260 
ASTRONOMY: J. STEBBINS 
stellar magnitude as the ordinary limit above which a star must vary 
in order to be detected, and if i represents the corresponding inclination 
the probabihty of an ecKpse of this or greater amount is given by cos i. 
Conversely, if we have found a certain number of stars with a given 
type of eclipse, we may multiply by sec i and obtain the corresponding 
number of such systems with orbit planes in all directions. 
Therefore, if we separate the known ecHpsing systems into classes 
according to the ratio P/D and multiply the number in each class by 
P sec i/D, we get numbers which represent the frequency of occurrence 
in space of the corresponding systems. From data already brought to- 
gether by Shapley (Contributions from the Princeton University Observa- 
tory, No. 3, 82, 1915), the tabulated results have been found. The third 
line has been derived from the second by the proper multiplication 
as described, the products being reduced in proportion to make the 
total of 88. 
Value of P/D 
Number of stars observed 
Relative number existing . 
2-4 5-7 8-10 11-13 14-16 17-19 20-22 
12 41 23 7 4 0 1 
3 24 26 16 13 0 6 
The interpretation of these results is that there are relatively few sys- 
tems with components nearly in contact, P/D = 2, and there is a dis- 
tinct preponderance oi P/D from 5 to 10, with maximum say at 8. 
This corresponds to a distance between centers of about 5 times the 
average radius of the two bodies. 
With more data we could derive similar results for each of the spectral 
classes. The systems with spectra of classes G and K seem to be quite 
different from the others, and omitting these we find for stars of B, A, 
and F spectra a close connection between the relative length of eclipses 
and the average periods. 
Value of P/Z) 2-4 5-7 8-10 11-13 14-20 
Number of stars 9 38 22 6 4 
Average period, days 1.0 2.4 5.0 11 15 
The increase of period with increasing P/D seems to mean, what has 
been pointed out before, that the stars which are farther apart move 
more slowly not only on account of the greater distance, but also because 
these systems are less dense. However, as the density seems to be a 
marked function of the spectral class, a further discussion with more 
material is essential. 
From these and other simple considerations, we may conclude: The 
preponderant type of close binary with components of the same order of 
size and of equal or unequal brightness, consists of bodies whose distance 
