December 16, 1910] 



SCIENCE 



883 



Hk) = 



sin' B, — sin'C; 

 sin" Sj — sin" 8,' 



Tables have been prepared giving the values of 

 0(k), taking 6, and 6, to correspond to obscura- 

 tions of GO and 90 per cent., and 8^ to a number 

 of values from to 100 per cent. From each 

 observed value of 6^, k may thus be determined. 

 If the values so found are not in agreement, they 

 may be improved by small modifications of the 

 assumed ff, and ^3. In this way a light-curve may 

 be found which represents closely the whole 

 course of the observations. When k is known, 

 R and i are very easily found. The whole com- 

 putation of the elements can be made in less than 

 an hour. When the eclipse is partial, the relative 

 brightness of the two stars is also unknown. By 

 assuming two or three values of this, light-curves 

 may be computed as above, and the best value 

 found by interpolation. If a secondary minimum 

 exists, the eccentricity of the orbit and longitude 

 of periastron may also be found by well-known 

 methods. 



Some Hints mi the Order of Stellar Evolution: 



Henry Nobris Russell. 



Let it be assumed that a star grows denser as 

 it advances in evolution; that it is in equili- 

 brium under its own gravitation, without sensible 

 external disturbance; and that the material of 

 which it is composed behaves like the gases with 

 which we are familiar. It has been shown by 

 Ritter and others that such a star will grow hot- 

 ter as it contracts (Lane's law) until its density 

 reaches a critical value, probably between those 

 of air and water, and nearer the latter. The tem- 

 perature then reaches a maximum and later de- 

 creases. The most massive stars will reach the 

 highest temperature at maximum. This is true 

 of both surface and internal temperatures, the 

 latter sufTering the greater relative changes. 

 Those stars that are hottest at any given time 

 will, therefore, be more massive than the average. 

 Stars whose surface temperature has a given 

 value less than the maximum will be of two kinds 

 — one early in evolution, of rising temperature, 

 large diameter and low density; the other late in 

 evolution, of falling temperature, small diameter 

 and high density. The former will give out many 

 times more light than the latter, on account of 

 their greater size; and the lower the temperature, 

 the more marked will be the differences between 

 these two classes. As contraction proceeds, the 

 stars, whose angular momentum is large, will 



break up into pairs, those formed earliest having 

 the longest periods. The farther evolution pro- 

 ceeds, the greater will be the proportion of such 

 pairs among tlie whole number of stars. Periods 

 less than a day or two can not arise unless the 

 density is already near or beyond the critical 

 value defined above. Recent work on spectroscopic 

 binaries has shown that the proportion of these 

 is greatest for type B and least for types K and 

 M; that short periods, especially those less than 

 two days, are practically confined to types B and 

 A; that the systems which give evidence of un- 

 usually great mass are almost all of type B; that 

 the relation between period and eclipse-duration 

 among the Algol variables (which are almost all 

 of types B and A) shows that their densities are 

 of the " critical " order of magnitude ; and that 

 the distribution of proper motions among the 

 stars of given apparent brightness and spectral 

 type shows (as Herzsprung has pointed out) that 

 the redder stars from type 6 onward fall into 

 two groups: one remote, of small proper motion 

 and great luminosity, the other near us, of large 

 proper motion and small luminosity. These two 

 groups overlap for type F, but are more and more 

 widely separated for the redder stars. The stars 

 of the first kind, being visible at great distances, 

 form a disproportionately large percentage of the 

 naked-eye stars — from 85 per cent, for type G to 

 100 per cent, for type il, for which even the near- 

 est of the stars of the second sort are invisible to 

 the naked eye. The following interpretation of 

 these facts is suggested: assuming, as is now gen- 

 erally believed, that stars of type B have the 

 highest surface temperature, and those of type M 

 the lowest, it appears that the stars of type B 

 show just the characteristics which the hottest 

 stars might be expected to have, and that they 

 represent a stage near the middle of evolutionary 

 history; and that the two groups, of difTerent 

 luminosity, among the redder stars, agree in char- 

 acteristics with those of rising and falling tem- 

 perature predicted by theory. The former, stars 

 of small proper motion, may be regarded as earlier 

 in evolution, the redder they are; and the latter, 

 stars of large proper motion, as later in evolution, 

 the redder they are. Since most of the redder 

 naked-eye stars belong to the former group, the 

 small percentage and long periods of spectroscopic 

 binaries among these spectral types are accounted 

 for. The scheme of evolution here suggested is 

 presented tentatively, as a working hypothesis. 

 Its fundamental conception is similar to that 

 underlying Lockyer's classification — from which, 



