CATALOGUE OF POLAE STARS. 



249 



The following cases occur in \Ybich this method of development is applicable : 



Case 



Given 



d*a 



From 



da 

 dt 



d^n 

 d(- 

 (Pu 

 df 

 d*a 

 dt* 



To find 



d a d'^ a d^ a d* a d° a 



dt dt^ dt^ dt* df 



d^u d'a d*a d' a d^ a 



dt- dt^ dt' dt' dt^ 



d^ a d* a d^ a d^ a (Pa 



dt' dt* dt^ dt^ df 



, &c. 



d* a d' a d^ a rf' a d^ a 

 'dt* ~dt^ 'df ~df ^' '*'■ 



d^a d'' a d" a d^ a 



df' df dt' dt^ dt'- 



, «fcc. 



, . ., , ^ ^ dS d-8 

 and smnlarly lor o, — , — , &c. 



■^ ' dt dt- ' 



For the application of this method in the computation of the differential coeffi- 

 cients of Groombridge 1119 we have the following data, for 1, 8, and 16 years. 



CASE (a). INITIAL FUXCTIOX = «. 



FOR w = \. 



