TRANSACTIONS OP THE SECTIONS. 15 



dence, and greatest when the incidence is most oblique. The absolute maximum is 

 given by the formula 



cot A =-?£-• 



** } 

 For ordinary flint-glass, A = 26° 0'. 



The difference of phase in the two component portions of the polarized beam is 

 the name in the reflected and in the transmitted pencils. 



There is no difficulty in extending the investigation to the more general case, in 

 which the media on the two sides of the plate are of unequal refract ire densities \ 

 but in this case the law last stated no longer holds. The general formulae for the 

 intensity explain not only the phenomena observed by Arago and by Sir David Brew- 

 ster, but likewise indicate some results hitherto unnoticed. 



On the Mixture of the Colours of the Spectrum. By Prof. J. C. Maxwell. 



The author described his apparatus for obtaining a uniform field, illuminated by 

 the light of any one or more definite portions of the spectrum, and comparing this 

 mixture with a field of white light in contact with it. The experiments consisted 

 in obtaining perfect equality between a combination of three definite portions of the 

 spectrum and this white light. The relations of these portions are then ascertained 

 by mathematical treatment of the equations so obtained, and it results that Newton's 

 " circle of colours " is found to be really two sides of a triangle ; red, yellow-green, 

 and blue being the angular points, and yellow being on the side between red and 

 green. The extreme red and violet form small portions of the third side, of which 

 the middle part representing purple is wanting in the spectrum. 



The peculiar dimness of the spectrum near the line F, as described to the Section 

 in 1856, was further investigated, and shown to be more marked to the author's eye- 

 sight than to that of others. It results from this that a mixture may be formed, 

 which appears green to one eye and red to another, and this was found experimentally 

 true. 



These results are only part of a complete investigation of the colours of the spec- 

 trum, of which the experimental portion is considerably advanced and will shortly 

 be published. 



On certain Laws of Chromatic Dispersion. 

 By Mungo Ponton, F.R.S.E. 



This paper is an attempt to trace the laws regulating the diminution of the wave- 

 lengths, corresponding to the fixed lines of Fraunhofer, in passing through various 

 refractive and dispersive media. If U be the length of the undulation, corresponding 

 to any line, in the free ether, and u its length after being subjected to the action of 



the medium, the relation between U and u may be expressed thus : — «— +#=w, or 



e 



e (u-f a+a') = U. Here e and a. are constant for the medium and temperature, while 



the quantity x, which is comparatively small, is peculiar to each wave. These 



quantities x represent that displacement or extrusion of the fixed lines, from their 



normal relative positions in the pure diffracted spectrum, which constitutes the 



irrationality of the various refracted spectra; and they are accordingly termed the 



extrusions of the fixed lines. Thus each medium is regarded as having a refractive, 



a dispersive, and an extrusive power, peculiar to itself at a given temperature. 



The constant e is found thus : B, C, D, &c. representing the normal wave-lengths 



corresponding to the fixed lines, and b, c, d, &c. these wave-lengths after refraction, 



calling (3B + 2C+D)-(F+2G+3H) = A and (3b+2c+d)- (f+2g+3h) = 8, then 



A 

 , Se =-. 



The constant x is found thus : S being the sum of the normal wave-lengths cor- 

 responding to the 7 lines, and s their sum after refraction, then is «=-} ( -— s). 

 The values of « and of log < for the different media are given in Table I. 



