404 Astronomical and Nautical Collections. 



same time, the quantity of white light to be added to these 

 tints, in consequence of the relative directions of the primi- 

 tive plane, of the primitive section of the plate, and of that 

 of the rhomboid of calcarious spar. 



The above expressions, cos ^9r-—, and sin ^ tt-:—, which 



show the respective intensities of the ordinary and extraor- 

 dinary image in a homogeneous light, of which the length of 

 the undulation is X, when the axis of the crystallized plate 

 makes an angle of 45° with the primitive plane of polari- 

 sation, and when the principal section of the rhomboid is 

 parallel to this plane, show us that the combination of the 

 systems of waves which emerge from the crystallized plate, 

 must be polarised in the primitive plane of polarisation, 

 when 0— e is either or equal to a whole number of undu- 

 lations, because then sin * tt — .— becoming = 0, the extraor- 

 dinary image vanishes. On the contrary, when o — e is equal 

 to an even number of semiundulations, it is cos ^tt — — that 



A 



becomes = 0, and consequently the ordinary image vanishes; 

 whence we may infer that the whole of the light is polarised 

 in the plane perpendicular to the principal section, which is 

 here precisely at the azimuth 2 i. But for all the interme- 

 diate values of X, the combination of the two systems of un- 

 dulations can only exhibit a partial polarisation : and it must 

 even appear completely depolarised when o—e is equal to 

 an odd number of quarters of an undulation, because then 



cos * TT —r- and sin ^ tt -r- becoming each equal to J , the 



two images are of the same intensity ; and this is the case 

 whatever may be the azimuth in which the principal section 

 of the rhomboid is placed, as we may find from the general 



formulas given above ; putting i = 45°, and sin ^ ir —- = J ; 



for they then give, 



Extr. image .... sin ^ 5 + ^ cos 2 s z= |. 

 Ord. image cos ^s — | cos 2 6* = |. 



It is easy to see in the same formulas, whatever may be 

 the value of i, that when o—e is equal to 0, or to an even 



