A. A. Michelson— Interference Phenomena, ete. 395 
Art. XLVI.—ZJnlerference Phenomena in a new form of Refrac- 
tometer ; by ALBERT A. MICHELSON, 
N an,experiment undertaken with a view to detecting the 
relative motion of the earth and the luminiferous ether (Am. 
Journal of Science, No. 128, vol. xxii,) it was necessary to pro- 
duce interference of two pencils of light, which had traversed 
paths at right angles with each other. This was accomplished 
foll he light from a lamp at a, fig. 1, was separated 
into two pecans at right angles, be, bd ‘by the plane-parallel 
viewed by the eye, or by a small eneope at e. 
It is evident that, so far as the interference is concerned, the 
apparatus may be replaced by a film of air whose thickness is 
—ed, and whose angle is that formed by the image of d in 4, 
with ¢ 
The problem of St hosiery in thin films has been studied 
by Feussner, but his equations do not appear to give the ex- 
planation of the phabunretia observed. In a articular, in the 
“Annalen der Physik und Chemie,” No. 12, 1881, on page 558, 
Feussner draws the conclusion that the taiteciens fringes are 
straight lines, whereas, in the above described apparatus they 
are in general curves: and there is but one case—that of the 
central fringe in white light—which is straight. 
e 
Fig, 1. Fig. 2 
I have therefore thought it worth while to sBemit the solu- 
tion of the problem for a film of air, for small angles of inci- 
dence and neglecting sia ontle reflections; and though the 
solution is not perhaps adapted to the eneral problem, it 
accounts for all the shaun phases in the special case. 
Let Om,, Om,, fig. 2, be two plane mirrors whose intersec- 
tion is projected at O, and whose mutual helaaion isg. The 
illumination at any point, P (not n ecessarily in the en of 
the figure), will depend on the mean difference of phase 
the pairs of rays starting from the source and reaching P, air 
