106 Rev. Mr Scoresby on the Unifdim Permeability of 



Fig. 4. 



Fig^ 5 



L«t M, Fig. 4, be a magnet, of which F is the focal point, 

 aad C a compass at the distance of at least four focal lengths. 

 Let 71 5 be the position of the needle under the influence of ter- 

 restrial magnetism only, and v! s' the position which it assumes 

 under the action of the magnet. Then the action of the nearest 

 pole F is represented by the sum of the squares of the distances 

 F y and F n' inversely, which does not, in this instance, mate- 

 rially differ from the sum of the squares of the distances F s and 

 F« inversely. 



But in the case represented in Fig. 5. the result is far other- 

 wise. Here the bar M, placed at the distance of one focal 

 length, occasions such a great deviation of the needle that a 

 very considerable increase of action on the pole / is gainej^, be- 

 yond the diminution of action sustained by the pole n', — the 

 increase of force being in the proportion in which the sum 

 of the reciprocals of the squares of the distances F s* and F n\ 

 expressed fractionally, exceeds the sum of the reciprocals of 

 the squares of the mean distances F .9 and F ti *. 



• The sum of these direct squares must in all cases be equal. For F sn 

 being a triangle which is bisected in the point C by a line FC drawn to the 

 apex, the sum of the squares of F s and F n, is equal to twice the squares of 

 FC and C s. In the triangle F s* n% for the same reason, the sum of the 

 squares F sf and F n', is equal to twice the squares of FC and C«'. But the 

 lines sn andVn', representing the same needle revolving]on a centre, are equal, 



and 



