DECEMBER 8, 1899. ] 
periods of about forty stars have been de- 
termined from measures made of 63 of these 
variables on nearly 100 plates by the author 
and Miss E. F. Leland. The period and 
light curve of one of the stars in this clus- 
ter were determined by Professor E. C. 
Pickering in 1896, and the periods of three 
others by visual observations with the 
Yerkes refractor. A tabular statement 
was given of the periods, maximum and 
minimum brightness and range, and dis. 
tance from the center of the cluster. Draw- 
ings were exhibited of the light-curves of 
the first eight variables in the group. The 
table disclosed a striking similarity among 
all these variables, not only in regard to 
length of period, but in magnitude and 
range of variation. Excepting No. 9, which 
has the exceptional period of 16" 47™, the 
longest period among the 40 stars is 14" 59”, 
and the shortest 10° 48". The average 
period is 12" 37", so that the greatest devia- 
tion in period from the mean is 2" 21™. At 
maximum these variables range between 
13.4 and 13.9 mags., and at minimum be- 
tween 14.5 and 14.9 mags. The uniform- 
ity of period, magnitude, and light-curve 
among so many variables in the same clus- 
ter points unmistakably to a common origin 
and cause of variability. No such uni- 
formity is found in the periods and light- 
curves of over one hundred variables deter- 
mined by the author in the great cluster 
w Centauri. 
A few of the variables in M.5 have been 
studied with special care for the exact de- 
termination of the form of the light-curve, 
and diagrams were shown of two of these, 
which represent what may be called the 
‘Cluster Type’ of variables. The decrease 
in brightness is rapid, but not nearly so 
rapid as the increase. The duration of 
maximum phase is exceedingly brief, if 
any ; the minimum brightness appears to be 
quite constant for several hours. The 
whole period may be divided as follows: 
SCIENCE. 
847 
Duration of maximum phase 0 per cent. 
a “ minimum ‘ ZO veya vite 
4 MCLECLEASIN OY beauau SOc mal 
a «increasing  ‘ LOE isis 
Note on the Relation between the Visual and 
Photographie Lnght-curves of Variable 
Stars of Short Period. 
With a visual telescope of sufficient power 
a series of frequent observations of a vari- 
able star will give the true form of its light- 
curve, since each observation consumes so 
little time that it is not affected by the star’s 
variability. The same would be true of 
photographic observations if the time of ex- 
posure could be made so short as to bear 
an inappreciable ratio to any change of 
phase. This applies to most long-period 
variables. Certain short-period variables, 
however, notably those belonging to dense 
clusters, are so faint and go through. their 
changes, especially the increase in light, so 
rapidly, that the necessary exposure bears 
a very large ratio to the duration of any 
phase and important modifications in the 
form of the light-curve follow. 
When the light of a star is changing ata 
uniform rate and in the same direction, the 
measured magnitude will approximately 
represent the actual photographic magni- 
tude at the middle time of exposure, but it 
is obvious that sharp changes in the light 
of a variable will not be well registered on 
photographs of relatively long exposure. 
A diagram was shown of an assumed light- 
curve, where the exposure required was 
one-half of the period of the star’s entire 
variation, and the rise and fall of the 
brightness were equally rapid. Here no 
photograph of the required exposure would 
record a complete minimum, but would fall 
above it, and similarly would fall below the 
true maximum. ‘Thus the tendency of the 
photographs is to smooth down the curve, 
reducing the star’s apparent range of varia- 
tion. 
Where the increase and decrease of light 
