126 



NA TURE 



\ytine 1 8, 1874 



Trnajjc Colours extinc;uished 



00 + EO B+A+B' + A=B + B'4A = A 

 OE + EE B'+A'+B + A'=B + B' + A'= A' 



And since the tints B, B' have disappeared from each of 

 these formula;, it follows that the second analyser P may 

 be turned round in any direction without altering the tints 

 of the overlaps in question. 



In like manner we may form the Table — ■ 

 OO-i-EE B+ A + B + A'= B+ A + A'- B 



O E + E O B'+ A'+ B'+ A = B'+ A + A'= B' 



Hence if the Nicol N be turned round, these overlaps 

 will retain their tints ; while if the analyser Pj be turned, 

 their tints will vary, although always remainmg comple- 

 mentary to one another. 



There remains the other pair of overlaps, viz. : — 

 OO + OE B + A + B'+ A 



E O + E E B'+ A + B + A' 



Each of these is deprived of the pair of complemen- 

 taries A, A', B, B' ; and therefore each, as it would seem, 

 ought to appear white of low illumination, i.e. grey. This 

 effect is, however, partially masked by the fact that the 

 dark bands are not sharply defined like the Fraunhofer 

 lines, but have a core of minimum or zero illumination, 

 and are shaded off gradually on either side until a short 

 distance from the core the colours appear in their full 

 intensity. Suppose, for instance, that IV and A' were 

 bright tints, the tints resulting from their suppression 

 would be bright. On the other hand, the complementary 

 tints A and 1! would be generally dim, and the image 

 B + A bright, and the overlap B + A + B' + A' would 

 have as its predominating tint that of B + A. And 

 similarly in other cases. 



There are two cases worth remarking in detail, viz. 

 first, that in which 



B = A', B' = A 

 i.e. when the same tints arc extinguished by the combina- 

 tion Q P and by Qi Pj. This may be verified by either 

 using two similar quartz plates O, O, ; or by so turning 

 the prism Pj that the combination Oj Pj used alone shati 

 give the same complementary tints as (] P when used 

 alone. In this case the images have for their formuUt 

 the following : — 



00 OE EO EE 



A + A' A -1- A' 2A 2A' 



in other words, O O and E O will show similar tints, and 



E O, E E complementary. A similar result will ensue if 



B = A, B' = A. 



Again, even when neither of the foregoing conditions 

 are fulfilled, we may still, owing to the breadth of the in- 

 terference bands, have such an effect produced that 

 sensibly to the eye 



B + A = B' + A' 

 and in that case 



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



= B -f A' + 2A - 2A' 

 which imply that the images O O and O E may have the 

 same tint ; but that E O and E E need not on that ac- 

 count be complementary. They will differ in tint in this, 

 that E E, 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 oj Coiiibi)iatio)i of two Colours. — A similar train 

 of reaboning 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 recombinition of all 

 four must reproduce white light. Hence the tint of each 

 triple overla]) is the same to the eye as the mixture of the 

 two tints suppressed in the remaining imaje. And since 

 by suitably turning the Nicol N or the prism Pj, or both, 

 we can give any required position to the two bands of 

 extinction, we have the means of exhibiting to the eye the 



results of the mixture of tints due to any two bands at 

 pleasure. 



Effect of Combinaiions of three Colours. — A further step 

 may be made in the combination of colours by using a 

 third quartz O2 and a third double-image prism P.,, which 

 will give rise to eight images. And if C C be the com- 

 plementaries extinguished by the combination O., P.,, the 

 formula; for the eight images may be thus written : — 



The total number of combinations of tint gi\'en by the 

 compartments of the complete figure will be 

 8 



I 



hJ 

 1 . 2 



8.7^6 



1 .2 . 3 



8.7.6.5 



1.2.3.4 



8^^. 6 

 1.2.3 



8.7 



8 single images 



= 28 overlaps of two 



S6 



= 5G 



three 



five 



I =1 „ eight 



Total . . 255 

 The most interesting features of the figure consists in 

 this, that the subjoined pairs are complementary to one 

 another, viz. :-- 



o n EOE 



C -t- B -f A C + B' + A' 



E O O (1 E 



C -f B -f A C -f B' + A' 



E E O OEE 



C + B' + A C + B -f A' 



EEE O E 



C -f B 4- A' C -I- B' -f- A 



And if the prisms P, Pj, P.j are so arranged that the 

 separations due to them respectively are directed parallel 

 to the sides of an equilateral triangle, the images will be 

 disposed thus : — 



OEO 000 

 EEO EOO OEE OOE 



EEE EOE 



The complementary pairs can then be read off, two 

 horizontally and two vertically, by taking alternate pairs, 

 one in each of the two vertical, and two in the one hori- 

 zontal row. And each image will then represent the 

 mixture of the three tints suppressed in the comple- 

 mentary image. 



Loiu-tint Colours. — A slight modification of the arrange- 

 ment above described furnishes an illustration of the con- 

 clusions stated by Ilehnholtz, viz. that the low-tint colours 

 (couleurs degradees), such as russet, brown, olive-green, 

 peacock- blue, iS:c., are the result of relatively low illumina- 

 tion. He mentioned that lie obtained these effects by 

 diminishing the intensity of the light in the colours to be 



