DYNAMICS. 



I . 



Another 

 measure of 

 prevure. 



ItnpulM 

 compared 

 with pres- 



deficient. It is different at different places, seems to 

 depend on the acciilent.il neighbourhood of the e.irth, 

 and (x-rhaps at a very great distance may vanish alto- 

 gether. A quality free from such objections is the 

 force necessary to give a body a certain vi-Wity. Sup- 

 pose that, by particular contrivances, we have render- 

 ed insensible the resistances arising from the weight of 

 a body, from friction and from the air, still force will 

 be necessary to put the Unly in motion ; but the small- 

 est force will be sufficient, and the same force \\ ill give 

 different bodies a differvnt \elocity. Now MI- may 

 consider the quantities of matter in two bodies to be 

 pro|wirtiona! to the forces, wliich, acting during the 

 same time, give them the Mine velocity. I'-timating 

 the quantity of matter in this way, we find, by ex- 

 periment* with Atwood's machine, that it is pro- 

 portional to the weight in the same place, which, being 

 csily measured, will serve conveniently to point out 

 the quantity of matter. The density of a body is the 

 quantity of matter in a certain bulk of it, and bears the 

 game relation to its whole quantity of ma^er, that the 

 specific gravity does to the whole weight. Hence the 

 mass is proportional to the bulk multiplied by the den- 

 sity, or m^M. It will sometimes facilitate our con- 

 ceptions, and perhaps the (Opposition is not far from 

 the truth, to suppose all bodies made up of small ele- 

 mentary particles possessing the same weight or quan- 

 ty of matter. In this view, the whole quantity of mat- 

 ter in a body will depend on the number of these ele- 

 mentary particles, and the density on the number in 

 a given bulk. 



5. Another Measure nf Pressure. When a pressure, 

 by conl'iiuing to art for some time, has produced mo- 

 tion, the product of the mass moved by the velocity 

 acquired in the same time will always be proportional 

 to the press- ure. That the mass is proportional to the 

 pressure when the velocity is the same, appears from 

 the very definition of mass ; and that the velocity is 

 proportional to the pressure when the mass is the same, 

 appears from further experiments with Atwood's ma- 

 chine ; and hence, in general, it will be proportional to 

 the product. This product, then, will serve as another 

 measure of the force of pressure, and the same ratio 

 will be obtained whichsoever of the measures we em- 

 ploy. The mass multiplied by the velocity of a body, 

 is often called its quantity of motion or momentum, 

 and hence a force of pressure may be said to be mea- 

 sured by the momentum or quantity of motion which 

 it can generate in a given time. Suppose that m v and 

 MV are two effects of the same force in the same time, 



then wr=MV, hence ' Y,and -_ r =M,also M : m:: 



v : V, or the masses will be reciprocally proportional to 

 the velocities generated. 



6 Impulse compared icith Pressure. A force of pres- 

 sure is supposed to act even 1 instant ; hence the veloci- 

 ty, and consequently the momentum, generated every 

 instant, must be infinitely small. A force of impulse 

 must art in a simibir manner, by making the body |i .. . 

 from the velocity (O), through all the intermediate de- 

 grees of velocity to that with which it sets out; hence 

 its effect also in an instant must be infinitely small, and 

 a finite time must elapse before any sensible motion can 

 ensue. It is not true, then, as it has often been said, 

 that a force of impulse, however small, is infinitely 

 greater than any force of pressure however great. The 

 true state of the matter is this : An impulse produces, 

 in a portion of time smaller than we can measure, a ve- 

 locity as great as any force of pressure with which we 



quainted can produce in a considerable time. N'-mw and 

 Hence the one must U- vastly greater than the CM ' 



when the mosses are the Mine ; it follow*, to,., thnt we totn *- 

 cuii in no case state the ratio ; but it follows, at the s.une ^^'^" 

 time, that the two forco may in some cases l-i- , 

 in consequence either of the mass moved by the foree 

 of pre^ure In-ing e \ceeilingly large, or that moved by 

 the force of impulse l>cing exceedingly small. Since, 

 however, we are always unacquainted with the time 

 during which the action of impulse contiim- 

 in no c.isv state the ratio of the two forces, and we can 

 only in any case infer their equality from their balan- 

 cing one another in like circumstances. 



7. One Impulse cum; urf nf'/'i nHo.'Acr. Though we 

 cannot comjiare an impulse with a pressure by the ,^1^."",,,,. 

 quantity of motion generated, yet we may by that prin- J|.ir,,i '*'')" 

 ciple compare impulses with one another; for the time another, 

 in which each produces its effect being exceedingly 



small, and to us unknown, may be considered as tl>- 

 same; and hence the force may naturally be regarded 

 as proportional to the momentum generated, or/==/f. 



8. firrce of a ]> di/ in Motion. As we estimate a 

 force by the quantity of motion which it communicates, b^jj 6 ^ k 

 so will we naturally estimate the force of a body in mo- motion. 

 tion by the quantity of motion which it is capable of 

 communicating by impulse before it is brought to rest. 



Now, it will appear afterwards from the third law of 

 motion, that a body communicates by collision just as 

 much motion as it loses ; hence it will be capable of 

 communicating before it is brought to rest just all the 

 motion it has, and hence its force will naturally be 

 estimated by its momentum or quantity of motion, or 

 /'== mv. Some effects which a body is capable of pro- 

 ducing before it is brought to rest, being proportional 

 to mv', have made some philosophers consider the force 

 ;;s following that ratio. But the quantity of motion 

 the body can communicate, seems to lie the most natu- 

 ral measure which we can assume, as it preserves n har- 

 mony between this and other forces. The subject, how- 

 ever, is now generally allowed to l>e entirely a matter of 

 definition ; if the measure we moan to employ is ex- 

 plained before we set out, and strictly adhered to in the 

 course of the investigation, it cannot alter the nature of 

 our deductions ; and the heat with which the contro- 

 versy was long carried on betwixt the most eminent 

 men, is a proof that sound metaphysics is not always 

 found in conjunction with profound skill in mathema- 

 tical and physical science. With regard to the force 

 which a body in motion actually exerts in any given 

 case of collision, it will be measured according to 1 i-i 

 article by the quantity of motion wliich it artiwliy com- 

 municates to the other bo;iy. The method of predict- 

 ing this will be given under (hii-fLsE). It will be 

 there seen that it depends partly on the mass struck, 

 but that whin ' . two masses arc the same, it is pro- 

 portional to the velocity of the striking body. 



SECTION II. 



Laws of Motion, or General Rules according to which 

 Forces, act. 



Tlcre are three general rules which a body obeys Laws of 

 in i,s. mot;.-, lever be the kind of body orthekind motion. 



,,f loa. th.- - it ; whether it be a particle of dust 

 driven l>v the > ind, or a pl.met revolving in conse- 

 quence, oi an o:iginal impulse throng!-, tlie celestial spa- 



These rults are the key that unlocks all the treasures 





