Determinations of Magnetic Susceptibility. 



435 



Similarly, 



and hence Ra'rrrQra', say (2), 



therefore R (a + a') = Pm + Qm', 



«= J (« + -') (3). 



Also, I=— (4), 



and hence, in the case of thin wires 



"=^ # < 5 >- 



The equation (2) gives ns a means of ascertaining the value of m', 

 if we know that of a, as in the case of 7 or 8, Table I. In the case 

 where a was not directly obtained by observation, m' was calculated 

 from the following formula, 



m f =cxA (6), 



where A is the area contained by all the turns of coil per unit length, 

 and c is the current strength in the coil. In the case of a cylindrical 

 coil, 



in which n is the number of turns of wire per unit length of the coil, 

 Jc the mean radius of the coil, p the number of layers, and b the mean 

 distance between any two adjacent layers. 



As to the evaluation of the magnetising force F. Let Jc be the mean 

 radius of the cylindrical coil, or what is equivalent to it if the coil 

 be not cylindrical ; then the magnetising force at a point in the axis 

 of the coil at a distance d from the centre, l\ c, and n retaining the 

 same signification as before, is, 



At the centre of the coil, if V be very great compared with Jc, 



¥=4<7rnc (8). 



Now it will be observed, as the equation (7) will show, that in my 



* Papers on " Electricity and Magnetism," Sir William Thomson, p. 472 ; or 

 Maxwell's " Electricity and Magnetism," yol. ii, p 68. 



VOL. XXXV. 2 G 



