2. _Luminous Appearances in the Atmosphere_.—An account is given at page 242 of our last volume, from Silliman’s Journal, of certain spots in the air near the horizon, which have been seen highly luminous in Ohio, United States, by Mr. Atwater, and which often induce the supposition that fires exist in their direction. Mr. Webster says—“I have observed similar phenomena in New England: I recollect one instance, when I resided at Amherst, in Hampshire County, Mass., a bright light in the north-east, near [p223] the horizon, appeared as the light of a building on fire appears at night, at the distance of several miles. I expected, in that instance, every hour to hear that some building in Shutesbury, or New Salem, had been burnt, and, so strong was my belief of it, that I repeatedly asked my neighbours whether they had heard of any such event. At last, I met a gentleman who had just come from one of those towns, who told me he had heard of no fire from that quarter, which convinced me the phenomenon was merely atmospheric.”—_Silliman’s Journal_, xii. 380. 3. _On the Determination of the Mean Temperature of the Air_.—This subject has been investigated by M. G. G. Hallstrœm, who gives the following algebraic formula, which correctly represents the mean temperature for all Europe. _v_ = 1/2 (_x_ _f_ + _x__e_)−0.33 + 0.41 sin. [(_n_−1) 30° + 124° 8′] _v_ = mean temperature. _n_ = the ordinal number of the month for which the temperature is to be calculated (thus, for March, _n_ = 3). 1/2 (_x_ _f_ + _x_ _e_) = the mean temperature taken as the mean of observations taken at ten o’clock in the morning and evening. In winter 1/2 (_x_ _f_ + _x_ _e_) = _v_ very nearly; whilst, in summer, this quantity is 3/4 of a degree greater than _v_ at Paris, Halle, and Abo.—_Annal. der Phys. und Chem._ 1825, p. 373.