﻿06 Prof. R. Threlfall on an Approximate Method 



Corollary (1). Tlie magnetic forces are independent of the 

 stresses in aether inside the iron. 



Corollary (2). Setting aside Professor J. J. Thomson's 

 stresses, the sether stress in air is less than that in iron — 

 assuming that Maxwell's " magnetic material " sufficiently 

 represents iron. The difference of tensions is 



This is an unbalanced stress ; and if the lines of induction 

 in the iron give rise to forces similar to those produced in 

 air, this must mean that the boundary tends to be pulled off 

 the iron. Taking Professor Thomson's stresses into account, 

 this effect may easily be reversed in any actual case. 



Referring to Professor Thomson's investigation (Physics 

 and Chemistry), I cannot avoid the impression that there still 

 remains a set of stresses depending on the variation of elastic 

 constants with temperature. This would further complicate 

 matters. 



§ 13. Each tube of induction is therefore a tube of force 

 within the usual definition ; but it does not follow that the 

 only forces are those represented by the tubes of induction. 

 If the tubes leave the iron surface normally, then the pressural 

 forces are tangential and we get the formula we have been 

 using ; and similarly if the tubes of induction are tangential 

 (i. e. when the infinitesimal air-gap separates similar poles), 

 the pressures operate alone, and w 7 e have a repulsion equal to 

 the former attraction as in the elementary theory. If the 

 tubes of induction leave the iron at any angle to the surface 

 between and 7r/2, we must consider the effect of the pressural 

 forces. 



To calculate these effects it is convenient and perhaps 

 correct to assume that just as the internal stresses of the iron 

 do not affect the forces which are the expression of the external 

 aether tensions, so they do not affect the forces corresponding 

 to the hydrostatic pressures. If, therefore, we consider a line 

 of force running out of iron into air and making an angle 

 with the normal, we can estimate the direction and magnitude 

 of the magnetic forces at once, thus : — 



Let AB be the trace of a plane boundary between air and 

 iron, and ON a normal drawn outwards into air. Let OP be 

 a vector in the plane of the paper representing the tensional 



