Colour-combinations by Polarized Light. 149 



Again, even when neither of the foregoing conditions is fulfilled, 

 we may still, owing to the breadth of the interference-bands, have 

 such an effect produced that sensibly to the eye 



B + A=B' + A'; 



and in that case 



B' + A=B + A-A' + A 



=B + A' + 2A-2A', 



which imply that the images O and E may have the same tint, 

 but that E O and E E need not on that account be complementary. 

 They will differ in tint in this, that EE, having lost the same 

 tints as E O, will have lost also the tint A, and will have received 

 besides the addition of two measures of the tint A'. 



Effect of Combinations of two Colours. — A similar train of rea- 

 soning might be applied to the triple overlaps. But the main 

 interest of these parts of the figure consists in this, that each of 

 the triple overlaps is complementary to the fourth single image, 

 since the recombination of all four must reproduce white light : 

 hence the tint of each triple overlap is the same to the eye as the 

 mixture of the two tints suppressed in the remaining image ; and 

 since by suitably turning the Mcol N or the prism P 1? or both, we 

 can give any required position to the two bands of extinction, we 

 have the means of exhibiting to the eye the result of the mixture 

 of the tints due to any two bands at pleasure, 



Eff'.Cv of Combinations of three Colours. — A further step may be 

 made in the combination of colours by using a third quartz, Q 2 , and 

 a third double-image prism, P 2 , which will give rise to eight images ; 

 and if C C be the complementaries extinguished by the com- 

 bination Q 2 P 2 , the formulae for the eight images may be thus 

 written : — 



OOO C+B+A. 



00 E C+B'+A'. 



OEO O'+B' + A. 



OEE C' + B+A'. 



EOO C' + B+A. 



EOE C+B'+A'. 



EEO C+B'+A. 



EEE C+B+A'. 



The total number of combinations of tint given by the compart- 

 ments of the complete figure will be : — 



