Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/37

Rh Page 26, l. 3 from bottom, dele 'As we have made no assumption', &c. down to l. 7 of p. 27, 'the expression may then be written', and substitute as follows:—

Let us now suppose that the curves for which $$a$$ is constant form a series of closed curves surrounding the point on the surface for which $$a$$ has its minimum value, $$a_0$$, the last curve of the series, for which $$a = a_1$$, coinciding with the original closed curve s.

Let us also suppose that the curves for which $$\beta$$ is constant form a series of lines drawn from the point at which $$a = a_0$$ to the closed curve s, the first $$\beta_0$$, and the last, $$\beta_1$$, being identical

Integrating (8) by parts the first term with respect to a and the second with respect to $$\beta$$, the double integrals destroy each other. The line integral,

is zero, because the curve $$a = a_0$$, is reduced to a point at which there is but one value of $$X$$ and of $$x$$.

The two line integrals,

destroy each other, because the point $$(a, \beta_1)$$ is identical with the point $$(a, \beta_0)$$.

The expressions (8) is therefore reduced to

Since the curve $$a = a_1$$ is identical with the closed curve s, we may write this expression

p. 80, in equations (3), (4), (6), (e), (17), (18), (19), (20), (21), (22), for $$R$$ read $$N1$$.

p. 82, l. 3, for $$Rl$$ read $$N1$$.

p. 83, in equations (28), (29), (30). (31), for $$(\frac{d^2 V_1}{dx^3})$$ read $$(\frac{d^2 V'}{dx dv})$$

in equation (29), insert - before the second member.

p. 105, 1. 2, for $$Q$$ read $$8 \pi Q$$.

p. 108, equation (1), for $$\rho$$ read $$\rho'$$.

(2), for $$\rho '$$ read $$\rho$$.

(3), for $$\sigma$$, read $$\sigma'$$.

(4), for $$\sigma'$$ read $$\sigma$$.

p. 113, l. 4, for $$KR$$ read $$\frac{1}{4\pi}KR$$.

l. 5, for $$KRR' cos \epsilon$$ read $$\frac{1}{4\pi} KRR' cos \epsilon$$.

p. 111, I. 5, for $$S_1$$ read $$S$$.

p. 124, last line, for $$e_1 + e_1$$ read $$e_1 + e_2$$.

p. 125, lines 3 and 4, transpose within and without; l. 16, for $$v$$ read $$V$$; and l. 18, for $$V$$ read $$v$$.

p. 128, lines 11, 10, 8 from bottom for $$dx$$ read $$dz$$.

p. 149, l. 24, for equpotential read equipotential.