228 Mr Allen, Notes on solid geometry. [March 20, 



the modulus being sin 75° ; then 



1 3 /Q sn7dn7 



and | snTdnT 



5 d (l+cnT)--" 



. sn Tdn T 



2/ 3 = 2+3* (i +C nT) 3 * 



By means of the cubic transformation it can be shown that 

 T—t^S, and if t be changed into cot or coH, then x 3 and ?/ 8 are 

 unaltered, but x is changed into cox and cole, y is changed into coy 

 and co 2 y respectively. 



(4) Notes on solid geometry. By A. J. C. Allen, M.A. 



The author gave a short proof of some properties of ruled sur- 

 faces, and also of the well-known theorem that if the ratio of the 

 curvature and torsion of a curve be the same at every point, the 

 curve is one traced on a cylinder, and cutting all the generators at 

 a constant angle*. 



May 1, 1882. 



Mr F. M. Balfour, President, in the chair. 



Professor Birkbeck and Mr J. E. Marr, M.A., St John's College, 

 were balloted for and duly elected Fellows of the Society. 



The President announced that the following resolution had been 

 passed by the Council : " That this Council desire to record their 

 sense of the extraordinary value of the scientific labours of the late 

 Charles Robert Darwin, M.A, LL.D., of Christ's College ; and that 

 a copy of this resolution be sent to Mrs Darwin as an expression of 

 the deep sympathy of the Council with herself and other members 

 of Mr Darwin's family for the irreparable loss they have sustained." 



* See Messenger of Mathematics, Vol. xn. pp. 26—28. 



