184 On tin Resistanct of Telegraphic Electromagnets. 



This increases with z\ therefore let -=?/, the inner radius of 

 the coil : let x be constant and?/ variable ; then A is a maxi- 

 mum when 



f! + If + 3 l ^'+^/ 

 / 2/ 27n/ 2 m a?— y 



is a minimum ; and that is when 



i-(>-5) 



2m7T 9 



— ar — 



3p ('-!)(■-!-.) 



The least value of - is 

 x 



X I 



4 

 Using the former value of p, viz. 1700 x — , also m = 807r and 



x=2 centimetres, then 



- == •? nearly. 



increases very slowly as x and m increase. 



v 

 In this determination of -, the outer radius has been sup- 



x 



posed to be constant, and the inner variable, and with it the 

 iron core. If, on the other hand, the inner radius is fixed and 

 the outer variable, a different ratio is obtained, viz. 



I 

 %nir o X 



x — 



X 



* C-I)('-5)' 



which gives lower values to - than before. 



x 



It also appears from (14) that the attractive force varies 

 inversely as the length of the coil. Though the formulas are 

 only true for long coils, yet it points in the direction of short, 

 flat coils; for the attractive force is also increased by increasing 

 the transverse dimensions of the coil, 



8. In paragraph 5 we found L x =173 and M = 5 approxi- 

 mately for iron wires of a certain size, distance apart, and 



