Thus, the total luminous energy falling per second from a standard candle on a square centimeter at a distance of 3 m. is 1 erg.[182] Hence the amount falling per second on a body of the size of an atom, i.e., of cross-section , is , but the energy with which an electron is ejected by light of wave-length (millionths millimeter) is , or four thousand times as much. Since not a third of the incident energy is in wave-lengths shorter than , a surface of sodium or lithium which is sensitive up to [Pg 252] should require, even if all tills energy were in one wave-length, which it is not, at least 12,000 seconds or 4 hours of illumination by a candle 3 m. away before any of its atoms could have received, all told, enough energy to discharge an electron. Yet the electron is observed to shoot out the instant the light is turned on. It is true that Lord Rayleigh has shown[183] that an atom may conceivably absorb wave-energy from a region of the order of magnitude of the square of a wave-length of the incident light rather than of the order of its own cross-section. This in no way weakens, however, the cogency of the type of argument just presented, for it is only necessary to apply the same sort of analysis to the case of -rays, the wave-length of which is sometimes as low as a hundredth of an atomic diameter ( cm.), and the difficulty is found still more pronounced. Thus Rutherford[184] estimates that the total -ray energy radiated per second by one gram of radium cannot possibly be more than . Hence at a distance of 100 meters, where the -rays from a gram of radium would be easily detectable, the total -ray energy falling per second on a square millimeter of surface, the area of which is ten-thousand billion times greater than that of an atom, would be . This is very close to the energy with which -rays are actually observed to be ejected by these -rays, the velocity of ejection being about nine-tenths that of light. Although, then, it should take ten thousand billion seconds for the atom to gather in this much energy from the -rays, on the basis of classical [Pg 253] theory, the -ray is observed to be ejected with this energy as soon as the radium is put in place. This shows that if we are going to abandon the Thomson-Einstein hypothesis of localized energy, which is of course competent to satisfy these energy relations, there is no alternative but to assume that at some previous time the electron had absorbed and stored up from light of this wave-length enough energy so that it needed but a minute addition at the time of the experiment to be able to be ejected from the atom with the energy . What sort of an absorbing and energy-storing mechanism an atom might have which would give it the weird property of storing up energy to the value , where is the frequency of the incident light, and then shooting it all out at once, is terribly difficult to conceive. Or, if the absorption is thought of as due to resonance it