596 FORMATION OF THE EQUATIONS OF CONDITION. 



Thus the values of x' m , y' m and z' m in the equations of condition given 

 in the previous Section (see pp. 520 553) have been determined. 



Each system of equations of condition will involve a single value of 

 m combined either with all even values of n or with all odd values of n. 

 There will be one system for the coefficients X', X'" n , another for the 

 coefficients F', Y' m _ n and a third for the coefficients Z'*, Z' m _ n . 



The belts of latitude, 5 in breadth, starting from 87 N. latitude, 

 are distinguished by the letters (a), (b), (c) &c., the centres of the belts 

 being 5, 10, 15 &c. from the pole respectively, and each belt of north 

 latitude combined with the corresponding belt of south latitude will con- 

 tribute an equation to each system. 



Thus for latitude 60 N. combined with 60 S., the set (/) will 

 furnish, for the g constants, the three following equations to the respective 

 systems X, Y, Z corresponding to m = 4 and n even : 



* -[9-6479108]^ -[9'6397698j(/l t -[9-3739435]^ 4 -[9-3627519]^ 6 -&c. 



= -( 4 -O for X, 



[9-7120302]0 4 * + [97022392]^ + [9-5314878]*/ 4 + [ 



= (b t + V t ) for Y, 



= - ( 4 + a' 4 ) for Z, 



and the three following equations to the similar systems corresponding to 

 odd values of n : 



-[9-547l920]# 4 -[9-5374280]#l 6 -[9a267y47]# 4 -[9-1145742]# 4 _ 7 -&c. 



= (a 4 + a' 4 ) for X, 

 [9'6499180]# 4 + [9-6379512] #1 6 + [9'3653414]# 4 +[9'3490233]#l v + &c. 



= -( 4 -a' 4 ) for Z. 

 where [9-6479108] is employed to express the number of which 9-6479108 is the logarithm. 



