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PROCEEDINGS OF THE NATIONAL ACADEMY QF SCIENCES Volume 1 I FEBRUARY 15, 1925 Number 2 CONDITIONS OF ELECTRIC EQUILIBRIUM AT BOUNDARY SURFACES; VOLTA EFFECT By EDWIN H. HALL JICFFRSON PHYSICAL LABORATORY, HARvARD UNIVERSITY Read before the Academy November 10, 1924 (but since revised) I shall here discuss more fully than I have done before the meaning and implication of two equations appearing in a paper which I published several years ago under the title Thermoelectric Action with Dual Conduction of Electricity.' These equations are (1) dP + dPaO, and (2) ne(dP + dPf)= -dp, and they were intended to express the conditions of electric equilibrium, no flow, at the junction of two metals, a and j3, at the same temperature. The differential form is explained by the fact that, for the purpose of discussion, I imagined the two metals to be joined by an "alloy bridge" varying in composition from pure metal a at one end to pure metal ,B at the other end; the equations were supposed to hold for any point on this bridge. The symbols in these equations require some explanation. P means electric potential in the ordinary sense, except as to the sign, which for all of the P's is so taken that an electron tends to move down the potential gradient. Thus e, the electron charge, is treated in my formulas as a positive quantity, so that any product eP will have the sign of the P factor. P, according to my view of the matter, is due to what is called a surface charge on the metals, that is, an excess or deficiency of electrons for each metal as. a whole compared with the number of positive ions for each metal as a whole. I am merely following unquestioned custom, based on Paraday's experiments, in assuming that any excess or deficiency of either kind of electricity shows as a surface charge, having no effect on the interior state of the metal except to raise or l