A singular instance of early mathematical talent has been made known by Mr. Gough, in the Philosophical Magazine.- Thomas Gasking, the son of a journeyman shoemaker of Penrith, was but nine years of age when the account was written : "he was, (says the writer), however, in consequence of the education given him by his father, (an acute and industrious man,) become well acquainted with the leading propositions of Euclid, reads and works algebra with facility, understands and uses logarithms, and has entered on the study of fluxions. On being examined, he demonstrated propositions from the first books of Euclid ; discovered the unknown side of a triangle, from the two sides and the angle given ; and solved cases in spherical trigonometry. In algebra, he gave the solutions of a number of quadratic equations; answered questions which contained two unknown quantities ; and applied algebra to geometry. He answered problems relating to the maxima of numbers and of geometrical magnitudes, with ease; and, on many other mathematical points, gave very high promises of future excellence."