210 
of just now, and which had already undergone the phase shifting 
discussed then, is besides subjected to a metal reflection, which can 
take place for all four of them in exactly the same way, this will 
mean for each of the beams a same phase shifting p. This latter 
does not deform the fan, as it revolves as a whole over an angle 8, 
since all the points P have participated in the new change of phase. 
For some four beams of other frequency the fan will indeed be 
rotated through another angle 8, but fans drawn up for different 
frequencies, must yet not be composed vectorially, because two 
different kinds of light can never interfere. Hence also when com- 
pound light falls on the apparatus, metal reflections will have no 
influence on the intensity, if each of the beams undergo them an 
equal number of times in the identical way; this latter peculiarity 
is always met with in the current interferometers for reasons of a 
practical nature. The same thing applies for the phase-shiftings 
which take place with total reflections. 
6. 
We must, therefore, devise an instrument in which first of all 
the condition of identical metal reflections and of identical 
total reflections is fulfilled, but that besides has the property to be 
illuminated for one half by rays which apart from metal and total 
reflections, have undergone none or only phase sbiftings of a, and 
to be illuminated for the other half by rays which apart from metal 
and total reflections, have been besides subjected to an extra 
phase shifting «, which differs from 2, and must be independent of 
the number of waves; the rays of the first and of the second kind 
must besides be coherent in order to be able to interfere. 
When we now put the question what constant phase-shiftings we 
have now at our disposal, we come to the following answer: 
1. a phase-shifting of in case of reflections against a denser 
medium ; 
2. a phase-shifting of 2, when a beam of light is narrowed to pass 
through a focus *); 
3. a phase-shifting > forward, when a beam must pass through 
a focal line *). 
The last two shiftings take place respectively in the focus and 
in the focal line; the latter alone differs from zr, and this is the 
only one we can therefore use for our purpose. We shall, therefore, 
1) Gouy, Ann. de Chimie et de Physique (6), 24. 1891. 
