29G 



not be overcome by due care in observing, we shall confine 

 our attention, in the present communication, to the latter. 



Two methods have been proposed for this second obser- 

 vation, one by Poisson, and the other by Gauss. The me- 

 thod of Poisson consisted in observing the thne 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 sus- 

 pended 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 deter- 

 mine 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 meridian, 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 co- 

 efficients, it is evident that observation must furnish as 

 many equations of condition, corresponding 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 num- 

 ber of unknown quantities thus eliminated, the greater will 

 be the influence of the errors of observation on the final re- 

 sult; and if, on the other hand, the distance between the 

 magnets be taken so great, that all the terms of the series 



