+ 



The Rev. Bbice Bronwin on the Theory of Planetary Disturbance. 55 



"T dr 



And by substitution, 



^ ' "^ d. 2l )dr^h, Ch cZr+ h, li^\;~^T^) 



£ 'li!^ + 3(po ,^ <!> (po. d(n en d{pf) a!=0 e« rf^(pO^') j^ 

 2 ^x^ '^'^'^^dr^-2^^^-dr+-h,—r-f'-d?+T,-dyt>£ 



To this we must add, 



^^^-^■^^ A rf^;+I;^?^■-I;-^?;^'^' 

 ^ '^"^ ''^Affo 'h,~dr^T,~d^'^' 



5. In concluding this paper, I will give a brief sketch of a transformation of 

 the differential equations which determine the place of a disturbed planet 

 which I have never seen noticed, but which I think is deserving of some con- 

 sideration. 



Make Q^-- + R; the equations with reference to a fixed plane are, 



df^^d.v-'"' df + d^-^' df+Tz=^- (1) 



Suppose now a plane always to make the constant angle i with the fixed 

 plane, i bemg the mean incUnation of the orbit to this plane. And let thi« 

 plane slide on the fixed plane in such a manner that their intersection may have 

 a uniform motion equal to that of the node, or so that the intersection of the 

 two planes may be always the mean place of the node. And let 6 - ant be the 

 longitude of this intersection, e being constant. 



Let now v, and y, be co-ordinates making the angle e - ant with .. and ,/ 

 ■X, lying m the intersection of the sliding and fixed planes. We have 



