"The torsion-balance is the most sensitive of all instruments. The largest rotating-masses, with which we can experiment, are probably the large fly-wheels in rolling-mills and other big factories. The centrifugal forces assert themselves as a pressure which tends from the axis of rotation. If, therefore, we set up a torsion-balance in somewhat close proximity to one of these large fly-wheels, in such a position that the point of suspension of the movable part of the torsion-balance (the needle) lies exactly, or as nearly as possible, in the continuation of the axis of the fly-wheel, the needle should endeavour to set itself parallel to the plane of the fly-wheel, if it is not originally so, and should register a corresponding displacement. For centrifugal force acts upon every portion of mass which does not lie exactly in the axis of rotation, in such a way as to tend to increase the distance of the mass from the axis. It is immediately apparent that the greatest possible displacement-effect is attained when the needle is parallel to the plane of the wheel."
This proposed experiment of B. and J. Friedländer is only a variation of the experiment which persuaded Newton to his view of the absolute character of rotation. Newton suspended a cylindrical vessel filled with water by a thread, and turned it about the axis defined by the thread till the thread became quite stiff. After the vessel and the contained liquid had completely come to rest, he allowed the thread to untwist itself again, whereby the vessel and the liquid started to rotate rapidly. He thereby made the following observations. Immediately after its release the vessel alone assumed a motion of rotation, since the friction (viscosity) of the water was not sufficient to transmit the rotation immediately to the water. So long as this state of affairs prevailed, the surface of the water remained a horizontal plane. But the more rapidly the water was carried along by the rotating walls of the vessel, the more definitely did the centrifugal forces assert themselves, and drive the water up the walls, so that finally its free surface assumed the form of a paraboloid of revolution. From these observations Newton concluded that the rotation of the walls of the vessel relative to the water does not call up forces in the latter. Only when the water itself shares in the rotation, do the centrifugal forces make their appearance. From this he came to his conclusion of the absolute character of rotations.
This experiment became a subject of frequent discussion later: and E. Mach long ago objected to Newton's deduction, and pointed out that it cannot be straightway affirmed that the rotation of the walls of the vessel relative to the water is entirely without effect upon the latter. He regards it as quite conceivable that, provided the mass of the vessel were large enough, e.g. if its walls were many kilometres thick, then the free surface of the water which is at rest in the rotating vessel would not remain plane. This objection is quite in keeping with the view entailed by the general theory of relativity. According to the latter, the centrifugal forces can also be regarded as gravitational forces, which the total sum of the masses rotating around the water exerts upon it. The gravitational effect of the walls of the vessel upon the enclosed liquid is, of course, vanishingly small compared with that of all the masses in the universe. It is only when the water is in rotation relatively to all these masses that perceptible centrifugal forces are to be expected. The experiment of B. and J. Friedländer was intended to refine the experiment performed by Newton, by using a sensitive torsion-balance susceptible to exceedingly small forces in place of the water, and by substituting a huge fly-wheel for the vessel which contained the water. But this arrangement, too, can lead to no positive result, as even the greatest fly-wheel at present available represents only a vanishingly small mass compared with the sum-total of masses in the universe.
[Note 20] (p. 42). We use the term "field of force" to denote a field in which the force in question varies continuously from place to place, and is given for each point in the field by the value of some function of the place. The centrifugal forces in the interior and on the outer surface of a rotating body are so distributed as to compose a field of this kind throughout the whole volume of the body, and there is nothing to hinder us from imagining this field to extend outwards beyond the outer surface of the body, e.g. beyond the surface of the earth into its own atmosphere. We can thus briefly speak of the whole field as the centrifugal field of the earth; and, as the centrifugal field, according to the older views, is conditioned only by the inertia of bodies, and not by their gravitation, we can further speak of it as an inertial field, in contradistinction to the gravitational field, under the influence of which all bodies which are not suspended or supported fall to earth.
Accordingly the effects of various fields of force are superposed at the earth's surface: (1) the effect of the gravitational field, due to the gravitation of the particles of the earth's mass towards one another, and which is directed towards the centre of the earth; (2) the effect of the centrifugal field, which, according to Einstein's view, can be regarded as a gravitational field, and the direction of action of which is outwards and parallel to the plane of the meridian of latitude; finally (3) the effect of the gravitational field, due to the various heavenly bodies, foremost amongst them, the sun and the moon.
[Note 21] (p. 42). Eötvös has published the results of his measurements in the "Mathematische und Naturwissenschaftliche Berichte aus Ungarn," Bd. 8, S. 64, 1891. A detailed account is given by D. Pekár, "Das Gesetz der Proportionalität von Trägheit und Gravitation." "Die Naturwissenschaft," 1919, 7, p. 327.
Whereas the earlier investigations of Newton and Bessel ("Astr. Nachr." 10, S. 97, and "Abhandlungen von Bessel," Bd. 3, S. 217), about the attractive effect of the earth upon various substances, are based upon observations with a pendulum, Eötvös worked with sensitive torsion-balances.
The force, in consequence of which bodies fall, is composed of two components: first the attractive force of the earth, which (except for deviations which may, for the present, be neglected) is directed towards the centre of the earth; and, second, the centrifugal force, which is directed outwards parallel to the meridians of latitude. If the attraction of the earth upon two bodies of equal mass but of different substance were different, the resultant of the attractive and centrifugal forces would point in a different direction for each body. Eötvös then states: "By calculation we find that if the attractive effect of the earth upon two bodies of equal mass, but composed of different substance, differed by a thousandth, the directions of the gravitational forces acting upon the two bodies respectively would make an angle of 0.356 second, i.e. about a third of a second with one another; "and if the difference in the attractive force were to amount to a twenty-millionth, this angle would have to be
th seconds; that is, slightly more than