EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 75 



so that B may be computed from this equation; or if three terms of the right- 

 hand member be taken and further observation made, B and C may be com- 

 puted without reference to A7V C ; i.e., without a knowledge of the displacement 

 due to the length of the column, for any color X, as a whole. With regard to 

 AN C , I may recall that this quantity is the difference of the air-paths, from the 

 respective points of intersection of the normal with the two faces of the grat- 

 ing at the place where the incident white ray impinges, to the two opaque 

 mirrors. 



41. Equations. Sensitiveness in terms of displacement. To the same 

 extent in which equation (i) applies, the sensitiveness dNJd\ may now be 

 computed, since 



(ii) 



and 



(12) dA/d8 = -D cos6 



where D is the grating constant and 6 the angle of diffraction for the color X. 

 Performing the operations and reducing, 



( \ d * * e ( 



~dN e cosR\ 



or, by inserting equation (5), 



, ^ dA tf ju cos R 



If R = o (normal incidence) , 



(15) 



or 



(16) N e -N?=i2eB/A* = -6eAdn/dA 



where Nf corresponds to X= , or to Cauchy's constant A. From equation 

 (15) it appears that the sensitiveness (d\/dN c ) is inversely as the thickness 

 e and directly as the cube of X, for a given glass. Since B/\ z depends on the 

 refraction of the glass, d\/dN c varies as \/e and as i/(5/X 2 ). It is this feature 

 that makes it ultimately unprofitable to use long columns. No additional sen- 

 sitiveness is gained ; the glass absorbs more and more fully. The columns are 

 not apt to be homogeneous, and the ellipses become excessively small and 

 sluggish in their motion. They offer, however, an excellent corroboration of 

 the sufficiency of equation (i). Writing this in the form (2), equation (17) 

 may be deduced on adding i/E\d 2 /j,/d\ 2 



/ % dX A s n ( cos R 



" dN e 2 B \ e(*B tan 



so that the predominating term for long columns is \*/6EB; or for normal 

 incidence, accurately \ z /6(E+e)B. 



