358 
PHYSICS: DA VIS AND TERRILL Proc. N. A. S. 
Since b is small, we write 
1^-2 = 1 + 25 
whence 
sin ^ = [1 - cos'^ ^ (1 + 2 b)y^' = [sin^ 6 -2b cos'' 6]'^' 
and again neglecting terms containing higher powers of 5 . 
sin = e - b (2) 
stnd ^ ^ 
Taking arc sin of each side, we have since b is small, 
e' = d-b — ^ • J- 
sin 6 cos 6 (3) 
e' = e - b cot d 
Now in this equation, B is the crystal angle measured, hence by determin- 
ing the angles of any characteristic line for several orders, it will be possi- 
ble to determine 5, or at least to find the limits of its magnitude. The 
angles being measured, those of higher orders are reduced to the equivalent 
first order angle, so that all angles may be compared directly. The pro- 
portion that each is affected by refraction being known from (3), the abso- 
lute value of b is readily determined. 
Instead of using (3), it is possible to substitute (2) in the relation 
n \ = 2 d sin ' 
obtaining, since b is small 
n X 
2 sin 6, 
d {I - b cot^ dn) (4) 
thus determining b from the increase in apparent grating space with order. 
However, since the limits of error have to be carried through in the compu- 
tations, the previous method seems to be more convenient. 
The spectrometer used has been described elsewhere. ^ The tube 
was of the water cooled type with a molybdenum target. Measurements 
of 6 were made for the first three orders of the Kai line, using a crystal of 
clear Iceland spar. The measurements w^ere gone over several times and 
it was found that the angles could be repeated to within 15'^ This is 
just about the limit of accuracy of the instrument which was determined 
by other methods to be about 20 '^ 
The following mean values were obtained. 
^ = 6° 42' 43'' ^ 10" 
62 = 13° 30' 45" ± 10" 
Os = 20° 31' 22" =t 10" 
where the additional terms represent the limits of error. 
