Scientific Memoirs/1/New Researches relative to the Immediate Transmission of Radiant Heat through different Solid and Liquid Bodies

←

Memoir on the Free Transmission of Radiant Heat through different Solid and Liquid Bodies

New Researches relative to the Immediate Transmission of Radiant Heat through different Solid and Liquid Bodies

Experiments on the Circular Polarization of Light

→

From the Annales de Chimie et de Physique, t. lv. p. 337.

1654660Scientific Memoirs — New Researches relative to the Immediate Transmission of Radiant Heat through different Solid and Liquid BodiesMacedonio Melloni

Article II.

New Researches relative to the Immediate Transmission of Radiant Heat through different Solid and Liquid Bodies; presented to the Academy of Sciences on the 21st of April, 1834, and intended as a Supplement to the Memoir on the same subject presented to the Academy on the 4th of February, 1833; by M. Melloni.

From the Annales de Chimie et de Physique, t. lv. p. 337.

Of the modifications which Calorific Transmissions undergo in consequence of the Radiating Source being changed.

THE experiments described in the former Memoir have shown that diaphanous bodies do not act in the same manner on the rays of heat and the rays of light simultaneously emanating from the most brilliant flame. We have seen, in fact, that thin flakes of alum and of citric acid, because of their transparency, perceptibly transmit all the luminous rays of an Argand lamp, and stop from eight to nine tenths of the caloric; while, on the other hand, thick pieces of smoky rock crystal intercept nearly the whole of the light and allow the radiant heat to pass freely. Do the different properties thus exhibited by each body, relatively to the two agents, and the relations of the calorific transmissions of the one screen to those of the other, remain constant, whatever be the source (luminous or obscure) whence the rays emanate? Such are the first questions that I have undertaken to solve in this second series of researches.

That the comparison between the quantities transmitted in each particular case might be fairly made, it was necessary to operate upon rays emitted by a source having a constant temperature. This condition could be complied with by means only of certain flames and boiling liquids. I was therefore unable to vary the experiments so much as I should have desired. The sources however which I have employed present the most remarkable phases of the hating and combustion of bodies. They are four in number; namely, the flame of oil without the interposition of glass, incandescent platina, copper heated to 390°, and boiling water. Thus I had two luminous and two non-luminous sources. The first is furnished by a Locatelli lamp^[1]; the second is a spiral of platina wire kept in a state of incandescence by means of a lamp fed with spirit of wine; the third is obtained by covering a flame of alcohol with a plate of copper, which soon acquires a fixed temperature whose mean value, as found by the method of immersion, is 390° Cent.(732° Fahr.); and the last source is merely a vessel of thin copper, blackened on the outside and filled with boiling water.

The intensities of the radiations have been always ascertained by the thermomultiplier. The means necessary to be adopted in order to obtain with this instrument the measure of the immediate transmission having been stated in the Memoir already quoted, I think it needless to enter here into further detail as to the arrangement of the apparatus and the nature of the galvanometric indications. I shall only remind the reader that as this method requires that the operation should be performed under the influence of a radiation equivalent to 30° of my thermomultiplier, the diaphanous substances, if placed at a suitable distance between the thermoelectric pile and the source of heat, cannot acquire a temperature sufficient to produce in the instrument any perceptible action. This is proved in three ways: first, by placing the screens on their stand after having exposed them to a calorific radiation of the same intensity as that to which they are exposed during the experiment; secondly, by substituting for the diaphanous body plates of blackened glass or metal, flakes of wood or stone, or sheets of paper; thirdly, by varying the nature and thickness of the medium (more or less transparent) through which the rays are to pass, from the thinnest plate of mica to pieces of rock crystal, glass, or Iceland spar several inches in thickness. In the first case the index of the galvanometer remains unmoved, ing the heat acquired by the screens; in the second case also it remains unmoved, although in this case the plates (blackened or opake) are submitted to the actual radiation of the source itself. In the third case the index of the galvanometer leaves its position of equilibrium and describes arcs of greater or less extent according to the quality and thickness of the screen. But the time which it takes to reach the extremity of these arcs is invariable, and equal to that which it takes to describe a deviation of 30° when there is no screen interposed.

This third proof, though indirect, is nevertheless the most convincing, and possesses the additional advantage of showing, as it were, palpably, that the manner in which radiant heat is transmitted in the interior of diathermanous substances is altogether analogous to that in which light is propagated through transparent media whether solid or fluid. For in respect to the latter we perceive no appretiable difference between the times which the luminous rays take to pass through layers of any quality and thickness whatsoever.

The analogy between the transmission of light and that of radiant heat is rendered still more striking if, by shaking or otherwise, a motion is produced in the mass of the screen submitted to the experiment. I have passed the different parts of a large square of glass rapidly before the narrow aperture of the metallic plate through which the calorific rays that strike the surface of the pile are transmitted. By means of a bow I made it vibrate; it emitted sounds more or less acute: the index of the galvanometer pointed invariably to the same degree of its scale. I found the deviation of the magnetic needle equally invariable when I measured the intensity of the calorific radiation through a layer of acidulated water, at first still, but afterwards set in motion by agitators or traversed by a strong electric current.

Here then, though under different forms, the fact observed in the experiments of Pictet and Saussure when we agitate the mass of air interposed betwen the reflectors is reproduced; namely, the impossibility of altering by these means the direction or the intensity of the luminous or the calorific rays passing through atmospheric air or any other diaphanous medium.

These different considerations seem to me well calculated to dispel every shade of doubt that may yet be entertained as to the immediate transmission of radiant heat by diathermanous bodies, whether solid or liquid. But (to return to the four sources) we have already observed that in our method of proceeding it is necessary to operate uniformly under the influence of a radiation equal to 30° of my thermomultiplier. Now to effect this with sources of various temperatures they must be brought more or less close to the thermoelectric pile until we have obtained the galvanometric indication required, and such is the way in which we have proceeded in all our experiments of transmission. The same screen being, in those different circumstances, submitted to the same quantity of radiant heat, the different degrees of diminution suffered by this heat in passing through it must evidently be attributed only to the peculiar quality of each radiation. This reflection will give still greater force to the truth of the consequences which we are about to deduce from the results of our experiments.

Seven plates of glass of different degrees of thickness submitted to the action of the four sorts of calorific rays in succession have given the following transmissions:

Thickness of the plates.	Transmissions of the glass out of 100 rays of heat issuing from
Thickness of the plates.	a Locatelli lamp.	incandescent platina.	blackened copper heated to 390° (732° Fahr.)	blackened copper heated to 100° (212° Fahr.)
0^mm·07	77	57	34	12
0 ·5	54	37	12	1
1	46	31	9	0
2	41	25	7	0
4	37	20	5	0
6	35	18	4	0
8	33·5	17	3·4	0

Although we do not exactly know the degree of heat given by the flame of oil or by platina kept in a state of incandescence by an alcohol lamp, we are nevertheless quite certain that the first of these possesses a higher temperature than the second, and that this again exceeds the 390° of the first plate of copper. Now a glance at the table is sufficient to show that the number of rays transmitted by the same plate decreases with the temperature of the calorific source, a fact which confirms the well-known law of Delaroche. But the decrease is more or less rapid in proportion to the greater or less thickness of the plate.

Let $OM$ , $ON$ , (Plate I. Fig. 1.) be two rectangular axes of the same length; let the first represent the thickness of the screen of 8^mm and the second the total quantity of incident heat. Let us divide $OM$ into six parts, $Oa$ , $Ob$ , $Oc$ , $Od$ , $Oe$ , $Of$ , respectively equal to 0·078 $OM$ , 0·58 $OM$ , 18 $OM$ , 14 $OM$ , 12 $OM$ , and 34 $OM$ ; and through the points of division let us draw the perpendiculars $aa'={\frac {77}{100}}ON$ , $bb'={\frac {54}{100}}ON$ , $cc'={\frac {46}{100}}ON$ , $dd'={\frac {41}{100}}ON$ , $ee'={\frac {37}{100}}ON$ , $ff'={\frac {35}{100}}ON$ , $Mg'={\frac {33.5}{100}}ON$ . The curve ( $a'b'c'd'e'f'g'$ ) passing through the extremities of these perpendiculars will represent the decreasing intensity of the Locatelli lamp at each point of the screen of 8^mm in thickness.

A similar construction will give the curves $a''b''c''d''e''f''g''$ , $a'''b'''c'''d'''e'''g'''$ , $a^{IV}b^{IV}$ , representing the decreasing intensities of the three other radiations.

Let us now suppose the screen cut by any plane ( $PP'$ ) parallel to $ON$ ; the emergent rays of the detached plate will be determined by the points at which the plane intersects the curves; so that $PP'$ , $PP''$ , $PP'''$ will represent the quantities of heat that issue from the plate $OP$ when exposed to the first three sources; for the rays of the fourth are completely extinguished at the distance of one millimetre. We now see that the ratios of the distance from those points of intersection to the axis $OM$ decrease in proportion as the thickness of the interposed layer is less. The distances from those points to the axis are pretty nearly equal when the section coincides with the ordinate $aa'$ at which the observations commence; they will become yet more so in the interior of the first layer $Oa$ , so that within a limit very close to the surface at which the rays enter the differences will almost vanish^[2].

The first infinitely thin plate will therefore transmit sensibly equal quantities of radiant heat from the four sources. The diminutions however which the rays from each source will suffer in the interior of this elementary plate, though so exceedingly small that they may be disregarded in reference to the quantities transmitted, must nevertheless bear very different ratios to one another; for it is to such diminutions, several times repeated by the action of the successive layers, that we are to attribute the remarkable differences in the quantities of heat transmitted from each source by a screen of a given thickness.

The law of Delaroche did not show whether the variable interception of the same flake arose from an internal or external action of the screen. Nay, more; the ordinary properties of the caloric seemed to lead to the far more probable consequence that the interception was entirely superficial; or in other words, that as the same plate of glass successively exposed to the radiations from several sources gave different calorific transmissions, it was natural to suppose that the heat was first stopped at the external surface in a proportion varying with the temperature of the source, and subsequently propagated inwards according to the known laws of conductibility. But the experiments which I have just mentioned seem to me to demonstrate clearly that the calorific rays from different sources are more or less quickly extinguished in the very interior of the mass.

Thus the molecules of glass act upon radiant heat with a real absorptive force, the activity of which is greater in proportion as the temperature of the source is lower. It will perhaps be now asked whether this kind of action be common to all diaphanous substances or peculiar to glass only.

To determine this, it is not necessary to repeat on all the bodies those experiments which we have made on different thicknesses of glass; for, the law of Delaroche being once established, it will follow that the substance of which the flake is composed operates on the rays of heat with an absorptive force inversely as the temperature of the source: and as this force acts from all points of the mass, it is clear that the difference between one transmission and another must decrease with the thickness of the screen. The question is therefore reduced to this; whether all bodies more or less transparent act upon heat radiating from different sources in a manner analogous to that which we have observed in one only of our flakes of glass.

I have registered in the following table the quantities of heat immediately transmitted from each of the four sources through plates of different kinds reduced to the common thickness of 2^mm·6. The transmissions are expressed in hundredth parts of the incident quantity. They are uniformly measured, like the preceding, under the action of a radiation of the same force derived from each source of heat.

Names of the interposed substances (common thickness, 2^mm·6.)	Transmissions from 100 rays of heat issuing from
	a Locatelli lamp.	incandescent platina.	blackened copper heated to 390° (732°)	blackened copper heated to 100° (212°)
Rock salt (diaphanous, colourless)	92	92	92	92
Fluate of lime (diaphanous, colourless)	78	69	42	33
Rock salt (diaphanous, dull)	65	65	65	65
Beryl (diaphanous, greenish yellow)	54	23	13	0
Fluate of lime (diaphanous, greenish)	46	38	24	20
Iceland spar (diaphanous, colourless)	39	28	6	0
Another species (diaph., colourless)	38	28	5	0
Mirror glass (diaphanous, colourless)	39	24	6	0
Another kind (diaph., colourless)	38	26	5	0
Rock crystal (diaphanous, colourless)	38	28	6	0
Rock crystal, smoky (diaph., brownish)	37	28	6	0
Acid chromate of potash (a vivid orange)	34	28	15	0
White topaz (diaphanous, colourless)	33	24	4	0
Carbonate of lead (diaph., colourless)	32	23	4	0
Sulphate of barytes, pure, (diaphanous, rather dullish)	24	18	3	0
White agate (translucid, pearly)	23	11	2	0
Adularia felspar (diaph., dull, veined)	23	19	6	0
Amethyst (diaphanous, violet)	21	9	2	0
Amber, artificial (diaph., yellow)	21	5	0	0
Emerald (diaph. bluish green)	19	13	2	0
Agate, yellow (translucid, yellow)	19	12	2	0
Borate of soda (translucid, white)	18	12	8	0
Green tourmaline (diaph., deep green)	18	16	3	0
Cowhorn (translucid, hazel)	18	4	0	0
Common gum (diaph., yellowish)	18	3	0	0
Sulphate of barytes (diaph., dull veined)	17	11	3	0
Sulphate of lime (diaph., colourless)	14	5	0	0
Sardoine (translucid, brown)	14	7	2	0
Citric acid (diaphanous, colourless)	11	2	0	0
Carbonate of ammonia (diaphanous, dull, striated)	12	3	0	0
Tartrate of potash and soda (diaphanous, colourless)	11	3	0	0
Amber, natural (translucid, yellowish)	11	5	0	0
Alum (diaphanous, colourless)	9	2	0	0
Glue, strong (diaph., yellowish brown)	9	2	0	0
Mother-of-pearl (translucid, white)	9	0	0	0
Sugar-candy (diaphanous, colourless)	8	0	0	0
Green fluate of lime (translucid, marbled green)	8	6	4	3
Melted sugar (diaphanous, yellowish)	7	0	0	0
Ice very pure (diaphanous, colourless)	6	0	0	0

Before we proceed to consider these results, it is necessary to recollect that they have all been obtained under the free action of an invariable radiation of 30° measured by the thermomultiplier. Now the half degrees of the galvanometer are very distinctly legible. Thus the transmissions are exact to 160th of the incident heat; but the observations being repeated, the hundredth part becomes easily appretiable.

In the quantity of rays transmitted through the same substance there is a variation of several hundredth parts according to its greater or less purity. It was therefore useless in giving the measure of this element to attempt a degree of exactness exceeding the hundredth part of the whole; but it was desirable to ascertain the limits of the insensible transmissions with more precision. In this case therefore I have always carried the approximation to 1200, and sometimes to 1300, so that if the zero does not represent a transmission really equal to nothing, it is at least certain that, if there are any rays of heat transmitted, their amount does not exceed 1200dth of the whole incident quantity.

In order therefore to reduce the probability of error, it has been found necessary to operate on stronger radiations. Now the table of intensities given in my first Memoir does not exhibit the forces which move the galvanometric index beyond the 45th degree. I could have extended it to the higher degrees of the quadrant by the method followed in its construction. But I thought it better to employ at each step a very simple artifice which immediately gives the force of any radiation whatsoever as well as the required limit of error. To make this clear, let us suppose that it is desired to verify a particular case of the transmissions in the table; for instance, that it is requisite to prove that the transmissions of alum, sugar, or ice exposed to the rays emitted by copper heated to 390° are either null or less than 1200dth of the whole of the incident heat.

The table shows that a plate of glass, of rock crystal, or of Iceland spar transmits from five to six hundredths of those rays; that is to say, that for a free radiation of 30° we obtain about 2° through the plate. We know moreover that in this feeble indication there is a possible error of 160th of the whole heat. The limit of error would be 170·6 if we wished to be rigorously exact, for by the table of intensities we see that, in the deviations below 20°, one degree is equivalent to 135·3 of the force which moves the needle to 30°. But let us admit only the limit 160, which will have the advantage of rendering the values independent of a knowledge of the ratios existing between the degrees of the galvanometer and the corresponding forces of deviation. Let us bring the source near, in order that We may obtain through the same plate of glass a deviation exceeding 2°; a deviation, for instance, of 8°. The quantity of incident heat is now increased fourfold, and the probablity of error is diminished in the same degree^[3]. Let us now substitute for the plate of glass a flake of alum, sugar, or ice; we shall find that the needle of the galvanometer is perfectly at rest: if there is any heat transmitted, it is therefore not more than ${\frac {1}{4}}\cdot {\frac {1}{60}}={\frac {1}{240}}$ of the whole radiation. Thus it is true that the transmission of these three substances reduced to plates of 2^mm·6 in thickness and exposed to the radiation of a body heated to 390° is null or less than 1200dth part of the whole incident heat. It is by operations analogous to this that I have been able to ascertain the limits of the values of the zeros of transmission.

Now that we know the degree of exactness to which the measures contained in our table have been carried, we may proceed to state the consequences to which they lead.

Let us, for the moment, not notice the results obtained with the rock salt. The order of the transmissions has no relation to the degree of transparency, as we have already determined in our first series of experiments. It is not strictly the same when we change the calorific source; but each substance exposed to the successive action of the four radiations presents a like order of decrease in respect to the quantities which it transmits from each of the sources; that is to say, that all the substances transmit quantities of heat which are feeble in proportion as the temperature of the radiating source is low. There are several cases in which the transmissions are nothing; but these cases do not make against the principle as the zero is never followed by appretiable transmissions.

The same principle holds in respect to all the liquids that I have been able to submit to experiment. It will be recollected that, in my mode of operating, the rays of heat, before they reach the liquid layer, must pass through a plate of glass. Now this substance becomes more and more interceptive in proportion as the sources employed are of a less elevated temperature, and consequently acts upon the calorific rays with an effect the same as that which a screen of variable transparency would produce in respect to light. The process therefore which I pursued in my first Memoir could not enable me to determine the exact ratios of the calorific transmissions through the same liquids when the source is changed; but it was possible to make it available for the purpose of establishing, in the greatest number of cases, the general law of decrease which we have just determined in respect to solid bodies.

Let us suppose that a thick plate of glass being submitted to the successive action of an equal quantity of heat, emanating from our four sources, gives these transmissions:

30,⁠ 18,⁠ 2,⁠ 0.

Let us suppose a parallelopiped, with sides parallel to the faces of the plate, to be cut out of the glass, and the cavity thus made to be filled with a given liquid: let us then suppose that the transmissions of the system become all respectively inferior to the preceding, and are reduced, for instance, to

20,⁠ 8,⁠ 1,⁠ 0,

it will be immediately concluded that the liquid acts on the calorific rays from different sources in the same manner in which its glass case does; that is, that it exhibits an order of decrease similar to that exhibited by the glass and by solid bodies in general. Now this is precisely the result furnished by the liquids contained in my glass vessels^[4].

In eight-and-twenty cases there have occurred but the three exceptions presented by carburet of sulphur, chloride of sulphur, and protochloride of phosphorus, in which the transmissions did not change when the liquid was substituted for glass. I found it therefore impossible to decide at first whether these three substances acted in the same manner as the others; for if they had acted even in a contrary way, provided their least transmission were equal to 30°, the result obtained would be the same. But in all probability these three anomalies are merely apparent; for the chloride of sulphur, the carburet of sulphur, and the protochloride of phosphorus being in a high degree permeable to radiant heat, the same thing will happen in respect to these three liquids inclosed in glass vessels that happens when very pure fluate of lime is substituted for them; that is to say, the transmissions of the system retain their proper values, though the fluate of lime itself be subject to the general law.

Thus the radiant heat from different sources is absorbed in greater or less proportions while it is passing through diaphanous bodies (solid or liquid); but while it is passing through the same body the absorption constantly increases as the temperature of the source decreases.

It happens quite otherwise to the luminous rays. Let us look through a plate of glass at the most vivid flame or at any other phosphorescent substance. If the plate is very pure, its interposition will produce no sensible effect, and the images will retain all the relations of intensity which they had when viewed directly. The pale phosphoric gleam therefore suffers in the interior of the glass screen the same absorption as the strong light of the flame does.

The bodies on which I have made my experiments have been taken indiscriminately from the three kingdoms of nature: some crystallized, others amorphous; some solid, others liquid; some natural, and others artificial: yet they all act in a similar order relatively to the rays of the different sources of caloric. Does not this constancy in their manner of acting, notwithstanding such great differences in their physical and chemical constitutions, indicate that this law of decrement belongs to the very nature of the heat? We should not however infer from this that there are not bodies which afford a passage equally free to calorific rays of every kind. For we see by the table that a flake of rock salt, whether exposed to the radiations of flame, of incandescent platina, of copper heated to 390°, or of boiling water, always transmits 92 of every hundred incident rays.

The same constancy of transmission is observable when we operate on sources of a temperature yet lower than that of boiling water; such, for instance, as vessels containing this liquid heated to 40° or 50°. It is observable also when we employ pieces of rock salt 15^mm or 20^mm thick. I have placed all the flakes of salt that I could dispose of side by side, so that the thickness of them all amounted to 86^mm. The quantity of heat transmitted by this series of flakes was considerably less than 93100 because of the great number of successive reflexions; but it was always invariable relatively to the four sources. Between these limits of thickness, therefore, rock salt really acts in respect to radiant heat just as colourless glass and colourless diaphanous bodies in general act in respect to light.

This being premised, it is clear that if each substance contained in the table acted like the second specimen of rock salt, that is, if it transmitted the heat in a proportion less than 93100 but always the same for each of the four sources, all these substances would be to radiant heat that which diaphanous bodies more or less dusky are to light. But they allow the rays from certain sources to pass through them and intercept the rays from others: they act therefore in respect to heat as coloured media act on light^[5].

What do we find when we expose the same coloured glass successively to differently coloured lights? Lights of the same tint as the glass pass abundantly, the rest are almost totally intercepted.

These analogies lead us therefore to consider the radiations from different sources of heat as not being of the same nature. This seems indeed sufficiently established by the mere fact that the calorific transmission of glass, Iceland spar, or any other diathermanous body varies with the temperature of the radiating source.

Thus boiling water, copper heated to 390°, incandescent platina, and the flame of oil will be to us the sources of a heat that is more or less coloured, that is to say, sources each of which gives out a greater quantity of calorific rays of a certain quality; but the flame will furnish caloric rays of every kind as it furnishes light of all colours.

We shall distinguish bodies into diathermanous and athermanous^[6]. The diathermanous we shall subdivide into universal and partial. The first of these subdivisions, which is analogous to colourless media, will contain but one substance, namely, rock salt; the second, which corresponds with the coloured media, will contain all the bodies comprised in our table, in addition to diaphanous liquids and diaphanous substances in general. As to the class of athermanous bodies I had supposed at first that every substance which completely intercepted light intercepted the whole of the radiant heat also. This is found to be the fact in the greatest number of cases. But subsequent experiments have shown me that flakes of black mica and black glass, though they completely intercept the most intense solar light, yet exhibit very strongly marked calorific transmissions. The following are the results:

	Transmissions out of 100 rays issuing from
	a Locatelli lamp.	incandescent platina.	copper at 390°.	copper at 100°.
Black glass(1 ^mm in thickness)	26	25	12	0
Ditto (2 ^mm ditto )	16	15.5	8	0
Black mica (0^mm.6 ditto )	29	28	13	0
Ditto (0^mm.9 ditto )	20	20	9	0

The black mica and black glass then, though perfectly opake, are diathermanous, but yet only partially diathermanous, because while they allow some rays of heat to pass they intercept others.

We may see, besides, that the heat of incandescent platina and that of the flame of oil are transmitted in nearly equal quantities by these two substances. As soon as I had made my first experiments on the transmission of opake bodies I found that the rays from incandescent platina pass through a plate of black glass in a greater proportion than those from an Argand lamp. Now as it happens quite otherwise in respect to transparent glass and other diathermanous bodies, I thought at first that, in the particular case of the black glass, the variation in the quantity of heat transmitted was inversely as the temperature of the radiating source^[7]. But it was not long before I discovered my mistake; for, exposing two flakes of glass, the one colourless and the other opake, first to the direct rays of a Locatelli lamp and next to the rays that passed through a screen of common glass, I found that if the transmission through the first plate increases, as I have already stated in my first Memoir, the transmission through the second decreases. These opposite variations exhibited by the transmissions of the black and the white glass relatively to the radiations from the Argand lamp, and the incandescent platina, do not arise from any peculiar action of the calorific sources on the two bodies, but from a particular modification which the cylindrical screen or glass funnel attached to the Argand lamp produces in the calorific rays passing through it, — a modification which changes their capability of ulterior transmission and enables them to pass through the other bodies in a greater or less quantity than if they were in their natural state. We shall presently see that almost all the screens produce analogous effects.

The similarity of the action of glass and transparent bodies in general upon radiant heat to that of coloured media upon light, is established even in its most minute details by all the phænomena of transmission that we have been able to observe. For we have seen that the calorific rays from the flame of an Argand lamp lose much of their intensity while passing into the interior of a thick piece of colourless glass, and that their subsequent losses decrease in proportion as the distance from the surface at which they enter increases. Now the same thing takes place if we expose to white light any coloured transparent body, a red liquid, for instance; for in this case nearly all the rays, blue, green, yellow, &c., which enter into the composition of this light are absorbed more or less rapidly by the first layers of the liquid, and the red rays alone penetrate to a certain depth.

It is also known from the experiments of Delaroche and others that the radiant heat which has traversed a plate of glass and suffered a certain loss will in passing through a second plate sustain a second loss proportionally less than the first. In the same manner does the incident white light in passing through the first layer of a coloured substance become considerably weaker, while the emergent coloured light parses almost without suffering any diminution of intensity.

By exposing a given plate of a diaphanous substance successively to equal quantities of calorific rays from different sources we have seen their transmissions vary with the temperature of the source, that is to say, with the nature of the rays emitted. We have seen moreover that the differences between one transmission and another decrease in proportion as the plates employed are thinner, until within a certain limit of tenuity they vanish or have a tendency to vanish altogether. All these effects are observable in the differently coloured lights transmitted through a coloured medium; for if the medium be red the quantities of light transmitted will be greater in proportion to the greater number of red rays contained in each radiation. The other rays will be absorbed in a greater or less degree. But the quantities of light transmitted approach more nearly to an equality in proportion as the plate to be passed through is thinner. In short, the coloured media become more faint as their mass is reduced, and when sufficiently attenuated retain no sensible tint whatsoever, in other words, they become permeable to luminous rays of all colours.

We have several times remarked the striking differences exhibited in the calorific transmissions of diaphanous substances. But this curious fact, which constitutes, as it were, the basis of our inquiries, ceases to surprise us as soon as we feel convinced that bodies which are transparent and colourless act upon heat in a manner similar to that in which coloured media act upon light. For, as upon the intensity of the colour depends the degree of transparency, that is, the number of luminous rays that pass through the coloured substances, in like manner upon this species of invisible calorific tint which diaphanous bodies possess will depend whether a greater or a less quantity of heat be transmitted^[8].

We shall presently see yet more striking analogies between the two classes of phænomena when we consider the modifications which the calorific rays undergo in their passage from one screen to the other. But before we dismiss the present subject it may be advisable to bestow a few moments' attention on the purposes to which the calorific properties of rock salt may be applied.

Glass is a substance but very slightly diathermanous, especially when the temperature of the source is low. The common prisms or convex lenses could not therefore be employed for the purpose of ascertaining whether radiant heat be subject to changes of direction analogous to those of light in penetrating to the interior of refracting media. It was owing to the use of such instruments that some who applied themselves to the investigation of this point attained but very indecisive results, and often drew from them very false conclusions. Scheele asserted that "bright points not possessing the least heat may be formed before the fire with burning-glasses^[9]." Carefully conducted experiments have more recently shown that a thermometer rises some degrees when placed in the focus of a lens exposed to the radiation of flame or of incandescent bodies^[10]. But as the heat is then luminous, and as no very decided effect is observed if the operation is performed with nonluminous heat, it was inferred that the elevation of temperature was owing to the light absorbed by the thermometer and that isolated radiant heat is not susceptible of refraction. This notion might derive additional support from the fact that lenses of rock crystal, Iceland spar, alum, and other diaphanous substances acted analogously to the glass lens: and yet it would have been wrong to attribute to the agent an effect which was due only to the particular structure of all those substances. To be satisfied of this we need only operate with a lens of rock salt; for the focal thermometer then always exhibits a marked elevation of temperature, even though the radiant heat be totally separated from the light. But it has been attempted to explain the effect of the lenses by an inequality in the heating of their different parts. It has been said that the heat is accumulated towards the centre, that the parts towards the margin, because of their thinness, quickly grow cold again, and that it is not surprising therefore to see the thermometer rise more rapidly when placed in the prolongation of the axis of the lens than in any other direction^[11]. It would however still remain to be explained why the experiment is no longer equally successful when for the salt we substitute alum or any other diaphanous substance. But as recourse might be had to supposed differences between the conducting, the absorptive, or the emissive powers of these bodies, it seems advisable first to prove the refraction of the nonluminous rays without using lenses.

With this view I place, at a certain distance from the thermoelectric pile and out of the direction of its axis, a plate of copper heated to 390° by an alcoholic lamp, or, what is still better, a vessel filled with water in a state of ebullition. The pile being lodged at the bottom of a metallic tube blackened inside, the rays of nonluminous heat emitted from the vessel in a direction oblique to the axis cannot reach the thermoscopic body, and the index of the galvanometer remains perfectly at rest. Matters being now in this state, I take a prism of rock salt and fix it at the mouth of the tube with its axis placed vertically and its refractive angle turned towards the angle formed by a line drawn from the source to the extremity of the tube. (See Plate I. fig. 2.) A considerable deviation is immediately perceived in the galvanometer. The rays of heat are therefore conveyed into the tube by the action of the prism.

To show that the effect is really due to the refraction and not to the heat of the salt it will be sufficient to turn the angle of refraction in a contrary direction; for as soon as this is done the needle falls again to zero, notwithstanding the presence of the prism. The experiment is no less successful with the heat of the lamp, or that of the incandescent platina. Calorific rays of every kind are therefore, like luminous rays, susceptible of refraction.

But on the principle of analogy, as each species of light, so will each species of heat possess a different refrangibility. Hence it is evident that if the prism be left in its position and the radiant source changed it would become necessary at the same time to change the angle formed by the axis of the pile with the direction of the rays, in order to obtain the desired effect on the galvanometer. If however we attempt to verify this conjecture we obtain no decisive result. This is easily conceived when we reflect that the aperture of the tube has a certain diameter and that it is placed quite close to the prism, so that the rays refracted at angles differing but very little from each other can alvays reach the pile though no change should be made in the inclination of the axis of the tube.

But there is another process by means of which, if we cannot exactly measure the refrangibility of each, species of calorific rays, we prove at least that the angle of refraction varies with the measure of the radiating source. I took a graduated circle $ABC$ (Plate I. fig. 3.) 22 inches in diameter carrying a ruler $CD$ as a moveable radius. At the extremity of this ruler I placed a thermoelectric pile $M$ composed of fifteen pairs disposed in one line perpendicular to the plane of the circle.

This apparatus being placed horizontally on a table, the centre $C$ was brought within a little distance of the bottom of a vertical prism( $N$ ) of rock salt, so that when the ruler $CD$ was properly placed the refracted parcel of hot rays fell on all the points of the linear pile.

By establishing the electric communications with the galvanometer and moving the ruler over the graduated arc, the point at which the deviation of the magnetic index attained its greatest value was easily determined. The radiating source was then changed while everything else was allowed to remain in the same state. We had now a calorific action more or less intense than the preceding; but in order to obtain the maximum of effect it was necessary to slide the ruler in one direction or the other. Thus, for instance, when I commenced the experiment with the incandescent platina, that is, when I had found the corresponding position of the pile that gives the greatest galvanometric deviation, it was necessary to move the ruler about two lines towards $B$ , on the side to which the most refrangible rays are directed, if I substituted the Locatelli lamp for the platina. But if I substituted for the platina a plate of copper heated to 390° I was obliged to slide the ruler three lines towards $A$ , in the direction of the less refrangible rays. The action of the boiling water in this experiment was too feeble to be compared with that of any of the three other sources.

The refraction and constant transmission of the calorific rays through the rock salt being placed beyond the possibility of doubt, we immediately see the use that may be made of this substance in investigating the nature of radiant heat. If, for instance, it is proposed to propagate to great distances the action of a heated body of small dimensions, we are now certain that we have only to place the body at the focus of a lens of rock salt, which will refract the calorific rays and make them form a real pharos of heat by issuing in a direction parallel to the axis. Is it desired that extremely feeble rays emanating from any source should be rendered perceptible? Let them be received on a lens of this substance having a thermoscopic body placed in its focus. In this manner we may, with the aid of an ordinary differential thermometer with small balls, obtain very decided indications of the heat issuing from a vessel filled with tepid water and placed at a great distance. In short, rock salt formed into lenses and prisms acts upon calorific rays in a manner perfectly analogous to that in which optical instruments act upon luminous rays. It constitutes then the true glass of radiant heat, and therefore the only glass that should be employed in appreciating the effects of its intensity. All other transparent bodies are but partial and incomplete transmitters of heat, totally intercepting calorific rays of a certain kind. It is easy to conceive, from these considerations, with what serious disadvantages those persons have had to contend who have undertaken to investigate the composition of solar heat with common prisms of flint or crown glass, water, alcohol, or some other diaphanous body. It was exactly the same as if they pretended to be able to analyse solar light with a prism formed of coloured glass.

Of the properties of the calorific rays immediately transmitted by different bodies.

The radiant heat which has passed through a plate of glass is transmitted in a greater proportion by a second plate of the same substance and the same thickness; the rays issuing from the second will be transmitted in a still greater proportion by a third, and so through any number of successive screens. The losses sustained by the calorific rays in their passage through a succession of screens, as compared with the quantity incident on each plate, will therefore form a decreasing series. But the difference between every two terms of this series becomes less and less as the number of terms increases, so that there must be somewhere a limit beyond which the difference has a tendency to vanish. We may conclude therefore that the rays after they have passed through a certain number of screens, will in their further transmission be subject to a loss reducible to a constant quantity as compared with the quantity of heat incident to each of the screens through which this further transmission is made.

The same phænomena may be traced in a continuous mass of diathermanous matter; that is to say, that if we imagine a piece of glass divided into several equal layers and measure the loss sustained by the radiant heat in its passage through each layer, the greater the distance of the layer from the surface at which the heat enters, the less will be the diminution suffered by the rays passing through that layer, and the losses have a tendency to become constant within a limit depending on the thickness of the layers. Some of these results Me have already verified in the preceding memoir, and it is easy to establish their truth, in reference to the sources of heat employed in our present inquiry, by means of the numbers which represent the transmissions of the plates contained in the first table^[12].

The only difference observable between the transmission through a continuous medium and the transmission through a series of detached screens is in the amount of the losses, which, for a given thickness, are found to be greater in the latter, because of the reflexions produced by each separate surface. These facts cannot surprise us after the idea we have formed to ourselves of the influence exercised by diaphanous substances on radiant heat. For the calorific sources always emit a certain portion of rays heterogeneous (if we may use the expression) to the calorific tint of the glass, which, through the absorbent action of the matter constituting the continuous medium or the detached screens, are successively extinguished until no rays remain but those that are homogeneous to this tint. Now these homogeneous rays must suffer a loss greater or less in its amount, but constant in respect to layers of equal thickness, as is the case, in the transmission of light, with red rays passing through a medium of the same colour, and with white rays passing through a medium diaphanous and colourless. What we have said of glass is equally true of every other partially diathermanous substance.

The calorific transmission through a series of homogeneous screens is then absolutely of the same nature as that which is effected through the interior of one continuous medium. This transmission we have examined, and, as we have just seen, it presents nothing contrary to its analogy with the transmission of light through coloured media. There is however a particular case in which two homogeneous screens act in so singular a manner in respect to light that it must be interesting to know whether something analogous does not take place in respect to caloric.

The optical phænomena presented by most of the slices of tourmaline cut parallel to the axis of crystallization are universally known. If these slices are placed one over the other and their axes laid in the same direction, they transmit light in considerable quantities. But if they be laid at right angles to one another, the light is totally intercepted. Do these phænomena, arising, as is well known, from the polarization of the light in the interior of the slices, take place in respect to calorific rays also; or, in other words, is radiant heat capable of being polarized in its passage through tourmaline?

In order to ascertain this I have taken two square plates of the same dimensions. I have made an aperture in the centre of each. This aperture was likewise a square having its sides parallel to those of the plate and each equal to the least breadth of the two polarizing slices. I then took some soft wax and attached a tourmaline to each aperture, holding the axis of the former parallel to one of the sides of the latter. These two plates being laid one over the other, it evidently depended on one of the sides of the one plate being placed parallel or perpendicular to a side of the other whether the light was to be transmitted or intercepted. Yet this pair of plates being placed vertically on the stand of my thermoelectric apparatus and exposed to the radiation of a lamp or incandescent platina, uniformly produced the same calorific transmission, whatever might be the relative direction of the sides of each plate.

That this fact might be put beyond the reach of doubt the galvanometric index was carried to the 18th or 20th degree, and the calorific communication now established was suffered to remain while we placed one of the plates on each of its sides in succession. The flame or the incandescent platina was then observed to appear and disappear alternately while the magnetic needle continued invariably at the same point of deviation.

This experiment was repeated many times with several tourmalines, and the angle formed by tlie intersection of their axes varied. The result was in all cases the same. The quantity of calorific rays transmitted through the two polarizing slices is then independent of the respective directions given to their axes of crystallization; that is to say, the heat radiating from terrestrial sources is not polarized in its passage through tourmalines^[13].

Let us now proceed to consider the transmission of heat through heterogeneous screens. The calorific rays emerging from each plate exposed to the action of the same source produce a particular elevation of temperature when they fall on the thermoscopic body of our apparatus. Whence we have inferred that the quantity of heat which passes through a given screen varies according to the quality and thickness of the substance. But, it may be asked, is this the only difference between the rays immediately transmitted through bodies of different kinds?

For the purpose of answering this question we have made the following experiments.

If the rays from a Locatelli lamp be brought to act on a thermoelectric pile after having previously passed through a screen of diaphanous matter (such as citric acid) but in a slight degree permeable to radiant heat, the effect obtained in the ordinary case, in which the whole action is equivalent to 30° of the thermomultiplier, will be very inconsiderable; but it may be increased by bringing the source of heat nearer, or by concentrating its rays on the plate with the help of metallic mirrors or lenses of rock salt. I suppose then that a deviation of 25° or 30° of the galvanometer has been produced through a plate of citric acid. I now interpose a plate of alum in such a manner that the rays emerging from the citric acid may be forced to pass through it before they can reach the thermoscopic body; the magnetic needle descends only about 3 or 4 degrees.

I now recommence the operation on any other diaphanous and colourless substance different from the citric acid; that is to say, I vary the distance from the lamp to the pile until I obtain the same galvanometric deviation of 25° or 30° by the action of the radiant heat on this new substance also. I then interpose the plate of alum, and the magnetic index, as in the case of the citric acid, descends again not more than about 3 or 4 degrees, but it approaches nearer to zero, and the retrograde movement is sometimes so marked that the needle nearly resumes its natural position of equilibrium.

If instead of alum other substances were employed as the invariable plate on which the rays issuing from each diaphanous body are successively made to fall, we should still observe differences in the corresponding deviations of the galvanometer; but they would be in general of a less decided kind. It is on this account that we have preferred the alum.

The following are the results, in hundredth parts, of the constant quantity of heat that falls on the plate of alum:

Screens from which there issue 100 rays of heat which are made to fall successively on the sample plate of alum.		Number of rays transmitted by this plate.
	No screen	9
	Rock salt (limpid)	9
	Rock salt (dull)	9
	Borate of soda	11
	Adularia felspar	14
	Iceland spar	22
	Rock crystal	25
	Mirror glass	27
	Carbonate of ammonia	31
	Sulphate of lime	72
	Tartrate of potash and soda	80
	Citric acid	85
	Alum	90

We see that radiations of the same intensity emanating from the diaphanous and colourless bodies contained in the tables pass through the same plate of alum in very different quantities. In the same manner sheaves of luminous rays issuing from different coloured media are transmitted some in greater and others in less proportions by a second transparent substance equally coloured, as the tint of each medium happens to be more or less analogous to that of the invariable substance through which they are to pass.

The calorific rays issuing from the diaphanous screens are therefore of different qualities and possess (if we may use the term) the diathermancy^[14] peculiar to each of the substances through which they have passed. The citric acid, the tartrate of potash and soda, and the sulphate of lime transmit rays which pass abundantly through alum; the diathermancy of these bodies therefore approximates nearly to that of the alum. The glass, the rock crystal, and the Iceland spar have evidently a different diathermancy, for the rays which pass through them are less transmissible by the invariable screen. The same may be said of borax, adularia, and carbonate of ammonia. As to the heat emerging from rock salt (limpid or dull) it acts in a manner similar to that in which the unobstructed light of the lamp would. The reason is evident, since the salt, acting equally on the different species of calorific rays, must transmit them all without reflecting their relative properties in any manner whatsoever.

These facts then completely confirm the conclusions which we had drawn from the preceding experiments: namely, that, 1st, flame sends forth rays of several kinds; 2nd, that diaphanous colourless bodies, with the exception of rock salt, act so as to extinguish certain caloric rays and allow others to pass, just as coloured media act in respect to light.

Here a very interesting question is naturally suggested. If the diathermancy or quality which constitutes the tint of a medium relatively to the radiant caloric is invisible, what part then do colours act in the transmission of heat?

When the quantity of radiant heat that passes through coloured glass is measured, it is always found to be less than that which passes through white glass of the same thickness. The difference indeed is sometimes considerable, though having no apparent relation to the prismatic order or intensity of the colour. We have already remarked this in the first memoir, and the truth of the remark will be readily admitted by any one who casts an eye over the following little table.

Screens of glass exposed to the radiation of a Locatelli lamp. (Common thickness 1^mm.85.)		Transmissions out of 100 rays of heat.
Glass,	white	40
—	red (deep)	33
—	orange	29
—	yellow (brilliant)	22
—	green (apple)	25
—	green (mineral)	23
—	blue	21
—	indigo	12
—	violet (deep)	34
—	black (opake)	17

It is therefore not to be doubted that an absorption of caloric is caused by the colouring matter. But is the power of absorption elective like the action of the invisible calorific tints in colourless diaphanous bodies, or does it affect all sorts of rays indiscriminately? We are about to investigate this point by means of experiments similar to the preceding, in which we have taken equal quantities of heat issuing from different screens of differently coloured glass, in order to make them pass through one common screen of alum.

Screens from which the 100 rays issue that are made to fall successively on the same slice of alum.		Number of rays transmitted by this slice.
Glass,	white	27
—	red	27
—	orange	27
—	yellow	27
—	green (apple)	5
—	green (mineral)	3
—	blue	27
—	indigo	27
—	violet	27
—	opake (black)	1

We see here that the rays emerging from the red, orange, yellow, blue, indigo, and violet are transmitted through the plate of alum in the same proportion as the rays that issue from the white glass. The colouring matter introduced into the composition of these different kinds of glass has no other effect than to extinguish part of the calorific sheaf which passed through the white, without perceptibly altering the relations of quantity between the several species of rays of which that sheaf is composed: they act in respect to radiant heat just as brown or blackish substances dipped in a transparent fluid would act in respect to light. But the case is different with respect to green and opake black; for these being introduced into the composition of glass, it will stop nearly all the rays that the alum is capable of transmitting. This effect arises from the green or opake colouring matter producing a certain modification in the diathermancy of the glass, and we have just seen that this species of calorific colouration is invisible and totally independent of coloration properly so called, since it exists in bodies possessing the greatest transparency. It is then extremely probable that the black or the green should not be supposed to enter as mere neutrals into this phænomenon, which will thenceforth depend on which or such a property of these colouring materials. I have found, in fact, some green glasses, which produced a much feebler action than others of the same tint but possessing a less brilliant colouration. The green glasses which act most powerfully are of a bluish cast; from which circumstance it would seem to follow that they contain a considerable quantity of oxide of copper. Whatever may be said of this singular property of green and black opake glasses and the cause by which it is produced, it is nevertheless an indisputable fact which every man can easily verify and of which we intend to give some new proofs presently. But it will perhaps be advisable previously to adduce the results furnished by several diathermanous substances examined by that process to which we have submitted the coloured glasses and the diaphanous colourless bodies.

Screens emitting 100 rays of heat which are made to fall successively on the same slice of alum.		Number of rays transmitted by this slice.
⁠	Mica, black opake ⁠	⁠	2
	Tourmaline, green		7
	Sulphate of barytes		12
	Acid chromate of potash		14
	Mica, white		15
	Beryl		19
	Emerald		19
	Agate, pearly		24
	Agate, yellow		24
	Amber, yellow		30
	Gum		45

On these numbers we have two remarks to make: first, that the green tourmaline and the black mica act in a manner analogous to glass of the same colour; second, that the beryl and emerald emit rays equally transmissible by the alum, although the colours of these two kinds of the same substance are different. The same happens to the two kinds of agate. These facts may perhaps be turned to some account by the mineralogist in examining certain coloured substances which belong to the different varieties of one mineralogical species.

We have been hitherto investigating the action of alum on a constant quantity of rays emerging from several diathermanous substances. Let us now reverse the problem and see what will be the effect when these substances are interposed in the passage of an invariable radiation issuing from alum.

In the third column of the following table will be found the results furnished by this class of experiments. It is almost unnecessary to observe that they have been obtained by successively placing the several bodies between the alum and the pile, after having produced in the galvanometer the ordinary deviation of 30° through the first substance. I have placed in the columns after the third the values of the transmissions of the same bodies exposed to the rays emerging from four substances different from alum; namely, sulphate of lime, acid chromate of potash, and green and black glass. The natural values of the calorific transmissions, that is to say, the results obtained under the immediate action of the lamp, are indicated in the second column.

Names of the substances interposed. (Those plates whose thickness is not specially indicated have the common thickness of 2^mm·6.)	Transmissions out of 100 rays.
	Rays immediately from the lamp.	Rays emerging from the alum, (thickness 2^mm·6.)	Rays emerging from the sulphate of lime, (thickness 2^mm·6.)	Rays emerging from the chromate of potash, (thickness 2^mm·6.)	Rays emerging from the green glass, (thickness 1^mm·85.)	Rays emerging from the black glass (thickness 1^mm·85.)
Rock salt	92	92	92	92	92	92
Fluate of lime	78	90	91	88	90	91
Beryl	54	80	91	66	70	57
Iceland spar	39	91	89	56	59	55
Glass (thick. 0^mm.5)	54	90	85	68	87	80
Glass (thick. 8^mm)	34	90	82	47	56	45
Rock crystal	38	91	85	52	78	54
Chromate of potash	34	57	53	71	28	24
Sulphate of barytes	24	36	47	25	60	57
White agate	23	70	78	30	43	17
Adularia felspar	23	23	58	43	50	23
Yellow amber	21	65	61	20	13	8
Black opake mica (thick. 0^mm9)	20	0·4	12	16	38	43
Yellow agate	19	57	64	24	35	14
Emerald	19	60	57	26	20	21
Borate of soda	18	23	33	23	30	24
Green tourmaline	18	1	10	14	24	30
Common gum	18	61	52	12	6	4
Sulphate of lime	14	59	54	22	9	15
Sulphate of lime (thick. 12^mm)	10	56	45	17	5	0·4
Carbonate of ammonia	12	44	34	11	6	5
Citric acid	11	88	52	16	3	2
Tartrate of potash and soda	11	85	60	15	2	1
Alum	9	90	47	15	0·5	0·3

Coloured glasses, (common thickness 1^mm.85.)

Glass, white	40	90	83	50	67	55
— violet	34	76	72	42	56	47
— red	33	74	69	41	54	45
— orange	29	65	58	36	48	39
— green (apple)	25	3	20	22	55	50
— green (mineral)	23	1	15	19	52	58
— yellow	22	49	46	27	35	30
— blue	21	47	42	26	34	29
— black (opake)	16	0·5	18	11	42	52
— indigo	12	27	26	14	20	17

Several of the numerical results contained in this table may be verified by calculation.

For, when two plates of different kinds are exposed together to the radiation of the source, their position relative to the entrance and the issue of the calorific rays does not affect the quantity of heat which passes through this system. This is easily proved by putting the first plate in the place of the second; for the thermomultiplier, notwithstanding this change of order, continues to mark the same degree of its scale. Let us now take two plates and place them alternately in each of the two positions, for instance, the plate of alum and the chromate of potash. These two substances, exposed separately to 100 rays of heat emanating directly from the source, transmit 9 and 34 respectively. The quantities of heat that should fall on each of the two plates in order that 100 may emerge in each case is easily determined by these simple proportions;

9	:	100	: :	100	:	x,
34	:	100	: :	100	:	x,

which give 1111 for the alum and 294 for the chromate of potash. Now we know by experiment that chromate of potash exposed to 100 rays issuing from alum transmits 57, and that alum exposed to 100 rays issuing from chromate of potash transmits 15.

But the order of succession has no influence on the transmission of the pair: let us therefore reverse the system only in one case or the other. We shall then have the same plates exposed in the same manner to the two radiations of 1111 and 294. The quantities transmitted under both circumstances should accordingly be proportional to the incident quantities, as is actually proved within the limits of approximation compatible with the nature of the experiments; for we have,

57 : 15 :: 1111 : 294.

The table contains ten pairs which are submitted in both ways to the radiations of the source; there are in it consequently twenty numbers which should be in proportions analogous to the preceding. It is evident too that these calculations require that the five plates emitting the 100 rays which fall successively on the whole series of diathermanous bodies should be those that are indicated by the same names in the first column. I have accordingly taken care that this condition should be satisfied.

The bodies submitted to the heat emerging from the screens present no longer the same order of transmission that they presented under the immediate action of the radiation of the lamp. The changes which take place have no apparent regularity whether we compare one series with another or consider only the different terms of the same series. Thus glass, Iceland spar, and rock crystal are more diathermanous to the heat emerging from the five screens than to that which comes directly from the source. Citric acid and tartrate of potash become more permeable to the rays issuing from the alum and sulphate of lime, and less permeable to those which proceed from black or green glass. With the opake mica and the tourmaline the case is directly the contrary. Some substances are equally permeable to the heat radiating from several screens. Others experience variations so great as to exhibit all the phases of the phænomenon, from an extremely abundant to an excessively feeble transmission^[15]. Through all these vicissitudes the action of the rock salt continues the same and uniformly transmits 92 rays out of 100. Hence follows the inverse proportion that if the series of plates be exposed to one hundred rays emerging from a plate of rock salt, the ratios of the quantities of heat transmitted would be the same as those obtained through the action of the immediate radiation; a proposition which I have besides verified by direct experiments.

After V hat we have so often repeated respecting the action of universal and partial diathermanous bodies, it would be superfluous again to point out the perfect similarity between these facts and the analogous phænomena presented by the transmission of light through diaphanous media, colourless and coloured. We shall therefore confine ourselves to a single observation on the nature of the rays which traverse certain screens.

The heat emerging from alum is almost totally absorbed by the opake screens, but is abundantly transmitted by all the diaphanous colourless plates. It suffers no appreciable loss when the thickness of the plates is varied within certain limits. Its properties of transmission therefore bear a close resemblance to those of light and solar heat. Let us now direct our attention to the rays which issue from the last two screens. The opake bodies transmit nearly the half of them; the diaphanous substances intercept them in very different quantities, and the portions transmitted are considerably diminished by increasing the thickness of the flakes. Thus, the rays emerging from the black or the green glasses are in respect to their properties of transmission as it were antagonist to the preceding, and analogous to those of the direct heat of the flame though still more decidedly marked, for they are almost completely absorbed by bodies possessing the greatest transparency.

I have availed myself of these last facts for the purpose of proving by a very simple process that solar light contains some calorific rays analogous to those which compose the radiant heat of terrestrial sources. With this view I introduced a solar ray into a dark room through an aperture having a screen of green glass as a stopper. To the light transmitted I exposed one of the blackened balls of a very delicate differential thermometer. The liquid column descended several degrees. I now placed quite close to the mouth of the aperture a thin plate of colourless glass; the liquid came back a little, but the retrograde movement became more decided when I interposed instead of the thin glass a plate of greater thickness. I took away the white glass and put in its place a plate of rock salt: the column was forcibly driven back, but reascended very nearly to its original position when I substituted for the salt a plate of very limpid alum. It is clear therefore that amongst the calorific rays of the sun there are some which have a resemblance to terrestrial heat. On the other hand we have seen that the rays from terrestrial flame which traverse a flake of alum suffer, like solar heat, only a very slight diminution in passing through glass and other diaphanous substances. Whence we infer that amongst the calorific rays from flame some are found similar to the heat of the sun. The differences observed between solar and terrestrial heat, as to their properties of transmission, are therefore to be attributed merely to the mixture, in different proportions, of several species of rays.

But, to return to the heat emerging from the screens exposed to the radiation of the lamp. We have said that the red, orange, yellow, blue, indigo, and violet matters which enter into the composition of the coloured glasses, act upon radiant heat as the black substances introduced into a coloured medium act relatively to light; that is, they diminish the quantity of heat transmitted by the glass without altering its diathermancy [diathermansie]. This proposition being admitted, it will necessarily follow, when rays of different species, such as issue from the five screens contained in the table, fall on a series of coloured glasses, that the calorific transparencies of these plates will be increased or diminished in proportion to the variation produced in the diathermancity [diathermaméité] of white glass. It has so happened in our experiments: for if we take the natural transmissions of the white, red, orange, yellow, blue, indigo, and violet, and compare these with their transmissions when submitted to the rays emerging from £uiy one of our live screens, we shall always find the same ratios between the different terms of each series.

As to the black and the green glasses, their changes of transmission occur sometimes similar, sometimes contrary to those of the other plates. We should not however be surprised at these irregularities, as the green and black colours alter the natural diathermancy of the glass and give it an aptitude to transmit quantities of heat which will be more or less considerable in proportion as the rays issuing from the different screens possess themselves a diathermancy more or less analogous to that introduced into the vitreous substance by these two colouring materials^[16].

Conclusion.

I had intended to introduce here some general reflections on the different hypotheses which have been proposed to explain the phænomena of heat, and on the question of the identity of radiant heat and light. But as these two agents are nowhere more intimately united than in the rays of the sun, such considerations should be preceded by a tolerably complete statement of the numerical results obtained by the application of our several processes to solar heat. The experiments however which I have hitherto been able to make with this view are too deficient in number and variety to justify my attempting any statement of the kind. I will therefore not enter, for the present, into any dissertation on the nature of heat, but will conclude with a recapitulation of the principal consequences to which I have been led by my inquiries into the properties of the radiant heat emitted by terrestrial sources, in order that being thus comprehended at a single glance they may be more easily compared with the analogous properties of light.

Radiant heat passes instantaneously, and in greater or less quantities, through a certain class of bodies, solid as well as liquid. This class does not consist exactly of diaphanous substances, since opake plates or plates possessing but a feeble transparency are more diathermanous or permeable to radiant heat than other plates possessing perfect transparency.

There are different species of calorific rays. They are all emitted simultaneously and in different proportions by flame, but in the heat from other sources some of them are always wanting.

Rock salt reduced to a plate and successively exposed to radiations of the same force from different sources always transmits immediately the same quantity of heat. A plate of any other diathermanous substance will, under the same circumstances, transmit quantities less considerable in proportion as the temperature of the source is less elevated: but the differences between one transmission and another decrease as the plate on which we operate is more attenuated. Whence it follows that the calorific rays from different sources are intercepted in a greater or less quantity, not at the surface and in virtue of an absorbent power varying with the temperature of the source, but in the very interior of the plate and in virtue of an absorbent force similar to that which extinguishes certain species of light in a coloured medium.

The same conclusion is attained by considering the losses which the calorific radiation from a source at a high temperature undergoes in passing through the successive elements which constitute a thick plate of any other diathermanous substance than rock salt. For if we imagine the plate divided info several equal layers, and determine by experiment what ratio the quantity lost bears to the quantity incident upon each of the layers, we find that the loss thus calculated decreases rapidly as the distance from the surface of entrance increases; but the diminution becomes less and less perceptible, so that it must become invariable when the rays have penetrated to a certain depth. This is precisely what happens to a pencil of ordinaiy light when it enters a coloured medium; for, those rays that are of a colour different from that of the medium being extinguished in the first layers, the losses of intensity sustained by the luminous pencil are at first very great, but they afterwards become gradually less and are at last very small, but constant when the only rays remaining are those of the same colour as the medium.

In fine the successive transmissions through heterogeneous screens furnish a third proof of the analogy which the action of diathermanous bodies on radiant heat bears to that of coloured media on light. The luminous rays issuing from a coloured plate either pass in abundance through a second coloured plate or undergo in it a powerful absorption according to the greater or less analogy of the colour of the second to that of the first plate. Now we observe facts perfectly similar to this in the successive transmission of radiant heat through screens of different kinds. And in this case too the rock salt acts in respect to the other bodies as it does in the case of rays emanating from sources of different temperatures. A given plate, if it be of rock salt, being successively exposed to calorific radiations of the same force emerging from different screens, transmits a constant quantity of heat; if the plate be of any other diathermanous substance the quantity transmitted will be variable.

There is therefore but one colourless and diaphanous body that really acts in the same manner on luminous and calorific rays. All other diaphanous bodies besides this indiscriminately suffer all kinds of light to pass through them, but of the rays of heat they allow some to pass while they absorb others: thus we discover in this one substance a real calorific coloration, to which, as it is invisible, and therefore totally distinct from coloration properly so called, we have given the name of diathermancy.

The colours introduced into a diaphanous medium always diminish its diathermancy in a greater or a less degree, without communicating to it any tendency to arrest certain calorific rays rather than others: they affect the transmission of radiant heat as dusky bodies affect the transmission of light. There is, it is true, an exception to be made in respect to green and opake black, at least in certain kinds of coloured glass. But these two colouring matters appear, in this case, to do no more than modify the quality to which we give the name of diathermancy, and which, as we have already seen, is totally independent of coloration.

The quantity of radiant heat which passes through polarizing plates of tourmaline is not affected by any change made in the angle at which their axes of crystallization are made to cross one another. Rays of heat are therefore not polarized in this mode of transmission and are in this respect entirely different from rays of light^[17]. But they resemble them in the property of refrangibility. This is completely proved by means of the rock salt, the only diathermanous body that is capable of transmitting the calorific rays emanating from every source.

As to lenses and common prisms they refract a certain portion only of the radiant heat; for the glass intercepts several sorts of calorific rays issuing from sources at a high temperature, and absorbs nearly the whole of the heat given out by bodies whose temperature is below incandescence. To this circumstance it is that we must attribute the doubt hitherto entertained as to the refrangibility of nonluminous heat.

NOTE.

[We annex to the foregoing papers of M. Melloni, various references to other Memoirs on the Transmission of Radiant Heat, and to former views of the results obtained by him.

In the "Report of the Third Meeting of the British Association," p. 381, is an "Account of some recent Experiments on Radiant Heat," communicated by Professor Forbes, and reciting M. Melloni's Experiments; and also, p. 382, an abstract of his subsequent discoveries communicated by himself to Professor Forbes, in order to be laid before the British Association.

The "Notices of Communications to the British Association at Dublin, August 1835," contains, p. 9, some remarks by Professor Powell on Melloni's repetition of his original experiment described in the Philosophical Transactions for 1825, and in the Philosophical Magazine, First Series, vol. lxv. p. 437, and a notice of Dr. Hudson's Experiments with the Thermomultiplier, rendering it questionable, in his judgement, whether the results obtained by Melloni on diathermanous bodies were not attributable to conduction. These notices will also be found in the London and Edinburgh Philosophical Magazine, vol. vii. pp. 296, 298.

Prof. Forbes's Memoir "0n the Refraction and Polarization of Heat" is contained in the Transactions of the Royal Society of Edinburgh, vol. xiii. p. 131, et seq.; and also in Lond. and Edinb. Phil. Mag., vol. vi. p. 134, et seq.

The following papers and notices have appeared exclusively in the London and Edinb. Philosophical Magazine:

A Note relative to the Polarization of Heat, by Professor Forbes arising from Professor Powell's remarks in the Notices of the British Association, referred to above, with a Postscript containing Professor Powell's explanation: vol. vii. p. 349.

M. Melloni on the Immediate Transmission of Calorific Rays through Diathermal Bodies, in reference to the objections of Dr. Hudson and Professor Powell, vol. vii. p. 475. Remarks on M. Melloni's paper by Professor Powell, vol. viii. p. 23. Remarks on both the foregoing papers, by Dr. Hudson, ibid., p. 109, confirming Melloni's original inductions. Professor Powell's Note on the Transmission of Radiant Heat, in reference to his remarks on Melloni's results, ibid., p. 187.

Professor Forbes's Note respecting the Undulatory Theory of Heat, and the Circular Polarization of Heat by Total Reflexion, ibid., p. 246. Dr. Hope's Address on the Delivery of the Keith Prize Medal to Prof. Forbes, giving a sketch of the history of our knowledge of radiant heat, ibid., p. 424.—Edit.]

In Part II. of Scientific Memoirs will appear translations of the subsequent papers of Melloni, and also of other memoirs relating to the same subject.

↑ The Locatelli lamp is merely a common lamp with one current of air and fed with oil. It has a wick of the shape of a quadrangular prism, which exactly fills the beak, but has no funnel. It gives a fine flame of constant temperature. The Argand lamp produces a flame of much greater intensity.
In the first series of experiments the main object was to determine the difference between the calorific and the luminous transparency. We therefore preferred the source which was least favourable to the establishment of the principal fact which it was then our purpose to verify. In the present experiments we proposed more particularly to examine the calorific transparency by itself. It was therefore necessary to operate upon rays that had not been forced to undergo a transmission previously to their being employed in the experiments.
↑ I have been unable to procure plates of glass thinner than ${\frac {7}{100}}$ of a millimetre. But we shall see presently that all other diaphanous substances, whether natural or artificial, are in their effects more or less analogous to glass. Now there are several crystals which spontaneously separate into plates of great tenuity, and are, consequently, well calculated to show that the ratios of the quantities of heat transmitted by a screen exposed to the radiations of the four sources approximate to equality in proportion as the thickness of the screen is reduced. Thus a plate of sulphate of lime 2^mm·6 in thickness gave for the four transmissions respectively,

14,⁠5,⁠0,⁠0.
These transmissions became

38,⁠18,⁠7,⁠0
when the thickness was reduced to 0^mm·4; and

64,⁠ 51,⁠ 32,⁠ 21
when the thickness was reduced 0^mm·01.

A plate of mica, 0^mm·02 thick, gave for the four transmissions

80,⁠ 76,⁠ 39,⁠ 26.

An extremely thin flake was taken from this plate (which was however not coloured): the four transmissions through this flake were,

86⁠,⁠ 85,⁠ 61,⁠ 46.
↑ This mode of estimating the energy of the calorific radiations enables us to determine without difficulty the ratios existing between the arcs described by the magnetic needle of the galvanometer and the corresponding forces. Let us suppose the calorific source removed sufficiently far from the pile to produce but a feeble deviation of the galvanometer; one of 10°, for example. In the passage of the calorific rays let there be interposed a plate which transmits a certain fraction of the incident heat. We shall suppose this fraction to be 12; the needle will descend to 2°. By bringing the source near, the deviation produced through the plate will be increased. Let us stop, when the needle shall have reached 4°, 6°, 8°, &c. successively; the calorific source will then emit upon the pile twice, thrice, or four times as much heat as before; for the transmission through the same plate exposed to a constant source of heat is always in a constant ratio, and the forces of deviation are proportional to the degrees in those arcs that are very near zero. Let the force which causes the galvanometer to describe the first degree of the scale be represented as 1, we shall then have 10 for the first force or quantity of incident heat, 20 for the second, 30 for the third, 40 for the fourth, &c. Now we know that the first force answers to 10°. In order to determine the deviation produced by the force 20 we have only to remove the plate when the galvanometer points to 4°; the calorific rays will then fall immediately on the pile, the angle of deviation will increase, and if the proportionality of the degrees to the forces continues through the whole extent of the arc of the first 20 degrees we shall see the index stop at 20°: at all events we shall have the corresponding indication. By repeating the same operation when the galvanometer points to 6°, 8°, we shall obtain the quantities sought, that is to say, the degrees answering to the forces 20, 30, 40, &c. Thus we may verify the results contained in the tables of intensities already made, or determine the elements necessary for the construction of new tables.
↑ In many instances I was unable to obtain any transmission, even by employing a very powerful radiation. It is thus that water, which transmits six or seven hundredths of the rays from a Locatelli lamp, completely intercepts the heat of the last three sources. Calculating the limit of error for the case least favourable to interception I found it 1616: the source was then brought very close to the liquid and an equal layer of oil employed, which caused in the index of the galvanometer a deviation of several degrees. Now if the water allows a passage to the radiation from bodies heated even to incandescence or brought to lower temperatures, the part transmitted must be less than 1616 of the incident quantity. I here speak of a layer of 3^mm or 4^mm in thickness: for it is possible and even very probable that layers much thinner than these may be in some slight degree permeable to rays of this kind. Thus we have seen glass of 0^mm·07 in thickness transmit 12100 of the rays emanating from boiling water, while a plate of 1^mm intercepted them totally. But as, in order to compare different transparencies, we must operate on a certain thickness of each medium (for the most opake bodies become diaphanous when they are sufficiently attenuated), so, in order to judge of the calorific transmissions through different bodies, we must take the greatest possible care not to employ excessively thin plates, or at least, if we are compelled by particular circumstances to use such, the substances compared should be perfectly equal in thickness; for in that state of tenuity the least difference of thickness might disturb the order of permeability and cause us to attribute a greater calorific transparency to substances possessing this property in an inferior degree. This is probably the cause of the mistake into which those have fallen who have fancied that they could prove by their experiments that water is more diathermanous than glass.
↑ It appears that Sir David Brewster had lately arrived at the same conclusion by means only of the experiments of Delaroche and Seebeck on the transmission through glass and on the distribution of heat in the solar spectra produced with different prisms, (See Report of the First and Second Meetings of the British Association for the Advancement of Science. London, 1833, p. 294.) But these experiments did not prove that the rays in passing through the different bodies suffer a real infernal absorption analogous to that which light suffers: above all, they were far from proving that this absorptive force, varying in each substance according to the temperature of the calorific source, could, in some particular cases, become constant, and in all respects similar to the action of colourless diaphanous media on luminous rays. On this ground it may be said that the inference of Brewster was yet premature; besides, the illustrious Scotchman rested his conjectures on the erroneous supposition that water has the same absorbent force in respect to all sorts of calorific rays. Experiment indeed leads to the opposite conclusion, as we have already proved in respect to solar heat by the different action of a layer of water on the temperatures distributed in each band of the solar spectrum; an action so widely different relatively to two different rays that all the heat of the violet light passes through the liquid without suffering any sensible diminution, while the nonluminous heat of the isothermal band is totally absorbed, (Annales de Chimie et de Physique, December 1831,) and we have just seen in the preceding note that analogous phænomena are observable in the radiations from terrestrial sources also; for a mass of water some millimetres in thickness intercepts all but a very small portion of the radiant heat issuing from flame and the whole of those rays that issue from any other source.
↑ Athermanous, in contradistinction to diathermanous, evidently signifies the absence of the power of transmitting heat. I adopt this term merely for convenience, without attaching to it a definite meaning; for, as there is no body which, if reduced to an extremely thin plate, may not become in some degree transparent, I think also that some rays of heat may pass through all substances in a state of great tenuity.
↑ Bulletin de la Soicété Philomatique, July 1833.
↑ Seeing that in respect to all the substances given in the table, the rock salt excepted, the order of decrement is similar though the sources of heat are different, one might be inclined at first to infer that they belong to the same species of partially diathermanous bodies, that is, that they may be compared with coloured media. But that such a conclusion is not legitimate will be shown by one example: let a be the species of rays transmitted by the medium A, b that species which is transmitted by the medium B, and c the rays intercepted by the same media. Let us suppose a calorific source that will give 30 a, 30 b, and 40 c; it is clear that the two media A and B will intercept 70 parts of the hundred and transmit 30. However, the rays emerging from A will be different from those which emerge from B. If we suppose a second source of heat such as will give 20 a, 20 b, and 60 c, we shall have 80 as the quantity intercepted and as the quantity transmitted by each of the screens. If the source gave 10 a, 10 b, and 80 c, the transmission would be 10 and the interception 90. Thus two substances exposed to different radiations may furnish calorific transmissions not only varying according to the same order of decrement, but equal in all their periods of variation, although the rays emerging from each may be of a different kind.
↑ Scheele, Traité de l'Air et du Feu, Paris, 1778, § 56.
↑ W. Herschel and Brande, Philosophical Transactions for 1800 and 1820.
↑ Philosophical Transactions, vol. cvi.
↑ Let us imagine the screen of 8^mm divided into seven layers having for their degrees of thickness the differences between two consecutive plates. (See the first table in this Memoir.) The quantities of heat incident on the layers when the radiation is from a Locatelli lamp are

100, 77, 54, 46, 41, 37, 35, 33.5,

and the quantities lost in the successive transmissions are

23, 23, 8, 5, 4, 2, 1.5.

Now the mean losses for the hundredth part of a millimetre of each screen will be

237, 2343, 850, 5100, 4100, 2100, 1.5100,

or 3.286, 0.535, 0.160, 0.050, 0.020, O.O1O, 0.007.

Hence the looses sustained by the rays of the lamp in the first hundredth part of a millimetre of each layer, when referred to the quantities of incident heat, will have the values

3.286100 0.53577 0.16054 0.05046 0.02041 0.01037 0.00735

that is, 0.0328 0.0070 0.0030 0.0011 0.0005 0.0003 0.0002.

By similar calculations the successive losses sustained by the radiations from the incandescent platina and the copper heated to 390° will be found to be

0.0614 0.0081 0.0032 0.0019 0.0010 0.0005 0.0003
0.0943 0.0155 0.0050 0.0022 0.0014 0.0010 0.0008.
Now the differences between every two terms of these series are for the

1st, 0.0258 0.040 0.0019 0.0006 0.0002 0.0001;
2nd, 0.0523 0.0049 0.0013 0.0009 0.0005 0.0002;
3rd, 0.0780 0.0105 0.0028 0.0008 0.0004 0.0002.
As to the fourth source it is useless to speak of it, as its rays are completely extinguished at the distance of one millimetre.

Thus, notwithstanding the inequalities of the increase of the distance from the second and the third layer to the surface of entrance, we observe in the three series the two principles we have laid down, namely, 1st, the decrease of the losses; 2nd, the tendency of this decrease towards a limit at which the loss becomes constant: but for each particular case the points of the medium at which the rays begin to suffer this constant action are evidently placed at a fixed distance from the origin. Therefore, if the glass be divided into equal layers, the limit of the decrease of the losses will be attained more slowly in proportion as the layers are more numerous, that is to say, thinner. It is for this reason that in each series the limit at which the losses become constant depends, as we have already said, on the thickness of the elementary layers.
↑ This result seems opposed to the experiments of M. Bérard on the polarization of reflected heat; but, ignorant as we are of the nature of the relations that caloric and light bear to one another, we have no means of proving that, as no polarization of heat is produced by the transmission through the tourmalines, none can be produced by reflexion at the surface of the glass. I am bound also to remark that some very able experimental philosophers having lately tried to polarize light by M. Bérard's process, their efforts proved unavailing. Mr. Powell informs us that although he had taken the necessary precautions against the heating of the glass and other causes of error he has never been able to discover the least appearance of polarization when operating with nonluminous heat. But he thinks that when he employed luminous sources he was enabled to observe a small perceptible effect by making the rays previously pass through a screen of glass (Edinb. Journal of Science, N. S., vol. vi.) Mr. Lloyd communicated at the last meeting of the British Association for the Advancement of Science (Cambridge 1833) some new results tending to support the conclusions derived by Mr. Powell from his own experiments. [No communication upon this subject by Professor Lloyd appears in the Report of the British Association for 1833.—Edit.]
↑ I employ the word diathermancy as the equivalent of calorific coloration or calorific tint, lest the latter should be confounded with tints or colours properly so called. The word has been suggested to me by M. Ampère, who has continued to assist me with his valuable advice in the composition of this Memoir, for which I here take the opportunity to tender him my grateful acknowledgements.

↑ This change in the faculty of ulterior transmission is not the only modification that radiant heat undergoes in passing through the diathermanous bodies. It becomes also more or less susceptible of being absorbed in different quantities by the black and the white surfaces. This fact can be thus proved by experiment:

We take two thermometers of equal sensibility, and after having coloured one of the balls black and the other white we expose them simultaneously to the radiant heat, sometimes direct, sometimes transmitted through a plate of glass. The two thermometers are then observed to rise unequally, but the inequality is greater when the transmitted heat is employed. Mr. Powell, to whom we are indebted for this ingenious experiment, has performed it on calorific radiations from a bright red hot iron and from an Argand lamp. The means of several series of observations furnished, as the ratio of absorption of the thermometer with the black to that of the thermometer with the white ball, 100 : 78 when the red hot iron was employed, and 100 : 72 when the lamp was used. These ratios became 100 : 50 and 100 : 57 when he operated on the rays transmitted through glass. (Report of the First and Second Meetings of the British Association for the Advancement of Science, pp. 274, 275.)

I have obtained numerical data perfectly analogous, by means of the thermomultiplier. The pile of the apparatus was well washed, afterwards whitened on one side and blackened on the other. The two colours were made from lamp black and Spanish white mingled with gumwater. Turning the pile on its stand I caused the direct or transmitted rays of a Locatelli lamp to fall successively on the two coloured surfaces, and observed the corresponding indications of the galvanometer. This experiment is promptly and easily executed. It has moreover the advantage of requiring no more than one thermoscopic body, a circumstance which makes it easier to compare the results than it is found to be when we are obliged to have recourse to two thermoscopes, which seldom or never possess the same degree of sensibility.

I shall now give the ratios derived from this process applied to direct heat, and to heat transmitted through several screens. The calorific effect produced each time on the black surface is represented by 100.

Radiant heat from a Locatelli lamp, (direct, or transmitted through several screens).			Absorbent power of the faces
			black.	white.

Rays direct from the lamp			100	80.5
Rays transmitted through rock salt				80.5
———————————————	alum			42.9
———————————————	glass,	colourless		54.2
——————————————————		bright red		60.6
——————————————————		deep red		77.8
——————————————————		bright yellow.		55.5
——————————————————		deep yellow		63.6
——————————————————		bright green		67.4
——————————————————		deep green		70.5
——————————————————		bright blue		61.0
——————————————————		deep blue		66.9
——————————————————		bright violet		67.6
——————————————————		deep violet		76.7
——————————————————		opake black		84.6

Thus the interposition of the rock salt has no influence on the ratio of the quantities of heat absorbed by tlie two surfaces ; but the alum affects it so strongly that the heat which has traversed a plate of this substance is much less capable than the direct heat is of being absorbed by the white surface. Colourless glass acts in a similar manner though with somewhat less energy. As to coloured glasses, their action is more feeble in proportion as their tint is less vivid. In short the greatest decrease in the absorption of the white surface is produced by the interposition of a yellow glass, and the least by the interposition of the red and the violet, and, as to each pair of plates of the same tint, the less effect is invariably derived from that in which the tint is deeper. This decrease of action which takes place in the vitreous matter in proportion as its transparency is diminished by addition of colouring substances more and more sombre, continues even when the glass loses its transparency altogether; for the plate of opake black glass is that which produces the least difference of absorption between the black and the white surfaces. It is however an exceedingly curious fact that the rays of heat in their passage through the black glass become more absorbable by the white surface than the rays issuing immediately from the lamp, so that the interposition of the black glass has on the direct heat an effect contrary to that produced on it by the interposition of the white glass.

↑ In a note to the preceding Memoir (page 8) I have said that, for the study of calorific radiations the thermomultiplier is preferable to every former thermoscopic apparatus. The great number of experiments that I have since performed by means of that instrument have produced in my mind a thorough conviction of the truth of that opinion. As there are still many experimental researches to be made not only in that class of phænomena, of the history of which we have scarcely given an outline, but in every branch of the study of radiant heat, it is to be wished, for the interests of science, that every investigator would furnish himself with a thermomultiplier. This apparatus, in the state of perfection necessary to ensure good observations, is unfortunately one of those which a person cannot construct for himself until he has made several attempts which are attended with a great loss of time, and which cannot succeed in many places for want of the requisite means. For these reasons I have thought it advisable to put some one in Paris in the way of supplying them to the public. There are excellent ones to be had at M. F. Gourjon's, rue des Nonandières, N° 2. The description of the ingenious means employed by this able mechanic to give to the instrument every improvement which 1 was desirous of having introduced into it would occupy too much time. I shall therefore confine myself to the mention of the principal defects found in the first instruments of this kind presented to the Academy of Sciences by M. Nobili and myself (at the sitting of the 5th of September 1831), but now laid aside for the improved thermomultipliers constructed by M. Gourjon.
In the first place the volume of the thermoelectric pile was too bulky, (being from 36 to 40 centimetres square in section,) a circumstance which rendered it impossible to operate on small pencils of calorific rays: in the next place the galvanometer did not mark fractions lower than half a degree, and the magnetic needles, instead of standing at the zero of the scale, settled sometimes to the right and sometimes to the left at a particular distance for each galvanometer, amounting in some instances to 10 degrees. In fine, the mountings being almost all of wood the pieces became warped by the hygrometrical variations in the atmosphere, and the instrument was rendered unserviceable.
The thermomultipliers of M. Gourjon have thermoelectric piles the acting surfaces of which are not larger than the section of a common thermometer (3 centimetres square). As to the galvanometers they are mounted entirely in copper with the exception of the small pieces necessary for the purpose of isolation: the minuteness of their indications extends to a fourth and even a sixth part of a degree, and the needles, when at rest, stand exactly at the zero of the scale. It is almost needless to add that with these improvements the instrument has lost nothing in sensibility.
↑ [Professor Forbee, however, in his Memoir, Lond. and Edinb. Pliil. Mag., vol. vi. p. 205, et seq., referred to in the Note which we have annexed, has established the fact of the polarization of rays of heat by this means, as well as by those of refraction and reflexion.—Edit.]

[1] The Locatelli lamp is merely a common lamp with one current of air and fed with oil. It has a wick of the shape of a quadrangular prism, which exactly fills the beak, but has no funnel. It gives a fine flame of constant temperature. The Argand lamp produces a flame of much greater intensity.
In the first series of experiments the main object was to determine the difference between the calorific and the luminous transparency. We therefore preferred the source which was least favourable to the establishment of the principal fact which it was then our purpose to verify. In the present experiments we proposed more particularly to examine the calorific transparency by itself. It was therefore necessary to operate upon rays that had not been forced to undergo a transmission previously to their being employed in the experiments.

[2] I have been unable to procure plates of glass thinner than ${\frac {7}{100}}$ of a millimetre. But we shall see presently that all other diaphanous substances, whether natural or artificial, are in their effects more or less analogous to glass. Now there are several crystals which spontaneously separate into plates of great tenuity, and are, consequently, well calculated to show that the ratios of the quantities of heat transmitted by a screen exposed to the radiations of the four sources approximate to equality in proportion as the thickness of the screen is reduced. Thus a plate of sulphate of lime 2^mm·6 in thickness gave for the four transmissions respectively,

14,⁠5,⁠0,⁠0.
These transmissions became

38,⁠18,⁠7,⁠0
when the thickness was reduced to 0^mm·4; and

64,⁠ 51,⁠ 32,⁠ 21
when the thickness was reduced 0^mm·01.

A plate of mica, 0^mm·02 thick, gave for the four transmissions

80,⁠ 76,⁠ 39,⁠ 26.

An extremely thin flake was taken from this plate (which was however not coloured): the four transmissions through this flake were,

86⁠,⁠ 85,⁠ 61,⁠ 46.

[3] This mode of estimating the energy of the calorific radiations enables us to determine without difficulty the ratios existing between the arcs described by the magnetic needle of the galvanometer and the corresponding forces. Let us suppose the calorific source removed sufficiently far from the pile to produce but a feeble deviation of the galvanometer; one of 10°, for example. In the passage of the calorific rays let there be interposed a plate which transmits a certain fraction of the incident heat. We shall suppose this fraction to be 12; the needle will descend to 2°. By bringing the source near, the deviation produced through the plate will be increased. Let us stop, when the needle shall have reached 4°, 6°, 8°, &c. successively; the calorific source will then emit upon the pile twice, thrice, or four times as much heat as before; for the transmission through the same plate exposed to a constant source of heat is always in a constant ratio, and the forces of deviation are proportional to the degrees in those arcs that are very near zero. Let the force which causes the galvanometer to describe the first degree of the scale be represented as 1, we shall then have 10 for the first force or quantity of incident heat, 20 for the second, 30 for the third, 40 for the fourth, &c. Now we know that the first force answers to 10°. In order to determine the deviation produced by the force 20 we have only to remove the plate when the galvanometer points to 4°; the calorific rays will then fall immediately on the pile, the angle of deviation will increase, and if the proportionality of the degrees to the forces continues through the whole extent of the arc of the first 20 degrees we shall see the index stop at 20°: at all events we shall have the corresponding indication. By repeating the same operation when the galvanometer points to 6°, 8°, we shall obtain the quantities sought, that is to say, the degrees answering to the forces 20, 30, 40, &c. Thus we may verify the results contained in the tables of intensities already made, or determine the elements necessary for the construction of new tables.

[p48-4] In many instances I was unable to obtain any transmission, even by employing a very powerful radiation. It is thus that water, which transmits six or seven hundredths of the rays from a Locatelli lamp, completely intercepts the heat of the last three sources. Calculating the limit of error for the case least favourable to interception I found it 1616: the source was then brought very close to the liquid and an equal layer of oil employed, which caused in the index of the galvanometer a deviation of several degrees. Now if the water allows a passage to the radiation from bodies heated even to incandescence or brought to lower temperatures, the part transmitted must be less than 1616 of the incident quantity. I here speak of a layer of 3^mm or 4^mm in thickness: for it is possible and even very probable that layers much thinner than these may be in some slight degree permeable to rays of this kind. Thus we have seen glass of 0^mm·07 in thickness transmit 12100 of the rays emanating from boiling water, while a plate of 1^mm intercepted them totally. But as, in order to compare different transparencies, we must operate on a certain thickness of each medium (for the most opake bodies become diaphanous when they are sufficiently attenuated), so, in order to judge of the calorific transmissions through different bodies, we must take the greatest possible care not to employ excessively thin plates, or at least, if we are compelled by particular circumstances to use such, the substances compared should be perfectly equal in thickness; for in that state of tenuity the least difference of thickness might disturb the order of permeability and cause us to attribute a greater calorific transparency to substances possessing this property in an inferior degree. This is probably the cause of the mistake into which those have fallen who have fancied that they could prove by their experiments that water is more diathermanous than glass.

[5] It appears that Sir David Brewster had lately arrived at the same conclusion by means only of the experiments of Delaroche and Seebeck on the transmission through glass and on the distribution of heat in the solar spectra produced with different prisms, (See Report of the First and Second Meetings of the British Association for the Advancement of Science. London, 1833, p. 294.) But these experiments did not prove that the rays in passing through the different bodies suffer a real infernal absorption analogous to that which light suffers: above all, they were far from proving that this absorptive force, varying in each substance according to the temperature of the calorific source, could, in some particular cases, become constant, and in all respects similar to the action of colourless diaphanous media on luminous rays. On this ground it may be said that the inference of Brewster was yet premature; besides, the illustrious Scotchman rested his conjectures on the erroneous supposition that water has the same absorbent force in respect to all sorts of calorific rays. Experiment indeed leads to the opposite conclusion, as we have already proved in respect to solar heat by the different action of a layer of water on the temperatures distributed in each band of the solar spectrum; an action so widely different relatively to two different rays that all the heat of the violet light passes through the liquid without suffering any sensible diminution, while the nonluminous heat of the isothermal band is totally absorbed, (Annales de Chimie et de Physique, December 1831,) and we have just seen in the preceding note that analogous phænomena are observable in the radiations from terrestrial sources also; for a mass of water some millimetres in thickness intercepts all but a very small portion of the radiant heat issuing from flame and the whole of those rays that issue from any other source.

[6] Athermanous, in contradistinction to diathermanous, evidently signifies the absence of the power of transmitting heat. I adopt this term merely for convenience, without attaching to it a definite meaning; for, as there is no body which, if reduced to an extremely thin plate, may not become in some degree transparent, I think also that some rays of heat may pass through all substances in a state of great tenuity.

[7] Bulletin de la Soicété Philomatique, July 1833.

[p53-8] Seeing that in respect to all the substances given in the table, the rock salt excepted, the order of decrement is similar though the sources of heat are different, one might be inclined at first to infer that they belong to the same species of partially diathermanous bodies, that is, that they may be compared with coloured media. But that such a conclusion is not legitimate will be shown by one example: let a be the species of rays transmitted by the medium A, b that species which is transmitted by the medium B, and c the rays intercepted by the same media. Let us suppose a calorific source that will give 30 a, 30 b, and 40 c; it is clear that the two media A and B will intercept 70 parts of the hundred and transmit 30. However, the rays emerging from A will be different from those which emerge from B. If we suppose a second source of heat such as will give 20 a, 20 b, and 60 c, we shall have 80 as the quantity intercepted and as the quantity transmitted by each of the screens. If the source gave 10 a, 10 b, and 80 c, the transmission would be 10 and the interception 90. Thus two substances exposed to different radiations may furnish calorific transmissions not only varying according to the same order of decrement, but equal in all their periods of variation, although the rays emerging from each may be of a different kind.

[9] Scheele, Traité de l'Air et du Feu, Paris, 1778, § 56.

[10] W. Herschel and Brande, Philosophical Transactions for 1800 and 1820.

[11] Philosophical Transactions, vol. cvi.

[p57-12] Let us imagine the screen of 8^mm divided into seven layers having for their degrees of thickness the differences between two consecutive plates. (See the first table in this Memoir.) The quantities of heat incident on the layers when the radiation is from a Locatelli lamp are

100, 77, 54, 46, 41, 37, 35, 33.5,

and the quantities lost in the successive transmissions are

23, 23, 8, 5, 4, 2, 1.5.

Now the mean losses for the hundredth part of a millimetre of each screen will be

237, 2343, 850, 5100, 4100, 2100, 1.5100,

or 3.286, 0.535, 0.160, 0.050, 0.020, O.O1O, 0.007.

Hence the looses sustained by the rays of the lamp in the first hundredth part of a millimetre of each layer, when referred to the quantities of incident heat, will have the values

3.286100 0.53577 0.16054 0.05046 0.02041 0.01037 0.00735

that is, 0.0328 0.0070 0.0030 0.0011 0.0005 0.0003 0.0002.

By similar calculations the successive losses sustained by the radiations from the incandescent platina and the copper heated to 390° will be found to be

0.0614 0.0081 0.0032 0.0019 0.0010 0.0005 0.0003
0.0943 0.0155 0.0050 0.0022 0.0014 0.0010 0.0008.
Now the differences between every two terms of these series are for the

1st, 0.0258 0.040 0.0019 0.0006 0.0002 0.0001;
2nd, 0.0523 0.0049 0.0013 0.0009 0.0005 0.0002;
3rd, 0.0780 0.0105 0.0028 0.0008 0.0004 0.0002.
As to the fourth source it is useless to speak of it, as its rays are completely extinguished at the distance of one millimetre.

Thus, notwithstanding the inequalities of the increase of the distance from the second and the third layer to the surface of entrance, we observe in the three series the two principles we have laid down, namely, 1st, the decrease of the losses; 2nd, the tendency of this decrease towards a limit at which the loss becomes constant: but for each particular case the points of the medium at which the rays begin to suffer this constant action are evidently placed at a fixed distance from the origin. Therefore, if the glass be divided into equal layers, the limit of the decrease of the losses will be attained more slowly in proportion as the layers are more numerous, that is to say, thinner. It is for this reason that in each series the limit at which the losses become constant depends, as we have already said, on the thickness of the elementary layers.

[p59-13] This result seems opposed to the experiments of M. Bérard on the polarization of reflected heat; but, ignorant as we are of the nature of the relations that caloric and light bear to one another, we have no means of proving that, as no polarization of heat is produced by the transmission through the tourmalines, none can be produced by reflexion at the surface of the glass. I am bound also to remark that some very able experimental philosophers having lately tried to polarize light by M. Bérard's process, their efforts proved unavailing. Mr. Powell informs us that although he had taken the necessary precautions against the heating of the glass and other causes of error he has never been able to discover the least appearance of polarization when operating with nonluminous heat. But he thinks that when he employed luminous sources he was enabled to observe a small perceptible effect by making the rays previously pass through a screen of glass (Edinb. Journal of Science, N. S., vol. vi.) Mr. Lloyd communicated at the last meeting of the British Association for the Advancement of Science (Cambridge 1833) some new results tending to support the conclusions derived by Mr. Powell from his own experiments. [No communication upon this subject by Professor Lloyd appears in the Report of the British Association for 1833.—Edit.]

[14] I employ the word diathermancy as the equivalent of calorific coloration or calorific tint, lest the latter should be confounded with tints or colours properly so called. The word has been suggested to me by M. Ampère, who has continued to assist me with his valuable advice in the composition of this Memoir, for which I here take the opportunity to tender him my grateful acknowledgements.

[p67-15] This change in the faculty of ulterior transmission is not the only modification that radiant heat undergoes in passing through the diathermanous bodies. It becomes also more or less susceptible of being absorbed in different quantities by the black and the white surfaces. This fact can be thus proved by experiment:
We take two thermometers of equal sensibility, and after having coloured one of the balls black and the other white we expose them simultaneously to the radiant heat, sometimes direct, sometimes transmitted through a plate of glass. The two thermometers are then observed to rise unequally, but the inequality is greater when the transmitted heat is employed. Mr. Powell, to whom we are indebted for this ingenious experiment, has performed it on calorific radiations from a bright red hot iron and from an Argand lamp. The means of several series of observations furnished, as the ratio of absorption of the thermometer with the black to that of the thermometer with the white ball, 100 : 78 when the red hot iron was employed, and 100 : 72 when the lamp was used. These ratios became 100 : 50 and 100 : 57 when he operated on the rays transmitted through glass. (Report of the First and Second Meetings of the British Association for the Advancement of Science, pp. 274, 275.)
I have obtained numerical data perfectly analogous, by means of the thermomultiplier. The pile of the apparatus was well washed, afterwards whitened on one side and blackened on the other. The two colours were made from lamp black and Spanish white mingled with gumwater. Turning the pile on its stand I caused the direct or transmitted rays of a Locatelli lamp to fall successively on the two coloured surfaces, and observed the corresponding indications of the galvanometer. This experiment is promptly and easily executed. It has moreover the advantage of requiring no more than one thermoscopic body, a circumstance which makes it easier to compare the results than it is found to be when we are obliged to have recourse to two thermoscopes, which seldom or never possess the same degree of sensibility.

I shall now give the ratios derived from this process applied to direct heat, and to heat transmitted through several screens. The calorific effect produced each time on the black surface is represented by 100.

Radiant heat from a Locatelli lamp,
(direct, or transmitted through several screens). Absorbent power of the faces
black. white.

Rays direct from the lamp 100 80.5
Rays transmitted through rock salt 80.5
——————————————— alum 42.9
——————————————— glass, colourless 54.2
—————————————————— bright red 60.6
—————————————————— deep red 77.8
—————————————————— bright yellow. 55.5
—————————————————— deep yellow 63.6
—————————————————— bright green 67.4
—————————————————— deep green 70.5
—————————————————— bright blue 61.0
—————————————————— deep blue 66.9
—————————————————— bright violet 67.6
—————————————————— deep violet 76.7
—————————————————— opake black 84.6

Thus the interposition of the rock salt has no influence on the ratio of the quantities of heat absorbed by tlie two surfaces ; but the alum affects it so strongly that the heat which has traversed a plate of this substance is much less capable than the direct heat is of being absorbed by the white surface. Colourless glass acts in a similar manner though with somewhat less energy. As to coloured glasses, their action is more feeble in proportion as their tint is less vivid. In short the greatest decrease in the absorption of the white surface is produced by the interposition of a yellow glass, and the least by the interposition of the red and the violet, and, as to each pair of plates of the same tint, the less effect is invariably derived from that in which the tint is deeper. This decrease of action which takes place in the vitreous matter in proportion as its transparency is diminished by addition of colouring substances more and more sombre, continues even when the glass loses its transparency altogether; for the plate of opake black glass is that which produces the least difference of absorption between the black and the white surfaces. It is however an exceedingly curious fact that the rays of heat in their passage through the black glass become more absorbable by the white surface than the rays issuing immediately from the lamp, so that the interposition of the black glass has on the direct heat an effect contrary to that produced on it by the interposition of the white glass.

[16] In a note to the preceding Memoir (page 8) I have said that, for the study of calorific radiations the thermomultiplier is preferable to every former thermoscopic apparatus. The great number of experiments that I have since performed by means of that instrument have produced in my mind a thorough conviction of the truth of that opinion. As there are still many experimental researches to be made not only in that class of phænomena, of the history of which we have scarcely given an outline, but in every branch of the study of radiant heat, it is to be wished, for the interests of science, that every investigator would furnish himself with a thermomultiplier. This apparatus, in the state of perfection necessary to ensure good observations, is unfortunately one of those which a person cannot construct for himself until he has made several attempts which are attended with a great loss of time, and which cannot succeed in many places for want of the requisite means. For these reasons I have thought it advisable to put some one in Paris in the way of supplying them to the public. There are excellent ones to be had at M. F. Gourjon's, rue des Nonandières, N° 2. The description of the ingenious means employed by this able mechanic to give to the instrument every improvement which 1 was desirous of having introduced into it would occupy too much time. I shall therefore confine myself to the mention of the principal defects found in the first instruments of this kind presented to the Academy of Sciences by M. Nobili and myself (at the sitting of the 5th of September 1831), but now laid aside for the improved thermomultipliers constructed by M. Gourjon.
In the first place the volume of the thermoelectric pile was too bulky, (being from 36 to 40 centimetres square in section,) a circumstance which rendered it impossible to operate on small pencils of calorific rays: in the next place the galvanometer did not mark fractions lower than half a degree, and the magnetic needles, instead of standing at the zero of the scale, settled sometimes to the right and sometimes to the left at a particular distance for each galvanometer, amounting in some instances to 10 degrees. In fine, the mountings being almost all of wood the pieces became warped by the hygrometrical variations in the atmosphere, and the instrument was rendered unserviceable.
The thermomultipliers of M. Gourjon have thermoelectric piles the acting surfaces of which are not larger than the section of a common thermometer (3 centimetres square). As to the galvanometers they are mounted entirely in copper with the exception of the small pieces necessary for the purpose of isolation: the minuteness of their indications extends to a fourth and even a sixth part of a degree, and the needles, when at rest, stand exactly at the zero of the scale. It is almost needless to add that with these improvements the instrument has lost nothing in sensibility.

[17] [Professor Forbee, however, in his Memoir, Lond. and Edinb. Pliil. Mag., vol. vi. p. 205, et seq., referred to in the Note which we have annexed, has established the fact of the polarization of rays of heat by this means, as well as by those of refraction and reflexion.—Edit.]

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

0.0614	0.0081	0.0032	0.0019	0.0010	0.0005	0.0003
0.0943	0.0155	0.0050	0.0022	0.0014	0.0010	0.0008.

1st,	0.0258	0.040	0.0019	0.0006	0.0002	0.0001;
2nd,	0.0523	0.0049	0.0013	0.0009	0.0005	0.0002;
3rd,	0.0780	0.0105	0.0028	0.0008	0.0004	0.0002.