HiNTON — Cayletfs Formuke of Orthogonal Transformaiioi. 65 



These formulae agree with Cayley's if ^ = ^, and y = ?^ + n', &c., 

 y' - n - n', &.Q., in which case the rotation is about a plane, by the 

 angle 2$. 



In no case, however, can they be made to assume his general form. 

 The reason appears to be that he starts from the determinants 



s 



b 



c d 



-b 



% 



f 9 



- c 



-d 



% h 



-d 



-9 



- h z 



and the form with the rows and columns interchanged in defining his 

 quantities a, b, c^f, g, h. Now an inspection of the form above shows 

 that the determinant of a transformation effected by any kind of 

 rotation cannot assume this form. Hence there is no geometrical 

 intei^retation of Cayley's constants with angles and axial planes. 



