455 



that in the general case the form of these equations is not 

 altered, and that the number of the constants remains the 

 same. But if it be supposed that the internal moments are 

 represented by the variation of a single function V, the pre- 

 sent supposition differs from the hypothesis of independent 

 action, in the absence of any restriction upon the form of V, 

 whose coefficients are now perfectly arbitrary, and may, there- 

 fore, be assumed to satisfy at pleasure any given relations. 



The Rev. Samuel Haughton communicated the following 

 Abstract of a new Method of deducing Fresnel's Laws of 

 Wave Propagation from a mechanical Theory. 



In a memoir on a classification of elastic media, presented to 

 this Academy in January, 1849, 1 deduced the general equations 

 of motion resulting from the hypothesis, that the function on 

 which they depend is a function of the nine differential coeffi- 

 cients of the displacements of each molecule. In that memoir 

 I have also shown the possibility of the laws of wave propa- 

 gation being the same in media of different molecular consti- 

 tutions, and have given some examples in the theories of Light. 

 The general function Fused in that paper contains forty-Jive 

 coefficients, and may be represented thus: 



2F= S(af) + 2S(ai|3,) + 2S(a2a3) + 2S(ai/32), (0 

 adopting the notation used in the memoir. The last term of 

 this equation consists of eighteen terms, while each of the 

 others contains nine. Among other hypotheses made by me 

 at the time of writing the memoir, 1 assumed the coefficients 

 of this last term to be equal in pairs, so as to reduce the total 

 number of coefficients to thirty-six. The consequences which 

 1 deduced from this hypothesis were interesting, but 1 did not 

 publish them in my memoir, as I could give no satisfactory 

 reason for the hypothesis itselt. As I conceived it at the time, 

 it was only a mathematical assumption made to simplify my 

 equations. Some days since, my friend Professor Jellett com- 



VOL. IV. 2 M 



