248 MR J. C. BEATTIE ON THE 



is present to such an extent that in the end it gives its sign to the total transverse 

 effect. 



This second effect is not to be confounded with the thermo-magnetic effect observed 

 by Ettingshausen and Nernst : the latter is evidently proportional to ( A nf and 

 positive in sign. 



The anomalous behaviour of the transverse effect in bismuth — which is hidden, if the 

 effect be represented in terms of the rotatory co-efficient R — has also been observed by 

 Ettingshausen and Nernst.* They found that in a specimen of pure bismuth, E 

 obtained a maximum value, — that is, both effects may appear in pure bismuth. Again, 

 Ettingshausen t has shown that, in an alloy of tin and bismuth, the transverse effect 

 changes sign. At high fields, when little tin is present : at lower, when more tin is added 

 until when the alloy contains 6 % tin, 94 °/ o bismuth, the positive sign alone is present. 

 The explanation lies in the presence of this second effect, which increases relatively to 

 the pure Hall effect as the proportion of tin to bismuth increases. 



It is interesting to note that the relation between transverse effect and resistance 

 variation holds, no matter what the percentage increase of resistance is, or how much the 

 transverse effects expressed in terms of R vary in the different plates. 



So far, the transverse effect has only been observed when the electrodes are at the 

 middle points of the sides. A number of experiments were next made with these 

 electrodes at different parts, while still kept opposite each other. In Plate Ia. the 

 numerical value of the transverse effect was found to have a maximum value with the 

 electrodes in the middle ; for other positions it was less. The greater the distance from 

 the middle points, the greater was the decrease. Next, the same plate was cut along the 

 middle line for about half its length. The electrodes were fixed at a b, c d, e f, 

 respectively, fig. 2, and the effect was found to be greatest at a b, less at e^and c d. 

 Finally, another slit was made along the middle line, and the electrodes were placed at 

 /'and g, fig. 3. The effect was qualitatively the same, but quantitatively less. 



The question to settle now is, Whether this decrease is due to a decrease in the pure 



Hall effect ? in the second effect ? or in both ? If we take the ratio for any one plate, 



n 



we get a number which may be looked on as characteristic of that plate ; it is 



independent of its dimensions, and depends only on its properties. If these are the 



same throughout — which we assume to be the case — and if we neglect the slight 



disturbances due to the fact that the temperature is not absolutely constant throughout 



the experiments, this number may be used to divide the transverse effect into its two 



constituents, and to give the relative values of these for any one plate, no matter how it 



is modified in size or shape. That is, we now apply the equation 



o(4-? + <ir>-± E • • < 3 >- 



* tiitz. bericht der hods. Akad. der JFissenschaft, Wien, 1886. 

 t Sitz. bericht der kais. Akad., Wien, 1887. 



