114 



PROCEEDINGS OP THE AMERICAN ACADEMY. 



The first condition is not very difficult to fulfil ; but, in consequence 

 of dust jiarticles which invariably deposit on the glass surfaces, — in 

 spite of the greatest possible precaution,  — it is practically impossible to 

 insure a perfect contact, or even constancy, iu the distances between 

 surfaces.* 



If now instead of the retardation by reflection we make use of the 

 retardation by transmission thi-ough the glass, the difficulty disappears 



almost completely. In particular the 

 air-films are compensated by equivalent 

 thicknesses of air outside, so that it is 

 no longer necessary that their thickness 

 should be constant. Besides, the ac- 

 curacy of parallelism and of thickness 

 of the glass plates necessary to insure 

 good results is now only one fourth 

 of that required of the reflection ar- 

 rangement. 



In Figure 3 let ab =^ s, the breadth 

 of each pencil of rays ; bd = t, the 

 thickness of each element of the eche- 

 lon ; 0, the angle of diffi'action ; «, the 

 angle adb; m, the number of waves 

 of length A corresponding to the com- 

 mon difference of path of the successive 

 elemeuts. The difference of path is 



cos (a + 0) ; or, since is always very 



Figure 3. 



mX 



H- 



t — ad. 



ac ^ 



cos « 



small, 



t 



ac 



(cos a — ^ sin tt) = < (1 — tan a), 



cos a ^ 



I. 



and m\— ijx— \)t ^ sQ 



To find the angle corresponding to a given value d\, differentiate for 



dp. 



A, and we find -— = - 

 a A s 



m — t 



dX 



Putting in this expression the approximate value of m 

 we have 



(.-»^, 



* Nevertheless I have succeeded with ten such plates, silvered on their front 

 surfaces, in obtaining spectra which, though somewhat confused, were still pure 

 enough to show phenomena such as the Zeeman effect, the broadening of lines 

 by pressure, etc. ; but evidently the limit had been nearly reached. 



