VOL. III.] PHILOSOPHICAL TRANSACTIONS. 3lf 



cities, also retain proper velocities after collision. And the bodies /?, .S", hav- 

 ing improper velocities, are restored to an equilibrium by collision : that is, as 

 much as R exceeds, and S is deficient of their proper velocity before impulse, 

 just so much by the impulse is taken from R, and is added to S : and con- 

 trary wise. 



Therefore the collision of bodies having their proper velocities, is equiva- 

 lent to a balance oscillating on its centre of gravity. And the collision of 

 bodies having improper velocities, is equivalent to a balance upon two centres, 

 which on each side are equally distant from the centre of gravity : the balance 

 beam being produced when necessary. 



Therefore there are three cases of the improper motions of equal bodies. 

 But of unequal bodies with improper motions, whether in the same or con- 

 trary ways, there are in all ten cases ; five of which arise by conversion. 



R, S, are the two bodies, either equal or unequal, R the greater, and S the 

 less {Jig. 12, 13, pi. 7) ; « is the centre of gravity, or the handle of the ba- 

 lance ; Z the sum of the velocities of both bodies. Then, 



OyS 7 ffiven velocity r -S* -> , ^ . , 

 Ro\ ofbodv ^{^jbeforeimpulse. 



i?e") given velocity ri?i , r ■ i 

 Ser of body ^{^jbeforeimpulse. 



oR^ required velo- cR^ r. • i 

 5} city of body { 5 } after .mpulse. 



Ro S of body 



e iS'i required velo- f-S" 1 n. • i 

 e/J I city of body {ij lifter impulse. 



The rule is. Re, S e, make o R, o S ; Ro, S o, make e S, e R. 



Read the syllables, though disjoined. Re, S e, o R, oS, or Ro, So, e S, 



skill in architectiire, he succeeded Sir John Denham in the office of surveyor-general of the king's 

 works ; and from tliis time he had the direction of a great many public edifices, by which he ac- 

 quired the highest reputation ; as in tlie theatre at Oxford, St. Paul's cathedral, London, the Monu- 

 ment, the churches of St. Stephen Walbrook, St. Mary-le-bow, with upwards of 60 other churches 

 which that dreadful fire had rendered necessary ; also Chelsea college, one of the wings of Green- 

 wich hospital, the modem part of Hampton Court, &c. He was one of the commissioners who, on 

 the motion of Sir Jonas Moore, surveyor-general of the ordnance, was appointed to find out a pro- 

 per place for erecting the national observatory 3 and he proposed Greenwich Park, which was ap- 

 proved of J the foundation stone of which was laid the 10th of August l675, and tlie building was 

 presently finished under the direction of Sir Jonas, with the advice and assistance of Sir Christopher. 

 He became architect and commissioner of Chelsea college ; also principal officer or comptroller of 

 the works in Windsor castle j and he sat twice in parliament, as a representative for two different 

 boroughs. He died in 1723, at 91 years, and was interred with great solemnity in the cathedral of 

 St. Paul's. As to his person. Sir Christopher was of alow stature, and thin frame of body 3 but by 

 temperance and regularity he enjoyed a good state of health, to a very unusual age. In his manners, 

 he was modest, devout, virtuous, and very communicative of his knowledge, of which he possessed 

 an extraordinary fund. — Sir Christopher never printed any thing himself; but several of his works 

 have been published by others ; some in the Philos. Trans, and some by Dr. Wallis and by other 

 friends. His draughts and posthumous works were published by his son. 



