Helmholtz calculated that the sun’s contraction over the 6000 years of recorded history would have reduced its diameter only 560 miles—a change that would not have been noticeable to the unaided eye. Since the development of the telescope, two and a half centuries earlier, the decrease in diameter would have been only 23 miles and that was not measurable by the best techniques of Helmholtz’s day. Working backward, however, it seemed that 25 million years ago, the sun must have been so large as to fill the earth’s orbit. Clearly the earth could not then have existed. In that case, the maximum age of the earth was only 25 million years. Geologists and biologists found themselves disturbed by this. The slow changes in the earth’s crust and in the evolution of life made it seem very likely that the earth must have been in existence—with the sun delivering heat and light very much in the present fashion—for many hundreds of millions of years. Yet there seemed absolutely no other way of accounting for the sun’s energy supply. Either the law of conservation of energy was wrong (which seemed unlikely), or the painfully collected evidence of geologists and biologists was wrong (which seemed unlikely),—or there was some source of energy greater than any known in the 19th century, whose existence had somehow escaped mankind (which also seemed unlikely). Yet one of those unlikely alternatives would have to be true. And then in 1896 came the discovery of radioactivity. The Energy of Radioactivity It eventually became clear that radioactivity involved the giving off of energy. Uranium emitted gamma rays that we now know to be a hundred thousand times as energetic as ordinary light rays. What’s more, alpha particles were being emitted at velocities of perhaps 30,000 kilometers per second, while the lighter beta particles were being shot off at velocities of up to 250,000 kilometers per second (about 0.8 times the velocity of light). At first, the total energy given off by radioactive substances seemed so small that there was no use worrying about it. The amount of energy liberated by a gram of uranium in 1 second of radioactivity was an insignificant fraction of the energy released by a burning candle. In a few years, however, something became apparent. A lump of uranium might give off very little energy in a second, but it kept on for second after second, day after day, month after month, and year after year with no perceptible decrease. The energy released by the uranium over a very long time grew to be enormous. It eventually turned out that while the rate at which uranium delivered energy did decline, it did so with such unbelievable slowness that it took 4.5 billion years (!) for that rate to decrease to half what it was to begin with.