Royal Society. 413 
wards with great rapidity, exactly imitating flames agitated to and 
fro by a violent wind.* 
««Démonstration compléte du Théoréme dit de Fermat: par 
Fran¢ois Paulet, de Genéve, ancien éléve de l’E’cole Polytechnique.” 
Communicated by P. M. Roget, M.D., Sec. R.S. 
The theorem of which the author professes to give, in this paper, 
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.” 
Dec. 17.—“ 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 Transactionst, 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 Arragonite 
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 
Fraunhofer’s results, and to afford a satisfactory extension of the 
theory to ten new cases, in addition to those already discussed ; 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. 
Jan. 7, 1836.—A paper was read, entitled, «‘ Meteorological Jour- 
nal kept at the Royal Observatory, Cape of Good Hope, from the 
1st of June to the 3lst of December, 1834.” Communicated by 
Capt. Beaufort, R.N., F.R.S., Hydrographer to the Admiralty. 
* Other particulars respecting this Aurora have been given in our late 
Numbers: by Mr. Sturgeon, p. 134; Dr. Robinson, p. 236; and Prof. Rigaud, 
p- 850.—Ebpir. 
+ An abstract of Prof. Powell’s preceding memoir will be found in Lond. 
and Edinb. Phil. Mag., vol. vi. p. 374: various papers on the subject, by-Prof. 
Powelland Mr. Tovey, have appeared in our last and present volumes.—Eprr. 
