668 
PHYSICS: C. BARUS 
This differs from the preceding by the deduction of 2x. The rays again 
terminate in the common wave front Piqs to enter the telescope. Here 
the long rigorous equation reduces practically to 
■n\ = 2ha'-2h''a/d 
The wv effect predominates, the cc' effect is intermediate and the xy 
effect very small if d is large, as already instanced. If a = = 1 
meter, d = \ kilom., X = 6 X 10~^ cm., the three terms of the first 
equation give respectively 6 X 10^, 10^, and 60 fringes. 
To the first order of small quantities the equations may be written, 
n \ = 2 b a (cosec /3 + cot jS) and n \ = & 2 a cot /3. They may also 
be obtained geometrically by letting fall a normal from to the near 
prism face, prolonging Tz backwards and using the isosceles triangle 
obtained. In this case x 2 { — w) cos^ (45° — a) — {z' — z) + 
y — CIS, the path difference and reduces to the above equation. So long 
as the nose of the prism is near the axis of rotation, the equation of 
first order quantities need not be modified. 
A very essential correction however is still needed. In the practical 
apparatus the mirrors m and n rotate on a rigid radius, h, whereas in the 
diagram (if 6 = j8 — a and o- = ^ -\- a), h elongates on the right and 
contracts on the left to h" = ^ sin /3 / sin 5, and h' = h sin ^ / sin cr. 
Hence the mirrors on the right and left are displaced normally by 
ih" — h) cos jS / 2 and {h — h') cos /3 / 2. The path difference introduced 
is thus {})" — h) (cos a + cos b) -\- {h — h') (cos a + cos d) which to the 
first order of small quantities may be written 2 h a { \ / sin j3 — sin |8 
+ cot jS). If this quantity is deducted from the right of the above 
equation for path difference and direct rays there remains simply X 
= 2 5 q: sin /3. This therefore is the equation to be used in interpreting 
the observations so that generally 2 A N cos i / A a = 2 b sin ^ where 
i = jS / 2 for the micrometer at n. 
In the case of reversed rays the conditions on the left remain the 
same as before ; whereas on the right the mirror is set at an angle 13/2 
to the rail. Hence the normal displacement is {b'^ — 6) sin /3 / 2 and 
the angle of incidence 90° — / 2 — a). Thus the full path difference 
here to be deducted is {b'' — b) (cos a — cos 6) + 2 (& — b') (cos a + 
cos 0-) which to the first order of small quantities reduces to 2 b a cot 
j8. Hence the equation for reversed rays is simply 2 A N / A a = 0 
and we have an interesting appearance of terms of the second order 
only, which I will here omit. In general glass paths may be compen- 
sated at pleasure. 
The observations made with the present apparatus, though quite 
interesting, are beyond the purpose of the present note. The two 
