METHOD OF OSCILLATIONS. 389 



We shall mention here the principal experimental methods used, 

 in order to define their theoretical meaning. 



414. Oscillations. This method, which was used by Coulomb, 

 consists in making a very small horizontal needle oscillate in front 

 of several points of a bar placed vertically in the meridian plane of 

 the needle. If n and N are the number of oscillations made by the 

 needle under the sole action of the earth, and under the combined 

 action of the earth and of the bar, the action of the bar on the 

 needle (the magnetism of which is supposed unchanged) is propor- 

 tional to the difference N 2 - 2 of the squares of the two numbers. 

 We measure thus the perpendicular component of the magnetic 

 force at the point in question. Coulomb assumed that this perpen- 

 dicular component was proportional to the density of the superficial 

 fictive layer at the nearest point of the needle, except quite close to 

 the end ; in this case he determined the density either by a graphical 

 method, or by doubling the value obtained for the oscillations of 

 the needle. It cannot be concealed that this mode of correction 

 is somewhat arbitrary ; it is, moreover, quite inexact, as we shall 

 afterwards see (419) that the perpendicular component at a point 

 is proportional to the density of the corresponding fictive layer, and 

 that it may directly give the distribution of magnetism. 



415. Torsion Balance. A second method, also due to Coulomb, 

 consists in measuring the repulsion exerted by every point of the 

 magnet, at a constant and very small distance, on the pole of a long 

 needle movable in a plane perpendicular to the axis of the bar. If 

 we regard the pole of the needle as unchanged, the torsion imparted 

 to the wire by which it is suspended to keep the needle in the desired 

 position, measures the perpendicular component of the magnetic 

 force with a certain degree of approximation. 



416. Use of Soft Iron. In the two preceding cases it is 

 assumed that the magnetism of the auxiliary magnet is invariable, so 

 that the action which it experiences is simply proportional to the 

 strength of the field. If the oscillating needle is of soft iron, and 

 the magnetisation of this needle is proportional to the strength of 

 the field, the action which it undergoes will be proportional to the 

 square of the perpendicular component. 



We may, in like manner, place a piece of soft iron (M. Jamin's 

 test nail} in different parts of the magnet, and determine the force 

 necessary to detach it ; this force of tearing away is still within 

 certain limits proportional to the square of the normal component. 



In these two methods, however, we do not take into consideration 

 either the variation of the coefficient k with the strength of the 



