PHYSICS: E. H. HALL 29 
straints. The optical properties of most substances show their electrons to 
be held rather rigidly, but many of the properties of metals, and especially 
of metals pronouncedly electro-positive in character, indicate a high degree 
of electronic freedom. 
It is therefore our belief that in the metals under consideration the differ- 
ence between the heat capacity observed and that calculated from the regular 
curve, which fits the experimental curve at low temperatures, may be re- 
garded as representing the actual heat capacity of their more loosely bound 
electrons. Whether these electrons are 'free' in the sense that each electron 
occupies a position symmetrical with respect to two or more atoms, or whether 
they remain attached to individual atoms, we should expect them to add to 
the heat capacity of the substance, provided that they are held by sufficiently 
weak constraints. 
We have thus an entirely new method of investigating the freedom of elec- 
trons in a metal, and it is to be hoped that when further quantitative data are 
available a comparison of the results obtained by this method with those 
obtained through a study of the photo-electric effect, or the Volta effect, will 
prove of interest. 
1 Lewis, /. Amer. Chem. Soc, Easton, Pa. 29, 1907, (1165); Zs. anorg. Chem., Hamburg, 
55, 1907, (200). 
2 Lewis and Adams, Physic. Rev., Ithaca, N. Y ., (Ser. 2), 4, 1914, (331). 
3 Langmuir, /. Amer. Chem. Soc, Easton, Pa., 38, 1916, (2236), calls attention to the 
possibility that the atom in a solid may not be vibrating in simple harmonic motion and 
hence that the potential energy may not be equal to the kinetic energy, as has been assumed. 
However, if this were the case the potential energy would in all probability be less than the 
kinetic energy and not greater. 
4 Dewar, London, Proc. R. Soc, A, 89, 158, 1913, (158). 
5 Nernst and Schwers, Berlin Sitz. Ber. Ak. Wiss., 1914, (1), (255). 
6 See Lewis and Gibson, J. Amer. Chem. Soc, Easton, Pa., 39, 1917, (2554). 
7 The four highest points of Nernst and Schwers have been omitted since they appear to 
us to be erroneous. 
THERMO-ELECTRIC DIAGRAMS ON THE P-V-PLANE 
By Edwin H. Hall 
Jefferson Physical Laboratory, Harvard University 
Read before the Academy, November 21, 1917 
About thirteen years ago I made an ill-directed and unfortunate attempt 
to analyze the electromotive force of a thermoelectric circuit, that is, to iden- 
tify and explain the local e.m.fs which, taken together, give the e.m.f. of 
the circuit as a whole. I am now making a new attempt. I know that my 
present effort is more intelligently directed than the former one, and hope 
that it will prove to be more fortunate; but I do not claim for it finality. 
