1273 
Further I wil substitute £/, by a, 7/, by 8, °/, by y,- then 
a’ + 6 + y?—1, thus in this notation we have to fix our attention 
upon the interference of the radiation from those points for which the 
numbers & satisfy the equation 
k, (1—a) — Bk,—y k, = 0. 
Now if this equation determines a great number of points, the 
pulses originating from the molecules will interfere without differ- 
ence of phase. 
This will be the case when the plane 
w (1—a) — yB—zy = 0 
passes through the molecules of the crystal. Now, a plane through 
molecules may in general be represented by 
A ae ali en ok enon EE ele) 
where abc are whole numbers, that we constantly suppose to be 
reduced to their smallest values possible. The values of afy, where 
maximal intensity is thus to be found on account of the cooperation 
of the points of a plane, we can find by putting 
ie 
a b C 
while «a? + 8? + y? must be 1. From this we find B=0, y= 0, 
a=1 (ie. the light transmitted directly, a point of interference 
that is not observable) and 
b? Het — aq? 
CS eS Se 
a? + b? +? 
dab 
= 2 2 ae 3 (5) 
0. + b +c 
; —2ac 
i | 
a +b? HC | 
Now we can easily show the direction thus found to agree with 
the direction in which the ROnrGEN-beam would be reflected if the 
chosen plane rich in molecules should be a mirror. For the angle 
of the normal of (4) forms with the z-axis an angle of which the 
= . a mew aS 
cosine is , the plane of incidence has for equation: 
OEE 
Cy —bz=—=0, the direction cosines of the reflected ray are a's’ y'. 
Thus we have 
at AE 
Bc—vy'b=—0 | ene ee 
a? pt y= 
