Astronomical and Nautical Collections, 405 



number of semiundulatlons, the extraordinary image vanishes 

 in the case s =0, and when o — e is equal to an odd number 

 of semiundulations the same expression becomes = when 

 s=z2i, and consequently the whole light is polarised in the 

 primitive plane, in the first case ; and in the second, at the 

 azimuth 2i; while, for all intermediate values of o— e, 

 neither image can wholly disappear, whatever may be the 

 direction of the principal section of the rhomboid. And all 

 these consequences of the theory are confirmed by experiment. 

 When we cause polarised light to pass through several 

 cystallized plates, of which the principal sections cross each 

 other in any manner, the phenomena become greatly compli- 

 cated, but may always be computed by the same theory. 

 The incident light is first divided, in the first plate, into two 

 systems of undulations, of which we may determine the in- 

 tensities of oscillation by the law of Malus, and the relative 

 positions by the difterence of their paths, as we have done 

 for a single plate : then each of these systems of undulations 

 is subdivided into two others in the second plate ; each of 

 these four new systems of undulations is again divided into 

 two in the third plate, and so forth. It is plain that when 

 the azimuths of all the principal sections are known, as well 

 as that of the rhomboid which affords the double image, we 

 can determine the comparative intensities of all the systems 

 of undulations which enter into each image, and that it is 

 equally easy to determine the difference of their paths, having 

 regard to the different species of refractions which they suc- 

 cessively undergo, when the thicknesses of the plates are 

 known, as well as the proportions of the velocities of the 

 ordinary and extraordinary rays which pass through them. 

 We shall, therefore, have for each image, the intensities and 

 the relative situations of all the systems of waves which con- 

 tribute to its formation, and the result of the whole may be 

 determined by the general method pointed out in my memoir 

 on Diffraction, p. 256. In these calculations, every thing is 

 theoretically determined from the fundamental principles 

 deduced from facts, and nothing has been borrowed from 

 experiment, even in the most complicated cases. It is in this 

 respect that the system here explained is greatly superior to 



