416 Scientific Proceedings, Royal Dublin Society. 



experiment, using tubes which more nearly correspond to the ideal cylindrical 

 shell, such as the tubing used in the frames of bicycles. 



This paper gives an account of an extended investigation into the 

 "Wiedemann effect, using such a steel tube 5 - 94 mm. mean radius, - 87 mm. in 

 thickness, and 95'1 cm. in length. The first problem which presented itself 

 was the measurement of the twist which would be produced in such a tube 

 under the available magnetic fields. We may state at once that it has been 

 found possible to measure a twist of the order of one second of arc, and to 

 investigate the Wiedemann effect over a sufficiently wide range of magnetic 

 fields to demonstrate a simple relation to the Joule effect indicated by 

 mathematical theory. 



The Twist of a Steel Tube in Spiral Magnetic Field. 



Theory of the Wiedemann effect. — We shall first consider the theory of 

 the effect, as this explains the special experimental conditions which have 

 to be complied with. Consider a thin cylindrical magnetic shell whose axis 

 coincides with the axis of z drawn downwards. Let S be a spiral magnetic 

 field whose axis coincides with the axis of z. This field produces a strain 

 consisting of &n elongation j t along the lines of force, and a contraction ej normal 

 to the lines of force. This elementary strain produces a twist of the cylindrical 

 shell (0) and an elongation along its length. Applying the usual transformation 

 of axes of the theory of elasticity, we obtain finally 



6 = (fi+Es) sin2o l/r. 



This equation has been given by Knott' in his investigation of the 

 Wiedemann effect in steel and nickel wires with a slightly different notation. 

 Here I = length of the tube, r = its mean radius, fi the elongation per unit 

 length parallel to the resultant field S, e 3 the transverse contraction per unit 

 length. The resultant field S acting on the tube is a spiral made up of the 

 longitudinal field H and the circular field F, where the pitch-angle a is given 

 by the equation tan « = H/F. The mathematical theory requires us to keep 

 S constant while varying H/F. Under these conditions 



6 oo sin2a. 



The observations given below show a satisfactory concordance with this 

 relation. 



Hysteresis effects. — As is well known, magnetic hysteresis presents great 

 difficulties in the examination of this phenomenon. We have not only to 



1 Knott, Trans. Roy. Soc, Edin,, vol. xxxv, p. 388. 



