338 PHILOSOPHICAL TRANSACTIONS. [aNNO 1 669. 



body, of a mean quantity, than if it was immediately struck by the body itself; 

 and if the interposing body be a mean proportional between the other two, its 

 action upon the quiescent body will be the greatest of all. 



In all these cases, the author, as he himself suggests, considers the bodies as 

 homogeneous, or of the same matter, or that their mass may be estimated by 

 their weight. He moreover subjoins, that he has observed a surprising law of 

 nature, which he can demonstrate in spherical bodies, and which seems to hold 

 universally in all others, either hard or soft, impinging either directly or ob- 

 liquely, viz. that the common centre of gravity of two or three, or more bodies, 

 always moves uniformly the same way in a straight line, both before and after 

 the stroke. 



On the Resolution of Equations in Numbers. By Mr. John Collins.* 



iV" 46, p. 929. 



It has been observed by several persons of this country, in any equation, 

 however affected, that if a series or rank of roots be assumed in arithmetical 



* In addition to the biographical account of this author at p. 207, it is further to be observed, 

 that he was of great benefit to the sciences in general} keeping up a constant correspondence 

 with many of tlie most learned men of his time, botli at home and abroad, and promoting the 

 publication of several valuable works, which without his encouragement would never have 

 been seen by the public; particularly Dr. Barrow's optical and geometrical lectures, also tlie 

 doctor's abridgement of the works of Archimedes, Apollonius, and Theodosius ; likewise Broun- 

 ker's translation of Rhonius's algebra, with Dr. Pell's additions^ &c. which were procured by his 

 frequent solicitations. Some time after his death, among his papers, were found a multitude of 

 manuscripts, on mathematical subjects, of Briggs, Oughtred, Barrow, Newton, Leibnitz, Pell, 

 and many others. From whose letters, and those of other celebrated mathematicians, it ap- 

 pears that Mr. Collins spared neither pains nor cost to procure what tended to promote real 

 science. Also many of the discoveries in physical knowledge owe their chief improvement to him j 

 for while he excited some to disclose every new and useful invention, he employed others in im- 

 proving them. Sometimes he was peculiarly useful, by showing where the defect lay in any branch 

 of science, pointing out the difficulties attending the inquiry j at other times explaining their ad- 

 vantages, and keeping up a spirit and energy for improvement. In short, Mr. Collins was like 

 the register of all the new acquisitions made in the mathematical sciences ; the magazine to which 

 the curious had frequent recourse j which acquired him the appellation of the English Mersenne. 

 And had not some of his correspondents obliged him to conceal their communications, there could 

 have been no dispute about the priority of the invention of a method of analysis, the honour of 

 which doubtless belonged to Newton ; as appears from the papers printed in CoUins's Commercium 

 Epistolicum ; a work which M^as made out from the letters left in possession of this author. 



Mr. Collins wrote and published himself a variety of useful works : as. An Introduction to Mer- 

 chants* Accounts, &c. 1652 ; The Sector on a Quadrant, l6"58 j Geometrical Dialling, l659 ; The 

 Mariner's Plain Scale new plained, l659 ', also several ingenious papers printed in the Phil. Trans, 

 besides some useful commercial tracts, highly acceptable to the public. 



