184 Literary and Philosophical Society. 



Theorems and Problems to elucidate the Mechanical Prin- 

 ciples called Vis Viva. By John Gough. 



Dr. Bottomley describes the paper thus : 

 * He starts with certain definitions of force and axioms. 

 Vis viva he defines as " the whole force opposed by a body 

 in motion to a retarding force which impedes its progress ; 

 and conversely, it is the whole force accumulated in a body 

 by the action of any motive force which puts that body in 

 motion." Also, he assumes that the vis viva of a body is 

 equal to the quantity of resistance which it is able to over- 

 come. Then follow certain theorems involving his defini- 

 tions and axioms. In his method of solution he uses 

 Euclid's doctrine of proportions and the fluxional calculus. 

 His paper concludes with mechanical problems the solu- 

 tions of which depend for the most part on the preceding 

 theorems, such as the penetration of plastic matters by 

 falling weights of known dimensions. 



' Determination of centre of gyration, and centre of 

 oscillation ; ratio of forces necessary to draw out ductile 

 cylinder of given proportions to other dimensions ; deter- 

 mination of the velocity with which one ball must strike 

 another so that it may break.' 



A Demonstration of Lawson's Geometrical Theorems. By the 

 late Rev. Charles Wildbore. 



Dr. Bottomley says here : 



' This paper consists of solutions by the late Rev. C. 

 Wildbore to all the sixty theorems in the well-known 

 pamphlet entitled, "A Dissertation on the Geometrical 

 Analysis of the Ancients, with a collection of theorems and 

 problems, without solutions, for the exercise of young 



