A.— MATHEMATICAL AND PHYSICAL SCIENCES 33 



Suppose we carry this dualism into concepts that are fundamentally 

 corpuscular and assert that matter may have a wave aspect ? This is 

 the notion put forward by Louis de Broglie, who postulated that, associated 

 with a particle having momentum mv, there is. a wave of wave-length X 

 given by X = hjtnv. As radiation which shows the fundamental wave- 

 property diffraction also exhibits corpuscular properties, so electrons 

 which are conceived primarily as corpuscular may be expected to exhibit 

 wave- properties ; and they do so. If a beam of electrons be passed 

 through thin foil, diffraction phenomena are observed which are perfectly 

 consistent with the wave-length postulated by de Broglie. If, moreover, 

 leaving the sub-atomic world, we deal with molecular rays of hydrogen or 

 helium, we may allow them to be reflected from a crystal surface and may 

 observe diffraction phenomena consistent with a de Broglie wave-length 

 of the right magnitude ; and we may collect the reflected waves as an 

 ordinary gas. 



But all this merely emphasises the dualism of the wave and corpuscular 

 aspects of matter — a dualism which is now disappearing under the analysis 

 of the last few years. The analysis, which is essentially mathematical, 

 has introduced the notion of probability into our estimates, say, of position. 

 We describe the wave which accompanies a corpuscle by means of an 

 equation which will contain an expression for the amplitude of the wave ; 

 and the amplitude at any point gives us a measure of the probability of 

 finding the corpuscle at that point ; if the amplitude vanishes anywhere 

 the probability of finding the corpuscle at that point vanishes also. The 

 concept of an electron as a definite entity at a definite point in space is 

 replaced by a probability pattern which, very dense in a certain locality, 

 rapidly thins as we move away from that locality. In fact, if we fix our 

 attention on the densest part of a given pattern, the probability of finding an 

 electron at a distance of io~ 13 cm. therefrom becomes vanishingly small, and 

 most of us may be content to use the concept of an electron almost in our 

 accustomed manner, realising that it has become a little fuzzy at the 

 edges. 



Despite the impending disappearance of this dualism, the story of the 

 discovery of sub-atomic particles is most easily told in particle fashion. 

 The discovery of the electron is now more than a generation old, as is the 

 discovery of the a-, (3- and y-rays of radium, and the a-rays or particles — 

 fast-moving helium nuclei — provided an atomic projectile which in the 

 hands of Rutherford became a most potent weapon for exploring the 

 intricacies of atomic structure. 



Electrons, a-particles and protons are electrical in origin ; they may 

 therefore be deflected by electrostatic fields. They move and so con- 

 stitute an electric current ; they may, therefore, be influenced by magnetic 

 fields. Information concerning their charges and masses may therefore 

 be deduced from their behaviour when subjected to such fields. Further, 

 special means have recently been devised for the generation of controlled 

 fields of high potential which may be used to accelerate charged particles 

 subjected to their influence. In this manner it has been found possible 

 to produce swift protons which may be used to bombard various elements. 

 We can in fact now load, aim and discharge our atomic rifle almost at 



