TO SPECTROSCOPIC MEASUREMENTS. 7 



tui'biiig causes, the result, after applying the correction, will rarely be in 

 eiTor by more than one tenth of its value, arid oi'dinarily the approximation 

 is much 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 diiference of path between the two interfer- 

 ing streams of light. 



The apparatus actually employed for this piu'pose was designed for the 

 comparison of wave-lengths, and while admu'ably adapted for the observa- 

 tion of visibility curves, it contains many parts not necessary for this use. 

 Fig. 1, Plate I., presents the plan of an arrangement which, while showing 

 all the essential parts, is much less comphcated. Starting from V, a vacuiun- 

 tube containing the substance whose radiations are to be examined (and 

 which is usually inclosed in a metal box in order that it may be raised to 

 any required temperature), the light is analyzed by one or more prisms 



* The formula for visibility deduced in the former paper {Phil. Ma<j., vol. xxi ; p. 340), is 



T7-2 C" + S' 



P' 



in which C = / 'f (oc) cos kr d.c, 

 8 = I 'f (.r) sill Iw clc, 

 P = f'f (x) dt, 



k = 2-n, 



D = Difference in path, 



and 'f (.r) 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 coiTeet 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 resulting vi.sibility ; then, by 

 definition, 



„,_(J.+6)-(J,+e)_ I,~I, . ^ -f 2e_ ^^ y._ 1,-1, 



(I,+e) + {I,+e)~ I,+I^+2e' I,+I^ ' {I,+I^)a + r) 



whence F= (1 + r) V. 



In the second case, let ? be tlie ratio of intensities of the interfering pencils ; then it can readily be 

 shown that the resulting intensity is / = (1 + p-) P + 2p (C cos ii-—S sin ft), 



and hence the visibility is F" = -^i£— . / C^ + S^ _ whence V= if — V 



l + p2 t p 2p 



If the interfering pencils differ by 25 per cent., the factor -^±f- differs from unity by about 4 per 

 cent. ; so that, in most cases, this cause of error may be neglected. 



