TO KNOW THE STARRY HEAVENS 
29 
in the telescope, but the discovery of 
their true nature and of their positions 
in space and distances from us has only 
very recently been made. All of these 
things are now known, at least approxi- 
mately, and it is the, at first, almost 
startling results of the long investiga- 
tions that have attracted the attention 
and interest of astronomers. 
In the first place, it may be said that 
no spherical cluster is so near us that 
any of its stars suffer any measurable 
displacement as we pursue our yearly 
path about the sun. Our position in 
space changes 186,000,000 miles during 
each six months, as we go around the 
sun, but if a heavenly body is so far 
away that its light occupies more than 
one hundred and fifty years in coming 
to us. its displacement owing to this 
change of position is too small to be 
measured, even in our largest tele- 
scopes. In fact at this distance away, 
a star will be displaced in a little 
“Parallactic Orbit,” the distance across 
which is almost exactly the same as the 
thickness of the finest spider thread. 
Since, therefore, we can detect no 
displacement of the stars of a spherical 
cluster directly, we must have recourse 
to indirect methods of finding their dis- 
tances from us. One of the most re- 
liable of all methods is by a study of 
the variable stars which many of the 
clusters contain. No less than twenty- 
five years ago, 132 of these variable 
stars were found in the cluster at C, 
85 were discovered in the cluster at D, 
while 122 were found in a cluster in 
Centaurus. This last is the largest and 
finest cluster of the entire heavens, but 
it is not visible from the United States. 
Some of the clusters contain but very 
few or no variable stars at all ; the 
cluster at'B, for example, has but seven. 
Many of these variable stars belong 
to a type known as Delta Cepheid vari- 
ables, because the typical variable star 
of this kind, discovered two hundred 
and forty years ago, is the fourth 
brightest star of the constellation 
Cepheus. This star will be found at 
A, Figure 1. Its light at a perfectly 
regular interval increases quite sud- 
denly to three times its usual amount 
and then it fades away somewhat more 
slowly. The intervals between the 
greatest brightness of the stars of a 
cluster range from ten to fourteen 
hours, the average period being a little 
more than twelve hours. It is believed 
that a Cepheid variable is a pulsating 
star, and that it is its periodic change 
in shape that causes its outbursts of 
light. 
It is remarkable that there has been 
established a definite connection be- 
tween the absolute brightness of a 
Cepheid variable and its period of 
variation. This connection is shown in 
Figure 2, which is a curve based upon 
• 
Sun 
• •• .. *111 
KY^ WAV 
cloud 
' 
• 1 
* _J 
Figure 3. Showing the situation of the spherical 
clusters with reference to our Milky Way cloud of 
stars. 
more than two hundred and thirty 
variables. Thus we see that the longer 
the period is the greater is the absolute 
brightness of the star. If the period is 
twelve hours, the star when placed at a 
unit’s distance would appear of mag- 
nitude — 0.3, which is about eighty times 
the brightness of our sun. If the period 
is ten days, however, the magnitude 
will be — 3.0; that is. the absolute 
brightness would be about ten times 
as great as in the other case. 
Thus we can find the absolute bright- 
ness of a star when we know its period. 
That these stars in the spherical clus- 
ters appear to us so very faint must 
be because they are so very far away 
from us. Thus, the average apparent 
brightness of the stars in the cluster in 
Centaurus is 12.3, while that of the stars 
in the cluster at C is 14.0. Evidently, 
the stars of the first cluster appear to 
us about six times as bright as those 
of the second because they are so much 
nearer to us. 
In this way (and by several other 
methods, which we have not space to 
describe), the absolute distances of the 
spherical clusters are found. The re- 
sults by all different methods are in 
excellent agreement. They all concur 
in showing that these clusters are en- 
tirely outside of ou- Milky Way cloud 
