120 EEPORT ON PHYSICAL OPTICS. 



amounts to 10. Generally the position of the three axes of elas- 

 ticity is invariable, and the optic axes for all colours are confined 

 to one plane ; but Sir John Herschel has lately observed that, in 

 borax, the optic axes belonging to different colours lie in different 

 planes ; and we are compelled to conclude that the direction of the 

 axes of elasticity in this, and probably in many other crystals, 

 varies with the colour. 



The first addition to the theory of Fresnel was made by M. 

 Ampere. The results alluded to are contained in two short papers 

 read to the French Academy in the year 1828, and since embodied 

 into one, and published in the Annales de Chimie* Fresnel had 

 arrived at the equation which belongs to all the tangent planes of 

 the wave-surface, and had shown in what manner the equation of 

 the surface itself might be thence deduced by differentiation and 

 elimination. This direct process, however, he seemed to think 

 would involve complicated and embarrassing calculations. The 

 method which he substituted for it consisted in verifying the 

 equation, to which he was led by reasonings not altogether rigo- 

 rous, and proving (by calculations which he found too tedious to 

 transcribe) that it satisfied the conditions already assigned. M. 

 Ampere has supplied the direct demonstration, and deduced the 

 equation of the wave-surface in the manner originally pointed out 

 by Fresnel. From this equation he has derived also the beautiful 

 geometrical construction given by Fresnel, and which the latter 

 had obtained indirectly. 



A very concise demonstration of the same theorem, and of the 

 other principal points of Fresnel's theory, was given not long after 

 by Mr. M'CuHagh.f This writer has shown that both the magni- 

 tude and direction of the resultant elastic force, called into action 

 by any displacement, may be represented by means of an ellipsoid 

 whose semiaxes are the three principal refractive indices of the 

 medium ; and from this ellipsoid, by the aid of a few geometrical 

 lemmas, he has deduced in a clear and simple manner the leading 



* " Memoire sur la Ddtermination'de la Surface courbe des Ondes lumineuses," 



&C., t 



t " On the Double Refraction of Light in a crystallized medium, according to the 

 principles of Fresnel," Transactions of the Royal Irish Academy, vol. xvi. A further 

 development of the principles of this memoir has been recently given by the author in 

 the 17th vol. of the same Transactions, under the title Geometrical Propositions 

 applied to the Wave-theory of Light." 



