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SCIENCE 



[N. S. Vol. XLI. No. 1047 



not in sucli a way as to permit the eclipse 

 explanation to apply. This circumstance 

 causes the observer once more to inquire 

 whether the shifts in the spectrum lines 

 that he observes are always velocity ef- 

 fects, or at any rate whether they are due 

 to orbital motion. These remaining cases 

 have another peculiarity; the period of the 

 secondary oscillation is always found to 

 be either just one half or just one third of 

 that of the principal oscillation. If we 

 interpret this in terms of a third body we 

 have a system in which the three compon- 

 ents are close together and revolve 

 around each other in simply commensu- 

 rate periods. It is for the mathematician 

 to say whether such a system can be stable, 

 and therefore whether such a third body 

 is possible. Although this is a problem of 

 many years' standing it has not yet been 

 approached from the mathematical side, 

 so far as, I am aware. It seems probable 

 to the speaker that such a system will be 

 found to be unstable, for reasons similar 

 to those that account for the dark divisions 

 in Saturn's rings and for the gaps in the 

 distances of asteroids from the sun, these 

 divisions and gaps corresponding to places 

 where the periods would be simply com- 

 mensurate to that of one of Saturn's satel- 

 lites in the one case, and to that of Jupiter 

 in the other. It is worthy of remark that 

 in not a single instance where a third body 

 has been inferred from a commensurate 

 secondary oscillation, has this body been 

 confirmed by a subsequent detection of 

 its spectrum or otherwise. It is true that 

 in Lambda Tauri two oscillations, both of 

 short period, have been detected ; but these 

 periods seem to bear no relation to each 

 other. 



A mathematical problem connected with 

 binaries, more important than either of 

 the above, has to do with the origin of 

 these systems. This is one of the few prob- 



lems in sidereal astronomy with which the 

 mathematician has concerned himself to 

 any great extent, but it is still far from 

 being in a satisfactory state. The past 

 history of the moon, in a dynamical sense, 

 formed the subject of an exceedingly la- 

 borious investigation by George Darwin 

 more than thirty years ago. He concluded 

 that the earth and the moon had once 

 formed a single body and that they had 

 broken away from each other by a kind of 

 fission induced by the rotation of the body 

 on its axis. Tidal friction is now set up; 

 it causes the two bodies to draw away from 

 each other, the month to become longer 

 and the orbit of the moon to become some- 

 what eccentric. Darwin and others have 

 extended this reasoning to double stars, 

 and here the recent work on spectroscopic 

 binaries seemed to afford a striking con- 

 firmation of the theory. It has been found 

 that close binaries almost invariably have 

 circular orbits and that their physical con- 

 dition, as revealed by their spectra, is of 

 the sort that is generally accepted as indi- 

 cating youth. Widely separated binaries, 

 on the other hand, are apt to have eccen- 

 tric orbits and to show signs of old age. 

 Still more recently the mathematical side 

 of the question has been reviewed by Moul- 

 ton, Jeans, Russell and others. It now ap- 

 pears that Darwin's results are at least 

 incomplete and that the causes he adduces 

 are not sufficient to account for the genesis 

 of the moon or for that of double stars. 

 The chief difficulty is that tidal friction is 

 not competent to drive apart to any great 

 distance two bodies of comparable mass 

 that have separated by fission. It appears 

 probable in this view that the separation 

 must have occurred long before the bodies 

 formed stars, that is, while they were still 

 nebulae. The difficulties of reconciling cer- 

 tain observational facts with this view are 



