235 



October 30, 1865. 

 The following officers were elected : — 



President Rev. W. H. Cookson, D.D. 



fMr. I. Todhunter. 

 Vice-Presidents. < Dr. Paget. 



(_ Professor Challis. 



Treasurer .... Rev. W. M. Campion. 



f Professor Cardale Babington. 

 Secretaries . . < Professor Liveing. 



[Rev. T. G. Bonney. 



["Professor Selwyn. 

 New Members J Rev. W. G. Clark. 

 the Council. 1 Mr. R. Potter. 



[Rev. N. M. Ferrers. 



The following communications were made to the Society : — 



By Mr. A. R. Catton— 



1 . "On the Synthesis of Formic Acid." 



2. " On the possibility of accounting for the double refraction of 

 Light by the vibrations of a continuous elastic medium kept in a state 

 of constraint by the action of the material molecules." 



By Professor Cayley — 



3. " A new Theorem on the Equilibrium of four Forces acting 

 on a solid Body." 



Defining the " moment of two lines " as the product of the short- 

 est distance of the two lines into the sine of their inclination, then, 

 if four forces acting along the lines 1, 2, 3, 4 respectively are in 

 equilibrium, the lines must, as is known (Mobius), be four genera- 

 ting lines of an hyperboloid ; and if 12 denote the moment of the lines 

 1 and 2, and similarly 13 the moment of the lines 1 and 3, &c, the 

 forces are as 



■s/23.34.42 : v/34.41.13 : \Al .12 . 24 : ^12.23.31. 



Calling the four forces P^ P 2 , P 3 , P 4 , it follows as a corollary that 

 we have 



P^ .12 = 12. 34v/l3.42 . \/l4 . 23= P 3 P 4 . 34 ; 



viz. the product of any two of the forces into the moment of the 

 lines along which they act is equal to the product of the other two 

 forces into the moment of the lines along which they act, — which is 

 equivalent to Chasles's theorem, that, representing a force by a finite 

 line of proportional magnitude, then in whatever way a system of 

 forces is resolved into two forces, the volume of the tetrahedron 

 formed by joining the extremities of the two representative lines is 

 constant. 



