Leaving actual figures aside for the moment, we may find it easier to think in terms of the scale-model we constructed in the first chapter (p. 88). We took our scale so small that the stars were reduced to tiny specks of dust; we noticed that space is so little crowded with stars that in our model the specks of dust had to be placed over 200 yards apart; to put it all in a concrete form, we found that Waterloo Station with only six specks of dust left in it is more crowded with dust than space is with stars. Now let the model come to life, so as to represent the motions of the stars. To keep the proportions right, the speed of the stars must of course be reduced in the same proportion as the linear dimensions of the model. In this the earth’s yearly journey round the sun of 600 million miles had become reduced to a pin-head a sixteenth of an inch in diameter, or, say, a fifth of an inch in circumference. As the stars move through space with roughly the same speed as the earth in its orbit, we may suppose the yearly journey of each speck of dust in our model also to be about a fifth of an inch. Thus each speck of dust will move about an inch in five years, roughly 16 feet in a thousand years—or say a ten-millionth part of a snail’s pace. Even if two specks started moving directly towards one another it would take them about 20,000 years to meet. For how long must six particles of dust, floating blindly about in Waterloo Station, move at this pace before each has had enough close meetings with other specks of dust for their energy of motion to become thoroughly redistributed? The mathematician, carrying out exact calculations with respect to the actual weights, speeds and distances of the stars, finds that the observed degree of approximation to equipartition of energy shews that gravitational interaction must have continued through millions of millions of years, most probably from 5 to 10 millions of millions of years. This, then, must be the length of life of the stars. It is a stupendous length of time, and before finally accepting it we may well look for confirmation from other sources. In estimating the age of the earth we were able to invoke assistance from all kinds of clocks, astronomical, geological and physical; happily they all told much the same story. In the present problem only astronomical clocks are available, but fortunately there are no fewer than three of these, and again they agree in saying much the same thing.