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

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1

ERRATA, VOL. I.

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,

$\int_{\beta_0}^{\beta_1}( X\frac{dx}{d\beta} )_{a = a_0}\ d\beta$ ,

in 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,

$-\int_{a_0}^{a_1}(X\frac{dx}{da})\ _\mathrm{\beta = \beta_1}\ da$ + $\int_{a_0}^{a_1}(X\frac{dx}{da})\ _\mathrm{\beta = \beta_0}\ da$ ,

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

The expressions (8) is therefore reduced to

$\int_{\beta_0}^{\beta_1}(X\frac{dx}{d\beta})\ _\mathrm{a = a_1}\ d\beta$

(9)

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.