212 ELECTROMOTIVE FORCE. chap.
Tammann, Heycock and Neville {10\ and others. The metals examined were found to be monatomic.
Helmholtz's Concentration Element. — In his theo- retical deductions (1877) Helmholtz {11) considered a combination consisting of two copper sulphate solutions of different concentrations, which were in contact, and into each of which was immersed a copper electrode. For the sake of simplicity, let us imagine that the difiference of concentrations of the two solutions is infinitesimally small, so that the €oncentration of one may be represented by C, and that of the other by C + dC, Let the Hittorf transport number for copper be m, then that for SO4 will be (1 — w) ; and, further, let the potential difference between the two electrodes be d V. If we pass through the combination —
dilute .> concentrated
Cu Cu I CUSO4 I CUSO4 CUSO4 I Cu,
2 X 96,500 coulombs (because a mol of CUSO4 corresponds with two gram-equivalents) in the direction indicated by the arrow, the concentration will then be represented by the following scheme : —
��On I PiiSO ^^ " ^) ^^
��"^^ CUSO4 I Cu Cu. mS04 '
��In the direction of the current (from left to right) vi gram-ions of copper have passed through the surface of separation of the two solutions, and (1 — m) gram-ions of SO4 have passed through in the opposite direction. A gram- ion of copper has dissolved from the left electrode, fuid this same quantity heis been deposited on the right electrode. This latter change is connected with no expenditure of work, for it consists simply in moving 63'6 grams of copper in a horizontal plane (if the copper electrodes were not at the same height, the work, which appears in the so-called gravita- tion elements, might be neglected, provided the diiference in the heights is not great).
The principal change consists in moving (1 — w)
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