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1434458Scientific Memoirs — On the Application of Electro-Magnetism to the Movement of MachinesMoritz von Jacobi

Article XXVI.

On the Application of Electro-Magnetism to the Movement of Machines; by M. H. Jacobi, Doctor of Science, and Professor at the University of Dorpat.

[Published at Potsdam, 1835.]

PREFACE.

The great discovery of M. Oersted, which has so much extended the limits of physical science, promises to open a new career to practical mechanics. The motive powers which have hitherto served for the movement of machines are not, properly speaking, forces; they are only masses animated by forces. These masses are made to act upon the point of application of a machine, and they consequently can only give it a velocity conformable to their own moving principle. But magnetism enables us to employ immediately a force; the point of application is the force itself. We thus perceive a considerable active force produced without any external influence. The interest of such a phænomenon is increased extremely by the simplicity of the apparatus and by the facility of conceiving its mode of action. But on examining it more closely, we find that the forces which are active in producing the movement present a great complication of circumstances. The study of the phænomena of electricity and magnetism is still in its infancy; and we are not surprised that every day makes us acquainted with new phænomena at once striking and unsuspected. The views which I had conceived of these forces have in part been confirmed during the course of my researches, and they have in part been shaken and even completely changed; as soon, however, as I was obliged to abandon one view, another presented itself which led to the disclosure of fruitful results. For example, the remarkable reaction which prevents the movement from becoming accelerated to infinity has become a new source of power; the exact knowledge of the galvanic action leads to a minimum of the expense attending its maintenance. I have restricted myself in my researches to such experiments as touch immediately upon the object itself; and from the number of these, I shall only publish those which have given results, or at least lead us to hope for them: I have suppressed as much as possible all purely theoretical considerations. As to the practical application, it appears to me decided by my experiments; to go further will be only to augment an effect, with which, laying aside sanguine expectations, we may already be content. It is no unusual thing to have electro-magnets which lift 2000lbs.; mine carried only from 30 to 40 at most: nevertheless, these feeble magnets furnished me with a mechanical action equal to half the force of a man. To maintain this action, during eight hours, scarcely half a pound of zinc is required, everything being properly arranged.

I have not yet been able to construct a larger apparatus, and I therefore wished to make as much use as I could of the one I possessed, since it was capable of showing completely the nature of the active forces. My experiments may be easily repeated; all depending upon carefully attending to the construction of the commutator, and likewise that of the galvanic apparatus. Those who are acquainted with electro-magnetic phænomena will easily be able to make the necessary arrangements, and to give the accurate proportion to the several parts. The object of this memoir will be attained if it inspire an interest for a subject which merits it.

Königsberg, August 21, 1835.

MEMOIR.

1.

In November 1834 I had the honour to lay before the Academy of Sciences of Paris a note upon a new electro-magnetic apparatus. That note was read at the meeting of December 1st; and an abstract of it was printed in the Institute, No. 82, of December 3rd, to which I refer. Since that time MM. Botto and dal Negro have claimed the priority of the invention, the former in the Institute (No. 110) of June 17th. The competition in which I find myself engaged with such distinguished men serves only to confirm my conviction of the importance of this new motive power. A discussion as to priority is only of historical interest. It is not astonishing that persons, who had scarcely any communication with each other, should have devoted themselves almost at the same time to the study of the same object. But we ought not to conceal from ourselves that, after the grand discovery of M. Oersted and the experiments of Mr. Sturgeon, who, it seems to me, first gave a great magnetic intensity to soft iron by means of an electric current, and viewing the instantaneous manner in which this magnetism may be destroyed or reversed, by merely changing the direction of the current,—it was not difficult to conceive the possibility that some motion or some mechanical operation might be produced by the electro-magnetic excitation of soft iron. In short we must award the palm to M. Oersted; whilst we who follow him shall have the merit of having known how to apply this new power to practical purposes and the wants of life: and this will be reserved for him who shall best have understood the mechanical and physical principles of this motive power.

2.

In May 1834 I constructed the first magnetic apparatus with a primitive continuous circular motion. It is true that, like M. dal Negro, (with whose labours I regret that I am not better acquainted,) I had several years ago conceived the idea of applying this power to mechanics: but I could not at first divest myself of the idea of making this application by means of an advancing and receding motion, produced by the attractive and repulsive power of magnetic bars,—a motion which, by known means, might have been changed into a continuous circular one. It seemed to me that an apparatus of this kind would have only the merit of an amusing toy, which might find a place in the cabinets of men of science, but would be entirely inapplicable on a large scale with any advantage.

For considering the general equation of active forces applied to the movement of machines

\Sigma \int _{0}^{a}M\,ds-\Sigma \int _{0}^{a'}P\,ds'=\Sigma mv_{'}^{2}-\Sigma mv_{0}^{2}

the magnetic action, during the amplitude $a$ , and represented by $\int _{0}^{a}M\,ds$ , could not be perfectly exhausted by the action $\Sigma \int _{0}^{a'}P\,ds'$ , unless the active force gained during the movement becomes zero, or $\Sigma mv_{'}^{2}-\Sigma mv_{0}^{2}=0$ . Now the magnetic attraction is a function of the space, the form of which we do not sufficiently know, this function being affected by the nature of the distribution of the magnetism in the body, of whatever form. The law of this distribution is scarcely established with regard to bars of steel of a regular form, magnetized to saturation and deprived of consecutive points. With regard to bars of soft iron of considerable dimensions, magnetized by an electro-conductive helix, we have analogies only, but no experiments. But however this may be, we know well that this function must be expressed by a very convergent series, so that the magnetic attraction will be in an inverse proportion to the square or to the cube of the distance, or, stopping at the three first members, will perhaps be composed of them. The magnetic points then approach each other with an accelerated motion; the active forces increase, and reach their maximum at the instant when the contact is completed: but this force ought then to be destroyed. It will destroy itself by the fixed points of the machine, and by the vibration of the system: but this will be in an unprofitable manner. There will be a complete loss of the active force obtained $\Sigma mv_{'}^{2}-\Sigma mv_{0}^{2}$ . We know the ill effects of shocks in the movement of machines, but there is here another inconvenience which is not simply mechanical. The soft iron, by these repeated shocks and vibrations, gradually acquires at the surface of contact the nature of steel; there will be a considerable permanent magnetism, and the transient magnetic force, which alone produces the movement, will be weakened in proportion. A number of experiments which I have made upon the magnetic force of a bar of soft iron bent into a horseshoe (of which I shall speak hereafter) has shown me the great disadvantages of oft-repeated shocks, proceeding from the sudden contact of the armature. But, if we stop at the mechanical principles of magnetism, it may be objected that the active force gained will not be absolutely lost for the purposes of utility; that in part the elasticity of the iron will itself reproduce it; that another portion may be regained by springs properly applied, or by other mechanical methods which may be invented. We leave the appreciation of all these factitious means and of these superadditions to those who are in the habit of constructing machines; they well know their insufficiency, the great loss of working power, and how rapidly all the systems are destroyed, unless the greatest care be paid to the preservation of the active forces. But we must seek the means of this preservation in the nature of the forces themselves. The history of the steam-engine teaches us that its improvement commences with Watt's ingenious idea of stopping the escape of the steam before the piston had accomplished its stroke, and of causing the steam afterwards to act by its own expansion. Watt understood the subject: all he did was to give to the function $P=\phi (s)$ , which expresses the action of the steam, such a form as $\int _{0}^{q}P\,ds=\int _{0}^{a'}P'ds'$ , and thus the active force gained becomes zero, all the prejudicial and destructive vibrations in the machines previously constructed cease, and the power of the motive force is converted for the most part into useful action. I must here cite the valuable researches of M. Poncélet on the construction of hydraulic wheels,—a work founded upon a profound comprehension of the same principles.

These considerations, at once clear and simple, have induced me to reject entirely every apparatus in which magnetism is applied to produce immediately an oscillating motion; these constructions being, as we have seen, as inadmissible as they are impracticable of execution on a large scale.

3.

In the note which I had the honour of laying before the Academy of Sciences of Paris I stated that, in accordance with all experiments, magnetism is a power acting like universal gravitation, solely in some function of space. The integral ${\frac {\int _{0}^{a}M\,ds}{a}}$ comparable with the known number $g$ , represents the mean action furnished by the attraction of two points, and is not at all affected by their relative velocity. The inversion of the poles being effected instantaneously, we should thus have a velocity infinitely accelerated. Now a system moving round an axis, and capable of a continuous circular motion, is that which is alone susceptible of such a velocity. It cannot become uniform, unless some resisting element, or some other action depending on the velocity, is introduced into the system. Putting aside the application to practical use which has to be made of such an apparatus, the obstacles to be overcome, inseparable from the system, consist only in the friction of the pivots in the sockets, and in the resistance of the air. As to the former, repeated experiments have proved that the friction is independent of the rapidity of rotation, at least within the limits of experiment; this resistance, therefore, can in no way contribute to render the accelerated motion uniform. It is in fact the resistance of the air which will act to produce this effect. Although it might be reduced at pleasure, principally by giving a suitable form to the rotatory system, it would not be entirely annihilated. But it will be allowed, that we should have reason to be well satisfied with the mechanical effect of magnetism, if this were the only cause which tended to reduce the accelerated movement to a uniform movement. The limits of such a uniform velocity must be very distant. I do not speak, of the great simplicity of a magnetic machine with a continuous circular motion, of the advantages of construction which are gained by being able to transform with ease this motion to any other which the working machine may require. These considerations had strongly impressed my mind, even whilst the means of execution were still unknown to me, but I always kept in sight the practical application, and the object appeared too important for me to exhaust my powers in the construction of see-saw toys, which might claim the honour of being placed in the rank with the electric chime relatively to their effect, and still more relatively to the tinkling with which they are accompanied.

4.

Fig. 1. of the annexed plate represents the magnetic apparatus of eight bars, arranged symmetrically upon a disc moveable round the axis $A$ , and of eight fixed bars similarly arranged upon a fixed platform. The arrangement of the bars admits of the greatest variety, provided it be exactly symmetrical, and that it allow the poles to approach each other as nearly as possible. To prevent the action being too oblique,—since the centre of magnetic gravity is probably at some distance from the extremity, as in the ordinary magnetic bars,—it is preferable to make this arrangement so that the axes of the cylindrical bars shall be situated rectangularly, and not parallel, as in the figure. It must be further observed, that there will be some difficulty in forging bars of considerable dimensions into the horseshoe form, so that the axes of the branches be situated exactly at the same distance, and that the branches themselves be exactly cylindrical. Filing them into shape will perhaps have the disadvantage of hardening too much the surface of the iron, and of rendering it less apt to receive and to part with the magnetism. The form proposed offers a further inconvenience, in the application of the copper wire helices, which have to be previously bent on another cylinder of the same dimension. These helices ought very nearly to touch the bars, which should be covered with silk on account of the insulation which is necessary. In future an arrangement similar to the one in fig. 2 will be preferred, in which $f$ are the fixed bars, and $m$ the bars moveable around the axis $a$ . We shall have the advantage of being able to employ cylindrical bars of soft iron, such as may be had of all dimensions in the shops. It will only be necessary to cut them into equal pieces, and the helices may be strongly wound round the bars by means of the lathe.

5.

As the magnetic attraction decreases rapidly as the distance increases, the integral $\int _{0}^{a}M\,ds$ will always be such a function of the amplitude $a$ , that its value will not greatly differ from a constant, $a$ being rather considerable. Admitting, for an instant, that the magnetic attraction is in an inverse ratio to the squares of the distances, we shall have $\int _{0}^{a}M\,ds=\int _{0}^{a}{\frac {f\,ds}{d^{2}+s^{2}}}={\frac {f}{d}}\;{\mbox{arc}}\,tg{\frac {a}{d}}$ , $d$ being the distance of the magnetic centres when the bars are placed the nearest possible; thus $d$ being very small with respect to $a$ , $\int _{0}^{a}M\,ds={\frac {f\pi }{4d}}\;{\mbox{or}}\;={\frac {nf\pi }{4d}}$ , representing the number of bars. We shall then have for the action of the motor, during one entire revolution, the expression ${\frac {n^{2}f\pi }{4fd}}$ . The radius of the circle upon which the bars are arranged does not enter into this expression; and for a stronger reason it will not enter into any of the other expressions, if the attraction still decreases more rapidly than the inverse ratio to the square of the distance. Thus the size of the circle for the same number of bars scarcely adds anything to the action of the motor.

I conceived that the system of bars, which in my apparatus are fixed, might also be rendered moveable. The rotation of the two systems will then be in a contrary direction and have the same velocity, the masses being equal. These two motions might be combined by means of conical wheels, in order to produce the motion of a second axis of rotation intended for the work. The action of the motor, during the amplitude $a$ , that is to say from one meeting of the poles to the other, would be as above ${\frac {nf\pi }{4d}}$ , but the poles meeting each other $2n$ times in one \revolution, we should have ${\frac {2n^{2}f\pi }{4d}}$ , or double the previous action. We might even construct wheel-work in such a manner that the velocities of the systems should be in the ratio of $m:1$ , and that the poles should meet $(m+1)n$ times, during one revolution. The action would then be $(m+1)n^{2}{\frac {f\pi }{4d}}$ , and this increase would be gained by purely geometrical means. This is a simple deduction from the fact that velocity does not enter into magnetic attraction. I have not as yet availed myself of this advantage in the construction of magnetic apparatus, since there are some remarkable circumstances, as we shall see hereafter, not sufficiently cleared up, and which may give rise to considerable modifications.

6.

The inversion of the poles is an object of the greatest importance. This inversion should take place instantaneously, and precisely at the place where the poles are situated opposite to one another. The mechanism intended to produce this operation should be put in motion by the apparatus itself, but no element should be introduced which is dependent in a geometrical manner upon the rotatory movement of the system. The velocity of the motion, however great it may be, should not at all affect this operation. The well-known bascule, an ingenious invention of M. Ampère, which is so advantageously employed in electro-magnetic experiments, cannot be employed in the magnetic apparatus with a continuous circular motion; for the number of inversions, in a given time, cannot be considerable without requiring extraordinary means; and even these means will not guarantee the certain result of an advancing and receding movement, repeated as frequently as may be necessary. I shall not recount here all the attempts I have made, both numerous and expensive, to arrive at the important result of an inversion of the poles, exact and precise, divested at once of every element depending on the velocity. But it is necessary to say that the greatest difficulties arose by employing mercury, as is usual in electro-magnetic experiments to form and to break metallic contact. In the liquid state the adhesion of the mercury to the metallic body plunged into it and afterwards withdrawn, varies with the rapidity of the motion and with the purity of the mercury. Frequently—I may say always—the inversion takes place too soon or too late, and thus gives rise to an attraction or repulsion, in a contrary direction to the rotation. Moreover it is very difficult to preserve the mercury pure when in contact with other metals; and even the purest mercury is disposed to oxidize easily under the influence of the electric sparks. These sparks are produced, under favourable circumstances, on establishing metallic contact, and always on breaking it. The result is, that the surface of the mercury is soon covered with a coating of oxide, which either entirely prevents the metallic contact, or at least weakens it. In employing amalgamated surfaces this effect is produced still more rapidly. Besides I have by incontestible proofs arrived at the conviction, that the simple contact of metals with a clean surface is quite sufficient to conduct the electric current, even of the weakest tension. The contact by means of mercury adds nothing to the energy of this current. It is erroneous to judge of this energy by the brilliancy of the spark, proceeding only from the combustion of the mercury. I have thought right to mention these circumstances, though apparently trifling. In a motor, from which we look to obtain an infinitely accelerated motion, the smallest details should not be disregarded; the most trivial are ultimately of importance.

7.

Fig. 3. represents the Commutator, adapted to the magnetic apparatus, so as to produce the inversion of the poles: $a,\,b,\,c,\,d$ are four discs of copper fixed upon the axis of rotation $e\,e$ . The discs $a,\,b$ and $c,\,d$ are united by copper tubes $f,\,f$ , entirely insulated from the axis by the interposition of a tube $g$ , of varnished wood or any other insulating substance.

The periphery of each disc is divided into eight exactly equal parts, of which four $h$ are cut into sectors and filled afterwards by pieces of ebony, forming with the metal an accurate and smooth surface. The discs are arranged upon the axis of rotation, so that the sectors of wood and of metal alternately correspond, as represented by the shaded parts of the figure. $ZZ,\,CC$ are bars of copper, formed as levers, very moveable in their supports: they are intended to conduct the current. The arm of the longest lever forms at its extremity an edge, which rests on the periphery of the corresponding disc. The other arm is bent and plunged into a little jar filled with mercury, $k$ . The jars $k\,k$ and $k'\,k'$ are united by plates of copper, as represented in figure 1. The action of this commutator will easily be understood. The levers are always in contact with the discs, and are alternately so with the metallic and insulating parts. By their mobility in their supports they yield to the slightest inequality of the surface. and the friction they occasion is very trifling. The helices which surround the moveable bars are united so as to form a continuous wire, the ends of which $l,\,m$ are soldered respectively to the systems of the discs $a,\,b$ and $c,\,d$ . The other helices, wound round the fixed bars, are also united, and the ends $n$ and $o$ immersed, the one in a jar of mercury $p$ , attached to the voltaic apparatus, and the other in the jar $k$ of the commutator. Thus all the sixteen helices form only one connecting wire, through the medium of the commutator. The voltaic apparatus consists of four troughs of copper, in which plates of zinc are immersed, all being united as in a pile. The direction of the current is shown in fig. 3 by little arrows; it is reversed each time the poles meet, provided the commutator be so placed that the edges of the levers shall quit one of the divisions in order to pass to the other. This inversion acts, as is seen, instantaneously, and quite independently of the velocity of rotation. The object is too simple, and sufficiently explained by the figures, to render it necessary to enter more into its details. I may add, further, that this same system of the inversion of the poles is applicable to any number of bars, provided that the sections of the discs are equal to them in number. I have constructed, for magneto-electric experiments, a double commutator of eight discs, with seventy-two divisions. In this apparatus there are also four levers similar to the former, which rest upon the cylinders ( $f$ ) that unite the discs in pairs. The other extremities of these levers are likewise immersed in jars of mercury, intended to receive the ends of a connecting wire, which is to be traversed by the voltaic or magneto-electric currents, sometimes in one direction sometimes in the other. The instrument is put in motion by a handle, which can be easily turned twice in a second, and effect in the same time 144 double inversions. It will be easy to change or completely interrupt the electric current 1000 or more times in a second. The nature of this current or of the magnetism will of course be better understood by decomposing it into a rapid succession of pulsations: I am persuaded, for instance, that we should succeed by this means in charging a Leyden jar, or in effecting any chemical decompositions by the thermo-electric current of a single pair of elements.

8.

The magnetic power is produced and maintained, as is well known, by the action of the voltaic apparatus. By using zinc as a positive metal, copper as a negative metal, and water acidulated with sulphuric acid as the conducting liquid, it is the transformation of the metallic zinc into sulphate of zinc which here constitutes the cost of keeping the apparatus in action. It is a matter of the greatest importance to reduce as much as possible this cost. Let us examine what is the relation between the magnetism of the connecting wire and the action of the voltaic apparatus. Since the discovery of electro-magnetism this object has engaged the attention of distinguished scientific men, but it presents so many difficulties and such a complication of circumstances, that we cannot be surprised that the theories and formulæ which they have endeavoured to deduce from experiments differ considerably.

This is not the place to enter into the criticism of these theories; but it appears to me that the theory established by M. Ohm, in a little work entitled "Die galvanische Kette, mathemutisch bearbeitet von Dr. G. S. Ohm (1827)," and developed more fully in various memoirs printed in the German Journals, presents so much simplicity, and agrees so well with all the phænomena of the voltaic pile, that I have not hesitated to adopt it, in order to obtain from it a general basis for the arrangement of the different elements of the magnetic apparatus. I may be permitted here to state the fundamental principles of this theory.

1. In a closed voltaic circuit the same quantity of electricity passes across each section which is perpendicular to the direction of the current, whatever be the form or the matter of the different parts of the circuit.

2. Whatever change is made in one part of the circuit, this change affects the entire action of the pile, and is not confined merely to the place where the change takes place.

3. The voltaic action, in whatever manner measured, is in the direct ratio of the electro-motive power, and inversely as the resistances which oppose themselves to the passage of the current, or $A={\frac {E}{R}}$ .

4. The resistances are composed of—

a) the resistance of the solid conductor or of the connecting wire. For the same substance this resistance is directly as the length of the wire, and inversely as the transversal section or as its thickness.

b) the resistance of the liquid conductor: this is in the direct ratio of the thickness of the liquid stratum which separates the positive and negative plates, and inversely as its transversal section, which coincides generally with the surface of the plates. During the action of the pile this last resistance increases, and at the same time the electro-motive power, or $E$ , is affected by it. This is caused by chemical effects which take place and change by degrees the nature of the liquids, the surface of the metals, and the electric tension. But fixing any state of the pile, the law cited always exists. The difficulty of making electro-magnetic experiments comparable with each other, and the still greater difficulty in obtaining absolute measures, consist principally in the continual change of these elements. Thus in expressing by $r$ the resistance of the connecting wire, we shall have ${\frac {rl}{d}}$ for the resistance of a wire, of a length $l$ , and of a thickness $d$ ; ${\frac {r'l'}{d'}}$ will likewise be the resistance of the liquid conductor, the surface and thickness of which are respectively expressed by $d'l'$ . Therefore the action of the current, or the quantity of electricity passing through the pile, will be $A={\frac {E}{{\frac {rl}{d}}+{\frac {r'l'}{d'}}}}$ .

5. The electromotive force is in the direct ratio of the number of voltaic pairs united in a pile, and at the same time the resistance $r'$ increases in the same proportion. Having one pile of $n'$ pairs, the force of the current will be expressed by $A={\frac {n'E}{{\frac {rl}{d}}+{\frac {n'r'}{d'}}}}$

6. If the electric current is divided into several branches, the lengths of which, reduced in an inverse ratio to their diameter, may be expressed by

l,\,l',\,l'',

&c., the total action will be the same as if there were only a single connecting wire whose length is expressed by the equation

{\frac {1}{L}}={\frac {1}{l}}+{\frac {1}{l'}}+{\frac {1}{l''}},

&c. Therefore having

n

wires of the same length, the total force of the current will be expressed by

A={\frac {n'E}{{\frac {rl}{nd}}+{\frac {r'l'n'}{d'}}}}={\frac {nn'dd'E}{rld'+r'l'dnn'}}

.

As we can avail ourselves of the magnetizing power of each unity of length of the connecting wire by coiling it round bars of the same dimension, the total power gained by a connecting wire

l

will be

A={\frac {lnn'dd'E}{rld'+r'l'dnn'}}

.

From this formula the limits of the action of the current may be deduced, which cannot be increased by the number or the surface of the voltaic pairs, by the length, the diameter, and the number of the connecting branches. Increasing only the surface of the pairs $d'$ , the limit of the total power of the current will be $A={\frac {nn'dE}{r}}$ ; increasing the number $n'$ , this limit is $A={\frac {ld'E}{r'l'}}$ .

Again this limit will be, by increasing the length of the wire $l$ , $A={\frac {nn'dE}{r}}$ ; the thickness of the wire $d$ , $A={\frac {l'd'E}{r'l'}}$ ; the number of the connecting branches $n$ , $A={\frac {ld'E}{r'l'}}$ .

In general, in order to increase the force of the current to any degree, it is necessary to enlarge the surface of the plates, and at the same time the thickness of the connecting wire or the number of the branches. The increase of the number of the pairs requires that of the length of the connecting wire, in order to attain the same end.

The experiments, as accurate as they are numerous, which M. Fechner has made on this subject, and which he has published in his work "Maassbestimmungen über die galvanische Kette (1831)," leave no doubt as to the justness of these laws, which express in a very simple manner all the relations of the different elements which constitute the voltaic pile. These experiments have been made for the most part by employing the method of oscillations, which M. Biot was the first to apply ingeniously to this kind of experiments.

9.

In admitting at first that the chemical effects which take place in the voltaic pile, and which represent the expense attending the magnetic apparatus, are in a direct ratio to the active surfaces, it seemed to me of great importance to establish the relation between the surface of a voltaic pair and the weight capable of being supported by a bar of soft iron submitted to the magnetizing power of the current. A bar of soft iron 1½ inch in diameter by 29 inches in length, weighing 14½lbs., was bent into a horseshoe, so that the centres of the branches were seven inches apart. The bar, covered with silk, was covered by a helix of copper wire of 1¼ line thick and 35 feet long. The magnetic power was measured by means of a steelyard, and a weight supported by rollers, in order to slip easily over the arm of the lever. The surface of the soft iron armature was of a somewhat convex form, in order that the extremities of the branches, forming a flat and smooth face, should only be touched in the direction of an edge, the position of which formed a right angle with the direction of the lever. The armature was in contact with the extremities of the branches when the lever was placed horizontally. Upon the latter had been marked a scale, the divisions of which indicated the thirtieth part of the sliding weight, to which was affixed an index: it was easy to estimate the tenths of these divisions. I had taken the necessary precautions to avoid as much as possible the errors of observation arising from the disposition of the apparatus. I shall not enter here into the details of the construction of this rather complicated apparatus, which I intend to give elsewhere, as it may be useful for experiments of this kind. The electromotors which I employed consisted of copper troughs three quarters of an inch wide, and sufficiently large to enable me to immerse in them respectively the plates of zinc of 4, 16, 36, 64, 100, 144 square inches. The contact of these last with the copper was prevented by the interposition of pieces of wood. The conducting liquid, of which I had previously prepared a sufficient quantity to serve for a series of experiments, was acidulated with ten per cent. of concentrated sulphuric acid of the specific gravity of 1·840. The experiments, with the same voltaic pair, were made without interruption; but after each one precautions were taken to cleanse carefully the zinc plates, to wash the trough with water and to renew the liquid, in order to restore the same state of action. But subsequent observations convinced me that the original state is restored more certainly by exposing the plates, and especially the negative one, to a current of air, until it is perfectly dried. It will then be no longer necessary to renew the liquid so frequently, especially when the observation is confined to the primitive state. It must be acknowledged that I subsequently found the copper troughs to be ill adapted for electro-magnetic experiments; concentric cylinders, which may be plunged in the liquid, are much better. These cylinders must be fixed firmly enough to remain at the proper distance, without recurring to the interposition of wood or of any other insulating matter. Much more constant galvanic effects may be obtained if the space occupied by the liquid between the two metals be not too narrow; at all events it ought to exceed half an inch. I have also made experiments with voltaic pairs arranged like the calorimotor of Hare, but there were reasons for rejecting these also. It is a very different thing to make an isolated observation, and to put in requisition the galvanic action for whole hours and days. It is in the latter case that for practical purposes measures are required, the necessity of which had not been before anticipated. It will be also necessary to reject the use of copper as a negative metal; the expense of employing silver, platina, or at least copper well plated with silver, gold, or platina, must be no obstacle. The solution of the copper in the sulphuric acid, however weak it may be, and its reduction into a metallic state, by the secondary effects of the nascent hydrogen, give rise to partial galvanic effects, by which the principal action is much affected, and to avoid which the greatest pains must be taken. In fact the motion of the magnetic apparatus was sometimes suddenly slackened or entirely interrupted, and on examining more closely I found that metallic particles of cementing copper or of iron had been deposited all along the pieces of wood interposed, or upon the bottom of the troughs, and thus formed a partial circuit. I shall speak of zinc hereafter. The following is the table of observations which I have made on the magnetic power of the horseshoe bar of iron above dsecribed.

Surface
of Pair.

No. 1.

No. 2.

No. 3.

No. 4.

No. 5.

No. 6.

No. 7.

No. 8.

No. 9.

No. 10.

Force.

mean.

calculated

square
inches

lbs.

4

41·46

40·31

47·19

43·18

45·47

48·88

46·52

55·21

54·07

47·75

47·3

16

126·32

123·43

125·21

125·67

128·47

130·16

124·39

120·55

130·16

136·16

126·45

126

36

156·98

216·54

180·04

189·73

184·31

185·30

205·91

211 —

157·38

162·77

185 —

182·3

64

201·72

208·29

195·14

197·33

199·99

198·32

201·25

202·92

197·41

203·83

200·62

216·1

100

266·63

243·21

236·45

235·65

229·93

232·75

228·79

227·11

236·05

236·3

144

311·8

221·46

210·17

198·88

210·17

198·88

192·23

……

144a^[1]

258·56

257·66

254·46

252·12

256·22

253·02

……

255·34

249

The values given in the last column have been calculated according to the formula $A={\frac {(233\cdot 6)x}{20+x}}$ , the constants of which were found by the method of the least squares. It is true that there are considerable differences between the observations of the same series, but there was no reason to choose those which agreed the best with each other, and to attribute the differences to an error of observation.

10.

I have read in an extract from the memoir of the Abbé dal Negro inserted in the "Annali delle Sc., 1813 [1833?], Marzo e Aprile, 105—120," that this author established a remarkable law, viz. that the magnetizing power is in the direct ratio of the perimeter of the electromotor, and that the surface has scarcely any effect in increasing this power. I did not delay making some experiments in order to confirm this law, which appeared to me of great importance for the œconomical effects of the magnetic machine. Two plates of zinc and copper, 36 inches long and 7 inches wide, were coiled into a helix, and separated from each other to a distance of one fourth of an inch by small pieces of wood in the manner of the calorimotor; the whole was plunged into water acidulated with ten per cent. of sulphuric acid. The mean weight which the bar was capable of supporting, whilst this pair of 252 square inches was employed, was taken from five experiments and amounted to 297·12 lbs.

From the same piece of copper and zinc I also cut two plates, 96 inches long and half an inch wide. These plates were coiled in the same manner and separated to an equal distance. The mean value of the magnetic force, when this electromotor of 48 square inches was employed, was also drawn from five observations and amounted to 133·79 lbs. By employing a liquid much more acidulated the weight might be increased to 180·49 lbs.

These two experiments cannot be classed with the others, as the circumstances attending them differed. But the perimeter of the first electromotive helix being 86 inches long, and that of the second 193 nches, it does not appear that the law of M. dal Negro is confirmed by these two experiments. There are many empirical formulæ in physics incapable of being carried out to the extremes, but they ought at least to be sufficiently general not to fail on the slightest attempt to extend their limits. Besides, I have taken the pains to calculate the experiments of M. dal Negro from the formula of M. Ohm. The fourth column of the following table indicates the results according to the ascertained formula $A={\frac {41\cdot 55x}{14\cdot 4+x}}$ , in which $x$ represents the surface of the pair of plates.

Surface.			Perimeter.		Force
Surface.			Perimeter.		observed.		calculated.
6	square	inches	14	inches	13·85	kilogr.	12·22	kilogr.
12	"	"	16	"	18·2	"	18·89	"
18	"	"	18	"	22·8	"	23·08	"
24	"	"	20	"	24·6	"	25·97	"
30	"	"	22	"	25·8	"	28·07	"
36	"	"	24	"	29·6	"	29·68	"
42	"	"	26	"	30·3	"	30·94	"
48	"	"	28	"	32·8	"	32	"
54	"	"	30	"	33	"	32·8	"
60	"	"	32	"	35·6	"	33·51	"

The second column of the preceding table, which contains the perimeter of the plates, represents at the same time the forces according to the law of M. dal Negro. That distinguished experimentalist did not make these experiments to verify the theory of M. Ohm; but the beautiful agreement of his observations with that theory sufficiently proves that they were made with great accuracy.

11.

Since 1831 Mr. Faraday has published from time to time experiments made with a view to investigate the nature of electricity and of its various effects. These experiments, both from their extent, the certainty and ingenious sagacity which they manifest, and the abundant results to which they have led, deserve to be ranked with the most eminent labours which have ever been made in physics. By a happy chance, which I cannot over-appreciate, these labours coincide with the efforts which I have made to render available the mechanical action of magnetism.

In observing a voltaic pair of plates of copper, silver or platina, and of common zinc plunged into acidulated water, we notice a great development of hydrogen gas. If the circuit be not closed this gas will be developed only on the surface of the zinc; but if the circuit be completed, there will be also a development of gas on the surface of the copper, or in general on the negative plate. This last quantity of gas is incomparably less than the first, and yet it is from this alone that the magnetic power of the connecting wire proceeds. The gas, abundantly disengaged on the surface of the zinc, does not contribute anything to this effect. On taking a plate of amalgamated zinc, instead of common zinc, or some amalgam of zinc, there will be no development of gas except when the circuit is closed; in breaking it this development ceases, the zinc in this combination not being attacked by the acid, or not being able of itself to decompose the water. It is not easy to explain this extraordinary fact. In such a pair of plates all the hydrogen gas, or its equivalent of zinc, serves to produce an electric current, whose magnetic force, calorifying power, and chemical action, are in a direct ratio to the quantity of disengaged gas or of oxidized zinc; and these different effects may equally serve to measure the quantity of electricity passing through the connecting wire, or even through the apparatus. The definite action of electricity, with regard to the chemical action, to decompose bodies, is incontestably proved by the numerous and ingenious experiments of Mr. Faraday. It will not be long before he will prove the law with regard to other effects; but the conviction of genius gives the right to anticipate experiment, and to announce great laws.

Amalgamated zinc is much more positive than common zinc, and its effects are much more decided. Moreover a voltaic pair of plates of this kind possesses a remarkable constancy, provided there are no secondary effects arising from the precipitation of the negative metal upon the positive plate. It may happen that some particle of the zinc may not be well amalgamated; in that case a direct action of the acid upon the zinc takes place, there is a development of hydrogen in that place, the negative metal accidentally dissolved in this liquid will be reduced in it by the gas, and there will be a partial pile, which will affect the principal action. These partial effects will be propagated by degrees over the whole surface, the positive state of which will then rapidly decrease. This will only take place when the negative metal is soluble in the acid.

12.

I have made many experiments on this subject. A thin plate of zinc of seven inches square, and weighing 848 gr., was amalgamated, in order to form a voltaic pair with a plate of copper of the same size. The liquid was sulphuric acid, of a specific gravity of 1·105. There was no development of gas on the surface of the zinc: the bubbles of air which formed there by degrees rose so slowly, that they might with propriety have been disregarded, even if there had not been reason to believe that they were for the most part the atmospheric air contained in the water. After five hours of action the plate was again weighed, and had lost only 112 gr.; during this time the pair of plates had been twice withdrawn from the acid, and dried for five or six minutes near a stove.

The following is the table of the deviations of the needle which denote the decrease of the energy of the current.

Time.	Deviation.	Time.	Deviation.
8ʰ 12′	61°	10ʰ	60°
8ʰ 22′	59°	10ʰ 30′	58°
8ʰ 30′	58°	11ʰ	57°
8ʰ 42′	57½°	the pile was dried
8ʰ 56′	56½°	11ʰ 5′	61°
9ʰ 10′	55½°	11ʰ 30′	60°
the pile was dried		12ʰ	59½°
9ʰ 16′	62°	12ʰ 30′	58°
9ʰ 30′	61°	1ʰ	57°

The following day the experiments were repeated with the same pair of plates. The decrease of the deviation was not so rapid as before, and the original energy always restorable by drying the plates; once it even increased to 65°. At 10ʰ 50′ in the evening the deviation was still at 55°. The action must have continued through the night, but the next morning the plate was found broken in pieces. Amalgamated zinc is too fragile to be employed in too thin plates. In order to compare the effects, a plate of common zinc of the same size was combined with a plate of copper and plunged into the same acid. The deviation was at first 55½°, after 43′ it lowered to 12°, and on drying the pair of plates 13° was the highest to which it could be restored. On being subjected to the action of the acid for 1¾ʰ, the plate had disappeared, and its insoluble parts only remained.

I have also made experiments upon a liquid amalgam of zinc poured into a porcelain basin covering a surface of 48 square inches; instead of a plate I employed a copper wire of 1¼in. diameter, coiled into a flat spiral, in order to let the gas escape more easily. The effects of this combination were very extraordinary; for, without anything being touched, the needle had during fifteen hours' action only receded 11½° from 60°, and remained fixed at 49½°. After breaking the circuit, and exposing the spiral to the air for some time, the deviation was restored to 59°. This experiment was the more striking as the multiplier of the galvanometer consisted only of a single coil of copper wire 1¼ lin. in thickness; for it is known that the decrease of the needle is much more feeble on employing a very long and slender wire.

A plate of gilt copper and an amalgam of zinc, composed of one atom of zinc and one of mercury (Zn. Hg.), a composition which is solid enough to be used in plates, gave also very good effects, both as to the constancy of the deviation and to its restoration.

In order to try some other compositions, which, according to Ritter, are still more positive than the amalgam of zinc, I had some plates cast, of an equal size, of lead, tin and zinc, of different alloys of these metals, and of different amalgams. The alloys were composed of atom to atom^[2], and moreover a plate of each composition was also amalgamated at its surface. The direction of the deviation of the needle of the galvanometer determined the place which each alloy ought to occupy. The liquid in which the plates were plunged was sulphuric acid diluted with four parts of water. I must remark, that the slightest change of the surface frequently affects the place of the metals the electrical relation of which does not differ much. It is chiefly in lead and its alloys that this phænomenon is most strikingly exhibited. Lead freshly polished is very positive in relation to lead exposed to the air for some minutes or steeped in any acid. The following is the result of two series of experiments, which I have made with the greatest care.

— ⁠Series I.
Tin.
Alloy of lead with tin. (Pl. Sn.)
Lead.
Tin amalgamated.
Lead amalgamated.
Amalgam of tin. (Sn. Hg.)
Alloy of zinc with tin, (Zn. Sn.)
Amalgam of lead. (Pl. Hg.)
Alloy of zinc with tin and lead. (Zn. Sn. Pl.)
Alloy of zinc with lead. (Zn. Pl.)
Alloy of tin with lead amalgamated.
Zinc.
Alloy of zinc with tin amalgamated.
Alloy of zinc with lead amalgamated.
Alloy of zinc, tin, and lead amalgamated.
Zinc amalgamated.
Amalgam of zinc. (Zn. Hg.)
Amalgam of an alloy of tin and lead. (Zn. Pl. Hg.)
Amalgam of an alloy of tin and zinc. (Sn. Zn. Hg.)
Amalgam of an alloy of tin, zinc, and lead. (Sn. Zn. Pl. Hg.)
Amalgam of an alloy of zinc and lead. (Zn. Pl. Hg.)
+

— ⁠Series II.
Tin.
Lead.
Tin amalgamated.
Amalgam of an alloy of tin with lead.
Alloy of lead with tin.
Lead amalgamated.
Amalgam of tin.
Alloy of zinc with tin.
Amalgam of lead.
Tin with lead amalgamated.
Alloy of zinc, tin, and lead.
Alloy of zinc and lead.
Zinc.
Zinc amalgamated.
Alloy of zinc, tin, and lead amalgamated.
Alloy of zinc and lead amalgamated.
Amalgam of zinc.
Amalgam of an alloy of tin and zinc.
Amalgam of an alloy of tin, zinc, and lead.
Amalgam of an alloy of zinc with lead.
Alloy of zinc with tin amalgamated.
+

We see by the above that the alloys, and principally the amalgams, are always positive with relation to the simple metals. Most of the amalgams, excepting those of tin and lead, may be used in plates. As to the chemical action upon these various compositions, it did not take place in the amalgamated zinc and the amalgam of zinc, any more than in any of the alloys and amalgams of tin and lead; but in all the other compositions of zinc the disengagement of gas was very brisk. In the first series, the amalgam of an alloy of tin and lead occupies a very positive place, but the hope of profiting by this is negatived by the second series. In employing the amalgamated plates or the amalgams of zinc, there occur various circumstances the cause of which I have not yet been able to discover. During the voltaic action particles of amalgam are often detached in the form of flakes, which float on the liquid, and are deposited on the copper or on the negative plates, so that these become by degrees amalgamated. By this the action is considerably weakened, or ceases altogether; for it is very remarkable that copper, silver, or platina, amalgamated on their surface, have scarcely any, or at most an extremely weak power of keeping up an electric current with any other metal. I have often remarked that the first deviation of the needle was very strong, and that at length it returned quickly to its first position of equilibrium, without exhibiting any deviation, whilst the voltaic circuit, composed of zinc and amalgamated copper, remained always closed. It appears to me also remarkable that a wire of copper, platina, or iron can be much more easily amalgamated under the influence of sulphuric acid by mercury containing other metals than by mercury entirely pure. It is desirable that this point should attract the attention of scientific men to make similar experiments with more attention.

Pure zinc has nearly the same qualities as amalgamated zinc or the amalgam of zinc, viz. of being very little acted upon by sulphuric acid. It is only subjected to chemical action when it enters into a voltaic combination. I refer, on this subject, to the important memoir of M. Aug. de la Rive, inserted in the Bibliothèque Universelle, vol. xliii. 1830. I have not yet been able to procure any pure zinc to repeat these experiments and to employ it in the magnetic apparatus. In zinc foundries pure zinc may easily be obtained in great quantity by re-distilling fit until it is purified of the cadmium and other extraneous metals. Its cost would not be much increased, but hitherto here has not been sufficient inducement to employ pure zinc to risk the expense of the repeated distillation. M. Fengler, manufacturing chemist at Myslowitz in Upper Silesia, has constructed the necessary apparatus for preparing pure zinc in large quantities; he could supply it for nine ecus the quintal, provided a quantity of three quintals were ordered, but unfortunately his foundry has since been burnt down. His process consists in interrupting the distillation when all the cadmium is driven off, in then changing the recipient and again interrupting the process as soon as he suspects that the other foreign metals are volatilized or mechanically drawn away. He repeats these operations as frequently as he thinks necessary. The zinc thus prepared should not be re-cast in iron crucibles.

13.

The rapid decrease of the voltaic effects in the ordinary voltaic piles opposes a great obstacle to the application of electro-magnetism. It may be overcome, partly at least, by an assiduous study of these effects. The motion of my magnetic apparatus was always very rapid at the commencement, but its velocity soon diminished, and ceased entirely after a lapse of time which never exceeded an hour. By employing amalgamated plates of zinc I have succeeded at three different times in making the apparatus work successively during 20, 22, and 24 hours without making any change whatever in the pile. The experiments were always interrupted by some accident, and I think that the action would otherwise have lasted still longer. The disengagement of gas was very inconsiderable, and took place only at the surface of the negative plate. The velocity was always at first from 120 to 122 revolutions in a minute, and decreased about half an hour after to 62 revolutions; a circumstance which is attributable to the commutator, which had not then the present construction. During the rest of the time the motion of the apparatus was remarkably uniform, making from 58 to 62 revolutions in a minute. I must however confess that I have obtained so extraordinary an effect only three times. There were always external circumstances, dependent upon the form of the voltaic apparatus, which counteracted the effect. I might be able to master most of these circumstances by constructing a new apparatus, the manipulation of which will be more convenient and the effect more certain.

14.

We have expressed by $A={\frac {E}{R}}$ the magnetic force of each section of a wire traversed by an electric current. This force is measured by the deviation of the needle or by the magnetizing power of the connecting wire. By adopting the law of Faraday we may equally measure this current by the disengagement of the gas, which represents at the same time the cost of maintaining in action a voltaic apparatus. If $D$ be the quantity disengaged, we shall have $D={\frac {E}{R}}$ . From this it follows that recurring to the formulæ of article 8, the œconomical effect may be expressed by the magnetic power of the whole extent of the connecting wire, divided by the development of the gas. This effect is in no respect changed either by the enlargement of the surface, or by the employment of various branches wound spirally around different bars of the same dimension. But by multiplying the helices, and uniting them to form a continuous wire, the œconomical effect may be increased as much as we please. For the disengagement of the gas, in employing $n$ helices or $n$ units of length, will be expressed by $D={\frac {E}{nr+r'}}$ ; but we may put in action the magnetizing power of the whole extent of the conducting wire, and we shall have for the total force $F={\frac {nE}{nr+r'}}$ or ${\frac {F}{D}}=n$ When the magnetic bars are intended to produce a mechanical motion, the increase of the œconomical effect will reach its limit; since by multiplying the number of the bars, the weight of the apparatus and the friction of the pivots in the sockets will be at the same time increased, so that that effect can only be expressed by ${\frac {F}{D}}=n-{\frac {(nr+r;)nf}{E}}$ . The maximum of the œconomical effect obtainable will depend on the value of $f$ or of the friction. By differentiating the second member with respect to $n$ , we shall have for this maximum $n={\frac {E-fr'}{2fr}}$ .

The bar which was used in the experiments of article 9 weighed 14½ lbs. Being adapted to any moveable apparatus, the friction it occasions would amount at most to ½ lb. It has been found by experiments: $E=283.6$ , $r'=20$ , $r=1$ , and $f={\frac {1}{2}}$ , thus $n=273.6$ ; that is to say, there would be the greatest possible advantage in employing about 273 bars wound round with helices of the same size. This number varies with the size of the plates: for a surface $m$ , we have $n={\frac {mE-fr'}{2fmr}}$ . In short the magnetic power available for practical purposes is ${\frac {nE}{nr+r'}}-nf={\frac {(E-fr')^{2}}{(E+fr')2r}}$ .

15.

In employing a voltaic battery, the œconomical effect will be diminished, unless at the same time the helices united in the same wire be multiplied; for Mr. Faraday has proved by the experiments reported in the articles 990, &c. of the Eighth Series of his Researches, that the same quantity of electricity passes through a voltaic battery of any number of pairs of plates which traverses a single pair of the same size. The quantity of gas disengaged at the surface of each plate of the battery is the same as at the surface of a single pair; this at first sight appears astonishing, and seems to contradict numerous experiments which have been made upon the pile; for every one knows that the quantity of gas disengaged by the decomposing apparatus, and at the same time the deviation of the needle, increase up to a certain point, by multiplying the number of plates.

In considering the formula $F={\frac {n'E}{n'r'+r}}$ where $n'$ represents the number of pairs of plates, $r'$ the resistance of each pair, and $r$ that of the connecting wire, or of the body which we wish to decompose, we must suppose that in the experiments of Mr. Faraday (990.) the connecting wire of the battery and of the single pair of plates were so short that its resistance $r$ might be entirely neglected in relation to $n'r'$ . We should not have obtained this striking result if we had employed a connecting wire of any considerable length, and still less if we had closed the circuits of the pair of plates and of the battery by any decomposing apparatus. Mr. Faraday has established a very exact distinction between the quantity and intensity of electricity set in motion. The first may be measured in different ways; but it will be difficult to find an exact measure for its intensity, nevertheless this would be very necessary for completing the theory. In admitting the important law of equivalents in galvanic decompositions, it appears that we ought to multiply these equivalents by the number of pairs of plates necessary to effect the decomposition. This would perhaps be the true measure, for after all it is necessary to consume a great number of atoms of zinc, in order to decompose a single atom of any other substance less decomposable. In what relates to the difference between quantity and intensity, caloric offers analogies; and in judging of a quantity of gas, we ought always to know its volume and its density. I must here quote another observation of Mr. Faraday, which is found in the Seventh Series, art. 853. He is speaking of a current which is, he says, "powerful enough to retain a platina wire 1104 of an inch in thickness red hot in the air during the whole time" (3¾ minutes); and he adds in a note: "I have not stated the length of wire used, because I find by experiment, as would be expected in theory, that it is indifferent. The same quantity of electricity which, passed in a given time, can heat an inch of platina wire of a certain diameter red hot, can also heat a hundred, a thousand, or any length of the same wire to the same degree, provided the cooling circumstances are the same for every part in both cases," &c. This is quite correct, but we may add that it would be necessary to multiply the number of pairs of plates in the same proportion with the length of the wire to obtain a current of the same quantity.

In short in order to heat a wire of 1000 inches to the same degree to which a wire of a single inch would be heated by a single pair of plates, it is necessary to disengage 1000 quantities of gas, proceeding from the same number of pairs. I have thought it right not to suppress this remark, considering that in the practical employment of the voltaic pile œconomy is requisite.

16.

The following is the table of experiments which I have made upon the deviation of the needle with relation to the quantity of gas developed at the surface of the negative plate of a voltaic pair of plates of silver and amalgamated zinc. The specific gravity of the sulphuric acid was 1·25.

Deviation of the Needle.	Time elapsed in the disengagement of 1 cubic inch of hydrogen.	Deviation of the Needle.	Time elapsed in the disengagement of 1 cubic inch of hydrogen.
42° 45′	50″	26° 30′	189″
41° 30′	57″·5	24° 52′	217″
39° 30′	64″·5	23° 52′	231″
34° 45′	89″	23° 7′	246″
32° 22′	108″·5	21° 30′	290″
29°	144″	20° 15′	312″
27° 30′	167″	20° 7′	330″
27° 15′	166″

The bubbles of air rising regularly enough to serve as a measure, I have reckoned, in another series of experiments, the time which elapsed in developing 10 bubbles of air. The following is the table:

Deviation of the Needle.	Time elapsed in the disengagement of 10 bubbles of hydrogen.	Deviation of the Needle.	Time elapsed in the disengagement of 10 bubbles of hydrogen.
34° 30′	22″·5	18° 22′	80″
32° 30′	25″	15° 15′	101″
31°	27·″5	14° 30′	124″
22°	56″	14° 20′	126″
21° 37′	57″	14° 10′	129″
21° 22′	59″	13° 20′	147″
19° 37′	67″	13°	160″

It is necessary to remark, that there was also a very feeble development of gas even at the surface of the zinc, which was taken into account. But the quantity of gas measured was, I believe, less than the quantity of gas developed; for there was a secondary action, which was manifested by the blackness of the plate of silver, and which we must attribute to a metallic reduction of the oxides dissolved in the acid. As it is very difficult to translate into forces the deviation of the needle^[3], these tables will not tend to confirm the law of Mr. Faraday: they only show that the deviation of the needle follows the same course as the development of the gas. I shall repeat the experiments, but reversing the process; that is to say, the development of gas will be taken for the most exact measure of the force of the current, and the value of the degrees of the galvanometer wall be deduced from it, either immediately, or by some formula of interpolation of convenient application. The experiments cited are not sufficiently rigorous to form the elements of calculation.

17.

To return to the magnetic machine. We had succeeded in obtaining an inversion of the direction of the current, both instantaneous and exact, by the commutator described above in article 7, the effect of which is not at all affected by the quickness of rotation. We had even succeeded in obtaining, at least for some time, a tolerably constant voltaic apparatus. In short, the means have been discovered of reducing the expense of maintenance to a minimum, by preventing the direct action of the acid upon the zinc, an action which cannot be turned to any use, and which, as is known, greatly surpasses that which serves to produce the voltaic current. Thus the most important difficulties in the practical application of electro-magnetism being overcome, it appeared to me time to examine more closely the nature of the forces which I desired to put in use, and principally to seek for the cause which limits a speed which we had reason to suppose must be infinitely accelerated. This speed had never surpassed 120—130 revolutions in a minute, on employing a pile of four pairs of plates two feet square. We must not lightly abandon conclusions founded on the nature of things, and those to which I refer are drawn solely from the integral $\int _{0}^{a}\,Mds$ , expressing the magnetic attraction and supposed to be independent of the speed. Besides, it rests upon the legitimate supposition that the electro-magnetic excitation of the soft iron operates instantaneously. If this were not the case, my apparatus would have shown that magnetism and electricity ought to be attributed to the motion of material particles, or to oscillations much more perceptible than are those of the propagation of sound. In short no one can deny that it is the nature of a force not to require time to act, and that, if its different effects were not instantly perceptible, it would then be some molecular motion, under the influence of mechanical laws, which takes place.

18.

At the end of my first note I said, that in using thermo-electric piles for the movement of machines, there was reason to fear the magneto-electric currents developed by magnetism in motion. The reaction which thence arises would be almost entirely destroyed in the hydro-electric pile, the liquid conductors offering too much resistance to the passage of these currents. These considerations were founded upon detached experiments. On employing a thermo-electric pile, the deviation of the needle was affected by a magnet which had been placed in a helix forming part of the circuit; this was not the case with a voltaic pair of plates of small dimension. The deviation of the galvanometer, extremely sensitive as it is, was not altered by it. This did not surprise me, since the conducting power of liquids is much below that of metals; but in making experiments on the magnetic force of a bar of soft iron, I have sometimes found considerable differences for which I could not account. I was curious to know if these differences proceeded from the weakening of the electric current produced by a pair of plates with a surface of half a square foot, or from the nature of the iron. I therefore inserted in the circuit a galvanometer at some little distance, that it might not be affected immediately by the magnetism of the bar. I was much astonished to see the needle recede upon my applying the armature, and advance as soon as it was taken off; for it was the first time that I had recognised the double office of the connecting wire, viz. that of conducting the voltaic current, and of representing at the same time a common wire subjected to the influence of a magnet in motion. The helix producing a magnet by the voltaic current is at the same time a magneto-electric helix in which a magnet is inserted. This is the explanation of the problem of the unifonn rapidity of the magnetic machine; for, being put in motion by the magnetizing power of a voltaic current, it represents simultaneously an apparatus composed of magnets in motion, and capable of producing a magneto-electric current, in a direction contrary to the voltaic current. The first is closed by the pile itself, which, being composed of a single pair only, does not offer too great a resistance to its passage.

In the connecting wire, formed by the union of the sixteen helices of the apparatus, I interposed a galvanometer; and then, by closing the circuit and preventing the motion of the machine, I observed the deviation of the needle: it amounted to nearly 60°. As soon as the motion of the apparatus commenced the needle began to recede, and continued to do so more and more as the speed became more accelerated. The motion having become uniform, at the rate of 60 revolutions in a minute, the needle became stationary at a deviation of about 47°. The needle always advanced when the motion was stopped or retarded; it receded, on the contrary, when it was mechanically accelerated. It appears that the deviation of the needle of 47° corresponds with the state of equilibrium; for the motion having of itself ceased, the needle did not quit this position. Thus in the different experiments, whether the first deviation of the needle exceeded 60°, or was less, it always became fixed at about 47°. The voltaic current having been weakened by the interposition of different branches, until the first deviation amounted only to 47°, the magnetism was not sufficiently strong to produce the movement of the apparatus. Repeated experiments will be necessary to investigate these interesting phænomena.

19.

I imagined that it would be useful to open two passages or two separate branches to the magneto-electric current; one of which should be the pile, and the other a second connecting metallic wire, so long and so thin as not too much to affect the quantity of electricity passing through the principal connecting wire. (Art. 8., No. 6.) There was reason to suppose that the counter-current would rather follow the metallic wire than the liquid of the pile: but it was not so. During the motion of the apparatus, the needle of the galvanometer being fixed at 47°, and the second circuit having been suddenly established, the needle was not much affected by it. It advanced, it is true, but only 1°·5. Neither did the speed of the apparatus sensibly change. On reducing the length of the second wire it was nearly the same. The passage of the counter-current across the metallic wire was proved, at least in part, by the interposition of a second galvanometer. During the accelerated movement the needle of this latter advanced in proportion as the needle of the former receded. This might have been expected, provided the counter-current in the secondary branch has the same direction as the voltaic current: it is quite conformable to the remark which M. Nobili has added to the end of his first memoir, upon the theory of the electro-dynamic induction. (Antologia di Firenze, 1832, No. 42.) The ends of the connecting wire surrounding the bars must be considered as the poles of an electro-motive apparatus: moreover the magnetizing power of this counter-current has been proved by making it pass through a helix bent round a bar of soft iron.

20.

In short all tended to prove that the greatest part of the counter-current might be rendered available by employing two apparatus of the same kind, the connecting wires of which, wound spirally round bars of each system, should terminate at the same pile. The counter-current produced by the movement of one apparatus would serve to strengthen the magnetism of the other, and vice versâ: the counter-currents would counterbalance each other to destroy their effects. The experiment could be made on a small scale with the bar above described, the branches of which were encircled with separate helices. Fig. 4. shows the form of the experiment. The two helices were connected by the dotted wire $c\,b$ plunged into the little cups filled with mercury $c,\,b$ . They thus formed a single connecting wire, the other ends of which $a,\,d$ were united with a pile $C\,Z$ . With my hands dipped in acidulated water I took hold of the connecting wire at the place $e,\,f$ , and I broke the circuit at the place $g$ or $h$ . I felt a violent shock. In other respects the experiment was the same as the beautiful one of Mr. Jenkins related by Mr. Faraday. By interposing the multiplying wire of a galvanometer $m$ in the circuit, the needle deviated to 48° by the voltaic current. Then applying the armature, it receded from 48° to 40°. The deviation on removing the armature was unobservable, the latter being too firmly attached. Now the helices were connected with the pile in two branches separated by means of the wires $a\,b$ and $c\,d$ . The wire $c\,b$ was withdrawn. I expected, on breaking the circuit, to find that the magneto-electric current excited in the helix $a\,c$ would be conducted quite entire by the helix $b\,d$ , and vice versâ; but I was mistaken: the shock was not much less: the needle nevertheless receded. I was struck by this experiment, but after all I believe I may regard this magneto-electric arrangement as an unclosed voltaic pile, consisting of two elements united in such a manner as to form only a single pair of plates, as is represented in fig. 5. The currents whose direction is opposed with relation to the wires $a\,b$ , $c\,d$ , unite in traversing a connecting wire placed in contact with the points $e\,f$ . If the galvanic excitation is not in perfect equilibrium, being stronger on one side than on the other, there will be a deviation of the needle proportional to the difference of the currents which traverse the wires $a\,b,\,c\,d$ . This agrees with the experiments which Mr. Faraday has related at the beginning of his Eighth Series, on the subject of decompositions produced by a single pair of voltaic plates. In short what is termed tension is the effect of forces equal and contrary in direction. In mechanics such forces destroy themselves, their sum being zero; but in physics it is different.

With regard to the direction of the magneto-electric current which occasions the shock, it is the same as that of the voltaic current. This was proved by a galvanometer, the multiplying wire of which terminated at the points $e,\,f$ . There was a deviation on a part of the voltaic current traversing the secondary branch $e,\,f$ . On applying the armature, the needle of this galvanometer advanced, at the same time that the needle $m$ receded. The contrary effect might be observed on removing the armature by the blows of a hammer.

21.

The following are some further experiments relative to this subject. The extremities of the bar were surrounded with a thin plate of copper, fig. 6, in the circuit of which was placed a galvanometer. On applying the armature, the needle was unaffected by it; but after having wound the ends of the multiplying wire around the points $e,\,f$ , and the circuit being thus closed, a considerable deviation took place.

An analogous result is shown in the following experiment. On plunging two thin plates of copper, held firmly in the hands, in the cups $a,\,b$ , or $c,\,d$ , of the bar, fig. 4, there was no shock when the circuit was broken by the separation of the wires $a\,b$ or $c\,d$ ; for the human body formed part of a circuit, in which equal excitations took place on two opposite sides. The thin plates being plunged into the cups $c$ and $b$ , a violent action took place at the instant of disjunction.

I formed a thermo-electric circuit of bismuth and antimony, in which was interposed a galvanometer: after having heated the two solderings to the same degree, there was no deviation of the needle; but the multiplying wire having been placed so as to form an intermediary branch, and the solderings being on opposite sides, there was a considerable deviation. This would not have taken place if the circuit of bismuth and antimony had been in its normal state, for then it would have had to conduct the greatest part of the thermo-electric current, provided that the multiplying wire was sufficiently long and thin to intercept only an extremely feeble part of it.

It seems to me that there are circumstances which cause metals to lose their conducting power, and that these same circumstances on the contrary increase that of liquids. Is this the state of bodies which Mr. Faraday calls electro-tonic?

22.

In the supplement of No. 105. of the Institute for May 13, 1835, there is a notice of a memoir by Mr. Faraday the publication of which we are looking for. The experiment cited at the end of this notice appeared to me so striking and important in connection with the subject of the present memoir that I did not delay repeating it. Two copper wires, 400 feet long and ¾ lin. in diameter, carefully covered with silk ribbon, were coiled together in a helix round a hollow cylinder of wood, 1½ inch in diameter. The ends of these two wires were united in a single one. The effect of this combination was beyond all my expectations; for by employing a voltaic pair of silver and zinc plates, which had only a surface of half a square inch, I obtained at the moment of disjunction a brilliant spark, and a violent shock which could scarcely be borne. The same effects took place when the pair of plates were reduced to a wire of platina and zinc. After having placed a cylinder of soft iron in the hollow of the wooden cylinder, the action was still more considerable. These effects were not much increased by the enlargement of the surface of the pair. A conducting wire of 400 feet having been employed alone, the spark and the shock were much more feeble; but on uniting in a circuit the two ends of the second wire of 400 feet, there was neither spark nor shock. This is perfectly conformable with Mr. Faraday's experiment.

Upon this I made the following experiment: In the hollow of the wooden cylinder I placed a cylinder of soft iron, 1½ inch in diameter, forming the armature of the bar of soft iron. We will call the corresponding extremities of the bar and the armature $A,a;B,b$ . The two wires of 400 feet of the helix coiled round the armature were united in one of 800 feet, the ends of which were conducted by a multiplier to the poles of a voltaic pair of plates about ¼ foot square. The helix surrounding the bar terminated at a pile of a foot square, by means of a commutator à bascule. The deviation was 16°. The current which magnetized the horse-shoe bar being directed so as to produce in $A$ the same magnetism as in $a(A_{n}a_{n},\,B_{s}b_{s},)$ , the needle advanced to 30°, and on reversing the current so as to produce contrary magnetisms $(A_{s}a_{n},\,B_{n}b_{s})$ the needle receded from 16° to 10°, returning after a few oscillations to its first position at 16°. By employing a single wire of 400 feet, the other wire not forming a circuit, the deviation of the needle was 21°. By the arrangement $A_{n}a_{n},\,B_{s}b_{s}$ , the needle advanced to 33½°; it receded on the contrary to 13° when the magnetism of the bar and of the armature attracted one another, $(A_{s}a_{n},\,B_{n}b_{s})$ . After having united in a circuit the second wire of 400 feet, the deviation of the needle having been the same as before, that is 21°, the needle advanced and receded by the arrangements above mentioned respectively to 30° and 40°. We see that in this case the needle is rather less affected than in the case of the disjunction of the second wire; but I expected, as a necessary consequence, that the needle would not be at all affected, for I had received no shock nor spark in the analogous experiment. I confess that at present I am unable to enter into an explanation of the striking difference which subsists between the current of reaction and the magneto-electric current.

23.

With regard to the magnetic machine, it will be of great importance to weaken the effect of the counter-current, without at the same time weakening the magnetism of the bars. It is the alternate combination of the pairs of plates or the voltaic pile which permits us to increase the speed of rotation at will. We know that the magnetic power of the current is not sensibly augmented by increasing the number of the pairs of plates, but the counter-current is considerably weakened by it, being forced to pass through a great many layers of liquid. In fact, on using twelve voltaic pairs, each half a square foot, instead of four copper troughs, each with a surface of two square feet, which I had hitherto used, the speed of rotation rose to at least 250–300 revolutions in a minute, a number which I was able only to estimate, having been unable to count them. The acid which I employed was extremely weak, and had served for many previous experiments. The development of gas was imperceptible either by sight or smell. Having immersed two thick copper wires in the cups $p$ and $o$ , and having taken hold of them with my hands dipped in salt water, I received during the motion of the apparatus violent shocks, and felt an extreme pricking sensation in the upper part of my body. The mechanical effect of the apparatus corresponding to the speed of 250 to 300 revolutions in a minute has been valued at half the force of a man. I shall at a future time apply to it an exact dynamometric apparatus.

I have not been able to make further experiments on this subject, and I am obliged to interrupt my investigations for a time; but from what precedes, I may perhaps be justified in maintaining, that the superiority of this new motor, with regard to the absence of danger, the simplicity of the application, and the expense of the materials necessary to keep it in action, is placed beyond doubt.

↑ The first series of experiments, which were made with the pair of plates of 144 square inches, presented such different values that no use could be made of them. I have sought in vain for the cause of these anomalies. After a fortnight the experiments were repeated, and gave values but little different. This is proved by the Table.
↑ In the alloys it is usual to combine the metals according to some relative proportion of weight. I united them by atoms, bearing in mind the general law of true chemical compositions.
↑ Becquerel's Treatise on Electricity and Magnetism, vol. ii. p. 20.

[1] The first series of experiments, which were made with the pair of plates of 144 square inches, presented such different values that no use could be made of them. I have sought in vain for the cause of these anomalies. After a fortnight the experiments were repeated, and gave values but little different. This is proved by the Table.

[2] In the alloys it is usual to combine the metals according to some relative proportion of weight. I united them by atoms, bearing in mind the general law of true chemical compositions.

[3] Becquerel's Treatise on Electricity and Magnetism, vol. ii. p. 20.

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