Interference Fringes and Focal Length. 767 



with considerable accuracy. This at once suggests an ex- 

 ponential equation of the form 



(i) 



d -l = -AY 



(where A is a constant), or 



J 



f = - jA .,N, 



(2) 



from which we obtain 



F = F £" AT * as the equation required, 



30 

 28 

 26 



5' 



10 J 3 



.1 



! 

























i 











\ 1 







































\l 















c 



-ysc. 



/ 



a. 

 12° 



Tan oc 

 ■ZJ2G 















\ 

















T. 





6" 



/4° 



■/. 



IS/ 

 f9S 















. ■ 



o 







































\ 



v \ 







































* 











































"e( 



3I.V 





































\ 







*\ 











































^ 



































V\ 

















































"* '• 



\' 



.-% 



?> 4 































v 







>«p 



<?w 



































*■*-.. 















Tot, 



^/77<? 



'//?e 





















**k 



% 



:*- 









^■■: 



""-• 



— 



"-- 







/Vo. o/" /P/>y^ 



Measurement of the angle made with the axis of N gives 

 the following values for A : — 



Quartz -2126 



Tourmaline *1051 



Mica -2492 



A is necessarily a mere number, and it is of great interest 

 to speculate as to its nature. Since monochromatic light was 

 not available, it is evidently useless to attempt to identify A 

 with any function of the index of refraction or bi-ref ringence 

 of the crystals used. 



If we invert equation (1), we obtain the result that the rate 

 of decrease of the number of fringes with focal length is 

 proportional to the reciprocal of the focal length itself. 



These results, though very elementary, seem to show that 

 another case in nature has been found to add to the list of 

 known phenomena following a logarithmic law of decay. 



