traced upon the Surface of the Sphere. 351 



XXXVII. 



We proceed now to consider a few circumstances connected with this 

 curve. The first form (5.) possesses that kind of analytical symmetry which 

 may claim for it some attention ; but it is of more importance, from its be- 

 ing the geographical equation of the lines of equal magnetic variation, 

 the needle being supposed constantly directed to the magnetic pole. In this 

 case, X is the colatitude of the magnetic pole, L is the f magnetic variation, 

 <J) the colatitude of any point in the curve, and 6 is the corresponding lon- 

 gitude, reckoned from the meridian in which the magnetic pole is situated. 

 If another meridian be taken as the origin of longitudes, such that, in re- 

 ference to it, the longitude of the magnetic pole is I ; then, the equivaria- 

 tion-curve is represented by the equation 



cot X sin 2 <j!> cotL sin (6 I) = cos<^> cos(0 I) (15.) 



The beautiful experiment of Mr BARLOW, which renders it highly pro- 

 bable that the phenomena of terrestrial magnetism result from thermo-elec- 

 tric causes, confers great philosophical interest upon this equation. The 

 resemblance of the lines along which the compass was carried in that expe- 

 riment to obtain a variation of L degrees, to the lines of equal variation 

 furnished by the observations of HALLEY, and his successors in the inquiry, 

 suggested that if we could assign this hypothetic path, in the form of an equa- 

 tion referred to our common geographical co-ordinates, we should greatly fa- 

 cilitate such comparisons as may be made between the phenomena and the 

 results of any presumed law of physical action by which that direction was 

 given to the needle. Independently, too, of this purpose, we should be 

 able, by means of that equation, to compare these hypothetical curves with the 

 curves furnished by observation, and thus (the general resemblance being ad- 

 mitted) find what deviations from these upon the surface of the earth, arising 

 from disturbing causes, or from " local attractions," But this is irrelevant. 

 The character of these curves is best obtained from equation (10.), and 

 we proceed to examine it. 



Let sin 6 = . . 6 = mr, and sin = sin a 

 . . 6 = 0, or 6 = TT, and < + a, or = a : 



