102 
MR. BARLOW ON THE PROBABLE ELECTRIC ORIGIN 
phenomena which M. Humboldt observed, and which MM. Biot and Kraft 
reduced to determinate laws of action * ; the two poles in this case, as in that, 
being indefinitely near to each other, and to the centre of the sphere. Hence 
then it follows, 
1 . That the laws of terrestrial magnetism are inconsistent with those which 
belong to a permanent magnetic body. 
2. That they are perfectly coincident with those which appertain to a body 
in a transient state of magnetic induction. 
These results were incontrovertible ; but an insuperable obstacle seemed 
still to oppose itself to any rational hypothesis relative to the cause of the 
earth’s magnetic power. Up to this period we knew of only one means of in- 
ducing magnetism, which was by the approximation of a permanent magnet to 
a ball or mass of simple iron, and one or two other metals : but what body 
could be imagined capable of inducing this power in the earth ; particularly as 
the earth preserved its magnetic energy constantly in nearly the same direction, 
whereas its position with regard to any exterior body was hourly changing ? 
Its magnetism could not therefore be induced by any foreign body; and as no 
* The formula indicating the position of a magnetic needle freely suspended from the combined 
action of the earth and an iron sphere upon it, is 
tan A = 
3 cos <p . sm q> 
<PM 
r 3 C 
+ 3 cos s <p — 1 
where A is the deflection from the axis of the sphere, <p the complement of the magnetic latitude, 
M the magnetic power of the earth, r the radius of the iron sphere, d the distance of the needle from 
its centre, and C a constant coefficient dependent on the magnetic power of the iron. In this expres- 
sion making M vanish according to the above supposition, and substituting <p + S' for A, so that S' 
becomes the complement of the dip, we have 
tan (<p + S') — 
3 cos i p sin <p 
3 cos 2 <p — 1 
which after an easy reduction becomes 
2 tan S' = tan <p, or tan S = 2 tan A 
where S is the dip, and A the magnetic latitude. By a similar process, calling I and I' the intensity of 
the dipping and horizontal needle, we find 
I = 2 A 4—3 sin* S an< l I' = 2 A y 3 _|_ sec 2 S 
which are precisely M. Biot’s formula;. — See Essay on Magnetic Attractions, page 195. 
