396 A. A. Michelson—Interference Phenomena 
reflection from the mirrors; a pair of rays signifying two rays 
which have originated at the same point of the source. 
If the area of the luminous surface is sufficiently ied the 
illumination at P will be independent of the distance, form, or 
position of the surface. Suppose, therefore, that the auicbos 
surface coincides with the surface Om,. Its image in Om, wi 
also coincide with Om,, and its image in Om, will be a ee 
” pre 
and the mirrors, and replacing them by t the two images, the 
onsider now a pair of points pp’. Let & be the angle 
formed by the line joining P and p (or p’) with the normal to 
the surface; # and g being both supposed small, 
4=Pp’—Pp=pp’. cos 3. 
The difference between this value of 4 and the true value is 
2Pp. sin’ where ¢ is the angle subtended by pp’ at P. If é 
is a small quantity, ¢ is a small quantity of the second order, 
and sin’ > is a small quantity of the fourth order; conse- 
quently 2Pp sin* — 9 may be neglected. We have therefore, to 
a very close kotlopiuaeee 4=pp’ cos 3; or, substituting 2¢ for 
pp, 2t being the distance base hi the ima ages, at the point 
where they are cut by the li 
4= “94 cos . 
Let cdef, c’d’e’f’, 3, represent the two images, and let 
their Raita be poe with cf, and their inclination be 
f i 
2g. Let P be the point considered ; P’, the projection of P on 
the surface cdef; and PB, the line forming with PP’ the angle 
