654 PROCEEDINGS OF THE AJMERICAN ACADEMY. 



Of the two, the Moreau formula seems to us the more likely to be 

 useful, as suggestive of true relations which it does not perfectly 

 express. The value of s<, which we need to know in order to use this 

 formula, we do know or can find. It is a definite property of iron and 

 of iron alone. But the value of Voigt's ©/, as we have shown, is merely 

 a property of iron with relation to lead. Now we know that the lead 

 line cannot be regarded as the real boundary of the thermo-electric 

 diagram. The lines for certain metals lie beyond it, below it in the 

 ordinary diagram, to the left of it in such a diagram as that of Figure 11. 

 These metals have a negative thermo-electric height, a negative thermo- 

 electric entropy, as regards lead. Reckoning thermo-electric heights 

 fi-om lead, taking lead as having zero thermo-electric entropy, is quite 

 as arbitrary as taking the freezing point of water for the zero of temper- 

 ature. We may do injustice here ; it is possible that we have not seen 

 the exact meaning of Voigt's 0'. 



However useful the formula of Moreau may be, his thesis that the 

 Hall effect and all the transverse effects associated with it are due to 

 some deformation of the metal plate in the magnetic field appears to be 

 incompetent to explain the observed facts, especially the Ettingshausen 

 effect, and, if taken alone, misleading rather than helpful. It is alto- 

 gether probable that the electron theory must be used, if aU the 

 phenomena observed are to be accounted for. 



The Longitudinal Effects. 



All of the transverse effects just considered change direction with 

 change of direction of the magnetic field, the sign of the coefiicient in 

 each case remaining unchanged. The associated longitudinal effects, 

 which are now to be described, remain, as the argument from symmetry 

 would predict, unchanged in direction with change of direction of the 

 field. One might, from this absence of dependence on the sign of the 

 field magnetism, expect the longitudinal effects to be proportional to 

 the square of the field-strength, and this may be true of some of these 

 effects in some metals, but in general it appears not to be true. The 

 fact seems to be, however, that the longitudinal effects are much less 

 simple functions of field-strength than the transverse effects are and 

 sometimes change direction with change of intensity of the field. 

 Whether they are strictly or very nearly proportional to the longitudinal 

 gradients of potential and temperature respectively, our own experiments 

 do not enable us to say. We shall, however, assume this proportion- 

 ality and shall accordingly define a certain coefficient for each of the 

 two longitudinal effects which we have found in iron. For the sake of 



