362 



the complete demonstration, is the following: "No power, beyond 

 the second degree, of any quantity, can exist, capable of being re- 

 solved into the sum, or the difference, of two other powers of the 

 same degree :" or, as it may still more generally be expressed, " If 

 the exponents of three powers be multiplied by the same number, 

 provided that number be greater than 2, neither the sum, nor the 

 difference, of any two of the resulting quantities can ever be equal 

 to the third quantity." 



It was resolved unanimously, — " That the thanks of this Society 

 be given to their Secretary John George Children, Esq., for the 

 zeal and ability which he has uniformly displayed, and the many 

 valuable services he has rendered, in promoting its objects." 



December 17, 1835. 

 SIR JOHN RENNIE, Knt., Vice-President in the Chair. 



" Researches towards establishing a theory of the Dispersion of 

 Light, No. II." By the Rev. Baden Powell, M. A., F.R.S., Savilian 

 Professor of Geometry in the University of Oxford. 



The author, in a preceding paper, published in the last part of 

 the Philosophical Transactions, commenced a comparison between 

 the results of M. Cauchy's system of undulations, expressing the 

 theoretical refractive index for each of the standard rays of the 

 spectrum, and the corresponding index found from observation in 

 different media. Since that paper was communicated, he has re- 

 ceived the account of a new series of results obtained by M. Rud- 

 berg, and comprising the indices for the standard rays in a prism of 

 calcareous spar, and in a prism of quartz, both for the ordinary and 

 the extraordinary rays ; and also the ratios of the velocities in the 

 direction of the three axes of elasticity, respectively, in Aragonite 

 and Topaz. The author was accordingly led to examine this valu- 

 able series of data, and the comparison of them with the theory forms 

 the subject of the present paper. He finds the coincidences of theory 

 and observation to be at least as close as those already obtained from 

 Frauenhofer's results, and to afford a satisfactory extension of the 

 theory to ten new cases, in addition to those already discussed j and 

 a further confirmation of the law assigned by the hypothesis of un- 

 dulations. 



A paper was in part read, entitled, « On the action of Light upon 

 Plants, and of Plants upon the Atmosphere." By Charles Daubeny, 

 M.D., F.R.S., Professor of Chemistry and of Botany in the Univer- 

 sity of Oxford. 



The Society then adjourned over the Christmas Vacation to meet 

 again on the seventh of January next. 



