REPORT ON PHYSICAL OPTICS. 401 



having any other value than those which exactly ansAver to 

 these intervals, the resulting light will be elUptically -polarized. 

 The ellipse will become a circle, and the light will appear to be 

 completely depolarized, when the two pencils are of equal in- 

 tensity, and the interval of retardatioh is an odd multiple of a 

 quarter of a wave. Here, then, is suggested an easy method of 

 putting the theory of moveable polarization to the test. If a 

 plate of sulphate of lime, whose thickness corresponds to such 

 an interval, be placed in a beam of polarized light of some 

 simple colour, so that its principal' section is inclined at an 

 angle of 45° to the plane of primitive polarization, the emergent 

 light should, according to the theory of waves, be circularly- 

 polarized; and the two pencils into which it is divided by the 

 analysing rhomb should not vary in intensity during its revolu- 

 tion. According to the theory of moveable polarization, on the 

 other hand, the light should be plane-jmlarized ; and one of the 

 images should vanish when the principal section of the rhomb co- 

 incided either with the primitive plane, or the plane perpendicu- 

 lar to it. This experimentum crucis was tried by MM. Fresnel 

 and Arago, and the result was just as had been predicted by the 

 wave-theory *. 



In the prosecution of their researches on the laws of inter- 

 ference of polarized light, MM. Fresnel and Arago discovered 

 further that two oppositely polarized rays will not interfere, 

 even when their planes of polarization are brought to coinci- 

 dence, unless they belong to a pencil, the whole of which was 

 originally polarized in one plane ; — and that, in the interference 

 of rays which have undergone double refraction, half an undula- 

 tion must be supposed to be lost or gained, in passing from the 

 ordinary to the extraordinary system. The latter principle is a 

 beautiful and simple consequence of the theory of transversal 

 vibrations. When a vibration in any given direction is re- 

 solved into two at right angles, and each of these again into a 

 second pair, in two fixed directions which are also perpen- 

 dicular, it will easily appear that, of the four components into 

 which the original vibration is thus resolved, the two in one of 

 the final directions conspire, while those in the other are 

 opposed. The tint produced by the interference of the former, 

 therefore, corresponds to the actual difference of routes of the two 

 polarized rays in the plate ; while that arising from the latter 

 is that due to the same difference augmented or diminished by 

 half an undulation. 



The former of the two laws now mentioned explains the office 



* Annales de Chimle, torn. xvii. 



1834. 2 D 



