THE PROBLEM OF THREE BODIES 487 



cusses cases of retrograde motions and the manner in which 

 certain direct orbits pass into the retrograde form. The im- 

 portant " orbits of ejection " when a body is ejected from the 

 Sun towards Jove, or from Jove towards the Sun, are discussed, 

 and the forms of the paths given for different values of the 

 energy constant C = 38, 34, 30, 26 and 20. For the value of 

 C = 20 the body ejected from the Sun starts in a straight line 

 towards Jove, and is gradually slightly deflected by the latter. 

 By the time it has reached and passed the place where Jove was, 

 the latter has passed away, and the body falls back again on the 

 Sun nearly in a straight line. This orbit is the limiting form of 

 four coalescent ones, the motion in which may be either direct 

 or retrograde. The ejectional stage affords one method of transi- 

 tion whereby direct paths may become retrograde or vice versa, 

 another way being passage through the apex of the equilateral 

 triangle on 5 / as base, this point being one of zero force, as 

 already mentioned. A body may reach this apex with an 

 indefinitely small velocity, either direct or retrograde, and the 

 direction of motion would then change. M. Burrau has also 

 treated the subject of orbits of ejection, and in addition he has 

 considered cases where the "Sun" and "Jove" are of equal 

 masses, which though not applicable to our own system may 

 have valuable bearings on the conditions of " other stars than 

 ours." Charlier has also discussed the problem of oscillating 

 satellites, and arrived at similar results to those given by Darwin, 

 whilst Professor Whitaker has given a criterion for the discovery 

 of periodic orbits, and important papers on this subject have 

 also been contributed by H. C. Plummer. There can be little 

 doubt that the further progress of theoretical astronomy will be 

 largely on these lines for some time to come, and it is to be 

 expected that much additional light will be thrown upon many 

 of the more obscure portions of the science. 



In connection with the application of these results to Cosmo- 

 gonic theory, one or two of which we have already briefly 

 outlined. Dr. See has suggested that an additional term might 

 be added to the Jacobian integral to represent the rate of increase 

 of the constant of relative energy as the particle revolves against 

 resistance and steadily drops nearer to the centre of attraction 

 {Astr. Nach. 4341-42). The action of a resisting medium diminish- 

 ing the velocity at every point and thus causing the resisted 

 particle to draw nearer the attracting centre or centres, it may. 



