Each end plate is connected with an insulated leaf of an electro- meter. When a charge is communicated to the centre plate under ordinary circumstances, the induction is equal on both sides, and the gold leaves are not disturbed. But if after uninsulating them, and again insulating them, a thick plate of shell-lac or sulphur be interposed between two of the plates, unequal induction will take place on the two sides, and the gold leaves will attract one another. By these means Dr. Faraday ascertained that, taking the specific
inductive capacity of air to be 1*
That of Glass is .1-76
Shell-lac 2*
Sulphur 2*24<
The results obtained with spermaceti, oil of turpentine, and naph- tha were higher than that of air, but their conducting powers inter- fered with the accuracy of the experiments.
By another form of apparatus he ascertained that all aeriform matter has the same power of sustaining induction ; and that no variations in the density or elasticity of gases produced any varia- tion in their electric tension until rarefaction is pushed so far as that discharge may take place across them.
Hot and cold air were compared together, and damp and dry air, but no difference was found in the results.
The great importance of the discovery and complete establishment of such a principle as that of specific inductive capacity, in all its relations both experimental and theoretic, is so palpable, that any comment must be superfluous ; and the Council have felt they can- not better mark their sense of the value of this discovery than by awarding the Copley Medal to its author.
The Council have awarded the Royal Medal for Mathematics to H. F. Talbot, Esq., for his two memoirs entitled, " Researches in the Integral Calculus," published in the Philosophical Transactions for 1836 and 1837.
Nothing perhaps tends more directly to bring the correctness of refined theoretical investigations in physics to the test of numerical results, than improvements in and extensions of the processes of integration. Any advance therefore which is made in this difficult branch of analysis must be viewed not merely in the light of a diffi- culty overcome in the progress of abstract science, but likewise as hav- ing an important bearing on the advancement of physical inquiry.
The branch of analysis to which Mr. Talbot's researches belong is one which is connected with a long series of valuable investiga- tions from the time of Fagnani and Eulerto that of Legendre, Jacobi, and Abel : it relates to integrals under the same form which are separately nonscendental, but which furnish, under particular con- ditions of the variables, an algebraical result when two or more of them are connected together with the signs + or — . The celebrated theorem of Abel, which may be made to comprehend some of Mr. Talbot's results, is the most comprehensive and most important of all the general conclusions which have been arrived at in this de-
