86 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



If the elementary equation of 47 is used, the results will not differ much 

 from those of the grating, provided the same approximations are made. For 

 if C is Airy's constant, we have in succession, d being the diameter of the 

 particle, 



(i) sin 



(2) sin i=(x y) /R', sin 6 = y/R z 



If y/R and (x y)/R f are small in comparison with i and R'i = R'i, practically, 



dx dx 



= CR' = 



or if y = o and the plate G is at F, 



Using the equation with lycopodium, a difficulty experienced is because the 

 colors, on projection, are reddish-brown or vague. But on reducing the red- 

 dish center at r to a dot, and treating it as a blue minimum, X = 49Xio~ 6 , 

 the following values for the diameter of the spores were obtained : 



C K x d 



1.22 250 cm. 5.7 cm. 0.0026 cm. 

 5-5 -0027 



This seemed to agree with the size of the particles seen under the microscope. 

 The diameter usually quoted is 0.0032 cm. The question would resolve itself 

 into a decision of the color, which is here a minimum and is therefore of no 

 further interest. If we regard the red edge of the disk as a blue minimum and 

 use the goniometer of chord 5 and radius R = ^o cm., s/2R= i.22\/d, whence 

 sd = 7 3. 2\ = 0.0036. In my experimental work with fog particles I used a 

 somewhat smaller constant, ds = 0.0032. 



50. Experiments with large coronas, annular source. Coronas by reflec- 

 tion. The coronas due to water particles are not intense enough to be avail- 

 able for projection, unless perhaps a fog-bank more than 12 inches thick is 

 used. The screen has to be placed so close to the fog-chamber (R very small) 

 and the color varies so rapidly along R, that the semblance of axial color (angle 

 of diffraction zero) found above, quite vanishes. The particles as a rule range 

 in size from somewhat above io~ 3 cm. to somewhat above io~ 4 cm., after 

 which the coronas become filmy. The work must therefore be done subjec- 

 tively, as usual, and the direct light to the eye may be blotted out by a small 

 screen or disk, placed between the point source and the eye. In such a case 

 the colors beyond the edge of the disk are very vivid. 



