34-2 Mr. Lubbock on the Variation of 



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



/ d R 



in 8 e or / j>, co] -r which are independent of c. 



<J Cl 



If ( -n J , as defined and limited in the expression for R in 

 p. 339, contains any term 



A cos (i (n t + c) -\-jmnt + lnt}, 

 d w contains the term 



[a, co] ^ cos (i (n t + c} + jmnt + lnt); 



and considering now only the constant portion of [, w], 8 <a con- 

 tains the term 



^ 



[a, a)] - : - =r s'm (i (n t + c) + j m n t + I n t}. 

 J (z + J m + 1} n 



Similarly, if ( -5 J contains the term 



B sin (i (n t + c) + jmnt + I' n t} 

 d e contains the term 



[o>, <?] B sin (i (n t + c) + j m n t + I' n t} 9 

 8 e contains the term 



TJ 



- l>> <3 (, + y OT + ^ n cos (< ( ^ + c ) +jmnt + l'nt} 9 

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



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

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



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

 tity 



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

 Let 



= C + D cos (i 2 +jmn t + Int) 

 a n 



