Obviously, however, we cannot carry out our calculations in this simple light-hearted way; it would be absurd to suppose that the sun’s last ton of substance will radiate energy at the same rate as his present stupendous mass of two thousand million million million million tons. A series of investigations which culminated in a paper published by Eddington in 1924, disclosed that, in a general sort of way, a star’s luminosity depends mainly on its weight. The dependence is not very precise, and neither is it universal, but when we are told a star’s weight we can say that its luminosity is likely, with a high degree of probability, to lie within certain fairly narrow limits. For instance most stars whose weight is nearly equal to the sun are found to have about the same luminosity as the sun. In general, as might be expected, stars of light weight radiate less than heavy stars, but also—and this could not have been foreseen—the differences in their radiations are far greater than the differences in their weights. The law which we have already noticed to hold for a few stars in the neighbourhood of the sun is true, although in a somewhat different sense, for the stars as a whole—the candle-power per ton is greatest in the heaviest stars. For example, the average star of half the weight of the sun does not radiate anything like half as much energy as the sun: the fraction is more like an eighth. This consideration extends the future life of the sun, and indeed of all the stars, almost indefinitely. A sort of parsimony seems to creep over the stars in their old age; so long as they have plenty of weight to squander, they squander it lavishly, but they contract their scale of expenditure when they have little left to spend. The sand runs slowly through the hour-glass when there is little left to run. In the same way, the average star of double the sun’s weight does not merely radiate twice as much energy as the sun; it radiates about eight times as much. We must keep this in view in estimating the past life of the sun; it shortens the sun’s past life just as surely as the opposite effect lengthens its future life. Observation tells us at what rate the average star of any given weight spends its weight in the form of radiation, and, on the supposition that the sun has behaved like this typical average star at the corresponding stage of its own past history, we can draw up a table exhibiting its gradual change of weight as its life progressed. Selected entries from this table would read somewhat as follows: