36 



3a e» 23 ' iy 



V 3* ' J/3 ' ay 



and, continuing the differentiations, 



J«" S«* 3,3' 3y* iiti^ «/3«y «y3<» 



3^'« — 3«* ^ S/3'' V 3«^^ ^/33y 3yJ« 



S't- ^, S*" , r'2 ^^ J. r'" i!H. . 2 CC — 4- 2 C'C" —4-2 C"C -- 



and substituting these values for 



l^v J"v S«u g^« l^v Vv . 



in the second member of (I''), and reducing by the relations (X"), 

 (L"), and (G), we obtain the function in the first member. This 

 function v", which composes the first member of (I"), may therefore 

 be obtained by assigning to the axes of coordinates, any arbitrary 



