186 Proceedings of the Royal Society 
The figure annexed shows that if the incident waves be inclined to 
the grating at such an angle that the perpendicular from any open- 
ing upon the wave surface 
passing through the next 
opening is equal to the wave 
length, the same phase will 
in this case also pass all the 
openings at the same in- 
stant, though derived from different incident waves, and the first 
lateral image will be seen in a direction normal to the grating. 
The same formula will give the wave length in this case, D being 
always the angular deviation from the true image or from the 
direction of the incident light. This is the condition approxi- 
mately realised in the arrangements for measuring the wave length 
about to he described, but as no provision is made for an exact 
adjustment of the grating to the inclination just indicated, and 
as a very minute error in such an adjustment would cause the 
conditions of the experiment to be altogether different from those 
indicated by the figure above, it is necessary to account for the 
appearance of lateral images in the case of light incident at any 
angle, and find a formula for the wave length applicable to that case. 
If, as in the figure below, the incident waves be so inclined to 
the grating that the perpendicular BC, together with the perpen- 
dicular BD, make up the wave 
length, the same phase of vi- 
bration will be situated at A 
and D ; for the same reason, 
behind every two consecutive 
openings, like phases will be 
situated upon surfaces inclined 
at the same angle as AD, that is to say, AD produced will en- 
velope like phases, and the first lateral image will be seen in the 
direction normal to AD. If we denote by I the angle of incidence 
CAB, and as before by D, the angle of deviation CAD, we get 
X = (a + e) {sin I + sin(D-I)}. So long as I and D are small, 
the latter factor is approximately = I + D - I = D = sin D, the 
same as before, so that in that case the error introduced by using 
the formula first obtained with only an approximate adjustment of 
