Philosophical Transactions/Volume 4/Number 45
Beginning the Fifth Year.
PHILOSOPHICAL
TRANSACTIONS.
March 25. 1669.
The Contents.
A PREFACE
To this Fifty Year of the Transactions.
IT may perhaps be expected, that here at the Entrance into the Fifth Year of these Philosophical Communications, something should be prefac'd, as hath been done formerly for an Introduction into each of the Four preceding years, beginning always (accordinq to the English Accompt) in the Moneth of March. Briefly then, I shall make a few fresh Reflections on what is past, to the purpose of Impressing some few things perhaps not altogether inconsiderable, And thence offer a Prospect of what may be hoped to be the Product of our future Endeavours, as God shall vouchsafe to prosper them.
In the first Volume, containing the Transactions of Two Years, 1665, 1666, though we were fatally interrupted by the Plague, Wars, and the horrible Conflagration of our Metropolis; yet we then made an Attempt of laying some Foundation for the Improvement of real Philosophy, and for the spreading of Useful knowledge; in publishing Advices and Directions for the writing of an Experimental Natural History; in pointing out Essays, Patterns and Exemplars, that have hitherto been designed in that kind; in giving notice of divers Artificial Engines and Instruments, which may be helpful for the further Discoveries of Nature, or for the greater performances of Art. We ought out, how far Art had then arriv'd towards the perfecting of the Microscope; and by what means that curious Instrument might be advanc'd; and what Informations it would afford us, either upon the view of minutest Bodies; or of the Texture, Surface, Porosities, Smoothness or Inequalities of other Bodies, that were in our power for such approaches. The like care we had for Telescopes, by what Operations, Engine, and Applications they might he further improv'd; and what was the most, they could thus far perform. Then we related the Finding out of the Rotation of some of the Planets, and the Changeableness, and Seasons of absence, or Obscurity in some of the Fixt Stars, or such as seem'd to he of their Train, And never, I think, were Comets so chaced, their Figures and Appearances so detected, their Motions almost reduced to Rule, and in a manner predicted; the Solar Eclipse in several and distant places carefully calculated. And not to recite here, what was attempted and done by Burning-Glasses; I shall but name the Instruments devis'd to Measure the Weight and the Changes of Weight of the Air, and other ascending and descending Fluids, either with the Pressure of the whole Atmosphere, or of smaller parcels freed from that Pressure; I mean the Baroscopes, and the Pneumatick Engins, There were also offred Hygroscopes, to note the degrees of Drought or Moisture in the Air; Thermometers to measure the degrees of Heat and Cold; and an Instrument to graduate Thermometers to make them Standards of Heat and Cold; an Instrument to measure the Refractions of Liquors of all kinds, for establishing the Laws of Refraction; Hydrostaticks to measure the Weight of Liquids, and divers other Contrivances to find out the Statical position, tendency and gravitation of Liquids in all parts. Besides, Engins to break the hardest Rocks; Huge Wheels and other Engins for Mines described; To raise Winds, by the fall of Waters; An Instrument to examine the greatest Depths of the Seas; Another, to try for fresh waters in the bottoms of some Seas; Pendulum-watches to ascertain Longitudes. But I must refer to a greater store of such useful Inventions commemorated by Mr Sprat in his History of the R. Society.
Neither had I here mention'd these, but to give this Advertisement; That sometimes one of these Instruments may open a fair Portal for more Volumes of the most obliging Philosophy, than can he absolv'd by many hands in some Ages. It will not be meer Preface, but closely agreeable to the Intention of these Tracts, if I here instance one particular, which may possibly seem to some of the lowest value, and yet may chance to prove of greater importance, than at first we are apt to imagine. I will name good Scales both of the nicest kinds, and some of a stronger frame. Now this I would represent. 'Tis certain, some Bodies do increase their weight in a strong Fire: See the Experiment in the said Hist. of the R. Society, p, 228. And Honorable Mr Boyle hath proved, That even Solid and Coldest Bodies have their Atmospheres; Some their Electricity; and same their Magnetismes: And 'tis palpahle, that some draw more Aliment, either from the Earth, or from subterraneous Liquors, or Spirits, or from the Nutritious parts of the Air, or other Influences, which descend through the Air, than they expend in their Atmospheres; And perhaps more at certain State times, till they have acquired their due Increment. This being observ'd, it seems easie to devise, How to examine by Scales, Glasses, and such slight furniture, whence Vegetables, many kinds of Stones, Metals, and other Minerals, have more or less of their Increment, and whence they obtain the stronger Fermentation, which conserves them, or promotes their perfection in their kind: Whether Glass, or what other Materials, do obstruct or retard the resort of any or all of these Spirits, Heats, or Influences: Whether Evergreens, the most fragrant or strong-senting, hot or cold Plants, draw more of their substance from the free Air; and which draw more from the subterraneal supplyes, And so we may examine Earths; and Minerals. We see many Tracts of Land, which yield peculiar Ferments, sometimes Vitriolate Earth, sometimes Aluminous, sometimes Nitrous, sometimes common-Saline, healing Bolus's, and Earth proper for Fullers, Tobacco-pipes, &c. Sometimes the ferment is so hot, as to hollow the surface faster than can easily be allay'd by Mixtures of a more sullen soyl. And sometimes the Natural surface is so sillen, as to swallow and devour the richest Compost, before it rewards the industrious Husbandman or Gardner: And some do highly pretend to make by Art Nitri-fodinas perpetuas; to devise the Magnets, which shall draw to our Use the Alimental Nitre of the Air. I shall not stay to engage for er against either of these, but by those curious Utensils we may soon examine, What may be done in good earnest, and how far clear Experiments will answer to those alluring promises. And though we should fail of the Particulars, yet thence we may chance to dive into some Secrets of very useful Philosophy, and find other Influences, than are either Electrical, or in the common sense Magnetical, but pregnant to disclose the Causes, and to remove the Defects of Fertility, and to impart other no less valuable vertues. For there are more kinds of Vegetables than are commonly so call'd, or so consider'd; as our History of Osteo-colla, and the beautiful Stone-plants growing on the hard Rocks in Jamaica (to omit many other Instances) do testifie. And we see by Experience, that peculiar Earths, Fullers Earth, Tarras for Vessels, and some kinds of Stones, and of Mineral Ores, have their real Increase of Substance in their times of Seasons, and proper plane. Many Noble Persons are Lovers of Gardens, and are willing to entertain Exoticks; and are provided of the Rocks, Grots, and Crypta's: Possibly, if they shall have a desire to search into the Causes of these over-hot ferments, and of the slow-pac'd duller Earth, they may happily fin unexpected Treasures in their own private Inclosures. The Spade and Pick-ax will shew the proximate Causes, or at least some of the Concomitants of every kind of Fertility, and of every kind of Barrenness; and the Scales will distinguish real and substantial growth, and the seasons of it, from deceiving Expansions: And then, by Arches and Vaults, by opening Springs, by heaps of Stones, here of Lime-stones, there of Marl-stones, and in severals of Pebbles, white and black Flints, Marcasites, Mineral Ores, Magnets, and Bodies of the strongest Electricity, where they may be had, some laid as in their Natural Beds, and some dislodged in an unkind posture, we may Artificially frame such subterraneous Furnaces and Stoves, as may, by a calm Process, afford us some of the Wonders of Divine Chymistry. And thus we may have refrigerating Conservatories for cooling Lenitives. Here we may feed moistning, drying, oily, acid, embalming, tartarous, and every other sort of Steams and Vapours: And what every Mass effects upon the Confiners at what seasons, and at what distance, the Scales and other Implements may detect. The Ingenious Sanctorius hath not exhausted all the results of Statical Indications. They may serve to calculate or weigh all sorts of Transpirations, to discriminate Generative, Nutritive, Sanative, Restorative, and Benigne, from Maleficiate and Noxious Spirits; and may instruct us how to guard from what is hurtful, and how to retain that which is congenial. This Memorandum was due to those Worthies, who have contrived these Philosophical Tools; and who, in despight of Calumny and Raillery, have in these and many other respects deserv'd as great Names (I must say this softly) as they, who have adorn'd the best Records of foregoing Ages. But to return; Here in their first Volume were also dispatch'd Enquiries and Directions for all Travellers by Sea and Land, for our Correspondents and all ingenious persons residing in the more famous parts of the World; to revise and return a safe Testimony of all such Observables of Nature and Excellencies of Art, as carry the greatest fame, or seem most considerable for Use or Instrustion. We have farnisht particular Inquiries for Mines, for Seas, for Springs, and for the Effects of the late Invention of Transfusing Bloud, and Medicated Liquours into the Veins of Animals.
In the second Volume, containing the Transactions of the Year 1667. we spread somewhat more largely abroad the Inquiries proper for more places of principal note; and then we received from our Correspondents, and publish'd, many not un-instructive Answers. And here were added more Instruments of Art, some newly devised, as an Instrument for Measuring the Diameters of Planets to great exactness. We offered fuller Directions for Sea-voyages; collected divers Anomatical researches; related many odd effects of the Transfusion of Bloud, and of Medicins into the Veins of Animals, a deeper Investigation and further Accompts of Respiration; a dissected Animal preserv'd alive by the Wind of Bellows; the Influence of Air upon the Life and Growth of Vegetables, upon Luminous Bodies, and Burning Coal, &c.
In the third Volume, for the Year 1668. (besides a good store of Instructive Answers to the former Inquiries, and some further Progress in the disclosures of Nature) hath been introduc'd something of Algebra, and other branches of the Mathematicks and Mechanicks, for the use of those that are studious in those Noble Arts, as well to direct in the best Methods, and to detect Erroneous adventures, for the behoof of generous Beginners, as for the satisfaction and further encouragement of them that have attain'd higher accomplishments.
Also, in each of these Volumes, hath been given the Breviate and Substance of such Philosophical Writings, as came abroad, and were thought of good worth. And all along we have interspers'd many Histories, Philosophical Observations and promiscuous Experiments.
And now, I think, we may take our Prospect, and see, that we have got more ground in our second Volume than in the first and more yet in the third than in either of the former; whence we take the liberty to ominate well for the future. Yet in all that I assume nothing to my self, but give all what it due to the merits of my generous Correspondents. And all that have affection for Arts and Sciences may rejoyce to see the late Proficiency of the Ingenious and Nobler Students in both our famous Universities, and tn all the Universities of Christendom. The Ingenious French have drawn the same Yoke with us, in publishing their Journal des Scavans; and the Romans have followed our Example in their Giornale de Letterati. And doubtless all Civil Nations, who have a Gust for useful knowledge, will, in good time, drive on this Example; and then, as the Light increaseth, and runs on, we shall in a like proportion become so many mutual Ayds to each other: And that will hopefully redound to the General good of Mankind.
I doubt not but the Reader will pardon the Prolixity of this Preface, since, as was promis'd, it is not onely Preface, but bears a part of my main business, which is, to excite and animate the Industry and free Communications of others; of some of whole Effects take for the present the Specimens following.
The Description
SEe Fig. I. Wherein A. is a small Sight with a short arm B. which may be turn'd round about, and mov'd up and down the small Cylinder CD. which is screw'd into the piece ED. at D. this piece E D moving round about the Center E; by which means the Sight may be remov'd either towards R or F.
EF is a Rule fastn'd onto the two Rulers GG, which Rulers serve both to keep the square Frame SSSS perpendicular, and by their sliding through the square holes TT, they serve to stay the Sight, either farther from or nearer to the said Frame; on which Frame is stuck on with a little wax she paper OOOO, whereon the Picture is to be drawn by the Pen I. This Pen I, is by a small Brass-handle V. so fixt to the Ruler HH, that the point I. may be kept very firm, so is alwayes to touch the Paper.
HH. is a Ruler, that is alwayes, by means of the small strings aaaabbbb, mov'd Horizontally, or Parallel to it self; at the end of which is stuck a small Pin, whose head P is the Sight; which is to be mov'd up and down on the Out-lines of any Object.
The Contrivance of the Strings is this. The two Strings aaa, bbb, are exactly of an equal length. Two ends of them are fastn'd into a small Leaden Weight QQ, which is mov'd in a Socket on the back side of the Frame, and serves exactly to counterpoise the Ruler HH, being of equal weight with it. The other two ends of them are fastn'd to two small Pins H. H, after they have been roled about the small Pulleys N, MM. LL. KK; by means of which Pulleys if the Pen I. be taken hold of and mov'd up and down the Paper, the Strings moving very easily, the Rule will always remain in an Horizontal position,
The manner of Using is is this: Set the Instrument on a Table, and fix the Sight A. at what height above the Table, and at what distance from the Frame SSSS, you please, Then, looking through the Sight A, and holding the Pen I. in your hand, move the Head of the Pin P. up and down the Out-lines of the Object, and the point I. will describe on the Paper OOOO, the Shape of the Object so trac'd.
An Observation
THe Observers, imploying a Telescope of 21 Foot, saw the Planet Saturn, as 'tis represented by Fig. II. the Globe in the midle manifestly appearing both above and below beyond the Ovale of his Anses; which was hardly discernable the last year.
They measur'd divers ways the Inclination of the Great Diameter of the Qvale to the Equator, which (Inclination) was found of about Nine degrees, although at that time it should not be but of Four degrees, according to what M. Hugens hath affirm'd in his Systeme of Saturn, viz. that the Plan of the Ring, which environs the Globe of this Planet, is inclin'd to the Plan of the Ecliptique but 23 deg. 30, m. Bur this last Observation and other like ones of this and the precedent Year being more exact, and made at a time more proper for measuring that obliquity, than were those, which had formerly served for a foundation to determine it; M. Hugens finds that, instead of 23 deg. 30. m. the Angle of the Plans of the Ring and of the Ecliptique must be of 31. deg or thereabout; and that being so, that not onely the Shape, which Saturn hath at present, but also all those, that have been noted since the true ones were observed, do perfectly agree with the Hypothesis of the Ring;See. Fig. 3. as 'tis be found in the French Letters, written by M. Auzout to M. L'Abbé Charles, and printed at Paris, A. 1665. upon the occasion of the Regguaglio di due Nuovo Osservationi da Giuseppe Campani. and particularly that of 1664. in the beginning of July*, which was made, and made publick by Signior Campani, wherein the Great Diameter is double to the Lesser.
As to the round Phasis of Saturn, that Change of the Inclination, was just now spoken of, cannot alter the time of it but very little or nothing; so that M. Hugens still expects this Apparance in 1671. when in the Summer of that Year Saturn will begin to loose his Anses, there being then to remain onely the Globe in the Midle; and will not recover them but about a year after, according to what he hath said in his Book of the Systeme of Saturn.
An Extract
IShall now answer to that particular of your Letter, which concerns Melons, as exactly as I can. All the Seeds, I sent you, produce Melons with a thin and somewhat embroider'd skin, not divid'ed by Ribbs: Some of them have their skin whitish, other of the Colour of Slate. The Melons themselves are not very great, their flesh very red, dry, melting upon the tongue; not mealy, and of a high mile. And these are the two onely kinds, which, after I have tried above an hundred different sorts, I make use use of, and send you, not having observ'd any change in them, after the use of 20 years.
As to the manner of cutting them, you know, that the first thing appearing of them, are two Leaves united, here called Ears (mark't in Figure IV. by 1.1.) Out of the midst of these two Ears there shoots, some days after, first one Leaf, which we call the first Leaf or Knot (mark't 2.) and out of the same place, after some days more, shoots a second, call'd the second knot (mark't 3.) Out of about the midst of the Stalk of this second knot shoots the third knot (mark't 4.) And this third knot it is, which must be cut at the place markt 6, without hurting the branch of the second knot, whence this third came; because that from that place will spring a branch, which we call the first Arm, and this Arm will shoot forth first one knot, then a second, then a third; and this third it is, you are to cut again in the same manner, as was said before. And you mutt be careful to cut these third knots, without staying for the shooting of the fourth or fifth ones. You'l see out of every knot come forth Arms or Branches like to the first, spoken of before; and it is at those Arms, that the Melon will be produced. And they will be good, if the foot or root be well nonurish't in good earth, and cherish't by a good hot-bed and the Sun. But let the foot of the Melon never pass into the dung, nor the earth be water'd but moderately, when you see it grows too dry, so as the shoot might thereby suffer; which yet you must not delay, till it happen, lest the remedy come too late. I water twice or thrice a week in very hot weather, and that about Sun-set; and I cover my Melons with a Straw-mat from eleven of the Clock in the fore- to two in the after-noon, when the heat of the Sun is too violent, and too quickly consuming that little moisture, which is necessary for the root. And when it raineth, I cover also my Melon-garden, lest too much wet hurt my fruit. There is some subjection in this, but 'tis also a pleasure to thrive in working by Rule.
If the root produce too many branches or arms, cut away the weakest of them, and leave none but 3. or 4. of the strongest and most vigorous, and such as have their knots nearest to one another. When I transplant my Melons from the Nursery-bed, I put commonly two roots together, except I find one very strong, which I then plant alone, cutting from it neither of the branches that shoot from each side (mark't 7.7.) betwixt the one Ear and the Leaf before spoken of. But when I joyn two roots together, I quite cut away both the branches, that shoot from the two Ears, standing one over against the other, to avoid the disordering abundance of branches; which also would wrong the foot.
The Melons being knit, I leave but two of them upon each foot, chusing those, that are best placed, and next to the first and principal Stalk, that is, to the heart of the foot. I also take care, to leave none but fair ones, and such as have a short and thick tail. The foot also of your Melon must be short, well truss'd, and not far distant from the ground. Melons of a long stem, and having the stalk of the Leaf too long and slender, are never vigorous, and cannot yield good Melons.
It happens sometimes, that at the very first there shoot out from between the two Ears, two Leaves, though I above spoke but of one; but this happens but seldom, and when it does, such two leaves must be reckon'd but for one knot; and afterwards there will shoot out a second, then a third, &c. and so on to 25 or 30, if you be not careful to cut in time: And it is at the extremity of those branches so distant, that Melons will grow; but they cannot be good, because they are so far from the place, which affords them their nourishment; and their Juyce is alter'd by the length of its passage through the branches, which the Sun spoileth; whereas the foot of the Melon being short and well truss'd, there are always leaves covering the branches and even the Melons themselves, until they be near ripe.
Too great heat patches them too much to take nourishment well; and this you must take care of. He that is curious, must every day walk often in his Melon-garden, to cut off all the branches, which he shall observe to be useless, or hurtful, You'l find of them to shoot forth almost to the Eye, and they are capable to alter all, if it be not remedied in time.
I must not forget to tell you, that from the midst betwixt the two Ears and the two first Leaves there shoots out yet one branch more, which ought to be kept, if vigorous, but cut, if weak.
In the Figure I have mark'd a Leaf with 5, shooting out from the midst of the fourth knot: I might have mark'd more, coming forth successively from one another, as you see the fourth come from the third, &c.
We may perhaps the next Moneth impart to the Reader another Letter from the same Generous and Intelligent person, upon the same Subject.
Ac Problematum omnium Solidorum effectio per easdem Curvas.
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Concerning this Probleme, the Author declares himself to be none of those, that search for that which cannot be found, to wit, to perform it by Right Lines and a Circle. 'Tis true indeed, it may be so done, to wit, by tryals and profers; as, who cannot in that manner divide an Arch into three Equal parts? But such Mechanismes are accounted ageometrick; and such operations may be well resembled to the vulgar Rule of False Position in Arithmetick, which cannot give an absolute true Resolution of one of the meanest of Questions, when the thing fought is Multiplex of it self, or Involved; for instance, what Number is that, which multiplyed in it self makes 9; who knoweth it not to be 3? But who can find it to be absolutely so by the aid of the ordinary rules of False Position, wherein the Extraction of a Square Root is not prescribed?
The Author observes; that amongst those, that solve this Probleme by the Conick Sections, they seem to have afforded fewer Effections thereof, than there have been Ages, since it was first proposed. Very few by ayd of a Circle and an Hyperbola or Parabola: by a Circle and Ellipsis none, that he could observe to have been published,
The which the Author considering, and studying how to supply, he found out not onely one, but infinite such Effections, and that not in one Method, but many; following the guidance of which Methods, by the like felicity he hath constructed all solid Problems infinite ways, by a Circle and an Ellipsis or Hyperbola.
1. His general Methods for finding two Means, by a Circle and either an Hyperbola or Ellipsis, are laid down in Prop. 1, 2, 16, and in this 16 Prop. he sheweth to do it with any Ellipsis and a Circle.
2. Particular Effections for finding but one or both of the Means, and Doubling the Cube, in Prop. 3. to 6,
3. And albeit all Cubick Æquations may be solved, either by the finding of two Means, or the Trisection of an Angle, yet he shews the Extent of his Method, in finding out other Infinite ways for the doing thereof, from Prop. 7. to 12.
4. The Trisection of an Angle by a Circle and Hyperbola, Prop, 13, and by a Parabola instead thereof, Prop. 15. And the finding of two Means by a Circle and Parabola, Prop. 14.
In the Second part of his Book De Analysis, the Author first gives you the Analysis or Algebra, whereby all his General Methods of finding two Means were invented. And afterwards, for the advancement of Geometry, gives you the Analysis, that relates to his particular Methods, as in case you would find but one of those Means, and afterwards by an easie operation the other. After that, he comes to shew, how the Effections or Delineations for Cubick Æquations were invented; And then, how those Constructions for the Trisection of an Angle were found out: the use whereof is, to give Lines in a known measure, equal to the quantity's sought, whereby either to give aid in the easie obtaining the first and second figures of the root, or controul the same.
Lastly, he comes to treat of General Constructions for the resolving of all solid Problems, without reduction of the Æquations proposed; and sheweth a general Construction for all Cubick and Bi-quadratick Æquations by ayd of a Circle and a Parabola, letting Ordinates fall from the points of Intersection on some Diameter of the Parabola (which is always parallel to the Axis,) whereas Des Chartes letting those Ordinates always fall upon the Axis, was forced to prepare and alter the Æquations by driving out or taking away the second term (which is next the highest,) that the sum of the Negative roots might be equal to the sum of the Affirmative ones, as his Constructions always require.
But how to find out all the variety's of solving all Solid Problems by the Conick Sections, hear the Author to the Reader: Methodum non adscripsi, tum quad gratius ac utilius futurum arbitratus sum, si eam ipse privato Studio, ex hisce Speciminibus eliceres, tum etiam quad judicium tuum de tota re præstolarer, Decrevi enim, si favor tuus accedat, non ipsam methodum tantum, sed & alia, quæ simul observavi, brevi, Deo bene juvante, censura tuae submittere.
We come next to speak of the last part of the Book, to wit, his Miscellanea, and because it fails in here somewhat properly, we therefore first mention his fourth Chap. De Maximis & Minimis, from which he derives this Proposition;
If any Magnitude (or Number, as the whole) be divided into such parts, that are to each other as a Number to a Number, the Product of those powers of the parts, that are of the same degree, as the parts themselves denominate, if the greatest of all Products of the like powers of the parts of the same magnitude when otherwise divided.
Concerning the Proposition the Author saith thus; Liceret hujus Propositionis Usum prolixius extendere ad determinandas nempe maximas & minima applicatarum in Curvis, tangentes, & similia; verum cum hanc materiam nuper in Exercitatione sua Geometrica; feliciter aggressus sit Vir Clarissimus Michael Angelus Riccius, doctrina & humanitate singulari, orbi literato notissimus, & justi operis spem faciat; frustra nunc pluribus insisterem, cum meliora & prefectiora ab ipso propediem expectari debeant.
That exercitation of Riccio hath been lately re-printed for Moses Pitts, Book-seller in Little-Britain, (and is annexed to Mercator's Logarithmotechnia) wherein the Author Riccio promiseth a new Rank of Conical Solids, which cut, do exhibit those Infinite Parabola's and Ellipses, whereby all Æquations may be easily resolved and determined. But the Learned and Modest Slusius in a private Letter concerning these matters, and Riccio's before-mention'd Geometrical Exercitation, saith somewhat more. Diu est etiam ex quo eandem materiam aggressus fueram, qua Methodo, videbis in Miscellaneorum meorum Cap. 4. ubi Propositionem universalem demonstravi, ex qua omnia deduci possunt; non tamen deduxi, ne viro amico, qui hanc materiam jam occuparat & a quo multa ac præclara expectari possunt, occasionem bene merendi de Rep. literaria præriperem.
Concerning the rest of the Miscellanies; Our Author in the 1. Chapt. treates De Infinitis Spiralibus, & spatiorum, ab iis & Radio Circuli comprehensorum, mensura. Concerning which he tells you, that Archimedes squared that Spiral, which was made b an equal motion both in the Radius and Circumference of the Circle: that Stephano Angeli hath done the like, when the Motion in the Radius is equal, but in the Circumference according to any degree of Acceleration; which gave him occasion to render this Doctrine easie and Universal by reducing it to one Analysis, when the motion is accelerate according to any degree either in the Radius or Circumference; and hence resolves this Probleme; In Circulo describere Spiralem ex talibus motibus compositum, ut Circulus ad spatium Spirale habeat rationem datam numeri ad numerum. And applies the same Doctrine in
Chap. 3. to another sort of Infinite Spirals.
Chap. 2. He treats De mesnura spatiorum, curva & recta Contentorum, & eorum Centri Æquilibrii; applying the former Analysis or Algebraick Calculation thereto.
Chap. 5. Treats De Puncto flexus contrarii in Conchoide Nicomedis prima: which Point he determines by the Intersection of a Parabola, whose Axis is situated in the same Line with that of the Conchoid; or by a Cubick Parabola, whose Axis is parallel to the Base of the Conchaid, and Vertex the same with the Pole of the Conchoid; and hence invents innumerable other Conchoids of like properties, and finds the Curve, passing through those points of flexure, that are made by Infinite Conchoids, described about the same common Pole and Base, which in the Common Conchoids he finds to be the Perimeter of the Cubick Parabola here mentioned: But in his own new Conchoids, it is the antient Cissoid; extended beyond a Quadrant and running Asymptotick: And he finds also the round Solids made by the Rotation of these infinite Curves; and of the Cissoid Line, about their Base Lines or Asymptotes equal to finite Solids.
Chap. 6. The Author considering; that Vincenzo Viviani in Book De Maximis & Minimis found, that if there were innumerable Parabolaſ described, having the same Axis and Vertex common, if from any point in that Axis, the shortest Lines were drawn to those Parabola's, all those points of Incidence would fall in an Ellipsis; and the Authors Analysis taught him, that the Prop. was Universal, wheresoever the point be assigned, from which the least lines are to be drawn; which he hath extended, and applyed to those infinite sorts of other Parabola's.
Chap. 7. Treats De Firurarum dimensione ex data Centro Æquilibrii: This he saith is accurately handled by the Learned already; Aliquot tamen modos adscribit, ut non difficules, uta nec inutiles ad investiganda Æquilibrii Centra: which may be applyed to good use; for, in any Curve, if there be Ordinates enough given, standing erect at an equal parallel distance, you may approach the Area, and if by ayd thereof, you find the Center of Gravity, then do you obtain the measure either of the Round Solid, or Spindle made by the Rotation of the given Figure, or of Hoofes raised upon it as a Base.
Chap. 8. The Author sheweth an easie way of finding the Center of Gravity of an Hyberbolical Conoid, and that in order to the resolution of this Probleme; Locum invenire, ad quem sunt omnia Centra Conoidum Hyperbolicarum, quæ fiunt ab Hyperbolis in dato Cono recto sectis, & quarum Axes sint Axi ejusdem Goni paralleli; which he finds to be an Hyperbole,
Chap. 9. He treats of the Center of Gravity of the Lunula of Hippocrates Chius, and sheweth, that if Hippocrates had given that, as he did the Quadrature of the Lunula, he had squared the Circle.
Chap. 10. Treats of Arithmetical Problems, wherein he asserts, that Diophantus was wont to solve Arithmetical Questions with great subtilty, but useth numbers only, whereas the same may often be more easily and universally solv'd by Algebra; and takes for examples, the third Question of the Fourth Book, which he reformes, and reduceth divers of the like kind, that Bachet hath added, to one Proposition and Resolution; the 44th of the Fourth Book of the same Diophantus, which being solved with much trouble, he sheweth to have a briefe Analysis; the 13th of the third Book, and the 36th of the fourth Book, by reason of the likeness of it's Operation with the former
Thus we have given an account of the Authors Book. What Repute he hath among the Learned, needs not to be insisted on. The famous Pascal Or Dettonville in a Letter to this Author, saith (to give it in English;) I believe, that to make it known that 'tis You, who hath round (for Example) this Parabola, which is the Place, than gives the Dimenlions of the Surfaces of the Solids of the Cycloid about the Base, it must be I, that must tell the World so; as well as the other Wonders of your New Analysis, and so many other things, which you have done me the honor to impart unto me, with that goodness you are pleas'd to have for me &c.
The Book here commended is the Second Edition of the Mesolabe of this Excellent Geometer, our Author; Concerning whose first Edition thus saith Stephano Angeli pag. 217. Accessionis ad Stercometriam & Mechanicen. Quomodo autem hujusmodi Problemata Solida construantur, edoctum fuit a quam plurimis; sed Herucleas metas in infinitum transcendit Nobilissimus & Clarissimus Geometra Renatus Franciscus Slusius Leodiensis in suo admirabili Mesolabo, in quo hæc infinitis enucleat modis.
Concerning this Book, we find it to be the judgement here, (and doubtless it will have the same esteem elsewhere among the Learned) that in it there is the most excellent Advancement made in this kind of Geometry, since the famous Mathematician and Philosopher Des Cartes.
THe Learned Author of this Treatise (a Member of the R. Society) considering with himself, how important it was, for the arraigning a full knowledge of the Nature and Qualities of the Blood, to investigate, besides the Circular Motion thereof, the Origin and Celerity of that Motion, and the various Changes thereof, together with the Causes of them; as also, to make an estimate of the Quantity of that Liquor emitted at every Pulsation; thought it very well worth while, to give, from his own best Observations, a clear and particular account of that whole matter, And for as much as he conceives, that the Motion of the Blood depends on that of the Heart, he begins with a Discourse concerning the Situation and Structure of the Heart, to shew, How exactly these two are calculated for its Motion, and how well adapted to distribute the Bloud into the parts of the whole Body.
In the First Chapter then, he considers the Diversity of the Situation of the Heart in different Animals, and the Reason thereof; proceeding to discourse of the Pericardium and its Use, together with the Origin and Use of the Serum therein; and why in Man onely that Case of the Heart grows to the Midriff, and what makes it to do so; as also, why the Cone in an Humane Heart bends much more to the Left side, than in Brutes: Then shewing, that Arteries have their rise from the Heart, but Veins terminate in it, and how and by what Vessels the Heart is nourisht by the Alimentary Juyce: treating also of the Vessels of the Heart, its Nerves, and the various Influx of the Animal Spirits through the Nerves into the Heart, according to the various shapes of Animals, together with the Cause thereof: Proving further, that the substance of the Heart is perfectly Muscular, and in perfection surpassing all other Muscles of the Body (where he expatiates into un-common Observations concerning Muscles in general;) then descending to a Minute Explication or the parts of the Heart, and there particularly shewing the Mechanical Contrivance of the Heart for its Systole and Diastole, together with an accurate description of the Foramen Ovale, and its Use in the Fœtus, the Clausure of the same in Animals born.
In the Second Chapter he treats of the Motion and Office of the Heart; Where, as he admits not of any Ferment or Eouilition of the Bloud in the Heart (which he affirms would be an Obstacle to its Systole, as 'tis needless to the Diastole,) so he assents, that the Motion of the Heart depends not from such an Eoullition (which he proves by Exoerimf nts, and vindicates from Objections;) but that the genuine and immediate Instruments of the Heart's Motion are its Fibres, Nerves, and Spirits flowing through them, the action of the Heart being altogether conform to that oi other Muscles: Where he takes occasion to make it out, that the Motion of Muscles is not caus'd by their being inflated, nor by any Explosion of the Spirits passing through them, out after the manner, as two men taking one another by their hands, draw themselves close together into mutual embraces: Whence he goes on to shew That the whole Motion of the Heart consists indeed in the Systole, that of the Diastole being onely a Motion of Restitution. Further, that there is a necessary Commerce betwixt the Heart and Brain (the Cause of all Sense and Motion:) but that both ultimately depend from the Stomack, as the constant Purveyor and Furnisher of Matter for Bloud and Spirits.
In the Third Chapt. he teacheth, with what Celerity all the Bloud passeth through the Heart, and what difference there is between the Venal Bloud and the Arterial. As to the former, he calculateth, that all the Bloud passeth through the Body, thirteen times, (not Six, as 'tis misprinted in the Book it self) in one hour. And concerning the latter, he is of opinion, that the Purpureous and florid color of the Blood in the Arteries proceeds not from its Accension in the Heart (if there he any such thing) but depends altogether from the Lungs, and the Admixture of the Air with the Bloud there: which he proveth by considerable Experiments; refuting withal the opinion of those that will derive it from the Comminution of the Bloud in the Lungs.
In the Fourth Chapt. he gives an Accompt of the Rise, Progress and Use of the Invention of Transfusing Bloud cut of one Animal into another: though in the History of this particular he commits (I know not by what over-sight) a mistake, in relating, that Monsieur Denys (call'd by him Dionysius) arrogateth to himself that Invention, whereas he onely tells us that some of his Nation do so. Besides which, we must needs take notice of another mistake in this part of the Book, viz. that the Author taking occasion to speak of the Philos. Transactions calls them the Transactions of the Society; which certainly he would not have done, if he had either but taken notice of what is said in Numb. 11. of the same; or else consider'd, that so Illustrious and so Learn'd a Body would certainly, if they thought fit to publish any thing as theirs, entertain the knowing World both with sublimer Mater, and with a sutable Eloquence: But this by the by.
In the Fifth Chapt. he treats of the Chyle, and its Change into Bloud; where he observeth, that nothing passes from the Spleen through the Vase breve into the stomack; but that the Ferment of the stomack proceeds immediately from the Blood it self: Explaining further, How the Separation of the Chyle is perform'd in the Intestins, and how the same, to facilitate the more its passage, is diluted and refined by the Juyce of the Pancreas, secreted into the Duodenum: Rendring also the Cause, Why all the Glanduls in the Abdomen and in all the lower parts of the Body do deposite their Lympha or Juyce into the Common great Receptacle of the Chyle, and Why that Receptacle is plac'd between the Tendons of the Daphragime; as also, Why those Channels, which convey the Chyle into the Subclavial Vein, are double. To which he adds, That all the Chyle is by the Ductus Thoracicus alone transmitted into the Bloud and Heart, which he proveth by several considerable Experiments, with some reflexion on the Bilsian Experiment alledged for the contrary. All which he concludes by shewing the degrees and ways of Change, whereby the Chyle is at last converted into Bloud; and how it serveth for the Nourishment and the several parts of the Body.
The Whole receives a singular Elucidation and Ornament by the Accurate Figures, in 6. Tables annexed.
Many Curious and important Observations are occasionally interspersed; such as are: That the Capillary vessels (of the same sort) do open into one another in all the parts of the Body: That all the Muscles of the Body, are Biventers or double belly'd: That as the Motion-of the Heart and Bloud is Circular, so the Fibres, as tke Moving Engines of them, are about the Cone of the Heart brought into a Circle and Center: That the Motion in the Muscles is not like Shooting, but Fencing; and many more, for which we must referr to the Book it self.
FINIS.
LONDON,
Printed by T. N. for John Martyn, Printer to the Royal Society, and are to be sold at the Bell a little without Temple-Bar, 1668.