- The
**logarithmic**formulae for these concentration cells indicate that theoretically their electromotive force can be increased to any extent by diminishing without limit the concentration of the more dilute solution, log c i /c 2 then becoming very great. - The results give equations of the same
**logarithmic**form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment. - On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar
**logarithmic**expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself. - A volume entitled Opera posthuma (Leiden, 1703) contained his "Dioptrica," in which the ratio between the respective focal lengths of object-glass and eye-glass is given as the measure of magnifying power, together with the shorter essays De vitris figurandis, De corona et parheliis, &c. An early tract De ratiociniis tin ludo aleae, printed in 16J7 with Schooten's Exercitationes mathematicae, is notable as one of the first formal treatises on the theory of probabilities; nor should his investigations of the properties of the cissoid,
**logarithmic**and catenary curves be left unnoticed. - When, by practice with logarithms, we become familiar with the correspondence between additions of length on the
**logarithmic**scale (on a slide-rule) and multiplication of numbers in the natural scale (including fractional numbers), A /5 acquires a definite meaning as the number corresponding to the extremity of a length x, on the**logarithmic**scale, such that 5 corresponds to the extremity of 2X.

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