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XXX. On the Application of Interference Methods to Spec- 

 troscopic Measurements. — II. By Albert A. Michelson*. 



[Plates V.-VIII.] 



THE theoretical investigation of the relation between the 

 distribution of light in a source, as a function of the 

 wave-length, and the resulting " visibility curve " has been 

 given in a paper bearing the same title as the present one in 

 the ' Philosophical Magazine ' for April 1891. 



The physical definition of " visibility " there adopted is 



in which Ij is the intensity at the centre of a bright inter- 

 ference-band, and I 2 the intensity at the centre of the ad- 

 joining dark band. In order to interpret the actual curves 

 obtained by observation of interference-fringes, it is first 

 necessary to reduce the results of the eye-estimates of visi- 

 bility, which may be designated by Y e , to their absolute 

 values as above defined. 



For this purpose two quartz lenses, one concave and the 

 other convex, and of equal curvatures, were mounted with 

 their crystalline axes at right angles to each other between 

 two Nicols. Under these conditions a series of concentric 

 interference-rings appeared. If a be the angle between the 

 principal section of the polarizer and the axis of the first 

 quartz, and a> the angle between the axis and the analyser, 

 the intensity of the light transmitted will be 



I = cos 2 (to— a) —sin 2a sin 2&> surV-Mr — — , 



where t x is the thickness through the first quartz and t 2 that 

 through the second. If the analyser and polarizer are 

 parallel, ft> = a, and 



1 = 1- sin 2 2a sinV * ( V* 9) > 



A. 



whence Ii=l> and I 2 = l — sin 2 2a, 



. Tr Ii — 1 2 1— cos 2 2a 



and V = i — -j- = ^— 53- • 



Jj + 1 2 l-fcos J 2« 



* Communicated by the Author. ( 



I take this opportunity of presenting my acknowledgments and thanks 

 to the Smithsonian Institution for the funds necessary to carry out this 

 research ; to the Clark University for the facilities it has placed at my 

 disposal; and especially to Mr. F. L. 0. Wadsworth, Assistant in Physics 

 of Clark University, for the valuable services he has rendered and his 

 unflagging zeal in furthering this investigation. 



