I9I0.] RESEARCHES IN COSMICAL EVOLUTION. 211 



nent professional astronomers since the celebrated work of Laplace 

 and Burkhardt, about 1805, on Lexell's comet of 1770. It is re- 

 markable that in the course of the past century the capture theory 

 of comets should have been highly developed by Leverrier, Adams, 

 Schiaparelli, H. A, Newton, Callandreau, Tisserand and many 

 others, while the capture of satellites should not have been seriously 

 considered prior to the publication of the writer's " Dynamical 

 Theory of the Capture of Satellites," in the Astronoinischc Nach- 

 ricliten, Nos. 4341-42 (July, 1909). 



The field of research opened up by the new theory is so large 

 that it doubtless will be many years before it is exhausted; yet 

 enough seems to have been done already to assure us that all the 

 satellites are captured bodies. The result of this line of thought will 

 be practically a new cosmogony. In order to render the results in- 

 telligible, we shall first outline the process of capture, and then re- 

 capitulate the conclusions at which we have arrived.* 



(a) In the year 1836 the celebrated German mathematician Ja- 

 cobi communicated to the Paris Academy of Sciences an integral of 

 the differential equations of motion for the restricted problem of 

 three bodies ; the system being made up of a sun attended by a planet 

 revolving about it in a circle, and a particle of insensible mass. 

 Jacobi remarks that the integral may be applied to a body such as 

 the terrestrial moon. 



(/3) In 1877 Dr. G. W. Hill developed and greatly perfected the 

 theory of Jacobi's integral, and applied it to the lunar theory in a 

 series of celebrated papers. Hill's work has since been the basis of 

 the profound researches of Poincare, Darwin and others on " Peri- 

 odic Orbits " and related topics in celestial mechanics. 



(7) Dr. Hill showed that in the restricted problem of three 

 bodies, implied in Jacobi's integral, there is a partition of the whole 

 space into three parts — one about each of the large bodies, the sun 

 and planet, and a larger domain enclosing both bodies — within which 

 the power of control over the particle is vested in the two bodies 

 individually and collectively, respectively. The closed surface about 

 the earth includes the orbit of the moon, and the orbits of the other 



*Cf. A. N., 4341-42, 4343, and Publications A. S. P., No. 127, August, 

 1909. 



