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XXIV. On Fresnel's Theory of Double Refraction. By R. 

 Moon, M.A., Fellow of Queeft's College Cambridge^ and of 

 the Cambridge Philosophical Society. 



[Continued from vol. xxvii. p. 559.] 



A FTER proving, as he imagines, the existence of the three 

 "*j« axes of elasticity, Fresnel enters into the most elaborate 

 calculations as to the motion of the originally disturbed par- 

 ticle, and then proceeds to discuss the laws according to which 

 the disturbance is transmitted from it to the rest of the me- 

 dium. His labours in this respect are perfectly futile. The 

 motion of the original particle, which is of the most simple 

 character, is altogether different from what he supposes; and 

 as to the laws according to which the disturbance is commu- 

 nicated from it to the rest of the medium, no disturbance what- 

 ever can be propagated. 



As to the first point, Sir John Herschel proceeds : — " Sup- 

 pose now any molecule set in vibration," in a plane passing 

 through the centre of the surface of elasticity, " then at any 

 period of its motion it will not be urged directly to its point 

 of rest; but obliquely so that it will not describe a straight 

 line, but will circulate in a curve more or less complicated; 

 its motion however will always be resolvable into two vibratory 

 rectilinear ones at right angles to each other, one parallel to 

 the greatest, and the other to the least diameter of the sec- 

 tion," which diameters it is shown, and this incontestable, are 

 at right angles to each other. " Each of these vibratory mo- 

 tions will, by the laws of motion, be performed independently 

 of the other; and therefore the motion propagated through 

 the crystal will affect every molecule of it in the same way as 

 if two separate and independent vibrations (at right angles, 

 as above) were propagated through it with different veloci- 

 ties." 



It is perfectly true that "the motion of the particle will al- 

 ways be resolvable into two vibratory rectilinear ones at right 

 angles to each other, one parallel to the greatest, and the other 

 to the least diameter of the section." But it is not true, as 

 Fresnel quietly assumes, that the motion will be the same as 

 if two separate disturbances were communicated, one in the 

 direction of the greatest, and the other of the least diameter of 

 the section. The distinction between the two cases is very 

 palpable. We may resolve the actual force on the particle 

 into two, one parallel to the greatest and the other to the least 

 diameter of the section ; and so the motions of the particle 

 parallel to those lines may be determined ; but these motions 



