Aston has recently discovered a new isotope (see p. 118) of uranium, called actino-uranium. As uranium and its isotope have different periods of decay, the relative abundance of the two is continually changing. From the ratio of the amounts of these substances now surviving on earth, Rutherford has calculated that the age of the earth cannot exceed 3400 million years, and is probably substantially less. These two physical estimates of the time which has elapsed since the earth solidified stand as follows: _Age of the Earth by the Radio-active Clock_ 1. From the lead-uranium } ratio in radio-active } More than 1400 million years. rocks } 2. From the relative abundance } of uranium and } Less than 3400 million years. actino-uranium } Various astronomical methods are also available for determining the time since the solar system came into being. Here the “clocks” are provided by the shapes of the orbits of various planets and satellites. The orbits do not change at uniform rates, but their changes are determined by known laws, so that the mathematician can calculate the rates at which change occurred under past conditions, and hence, by totalling up, can deduce the time needed to establish present conditions. The following two estimates are both due to Dr H. Jeffreys: _Age of the Solar System by the Astronomical Clock_ 1. From the orbit of Mercury ... From 1000 to 10,000 million years. 2. ” ” the Moon ... Roughly about 4000 million years. While these various figures do not admit of any very exact estimate of the earth’s age, they all indicate that this must be measured in thousands of millions of years. If we wish to fix our thoughts on a round number, probably 2000 million years is the best to select. THE AGES OF THE STARS We now turn to the far more difficult problem of determining the ages of the stars. We shall not approach it by a direct frontal attack, but start far away from our real objective. Let us in fact start at the extreme other end of the universe, and delve a bit further into the properties of a gas. EQUIPARTITION OF ENERGY IN A GAS. We have pictured a gas as an indiscriminate flight of molecule-bullets. These fly equally in all directions, occasionally crashing into one another, and in so doing, changing both their speeds and directions of flight. We have seen that the total energy of motion undergoes no decrease when such collisions occur. If one of the molecules taking part in a collision has its speed checked, the other has its speed increased by such an amount that the energy lost by one molecule is gained by the other. Total energy of motion is “conserved.”