472 Mr. J. Walker on the Admissible Width of 



mentally by employing very dilute solutions and a large 

 accumulator-battery, such as that recently employed by Pro- 

 fessors Trowbridge and Richards *. 

 20th May, 1898. 



Note added May 27th. — Dr. Van Everdingen informs me 

 that he has discovered the slip in his calculation, and agrees 

 with the remarks made above concerning the experiments of 

 Florio and Bagard. 



XLYIII. On the Admissible Width of the Slit in Interference 

 Experiments. By James Walker, M.A.\ 



1. TNa paper published in the Philosophical Magazine for 

 JL August 1889, Lord Rayleigh has discussed the question 

 of the admissible width of the slit forming the proximate 

 source of light in interference experiments, and has pointed 

 out that " In Fresnel's experiment, whether carried out with 

 mirrors or with biprism . . . the condition for distinctness is 

 simply that the width of the slit be a small proportion of the 

 width of the bands \" This rule, which applies to the case 

 in which the variation of the width of the bands is produced 

 by a change in the mirrors or biprism, the distances of 

 the slit and screen of observation from the apparatus 

 remaining constant, requires modification when it is the 

 variation of the distances that causes the alteration of the 

 width of the bands, the apparatus remaining otherwise 

 unchanged ; for it is an experimental fact that in this latter 

 case, as the bands become finer, the slit may be made wider 

 without loss of distinctness. A more detailed investigation 

 leads to this result, and shows moreover that a progressive 

 widening of the slit causes a periodic disappearance of the 

 bands, the system of bands at the successive reappearances 

 being alternately bright and dark centred §. 



2. We require first the relative retardation at a point of 

 the screen of observation of the streams emanating from any 

 point of the slit. 



FresneVs Mirrors. — Let the line of intersection of the 

 mirrors be the axis of ?/, and let the axis of z be taken so as 

 to pass through the image of the centre of the slit in the 



* Phil. Mag. February (1897). 



t Communicated by the Author. 



\ Phil. Mag. [5] xxviii. p. 80 (1889). 



§ I find that this result of the progressive widening of the slit has 

 already been given by M. Ch. Fabry in his thesis for the degree of Doctor 

 of Science, published at Marseilles in 1892, and regret that I was not 

 aware of this interesting work until my paper was in type. 



