152 ON A NEW CASE OF INTERFERENCE 



a must be very small, or the incidence very oblique, in order that 

 the fringes should have any sensible breadth. 



We have hitherto assumed that the light has undergone no 

 change by reflexion, excepting the change of direction. Let us 

 now suppose that the phase of the vibration is accelerated, and let 

 us examine the effect produced in the position of the fringes. 



Let the amount of this acceleration be denoted by the angle 

 fnr ; then the differences of the phases will be 



So that the successive fringes will be formed at the points for 

 which 



m being any number of the natural series. But we have already 

 found that X - S = 2 tan ax; so that the points in question are 

 given by the formula, 



x = | (m + /x) A cotan a ; 



the even values of m corresponding to the bright fringes, and the 

 odd values to the dark ones. It is evident from this that the 

 magnitude of the fringes will be unaltered ; and that the only 

 effect of the acceleration is to push the entire system from the 

 edge, the amount of the shifting being equal to juA cotan a. 



In order to submit these results to the test of trial, I employed 

 the apparatus consisting of two moveable metallic plates, which is 

 of so much use in experiments of interference. The plates being 

 closed, so as to form a narrow horizontal aperture, the flame of a 

 lamp was placed behind ; and the light thus diverging from the 

 aperture was received, at the distance of about three feet, on a 

 piece of black glass truly polished, and also horizontal. This 

 reflector was then adjusted, so that its plane might pass a little 

 below the aperture ; or, in other words, that the light might be 

 incident upon it at an angle of nearly 90. It is evident, then, 

 that the light thus obliquely reflected will meet the direct light 

 diverging from the aperture under a very small angle, and with a 

 difference in the lengths of their paths which is capable of indefi- 

 nite diminution. The two lights, therefore, are in a condition to 

 interfere ; and I found, accordingly, that when they were received 

 upon an eyepiece, placed at a short distance from the reflector, a very 



