It is one thing to feel a limitation of time-scale irksome, ruling out ideas and explanations which are otherwise plausible and attractive; it is another thing to produce definite evidence against the time-scale. I do not think that astronomers had _in their own territory_ any weapon for a direct attack on the Helmholtz-Kelvin hypothesis until the Cepheid variables supplied one. To come to figures: δ Cephei emits more than 700 times as much heat as the sun. We know its mass and radius, and we can calculate without difficulty how fast the radius must contract in order to provide this heat. The required rate is one part in 40,000 per annum. Now δ Cephei was first observed carefully in 1785, so that in the time it has been under observation the radius must have changed by one part in 300 if the contraction hypothesis is right. You remember that we have in δ Cephei a very sensitive indicator of any changes occurring in it, viz. the period of pulsation; clearly changes of the above magnitude could not occur without disturbing this indicator. Does the period show any change? It is doubtful; there is perhaps sufficient evidence for a slight change, but it is not more than ¹⁄₂₀₀th of the change demanded by the contraction hypothesis. Accepting the pulsation theory, the period should diminish 17 seconds every year--a quantity easily detectable. The actual change is not more than one-tenth of a second per year. At least during the Cepheid stage the stars are drawing on some source of energy other than that provided by contraction. On such an important question we should not like to put implicit trust in one argument alone, and we turn to the sister sciences for other and perhaps more conclusive evidence. Physical and geological investigations seem to decide definitely that the age of the earth--reckoned from an epoch which by no means goes back to its beginnings as a planet--is far greater than the Helmholtz-Kelvin estimate of the age of the solar system. It is usual to lay most stress on a determination of the age of the rocks from the uranium-lead ratio of their contents. Uranium disintegrates into lead and helium at a known rate. Since lead is unlike uranium in chemical properties the two elements would not naturally be deposited together; so that the lead found with uranium has presumably been formed by its decomposition.[30] By measuring how much lead occurs with the uranium we can determine how long ago the uranium was deposited. The age of the older rocks is found to be about 1,200 million years; lower estimates have been urged by some authorities, but none low enough to save the contraction hypothesis. The sun, of course, must be very much older than the earth and its rocks.