100 
PHYSICS: E. H. HALL 
Proc. N. A. S. 
Thus for two metals, a and /?, with twelve characteristic quantities to 
be determined, I have ten equations given by the properties of the metals, 
each metal being considered separately. When the two metals are brought 
into contact at 0° C. and again at 100° C, I have two Peltier-effect equa- 
tions of the form 
(i0> (6) 
one for each temperature, where X^ is the heat, in ergs, required to free 
(1 -r e) electrons within /?, and X a has a like meaning for a. 
Thus I have twelve equations to determine the twelve constants in 
question. 
If my theory were perfect and my experimental data complete, every 
constant could be found exactly, or to any desired degree of precision, by 
means of the equations here mentioned; but neither of these conditions is 
fulfilled. It is unlikely, for example, that equation (1) holds strictly 
through any considerable range of temperature. The experimental 
data I have used are doubtless incorrect to some extent, and in several 
places I have had to fill observational gaps by rather hazardous methods, 
particularly in values of thermal conductivity. Somewhat arbitrarily 
I have chosen to treat Bridgman's values of <j as strictly correct, though 
he does not so regard them. I have done the same with regard to the 
available values of k 0 , ki 0 », B 0 , and n Q . Accordingly the values of 0i O o 
and IIioo worked out from my equations are subject to the accumulated 
errors of theory and data, and it is not very disconcerting to find them 
differing considerably in some cases from the observed values or those indi- 
cated by other evidence. 
If the question is raised why values of the constants cannot be found 
that will satisfy all of the equations, even if some of the data are inaccurate, 
the answer is that not all values are available for these constants, thus 
C, q, \ c , and s must all be positive quantities. 
Below are given for each of many metals, and for two alloys, the values 
of the six constants that I have hit on to account, as well as may be, for 
the observed or estimated values of the Thomson effect, thermal con- 
ductivity, and Peltier effect with respect to bismuth, in these substances. 
It is to be remembered that the algebraic sign which I give to the Thomson 
effect in any metal is opposite to the one ordinarily used; for example, I 
call a positive in iron and negative in copper. The Peltier effect, II, 
is given as the amount of heat, in ergs, absorbed by (1 -5- e) electrons in 
going from the metal in question to bismuth. Thermal conductivities 
are given in calories/cm., sec, deg. C. The constant part, X c , of X' 
is given in ergs; 8 C is the "ionizing potential," in volts, corresponding to 
X c ; d Q and 5i 0 o> respectively, are the ionizing potentials, in volts, for the 
total work of ionization at 0° C. and at 100° C; k is electric conductivity 
in absolute measure. The numbers in the horizontal lines marked Calc. 
