CLASSICAL THEORY OF LIGHT 739 



the case when the grathig is a series of windows letting Hght through 

 towards the camera, separated by walls which intercept the light. 

 Such is also the case when the grating is a series of mirrors reflecting 

 light towards the camera, separated by windows which let it escape 

 or by absorbing surfaces which swallow it up. Such is the case when 

 the instrument is a surface of metal ploughed into furrows, so that 

 the reflecting-power towards any assigned direction varies from point 

 to point across the furrow, and varies periodically as one moves across 

 the system of furrows. Such is the case if the waves traverse or are 

 reflected from all points of the grating equally, but with phase- 

 retardations which vary periodically across the grating-surface. Such 

 is the case when the instrument is a surface containing oscillators 

 able to vibrate in unison with the incident waves and able to radiate 

 new waves because of their vibration, these oscillators being evenly 

 spaced or else clustered in identical groups which themselves are 

 evenly spaced. Such in fact is in general the case whenever the 

 "grating" is any object with a periodic structure, the details of which 

 are able in any manner known or unknown to perturb the passage of 

 the waves; for anything which confuses or impedes the even onward 

 progress of a train of waves, whether it be a vibrator which they set 

 into oscillation or merely an inert impenetrable obstacle in their way, 

 becomes thereby the source of a new system of undulations. 



Wave-lengths of light therefore are determined by setting up in the 

 path of the light-stream something which has a periodic structure, of 

 which the period is known; locating the diffraction-maxima, if such 

 there be; and using the formula (7), provided that the object is plane 

 (another, which we shall eventually derive, is used if the object is 

 three-dimensional and the waves travel across its structure). Location 

 of one maximum would not as a rule suffice, for without further 

 knowledge its order could not be identified. One must measure 

 sufficiently many maxima to infer from the ratios of their values of 

 sin d what their orders are. On the other hand, understanding of the 

 precise mode and mechanism of the action of the elements of the 

 grating upon the light is not required, desirable as it may be. Perhaps 

 we do not properly understand how the atoms of a crystal scatter even 

 X-rays; and certainly the founders of the wave-mechanics did not 

 foresee that crystals scatter electron-waves. Yet Davisson and Ger- 

 mer determined the wave-lengths of these latter in 1927 with the 

 same equation wherewith Fraunhofer in 1821 had ascertained the 

 wave-lengths of the lines of the solar spectrum — the very equation, 



X = -sin dn, 

 n 



