Reflecting telescopes are those which represent the images of distant objects by reflection, chiefly from concave mirrors. Before the achromatic telescope was invented, there were two glaring imperfections in refracting telescopes, which the astronomers of the 17th century were anxious to correct. The first was its very great length when a high power was to be applied, which rendered it very unwieldy and difficult to use. The second imperfection was the incorrectness of the image as formed by a single lens. Mathematicians had demonstrated that a pencil of rays could not be collected in a single point by a spherical lens, and also that the image transmitted by such a lens would be in some degree incurvated. After several attempts had been made to correct this imperfection by grinding lenses to the figure of one of the conic sections, Sir I. Newton happened to commence an examination of the colours formed by a prism; and having, by the means of this simple instrument, discovered the different refrangibility of the rays of light--to which we have several times adverted in the preceding descriptions--he then perceived that the errors of telescopes, arising from that cause alone, were some hundred times greater than such as were occasioned by the spherical figure of lenses; which induced this illustrious philosopher to turn his attention to the improvement of telescopes by reflection. It is generally supposed that Mr. James Gregory--a son of the Rev. John Gregory, minister of Drumoak in the county of Aberdeen--was the first who suggested the construction of a reflecting telescope. He was a young man of uncommon genius, and an eminent mathematician; and in the year 1663, at the age of only 24, he published in London, his treatise entitled ‘Optica Promota,’ in which he explained the theory of that species of reflecting telescope which still bears his name, and which he stated as being his own invention. But as Gregory, according to his own account, was endowed with no mechanical dexterity, and could find no workman capable of realizing his invention--after some fruitless attempts to form proper specula, he was obliged to give up the pursuit; so that this telescope remained for a considerable time neglected. It was several years after Gregory suggested the construction of reflecting telescopes, till Newton directed his attention fully to the subject. In a letter addressed to the secretary of the Royal Society, dated in February, 1672, he says, ‘Finding reflections to be regular, so that the angle of reflection of all sorts of rays was equal to the angle of incidence, I understood that, by their mediation, optic instruments might be brought to any degree of perfection imaginable, providing a reflecting substance could be found which would polish as finely as glass, and reflect as much light as glass transmits, and the art of communicating to it a parabolic figure be also obtained. Amidst