The NIST Reference on Constants, Units and Uncertainty

Fundamental Physical Constants


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Introduction to the constants for nonexperts

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Velocity of light in vacuum (c)

    To determine a velocity requires knowledge of both a distance and a time. Attempts to achieve measurements of the speed of light (c) date back to the 16th- and 17th-century Italian scientist Galileo Galilei, who supposedly tried unsuccessfully to determine c by having two men stand at a known distance from each other and alternately cover and uncover their handheld lanterns as soon as they saw the light from the other man's lamp, thus seeking to determine the elapsed time for light to travel the known distance between the two men. A 17th-century Danish astronomer, Ole Rømer, calculated a value of c from the dependence of the period of revolution of a moon of Jupiter on the Earth's orbital position about the Sun. Similarly, in 1726, an English astronomer, James Bradley, determined c from the apparent change in position of a number of stars in the sky as the Earth moved about the Sun.

    The problem of overcoming the short time interval associated with light traveling a readily measured distance on the Earth's surface was first solved by a French physicist, Armand-Hippolyte-Louis Fizeau, in the mid 19th century. He did this by having the light pass through a gap between the teeth of a toothed wheel rotating at a known rate, reflect off a fixed mirror a known distance away, and return to the wheel. A related method utilizing a rotating mirror was also employed by another French physicist, Jean Foucault, in 1862.

    The classic pre-World War II measurements of the constant c are associated with Albert A. Michelson, a physicist in the United States. From 1924 to 1926, Michelson measured c by reflecting light between a rotating mirror with a number of faces and a fixed mirror some 35 kilometers (22 miles) away. A second measurement using essentially the same method but in a 1.6 kilometer (one-mile) evacuated tube was carried out by Michelson and his associates over the period 1931 to 1935.


The Newtonian gravitational constant (G)

    The universal, or Newtonian (after Isaac Newton), gravitational constant (G) is the constant of proportionality in the equation relating the gravitational force between two separated bodies to their respective masses. There have been two different classes of experiment to measure the constant G. The first involves estimating the mass of the Earth and separately determining the radius of the Earth and the acceleration of an object falling toward the Earth because of gravity at its surface. Attempts to measure the mass of the Earth have been of two kinds. In 1775, a British astronomer, Nevil Maskelyne, used the deflection of a plumb line from the vertical when placed on either side of a mountain of known shape and density. In 1854 another astronomer, George Biddell Airy, of England, measured the gravitational constant by comparing the period of a pendulum's swing at the Earth's surface and at the bottom of a mine shaft of known depth.

    The second general class of experiment for determining the gravitational constant, a significantly more accurate one, consists of measuring the gravitational force attracting two masses in the laboratory. In 1798 Henry Cavendish of England using a torsion balance designed a few years earlier, carried out the first such experiment. He suspended by a thin fiber a light, stiff rod with two solid five-centimeter (two-inch) diameter lead spheres attached at either end. He then brought two 30-centimeter diameter (12-inch) lead spheres near the smaller spheres. The gravitational attraction between them produced a torque, or turning force, that twisted or deflected the suspension fiber. More recent measurements of G using an oscillating torsion balance and gold, platinum, and glass small spheres were carried out by physicist P. R. Heyl at the U. S. National Bureau of Standards from 1925 to 1928.

Ratio of the electron charge (-e) to the electron mass (me), -e/me

    Numerous direct measurements of this quantity were carried out over the period 1897 to 1938. The experiments usually involved the deflection of beams of free electrons by electric and magnetic fields. Many of the experiments required the measurement of the velocity of the electrons combined with a simultaneous determination of the voltage used to initially impart kinetic energy (i.e., velocity) to the electrons. Often the electron velocity was determined by a null deflection method in which the magnitudes of crossed electric and magnetic fields, through which the electron beam traveled, were so adjusted that the electric and magnetic deflecting forces just balanced each other. An English physicist, Joseph John Thomson, was the first to use this technique in 1897.


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Reproduced with permission from Encyclopaedia Britannica, 15th edition. © 1974 Encyclopaedia Britannica, Inc.