;o6 



NATURE 



[April 14, 192 1 



uncertainty in the parallax determination begins 

 to become comparable with the value of the paral- 

 lax (say, CT<o"-o2 5 in the case of modern photo- 

 graphic determinations). Adams, therefore, has 

 replaced the determination of each single parallax 

 by a collective result, and has, in effect, reversed 

 the former procedure, so that now, from a deter- 

 mination of the absolute magnitude and the ap- 

 parent magnitude, the parallax may be derived 

 with a high order of accuracy. 



Another indirect method, 

 discovered independently and 

 almost simultaneously by 

 Hertzsprung and Russell, en- 

 ables a hypothetical value to 

 be derived for the parallax of 

 any physical double star of 

 which the components show 

 even a trace of relative motion. 

 If TO is the observed relative 

 motion in seconds of arc per 

 year and 5 the observed separa- 

 tion of the components in 

 seconds of arc, then the paral- 

 lax is given by V^'^ = s'w''-l\\-(im^ 

 where m denotes the combined 

 mass in terms of that of the 

 sun as a unit. The masses of 

 the stars do not show a wide 

 variation, and Russell finds 

 that, assuming the mass of the 

 binary system to be double that 

 of the sun, the resulting error 

 in the absolute magnitude de- 

 duced from this hypothetical 

 parallax will not exceed + loM 

 in 89 per cent, of all the cases. 



A third method of some in- 

 terest may also be briefly re- 

 ferred to. There is a type of 

 variable star the light variation 

 of which is characterised by 

 certain peculiarities which 

 seem to indicate that the varia- 

 tion is due to an actual pulsa- 

 tion in the star. Such variables 

 are termed Cepheids, after the 

 typical example, S Cephei. 

 In the Magellanic clouds is a 

 large number of these variables, 

 and it was discovered by Miss 

 Leavitt that there is a definite 

 relationship between the 

 periods of these Cepheids and their apparent mag- 

 nitude, or, since they are all at appreciably the same 

 distance, between their period and absolute magni- 

 tude. Their absolute magnitude, however, is not 

 a priori known, but the near Cepheids may be 

 used to fix a point on the curve, and then the 

 absolute magnitude of any Cepheid can at once 

 be found if its period is determined. This has 

 the following important application : the large 

 majority of the variables which occur in stellar 

 clusters are of the Cepheid type, and this relation- 

 ship, therefore, provides a basis for the deter- 

 NO. 2685, VOL. 107] 



mination, with a relatively small uncertainty, of 

 the distances of stellar clusters. The result is 

 the more valuable because the clusters are at such 

 great distances that there is, at present, no reason- 

 able expectation of the possibility of their direct 

 determination. With the aid of the large reflectors 

 at Mount Wilson, much valuable work has been 

 done in determining the apparent magnitudes of 

 cluster stars and, the parallax of the clusters 



Fig. 6. — Absolute magnitudes of stars in relation to spectral type. 



having been determined, these can at once be 

 turned into absolute magnitudes. 



It will be evident from the preceding remarks 

 that our knowledge of the absolute magnitudes 

 of stars has within recent years increased very 

 rapidly. What are the absolute magnitudes of 

 the stars in the neighbourhood of the sun? The 

 values show a very marked dependence upon the 

 spectral type of the star. It was shown by Russell 

 that for any given type there is a limiting abso- 

 lute magnitude below which, in general, stars 

 of that type do not occur. The redder the 



