221- 
to advance. He then') gets Ci) =P» V(U, and will therefore 
find from (7): 
p (2) = evo cos 4 lx dl 
0 
mt (26) 
in which P= |¢(«) dz is therefore a constant. 
We need not make this hypothesis; and it is exactly in this that 
the great significance of the method lies. When in spite of this we 
do submit to this restriction, we shall find that the curves I and II 
become dependent on each other. According to equation (23) and 
(24) we have namely: 
2 cos 42 lm C (I) — 2 sin Aar Im 8 (I) = fl (cl) 
2 sin Aar lin C (1) + 2 cos 42r lm S (l) = — FIT (cl) 
so that SO would lead to: 
— II (cl) — tg Aa lm X I (cl)?) 
Further the quantity V was a quantity that was not easy to 
estimate, and could, strictly speaking, only be determined from 
photometrical observations; it appears from its intricate definition 
J, a ae tee : 5 
= that it is not continuous, and accordingly can never 
ee y ee ee 
be registered, but must be determined point for point. Equation (26), 
which is based on Micnerson’s visibility curve, holds therefore only 
for a symmetrical distribution of the energy and is not quite exact 
even in this case, while the V-curve is difficult to obtain, and then 
only very faint. 
Summing up we come to the conclusion that in the discussed 
arrangement we have found a means to read the distribution of 
energy, both over a narrow and over an extensive spectral region 
1) After neglecting some terms mentioned in footnote 2. 
*) Substituting this in equation (25), we should have expressed © (x) only by 
the aid of the curve J, and in this special case the cylinder lenses seem not to 
have been required; but in order to know m we must know ZI at least for one 
value of cl; hence the use of the cylinder lenses is inevitable even in this simple 
case, when we wish to work mathematically exactly. For the determination of 
Jmax — Jmin MICHELSON has considered C(/) and S(l) as constants in the 
differentiation with respect to /; besides for S=O we find ((l) = PX V(U) only 
for those values of / that satisfy S (J) = — tg 4 lim XC (U), hence for an infinite 
number of values of 7, but not for a continuously infinite number, which would, 
however, be required by mathematics if equation (26) is to follow from equation (7). 
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