ON THE PHENOMENA OF TERRESTRIAL MAGNETISM. 85 
4° 20' N. and S. latitude, and in 14° and 194° E. longitude. Cal¬ 
culated from the hypothetical elements above stated, they should 
be in 3° 55 N. and S. latitude, and in 6° 56' and in 186° 56' E. 
longitude. The differences 0° 25 ' of latitude and 7° 4' of lon¬ 
gitude show that the errors of the elements of calculation are 
not very great even on the first approximation. We may here 
perceive the particular value which would attach to careful ob¬ 
servations in the line of no dip in the vicinity of these two 
geographical positions ; in the means afforded of correcting the 
situation of the poles of the magnetic equators. 
M. Hansteen next proceeds to deduce more correctly the si¬ 
tuation of the terminations of the magnetic chords, and to sub¬ 
stitute these for the points of convergence hitherto employed 
instead of them. To explain this, let E B F A (fig. 4.) be a section 
of the earth in the plane of the first magnetic meridian, having an 
infinitely small magnet in y, of which C y measures the eccentri¬ 
city ; A B is the prolongation of the magnetic axis or the mag¬ 
netic chord ; a b a diameter parallel to it; and r F points where 
the magnetic line of repose is perpendicular to the surface, or 
where the dip is 90°. If the earth had but one magnetic axis, 
and that eccentric, the two points of the dip 90° would fall in 
the first magnetic meridian, each between the termination of 
the magnetic chord and the pericentric point F. Now it may 
easily be shown that when the eccentricity is sufficiently small 
to admit of the sine of the arc being taken for the arc itself, 
B b = A a = \ h r = J a F ; or that the distance of the points 
where the dip is 90° from the poles of the magnetic equator is 
equal to three times the eccentricity. If now we imagine the ar¬ 
rows to represent the directions of the needle freely suspended, 
and further imagine the arrows to be brought down to a hori¬ 
zontal direction, as in the case of the compass needle by weight¬ 
ing the upper end, all the arrows between h and r will point in 
the direction b r, and all those between r and F in the direction 
F r ; and in like manner the arrows between F and F will point 
(though with the other end) in the direction F F, and those be¬ 
tween F and a in the direction a F ; consequently the points of 
dip 90° (or r F) will be also the points of convergence of the 
horizontal needle : and the arc a which measures the distance 
between the poles of the magnetic chord and the poles of the 
magnetic equator should be the arc b B or a A, and not the arc 
b r or a F, which have been hitherto used for a. 
On the supposition of a single magnetic axis then the proper 
value of & could be easily derivedfrom the value hitherto employed, 
of which it would be just one third. But the points of conver¬ 
gence obtained in the third chapter were not the points due to 
