CHAP, ii.] ELECTRICITY AND MAGNETISM. 101 



12 times a minute, we know that the force will be pro- 

 portional to I2 2 3 2 = 144 9= 135. So we shall find 

 that as the force falls off the oscillations will be fewer, 

 until, when we put the oscillating magnet opposite the 

 middle of the vertical magnet, we shall find that the 

 number of oscillations is 3 per minute, or that the 

 earth's force is the only force affecting the oscillations. 

 In Fig. 57 we have indicated the number of oscillations 

 at successive points, as 14, 12, 10, 8, 6, 5, 4, and 3. 

 If we square these numbers and subtract 9 from each, 

 we shall get for the forces at the various points the 

 following: 187, 135, .91, 55, 27, 16, 7, and o. These 

 forces may be taken to represent the strength of the 

 free magnetism at the various points, and it is convenient 

 to plot them out graphically in the manner shown in 



\ 





Fig, 57- 



Fig. 57) where the heights of the dotted lines are chosen 

 to a scale to represent proportionally the forces. The 

 curve which joins the tops of these " ordinates " shows 

 graphically how the force, which is greatest at the end, 

 falls off toward the middle. On a distant magnet pole 

 these forces, thus represented by this curvilinear triangle, 

 would act as if concentrated at a point in the magnet 





