Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/157

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472.]

subterranean or celestial?.

125

V=A_{1}{\frac {r}{a}}+\mathrm {\&c.} +A_{i}\left({\frac {r}{a}}\right)^{i},{}+B_{1}\left({\frac {r}{a}}\right)^{-2}+\mathrm {\&c.} +B_{i}\left({\frac {r}{a}}\right)^{-(i+1)}

.

The first series represents the part of the potential due to causes exterior to the earth, and the second series represents the part due to causes within the earth.

The observations of horizontal force give us the sum of these series when $r=a$ , the radius of the earth. The term of the order $i$ is

V_{i}=A_{i}+B_{i}

.

The observations of vertical force give us

Z={\frac {dV}{dr}}

,

and the term of the order $i$ in $aZ$ is

aZ_{i}=iA_{i}-(i+1)B_{i}

.

Hence the part due to external causes is

A_{i}={\frac {(i+1)V_{i}+aZ_{i}}{2i+1}}

,

and the part due to causes within the earth is

B_{i}={\frac {iV_{i}-aZ_{i}}{2i+1}}

.

The expansion of $V$ has hitherto been calculated only for the mean value of $V$ at or near certain epochs. No appreciable part of this mean value appears to be due to causes external to the earth.

471.] We do not yet know enough of the form of the expansion of the solar and lunar parts of the variations of $V$ to determine by this method whether any part of these variations arises from magnetic force acting from without. It is certain, however, as the calculations of MM. Stoney and Chambers have shewn, that the principal part of these variations cannot arise from any direct magnetic action of the sun or moon, supposing these bodies to be magnetic^[1].

472.] The principal changes in the magnetic force to which attention has been directed are as follows.

↑ Professor Hornstein of Prague has discovered a periodic change in the magnetic elements, the period of which is 26.33 days, almost exactly equal to that of the synodic revolution of the sun, as deduced from the observation of sun-spots near his equator. This method of discovering the time of rotation of the unseen solid body of the sun by its effects on the magnetic needle is the first instalment of the repayment by Magnetism of its debt to Astronomy. Akad., Wien, June 15, 1871. See Proc. R. S., Nov. 16, 1871.

[1] Professor Hornstein of Prague has discovered a periodic change in the magnetic elements, the period of which is 26.33 days, almost exactly equal to that of the synodic revolution of the sun, as deduced from the observation of sun-spots near his equator. This method of discovering the time of rotation of the unseen solid body of the sun by its effects on the magnetic needle is the first instalment of the repayment by Magnetism of its debt to Astronomy. Akad., Wien, June 15, 1871. See Proc. R. S., Nov. 16, 1871.

[1]