PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 37 



collar carried simply a pointer. To stop the second pencil, I attached a wooden collar to the 

 brass collar, and inserted in it a Nicol's prism, which was turned till the more refracted pencil 

 was extinguished. In a few of the latest experiments the Nicol's prism was dispensed with, 

 and the more refracted pencil stopped by a screen with a hole which allowed the less refracted 

 pencil to pass. In the other instrument, which I used for the analyzer, the brass collar carried 

 a vernier reading to 5'. In this instrument the doubly refracting prism admitted of being 

 removed, and I accordingly removed it, and substituted a Nicol's prism, which was attached by 

 a wooden collar. The Nicol's prism was usually inserted into the collar at random, and the 

 index error was afterwards determined from the observations themselves. 



The light employed in all the experiments was the sun light reflected from a mirror placed 

 at the distance of a few feet from the polarizer. On account of the rotation of the earth, the 

 mirror required re-adjustment every three or four minutes. The continual change in the 

 direction of the incident light was one of the chief sources of difficulty in the experiments and 

 inaccuracy in the results ; but lamplight would, I fear, be too weak to be of much avail in 

 these experiments. 



The polarizer, the grating, and the analyzer stood on the same table, the grating a few 

 inches from the polarizer, and the analyzer about a foot from the grating. The plane of 

 diffraction was assumed to be parallel to the table, which was nearly the case ; but the change 

 in the direction of the incident light produced continual small changes in the position of this 

 plane. In most experiments the grating was placed perpendicular to the incident light, by 

 making the light reflected from the surface go back into the hole of the polarizer. The angle 

 of diffraction was measured at the conclusion of each experiment by means of a protractor, 

 lent to me for the purpose by Prof. Miller. The grating was removed, and the protractor 

 placed with its centre as nearly as might be under the former position of the bright spot 

 formed on the grating by the incident light. The protractor had a pair of opposite verniers 

 moveable by a rack ; and the directions of the incident and diffracted light were measured by 

 means of sights attached to the verniers. The angle of diffraction in the different experiments 

 ranged from about 20° to 60°. 



The deviation of the less refracted pencil in the doubly refracting prism of the polarizer, 

 though small, was very sensible, and was a great source both of difficulty and of error. To 

 understand this, let AB be a ray incident at B on a slip of the surface of the plate contained 

 between two consecutive grooves, BC a diffracted ray. On account of the interference of the 

 light coming from the different parts of the slip, if a small pencil whose axis is AB be incident 

 on the slip, the diffracted light will not be sensible except in a direction BC, determined by 

 the condition that AB + BC shall be a minimum, A and C being supposed fixed. Hence 

 AB, BC must make equal angles with the slip, regarded as a line, the acute angles lying 

 towards opposite ends of the slip, and therefore C must lie in the surface of a cone formed by 

 the revolution of the produced part of AB about the slip. If AB represent the pencil coming 

 through the polarizer, it will describe a cone of small angle as the pointer moves round, and 

 therefore both the position of the vertex and the magnitude of the vertical angle of the cone 

 which is the locus of C will change. Hence the sheet of the cone may sometimes fall above 

 or below the eye-hole of the analyzer. In such a case it is necessary either to be content to 



