This method of estimating geological time has been described as the “Geological hour-glass.” We see how much sand has already run, we notice how fast it is running now, and a calculation tells us how long it is since it first started to run. The method suffers from the usual defect of hour-glasses, that there is no guarantee that the sand has always run at a uniform rate. Geological methods suffice to shew that the earth must be hundreds of millions of years old, but to obtain more definite estimates of its age, the more precise methods of physics and astronomy must be called in. Fortunately the radio-active atoms discussed in the previous chapter provide a perfect system of clocks, whose rate so far as we know does not vary by a hair’s breadth from one age to another. We have seen how, with the lapse of sufficient time, an ounce of uranium disintegrates into 0·865 ounce of lead and 0·135 ounce of helium. The process of disintegration is absolutely spontaneous; no physical agency known in the whole universe can either inhibit or expedite it in the tiniest degree. The following table shews the rate at which it progresses: _History of One ounce of Uranium_ Initially: 1 oz. uranium No lead After 100 million years 0·985 oz. uranium 0·013 oz. lead ” 1000 ” 0·865 ” ” 0·116 ” ” ” 2000 ” 0·747 ” ” 0·219 ” ” ” 3000 ” 0·646 ” ” 0·306 ” ” and so on. Thus a small amount of uranium provides a perfect clock, provided we are able to measure the amount of lead it has formed, and also the amount of uranium still surviving, at any time we please. When the earth first solidified, many fragments of uranium were imprisoned in its rocks, and may now be used to disclose the age of the earth. We are not entitled to assume that all the lead which is found associated with uranium has been formed by radio-active integration. But, by a fortunate chance, lead which has been formed by the disintegration of uranium is just a bit different from ordinary lead; the latter has an atomic weight of 207·2, while the former is of atomic weight only 206·0. Thus a chemical analysis of any sample of radio-active rock shews exactly how much of the lead present is ordinary lead, and how much has been formed by radio-active disintegration. The proportion of the amount of lead of this latter kind to the amount of uranium still surviving tells us exactly for how long the process of disintegration has been going on. In general all the samples of rock which are examined tell much the same story, and the radio-active clock is found to fix the time since the earth solidified at 1400 million years or more. The clock cannot tell us for how long before this the earth had existed in a plastic or fluid state, since in this earlier state the products of disintegration were liable to become separated from one another.