“Both the law of inertia and the law of gravitation contain a numerical factor or a constant belonging to matter, which is called mass.”

— Willem de Sitter

We have thus two definitions of mass; one by the law of inertia: mass is the ratio between force and acceleration. We may call the mass thus defined the inertial or passive mass, as it is a measure of the resistance offered by matter to a force acting on it. The second is defined by the law of gravitation, and might be called the gravitational or active mass, being a measure of the force exerted by one material body on another. The fact that these two constants or coefficients are the same is, in Newton's system, to be considered as a most remarkable accidental coincidence and was decidedly felt as such by Newton himself. He made experiments to determine the equality of the two masses by swinging a pendulum, of which the bob was hollow and could be filled up with different materials. The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i.e., the inertial and the gravitational mass are the same. These experiments have been repeated in the nineteenth century by Bessel, and in our own times by Eötvös and Zeeman, and the identity of the inertial and the gravitational mass is one of the best ascertained empirical facts in physics-perhaps the best. It follows that the so-called fictitious forces introduced by a motion of the body of reference, such as a rotation, are indistinguishable from real forces. ...In Einstein's general theory of relativity there is also no formal theoretical difference, as there was in Newton's system. ...the equality of inertial and gravitational mass is no longer an accidental coincidence, but a necessity.
"The Astronomical Aspect of the Theory of Relativity" (1933)

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Willem de Sitter 44

Dutch cosmologist 1872–1934

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“Both the law of inertia and the law of gravitation contain a numerical factor or a constant belonging to matter, which is called mass. We have thus two definitions of mass; one by the law of inertia: mass is the ratio between force and acceleration. We may call the mass thus defined the inertial or passive mass, as it is a measure of the resistance offered by matter to a force acting on it. The second is defined by the law of gravitation, and might be called the gravitational or active mass, being a measure of the force exerted by one material body on another. The fact that these two constants or coefficients are the same is, in Newton's system, to be considered as a most remarkable accidental coincidence and was decidedly felt as such by Newton himself. He made experiments to determine the equality of the two masses by swinging a pendulum, of which the bob was hollow and could be filled up with different materials. The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i. e., the inertial and the gravitational mass are the same. These experiments have been repeated in the nineteenth century by Bessel, and in our own times by Eötvös and Zeeman, and the identity of the inertial and the gravitational mass is one of the best ascertained empirical facts in physics-perhaps the best. It follows that the so-called fictitious forces introduced by a motion of the body of reference, such as a rotation, are indistinguishable from real forces…. In Einstein's general theory of relativity there is also no formal theoretical difference, as there was in Newton's system…. the equality of inertial and gravitational mass is no longer an accidental coincidence, but a necessity.”

Willem de Sitter (1872–1934) Dutch cosmologist

p, 125
"The Astronomical Aspect of the Theory of Relativity" (1933)

“Gravitation is not only similar to inertia in its generality, it is also measured by the same number… the mass. The inertial mass is what Newton calls the "quantity of matter": it is a measure for the resistance offered by a body to a force trying to alter its state of motion. It might be called the "passive mass." The gravitational mass, on the other hand, is a measure of the force exerted by the body in attracting other bodies. We might call it the "active" mass. The equality of active and passive, or gravitational and inertial, mass was in Newton's system a most remarkable accidental co-incidence, something like a miracle. Newton himself decidedly felt it as such, and made experiments to verify it, by swinging a pendulum with a hollow bob which could be filled with different materials. The force acting on the pendulum is proportional to its gravitational mass, the inertia to its inertial mass: the period of its swing thus depends on the ratio between these two masses. The fact that the period is always the same therefore proves that the gravitational and inertial masses are equal.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“In many different fields, empirical phenomena appear to obey a certain general law, which can be called the Law of Large Numbers. This law states that the ratios of numbers derived from the observation of a very large number of similar events remain practically constant, provided that these events are governed partly by constant factors and partly by variable factors whose variations are irregular and do not cause a systematic change in a definite direction.”

Siméon Denis Poisson (1781–1840) French mathematician, mechanician and physicist

Statement of Poisson's law also known as the Law of Large Numbers (1837), as quoted by [Richard Von Mises, Probability, Statistics and Truth, Allen and Unwin, 1957, 104-105]

“In Einstein's general theory of relativity the identity of these two coefficients, the gravitational and the inertial mass, is no longer a miracle, but a necessity, because gravitation and inertia are identical.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“Some mechanism seems to be needed, whereby either gravitation creates matter, or all the matter in the universe conspires to define a law of gravitation.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Space, Time and Gravitation (1920)
Context: We can see that, the constant in the law of gravitation being fixed, there may be some upper limit to the amount of matter possible; as more and more matter is added in the distant parts, space curves round and ultimately closes; the process of adding more matter must stop, because there is no more space, and we can only return to the region already dealt with. But there seems nothing to prevent a defect of matter, leaving space unclosed. Some mechanism seems to be needed, whereby either gravitation creates matter, or all the matter in the universe conspires to define a law of gravitation.<!--p.163

“In developing his theory of gravitation, Newton assigned to every material body another property which is called its gravitational mass. Gravitational mass determines the force exerted by the body on other bodies, and so its function appears to be quite distinct from that of inertial mass. Nevertheless, the two are found to be identical in magnitude. Newton made experiments to verify this remarkable equality by swinging a pendulum with a bob which could be made with different materials. The period of the swing depended on the ratio of the inertial and gravitational masses of the pendulum, but in all cases it was found to be the same… In 1890 Eötvös made a much more refined test with the aid of a… torsion balance. Repeated experiments showed that inertial mass and gravitational mass were equal to within one part in 100 million. Einstein suggested that this was because inertia and gravitation are identical.”

Gerald James Whitrow (1912–2000) British mathematician

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

“Analogy would lead us to conclude that the combinations of the primordial matter, forming our so-called elements, are as universal or as liable to take place everywhere as are the laws of gravitation and centrifugal force.”

Robert Chambers (publisher, born 1802) book Vestiges of the Natural History of Creation

Source: Vestiges of the Natural History of Creation (1844), p. 28
Context: Analogy would lead us to conclude that the combinations of the primordial matter, forming our so-called elements, are as universal or as liable to take place everywhere as are the laws of gravitation and centrifugal force. We must therefore presume that the gases, the metals, the earths, and other simple substances, (besides whatever more of which we have no acquaintance,) exist or are liable to come into existence under proper conditions, as well in the astral system, which is thirty five thousand times more distant than Sirius, as within the bounds of our own solar system or our own globe.

“The matter of jurisprudence is positive law: law, simply and strictly so called : or law set by political superiors to political inferiors.”

John Austin (legal philosopher) (1790–1859) legal philosopher

Source: The Province of Jurisprudence Determined (1832), p. 1; opening line

“Fabricating astronomical data going back thousands of years calls for knowledge of Newton’s Law of Gravitation and the ability to solve differential equations.”

N. S. Rajaram (1943–2019) Indian mathematician

N.S. Rajaram: The Politics of History, p.47.

“Gradually, during the eighteenth century, physicists and philosophers had become so accustomed to Newton's law of gravitation, and to the equality of gravitational and inertial mass, that the miraculousness of it was forgotten and only an acute mind like Bessel's perceived the necessity of repeating those experiments. By the experiments of Bessel about 1830 and of Eötvös in 1909 the equality of gravitational and inertial mass has become one of the best ascertained empirical facts in physics.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“Both the law of inertia and the law of gravitation contain a numerical factor or a constant belonging to matter, which is called mass.”

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Willem de Sitter 44

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