204 
These have been joined to one vector in fig. 1. Thas the action 
of every instrument where only normally propagated light is used, 
can be determined in any point Q by the aid ofa vector fan, which 
revolves round O as a whole in the direction of the 
A arrow. The intensity of the square will be the result 
2 of the vectors. Suppose that for all the points P,, P,, 
P,,...P; the phases of their disturbances in Q are 
Aj compared with the phase of the disturbance given by 
a point P,, the vector of which be AO,, hence a 
0 point over which the shortest optical way passes from 
Fig. 1. the source to the point of observation, then 
LAGOA is=em, 7 A,OA,=c,m, ete, in which the constants 
¢c,,c, ete. depend on various lengths, angles, and indices of refraction. 
We shall call the direction of the vector OA, the time-direction 
for the sake of brevity, because it only depends on time; it will 
appear to play a prominent part in our reasoning, and we shall 
henceforth draw it always vertical, and omit the axis of projection. 
We have drawn here a fan whose vertex is small; in reality it will 
probably contain several times 27. Vectors namely corresponding 
with paths LQ, which differ a whole number of waves in length, 
will indeed be superposed in the figure, but will not be drawn as 
one vector. This happens only when the paths are optically of 
exactly the same length. Nor need the end points of the vectors 
form a continuous curve. 
Let us elucidate this by constructing the fan for an echelon. It 
consists of a few smaller fans, which are arranged in O like spokes 
in a wheel, and whose number is equal to the number of plates of 
the echelon. Only three of them are drawn in fig. 2. 
All the points P, lying in a vertical line on the front plane of 
a plate lie optically equally far from the source *), and at the same 
time equally far from Q. Their vectors are therefore united to a 
single vector OA, the length of which is accordingly proportionate 
to the length of the vertical line ®). Any given point of the lefthand 
side of the first plate can, therefore, be considered as the point 
P, just mentioned. : 
The indices at the points P of fig. 3 indicate which vector in 
fig. 2 originates from their vertical line. When the echelon is viewed 
at an angle @ with the normal, the rays from P, and P, will 
dan 
1) The light strikes in the direction d in fig. 3. 
2) In this way it is also possible to find the influence of diaphragms placed before 
the plates, which will later on be made use of. 
