A Treatise on Electricity and Magnetism/Errata

by James Clerk Maxwell

Layout 2

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,

$\int _{\beta _{0}}^{\beta _{1}}(X{\frac {dx}{d\beta }})_{a=a_{0}}\ d\beta$,

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,

$-\int _{a_{0}}^{a_{1}}(X{\frac {dx}{da}})\ _{\mathrm {\beta =\beta _{1}} }\ da$ + $\int _{a_{0}}^{a_{1}}(X{\frac {dx}{da}})\ _{\mathrm {\beta =\beta _{0}} }\ da$,

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 $({\frac {d^{2}V'}{dxdv}})$

p. 83,„ 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 $\rho '$.

p. 108,„ equation„ (2), for $\rho '$ read $\rho$.

p. 108,„ equation„ (3), for $\sigma$, read $\sigma '$.

p. 108,„ equation„ (4), for $\sigma '$ read $\sigma$.

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

p. 113,„ 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. p. 159, l. 3, for $F$ read $f$.

p. 159,„ l. 2 from bottom, for $M$ read $M_{2}$.

p. 163, l. 20, for $\lambda _{i-s+1}$ read $\lambda _{i-\sigma +1}$.

p. 164, equation (34), for $(-1)^{i-s}{\frac {\left|{\underline {2s}}\right.}{2^{2}s\left|{\underline {i}}\right.\left|{\underline {s}}\right.}}$ read $(-1)^{i-\sigma }{\frac {\left|{\underline {2\sigma }}\right.}{2^{2}\sigma \left|{\underline {i}}\right.\left|{\underline {\sigma }}\right.}}$

p. 179, equation (76), for $i+l$ read $2i+1$.

p. 185, equation (24), for ${\frac {x^{2}}{b^{2}}}-{\frac {z^{2}}{c^{2}}}=1$ read ${\frac {x^{2}}{b^{2}}}-{\frac {z^{2}}{c^{2}-b^{2}}}=1$.

p. 186, l. 5 from bottom, for 'The surface-density on the elliptic plate' read The surface-density on either side of the elliptic plate.

p. 186, equation (30), for $2\pi$ read $4\pi$.

p. 188, equation (38), for $\pi ^{2}$ read $2\pi ^{2}$.

p. 196, l. 27, for $e..e$ read $e_{1}..e_{2}$.

p. 197, equation (10) should be $M={\frac {E\,e}{f}}-{\frac {1}{2}}{\frac {e^{2}a^{3}}{f^{2}(f^{2}-a^{2})}}$.

p. 204, l. 15 from bottom, dele either.

p. 215, l. 4, for ${\sqrt {2k}}$ read ${\sqrt {2}}k$.

p. 234, equation (13), for $2E$ read ${\frac {E}{2\pi }}$.

p. 335, dele last 14 lines.

p. 336, l. 1, dele therefore.

p. 336,„ l. 2, for 'the potential at $C$ to exceed that at $D$ by $P$,' read a current, $C$, from $X$ to $Y$.

p. 336,„ l. 4, for '$C$ to $D$ will cause the potential at $A$ to exceed that at $B$ by the same quantity $P$,' read $X$ to $Y$ will cause an equal current $C$ from $A$ to $B$.

p. 351, l. 3, for $R_{1}^{2}u^{2}+R_{2}^{2}v^{2}+R_{3}^{2}w^{2}$ read $R_{1}u^{2}+R_{2}v^{2}+R_{3}w^{2}$.

p. 351,„ l. 5, read $+2\iiint (u{\frac {dV}{dx}}+v{\frac {dV}{dy}}+w{\frac {dV}{dz}})\,dx\,dy\,dz$.

p. 355, last line, for $S'$ read $S$.

p. 356, equation (12), for ${\overline {\left.{\frac {db}{d}}\right|}}^{2}$ read ${\overline {\left.{\frac {db}{dx}}\right|}}^{2}$.

p. 365, in equations (12), (15), (16), for $A$ read $Ar$.

p. 366, equation (3), for ${\frac {E_{2}}{r_{1}}}$ read ${\frac {E_{2}}{r_{2}}}$.

p. 367, l. 5, for $2k_{1}S$ read $2k_{2}S$.

p. 368, equation (14), for $J_{2}^{'}$ read $I_{2}^{'}$.

p. 397, l. 1, for ${\frac {D'}{E}}\delta '$ read ${\frac {D'}{E'}}\delta '$.

p. 404, at the end of Art. 350 insert as follows:—

When $\gamma$, the resistance to be measured, $a$, the resistance of the battery, and $\alpha$, the resistance of the galvanometer, are given, the best values of the other resistances have been shewn by Mr. Oliver Heaviside (Phil. Mag., Feb. 1873) to be

$c={\sqrt {a\alpha }},\quad b={\sqrt {a\gamma {\frac {\alpha +\gamma }{a+\gamma }}}},\quad \beta ={\sqrt {\alpha \gamma {\frac {a+\gamma }{\alpha +\gamma }}}}$.

 

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