VOL. XXXIV.] PHILOSOPHICAL TRANSACTIONS. l( 



The Forces in. Force communicated by the Stroke. Proportion. 



Before After 



o i6 i6 



4 36 32 



36 100 64 



100 196 96 



J 96 324 128 



324 484 160 



Before After 



1 



2 

 4 



6 



8 

 10 



the stroke. the stroke. 



If it be said, that Mr. E. has not considered the other part of the entire 

 effect of the stroke, the intropression of the parts; he replies, this will make 

 but a small alteration in the matter; since the intropressions in all these cases 

 are equal, the relative velocities being by supposition the same: so that not- 

 withstanding, upon the whole, one and the same, or equal causes, will produce 

 unequal effects. 



Remarks on a supposed Demonstration, that the moving Forces of the same 

 Body are not as the Velocities, but as the Squares of the Velocities. By the 

 same. N° 396, p. 188. 



The demonstration runs thus: " 1 conceive that the body c, fig. 14, pi. 3, 

 impinges obliquely on the spring l with the velocity cl, as 2, the angle of in- 

 clination CLP being of 30 degrees, whose sine c? is half the radius cl. I sup- 

 pose the resistance of the spring to be such, that to bend it, there is precisely 

 required one degree of velocity in that body, should it impinge perpendicularly; 

 what then, shall be the consequence after an oblique impulse of c against the 

 spring L? since the motion in cl is compounded, as is well known, of the two 

 collateral motions in cp and pl; and since cp, according to which the body 

 directly impinges on the spring l, represents half the velocity of the body 

 through cL, this motion through cp will be destroyed, when the spring is bent; 

 for it would be the same thing, as if the body c should with the velocity cp, 

 perpendicularly impinge on the spring, which by the hypothesis might destroy 

 that velocity, the velocity of the body and the direction pl continuing the same; 

 producing therefore, pl to m; so that lm be = pl = \/3, for cl is supposed 

 = 2, and applying in M another similar spring, forming with lm the angle 

 LMQ, whose sine lq = cp = 1 ; by the same reason it is manifest, that the 

 body c, after the bending of the spring l, will bend the spring M, losing the 



VOL, VII, Z 



