_ 1 1 (n + m)\ n + m ~ m 



"" = 2* ml 1.3.5 ... (2-l) ~ 2n-l "''' 



ON THE EARTH'S SURFACE REGARDED AS A SPHEROID, 

 and generally 



.__L_L_fe<_ ni 



(2-l)' 



The value of JT n m is always 0, except when m=l. 



The value of Y" is always 0, except when m=l, 



and the value of Z" 1 is always 0, except when m Q. 



469 



Z= n _2(j Z =-m- 1 G 



n ^,n+2 ' -* * 



/ 2 = l-e 2 and log (-] = 0'0014542. 



The logarithms of the values of the coefficients X?, Y, Z at the Pole 

 for m = 0, m = 1 and for the several values of n are here given. 



For X these are to be multiplied by (</cosX + &'sinX), and for Y 

 they are to be multiplied by (g r sin X h' cos X). 



NOTE. In the tables n before a logarithm indicates that the corre- 

 sponding number is negative. 



