264 USEFUL FORMULAE, CONNECTING LEGENDRE'S COEFFICIENTS, WHICH 

 When m = 0, then Q% is reduced to P n and we should have 





which is identical with equation (14). 



25. From equation (19) we may derive a scheme of calculation, by 

 means of which the numerical values of G for different values of n and 

 m may be obtained. 



This is the equation employed by Mr Graham in the calculation of 

 these functions. 



From equation (18) we may also derive a scheme of calculation by 

 means of which the numerical values of G for different values of n and m, 

 may be obtained. 



In the latter case the value of each function is derived from the values 

 of the two previous functions with the same value of m. 



This is the equation employed by Mr Wright in 1873 74 in the calcu- 

 lation of all the values of G up to 6rJ to ten places of decimals for all 

 values of //. differing by '01 from to 1. 



The functions 6r, H, &c. are functions of p., the cosine of the geo- 

 centric co-latitude. 



The values of 6r for different values of n and m up to 6rJ have been 

 determined for every degree of latitude on a sphere of radius unity. They 

 have also been determined for every degree of the geographical co-latitude, 

 taking into account the spheroidal figure of the Earth. 



The values of these functions are given in the tables. 



