398 A, A. Michelson—Interference Phenomena 
same sign as g, the fringes appear in front of the mirrors; if ¢ 
has the opposite sign, the fringes appear behind the mirrors 
To find the form of the curves as viewed by the eye at EK, 
let SE=D; call T the distances between the surfaces at E’, the 
projection of E. From P draw PR parallel to DP’, and RS at 
right angles, and let RS=c. We have then 4, =T +c tan g, 
whence, substituting for c its value D tan 7 
T+(D+P) tan ¢ tani 
/1+tan? i+tan? 6 
If on a plane perpendicular to EEK’ at distance D from E, we 
call x distances parallel to P’C, and y distances parallel to P’D, 
reckoned from the projection of E on thi s plane, then, putting 
a2 (5) 
tang=K a +P=S, we have for the equation to the curves, 
as they would appear on this surface to an eye at 
see ae, or 
/ D? +x? +y? 
A?y? = (48? K? — 4?)x? + 8TSK Dz + (4T?— 4?)D? (6) 
If, numerically, 
4<2SK the curve is a hyperbola, 
4=2SK the curve is a parabola, 
4>2S8K the curve is an Lene 
=0 thecurveisac 
4=0 the curve isa ateatih line, 
All the deductions from equations (4) and (6) have been 
ag Reg rag came verified by experimen 
served that in the most important case, and 
that most likely is occur in practice, namely, in the case of the 
central fringe in white light, we have 4=0, and therefore also 
t,=0; and in this case the central fringe is a straight line 
formed on the surface of the mirrors. Practically, however, it 
is impossible to obtain a roe gas straight line, for the surface 
of the mirrors is never 
It is to be noticed that the central fringe is black, for one of 
the pencils has experienced an external, the other an internal 
reflection from the surface 4, fig. 1. This will not however be 
true unless the plate g (which is employed to compensate the 
effect of the plate aoe is of sada the same thickness as 5, and 
placed parallel wit these conditions are not ful- 
filled, the true result is oe by the effect of “achromatism” 
investigated by Cornu (Comptes Rendus, vol. xciii, Nov. 21st, 
1881). This remark leads naturally to the investigation of the 
effect of a plate of glass with plane sere surfaces, interposed 
in the path of one of the pencils. 
