Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/389

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300.]
COEFFICIENTS OF CONDUCTIVITY.
347
(8)
(9)
(10)


By a proper choice of axes, either of the two latter equations may be deprived of the terms involving the products of or of The system of axes, however, which reduces to the form



is not in general the same as that which reduces it to the form



It is only when the coefficients are equal respectively to that the two systems of axes coincide.

If with Thomson[1] we write

and (11)


then we have


(12)
and (13)


If therefore we cause to disappear, will not also disappear unless the coefficients are zero.

Condition of Stability.

300.] Since the equilibrium of electricity is stable, the work spent in maintaining the current must always be positive. The conditions that must be positive are that the three coefficients and the three expressions


(14)


must all be positive.

There are similar conditions for the coefficients of conductivity.

  1. Trans. R. S. Edin., 1853-4, p. 165.