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



\ h- J h dv "^ ' h dj 



We eliminate C from this by putting p^j-^ (l~5"7^ + l ~5^ ) for p = /)^^. 

 Let {S) be the value of S when /s is changed into p, v-| , and we have 



Sn d r ^ /d<f) d<p^\ 1 



T, ^ 1''' v^ ~d?yj' 



Eliminate (p, cos \3f + p, sin \N) ~ (^i| - | -^ j by 



,„, /I 2upN rfi? /t* ^ ,r • ^ »r. ^n d(p-,) 



\/i h^^hy dv 

 and we find as the result, 



^ d ^ Jd^ _ d<jr\ I 



Make (P) = (S) -1^+5^^. Then, 

 ^ ^ ' h dv li^ dr 



We now develope p^ and \, by the powers of 0; so that {S") and (P") will 

 have only p] and X", which are elliptic functions of t only, with the constant 

 elements a^, e,, &c. 



