COLOURS OF CRYSTALLINE PLATES. 137 



continuously ; and that in each system of waves there are probably 

 several hundred successive vibrations, which are all similar, 

 although the vibrations of one system bear no relation to those of 

 another, and the different systems succeed one another with such 

 rapidity as to obliterate all trace of polarization. This per sattum 

 transition from one system of waves, to another in which the 

 vibrations are wholly different, seems a complication in the 

 machinery of light, for which the elegant simplicity of the parts 

 better known has not prepared us ; and I cannot but indulge the 

 hope that the hypothesis, which now stands as the representative 

 of experimental laws, may be found to merge in some simpler 

 physical principle. 



The laws of interference of polarized light have thus supplied 

 the defective link in the explanation of the colours of crystalline 

 plates first suggested by Young. The magnitudes of the resolved 

 vibrations are known, when the planes of polarization of the two 

 pencils are given with respect to the plane of primitive polari- 

 zation, and the plane of analyzation ; and as the laws of double 

 refraction enable us to find the interval of retardation of these 

 pencils, we have all the data necessary for the computation of the 

 intensity and colour of the light resulting from their interference. 

 This computation has been given by Fresnel, not only for a single 

 plate, but likewise for two plates superposed ;* and the theory has 

 been since more fully developed by Professor Airy.f The results 

 are found to be, in all cases, in exact accordance with the observed 

 facts ; and all the circumstances of the coloured rings in uniaxal 

 and biaxal crystals are completely explained. 



The form of the rings, or isochromatic curves, depends upon 

 the interval of retardation alone ; and the value of this interval 

 had been deduced but approximately. Mr. M'Cullagh has recently 

 given a general and exact method for its calculation, and for the 

 determination of the forms of the rings for any plate of a double- 

 refracting crystal bounded by parallel planes. This method is 

 made to depend upon the properties of the surface of wave-slowness, 

 of which I have spoken in another place ; and it is found that if 

 the incident ray be produced to meet the sphere (which is the 

 surface of wave-slowness for air), and through the point of inter- 



* Annales de Chimic, torn. xvii. 



t Cambridge Tra>tsactions, 1831, and Math. Tracts. 



