C. Bar us — Axial Colors of the Steam Jet and Coronas. 225 



Axial 



Disc 



d 



n 3 



cl/D 



color 



color 



cm 



cm 





b 



{fog) 



(-00015) 



•008 



8-8 



y 



bg 



22 



•on 



1-1 



p 



gy 



25 



13 



6-1 



V 



y 



27 



14 



6-4 



b 



ro 



29 



15 



6-5 



From this it appears that the strong axial blues of the first 

 order must belong to particles even larger than -0001 cm in 

 diameter, and that all particles are more than six times larger 

 than would be demanded for interferences. 



3. .Recently I have considered the case of a lamellar grating, 

 in which diffractions are obtained from a uniform succession 

 of alternately different thicknesses of clear glass. Experiments 

 with such gratings were originally made by Quincke and there 

 is a full theoretical treatment by Verdet. The behavior of 

 this grating differs from that of the usual kind in the occurrence 

 of an additional factor 



cos 2 (-n-d(n — 1) +7ra sin 8)/X 



where n is the index of refraction, d the difference in thick- 

 ness between thin strips of width a and of thick strips of width 

 b, 8 the angle of diffraction. Hence for axial color, 8= 0, minima 

 occur at (n — l)d = (2m-\-l).\/2, whereas for Newton inter- 

 ferences the minima occur for a thickness of D in case of 

 transmitted light, where 2/u,_Z)=(2m4-l)A/2 ; whence 



d[D = 



n — 1 



In case of water n—1'33, or d/D= 8*0. This result holding for 

 a grating of transparent strips, is so near the above datum 

 d/D^>6 for a medium of transparent particles (for which there 

 is no theory), that it seems reasonable to conclude, that the 

 actual colors are referable to the same type of phenomenon in 

 both cases. The need of observations through long columns 

 in case of fog particles suspended in air is additionally con- 

 firmative, since the contribution of color due to one particle 

 must be exceedingly small. 



4. One might be tempted to explain the disk colors in the 

 same way, for in case of deviation 8 from the axial ray 



D/d= (n — 1 )/2w + a sin 8/2dn. 



But here there are several insuperable difficulties, which refer 

 the disk color to a different origin. In the first place, they 

 are much more intense than the axial colors and are seen dis- 

 tinctly through very small thicknesses of fog ; disk colors are 

 ^apparently abruptly complementary to the axial colors and 



