in 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



Tin- first condition is oof very difficult to fulfil; but, in consequence 

 of dust particles which invariably deposit <>n the glass surfaces, — in 

 Bpite of the greatest possible precaution, — it is practical!} impossible to 

 insure a perfect contact, or e\en constancy, in the distances between 

 surfaci " 



[f now instead of the retardation by reflection we make use of the 

 retardation by transmission through tin- glass, tin- difficulty disappears 



almost completely. In particular the 



air-films are compensated 1>.\ equivalent 



i i thicknesses of air outside, so that it is 



no longer necessarj that their thickness 

 should In- constant. Besides, the ac- 

 curacy uf parallelism and of thickness 

 of the gla<s plates invc.-*ary t" insure 

 gund results is now only one fourth 

 of that required of the reflection ar- 

 rangement. 



In Figure 3 let a b = s, the breadth 

 of each peucil of rays ; b d = <. the 

 thickness of each element of the eche- 

 lon ; 9, the angle of diffraction ; «. the 

 angle adb; in, the number of waves 

 of length A. corresponding to the com- 

 mon difference of path of the successive 

 elements. The difference of path is 



cos (a + 6) ; or, since 6 is always verj 



m\ 



Figure 3 

 fit — ad, 



a c = 



cos a 



t 



- (cos a — 6 sin a) = t (1 — tan a), 

 cosu 



small, 



cos a 



and m A = (/x — 1) t -f s 0. I. 



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



o i d0 ] ( '' " 



A, and we find -r- = - ( m — i , 

 dk s \ d\ 



Putting in this expression the approximate \alue of m = (fi — 1 I , 

 we have 



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



surfaces, in obtaining Bpectra which, though somewhat confused, were still pore 



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

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



