332 Dr. J. Kerr's Experiments on the 



that the absolute retardations also are sensibly proportional 

 to the strain. 



Proposition VI. 



To analyse the two strain-generated absolute retardations 

 which are compared in proposition IV., these retardations being 

 now viewed as composite effects of the strain, due partly to 

 change of refringent power of the glass, and partly to change of 

 thickness of the plate. 



12. An elementary solution of this delicate problem is 

 attempted under the present proposition and the two follow- 

 ing, by means of the winged plate and refractor. 



When the winged plate is unstrained, let e be its thickness, 

 and m its index of refraction ; when the central pillar, stand- 

 ing vertically, is compressed by a given weight, let e + Be be 

 its thickness, m -f 8m and m + B'm its indices of refraction for 

 the pencils V and H respectively ; also let m' be the index 

 of the medium in which the plate is immersed. If the two 

 pencils of the refractor pass through the plate, V through 

 strained pillar, and H through unstrained wing, the strain- 

 generated difference of their retardations 



= {m + Bm) (e + Be) — (me + m'Be) 

 = eBm + (m — m ! ) Be = V. 



In the same way, the difference of retardations of H through 

 strained pillar and V through unstrained wing 



= eB'm + (m — m')Be = IF. 



Let the winged plate be immersed first in common air 

 (index = l), and then in any convenient liquid (index=m / ) ; 

 and let a and a! be the values of the retardation V, measured 

 by the refractor in the two cases respectively ; then 



eBm-\-(m — 1) Be— a, (1) 



eBm + (m — m')Be=a' (2) 



Hence immediately, 



(m f -l)Be=a-a ! , (3) 



(m' — 1) eBm = (m— l)a' — (m— m f ) a . . (4) 



Eqs. (3) and (4) indicate a complete experimental solution 

 of the first part of our problem, that namely which regards 

 the pencil V ; for these equations enable us to express the 

 two terms of the first member of equation (1) separately, in 

 terms of only the measured quantities m, mf, a, a'. 



In the same way, if b and V be the measured values of 



