Ratio of Mass to Weight for Crystals and Radioactive Substances.

P. Zeeman. Some Experiments on gravitation. The ratio of mass and weight for crystals and radioactive Substances. Koninklijke Akademie van Wetenschappen. The Amsterdam. Proceedings Vol. XX No. 4, p. 542.

The author first of all points to the interest which the question of the ratio of mass to weight has recently acquired in connection with the general principle of relativity. Only in the case where there exists a force field giving the same acceleration of weight to bodies is it possible to “create” a gravitational field by a transformation of coordinates.

The most sensitive method for determining this ratio must be recognized as Eötvös’s method, which used a torsion balance in the following way. Two different masses (for example, cork and brass) of equal weight are suspended from the two ends of the rod of a torsion balance. This rod has the direction \(WO\). The forces acting on both masses will be: 1) the force of gravity, proportional to the weight, and 2) the centrifugal force, proportional to the mass. If the weights of both masses are the same, but the masses are different in magnitude, then the resultants for the two masses have different directions, which creates a couple of forces twisting the balance through a certain angle \(\alpha\). If the balance is turned through 180, then the couple of forces will have the opposite direction and the twisting will occur in the opposite direction, through the angle \(-\alpha\); the angle \(2\alpha\) can easily be determined from experiment. According to Eötvös’s experiments, taking into account possible errors in the observations, the ratio of weight to mass remains constant with an accuracy up to

\[ \frac{1}{2 \cdot 10^7}. \]

Zeeman repeats Eötvös’s experiments in order to clarify this ratio for “oriented” crystals and for radioactive substances. Zeeman

first of all improves the torsion balance of Eötvös, making it more sensitive. The results of his experiments are as follows:

1) The influence of the orientation of a quartz crystal on the ratio of mass to weight is less than \(\dfrac{1}{30{,}000{,}000}\) of the weight of the crystal.

2) For uranium, the deviation from the law of constancy of the ratio of weight to mass is less than \(\dfrac{1}{20{,}000{,}000}\) of the weight of the substance.

The significance of this second conclusion is also important in the following respect: radioactive substances contain enormous quantities of energy; thus one gram of radium during its lifetime, not counting the decay products, including emanation and radium \(F\), releases \(3.7 \cdot 10^9\) calories, which, according to our present views on energy, corresponds to \(0.6 \cdot 10^{-4}\) g of mass. Does this energy, which is contained in a radioactive substance and which in the course of its lifetime will be lost by it in the form of a definite number of calories, have not only mass but also weight? To this extremely interesting question Zeeman’s experiment gives an affirmative answer, since the quantity of energy contained in the radioactive substance is quite sufficient for its weight to be detected, if one assumes, as is now usually done, that it has mass1.

V. Frederiks.

1. By the word “mass” here one should understand what is now often called more precisely “inertial mass.” ↩