CONCERNING TERRESTRIAL MAGNETISM. 235 



discrepancies were such as to admit of account from the errors of observation and 

 the imperfection of instruments. However, it is much simpler to ascertain whether 

 the axis thus determined agrees with the observation made at a fifth or a sixth place. 

 Let us take the Parisian needle as an instance. 



By recurring to equation (36.), and putting the values o^ ah and a |3 just deter- 

 mined and those of a7 b^ and a^ |3^ found in the table of section XI. for Paris, we have 

 the least distance between the Parisian needle and the magnetic axis either •173341 r 

 or '189540 r, according as the + or — sign above mentioned is employed. 



These are between a fifth and a sixth part of the terrestrial radius. We may now, 

 were it necessary, seek the coordinates of the points in which the line of shortest 

 distance intersects the two different magnetic axes and the Paris needle, and thence 

 the equations of the lines drawn from those points to Paris, and thence again the 

 angle formed by the Paris needle, and each of the other lines : that is, we should find 

 the error of observation in the Paris needle if we suppose the magnetic axis correctly 

 determined from the other four needles. But it is unnecessary to go through the 

 computations, as it is easy to see that this angle will not be very different from (but its 



difference, whatever it be, will be greater than it,) tan"" '173341, and tan"^ '189540, 

 that is, about 10° or 11°. The discrepancies in every other case that I have tried are 

 as great as, and in most of them still greater than, in that just examined. The further 

 prosecution of this branch of the inquiry, with our present data, must therefore be 

 abandoned. 



XIII. — So far as method is concerned, the previous processes are perfectly adapted 

 to decide the question of the duality and the equality of intensity of the magnetic 

 poles. In the absence, however, of data upon which full reliance can be placed, we 

 are not at present able to apply that method to the actual circumstances of the earth. 

 It hence becomes desirable to examine certain other phenomena, to ascertain whether, 

 in their general bearings and character, they also are compatible with the hypothesis 

 of two such centres of force. These are : — the^points at which the needle becomes ho- 

 rizontal, constituting the magnetic equator ; the points at which the needle becomes 

 vertical ; the curves of equal dip ; the Halleyan lines, or curves of equal variation ; 

 the lines of equal magnetic intensity, or isodynamic lines of Hansteen ; and those 

 particular cases where the isodynamic line is reduced to a point, which constitutes 

 the "pole" in the language of Hansteen and a considerable number of modem writers. 

 The first two of these I shall examine in the present, and the remaining ones in a 

 subsequent paper. I then propose to enter into a minute numerical discussion of 

 such observations as I may be able to obtain in the interim ; and of course attempt 

 to ascertain how far any one may be vitiated by instrumental or local circumstances, 

 and how far the geometrical peculiarity of the observation itself may render it unfit 

 for our present method of investigation. 



I do not propose this course without being fully sensible of the difficulty and 

 labour it entails upon me ; but at the same time I feel perfectly assured that any 



2 H 2 



