344 
ASTRONOMY: H. SHAPLEY 
the result is 
aAB^ = ^JzA/y (9) 
1 + Cy , ^ 
Here y is the ratio of solid and liquid sections and we inquire what 
value of y will make Ad' a maximum provided A, B, C are constant. 
If the thermal and elastic elongations are to be equal A = 2B, Dif- 
ferentiating (9) and reducing: 
l/y = C{ Vl + A/BC - 1) (10) 
and since y must be positive the radical is positive. Now if ^ = 2B, 
for example, the ratio of diameters 2ri to 2^2 would in all cases have to 
exceed 0.65. li A = SB, the case of water remains nearly the same, 
but for ether and alcohol the diameter ratio approaches 0.9. 
1 These Proceedings, 5, 1919, (267-272) . 
2 Carnegie Publ. No. 249, 1917, pp. 84-94. 
STUDIES OF MAGNITUDES IN STAR CLUSTERS, IX. THE 
DISTANCES AND DISTRIBUTION OF SEVENTY 
OPEN CLUSTERS 
By Harlow Shapley 
Mount Wilson Observatory, Carnegie Institution of Washington 
Communicated by G. E. Hale, June 14, 1919 
The question of whether globular clusters are really or only appar- 
ently absent from the mid-galactic segment makes the study of the dis- 
tances of open clusters particularly important. These objects are rela- 
tively near to the galactic circle, and many appear to be at such great 
distances along the plane as to support the hypothesis that obstructing 
matter is insufficient to occlude globular clusters in mid-galactic re- 
gions. ^ On the other hand there is evidence that globular clusters 
actually may not be absent from low galactic latitude,^ and the follow- 
ing discussion of open clusters and other relevant factors suggests that 
the question must be considered an unsettled one for the time being. 
Although the question of the reality of the region of avoidance affects 
but little the general conclusions reached in earlier papers regarding 
globular clusters, spiral nebulae, and the Galaxy, two modifications 
should be made to previously suggested interpretations,^ in case we 
demonstrate the existence of much obstructing matter along the galactic 
