Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/412

370 of conductivity, Art. 298. If we put $$D$$ for the determinant of the coefficients of resistance, we find

Similar equations with the symbols accented give the values of $$ u',\, v'$$ and $$z'.$$ Having found $$ \overline{u},\, \overline{v} $$ and $$\overline{w}$$ in terms of $$ \overline{X},\, \overline{Y} $$ and $$ \overline{Z}, $$ we may write down the equations of conductivity of the stratified conductor. If we make $$ h = \frac $$ and $$ h' = \frac,$$ we find

320.] If neither of the two substances of which the strata are formed has the rotatory property of Art. 303, the value of any $$P$$ or $$p$$ will be equal to that of its corresponding $$Q$$ or $$q.$$ From this it follows that in the stratified conductor also or there is no rotatory property developed by stratification, unless it exists in the materials.

321.] If we now suppose that there is no rotatory property, and also that the axes of $$x,\, y$$ and $$z$$ are the principal axes, then the $$p$$ and $$q$$ coefficients vanish, and