If the propounders of this theory had from the first explained that they
do not claim, for _the plane of oscillation_, an exemption from the
general rotation of the earth, but only 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, it would have saved a
world of fruitless conjecture and misunderstanding.
For myself I can say that it is only recently I have become satisfied
that this is the real extent of the claim; and I confess that had I been
aware of it sooner, I should have regarded the theory with greater
respect than I have hitherto been disposed to do. Perhaps this avowal
may render more acceptable the present note, in which I shall endeavour
to make plain to others that which so long remained obscure to myself.
It is well known that the more we advance from the poles of the earth
towards the equator, so much greater becomes the velocity with which the
surface of the earth revolves--just as any spot near the circumference
of a revolving wheel travels farther in a given time, and consequently
swifter, than a spot near the centre of the same wheel: hence, London
being nearer to the equator than Edinburgh, the former must rotate with
greater velocity than the latter. Now if we imagine a pendulum suspended
from such an altitude, and in such a position, that one extremity of its
line of oscillation shall be supposed to reach to London and the other
to Edinburgh; and if we imagine the ball of such pendulum to be drawn
towards, and retained over London, it is clear that, so long as it
remains in that situation, it will share the velocity of London, and
rotate with it. But if it be set at liberty it will immediately begin to
oscillate between London and Edinburgh, retaining, _it is asserted_, the
velocity of the former place. Therefore during its first excursion
towards Edinburgh, it will be impressed with a velocity greater than
that of the several points of the earth over which it has to traverse;
so that when it arrives at Edinburgh it will be in advance of the
rotation of that place; and consequently its actual line of oscillation,
instead of falling directly upon Edinburgh, will diverge, and fall
somewhere to the east of it.
Now it is clear that if the pendulum ball be supposed to retain the same
velocity of rotation, _undiminished_, which was originally impressed
upon it at London, it must, in its return from Edinburgh, retrace the
effects just described, and again return to coincidence with London,
having all the time retained a velocity equal to that of London. If this
were truly the case, the deviation in one direction would be restored
in the opposite one, so that the only result would be a repetition of
the same effects in every succeeding oscillation.
It is this absence of an element of increase in the deviation that
constitutes the first objection to this theory as a sufficient
explanation of the pendulum phenomenon. It is answered (as I suppose,
for I have nowhere seen it so stated in direct terms) that the velocity
of rotation, acquired and retained by the pendulum ball, is _not_ that
of London, but of a point midway between the two extremes--in fact, of
that point of the earth's surface immediately beneath the centre of
suspension.
There is no doubt that, if this can be established, the line of
oscillation would diverge in both directions--the point of return, or of
restored coincidence, which before was in one of the extremes, would
then be in the central point; consequently it would be of no effect in
correcting the deviation, which would then go on increasing with every
oscillation.
Therefore, in order to obtain credence for the theory, satisfactory
explanation must be given of this first difficulty by not only showing
that the medium velocity _is really that_ into which the extreme
velocity first impressed upon the ball will ultimately be resolved; but
it must also be explained _when_ that effect will take place, whether
all at once or gradually; because, it must be recollected, the
oscillations of the experimental pendulum cannot practically commence
from the central point, but always from one of the extremes, to which
the ball must first be elevated.
But this is not enough: there must also 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 over which it passes; and
that, although in motion, it is _not_ as really and as effectually a
partaker in the rotation of any given point, during its momentary
passage over it, as though it were fixed and stationary at that point.
Those who maintain that this is not the case are bound to state the
_duration of residence_ which any substance must make at any point upon
the earth's surface, in order to oblige it to conform to the exact
amount of velocity with which that point revolves.
Lastly, supposing theses difficulties capable of removal, there yet
remains a third, which consists in the undeniable absence of _difference
of velocity_ when the direction of oscillation is east and west. It has
been shown that the difference before claimed was due to the nearer
approach to the equator of one of the extremities of the line of
oscillation in consequence of its direction being north and south; but
when its direction is east and west both extremities are equally distant
from the equator, and therefore no difference of velocity can exist.
I have directed these observations to the fundamental truth and reality
of the alleged phenomenon; it is quite clear that these must first be
settled before the laws of its distribution on the surface of the globe
can become of any interest.