172 BEPORT— 1892. 



The curves show a general tendency to estimate the visibility too 

 high when the interference bands are clear, and too low when they are 

 indistinct. This tendency may be modified by a number of circum- 

 stances ; thus it increases with the refrangibility of the light used ; it 

 is greater when the field contains a large number of bands than when 

 there are but few ; it is greater while the visibility carve is falling than 

 when it is rising ; it does not seem to be greatly affected by the intensity 

 of the light ; finally it varies on different occasions and with different ob- 

 servers. Notwithstanding these disturbing causes, the result, after 

 applying the correction, will rarely be in error by more than one-tenth of 

 its value, and ordinarily the approximation is nauch closer than this.' 



The observations necessary to construct the visibility curves, from 

 which the distribution of light in any approximately homogeneous source 

 is to be deduced, may be made with any form of interference apparatus, 

 which allows a considerable alteration in the difference of path between 

 the two interfering streams of light. 



The apparatus actually employed for this purpose was designed for 

 the comparison of wave-lengths, and while admirably adapted for the 

 observation of visibility curves it contains many parts not necessary for 



• The formula for visibility deduced in the preceding paper is 



in which 



C = \<p(x) cos kxdx, 



S = U) («) sin Jixdx, 



P= [<)(«) <^a-, 



ft = 2irD, 



D = Difference in path, 



and <p(x) represents the distribution of light in the source. 



In this expression no account was taken of the effect of extraneous light, and it 

 was assumed that the two interfering pencils were of equal intensities. It can be 

 shown that the error due to both these causes tends to lower the visibility ; but in 

 either case the correct values may be obtained by multiplying by a constant factor. 



In the first case let e be the intensity of the extraneous light, and V the result* 

 ing visibility ; then by definition — 



^ -(I,+e) + (I. + e)~I, + I., + 2e ' ^"^ ^"^ I. + Ij" ' " (I, + 1.,) (1 + r) ' 



whence V = (1 + r) V. 



In the second case, let p be the ratio of intensities of the interfering pencils ; 

 then it can readily be shown that the resulting intensity is 



I = (l + p-)P + 2p (C cos a-S sin »), 



and hence the visibility is 



^ "l + p2 P ' 

 whence 



2p 



l+p- 

 If the interfering pencils differ by 25 per cent, the factor —x — differs from unity 



by about 4 per cent., so that, in most cases, this cause of error may be neglected. 



