:N8 professor KNOTT on some relations between 



have to solve equation (3), putting for p its proper value for the maximum radius ; in 

 this case 1w v Then if is the required angle, we get 



tane=-^= 6 -y—=+ f ^ . . . (5). 



And now let us make the assumption, plausible enough and certainly the simplest that 

 can be made in the circumstances, that this direction of maximum elongation coincides 

 with the direction of the resultant magnetising force, as it may be assumed to exist in the 

 experiments which give the Wiedemann effect. It will be remembered that we are 

 applying the calculation to a cylindrical tube, although so far as the problem is an 

 "elasticity" one there is no necessity for such a limitation. By so confining our attention 

 to a thin- walled tube, we are able to regard the equation £, = zsz as a sufficiently near 

 approximation to what might reasonably be expected to hold good if the experiment 

 giving the Wiedemann effect were made with a tube instead of a wire, the tube being 

 under the influence of an axial current and of a uniform longitudinal field. The magnetic 

 distribution in an iron or nickel wire due to a current passing along it is something of 

 which we know absolutely nothing, so that to make a calculation based upon an assumed 

 expression for £ involving x and y in some simple manageable way, would probably ill 

 repay the extra labour. 



Eeturning then to the equation (5), let us take a and ft as the circularly and longi- 

 tudinally magnetising forces. Then, assuming that the maximum elongation ts 1 takes 

 place in the direction of the resultant magnetising force, we may put tan 6 = a/ ft, and 

 hence by a simple reduction, 



6y a/3 



2(sr 1 -cr 1 )~a2+/3 2, 



Here y is the radius of the tube. Writing it r, we obtain finally.* 



6 r oM--^ (6) ' 



that is, the twist 0, which measures the Wiedemann effect, is given in terms of the 

 magnetising forces a, /3, the radius of the tube r, and the Joule elongation zf v together 

 with cr 1; the accompanying elongation at right angles to vj v Of o^ we have no direct 

 measurement. Joule, however, found that iron longitudinally magnetised did not change 

 appreciably in volume. This would make o^ = — &J2 for the moderate magnetising 

 forces with which Joule worked. 



In comparing this formula with results of experiments as obtained till now, we must 

 remember that in the experiment we are dealing with a wire circularly magnetised 

 throughout its interior in a complicated and altogether unknown manner ; whereas in the 

 expression just given we are dealing with a thin-walled tube. Nevertheless, it is easy 

 to see that the formula does to a certain extent apply even to the wire. Thus the twist 



* This expression differs from the one given in my earlier paper (p. 198). That, however, was incompletely worked 

 out with a too early assumption of the law connecting the elongation with the magnetising force. 



