X-RAYS AND CRYSTALS 377 



This may readily be shown to be so if 



aa = h|\ 



a|3 = h 2 \ (I) 



a(i-y) = h 3 X 



where h lt h 2 , h 3 are integers and a,/3, 7 the cosines of the angles 

 which the direction considered makes with the cubic axes. 



This is analogous to the equation which holds for a line 

 grating: 



X sin 6 = nA 



where n is the order of the spectrum ist, 2nd, 3rd, etc., a 

 the "constant" or interval between successive lines and 6 the 

 angle which the direction of the telescope axis makes with 

 the normal to the grating when a line of wave length X lies on 

 the cross wire. It means that the wave from the atom at the 

 origin is hj and h 2 wave lengths behind that from its neighbours 

 along O X and O Y respectively, h 3 ahead of that from its 

 neighbour along O Z. 



These equations can at once be tested. By knowledge of the 

 position of a spot on the photographic plate, the a (3 7 of its pencil 

 can be calculated and since from equation (I) 



£. = £ _ l ~y 



h, h 2 h 3 



the values of a, /3, 1—7, for the spot ought to be in a simple 

 numerical ratio. As a matter of fact, this is found to be so ; the 

 values of a,/3,i—y for spots are in ratios such as 1:3:1 or 

 1:9:3. In no case is it necessary to assume a number h x , h 2 or h 3 

 greater than 10 in order to fit these values of a, /3, 1 —7 to a whole 

 number ratio. This affords strong confirmation to the theory 

 that the spots are due to interference. 



The numbers h 1( h 2 , h 3 are the most convenient parameters 

 with which to define an interference maximum. They give at 

 once the position of the spot on the photographic plate and the 

 wave length to which it corresponds. 



By choosing for h u h 2 , h 3 any three integers, one obtains the 

 position of a spot which ought to appear in the photograph, if 

 the incident radiation contain the wave length corresponding to 

 these three integers. 



To each spot in the photograph in fig. 2 numbers h lf h 2 , h 3 

 can be assigned in this way. If this be done and the numbers 

 corresponding to the most marked spots are arranged approxi- 



