386 PROFESSOR KNOTT ON SOME RELATIONS BETWEEN 



beyond the power of direct experiment to investigate the real reciprocal phenomena con- 

 nected with what has been called in this paper the Wiedemann effect. 



Some of the weaknesses of Professor Wiedemann's own theory of frictionally restrained 

 or rotating molecules as applied to these phenomena, have been very effectively exposed 

 by Mr Bid well.* There are, besides, several objections of a general character which 

 might be urged. For example, the theory is incapable of predicting phenomena. 

 Maxwell's explanation, however, taken in conjunction with Bakrett's discovery of the 

 shortening of nickel, at once suggested that the Wiedemann effect in nickel was opposite to 

 that in iron ; and so I found it to be. Again, the shortening of iron in high fields at once 

 suggested that in such fields iron should twist the other way ; in other words, behave like 

 nickel in all fields ; and this Mr Bidwell found to be the case. Arguing from Mr Bidwell's 

 recent work, we may expect to find that the Wiedemann effect in cobalt is in low fields 

 as in nickel, but becomes reversed in high fields. In fact, if we call that twist positive 

 which is shown by iron in low and moderate fields, we may state the relations of the 

 Wiedemann effect in the three magnetic metals thus : in iron it is positive in low fields and 

 negative in high ; in cobalt, it is probably negative in low fields and positive in high ; in 

 nickel, it is always negative. 



Then, again, it is impossible to apply to Wiedemann's theory any numerical test, 



whereas, as I now proceed to show, Maxwell's explanation enables us to institute a 



numerical comparison between the Joule and the Wiedemann effects. We know by 



experiment that both phenomena exist ; and that, whether the latter is to be explained 



in terms of the former or not, they must at any rate coexist in the form of experiment 



more particularly under discussion. Let us then consider the distribution of stress and 



strain in a cylindrical tube which, as a whole, is subjected to the three strains — uniform 



elongation in the direction of its length, uniform expansion in directions at right angles 



thereto, and a simple twist about the axis of the cylinder. Let this axis be the z axis, 



and let the twist 6 be taken right-handedly with reference to it. The x and y axes 



will then lie in a section of the cylinder. If 73 is the elongation in the direction of the 



cylinder, and <r the elongation in any direction perpendicular thereto, we may express 



the displacements £, 77, £ of a point originally at x, y, z (z very small) by means of the 



following formulas: — 



£= — 6yz+o-x\ 



r)=+6xz+a-yY (1) 



From these we get, in the usual way, 



dx dz dy 



dy dx dz y 



dz dy dx 



* Phil. Mag., September 1886. 



