28 The Rev. Brice BRomviu on the Theory of Planetary Disturbance. 

 And difFei'entiating relative to t, 



1 dr Ate . , .dv . 2 ^^ ;, 



= ^ sin (u - tt) -^ ; or, since r^ — = h. 



r" dt K- 



dt 



1 dr ue . , . fie , . ■ -, 



- -;- = Vt sin (i; — TT ) = V^ (cos tt sin t; - sin tt cos v). 

 h dt h- ^ ' /r "- 



Whence we easily deduce 



In like manner, 



1 u\ 1 dr . /ue 



___jcos. + ^^sm« = pCos.. 



1 u\ . \dr fxe . 



fr, Sin u - y -r- cos z; = 7:; sin tt. 



r h- h dt h- 



1 u\ ^ Idp . fie 



- - -fr, ) cos \ + y j^ sin \ = ^ COS m. 



p h-J hdr h' 



1 m\ . ^ 1 c?P -, M« • 



fie 



fxe 



Equating the two sets of values of yj cos tt and ^ sin tt. 



h- 

 1 m\ Idr . A m\ ^ , 1'^/' ■ ^ 



h 



r 



1 M 



,, , sin u - y-j- cos u = ^, sm \ - y -y- cos X. 



(5) 



Multiplying these by cos u, sin v, cos X, and sin X, and adding and sub- 

 tracting results, 





ArfT 



A (/< 



(6) 



