GAUSS'S THEORY OF TERRESTRIAL MAGNETISM. 119 



at London = 1732 (it having been customary in former 

 times to call that force 1*732). The first or constant 

 term, which does not appear in our formula for V, pro- 

 bably arises from the conversion of powers of cosines &c. 

 into cosines of multiple arcs. The letter e stands for 

 cos u and f for sin u. 



-= - 1-977 + 937103e+71'245 e 2 - 



+ (64-437-79-518 e + 122-936 e*+ 152-589 e 3 )/cos \ 

 + ( - 188-303 -33-507 e + 47794 e* + 64-112 e 3 )/sin \ 

 + (7-035 - 73-193 e - 45791 e 2 )/ 2 cos 2X 

 + ( - 45-092 - 22-766 e - 42-573 e 2 )/ 2 sin 2X 



+ (l-396 + 19774e)/ 3 cos3X+ (-18750 -0-l78e)/ 3 sin3X 

 + 4-127/ 4 cos 4X + 3-175/ 4 sin 4X. 



From these, by the formulae in Article 47, are formed 

 numerical values of N, W, and C, for numerous latitudes 

 and longitudes : and from them are derived numerical 

 values of Declination, Horizontal Force, and Dip. By 

 means of the values of Declination, curves of Places of 

 Equal Declination were laid down by Gauss upon a map, 

 from which the writer of this Treatise has formed the 

 Magnetic Meridians in Figures 20 and 21. The Mag- 

 netic Meridians may also be traced by the following 

 process. Conceive fictitious ordinates x, y, z, as in 

 Article 47, where x and y are on the tangent-plane 

 of any point on the earth's surface, and x is in the 

 direction in which V does not alter, that is, in the direc- 

 tion of a curve of Equal Values of V. The general 



