CAPACITY FOR HEAT OF METALS AT LOW TEMPERATURES. 339 
For iron, cadmium, and sodium, which Nernst has not investigated, the mean values 
obtained by Dewar over the range from liquid nitrogen to liquid hydrogen have 
been utilized for the purpose of extending the curves to low temperatures. 
Whilst Dewar’s method is of great use for obtaining comparative values, especially 
of organic substances and poor heat conductors, it cannot, when applied to metals, 
claim to be capable of giving absolute values with the same precision as the electrical 
methods, and it is noticeable that Dewar used a mass of only 1 gr. of lead as 
compared with 400 gr. by Nernst and 2200 gr. in the investigation recorded in this 
paper. 
Moreover it should be remembered that, where the curvature is marked, the 
mean value over a range may depart appreciably from the real value at the mid 
point; and, for this reason also, values obtained by an electrical method are to be 
preferred. 
Dewar’s Mean Values at 50° C. Absolute. 
. 
Fe, 0-98 
Cel, 3 • 46 
Na, 3’50 
(10) Discussion of the Results. 
The question of the variation of atomic heat with temperature has recently received 
a considerable amount of attention, chiefly on account of its bearing on Planck’s 
“ quantum ” theory. 
The theoretical formulae are concerned with C„ (the atomic heat at constant 
volume), while the quantity experimentally investigated is C ? , the atomic heat when 
the solid is free to expand with temperature. 
It is necessary to know the values of the compressibility and expansion coefficients, 
in order to apply the well-known thermodynamical relation 
O p —C v = a 2 evt . (5) 
where a is the coefficient of cubical expansion, e is the coefficient of volumetric 
elasticity, v is the reciprocal of the density, and t the absolute temperature. 
The values of e* obtained by Richards have been assumed, but, on account of 
lack of data, we have been compelled to disregard the variation of the compressibilities 
with temperature. 
The coefficient of expansion of metals decreases with temperature, as shown by the 
work of Fizeau, Dorsey,! Ayres, | and others. 
* ‘ Journ. Chem. Soc.,’ 1911. 
t ‘ Phy. Rev.,’ vol. xxv., p. 97, 1907. 
| ‘ Phy. Rev.,’ vol. xx., p. 38, 1905. 
2x2 
