406 Astronomical and Nautical Collections, 



that of moveable polarisation, which becomes so embarrassing 

 when we wish to inquire how the oscillations of the axes of 

 the luminous particles are continued in their passage from 

 one plate to another, in which the principal section makes 

 any angle with that of the first. Thus the h)^pothesis of Mr. 

 BioT has not enabled him to determine all the coefficients of 

 his formulas for two plates placed on each other, except in 

 very particular cases ; and there is even one case in which 

 his formulas do not accurately agree with the phenomena, as 

 I found by comparison with my own: it is that in which two 

 plates of the same kind have their axes crossed at an angle 

 of 45°. The discussion of this particular case, and the 

 general formulas for the tints given by two plates, will be 

 found in the second note added to the report of Mr. Arago 

 on my Memoir, page 267 of the seventeenth volume of the 

 Annales de Chimie et de Physique, 



I have shown, in the same note, that we may explain in 

 the simplest manner the principal properties of polarised 

 light, the law of Malus, and the singular character of dou- 

 ble refraction, if we suppose that, in the luminous undula- 

 tions, the oscillations of the particles are executed in direc- 

 tions perpendicular to tlie rays, and to that which we have 

 called the plane of polarisation. Adopting this hypothesis, 

 it would have been more natural to have called the plane of 

 polarisation that in which the oscillations are supposed to be 

 made : but I wished to avoid making any change in the 

 received appellations. This hypothesis, particularly pointed 

 out by the laws observed by Mr. Arago and myself, in the 

 interferences of polarised rays, shows how these laws must 

 necessarily result from the nature of the undulations ; so 

 that the formulas which I have just given for crystallized 

 plates, as well as those which represent the phenomena of 

 diffraction, reflection, refraction, and the coloured rings, are 

 thus reducible to a single supposition : for it agrees, as well 

 as that which we at first adopted, with the calculations of 

 the interferences which served to explain these phenomena : 

 since it is indifferent in these calculations, as was observed at 

 the beginning of this essay, whether the oscillating motions 

 to be combined, were parallel or perpendicular to the rays, 



