342 Mr. Lubbock on the Variation of 



It must be recollected that in this expression no terms are included 



in $ e or / [e 9 at] — pr which are independent of c. 



If (-5 — ), as defined and limited in the expression for R in 



p. 339, contains any term 



A cos (i(nt + c) + j mnt + In t) 9 



d G) contains the term 



[a 9 at] A cos [i {lit + c) +jmnt + lnt); 



and considering now only the constant portion of \a 9 ©], 80 con- 

 tains the term 



favi fi+jm + /) w sin (*'(** + c ) +J mni + lnt). 

 Similarly, if ( -= — \ contains the term 



B sin (i (nt + c) + j mnt + V n t) 

 d e contains the term 



[«, e] B sin (i (nt + c) + j mnt + V n t) 9 

 8 e contains the term 



"" 1>> g 3 (i + j m + V) n C ° S ( * ^ * + C) +J mnt + *"*)> 

 and these terms give, after well-known reductions, in J — — d t 



r&>, e] —r- s 7T-7-. • 7-w; cos (I' — I) t 9 



L ' J n(i +jm + l){i +jm + V) K J ' 



which is evidently of the order m\ A and B being each of the or- 

 der m 2 , and i of necessity not equal to zero. 



I now proceed to consider the effect of the variation of the quan- 

 tity 



0, &>] 



which may be taken as the type of other similar quantities. 

 Let 



L^J = C+ Dcos(int +jmnt -f Int) 



