(154 1'HILOSOPHTCAL TRANSACTIONS. [aNNO 1775. 



Times of the middle of its obscura- 

 tion in the 3d point. 

 17S4, Oct.^fj . . . . 1*? on]ya single period of 12 a 21 i 



18 -J. |2 17 



31 15/ " 



o, , r \ 2 periods, each of. . . . 12 



31 ... . 1 J J 



19 



Hence the period on a mean is 12 19± 



111 ascertaining the above times, I attended particularly to the nearest obser- 

 vations both preceding and following. In the manner above stated the period 

 may also be deduced from the middle of its obscuration in the 7 th point ; but as 

 these observations are not so exact as the above, I shall only, as a further con- 

 firmation, compare 2 of the most distant of them, viz. Sept. 2Q, 22 h and Nov. 

 20, 6 h , which interval I find contains 6 periods, each of 12 d 20 h + . 



X. On the Motion of Bodies affected by Friction. By the Rev. S. Vince, A. M. 



p. J 65. 



The law by which the motions of bodies are retarded by friction has never, 

 that I know of, been truly established. Musschenbroek says, that in small 

 velocities the friction varies very nearly as the velocity, but that in great veloci- 

 ties the friction increases ; he has also attempted to prove, that by increasing the 

 weight of a body the friction does not always increase exactly in the same ratio ; 

 and that the same body, if by changing its position you change the magnitude of 

 the surface on which it moves, will have its quantity of friction also changed. 

 Helsham and Ferguson, from the same kind of experiments, have endeavoured 

 to prove, that the friction does not vary by changing the quantity of surface on 

 which the body moves ; and the latter of these asserts, that the friction increases 

 very nearly as the velocity ; and that by increasing the weight, the friction is in- 

 creased in the same ratio. These different conclusions induced me to repeat 

 their experiments, in order to see how far they were conclusive in respect to the 

 principles deduced from them : when it appeared, that there was another cause 

 operating besides friction, which they had not attended to, and which rendered 

 all their deductions totally inconclusive. Of those who have written on the 

 theory, no one has established it altogether on true principles : Euler (whose 

 theory is extremely elegant, and which, as he has so fully considered the subject, 

 would have precluded the necessity of offering any thing further, had its princi- 

 ples been founded on experiments) supposes the friction to vary in proportion to 

 the velocity of the body, and its pressure on the plane ; neither of which are 

 true : and others, who have imagined that friction is a uniformly retarding force 

 (and which conjecture will be confirmed by our experiments,) have still retained 

 the other supposition, and therefore rendered their solutions not at all applicable 



