MAGNETISM 



which represent them. The angles of 

 these triangles, the dip being one of 

 these angles, may be determined by the 

 trigonometrical relations of these lines 

 when two of them are given. All that 

 is required for this purpose is to ascer- 

 tain the ratio of the forces which act in 

 directions parallel to these lines, and are 

 proportional to them. Of the methods 

 by which the intensity of these forces is 

 to be measured, we shall proceed to treat 

 in the next section. 



6. Methods of determining the inten- 

 sities of the Magnetic Forces. 



(317.) When a magnetic needle is 

 moveable in any plane on an axis that 

 passes through its centre of gravity, so 

 that its movements are simply the ef- 

 fects of the magnetic forces of the earth 

 acting upon the two polarities of the 

 needle (which may be considered as 

 concentrated in its poles), it takes a 

 certain position, which is that in which 

 the forces are in equilibrium. Let 

 needle SN, fig. 70, for example, be 

 moveable on an axis at X, perpendi- 

 cular to the plane of the figure ; and let 

 Fig. 70. ; 



\ 



NE be the direction in that plane of 

 the force of terrestrial magnetism acting 

 upon the pole N ; while S e, opposite 

 and parallel to NE, is the direction of 

 the force in the same plane, acting upon 

 the pole S. The position to which the 

 needle is brought by these forces is s n, 

 parallel to the common direction of 

 these forces, when they are in direct 

 opposition to each other, and therefore 

 in equilibrium. In order to estimate 

 the rotatory efficiency of the forces in ope- 



ration in any "other position, as SN,we 

 must resolve the force represented by the 

 line NE into two others ; the one, N x, 

 in the direction of the radius of rotation 

 XN, prolonged ; and the other in the 

 direction NR, perpendicular to it. The 

 force N x, being opposed by the fixed 

 axis at X, contributes in no respect to 

 produce motion ; NR is the only part 

 of the terrestrial force that turns the 

 needle upon its axis. Now it is evi- 

 dent that NR is to NE, as the sine of 

 the angle NER, or its equal EN#, to 

 the radius; but the force represented 

 by the line NE being a constant force, 

 the rotatory force NR will, in every po- 

 sition of the needle, be invariably as the 

 sine of the angle EN#, made by the 

 needle, on its prolonged direction, with 

 the direction of the terrestrial force. 

 The same reasoning, in all respects, ap- 

 plies to the force S e acting on the pole 

 S ; but since it acts on the other side 

 of the axis in a contrary direction, it 

 will concur with the force acting on 

 the pole N, in giving the same rotatory 

 motion to the needle. The effect will, 

 therefore, be equal to the sum of these 

 two rotatory forces, and will be twice 

 as great as either of them taken sepa- 

 rately; and the resultant will still be 

 proportional to the sine of the angle of 

 inclination. 



(318.) A little consideration will en- 

 able us to perceive that the condition of 

 the needle, with regard to the magnetic 

 forces, is analogous to that of a lever 

 moveable on a horizontal axis, and 

 acted upon by the force of gravity. If 

 we suppose a straight lever, AB, fig. 

 7 1 , moveable upon an axis X, at right 

 angles to it, to be raised from the ver- 

 tical position a b, which is that of equi- 

 librium, inasmuch as gravitation acts in 

 Fig. 71. 



A <- 



