ON THE PH ENOMENA OF TERRESTRIAL MAGNETISM. 8 
H) 
19. cot o = 
20 . D = D 
M F.cos I 
M'T“ cos I. sin (D 
— o. 
+ cot (D 
The 7th chapter is occupied in an endeavour to assign more ex¬ 
actly the situation of the magnetic poles, the length of the mag¬ 
netic axes, and their relative force in M. Hansteen’s hypothesis. 
Reverting to the four points of convergence found in the 3rd 
chapter, M. Hansteen shows that they are not identical with 
the situations of the ends of the magnetic chords. They would 
be so if the three following conditions were fulfilled, viz. 1 st, 
If the earth had but one magnetic axis 5 2 nd, If the horizontal 
needle were always in the magnetic meridian ; 3rd, If the mag¬ 
netic meridians were all great circles. Unless these three con¬ 
ditions are fulfilled, the points of convergence must differ more 
or less from those points where the magnetic axis prolonged 
meets the earth’s surface. 
In the case of a single eccentric magnetic axis, the point of 
convergence belonging to each pole will fall in the first meridian 
between the extremity of the prolonged axis and the pericentric 
point. In the case of two such axes, the points of convergence 
will differ still more from the extremities of the chords : and the 
amount of difference will depend on the positions and propor¬ 
tionate forces of the axes. If the points of convergence are 
derived from observations made in the vicinity of the poles of 
the stronger axis, the deduction of the geographical situation of 
the magnetic chord may be made with the less uncertainty, be¬ 
cause the intensity of that pole will predominate considerably 
over the influence of the weaker axis 5 but that axis will still 
have a sensible disturbing influence if, as is probable, the length 
of the ^ axis of the magnet is less than half that of the earth’s 
radius. 
M. Hansteen here remarks that the study of the pluenomena 
thus far has placed beyond question their entire inconsistency 
with a single magnetic axis ; that it has further manifested their 
general accordance with such an arrangement of the lines of dip, 
variation, and intensity as would follow on an hypothesis of two 
magnetic axes ; but it has given as yet no precise knowledge 
of any of the particulars of these axes except their number. 
Their exact situation, their length, and other dimensions, as 
well as the proportion of their forces, yet remain to be de¬ 
duced. Their length is determinable were their situation and 
relative force exactly known. Their relative force would be 
deducible did we know their position and their length. But 
the preliminary determination of their situation is by no means 
easy to be accomplished. There are no less than eleven imper- 
