212 
VARIABLE STARS 
in the ratio L 2 + \L x R<?\a‘ l : L 2 . This, however, is not true. A globe 
illuminated from without does not present a uniformly bright disc, and 
the formula (144-1) tells us nothing about the brightness as seen in a 
specified direction. Allowing for this, the simple geometrical theory gives 
the ratio L 2 + f L^ja* : L 2 (144-2). 
In addition, there is a small effect due to “darkening at the limb” 
which affects both the ordinary emission and the re-emission (§ 227). 
At full phase the reflected radiation has an advantage, since it comes 
mainly from the centre of the disc and avoids the darkening. This is found 
to increase the albedo in the ratio -j-|, the increased brightness for the 
observer who sees the full phase being at the expense of reduced brightness 
in other directions. 
Since R 2 /a is often rather large it is well to retain higher powers. A 
more accurate expression for the increase is then 
^L x {sin 2 <f> + (2 + cos 3 <f> — 3 cos (/>)/sin <p} (144-3), 
where sin </> = R 2 /a. 
It may be added that the variation of this added brightness with phase 
is proportional to - (sin i p — ip cos ip), the phase-angle ip being reckoned 
77 
from zero at “new.” The observed reflection coefficients have been cal 
culated on the assumption that the variation is proportional to |(1 — cos ip). 
It so happens that this introduces no error in the reflection coefficient, but 
it makes an appreciable difference in the calculation of the ellipsoidal 
elongation of the stars. Determinations of the elongation of the stars 
under each other’s attraction must ultimately yield important information 
for the development of our theory; but at present the treatment is too 
crude for our purposes. 145 
145. Results for those variables in which the reflection effect has been 
thoroughly studied are collected in Table 28 a. 
The type given is that of the brighter component; the type of the 
fainter can be estimated from the ratio of the surface luminosities 
by reference to Table 16 (where J is measured in magnitudes). The unit 
of heat intensity used for L x and L r is the maximum for the system, 
i.e. L x + L 2 + L r = 1. The calculated value of L r is found from (144-3), 
and the observed value is taken directly from the published discussions of 
the photometric data; the probable error assigned by the investigator is 
given in the last column. (The V s in the table refer to the light or heat 
in the direction towards the observer, and seen by him except in so far as 
the eclipse interferes.) No. 9 depends on selenium photometry; the others 
depend on visual observations.