220 Proceedings of the Royal Society of Edinburgh. [Sess. 
and may of course vary in sign from metal to metal, but R and S will both 
have the same sign in the same piece of metal. This is quite in accordance 
with experiment. 
In the case of the coefficient Q, it will be seen that a diversity of sign 
can only occur if x x and x 2 have opposite signs, which is not a very likely 
proposition. In any case, there would be no reason to expect any close 
relation between the sign of Q and the sign of R. Experiment shows, 
however, that these coefficients have in general, though not always, the 
same sign. 
R 
Again, in order to account for the fact that the ratio -g has nearly 
the same value for all metals, it must be supposed that one group of 
carriers is of small importance compared with the other. 
It would seem, therefore, that the difference in the signs of the 
transverse effects in different metals must be referred to some cause 
other than the participation of positive as well as of negative carriers 
in the transmission of the current. 
Sir Joseph Thomson * has suggested that the reversal of the Hall 
effect in iron may be due to the fact that the magnetic field close to a 
molecule is in the opposite direction from the magnetic field in the free 
space between molecules. The Hall effect would thus be a differential 
effect, and the reversed sign would be easily accounted for. 
A. W. Smith f has put this to the test of experiment by measuring 
the Hall effect in iron at various temperatures up to 1000° C. No 
reversal of the sign of the Hall effect was observed, although iron loses 
its magnetic properties at a temperature considerably below 1000° C. A 
simple inspection of the values of the Hall effect for different metals 
is sufficient to show that there is no direct relation between the sign 
of the Hall effect and the magnetic properties of the metal, for the 
effect is positive in both iron and zinc, while it is negative in both 
nickel and copper. 
Nevertheless, a differential action such as Thomson has suggested would 
carry us far towards an explanation of the experimental results, if it could 
be supposed to occur in all metals whether magnetic or not. Such a 
differential action would apply with equal force to all the transverse 
effects, and would thus account for the experimental relation between 
R and S. The fact that the relation between Q and R is not so simple 
is not difficult to understand, for in the case of the thermomagnetic effect 
the temperature gradient in the plate sets up a potential gradient along 
* Corpuscular Theory of Matter. 
t Phys. Rev., Jan. 1910. 
