The author, after referring to a communication made to this Society, on the 18th March 1839, on this subject, and noticed in the “Proceedings” of that date, stated, that being about to recommence his observations on radiant heat, so long and unavoidably interrupted, he had carefully examined the unpublished observations on which the previous notice was founded, with a view to ascertain what might be the numerical discrepancy which they present from Fresnel's Theoretical Law. The variation in the results of experiment for each of the angles was very considerable, arising from a multitude of causes as yet imperfectly estimated, but which appear to have been encountered by other observers, who, since that time, have undertaken the same research. Under the circumstances, the mean of the whole observations made between November 1838 and March 1839, have been taken for each angle of incidence; and the results being projected in the usual manner, the angles of incidence forming the line of abscissæ, and the intensities the ordinates, an interpolating curve was drawn through the whole. The numbers thus obtained (which are presented as only a rude first approximation), are shewn in the following table, and compared with Fresnel's Formula, calculated for an index of refraction of 1·50.