154 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1924 



fiftieth of the radius of an electron. This single illustration will 

 show, and with some margin to spare, that under normal conditions 

 the tidal influence between neighboring stars is utterly insignificant. 

 For tidal forces to become important to cosmogony, conditions 

 must be abnormal. 



Our sun happens at the present moment to have no especially near 

 neighbor; but it is fairly certain that at some time, in its wander- 

 ings through the stars, it must have passed stars within a much 

 less distance than that which now separates it from Proxima Cen- 

 tauri. The most trustworthy lines of evidence as to the earth's age, 

 namely, those from geology and radioactivity, indicate an age of 

 from 800 to 1,100 million years. For precision, let us think of the 

 sun's age as 1,000 million years. Let us imagine for the moment, 

 what is no doubt very far from the truth, that throughout all this 

 thousand million years the sun and all the stars have moved just 

 as they are moving now, with the same average velocities as now, and 

 keeping at the same average distance apart. Throughout this thou- 

 sand million years the distance of our sun from its nearest neighbor 

 will have been continually changing, and one star after another will, 

 of course, have taken up the role of nearest neighbor. I5ut there 

 must have been some one instant in this thousand million years at 

 which our sun was nearer than at any other instant to its nearest 

 neighbor. A calculation based on the theory of probability indicates 

 that this nearest distance is likely to have been of the order of 

 7X10^^ cm., a distance which, although only a six-hundredth of that 

 which now separates us from Proxima Centauri, is still equal to 

 fifteen times the radius of Neptune's orbit. Even if the sun had 

 filled the whole of Neptune's orbit, the tidal fraction at this closest 

 encounter, on the supposition that the nearest star had a mass equal 

 to the sun, would only be equal to 1/(15)' or 1/3375, giving a height 

 of tide which is quite unimportant from the point of view of cos- 

 mogony. So long as things have been as they now are, tidal actions 

 between separate stars must have been quite devoid of cosmogonic 

 interest, except possibly in very special cases of quite exceptionally 

 close approaches. 



It is, of course, possible that our sun was the victim of one of 

 those exceptionally close encounters. Nothing can l)e brought against 

 the supposition of such an event, except its a priori improbability. 

 The result of such a close encounter might, as we shall see, be the 

 creation of a system in many ways resembling our solar system. 



Our calculations of probabilities and improbabilities have, how- 

 ever, rested upon the admittedly erroneous assumption that stellar 

 conditions have been similar to the present ones for a period of 

 a thousand million years. On looking back through the past history 

 of the universe, we come to a time when conditions must have been 



