(Vol. iv., p. 129.)
I beg to send you a few remarks on the note of A. E. B., concerning the
"Pendulum Demonstration of the Earth's Rotation."
Your correspondent appears to consider that the only fact asserted by
the propounders of the theory, is a variation in the plane of
oscillation, caused by "the difference of rotation due to the excess of
velocity with which one extremity of the line of oscillation may be
affected more than the other;" the probable existence of which he proves
by imagining a pendulum suspended over a point half-way between London
and Edinburgh, and set in motion by being drawn towards and retained
over London, and thence dismissed on its course. It is clear that in
such a case the pendulum would at starting be impressed with the same
velocity of motion in an eastern direction which the retaining power in
London had, and that its path would be the result of this force
compounded with that given by gravity in its line of suspension, _i.e._
towards the north, and its course would therefore be one subject to easy
calculation. I should imagine that this disturbing force arising from
the excess of eastern velocity possessed by the starting point over that
of suspension, would be inappreciable after a few oscillations; but at
all events it is evident that it might readily be avoided by setting the
pendulum in motion by an impulse given beneath the point of suspension,
by giving to it a direction east and west as suggested by A. E. B., or
by several other expedients which must occur to a mathematician.
Your correspondent proceeds by requiring that there should be shown
"reasonable ground to induce the belief that the ball is really free
from the attraction of each successive point of the earth's surface,"
and is not as "effectually a partaker in the rotation of any given
point" as if it were fixed there; or that "the duration of residence"
necessary to cause such effect should be stated. Now I certainly am
aware of no force by which a body unconnected with the earth would have
any tendency to rotate with it; gravity can only act in a direct line
from the body affected to the centre of the attracting body, and the
motion in the direction of the earth's rotation can only be gained by
contact or connexion, however momentary, with it. The onus of proving
the existence of such a force as A. E. B. alludes to, must surely rest
with him, not that of disproving it with me. What the propounders of
this theory claim to show is, I humbly conceive, this,--that the
direction in which a pendulum oscillates is _constant_, and not affected
by the rotation of the earth beneath it: that as when suspended above
the pole (where the point of suspension would remain fixed) the plane of
each oscillation would make a _different_ angle with any given meridian
of longitude, returning to its original angle when the diurnal rotation
of the earth was completed; and as when suspended above the equator,
where the point of suspension would be moved in a right line, or, to
define more accurately, where the plane made by the motion of a line
joining the point of suspension and the point directly under it (over
which the ball would remain if at rest) would be a flat or right plane,
the angle made by each successive oscillation with any one meridian
would be the _same_, so, at all the intermediate stations between the
pole and the equator, where the point of suspension would move in a
line, commencing near the pole with an infinitely small curve, and
ending near the equator with one infinitely large (_i.e._ where the
plane as described above would be thus curved), the angle of the plane
of oscillation with a given meridian would, at each station, vary in a
ratio diminishing from the variation at the pole until it became extinct
at the equator, which variation they believe to be capable both of
mathematical proof and of ocular demonstration.
I do not profess to be one of the propounders of this theory, and it is
very probable that you may have received from some other source a more
lucid, and perhaps a more correct, explanation of it; but in case you
have not done so, I send you the foregoing rough "Note" of what are my
opinions of it.