SIZE AND AGE OF THE UNIVERSE— JEANS 133 



pendulum swinging, it comes to rest after a short time. It has been 

 reduced to rest by its continued impact with molecules of air; in 

 brief, it has shared its energy with these molecules. 



Actual experiment may show that this pendulum comes to rest in 

 a few minutes, but I could calculate this out without experiment. 

 All I need to know is the size and weight of the pendulum, and the 

 density of the air in which it swings. Thus if I come into the room 

 and find the pendulum swinging vigorously, I can conclude, from 

 purely abstract calculations, that it has not been swinging for many 

 minutes; it must have been set into motion only a few minutes ago. 

 But if I find that it is at rest, and that hundreds of other similar 

 pendulums are also at rest, I can conclude that they have stood un- 

 disturbed for many minutes — they may previously have been in 

 motion, but if so, they have already shared their energy with the 

 surrounding molecules of air. 



This tendency to sharing energy pervades the whole of physics 

 and prevails also in astronomy. The laws which govern the motions 

 of the stars show that these also must share their energies with one 

 another, and if they have been left undisturbed for a sufHciently 

 long time, this sharing of energy will be complete. We can calculate 

 how long a time is needed for the process to be effected, and it proves 

 to be a matter of millions of millions of years. Thus if we find that 

 the stars have already shared their energy, we know that they must 

 be millions of millions of years old. 



The method admits of greater refinements. Suppose I have a row 

 of pendulums of different sizes and weights, one of which comes 

 approximately to rest in 2 minutes, while the next requires 4 minutes, 

 others require 6, 8, 10, and 12 minutes, respectively. Suppose a 

 cataclysm of some kind occurs — saj^, an earthquake — and after a time 

 I come into the room and find that the 2, 4, and 6 minute pendulums 

 have already come to rest, while the 8, 10, and 12 minute pendulums 

 are still swinging with varying degrees of force. It is reasonable to 

 conclude that the cataclysm occurred between 6 and 8 minutes ago. 

 With a sufficient number of pendulums, it might be possible to fix 

 the time with considerable precision. 



Now the different kinds of stars form just such a range of pendu- 

 lums. Fortunately, they share their energies at very different rates. 

 When we proceed to observation, we find that in actual fact some 

 types of stars have already shared their energies almost completely, 

 both with other stars and with one anotheu; for other types the 

 process has barely begun. This is shown in the three following 

 tables. 



