134 The Eev. S. Haughton on a Classification of Elastic Media, 



moil- published in the Journal de PEcole Polytechnique ;* and, more recently, 



M. Bakre de Saint VENANxf and Mr. StokesJ have written on the friction of 



fluids in motion. 



The quantities to be added to the ordinary equations of hydrodynamics are 



/ 4P' 

 the right hand members of equations (37), introducing the relation {A=-^ 



which expresses that a displacement produces no molecular force. 



The equations of the motion of gases have been already given, on the sup- 

 position that there is no tangential action, which is equivalent to assuming that 

 the vibrations are normal, and therefore {P = 0). If we wish to take account 

 of the friction of gases, we should use the equations which have just been indi- 

 cated for liquid motion. 



section v. compakison of mechanical theories of light. 



It is well known that different mechanical theories have been proposed to 

 account for the phenomena of the movement of light in crystalline bodies, and 

 that, although these theories differ in their fimdamental hj'potheses, yet, to some 

 extent, they agree in representing the most obvious phenomena of double re- 

 fraction. The laws of wave-propagation in crystals, are geometrical conse- 

 quences of the properties of Fresnel's wave-surface; and no mechanical theory 

 of light can be considered as even an approximation to the truth, unless it con- 

 tains, as a deduction from its hypotheses, the wave-surface of Feesnel. But 

 it would be an error to conclude that any theory is correct, which satisfies this 

 condition. Tliere are, in fact, three different theories which satisfy this funda- 

 mental condition, and it is evident that they cannot all be true. The first of 

 these theories was propounded by Fresnel himself, in his memoir on Double 

 Refraction. § It is based on the hypothesis, that the luminiferous ether is com- 

 posed of attracting and repelling molecules. The form of wave-surf ace known 

 as Fresnel's is deduced by its author from this hypothesis, with the peculiarity 

 that the vibrations of the molecules are perpendicular to the plane of polarization. 



* Cahier xx. p. 139. t Comptes Eendus, torn. xvii. p. 1240. 



J Transactions of Cambridge Philosophical Society, yoI. viii. part 3. 

 J Memoires de I'Institut, torn, vii., p. 45. 



