EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 87 



When an annular source is used, the path of the cone or cylinder of light 

 through the fog is highly illuminated and the diffraction is both inward and 

 outward from this shell. The shadow of the disk of the annulus, therefore, 

 necessarily remains permanently dark, so that this should be small and the 

 cone as divergent as the fog-chamber permits. The colors are quite brilliant, 

 in spite of the fact that fewer particles are used than in the case of an unob- 

 structed point source. 



In fig. 48, if FF is a fog-chamber, ww and w'w' elements of the conical shell 

 of light, a position of the eye of E behind the fog-chamber may be found, at 

 which the whole interior of the cone flashes into the uniform color of the 

 disk. For this purpose i must be small or zero, or the shell nearly cylindric, 

 in which case, if R is the distance of the eye from the center of the chamber, 

 s/R the aperture of a given color minimum, the elementary equation 

 becomes 



In this case 5 is constant and R is variable. It is found difficult to use this 

 method practically. 



An interesting accompaniment of these experiments is the occurrence of 

 vivid color when the eye is in a proper position on the illuminated side of the 

 fog-chamber, as, for instance, at E' or E". In other words, there is also vivid 

 diffraction in connection with the reflected light, a phenomenon which it is 

 difficult to detect in case of the absence of the annular screen A , since all the 

 fog is illuminated. These colors come from both the outside and the inside of 

 the cone. When the colors fade, or when there is much directly reflected 

 light, they may be restored by a Nicols prism, as this on orientation cuts off 

 the reflected light only. The diffracted colors are in no case polarized, whether 

 seen by transmitted or reflected light. 



c/l 



FIG. 48. 



Experiments made at some length with these annular sources, supplied 

 with both polarized and unpolarized light, did not lead to further results 

 worthy of note. They showed clearly that the axial and disk colors can not 

 be explained as suggested and produced above, in case of the grating, however 

 many points of resemblance there are. In fact, if with regard to fig. 48 we 

 write 



sin (*+0) = Cl/d 



