4 The Rev. H. Lioyp on the Determination of the Intensity 
Two methods have been proposed for this second observation, one by Poisson, 
and the other by Gauss. The method of Poisson consisted in observing the 
time of vibration of the second magnet, under the combined action of the first and 
of the earth, the acting magnet having its axis in the magnetic meridian passing 
through the centre of the suspended magnet. In the method of Gauss, which is 
now universally adopted, we observe the position of equilibrium of the second 
magnet, resulting from the action of the same forces. The acting magnet being 
placed transversely with respect to the suspended one, the latter is deflected from 
the meridian, and the amount of this deflection serves to determine the ratio of 
the deflecting force to the earth’s force. The position chosen by Gauss for the 
deflecting magnet is that in which its axis is in the right line passing through 
the centre of the suspended magnet, and perpendicular to the magnetic meri- 
dian, in which case the tangent of the angle of deflection is equal to the ratio 
of-the two forces. From this ratio it remains to deduce that of the magnetic 
moment of the deflecting bar to the earth’s force. 
The difficulty of this process arises from the form of the expression of the 
force of the deflecting bar. This force being expressed by a series descending 
according to the negative odd powers of the distance, with unknown coefficients, 
it is evident that observation must furnish as many equations of condition, cor- 
responding to different distances, as there are terms of sensible magnitude in the 
series; and from these equations the unknown quantities are to be deduced by 
elimination. Now, the greater the number of unknown quantities thus elimi- 
nated, the greater will be the influence of the errors of observation on the final 
result; and if, on the other hand, the distance between the magnets be taken 
so great, that all the terms of the series after the first may be insensible, the 
angle of deflection becomes very small, and the errors in its observed value bear 
a large proportion to the whole. 
It fortunately happens, that at moderate distances (distances not less than 
four times the length of the magnets) all the terms beyond the second may be 
neglected. The expression for the tangent of the angle of deflection is thus re- 
duced to two terms, one of which contains the inverse cube of the distance, and 
the other the inverse fifth power ; that is, if « denote the angle of deflection, 
and p the distance, 
Q 
tan u = Soingee 
