98 Rev. Mr Scoresby on the Uniform Permeability of 



When the bar is placed in the prescribed position, with the 

 north pole at the distance of 07ie length from the compass, then 

 the action of the south pole, tending to counteract that of the 

 north, will be in the inverse relation with the nearest pole of 2* 

 to 1^ That is, if the force of the nearest pole be called 1, then 

 the force of the remote pole will be inversely as 4 or -jth, which 

 being in the contrary direction to that of the nearest pole, re- 

 duces its action to ^ths. In like manner, at two lengths of the 

 bar, the force of the nearest pole being now inversely as the 

 square of 9> or jth is reduced by the remote pole at three lengths 

 distance, the action of which is inversely as the square of 3 or 

 i-th ; hence \ — i = 36» representing the actual influence or 

 general resultant of the whole of the magnetic forces in the 

 magnet acting upon the compass. 



But we may obtain a general expression for all distances, 

 either in lengths or fractions of lengths of the bar. 



Let F be the influence of the nearer pole at the distance a. 



Then will -—r represent the influence at the distance a:, and 

 Fa* 



i , the counteracting influence of the remote pole at the dis- 

 tance X + \' 



Hence the resultant influence is, 



As the force F, however, being the separate action of a pole 

 not practicably separable, is not a quantity that can be imme- 

 diately ascertained by experiment, this expression requires to 

 be extended so as to connect it with the value of the assumed 

 force : — 



Let R be the resultant influence of a magnet on the compass 

 at distance a, and, in the first instance, let a be equal to x. 



Then B = Fa'-f==. = F--^ 



«* . o + 1 a + 1 



Therefore F =: R ^±J_: Hence, 



2 a + 1 



F a* ^"'^ ^ = R fli±i! ^^_+ V 



*'.*+ 1' 2a+ 1 ' X* .x-k-V 



