Retardations, and on the Theory of FoucauWs Test. 165 



appear from the sketch that the whole of it was not used. 

 Thus in (1) X/ia would be about 5X10 -5 ; and the accuracy 

 with which yu, was determined (about + '00002) is of the order 

 that might be expected. 



It is of interest to trace further and more generally what 

 the wave theory has to tell us, still supposing that the source 

 of light is from an infinitely narrow slit (or, what comes to 

 the same, a slit of finite width at an infinite distance), and 

 that the apertures are rectangular. The problem may then 

 be supposed to be in two dimensions*, although in strictness 

 this requires that the elementary sources distributed uni- 

 formly along the length of the slit should be all in one phase. 

 The calculation makes the usual assumption, which cannot 

 be strictly true, that the effect of a screen is merely to stop 

 those parts of the wave which impinge upon it, without 

 influencing the neighbouring parts. In fig. 1, A represents 



Fig. :. 



Q 



A 



•3 



the lens with its rectangular aperture, which brings parallel 

 rays to a focus. In the focal plane B are two adjustable 

 screens with vertical edges, and immediately behind is the 

 eye or objective of a small telescope. The rays from the 

 various points Q of the second aperture, which unite at a 

 point in the focal plane of the telescope, or of the retina, may 

 be regarded as a parallel pencil inclined to the axis at a small 

 angle </>. P is a point in the first aperture, AP = «£, BQ = £, 

 AB=/. Any additional linear retardation operative at A 

 may be denoted by R, a function of x. Thus if Y be the 

 velocity of propagation and /e = 27r/\_, the vibration at the 



* Compare Wave Theory, Encyc. Brit. 1888; 'Scientific Papers,' 

 vol. iii. p. 84. 



