64i Mr. Spottiswoode — Equations of Rotation. [1863. 



Now it is known by the theory of elliptic functions that 



d cos amx 



= — sm am am x. 



dx 

 d sin am x 



= cos am X A am X, 



dAamx _ „ . 



— ^ — = —kj^ sm am x cos am x. 



Whence P^^, Q^, being the moments of the disturbing forces about the 

 present axes. 



If dm . / dn df\\ 



■ 1 r dn ^ ^ . dn dfW 



From these we derive 



^= \/0^.PxCOSx+\/V^QiSinx, 



J^) = -V^0^PxSinx+v'"^^QxCOSx, 



dn . n ^^sinvcosv-- , , 



^X;77^\/^^-^^i+ Av {--\/0-0.PxSinx+x/0,-0Acosx}> 



or 



dn , R, — 0»2sinycosYr / , 



, , 0,-0 1 sin X cos x r , / 



■=^/Q-Q-^■^ -QZZe^ ~ CAx)^ ^ ~ v^^PiSinx + \/A - cosx} 



^{^f~e^-p,cosx+\/d,-e,Q, sm^dt. 



And lastly, 



^__jf^__L -\/e^,Pi sin x + \/0i-eA cosx 

 dt dt AxJI^eZZa^p^cosxTv^eF^Asinxl^^* 



