The Rev. Brice Bronwin on the Theory of Planetary Disturbance. 43 

 M. Hansen employs this method, and differentiates relative to t, by whicli 

 means he gets rid of ^ log {^]. Thus we have 



d^ 





. ~ 2 



1 + 



and changing t into t, 



Tt 



'dj 



d^ \ 



Or, by (7) of the section referred to, 

 rf/3 _ Snr dr^ 



dd> 



dr' 



dt 



h, dz 



1 + t 

 dr 



In this form M. Hansen leaves it. But we might employ (8) of the same 

 section to reduce it, or to give a distinct form ; but that would introduce 



h 



r- agam. 



A, ^ 



4. We now proceed to the determination of the latitude, and the reduction 

 to a fixed plane. Make a the sine of the latitude, i the inclination, and b and 

 e the longitude of the node on the plane of the orbit and on the fixed plane 

 respectively, ^ having an origin fixed on the former plane. By making the 

 plane of the orbit to turn round the radius vector an infinitesimal space, it is 

 easily seen that, 



d^ = cos idO; (l) 



and we have the known formulffi, 



di_ 1 dR _ cos i dR 

 dt 



h sin i dd h sin i d^ ' 

 d^ _ cos i dR 

 dt h sin i di 



g2 



(2) 



