ON THE PHENOMENA OF TERRESTRIAL MAGNETISM. 75 
variations shown by observation fall between the limits assigned 
by the consideration of each axis taken separately. There are 
two exceptions to this rule, which are in Java, and from Mex¬ 
ico to the Isthmus of Panama. But these apparent anomalies 
are also capable of being explained, and disappear when a cor¬ 
rection is introduced, which M. Hansteen points out in Euler’s 
investigation, which in certain cases slightly affects the calcula¬ 
tions here made in strict accordance with Euler’s formulae; and 
when the true magnetic poles are substituted in the calculation 
for the points of convergence, which have hitherto been consider¬ 
ed as coincident with them. 
In concluding this chapter, M. Hansteen remarks, that as the 
curves of variation computed on the hypothesis of two magnetic 
axes either represent well the actual phenomena, or assign the 
limits within which the observations are found to fall,—and as 
four magnetic poles sufficiently explain the double flexure of the 
lines of dip,—and as the alterations of variation and dip are fully 
explained by the motions above described of the four poles,—and 
as, lastly, the phenomena of the intensity indicate a double mag ¬ 
netic axis,—we may consider this hypothesis to be as well esta¬ 
blished, as a means of representing the phenomena, as any hypo¬ 
thesis whatsoever introduced in physical illustration. 
Chapter fifth is entitled <e On the Theory of Magnets.” Hav¬ 
ing shown that when two magnetic points act on each other, 
their mutual action, whether of attraction or repulsion, is the 
product of the absolute magnetic force of the two points into some 
function of their distance apart, M. Hansteen proceeds to inves¬ 
tigate the elementary laws which regulate the action of a linear 
magnet upon a magnetic point situated, first, in the prolongation 
of its axis; second, in the perpendicular passing through its cen¬ 
tre, or its equator. The action depends in both cases, first, on 
the distance of the point from the centre of the magnet; second, 
(and particularly if the distance be inconsiderable in proportion 
to the length of the magnet,) on the distribution of the magnetic 
intensity in the magnet itself. These, therefore, form the sub¬ 
ject of two elementary laws, deduced from experiments, which 
consist in drawing a small compass-needle from its line of repose 
in the magnetic meridian by a linear magnet, placed horizontally, 
at different distances in succession, from four to twelve times the 
half axis of the magnet, in a line through the centre of the needle 
perpendicular to the magnetic meridian, and in noting the dis¬ 
placements occasioned thereby in the direction of the compass- 
needle. The displacements so occasioned are then compared 
with computed expressions, in which the influence of the mag¬ 
net is considered to vary inversely, first, as the distance itself; 
