DETERMINATION OF THE GAUSSIAN MAGNETIC CONSTANTS. 133 



The following tables give some comparisons. The first of these tables 

 "ives the values of the first twenty-four constants (i.e, of those to the 

 fourth order) as determined by Gauss for 1830, by Erman and Petersen, 

 by Adams (1) from Sabine's charts for the epoch from 1842-45, and (2) 

 from the Admiralty charts for 1880, and by Neumayer for 1885, as pub- 

 lished in Berghaus' ' Physical Atlas.' 



If we had expressed the magnetic potential and the magnetic forces, 

 X, Y and Z in terms of the functions Q™, Q™, Ac, instead of in terms of 

 jjm jjm ^Q -vpe should have obtained another series of magnetic constants 

 but the two series are related to one another, and the one series may be 

 derived from the other by multiplying each constant in one series by a 

 factor depending on the values of n and vi. 



Thus let «™ and 6™ be two magnetic constants derived from the 

 function Q,7 (as defined above), and let a„ and /?„ be the corresponding 

 Gaussian magnetic constants as derived from the function H™. Then these 

 magnetic constants a™ and 6™ are connected with a„ and ^„ by the relations 



A>_Q._l-3.5'---(2«-l) 



On 



H„ 



(n—m) 



for a given value of m ; and similarly 



and in particular 



a„.^A.._Q». _ 1-3.5 • • • • (2n. 



■1) 



and 



''ji=l=^^=9:^= 1-3-5 {2n- 



«,.-2 &«-2 H„_2 {n-m—2) ! 



^rH-2 fin + i^^Qn + i __ 1-3.5 



i. Q AJ. ,, + .> 



-5) 



(2« + 3) 



•-li+a 



{n-m + 2) 



