270 The Rev. Prof. Powell's Note to a former Paper. 



greater than, or equal to y, the preceding result, so treated 

 and reduced, becomes 



(N , ,-N ,)u+N ,-N 



V X— l,y— 1 x—\,y' x,y—l x,y 



D 



while if ?/ — J be greater than, or equal to x, it becomes 



D 



x,y 



These results agree with those of Mr. Jones (p. 176), if in 

 the formulae cited N be substituted for its equivalent 



N , — D . If ever the time should arrive when 



^^x—\,y—\ x,y 



tables of this sort are calculated for three lives, it should be 

 by the formula 



= a a a v^^ ^ ^^' 



m, n, p m n p 



and so on. In such a case, the method now in use would 

 become intolerable, from the large number of cases into 

 which different orders of survivorship would require formulae 

 to be subdivided. 



XLVJ. Note to a Paper "On certain points in the Undulatory 

 Tlieory, S^c." in the last Number of the Philosophical Maga- 

 zine. By the Rev. Baden Powell, M.A., F.R.S., Sfc.^ Sa- 

 vilian Professor of Geometry, Oxford*. 



IN referring to the establishment of the principle of a rela- 

 tion between the symmetrical or unsymmetrical arrange- 

 ment of the ffitherial molecules, and the rectilinear or elliptic 

 nature of the vibrations, I was led at the suggestion of a 

 friend to add a note (p. 161) while the paper was in the press, 

 with respect to the share which M. Fresnel might be supposed 

 to have in disclosing that principle. 



Having since looked more closely into the matter, I think 

 it right to take this opportunity of stating the result. 



Fresnel devotes a section of his admirable Memoir on 

 double refraction to the consideration pf the mechanical 

 theory of setherial vibrations. But this, though characterized 

 y all the profound ability of the author, is discussed almost 

 entirely in general terms, and the results are not connected 

 with any mathematical development of equations of motion. 



* Communicated by the Author. 



