VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 66l 



very strong cohesion to it. 2dly, A body whose weight was ] 6 oz. was laid at 

 rest on the horizontal plane, and it was found that a moving force of 6 oz. 

 would just put it in motion ; but that a moving force of 4 oz. would, when it was 

 just put in motion, continue that motion without any acceleration, and there- 

 fore the accelerative force must then have been equal to the friction, and not 

 when the moving force of 6 oz. was applied. 



From these experiments therefore it appears, how very considerable the 

 cohesion was in proportion to the friction when the body was in motion ; it 

 being, in the latter case, almost J-, and in the former it was found to be very 

 nearly equal to the whole friction. All the conclusions therefore deduced from 

 the experiments, which have been instituted to determine the friction from the 

 force necessary to put a body in motion, have manifestly been totally false ; as 

 such experiments only show the resistance which arises from the cohesion and 

 friction conjointly. 



8. I shall conclude this part of the subject with a remark on art. 5. It ap- 

 pears from all the experiments which I have made, that the proportion of the 

 increase of the friction to the increase of the weight was different in all the dif- 

 ferent bodies which were used; no general rule therefore can be established to 

 determine this for all bodies, and the experiments which I have hitherto made 

 have not been sufficient to determine it for the same body. At some future op- 

 portunity, when I have more leisure, I intend to repeat the experiments in order 

 to establish, in some particular cases, the law by which the quantity of friction 

 increases by increasing the weight. Leaving this subject therefore for the pre- 

 sent, I shall proceed to establish a theory on the principles which we have already 

 deduced from our experiments. 



Prop. 1. — Let efg, fig. 1, pi. Q, represent either a cylinder, or that circular 

 section of a body on which it rolls down the inclined plane CA in consequence of its 

 friction; to find the time of descent and the number of revolutions. 



As it has been proved in art. 5, that the friction of a body does not increase 

 in proportion to its weight or pressure, we cannot therefore, by knowing the 

 friction on any other plane, determine the friction on ca; the friction therefore 

 on ca can only be determined by experiments made on that plane, that is, by 

 letting the body descend from rest, and observing the space described in the first 

 second of time; call that space a, and then, as by art. 3, friction is a uniformly 

 retarding force, the body must be uniformly accelerated, and consequently the 

 whole time of descent in seconds will be = </ — . Now to determine the num- 

 ber of revolutions, let .s be the centre of oscillation to the point of suspension a ;* 



* a and * are not fixed points in the body, but the former always represents that point of the body 

 in contact with the plane, and the latter the corresponding centre of oscillation. — Orig. 



