187 
of Edinburgh, Session 1869 - 70 . 
the grating is inconsiderable. The same is the case if either I 
alone or D - I be very small. 
By differentiating the formula we get 
cos I + cos (D - I) -1^=0 . (2). 
dD _ cos (D - I) - cos I _ _ cos I 
’ ’ dl cos (D - I) cos (1) - 1) ' 
(and if D = 21) = 1 - cos 1 = 0, 
cos I 
that is, D is constant for small variations of the position of the 
grating, or angle of incidence, while the variation of the latter 
by condition (2) does not affect the value of X calculated from the 
formula. There is, therefore, an advantage in observing with the 
grating adjusted to bisect the angle between the directions of in¬ 
cidence and diffraction, that being the position in which a small 
error in the adjustment has the least effect upon the result given 
by the formula, which becomes in this case, 
X = 2(a + e) sin 5. . 
-J 
In the arrangements now to be described, in which we use two 
sources of light, one on each side of the normal to the grating, 
we make the angle (D — I) approximately vanish, and use the mean 
of the two angles of incidence in the formula 
X —- (a + e) sin I. 
By neglecting the part (a + e) sin (D - I), which is positive for 
the one light, and negative and of the same magnitude for the 
other, as is plain from the method of observing, we introduce no 
error into the result. 
AC, BD, are sections of two rectangular pieces of tin bent into 
a cylindrical form round the glass funnels of two paraffin lamps. 
Their edges come short of meeting so as to leave a slit at A and B 
of about 1 millimetre in breadth. These slits are partially covered 
with tin as shown immediately below, where they are drawn as 
they appear to the eye of the observer. A thread is stretched 
round the two cylinders, partly shown between A and B. EE 
