A.— MATHEMATICAL AND PHYSICAL SCIENCES 31 



wave-length. What have nineteenth-century theories of radiation to say 

 to this ? Their answer is clear, and gives a curve which coincides with 

 the cocked-hat curve in the region of long wave-lengths but exhibits 

 no maximum, and moves completely away from the experimental curve 

 as the wave-length decreases. It was this complete disharmony between 

 classical theory and experimental fact that led Planck, in the last year of 

 the nineteenth century, to supply a solution giving a curve which closely 

 fits the cocked-hat curve, which has revolutionised physical science and 

 which has incidentally provided the language with a new verb, ' to 

 quantise.' What do we mean when we speak, for instance, of quantising 

 energy ? To quantise a physical quantity is to restrict its magnitude 

 to a number of discrete, separated values, which are integral multiples of a 

 certain selected unit. Planck assumed that a hot body consisted of a 

 number of oscillators which in their simplest form may be conceived as 

 massive particles oscillating in straight lines with definite frequencies, 

 in simple harmonic fashion. The energy of such an oscillator is easily 

 enough calculated, and the drastic assumption made is that the possible 

 values of the energy of the oscillator are to be restricted to a series of 

 integral multiples of a unit which is itself proportional to the frequency, 

 so that the unit may be written as hn, where n is the frequency and h is a con- 

 stant known as Planck's constant. And energy is emitted in integral bundles 

 or quanta, the indivisible unit of measurement having the magnitude hn. 



Turn now to another experiment, quite inexplicable on the lines of the 

 older wave-theory. An insulated negatively- charged plate of zinc, when 

 exposed to ultra-violet light, loses its charge— loses electrons, that is, in 

 terms of our picture. Certain facts emerge from a close study of the 

 experimental conditions. If, for example, the frequency of the light is 

 below a certain threshold value, then, however great the intensity may be, 

 and whatever the length of time of the exposure, the zinc plate keeps its' 

 charge. If, however, the frequency is raised above this threshold value 

 the charge begins to leak away at once, and this, though the intensity of 

 the incident light be so small that, on the basis of the wave-theory, it 

 would take days to accumulate sufficient energy to release an electron 

 with the kinetic energy which it is observed to possess. Moreover, the 

 rate of emission of electrons increases proportionately with the increase 

 of intensity of illumination. If we take the view that light consists of 

 photons, bundles or quanta of energy each of magnitude hn, travelling 

 with the velocity of light, then if, say, a surface atom is struck by a photon, 

 and emits an electron which has to do work in freeing itself from the 

 surface, we may equate the sum of this work and the kinetic energy with 

 which the electron leaves the surface to the energy possessed by the original 

 photon. A little consideration will show that this explanation meets 

 observed facts in a way quite impossible to a classical wave-theory. 



Here, then, in this so-called photo-electric effect, and in the experi- 

 mental facts of the distribution of energy in the spectrum, we have two 

 simple happenings which cannot in any way be squared with classical 

 theory. Consider, now, very briefly some of the elementary facts of 

 spectroscopy— another region of physics to which quantum ideas have 

 been applied with brilliant success. We have travelled far to-day from 



