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



dp d\ _dp d\ _ J, 



dt dr d-T dt~ ' ^ > 



which is a very remarkable equation. 

 From this we deduce successively, 



dp d\j dp d\ rp f, dp 

 dt dr dr dt ~ c/t' 



h^(dp(!l_dpdj\ ^j^^^^dp 

 p'f \dt d-T dr dt) dr' 



but 



dt P' dt'^^ d^ dt' dr P'dr^^ d^ dr' 

 Therefore, by substitution in the above, 



i^mq_c^dj\^ dp 



p, \dt dr (It dt) dr ^ ' 



This again is a very remarkable equation, and has a remarkable corres- 

 pondence with (7). Dividing it by — -=^ = — -, = — , we have 



P,dr p,^- p^ 



d^_d^\±\ _1 .yr , ew| ([p 



dt drld^j ~ h''^ h '' dr' 



or, 



dt h''^ "^ 2/j dr "•■ drld^ ' 



\dJ 

 Equation (7) multiplied by 2p gives 



^ dp d\ „ dp d\ ^ _, 

 '^ dt dr '^dr dt '^ 



But differentiating p- — = h, relative to t, we have 



2 d-\ dp dX _ dh 



^ drdt ^~dt 'dh~'dt' 



(9) 



