504 Mr. A. Ferguson on certain Small 



parallel to the plane of xy. We shall consider the magnitude 

 of the correction to be applied for light which, after re- 

 fraction at the upper surface of the lens, is incident at the 

 symmetrical points P and P'. 



Let R be the radius of the lens-surface and x the radius 

 of the wth dark ring, and let us assume in what follows that 



^andtan 2 ^ (tan^^^j are negligible compared with 



unity. Taking first the case in which the refraction occurs 

 at P, we have from fig. 3 



Fig. 3. 



fy — i' — r' + r, .. . . 

 and ijr — i' — (l). 



Also, if the origin be at 0, 



and therefore , , dy x 



y 



giving 



.!• 



sini|r=g =p, say. 



