420 
ASTRONOMY: SHAPLEY AND NICHOLSON 
were strictly monochromatic the spectral lines would have a finite width 
since the resolving power of a spectrograph is not infinite. As is well 
known, however, the light giving rise to an absorption line is by no 
means monochromatic. Its distribution may be represented satis- 
factorily by 
where Vn is the value of v for intensity /$, corresponding to maximum 
absorption. The form of the resulting line, as reproduced by the 
spectrograph, has been discussed in detail by Wadsworth.^ 
Rotation of the star will also contribute to the widening of spectral 
lines. Since v, the projection of the rotational velocity in the Hne of 
sight, is numerically equivalent to the distance on the stellar disk 
from the axis of rotation, we may write r 2 ^ ^2 _|_ ^2 Therefore the 
total Hght of the star is 
+ V/I^2 +1 
L = J Jj dvdy = ^ \ [{1 - x) ^ xV\ - v'' - y'']dvdy 
-1/1^2 -1 
and 
— = 2 (1 - xW\ - + ^ (1 - 
Iji 2 
In this case 7^? is a function of the degree of darkening, being the in- 
tensity for maximum absorption (when = 0) divided by 2 (l — x) -f — 
2 
Then for x = 0 
L = 2 Vl-v' (7) 
and for x = 1 
^=^(1-.^) (8) 
J R A * 
For comparison with figure 1, the intensity curves of the absorption 
lines for a rotating star (assuming monochromatic radiation and infinite 
resolving power) are shown in figure 2. 
It can be shown without difficulty that if for an average Cepheid the 
period of rotation is less than two months the widening of the lines 
due to rotation will be decidedly greater than the widening due to 
pulsation. 
Obviously, then, rotation of the star, resolving power, and the in- 
herently finite width will all affect the appearance of the absorption 
lines, independently of changes due to pulsation. If the resolution is 
