On ihe Motion of^Bodics affected Ixj Friction. 5 1 



moving- force expressed by its weight; F = the friction- W 

 = the w eight of the body upon the horizontal plane ; S = 

 the space through \\'hieh the moving force descended in the 

 time t expressed in seconds; ;•= Ifi^V feet; tiien the whole 

 accelerative force (the force of gravitv being unity), will be 



-^ , .■■ ; hence, by the laws of uniformly accelerated mo- 



JVl -J- Vv 



tions, ^inl X r/^- =S, consequently F = M-^l-!l^ii?. 



To exemplify this, let us .take the case of tlie last experi- 

 nient, whuvc M = 7, W = 25|, S = 4-=-^ feet, t = 4'': 



" - 7 — ''■*^' '^'^ = G. 1 1 7 j consequently the friction 

 was to the wei^i.ii ^ "" 



And the great accurat'f rubbing body as 6.4167 to 25.75. 

 method is manifest from hehtcrmining the friction by this 

 had been made in the descent (afidf an error of one inch 

 made may always determine the space euments carefully 

 exactness), it would not have afieeted tlieconcliw.h greater 

 part of the whole. '-,dtli 



5. We come in the next place to determine whcthe. 

 friction, cceteris paribus, varies in proportion to the weight 

 or pressure. Now if the uhole quantity of the friction of 

 a body, measured by a weight without inertia equivalent to 

 the friction drawing the body backwards, increases in pro- 

 portion to its weiglit, it is manifest that the retardation of 

 the velocity of the body arising from the friction will not 



, , 1 r 1 , 1 • • Ouarti;v of fn'ctiDU 



be altered : for the retardation varies as r^ — ^ ; 



' yuAiitity ot luatlcr 



hence, if a body be put in motion upon the horizontal plane 

 by any moving force, if both the weight of the body and 

 the moving force be increased in the same ratio, the acce- 

 leration arising from that moving force w ill remain the same ; 

 ijecause the accelerative force varies as the moving force di- 

 \ided by the whole quantity of matter, and both are in- 

 creased m the same ratio ; and if the quantity of friction 

 increases also as the weight, then the retardation arising 

 from the friction will, from what has been said, remain the 

 same; and therefore tlie whole acceleration' of the body w ill 

 not be altered : consecjuently the body ought, upon this 

 supposition, still to describe the same space in the same 

 lime. I ience, bv observing the spaces described in the same 

 lime, when both the body and the moving force are increased 

 in the same ratio, we may determine whether the friction 

 increases in projiortioii to ihi- weight. The following ex- 

 1) 2 periments 



