Vol.. 8, 1922 
ASTRONOMY: H. SHAPLEY 
69 
nent maxima or minima encountered during the march of the reflector 
in y, be taken, a circle is to be drawn with a center at R and a radius RP. 
In case of the first minimum at :v = 40 cm., the image is 7 at 2 = 40, 
;V = 80. Hence IC = 27 cm. is the path difference from the minimum 
at :V = 40 cm. which is placed a little too high. The following data so 
measured, may be given as examples. 
Minimum y = ^0 cm., X/2 = 27cm. y = 110 cm., 7X/2 = 179 cm. 
70 cm., 3X/2 = 82 9X/2 = 220 
93 cm., 5X/2 = 126 
Maxima 3; = 53 cm., IX = 50 cm. y = 130 cm., 4X = 198 cm. 
83 cm., 2X = 105 155 cm., 5X = 248 
103 cm., 3X = 148 25 cm., OX = 4 
These results in their entirety are convincing, being quite as accurate 
as the location of maxima and minima admits. The minima of figure 2 
treated by the same method give, for instance, 
Minimum 3; = 25 cm., X/2 = 24 cm. y = 103 cm., 7X/2 = 170 cm. 
50 cm., 3X/2 = 68 126 cm., 9X/2 = 215 
80 cm., 5X/2 = 125 etc. 
with similar data for the maxima. 
* Advance note from a report to the Carnegie Institution, Washington, D. C. 
NOTE ON THE PROBLEM OF GREAT STELLAR DISTANCES 
By HARI.OW Shaplky 
ASTRONOMICAI. OBSERVATORY, HARVARD UNIVERSITY 
Communicated by Edwin B. Wilson, February 27, 1922 
Through a study of the faint variable stars in the Small Magellanic 
Cloud it has been possible to check the photometric methods of measuring 
the parallaxes of globular clusters. 
The great distances now ascribed to the globular systems require that 
the cluster type variables, with periods less than one day, be of high 
luminosity. The high absolute brightness of typical Cepheids, with periods 
longer than one day, is commonly accepted ; but the f aintness of the galac- 
tic variables of the cluster type, and their peculiarly large radial velocities* 
suggest that studies of their proper motions and trigonometric parallaxes 
will contribute little in the near future to the problem of their average 
absolute magnitude. It is now found, however, that the faintest variables in 
the Small Magellanic Cloud are Cepheids of the cluster type, and they are but 
one magnitude fainter than the typical Cepheids with periods of three days. 
In 1904 and 1905 Miss Leavitt discovered nearly a thousand variable 
stars in the Small Magellanic Cloud from photographs made at Harvard's 
observing station at Arequipa, Peru. In addition, she found more than 
eight hundred variables in the Large Magellanic Cloud. Miss Leavitt 
