ON THE PILENOMKNA OF TERRESTRIAL MAGNETISM. 
dicularly on the weaker axis a b, and prolonged, would meet the 
surface in about 217° E.; this point would be the nearest to, and 
a point 180° from it, or about 37° E., near the east coast of Africa, 
would be the most distant from, the middle of the axis ab } and 
consequently about 37° E. would be the minimum of intensity 
if ah were the only axis. Hence it follows that the point of 
minimum intensity in the line of no dip resulting from both axes, 
must be somewhere in Africa between the two points of 17° E. 
and 37° E. From this point, then, we may imagine a curve to 
commence, passing northward through Europe, and southward 
through Africa, and cutting every line of dip at its point of mini¬ 
mum intensity. This curve, prolonged through all the lines of 
dip, would at length pass into the points where the dip is 90°, 
where the character of the curve would change from the curve of 
minimum to the curve of maximum intensity in the several lines 
of dip, which it would successively intersect till it again reached 
the geographical equator at some intermediate point between the 
meridians of 197° E. and 217° E., which are the points of greatest 
intensity of the two axes respectively, on the line of no dip. 
At the date of publication of M. Hansteen’s work there ex¬ 
isted very few observations of the intensity with which to com¬ 
pare the system of intensities here presented. Those which did 
exist were, however, conformable to it. The intensities under 
equal dips diminished from the west side of America (beyond 
which, on the side of the Pacific, no observations had been 
made,) to the coasts of Europe and Africa ; where the existence 
of a minimum must be supposed, since, in proceeding still further 
to the eastward, the force was again found to increase, under dips 
of the same amount. 
In the fourth chapter, M. Hansteen passes under examination 
Euler’s investigation of the mathematical theory of the lines of 
variation due to a single magnetic axis under various assumed 
conditions. Of these, the fifth case discussed by Euler is, when 
the poles of the axis are in different meridians, and at different 
distances from the poles of the earth. This case meets precisely 
the present conditions of both the axes in M. Hansteen’s hypo¬ 
thesis. Having premised Euler’s formulae in this case, he em¬ 
ploys them in calculating successively the lines of variation cor¬ 
responding to each of the axes A B and a b , in the positions they 
are supposed to have occupied in the year 1739. These lines 
are delineated on maps of both hemispheres, exhibiting separately 
the variation corresponding to each axis. These maps are then 
compared with the map showing the actual phaenomena in the 
year 1773 ; and the result of the comparison maybe summed up 
as follows : 1st, The variation computed from the axis A B agrees 
