FUNDAMENTAL IDEA OF WAVE MECHANICS 313 ally operating with isolated mutually independent light rays. The new undulatory mechanics corresponds to the wave theory of light. What is gained by changing from the old view to the new is that the diffraction phenomena can be accommodated or, better expressed, what is gained is something that is strictly analogous to the diffraction phenomena of light and which on the whole must be very unimportant, otherwise the old view of mechanics would not have given full satisfaction so long. It is, however, easy to surmise that the neglected phenomenon may in some circumstances make itself very much felt, will entirely dominate the mechanical process, and will face the old system with insoluble riddles if the entire mechanical system is comparable in extent with the waveleng ths of the"waves of matter"which play the same part in mechanical processes as that played by the light waves This is the reason why in these minute systems, the atoms, the old view was bound to fail, which though remaining intact as a close approximation for gross mechanical processes, but is no longer adequate for the delicate interplay in areas of the order of magnitude of one or a few wavelengths It was astounding to observe the manner in which all those strange addi- tional requirements developed spontaneously from the new undulatory view, whereas they had to be forced upon the old view to adapt them to the inner life of the atom and to provide some explanation of the observed facts Thus, the salient point of the whole matter is that the diameters of the atoms and the wavelength of the hypothetical material waves are of approxi- mately the same order of magnitude. And now you are bound to ask wheth- er it must be considered mere chance that in our continued analysis of the structure of matter we should come upon the order of magnitude of the wavelength at this of all points, or whether this is to some extent compre- hensible. Further, you may ask, how we know that this is so, since the material waves are an entirely new requirement of this theory, unknown anywhere else. Or is it simply that this is an assumption which had to be made? The agreement between the orders of magnitude is no mere chance, nor is any special assumption about it necessary; it follows automatically from the theory in the following remarkable manner. That the heavy nucleus of the atom is very much smaller than the atom and may therefore be consid ered as a point centre of attraction in the argument which follows may be onsidered as experimentally established by the experiments on the scatteringFUNDAMENTAL IDEA OF WAVE MECHANIC S 313 tually operating with isolated mutually independent light rays. The new undulatory mechanics corresponds to the wave theory of light. What is gained by changing from the old view to the new is that the diffraction phenomena can be accommodated or, better expressed, what is gained is something that is strictly analogous to the diffraction phenomena of light and which on the whole must be very unimportant, otherwise the old view of mechanics would not have given full satisfaction so long. It is, however, easy to surmise that the neglected phenomenon may in some circumstances make itself very much felt, will entirely dominate the mechanical process, and will face the old system with insoluble riddles, if the entire mechanical system is comparable in extent with the wavelengths of the "waves of matter" which play the same part in mechanical processes as that played by the light waves in optical processes. This is the reason why in these minute systems, the atoms, the old view was bound to fail, which though remaining intact as a close approximation for gross mechanical processes, but is no longer adequate for the delicate interplay in areas of the order of magnitude of one or a few wavelengths. It was astounding to observe the manner in which all those strange addi￾tional requirements developed spontaneously from the new undulatory view, whereas they had to be forced upon the old view to adapt them to the inner life of the atom and to provide some explanation of the observed facts. Thus, the salient point of the whole matter is that the diameters of the atoms and the wavelength of the hypothetical material waves are of approxi￾mately the same order of magnitude. And now you are bound to ask wheth￾er it must be considered mere chance that in our continued analysis of the structure of matter we should come upon the order of magnitude of the wavelength at this of all points, or whether this is to some extent compre￾hensible. Further, you may ask, how we know that this is so, since the material waves are an entirely new requirement of this theory, unknown anywhere else. Or is it simply that this is an assumption which had to be made? The agreement between the orders of magnitude is no mere chance, nor is any special assumption about it necessary; it follows automatically from the theory in the following remarkable manner. That the heavy nucleus of the atom is very much smaller than the atom and may therefore be consid￾ered as a point centre of attraction in the argument which follows may be considered as experimentally established by the experiments on the scattering