PHYSICS: C. BARUS 
671 
duced will be 2e cos i. Similarly if the normal displacement of the plate 
P is ^'and the angle of incidence i' , the path difference will be 2e' cos i' . 
As in the preceding experiment the mirror at n may be a half silver, 
so that the ray, d, passes through it and may then be returned in its 
own path by a mirror at n" , on a fixed standard but provided with a 
micrometer. The displacement of this mirror parallel to itself over a 
distance introduces the path difference 2e, while during this motion 
the rays np or n'q are now stationary. Beams of light do not pass 
through each other and the interferences are kept at full intensity 
throughout. The glass path at n compensates the glass path PP' 
The air path excess Inn" on the right must be specially compensated 
by an offset in d, as explained above. 
7. Equations. — The rigorous equations for this case are cumbersome. 
If in figure 4, m and n are in the same phase and Pp is symmetrical, 
there will be no path difference at p. When Pn is rotated over an 
angle a into Pn' , the path on the right becomes nn' + n'g + qs while 
{ps, wave front) the path on the left remains mp as before. The path 
difference is thus the difference of these quantities to which however 
the increased glass path at PP' would have to be deducted. If the 
angle SnP is j8 and Pnp y, the values of the branch paths may be found 
to be (since nP = mP = b) is ^ — a = 8 and y — a = t 
mp = np = h / cos y 
nn' = & sin a / sin b 
n'q = 5 sin /3 / sin 5 sin r 
Hence qs and the path difference are compHcated expressions which 
need not be inserted here. 
If a is small, so that differential expressions may be introduced, the 
rigorous equation (to an approximation of the second order in a) is 
finally equivalent to n \ = h a {\ cos - y) ) /sin /?. If /3 = 90°, 
n \ = h a -\- p a cos 7, where p is the distance Pp. The same expres- 
sions may be obtained geometrically by prolonging n'P and T'q and 
treating the isosceles triangle produced. 
For the case where the ray Sn prolonged returns on itself as from 
n" , in figure 4, n being a half silver plate, the quantity nn' = 2x = 
2 b a / sin 8 must be deducted. Hence n \ = b a (1— cos {(3 — y) ) / 
sin /3. When 7 = 0, this equation coincides with the case of the prism 
method apart from the factor 2. 
It is finally necessary to apply the correction for the occurrence of a 
constant radius of rotation, whereby the mirror n is both rotated and 
displaced. If the distances Pn = b and Pn' = b", the normal displace- 
ment is e (b" — b) cos — y) / 2. The angle of incidence being 
