LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 159 



by a somewhat thin plate of doubly-refracting material, such as mica, the plane 

 of analysis being perpendicular to that of primitive polarisation. To this case 

 also our calculations are applicable, if we neglect the dispersion, and (as is 

 usual) the light transmitted after two or more reflections at the surfaces of 

 the plate. 



If the analyser be turned through 90°, a new series of colours is exhibited 

 complementary to the first series. The purity of the colours, as regards 

 freedom from admixture with white, is greatest when the principal section of 

 the crystal is inclined at 45° to the plane of polarisation, and it is in this case 

 also that the colours of the first series attain their maximum brightness. If 

 we represent the first series by sin 2 (7r V/X), the second series in the case referred 

 to will be represented by cos 2 (7rV/X). It should be noticed that the colours of 

 Newton's rings seen by transmitted light are complementary to those seen 

 by reflection; but the scale of colours is far more dilute than that obtainable 

 as above with the aid of double refraction. 



The colours of the first series are met with also in other optical experi- 

 ments, e.g., at the centre of the illuminated patch, when light issuing from a 

 point passes through a small round aperture in an otherwise opaque 

 screen.* 



§ 3. In order to be able to calculate the colour of any given mixture of light, 

 it is necessary to know the exact chromatic relations of the spectral rays them- 

 selves. This is precisely the question investigated by Maxwell, t Selecting 

 three rays as standards of reference, he expresses the colours of other rays in 

 terms of them. The actual observations in all cases consisted in matches of two 

 whites, one the original white which had not undergone prismatic analysis, the 

 other a white compounded of three rays, — first of the three standard rays 

 themselves, then of two standard rays in combination with a fourth ray which 

 it was desired to express in terms of the standards. The auxiliary white was 

 then eliminated. 



The three points selected were at 24, 44, and 68 of the scale to which 

 the spectrum was referred. "I chose these points, because they were well 

 separated from each other on the scale, and because the colour of the spectrum 

 at these points does not appear to the eye to vary very rapidly, either in hue or 

 in brightness, in passing from one point to another. Hence, a small error of 

 position will not make so serious an alteration of colour at these points, as if 

 we had taken them at places of rapid variation; and we may regard the 

 amount of the illumination produced by the light entering through the slits in 

 these positions as sensibly proportional to the breadths of the slits. 



* Airy's Tract on Optics, § 79. 



f "On the Theory of Compound Colours," Phil. Trans., 1860. 



