[delury] convection .\ND STELLAR VARIATION 229 



and hence for each element in the atmosphere affected there may be 

 written : 



Ej£ = P ^ + Ijj, for hydrogen ; Eq^j^ = Fq^ + Iqw ^^^ calcium; 



and so on. These differing effects are illustrated in the spectrohelio- 

 grams taken by Hale, Deslandres, Fox and others. In any variable star 

 the effects for the different elements may or may not be the same depend- 

 ing on whether or not the elements occupy the same regions affected 

 during the changes. 



§5. Changes in the atmospheric convection currents produce varia- 

 tions in luminosity and changes in the character and position of the 

 spectral lines. Varia4:ions in brightness may be caused by changes in 

 the quantities of heated matter brought out to the surface of the star, 

 or by changes in the depth and pressure of the absorbing layers of the 

 atmosphere, or by changes in the intensity or position of electrical dis- 

 charges. Alterations in the character of the spectral lines may be due 

 to these same causes and also to changes in the vapor-density of the 

 elements and compounds. Shifts in the lines of the spectrum may be 

 produced by changes in pressure, a lessening of ])rci-pu]e in general 

 lessening the wave-length,^ or by rapid variations in the length of the 

 optical path of the light brought about either by rapid motions of the 

 luminous masses or by rapid changes in the density of the media through 

 which the light passes caused either by radial or transversal currents or 

 by sudden changes in the positions of electrical discharges or glows. 

 These latter effects are included in the formula given by Michelson : 2 



1 dL 1 dl da 



N' = N {1 - - . - ) = N ll 2 {pi - -\- I -)\ 



V dt V dt dt 



where V is the velocity of light in ether, N the vibration-frequency of 

 the line under consideration, N' the observed frequency and L the length 

 of the optical path which is equal to ^ I n, that is, the sum of the 

 optical paths of the various media through Avhich the liglit pasfios, I re- 

 ferring to tha linear distances and ;/ to the refractive indices of these 

 media. It will thus appear that a rapid lessening of the distance away 

 of the source of light from the observer, or of the densities of the media 

 traversed by the light will introduce an increase in the value of N', the 

 observed frequency, and therefore a decrease in the wave-length of light. 



1 Humphreys. Astrophysical Journal, 6, 169-232, 1897. 



2 /Md., 13, 192-198, 1901. 



Sec. III., 1009. 14. 



