VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 657 



contrary to the moving force, may be immediately deduced from the foregoing 

 experiments. For let m = the moving force expressed by its weight ; p = the 

 friction ; w = the weight of the body on the horizontal plane ; s = the space 

 through which the moving force descended in the time t expressed in seconds ; 

 r= 16-jV feet; then the whole accelerative force (the force of gravity being 



unity) will be '■ ; hence, by the laws of uniformly accelerated motions, M ""— - 



J ' M + w ■> •> ' M + w 



| « _L- \y) v c 



X r? = s, consequently f = m — - — — 2 . To exemplify this, let us take 



the case of the last experiment, where m = 7, w == 25^-, s = 4 T 7 T feet, t = A"; 



hence f = 7 — tjt\ 7# = 0-417 ; consequently the friction was to the weight 



of the rubbing body as 6.417 to 25.75. And the great accuracy of determining 

 the friction by this method is manifest from hence, that if an error of 1 inch 

 had been made in the descent (and experiments carefully made may always deter- 

 mine the space to a much greater exactness) it would not have affected the con- 

 clusion -5-1-5- part of the whole. 



5. We come in the next place to determine, whether friction, caeteris paribus, 

 varies in proportion to the weight or pressure. Now if the whole quantity of 

 the friction of a body, measured by a weight without inertia equivalent to the 

 friction drawing the body backwards, increases in proportion to its weight, it is 

 manifest, that the retardation of the velocity of the body arising from the fric- 

 tion will not be altered ; for the retardation varies as - " a °'^ -°, - r — — ; hence, if 



Quantity of matter ' 



a body be put in motion on 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 

 acceleration arising from that moving force will remain the same, because the ac- 

 celerative force varies as the moving force divided by the whole quantity of mat- 

 ter, and both are increased in the same ratio ; and if the quantity of friction in- 

 creases also as the weight, then the retardation arising from the friction will, from 

 what has been said, remain the same, and therefore the whole acceleration of 

 the body will not be altered ; consequently the body ought, on this supposition, 

 still to describe the same space in the same time. Hence, by observing the 

 spaces described in the same time, when both the body and the moving force are 

 increased in the same ratio, we may determine whether the friction increases in 

 proportion to the weight. The following experiments were therefore made in 

 order to ascertain this matter. 



Exper. 1. A body weighing 10 oz. by a moving force of 4oz. described in 2 s a 

 space of 51 inches; by loading the body with lOoz. and the moving force with 

 4 oz. it described 56 inches in 2 s ; and by loading the body again with 10 oz. 

 and the moving force with 4 oz. it described 63 inches in 2 s . 



Exper. 2. A body, whose weight was l6oz. by a moving force of 5 oz. de- 



VOL. XV. 4 P 



