PHYSICS: C. BARUS 
121 
to ascertain whether this would still be feasible in the apparently more favor- 
able, but also more difficult case of two internal reflections. In figure 3, white 
light arrives from a collimator at L and strikes an auxiliary mirror m, before 
reaching the half silver N. If m is capable of rotating both on a horizontal 
and vertical axis as well as sliding right and left in the diagram, it greatly 
facilitates adjustments of angle and location of rays. The two beams bcdef 
and bfedc reunite at b after passing the glass cylinder G (rotating around the 
axis a) and are observed by the telescope at T. As the spectra (after refrac- 
tion at c and /) are reflected 3 and 2 times respectively, the fringes of non- 
reversed spectra will be obtained covering the whole length of spectrum. A 
glass G of low index of refraction will here usually be preferable. 
In case of a half silver mirror at a small glancing angle there are usually 
two pairs of bright spectrum images, and one fainter pair, apart from very 
faint ones. One bright and one faint pair carry identical fringes and the 
spectrum images may be small enough to be separated. In case of clear 
glass, however, there is practically but one pair of bright images, and they 
carry fringes when properly superposed. 
3, Equations. — The first question to be elucidated is the nature of the con- 
ditions of refraction. From the figure, in view of the symmetry of the ar- 
rangement, if b is the breadth of the ray parallelogram and R the radius of 
the cylinder, ^ its index of refraction, h the distance of the chord C from the 
axis A, i and r the angles of incidence and refraction of the rays dC or d'C': 
sin i = sin 2r = b/2R (1) 
sin r = h/R (2) 
Ij, = 2 COST = b/2 h (3) 
The relations remain the same iib/2r is constant. If the (small) value b = 
10 cm. is inserted into the equation, the conditions may best be shown by a 
graph for i and //. It will then be seen that for diameter 2r between 10 and 
11 cm., the available indices of refraction of the glass would increase from 1.4 
to 1.7 roughly, while the angle i falls from 90° to about 65°. Hence the 
experiment requires the interfering rays to impinge near the outer limits of the 
cylinder. 
