th of a second; and later:
"I attached separate bodies of about 30 grms. weight to the end of a balance-beam about 25 to 30 cms. long, suspended by a thin platinum wire in my torsion-balance. After the beam had been placed in a position perpendicular to the meridian, I determined its position exactly by means of two mirrors, one fixed to it and another fastened to the case of the instrument. I then turned the instrument, together with the case, through 180°, so that the body which was originally at the east end of the beam now arrived at the west end: I then determined the position of the beam again, relative to the instrument. If the resultant weights of the bodies attached to both sides pointed in different directions, a torsion of the suspending wire should ensue. But this did not occur in the cases in which a brass sphere was constantly attached to the one side, and glass, cork, or crystal antimony was attached to the other; and yet a deviation of
th of a second in the direction of the gravitational force would have produced a torsion of one minute, and this would have been observed accurately."
Eötvös thus attained a degree of accuracy, such as is approximately reached in weighing; and this was his aim: for his method of determining the mass of bodies by weighing is founded upon the axiom that the attraction exerted by the earth upon various bodies depends only upon their mass, and not upon the substance composing them. This axiom had, therefore, to be verified with the same degree of accuracy as is attained in weighing. If a difference of this kind in the gravitation of various bodies having the same mass but being composed of different substance exists at all, it is, according to Eötvös, less than a twenty-millionth for brass, glass, antimonite, cork, and less than a hundred-thousandth for air.
[Note 22] (p. 44). Vide also A. Einstein, "Grundlagen der allgemeinen Relativitätstheorie," "Ann. d. Phys.," 4 Folge, Bd. 49, S. 769.
[Note 23] (p. 46). The equation
asserts that the variation in the length of path between two sufficiently near points of the path vanishes for the path actually traversed; i.e. the path actually chosen between two such points is the shortest of all possible ones. If we retain the view of classical mechanics for a moment, the following example will give us the sense of the principle clearly: In the case of the motion of a point-mass, free to move about in space, the straight line is always the shortest connecting line between two points in space: and the point-mass will move from the one point to the other along this straight line, provided no other disturbing influences come into play (Law of inertia). If the point-mass is constrained to move over any curved surface, it will pass from one point to another along a geodetic line to the surface, since the geodetic lines represent the shortest connecting lines between points on the surface. In Einstein's theory there is a fully corresponding principle, but of a much more general form. Under the influence of inertia and gravitation every point-mass passes along the geodetic lines of the space-time-manifold. The fact of these lines not, in general, being straight lines, is due to the gravitational field, in a certain sense, putting the point-mass under a sort of constraint, similar to that imposed upon the freedom of motion of the point-mass by a curved surface. A principle in every way corresponding had already been installed in mechanics as a fundamental principle for all motions by Heinrich Hertz.