658 PHILOSOPHICAL TRANSACTIONS. [ANNO 1785. 



scribed a space of 49 inches in 3 s ; and by loading the body with 64 oz. and the 

 moving force with 20 oz. the space described in the same time was 64 inches. 



Exper. 3. A body weighing 6 oz. by a moving force of 2|oz. described 28 

 inches in 2 s ; and by loading the body with 24 oz. and the moving force with 10 

 oz. the space described in the same time was 54 inches. 



Exper. 4. A body weighing 8 oz. by a moving force of 4 oz. described 334- 

 inches in 2 s ; and by loading the body with 8 oz. and the moving force with 4 oz. 

 the space described in the same time was 47 inches. 



Exper. 5. A body whose weight was Q oz. by a moving force of A\ oz. described 

 48 inches in 2 s ; and by loading the body with Q oz. and the moving force with 

 4-i- oz. the space described in the same time was 60 inches. 



Exper. 6. A body weighing 10 oz. by a moving force of 3 oz. described 20 

 inches in 2 s ; by loading the body with 10 oz. and the moving force with 3 oz. 

 the space described in the same time was 31 inches ; and by loading the body 

 again with 30 oz. and the moving force with 9 oz. the space described was 34 

 inches in 2 s . 



From these experiments, and many others which it is not necessary here to 

 relate, it appears, that the space described is always increased by increasing the 

 weight of the body and the accelerative force in the same ratio ; and as the acce- 

 leration arising from the moving force continued the same, it is manifest, that 

 the retardation arising from the friction must have been diminished, for the 

 whole accelerative force must have been increased on account of the increase of 



the space described in the same time ; and hence (as the retardation from 



-. . . Quantity of friction x , c c . . , 



friction vanes as — -r- — 7 — - — ) the quantity ol friction increases in a less ratio 



Quantity of matter ' * J 



than the quantity of matter or weight of the body. 



6. We come now to the last thing proposed to determine, that is, whether the 

 friction varies by varying the surface on which the body moves. Let us call two 

 of the surfaces a and a, the former being the greater, and the latter the less. 

 Now the weight on every given part of a is as much greater than the weight on 

 an equal part of A, as a is greater than a ; if therefore the friction was in pro- 

 portion to the weight, caeteris paribus, it is manifest, that the friction on a 

 would be equal to the friction on a, the whole friction being, on such a supposi- 

 tion, as the weight on any given part of each surface multiplied into the number 

 of such parts or into the whole area, which products, from the proportion 

 above, are equal. But from the last experiments it has been proved, 

 that the friction on any given surface increases in a less ratio than the 

 weight ; consequently the friction on any given part of a has a less ratio to the 

 friction on an equal part of a than a has to a, and hence the friction on a is 

 less than the friction on a, that is, the smallest surface has always the least 

 friction. But as this conclusion is contrary to the generally received opinion, I 

 have thought it proper to confirm the same by a set of experiments. But before 



