CONCERNING TERRESTRIAL MAGNETISM. 
105 
and only two, points on the earth's surface, at which the needle can take a position ver- 
tical to the horizon. 
Whether this be the number actually existing on the surface of our earth, we are 
not at present in a condition to determine. One such undoubtedly there is, and a 
second is probable, but its position has not been assigned ; neither from any obser- 
vations yet published, can it be even approximately determined, nor, therefore, its 
existence positively affirmed. I am not aware that any observations give reason to 
suspect the existence of more than these two ; and hence, so far as we can judge from 
the data before us, the conclusion now obtained as a consequence of two magnetic 
centres of force, is consistent with the phenomena for which the hypothesis is required 
to account. It is therefore a strong argument, in the present state of our actual know- 
ledge of the phenomena of teirestrial magnetism, for the truth of that hypothesis. 
XXXIII. — No particular specification of the cases which can arise from the relative 
positions of the centre of the earth, and the coordinates of the centres of force, is here 
necessary ; as, except in the case of the magnetic axis passing through the centre of 
the earth, no considerable simplification of the equation, nor, therefore, any essential 
variation in the form of the curve of verticity, so far as I have remarked, can arise. 
When O is in the line y M y l (fig. 18 .) the branches are symmetrical, it is true, and the 
form rather more simple than when it is in any other position ; and as we remove O 
to points further on either side from that line, the curve becomes more and more 
bizarre, but still it retains the same general features as in its more simple case ; and 
its branches have in all cases the same character, whatever be the coordinates of O 
with respect to the magnetic poles, and not situated in the same line with them. 
If, moreover, we have determined two points on the surface of the earth at which 
the needle can become vertical, and describe the great circle passing through them, 
we know that the poles themselves are in this plane, and situated somewhere in the 
concave angle formed by drawing the radii from those points to the centre. As, how- 
ever, four quantities are necessary to express the coordinates of those poles, and we 
have only two conditions given, the actual position of the points themselves cannot 
be determined from these data. The problem is hence, even when both points of ver- 
ticity are known, still left indeterminate. Nevertheless, by combining these with other 
observations upon the dip and variation made at different, and still better at distant, 
places, the problem becomes capable of solution. 
Again, if we could determine the points on the earth’s surface at which the intensity 
is a maximum (in respect to its contiguous points, in all directions from it), we should 
obtain other conditions, which united with those of the two points of verticity, from 
which the positions of the magnetic poles might be determined. To the solution of 
this problem, the determination of maximum-intensity points, I shall next direct the 
attention of the Royal Society. The investigations are already completed, and I hope 
shortly to find leisure to put them into order ; and shall only premise here, that as 
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