608 SOLUTION OF THE EQUATIONS. 



13. In order to test the accuracy of the work in the determination of 

 the magnetic constants we may substitute their values in the theoretical 

 expressions for X, Y and Z and compare the results with the values of 

 X, Y and Z as taken from the charts. 



For this purpose we have to form for each parallel of latitude the 

 value of the expression 



\ K + ') = W + xw + xw 



+ (XM + X& + X,W) cos X + (XM + XM + XM) sin X 

 + (X?g t * + Xigi) cos 2X + (Xfh? + Xfhf) sin 2X 



+ (Xfa 1 + Xfa>) cos 3X + (XW + Xfhf) sin 3X 



+ X*g* cos 4X + X*g* cos 5X + X 5 \ l sin 4X + Xfhf sin 5X, 

 and also the value of the expression 



X& + X& + X&) cos X + (XW + XM + XW) sin X 

 Xfa* + X;g? + AVflf.') cos 2X + (Xfh? + Xfa* + Xft) sin 2X 

 Xfa> + XW) cos 3X + (XM + XM) sin 3X 



X& + X&) cos 4X + (Xft + XM) sin 4X 



* cos 5X + Xfgf cos 6X + JT.V sin 5X + Xfh* sin OX, 



and then to form the sum and difference of these expressions for the 

 values of X in northern or southern latitudes respectively, which may then 

 be directly compared with the charts. 



Similar expressions must be formed in the same way for Y and Z 

 for each parallel of latitude, and their sums and differences taken as in 

 the case of X. 



When the values of the magnetic constants had been determined, they 

 were substituted in the equations of condition for each belt of latitude, 

 the terms of which when added up gave the theoretical value of the 

 absolute term for that latitude. This calculated value of the absolute term 



