DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 277 



10~ 6 .2W. Thus for the extreme load of 50 kilogs. it is only 10"*, and may be 

 disregarded. 



9. Imperfect Adjustment of the Inclination of the Slit. 



If the slit he not horizontal its different parts will act as different sources of light 

 at different heights h. 



It is clear that if the inclination be too great the different parts of the slit will 

 give different dark bands in the spectrum, all overlapping. The integral band will te 

 diffuse in consequence and not readily measureable. It is quite easy, however, to 

 make this adjustment to a nicety, as follows : 



Let AB (fig. 5) be the slit, A'B' the image of AB in the cylindrical lens (Y of fig. 2) 

 for rays proceeding in a horizontal plane. Then each element P of the slit gives a 

 vertical line of light through P'. Let 8,8., 

 be the opening of the slit of the spectro- 

 scope. The latter is a good deal smaller 

 than the image A'B', so that in practice 

 only a moderate length of the luminous slit 

 is used. If now the cylindrical lens be 



moved to one side or the other, so that Fig. 5. 



S,S, travels from one end of A'B' to the 



other, then, if the luminous slit be not horizontal, the band will shirt in the spectrum 

 in consequence. When no such shift occurs, we know that the adjustment is very 

 exact. There is very little difficulty in making this adjustment, and accordingly 

 there is no reason for anticipating any sensible error from this cause. 



10. Imperfect Horizontal Adjustment of the Knife-edges. 



In practice it is impossible to ensure that the two pairs of knife-edges shall be 

 exactly symmetrical with regard to the vertical through the load. Failure to satisfy 

 this condition introduces shearing stresses in the l)eams, so that the axes of 

 polarization are no longer horizontal and vertical and further the bending moment 

 varies from cross-section to cross-section. 



The complete analytical investigation of the correction in this case is long and 

 difficult, but the results may he summed up as follows, for the simplest case, when 

 only one of the slabs is supposed imperfectly adjusted. 



In general there is no longer perfect extinction, so that the band is not quite black. 



Assuming that the " overlap " of the two slabs is half their height, the position of 

 the band for rays passing through the edge of either slab is unaltered. 



The position of the band for a ray passing exactly at mid-level is shifted towards 

 the red end of the spectrum by an amount not exceeding O'G of a tenth-metre. 



Thus, remembering that rays which have passed through the glass at different 



