the Interferences of Light. 5 



the very small angle at which the rays meet, then we shall 

 readily deduce the relation 



>^ 



c = — cot Q, 



an expression which is in fact identical with that referred to 

 above. Similar expressions will follow for successive values of 

 c measured from the same central point, involving successive 

 multiples of A. 



In reference to the supplementary experiment on the effect 

 of retardation of the undulations, in the displacement of the 

 stripes upon interposing a plate of glass or other medium in 

 the path of one of the rays, we may easily obtain an expression 

 by which the displacement may be calculated : for according 

 to the undulatory theory the velocities in different media be- 

 ing inversely as the refractive powers, we shall have for a 

 thickness t of glass whose refractive power is m, that of air 

 being 1, the difference, or effect of retardation in the two rays, 

 equivalent to what would arise from a difference in the length 

 of their i-outes expressed by 



d = t{m — 1). 



This difference being substituted for the particular multiple 



of A which expresses the difference of routes of the two rays 



in the previous formula, we shall have the displacement of the 



corresponding stripe from the expression, 



w ,N cote 

 c = t{m-\) — 2— • 



(9.) It is obvious that if a piece of clear glass be placed in 

 the diverging beam of light, there is a diffraction both within 

 and without its edge. This circumstance may affect the ex- 

 periment of intercepting' by glass plates one of two interfering 

 rays, in order to show the effect due to the retardation of the 

 undulations in passing through the denser medium. 



Proper precautions are easily taken when we use the light 

 from two small apertures, or (what is the same thing) that from 

 the two sides of an opake object. 



In the corresponding experiment with the obtuse prism, or 

 two reflectors, the same cause produces some little confusion 

 in the appearance, which it is impossible to avoid, and which 

 may at first embarrass the experimenter ; especially when 

 the object is to show, by the shifting of the stripes, the effect 

 of retardation due to the difference of thickness of two plates 

 of glass by slightly inclining one of them; and particularly if 

 the glasses be of any considerable thickness. 



(10.) The following is a simple variation of the experiment 

 which I have adopted, as both completely avoiding any incon- 

 venience 



