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.