tion, and Measure of the Powers and Actions of Bodies; efpecially after a diligent Enquiry into the Subject. But the Powers and Actions of Mathematical Bodies are circumfcribed and measured; either, (1.) by Space of Place *; Inftances. (2.) by Moments of Time; (3.) by the Correspondence or Proportion of Quantity; or, (4.) by the Predominancy of Virtue and unless thefe four Things are well and diligently weigh'd, the Sciences indeed, may, perhaps, be beautiful in Show and Appearance; but they will remain unfruitful, or barren of Works. And the four Inftances, with regard to these four Particulars, we call, in general, Mathematical Inftances; or Inftances of Menfuration. Practice, how 207. Practice proves burdenfome either, (1.) from the admixture of rendered bur- ufelefs Things; (2.) from a Multiplicity of Inftruments; or, (3.) from denfome. the Bulk of the Matter, and Bodies required, in certain Works. Thofe Inftances, therefore, ought to be highly efteemed, which either, (1.) direct and determine Practice to fuch Things as chiefly regard the Benefit and Advantage of Mankind; or, (2.) retrench the Number of Inftruments required; or, (3.) fave and leffen the Materials to be employ'd. Propitious InStances. (21.) Instances of the Staff. 208. And the three Inftances correfponding to thefe three Particulars, or Requifites, we call by the fingle Name of Propitious or Benevolent Inftances. We fhall fpeak of these feven Inftances, feparately; and with them conclude this Section of the Doctrine of Prerogative Inftances. APHORISM XLV. 209. In the twenty-first Place, therefore, among Prerogative Inftances, come Inftances of the Staff, or Measuring-Rod; which we alfo call Permeating, or Teminating Inftances; for the Forces and Motions of Things operate and exert themfelves in certain Spaces, that are not indefinite or fortuitous, but determinate and finite: and the due Observance and marking of these Spaces in every Nature fought, is of great Importance to Practice; not only in preventing us from being deceived by it; but alfo in enlarging and rendering it more extenfive and powerful: For it at a Diftance. is fometimes poffible to extend Virtues and Powers; and, as it were, bring Distances nearer, as we fee in Telescopes. Virtues bave their Sphere of Activity. Some operate 210. There are alfo many Virtues that operate and extend their Force only by manifeft Contact; as in the Percuffion of Bodies; where one Body does not move another, unless the impelling Body touches the Body impelled. So, likewife, external Remedies, as Unguents and Plaifters, * See below, Aph. 45. y See below, Aph. 46. See below, Aph. 48. b Which fee below, Aph. 45-48. See below, Aph. 49. • See below, Aph. 51. fters, exert not their Virtues, without touching the Body. And, lastly, 211. There are alfo other Virtues, which operate at a finall Diftance; Others operate 212. Again; if there be any magnetic Virtue, which operates by Con- Some at very fent, between the Globe of the Earth, and ponderous Bodies; or between great ones. the Globe of the Moon and the Waters of the Sea; which feems highly probable from the Spring-Tides; or between the Sphere of the Fixed Stars and the Planets, fo as to attract the Planets to their Apogeés; all thefe muft operate at very great Distances. and Cold. 213. There are alfo found certain Communications of Flame, to con- Inftanced in fiderable Distances, in certain Materials: as they relate, in particular, Flame, Heat, of the Naphtha of Babylon. Heat, likewife, infinuates itself to great Distances; and fo does Cold: infomuch, that the huge Maffes of Ice broke off, and floating in the North Sea, and thence coming into the Atlantic Ocean, ftrike a Coldnefs many Leagues off, perceptible to the Inhabitants about Canada ". 214. Odours, likewife, tho' thefe feem always attended with a corpo- In Odours, real Emiffion of the odoriferous Subftance, operate at confiderable Di-Sounds, and Light. ftances; as appears to fuch as fail along the Coafts of Florida, or fome Parts of Spain, where there are whole Groves, or Woods of Lemmons, Oranges, and the like odoriferous Trees; or Thickets of Rosemary, Marjoram, &c. And lastly, And laftly, Sounds, but particularly the Rays of Light, operate to prodigious Distances *. 215. But all thefe Virtues, whether they operate to fmall, or large All Virtues Distances, certainly operate to finite ones, and fuch as are known to limited. Nature fo that there are certain fixed Bounds, which they cannot exceed; and that in Proportion, either (1.) to the Bulk and Quantity of the Bodies; or, (2.) to the Strength or Weaknefs of the Virtues; or, (3.) to the Suitablenefs or Unfuitablenefs of the Medium: all which, See Vol. III. p. 614, &c. See Mr. Boyle's History of Cold, paffim. iSee Mr. Boyle of Effluvia. ought Sce Mr. Boyle, Dr. Hook, Sir Ifaac Newton, the Philosophical Transactions, French Memoirs, &c. Some act at a ought to be carefully obferved, and brought to Computation'. And again; the Measures of thofe called Violent Motions, or the Motions of Projectiles, as Bullets from Guns, the Motions of Carriages, &c. ought to be observed and determined: for these also have manifeftly their fixed Limits. 216. There are, likewife, certain Motions and Virtues, contrary to Distance, and thofe that operate by Contact, and not at a Distance; as acting at not by Contact a Diftance, and not by Contact: and again; others that operate weaker at a small Distance, and stronger at a greater. Thus Vifion is not well performed in Contact; but requires a certain Medium, and a certain Distance, to be perfect: tho' I have been affured, by a Perfon of Veracity, who was couched for Cataracts in his Eyes, (which is an Operation performed by means of a small filver Needle, thruft between the first Coat of the Eye, to remove and force away the Film of the Cataract into the Corner of the Eye,) that he clearly faw the Needle moving over the Pupilla, or Sight of the Eye". Exemplified in Vifion. 217. But allowing this, 'tis manifeft, that larger Objects cannot be well or diftinctly feen, except in the Vertex of a Cone, made by the converging of the Rays from fome Distance. Thus old Men fee better when the Object is removed a little farther off, than when it is near. And it is certain, that in Projectiles, the Percuffion is not fo strong at too small a Diftance, as it is foon after, or at the due Distance. The Measures, therefore, of thefe Things, and others of the like Kind, are to be fet down, to determine their Motion in Point of Distance. The Motions of 218. We must not omit another Kind of Local Measure of Motions, Expanfion to which regards not progreffive, but Spherical Motion; that is, the Exbe measured. panfion of Bodies into a larger Sphere, or their Contraction into a less. For we fhould enquire, among the Meafures of Motion, what Degree of Compreffion or Extenfion, Bodies, according to their Nature, may eafily and readily fuffer; and at what Point they begin to refift; and at length, will fuftain no more. Thus when a blown Bladder is comprefs'd, the Exemplified in Air fuftains fome Degree of Compreffure; but if the Compreffure be a blown Blad- too great, the Air enduring it no longer, burfts the Bladder, and frees der. In Air under itself. 219. But to make a more exact Experiment to this Purpose, we took a fmall, light, and thin metalline Bell; and plunged it into a Bafon of Water, fo that it carried down along with it the Air contained in its Cavity, to the bottom of the Veffel; where we had first placed a little Ball, which the Cavity of the Bell was to fall upon. When this Ball was little in Proportion to the Cavity of the Bell, the Air fhrunk itself into a lefs Compafs, without efcaping; but if the Ball was fo large, that the Air could not freely yield, the Air would then, as being impatient Here we may obferve the proper Ufe of Calcalation, or Mathematics, in Phyfics. of of a greater Preffure, raife up the Bell, on one fide, and afcend in Bubbles". 220. Again; to try what Degree of Extenfion Air is capable of, we The Rarifatitook a Glafs-Egg, with a fmall Orifice at one End thereof; and by on of the dir. ftrong Suction drew out the Air; then immediately stopping the Orifice with the Finger, we plunged the Glafs in Water; where the Finger being removed, the Air that was stretched and dilated by the Suction, now endeavouring to contract itfelf; (fo that if the Glafs had not been plunged in Water, it would have drawn in the external Air with a hiffing Noife ;) it drew in fuch a Quantity of Water, as fufficed to rccover the remaining Air to its former Bulk or Dimension °. dies hard to comprefs. 221. And it is certain, that pneumatical, or rare Bodies, fuch as the Tangible BAir, will fuffer a remarkable Contraction; but that tangible Bodies, fuch as Water, fuffer Compreffion with much greater Difficulty, and in a lefs Degree. What this Degree might be, we attempted to difcover by the following Experiment. 222. We caufed a hollow and strong Globe of Lead to be formed, ca- Water compable of containing two Wine Pints; and having made a Hole therein, we press'd. fill'd the Globe with Water; then folder'd up the Orifice with Lead; and now beat the Sides of the Globe flat out with a large Hammer: whence the Water was of neceffity contracted; because a Sphere is the Figure of largest Capacity. And when hammering was of no farther Service, in making the Water shrink; we put the Lead Veffel into a Prefs, and fqueezed it; till at length the Water forced itself thro' the foiid Lead; and stood upon its Surface, like a Dew. We afterwards computed into how much lefs Space the Water was driven, by this violent Preffure P. 223. But folid, dry, or more compact Bodies, as Stones, Wood, and Solids harder Metals, fuftain a much lefs, and almoft imperceptible Compreffion, and to-comprefs. Extenfion; and either releafe themfelves by breaking, moving, fqueezing out, or other Evafions; as appears in the bending of Wood, or Metal; in Spring-Clocks, or Watches; in Projectiles, Hammering, and numerous other Motions. 224. But all thefe Particulars, together with their Measures, are to Calculations, be discover'd and fet down, in the Enquiry into Nature, either in the Way or Eftimations, of certain Calculation, Eftimation, or Comparison; as the Cafe will admit. n The Defign was here, to eftimate the Force wherewith Air refifts its own Condensation, or endeavour to escape. See Mr. Boyle's Pneumatical Experiments; particularly Abridgm. Vol. II. p. 670---672. See Mr. Boyle's Works, Abridgm. Vol. II. p. 414. P Sce the Experiments of the Academie del Cimento; and Mr. Boyle's Works, Abridgm. Vol. I. p. 628, 629. Vol. II. p. 290, 666, 703, &c. to be made of every kind. VOL. II. X x x APHORISM Their Office. APHORISM XLVI. (22) Inftances 225. In the twenty-fecond Place, among our Prerogative Inftances, come of the Course. Inftances of the Course, or Stage; which we alfo fometimes call Hydrometrical Inftances; deriving the Term from the Hour-Glaffes of the Ancients, wherein they ufed Water inftead of Sand. Thefe Inftances measure Nature by Moments of Time', as the Inftances of the Staff' meafure them by Degrees of Space. For all Motions, or natural Actions, are perform'd in Time; one indeed fwifter, and another flower; but all Actions perin certain Moments well known to Nature. Even thofe Actions which form'd in dif- feem fuddenly performed, or in the twinkling of an Eye, as we phrase ferent Times. it, are yet found to differ in Time, as to more or less. Exemplified in 226. And, firft, we fee that the Revolutions or Returns of the Cemany Particu- leftial Bodies are performed in certain Times or Periods; fo likewife is the Flux and Reflux of the Sea. The Defcent of heavy Bodies towards the Earth, and the Afcent of light Bodies towards the Heavens, is perform'd in certain Moments; according to the Nature of the Body, and the Medium it moves in. The Motions of a Ship, in failing; of a Horse, or other Creature, in running; of a Projectile, in flying, &c. are all, in like manner, performed in certain Times, measurable in the Amount or Refult. And, with regard to Heat, we fee that Boys, in the Winter, will wafh their Hands in the Flame of a common Fire, without burning themselves; and, in the way of Sport, others will, by a nimble and equible Motion, turn Glaffes of Wine, or Water, upfide-down, and recover them again, without fpilling: and there are many Particulars of the fame Kind. lars. In Sound. And Vision. 227. So, likewife, fome Compreffions, Dilatations, and Eruptions, or Explofions of Bodies, happen fwifter, and others flower, according to the Nature of the Body, and the Motion; but they happen in certain Moments of Time. Thus, in the joint Explofion of feveral large Cannons, which may be heard fometimes to the Distance of thirty Miles, the Report is firft audible to those near the Place, where the Discharge is made; and afterwards to thofe who are farther off'. 228. And in Vilion, where the Action is exceeding fwift, 'tis plain, that certain Moments of Time are required to its Performance: as is plain from hence, that Bodies are rendered invifible through too great a Velocity of Motion; as in the Discharge of a Bullet from a Gun; where the Ball flies too fwift to have its Impreffion received by the Eye. As if it were Inftances of the Time-Keeper, or Hour-Glafs. See above, Aph. 44. See above, Aph. 45. 229. And, Sce Mr. Whiston's Second Edition of his Effay upon the Longitude; and Dr. Derban's Paper upon the Motion of Sounds, in the Pbilofophical Tranfactions, N° 313. |