REVERSED AND NON-REVERSED SPECTRA. 73 



% be the number of long fringes, to restore the original coincident phase; i.e., 

 let x longer fringes gain one long fringe on the x shorter fringes. Then 



that is, x fringes constitute a new period. From the above data 



It follows that the length of coincident strips is subject to 

 e = CI(HI i ) = Cznz = Cnz/x or C = 7 



C\ Cz 



where C is the new constant. This would place the fringes beyond the coarse 

 group below, but naturally C is enormously dependent on small errors in C\ 

 and Cz. 



Finally, if equation (9) be taken, the X is to be increased to 



M = X/(i -cos 6> m ) =X/(i - Vi - (wX/D) 8 



in order that equations similar to the above may apply. Thus 



n'M MM' 



In the diffractions of the first order of spectra m = i and 



io 3 M' = 4.747 C' 3 = 0.0330 



These are the coarse order of fringes, so that 



n= i 2^ = 0.033 



10 0.33 



100 3.3 , etc. 



Fringes are thus still strongly available, even if the distance apart of the 

 plates is over 2 cm. 



If the diffractions are of a second order of spectra, m = 2 , 



ioW=i.oi6 io 3 M'=i.i6s C"' 3 =io- 3 X7.85 



These fringes are therefore of intermediate order, since 



n= i 2 = 0.0078 cm. 



10 0.0785 



100 0.785 



They would be enhanced, since they cooperate with the double diffractions 

 of the first order. 



33. Observations and corrections. Preliminary work. The following 

 work was done merely with a view to testing the equations and with no 

 attempt at accuracy. The grating was left unsilvered, so that the ruled sur- 



