CONCERNING TERRESTRIAL MAGNETISM. 



223 



The nature of this paper does not allow of much numerical experiment upon the 

 observation-data ; but still, in illustration of the method of determining the position 

 of the magnetic axis, I have entered into a little. The results are not very favourable 

 to the hypothesis ; but when it is considered that the observations were selected almost 

 at hazard, all made with different instruments, by various persons, and in geological 

 regions extremely dissimilar, we could hardly, in the confessedly imperfect state of the 

 art of observation, expect to obtain satisfactory results. Taking all things into 

 account, the results are, unfavourable though they be, as satisfactory as we could 

 expect. However, whatever conclusion may be drawn from them, they furnish at 

 least a pattern for calculating any better and more consistent observations we may at 

 any future time be able to procure ; and if any that are beyond question can be ob- 

 tained, it will enable us to bring the linearity of the magnetic axis to an indisputable 

 test. The duality, should the linearity be established, can be at once put to the test 

 by means of the process in Section III. 



Now that this method of investigation is proposed, it will doubtless occur to some 

 of my readers that a more direct course would have been to assume the undetermined 

 coordinates a^ b^ c^, a,, b^ c,,, of the two poles, and express the equation of the sphere in 

 reference to the same axes, and hence the directive effect of the two poles upon a 

 needle placed at a point xy z on the spherical surface. Such a method, they will 

 believe, must also have occurred to me as the most natural ; but if they will take 

 the trouble to form the equations of condition that this method will require, they will 

 see the utter impracticability of effecting the reductions under the mere motive of 

 making an experiment upon the results of an hypothesis when no confidence was felt 

 in the numerical data which entered into the formula. The reason for adopting the 

 less direct, but incomparably more simple, preliminary test illustrated by Sections XI. 

 and XII. will then be suflicientlv obvious. 



I. — Given the dip and variation of the magnetic needle and the geographical coordi- 

 nates of the place of observation, to find the geographical coordinates of the 

 place where the needle, sufficiently prolonged, will intersect the surface of the 

 earth again. 



We assume, for reasons too well known to need spe- 

 cification here, that the orthogonal projection of the dip- 

 ping-needle upon the horizontal plane gives the position 

 of the horizontal needle ; or, which comes to the same, 

 that the dipping-needle and the horizontal needle are in 

 the same vertical plane. This plane cuts the sphere in 

 a great circle, which we shall for the present suppose to 

 coincide with the plane of the paper, and to be repre- 

 sented in the annexed figure by C K B. Let E C be the 



