VOL. LXX.] PHILOSOPHICAL TRANSACTIONS. 73g 



motion of each body after the stroke may easily be determined: for considering 

 p as acting on q with the velocity v — v, putting 2m = 



P X GC X GO 



Q X GC X FO + P X go X DC 



we shall have, by this prop, (v — v) X 2m = the velocity communicated to g ; 

 therefore v -^ {v — v) x 2m = the velocity of a after the stroke: also (v — v) 

 X M X — = the velocity gained by the point d from simple impact, and con- 

 sequently the velocity of that point after =zv -\- {v — v) Xm x — , hence v — 



t' — (v — u) X M X — = the velocity lost by p at the point f from simple im- 

 pact; therefore p's velocity after the stroke = v — [v — v — (v — v) X m x 

 —1 = -" . In the same manner it might have been determined had a moved in 



CG-' FO ° , 



an opposite direction. 



Cor. 4. Hence also we may easily determine the motion of each body after the 

 stroke, supposing q had not been moving in a direction parallel to the motion of 

 p, by resolving q's motion into two parts, one parallel to the motion of p, and 

 the other perpendicular; and finding by the preceding what would be the effect 

 of the parallel motions, and then compounding q's motion after the stroke, from 

 that consideration, with the motion it had in a direction perpendicular to it before 

 the stroke. 



Cor. 5. The point a of the body p will describe the common cycloid, when that 

 body after the stroke has any progressive motion. 



Cor. 6. Hence therefore the times of the revolutions of each body may be 

 determined as in prop. 6. 



Cor. 7- If the bodies had any rotatory motion before impact, every thing 

 relative to the motion of the bodies after the stroke might have been determined 

 from the same principles. 



XXXIII. The Case of James Jones, continued from p. 684. By Richard 



Browne Cheston. p. 578. 



Mr. C. now could announce the state the bones of the pelvis appeared in after 

 a maceration of 5 months : for though by very seldom changing the water, and 

 keeping the vessel containing it rather in a warm place, he suffered the highest 

 putrefaction to come on, it took up that space of time before the soft parts were 

 entirely destroyed. Maceration has now shown, that the depth the probe entered, 

 and the gritty resistance felt in the body of the tumor, was not from its passing 

 through a carious or diseased part, as there was reason then to suppose, but from 

 the quantity of osseous matter deposited on the outer side of the os innomi- 

 natum; and that the part so loaded with it externally, and as it afterwards 

 proved to be internally, was apparently in a sound state. 



As tlie soft parts of the tumor decayed in maceration, great quantities of 



5 B 2 



