Vol. 6, 1920 
PHYSICS: E. H. HALL 
143 
(13) 
(14) 
I shall, moreover, assuming that the total heat of ionization per elec- 
tron is made up of a part X'o, due to the overcoming of atomic attraction, 
a part 1.5RT for the kinetic energy gained, and a part RT for the pv 
potential energy gained, write 
X' = X^^ + 2.5RT = + 2.5i?(273 + t). (11) 
Keeping to hypothesis (A), and so using equation (8) for a, I get by 
substitution according to eqs. (9), (10) and (11), 
a = K -h {K, + K4)T, (12) 
where K, Ki and K2 are constants,^ defined by the equations 
K =^[c(1.5-g)+G(^^-273(L5-g)) 
— 273C2(^?^- 273(1.5 -g))] 
K, = :?[g(4 -q)-\- .cl^^ - 273(1.5 - g))] 
i^2= - .C2(6.5 — g). (15) 
e 
I have put a into the form shown by equation (12) in order to make 
my expression for it correspond as nearly as may be to that used by Bridg- 
man to set forth the results of his experiments. He writes, in substance, 
a = {A -\- Bt)T, (16) 
where A and B are constants, the latter being zero in many metals. 
Bridgman finds nothing corresponding to my constant K, and I have 
spent much labor in attempting to get rid of this constant; but no reason- 
able assumption that I can make eliminates it from my general expression 
for a. On the other hand, equation (13) shows that K is the sum of many 
terms, some positive, some negative, and there is nothing to show that it 
may not be very small, too small to appear in such experiments as those 
of Bridgman. Accordingly, in dealing with his observations I put K, and 
so the second member of (13), equal to zero. This gives me an equation 
of which I make frequent use in the form 
C= \—C 
-273(1.5-^)) + 273g(?^° -273(1.5 -g))] 
{1.5 -q). (17) 
As to the A and B of equation (16), I take these to be, respectively, 
the Ki and the K2 of my equations, and, as Bridgman gives the value of 
A and B for every case dealt with, I have the K, Ki and K2, of equations 
(13), (14) and (15), replaced by definite numerical terms. 
These three equations now contain the five unknowns, C-, Ci, C2, X'o, 
and q. Accordingly, I must assume values for two of these quantities 
in order to evaluate the other three. As a rule, I have assumed values of 
