1 54 Prof. Baker, On a set of transformations of rectangular axes 



The latter of these expresses Hamilton's law that a rotation of 

 amount 2C about the vertex C of a spherical triangle ABC, followed 

 by a rotation of amount 25 about the vertex B, gives a rotation 

 about the vertex A of amount 2tt — 'iA. The former expresses that 

 if be the pole of the arc BG, and P be any point of the sphere, 



cos PO sin a sin B sin C 



= cos PA sin A — cos PB sin B cos C — cos PC sin C cos B. 

 The transformation here denoted by P is that called by Clifford a 

 right (or left) vector. It can also be represented in the form 



where 



is such that m'^ 



P = cos 19 . CO + sin 1$ . m, 

 0, — n, m, I 

 n, 0, — I, m 



— 771, I, 0, n 



— I, — m, —n, 

 co; this is the same as P = e^'^^. 



I 



