172 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1944 
the pictures go to more and more distant nebulae. The amount of the 
shift gives the velocity of recession. Many nebulae have been ob- 
served and the conclusion is reached that for every million light-years’ 
distance from the earth the velocity of recession is increased by 
about 100 miles per second. The farthest nebulae observed are flying 
away from us with a speed of about 25,000 miles per second. 
It is well to weigh critically the evidence for results like these. As 
regards estimates of nebular distances, the methods used by astrono- 
mers seem entirely adequate. In the nearest nebula individual stars 
can be seen. Some of these stars fluctuate in brightness with a period 
of 514 days. Similar stars, known as Cepheid variables, are found in 
our own nebula, and the distances of a few of them have been deter- 
mined by ordinary engineering methods. It is found that these stars 
are all of about the same size, so that if one Cepheid variable is much 
fainter than another its faintness may be attributed solely to its greater 
distance. The distance of the nearest nebula can thus be determined 
with considerable accuracy by comparing the brightness of one of its 
Cepheid variables with the brightness of a similar star in our own 
galaxy—a star whose distance has been measured by reliable methods. 
Having a good estimate of the distance of one nebula it is legitimate to 
infer that other nebula of the same type are fainter and smaller only 
because they are farther away. It is thus possible to estimate their 
distances. The results of these estimates might give occasional large 
errors, but when a great number of observations are made the indi- 
vidual errors must average out fairly well. 
As regards the shift of the absorption line toward the red, a good 
many attempts have been made to explain it in some other way than 
by the Doppler effect. So far, all these attempts have failed or en- 
countered logical difficulties. During the last few years, however, 
certain evidence has accumulated which has brought about a para- 
doxical situation in the theory of the expanding universe. There are 
some very serious objections to the theory. First, let us suppose that 
our explosion hypothesis is more or less in accord with the facts. After 
all, if the nebulae are now observed to be scattering they must at some 
previous time have been more closely bunched. It is not difficult to 
calculate how long ago it was when the nebulae were all together and 
touching each other. We know how far away they are now, we know 
how fast they are receding, and how their velocity of recession varies 
with the distance from us. These data enable us to calculate the time 
when they must have started. According to Hubble, after all correc- 
tions have been made this starting time was about 1,000 million years 
ago. Unfortunately this is only a fraction of the age of the earth— 
indeed there is evidence that life actually existed on earth that long 
ago. It is difficult to see how our earth could exist in its present form 
