63 Mr. Spottiswoode — Equations of Rotation [1863. 



in virtue of (1 1). Hence the wliole expression vanishes, or 



and similarly 



Moreover, in virtue of (23), we have 



Hence multiplying (25) first by f^o» respectively and adding, 

 secondly by B^, f^, 



thirdly by (&^, C^, 



we shall obtain the inverse system 



(27) 



Returning to the integrals (13), we derive 



(0x-%i' + (92-eX'=^'-(S + 



(0 -0,)i.,H(0x-0j?,^=>^^-(S + 0,)^. 



Let 



then 



and 



M, =c A / — ^ cos Y 



_ /p-(s+e)A / 

 _ / A'-(S+9)A /r"eFelEM»Ssi„'v 



Substituting in the equations of motion (21) {e. g. the first of them) 

 and dividing throughout by sinx\/ — {^•\-Q^hj we have 



