120 ON MAGNETISM. 



dV 

 expression for force in the direction x is -j- . But in 



this instance, V does not alter with alteration of x ; 



dV 



therefore -7- is 0, and there is no force in the direction 

 dx 



of x. Consequently the whole horizontal force is in the 

 direction of y, or perpendicular to the curve of Equal 

 Values of F Now Gauss has prepared curves of Equal 

 Values of F(not copied in this Treatise), and therefore 

 it is only necessary to draw trajectory-curves cutting all 

 the Equal- F-curves at right angles, and the lines so 

 drawn will be the lines of direction of total horizontal 

 force, or the Magnetic Meridians. 



The curves of Equal Horizontal Force in Figures 28 

 and 29, those of Equal Total Intensity in Figures 35 

 and 36, and those of Equal Dip in Figures 20 and 21, 

 are copied immediately from Gauss. 



The elements from which these curves have been 

 formed having been deduced from 24? magnetic measures 

 made at different places, those measures are necessarily 

 exhibited correctly in the curves. And now the ques- 

 tion arises, whether all other measures made since that 

 time are exhibited accurately by the curves. And the 

 answer is, that they are exhibited so accurately as to 

 leave no doubt on the fundamental correctness of the 

 theory, and yet with small discordances which render it 

 desirable that the formulae should be extended and 



compared with a greater number of measures for nu- 



y 



merical determination of the constants in ~ I* 1 the 



M 



