98 SCIENCE PROGRESS 



for two given lines a smooth curve could be drawn connecting 

 their difference of intensity with the type, and such curves 

 were constructed for a number of pairs of lines. If, then, for 

 a given spectrum these differences of intensity are measured 

 the type can be read from the curves and a mean value taken. 

 This method is an accurate, rapid, and easy method of de- 

 termining the type of a star. 



In the second investigation the method of studying the 

 intensities of spectral lines is applied to the determination of 

 stellar parallaxes or distances. There are certain spectral lines 

 which are peculiarly sensitive in their behaviour to the physical 

 condition of the gases which give rise to them ; now two stars 

 of the same type may differ greatly in size, mass, and intrinsic 

 brightness and therefore presumably in the atmospheres in 

 which the spectral lines find their origin. Such differences 

 should be evidenced in the behaviour of certain spectral lines. 

 This is found to be the case, and by a comparison of intensities 

 with other lines for stars of known parallax (tt) and hence 

 known absolute magnitude (M), linear relations are derived 

 connecting the difference of intensity and magnitude for stars 

 of different types . Thus, for any star of known type by measur- 

 ing the intensity difference, M may be derived and — m being its 

 apparent brightness — it can be deduced from the relation 



5 log 7r = M — ra — 5 . 



The third investigation tests this method by comparing 

 the parallaxes of stars so calculated with measured values, 

 and the agreement in almost all cases is so close as to indicate 

 that a method has been discovered which may revolutionise 

 our knowledge of stellar parallaxes, an account of the gradual 

 development of which has been given in these notes, Science 

 Progress, x. p. 121, July 1915. The method is particularly 

 important in that it will provide good determinations of the 

 parallaxes of bright stars of small proper motion of which 

 comparatively few direct measures have been made. 



The curves mentioned in the first investigation were based 

 on stars of low luminosity and large proper motion. In the 

 fourth investigation, an account is given of the application 

 of this method for determining type to late type stars of high 

 luminosity : it was found that the hydrogen lines in such 

 cases were abnormally intense, and regarded by themselves 



