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IN December, 1913, Jeans wrote an important paper in what was to him a new, though at the same time familiar, field. It was entitled ‘The kinetic theory of star clusters'. It was his first paper in the Monthly Notices of the Royal Astronomical Society. The field was familiar, because it made a calculation similar to those Jeans had been frequently making in his work on the kinetic theory of gases; it was new, because it was the first occasion on which Jeans ventured into the theory of star clusters. Its object was to determine the deviation of direction in the motion of stars due to close approaches by other stars.
The formula I need not quote. But some of Jeans's applications of it are of interest. Assuming 109 stars within a distance of 1000 parsecs, assuming each star to be on the average five times as massive as the sun, and assuming a typical relative velocity between members of a pair of stars ‘in collision’ to be 60km. sec.-1, he calculated that a gross deflexion of 1° would be acquired after a distance of 4 x 1023 cm., or, with an individual star velocity of 40 km. sec.-1, after an interval of 3200 million years, which is the present estimate of the age of the universe. This is the result of the accumulation of small deflexions, excluding ‘violent’ deviations. A sudden deviation of, say, 5° would occur once in 5 million million years; and one of 2°, once in 8 x 1011 years.
He further summarized what might be deduced from his formula in the following vivid passage:
… let us take a definite instance of a star stream in which the stars all start with equal and parallel velocities of 40 km. sec.-1. Let us suppose that a star is still considered to belong to the main stream as long as its direction of motion makes an angle not greater than 2° with the main stream. After 100 million years, the stream will have lost only one in 8000 of its original members, and the remainder will make angles with the main stream of which the average amount is only 10′.