672 
PHYSICS: C. BARUS 
(/5 + 7) / 2 — a, the corresponding partial path difference works out as 
{h" — b) (cos (/3 — a) + cos (7 — a) ) ; or finally in full as & a (cos^ ^ 
+ cos cos 7) / sin ^. Subtracting this from the first equivalent of 
n X above, the equation to be used for non-reversed rays becomes 
n \ = b a (sin jS + sin 7) when a is small. As the angle of incidence at 
the mirror at # is (/3 + 7) / 2, and if A iV is the displacement of this 
micrometer, the practical equation is thus 2 A N cos (jS + 7) / 2 = 
b (sin jS + sin 7) A a. 
For reversed rays the norma] displacement is {b'^ — b) sin (/3 — 7) / 2 
and the path difference for small a therefore b a cot /3 (cos (7 — a) 
— cos (/3 — a) ). Subtracting this from the corresponding equivalent 
of n X, the equation for reversed rays is thus n \ = b a (sin ^ — sin 7) 
or in the practical form as the incidence is now zero, 2 A N — b (sin jS 
— sin 7) A a. 
All equations contain the distance of the remote object at 5, in 
sin jS, so that d occurs as a second order quantity. 
Observations (also to be omitted here) were made in great variety 
with this apparatus, a knife edge prism at S cleaving the white beam 
from a collimator. To obtain strong ful] spectrum ellipses, the rays 
T and must not only be parallel but interpenetrate so far as possible. 
If p and q are a few millimeters apart all fringes vanish. For this ad- 
justment the compensator is again convenient and for reversed rays it 
must be of the offset type described. One may notice that the slit 
images are here mirror images of each other. Nevertheless brilHant 
achromatics may be obtained even from rough surfaces, if narrow, by 
the succession of operations given above. Both these and the spectrum 
fringes are available for measurement. The achromatics are most 
serviceable if tranverse to the slit image as they then rise and fall with 
the play of the micrometer. To obtain them, the center of ellipses 
must be placed in the vertical through the telescopic held; but above or 
below it. In other words the spectrum fringes are to be horizontal. 
Even when (as in the preceding section in view of the half ellipses) 
horizontal spectrum fringes are precluded, the achromatic fringes will 
be found by adjusting as if the former were to appear. The best ach- 
romatics consist of but one or two fringes, sharply in black and white, 
with three or four much fainter fringes on either side. These occur 
frequently, but how to differentiate them systematically from the other 
groups of 10 or 20, more nearly uniform and therefore less serviceable 
fringes, I have yet to learn. All must be treated with caution, however, 
for they move through the field of the telescope so rapidly that if lost it 
is usually expeditious to seek for them again through the spectrum fringes. 
