208 
contain J cos4a lr for absolutely monochromatic light, for which 
can also be written J cos 4 al (m—m). But for single light the intensity 
must be an even function in m, as we saw; hence cos 4a lm—m) 
can only occur in that combination which reduces it to 
J cos a Im, which is even in m, i.e. it can only be met with in 
forms like: 
cos Anr lm J cos Aar | (m—m) — sin An lm J sin 40 1 (m—m)_ or 
cos An Um J cos An la — sin Anlm Jsin4ale. . . . . . .. (8) 
ba 
To extend reversely the formula of intensity for single light to 
that for compound light we must substitute y («)d«# for J in the 
former, and then integrate with respect to «. The grouping (8) then 
passes into cos 4x lm C—sin4almS, exactly that of equation (4). 
The preceding has therefore proved that none of these instruments 
can yield a second equation between C’ and S which is independent 
of equation (4). C and S can, therefore, not be separated from 
‘their combination, it seems, therefore, that p («) cannot be solved. *) 
5. 
It is now obvious that the first thing to do is to examine whether 
the function ~(#) can perhaps be determined, if the light in some 
instrument or other can undergo a phase shifting «, which differs 
from ze, it being of no consequence whether it is caused by metal 
reflections or other phenomena. Suppose that part of these points P, 
now marked by double or triple accents, receives such light. The 
angles of the corresponding vectors with the time direction would 
have to be c,"m, c,'m..., ¢,'"m, cm, if the light travelled in the 
same directions, but everywhere in a normal way; now they are, 
therefore, c'm + «or c''m tata, according as on the point P" 
1) In passing we may remark that C and S do not occur combined in another 
way in the formula of intensity that determines the distribution of intensity for 
the echelon over the whole focal plane of the telescope. This depends for the different 
points on-a parameter, which we might call /’. | have proved by a computation 
which is left out here that this function of /’ satisfies a differential equation of the 
second order, in which only combinations of C and S of the kind as in equation 
(4), to be taken for some values of / in connection with /’, occur as coefficients. 
Thus the dependence between the intensities in the image of reflection of the 
echelon and that in the image of interference in MicHELSoN’s interferometer had 
been proved purely analytically. Though the formula of intensity for the echelon 
could be greatly modified by the supposition that diaphragms of a particular shape 
were placed before the glass plates, such a differential equation of the second order 
remained of force all the same, and so the dependence continued to exist. 
