ioo ELEMENTARY LESSONS ON [CHAP. n. 



two places will be to one another in the ratio of <z 2 

 to a. 



Again, we may use the method to compare the force 

 exerted at any point by a magnet near it with the force 

 of the earth's magnetism at that point. For, if we swing 

 a small magnetic needle there, and find that it makes m 

 oscillations a minute under the joint action l of the earth's 

 magnetism, and that of the neighbouring magnet, and 

 that, when the magnet is removed, it makes n oscillations 

 a minute under the influence of the earth's magnetism 

 alone, then m* will be proportional to the joint forces, 

 H* to the force due to the earth's magnetism, and the 

 difference of these, or nP ril will be proportional to the 

 force due to the neighbouring magnet. 



122. We will now apply the method of oscillations to 

 measure the relative quantities of free magnetism at 

 different points along a bar magnet. The magnet to 

 be examined is set up vertically (Fig. 56). A small 

 magnet, capable of swinging horizontally, is brought near 

 it and set at a short distance away 

 from its extremity, and then oscillated, 

 while the rate of its oscillations is 

 counted. Suppose the needle were 

 such that, when exposed to the earth's 

 6 magnetism alone, it would perform 3 



complete oscillations a minute, and 

 3."~"~H that, when vibrating at its place near 



the end of the vertical magnet it 

 oscillated 14 times a minute, then 

 the force due to the magnet will be 

 proportional to I4 2 3 2 = 196 9 = 

 187. Nextly, let the oscillating mag- 

 net be brought to an equal distance 

 opposite a point a little away from 

 the end of the vertical magnet. If, here, it oscillated 



1 We are here assuming that the magnet is so placed that its force is in a 

 line with that of the earth's magnetism at the point, and that the other pole 

 of the magnet is so far away as not to affect the oscillating needle. 



Sp 



