The optical theory referred to in the title of this communication is now fully half a century old; and has, moreover, been well expounded in the standard English treatises of Pendlebury and Heath. Still, notwithstanding its elegance and simplicity, and its great practical importance as giving the first approximation to the theory of the great majority of the optical instruments in ordinary use, its filtration into the strata of popular knowledge has been remarkably slow. It seems, therefore, to be worth while to offer a brief summary of its leading principles, freed as much as possible from the detailed calculations which become necessary when the constants of the optical system have to be deduced from the data of construction, and to indicate methods for experimental verification. In giving this summary, I shall omit the demonstrations of some of the propositions, which can be found by those who desire them in the well known Treatise on Geometrical Optics, by Heath