Astronomical and Nautical Collections. 399 



ference of the paths described, in order to calculate the 

 proportion of the extraordinary image produced by polarised 

 light in the first plane, it must not be added for the extraor- 

 dinary image from the light polarised in the second plane ; 

 so that the two tints which they exhibit, either at once or in 

 rapid succession, in the extraordinary image, will be com* 

 plementary to each other. Hence, this kind of compensa- 

 tion, which occurs at every possible azimuth, prevents our 

 perceiving the effects of interference. 



Returning to the case represented by the figure, when the 

 incident light has undergone a previous polarisation in the 

 plane PP', before it passes through the crystallized plate, of 

 which the principal section 00' makes an angle i with this 

 plane ; if we inquire, for a particular kind of homogeneous 

 light, having its undulations of the length X, what must be 

 the intensities of the ordinary and extraordinary images given 

 by the rhomboid of calcarious spar, of which the principal 

 section SS' makes an angle s with the primitive plane PP' : 

 we may neglect in the calculation the loss of light occasioned 

 by the partial reflections of the two surfaces of the plate and 

 of the rhomboid, because it only affects the total brightness 

 of the images, without any alteration of their comparative 

 intensities, which alone we are considering. If the actual 

 velocity of the oscillating particles be represented by F, for 

 the incident polarised pencil, the brightness of the light will 

 be expressed by F^, which is the living force, in the common 

 sense of the term ; this being the true mode of estimating 

 the intensity of light in all optical experiments: since it is 

 the sum of the living forces, and not that of the simple 

 velocities, which remains constant, as the total intensity, in 

 all the subdivisions to which the light is subjected. This 

 being granted, the incident pencil, in passing through the 

 crystallized plate, is divided into two others, of which the 

 luminous intensities must be equal, according to the law of 

 Malus, to F * cos * I, for the ordinary refraction, and F^ 

 sin* i for the extraordinary: consequently the actual veloci- 

 ties, in the former, will be expressed by F cos i, and in the 

 latter by F sin i; hence the incident light, in passing through 

 the plate, is divided into two systems of undulations, which 

 may be thus represented — 2 E 2 



