126 REPORT— 1898. 



Adding these together, we have 



(for g^) (for Al) 



•0417859 a^ + 1-2255712 a^=-0714734 or -1395649 (/3). 



Eliminating u\ from the equations (a) and (/3) we have 



1-2255093 a^,=-0703382 or -1388117. 



1 Hence (/<=-0573951, and A^=-1132686. 



Substituting in the first equation, we get 



i7^=-0270832 and 74=-0178567. 



Hence it appears to be important to take g\ and h\ into account, as 

 they are larger than gl and h\. 



Similarly in solving the equations with ni=4 and n even, it is found 

 that 



^1='0029684, 74=-0217744 

 (^^=-0642604, 74=-0603230. 



So that g\ and h^ are more important than g\ and h\. 



The relative importance of magnetic constants of different orders is well 

 shown by the solution of the final equations for lif^ hi and /t, for the period 

 1880. Keeping in the terms containing lii, the final equations derived 

 by combining the equations for X, Y and Z are 



24-1400624 Al- -2579706 Ah--1213933 ;4=-19111, 

 — -2579706 A:i + 2-17S4697 7i?--0719819 A— -13841, 

 -•1213933 /(;i--0719819 7tl + -1887180 A?=--02852. 

 The solution of these equations gives the values 



74=-00794, 7i?=-06041, 74=--12298 British units. - 

 Converting these into c.g.s. units we get 



A;:;= -000366, 7i?= -0027855, 7^=- -00567. 



Comparison with the tables shows that the effect of keeping in the 

 constant h\ is to make a considerable change in the values of the con- 

 stants lii and lil. 



The corresponding equations for gl, g\ and .7^ are 



-14-62295=24-1400624 ^^--2579706 ^^--1213933 g-'i, 

 -l-11044=--2579706 ^^2-1784697 ^5--0719819 g":, 

 •05785= - -1213933 f7l--0719819 g\ + -1887180 g\, 



and the solution of these equations gives the values 



^:^=- -613670, ,y?=- -592789, (/■^=- -314308 British units, or 

 ^2= -•028295, r/:^=- -027332, y?=- -014492 c.g.s. units. 



These values of g\ and gl do not differ much from the values previously 

 obtained, which are given in the following table. 



Let us fui-ther illustrate the mode of solving these final equations by 

 taking the case of m=:0 and n odd. 



Since the observations of magnetic elements in high latitudes appear 

 to be doubtful, we will form the equations of condition, taking into 

 account the data only up to 67^° N. and S. latitudes. 



' The two extra magnetic constants i^j and h'\ here determined make up the 

 number of constants which have been determined to 50. 



