203: 
Prof. Ornstein requested me to investigate whether such an equation 
might not be obtained from the distribution of intensity in the 
refraction image in the echelon. The result of this investigation is 
that if the intensity formula no matter of what instrument, contains 
C or S, it must always contain both of them. And that in the 
combination in which they already occurred in equation (4), unless 
one makes use of an artifice to be specified later on. Without this 
C and S cannot be solved, and ¢ (2) can, therefore, not be determined. 
We shall first prove that for absolutely monochromatic light the 
intensity is always an even function of the number of waves, when 
we premise that the light in the apparatus propagates normally, 
1. e. that a change of phase is accompanied with a proportional 
variation of path, so that e. g. reflection against a denser medium, 
inetal and total reflection must be excluded. 
A point Q, where we measure the intensity, receives its light 
from certain points P of the instrument, which in their turn are 
again illuminated by the source L. The points P are in different 
phases, because they receive the light from the source each by 
another way. As we have everywhere assumed the normal propa- 
gation of the light, the differences of phase will exclusively depend 
on differences of paths expressed in numbers of waves, and therefore 
1 = ; : en 
be proportionate to En which the factors of proportionality 
depend on lengths, angles, indices of refraction ete. We shall leave 
dispersion out of consideration, because in the instrument that is 
to be devised later on this will be anyway excluded. Also optically 
the paths, which the light from the points P must still pass over 
before it arrives at the point of observation Q, will not be of 
equal length, so that other differences of phase are added to the 
already existing ones, which others on account of the normal propa- 
gation of the light will exclusively rest on differences of path, and 
will therefore be proportional to m, so that the deviations to which 
the points P finally give rise in Q, present mutual differences of 
phase which are proportional to 1. When these deviations are 
represented as projections of vectors whose angle with the axis of 
projection is equal to the corresponding phase, then the points P, 
over which paths of light run from ZL to Q, which are equally 
long in number of waves, give vectors that overlap. 
14 
Proceedings Royal Acad. Amsterdam. Vol. XXII. 
