lUSl'KKSION IN ARTIFICIAL DOUBLE U.FIIACTION. 269 



The two slabs were cut from the same piece of glass, and every precaution was taken 

 to ensure that they should )>e as nearly identical us possible. The dimensions of the 

 cross-sections were practically the same, namely, in the notation of the last section, 

 2<i = 2a t = 3 centims. and 2&i = "2b t = 1 centim. 



The length of each slab was about 13 ceutims. 



Bending moments of opposite sign, in a vertical plane, were applied to these, so 

 that the light passed through parts of the glass either altogether under tension, or 

 altogether under pressure, according to the manner in which the bending moment 

 was applied. Of the method of applying such bending moment a fuller account will 

 be given below. 



After emerging from the two beams the pencil of light traversed a Nicol A, which 

 was crossed with the Nicol P. It was then focussed by a cylindrical lens Y (which 

 consisted in practice of a glass beaker filled with water) upon the vertical slit of a 

 spectroscope Q and the spectrum observed in the usual way. 



The condensing lens C was focussed approximately upon the Nicol P ; both and 

 Y were introduced in order to improve the illumination. It was found otherwise 

 that so much light was lost that only a very faint spectrum could be obtained, and 

 this was useless for the purpose of the observations. 



The latter consisted in measuring accurately the position in the spectrum of the 

 black bands corresponding to light completely quenched between the Nicols P and A. 

 Light of any colour will, of course, be quenched between crossed Nicols when the 

 relative retardation of the two rays (polarized in horizontal and vertical planes 

 respectively) in which it is split up by the strained glass amounts to an integral 

 multiple of the wave-length. 



Referring to formula (7) this occurs when 



-A)] ....... (8), 



71 being an integer. If C, were independent of the wave-length, as WERTHEIM'S law 

 would require, then, for a baud of a given order, n is fixed and the wave-length X of 

 extinction is proportional to M 



If, however, C, varies with X, then X/C, is proportional to M* 



By observing the values of X corresponding to a given M f , and varying M,, we 

 obtain the relative magnitude of the coefficient C, for these varying values of X. 



The probable error of setting on the centre of a black band was calculated by the 

 author in the ' Camb. Phil. Soc. Proc.,' vol. XII., Pt. V., pp. 314-315, and was found 

 to be about 1', so that the wave-length of extinction is determined with a propor- 

 tional error smaller than - 002. The average error due to inaccuracy in setting the 

 cross-wires in the eye-piece upon the centre of the black baud is then about 8 to 

 10 tenth-metres, so that the wave-lengths may be considered known accurately to 

 three figures. 



The bending moments were applied to the slabs by means of the apparatus shown 



