For the sake of being more easily understood, I will suppose a tube A B C D.[7] Let E be the eye of the observer; then, when there are no lenses in the tube rays from the eye to the object F G would be drawn in the straight lines E C F, E D G, but when the lenses have been inserted, let the rays go in the bent lines E C H, E D I,—for they are contracted, and those which originally, when unaffected by the lenses, were directed to the object F G, will include only the part H I. Hence the ratio of the distance E H to the line H I being known, we shall be able to find, by means of a table of sines, the magnitude of the angle subtended at the eye by the object H I, which we shall find to contain only some minutes. But if we fit on the lens C D thin plates of metal, pierced, some with larger, others with smaller apertures, by putting on over the lens sometimes one plate, sometimes another, as may be necessary, we shall construct at our pleasure different subtending angles of more or fewer minutes, by the help of which we shall be able to measure conveniently the intervals between stars separated by an angular distance of some minutes, within an error of one or two minutes. But let it suffice for the present to have thus slightly touched, and as it were just put our lips to these matters, for on some other opportunity I will publish the theory of this instrument in completeness. [7] [Illustration] The line C H in Galileo’s figure represents the small pencil of rays from H which, after refraction through the telescope, reach the eye E. The enlarged figure shows that if O P be the radius of the aperture employed, the point H of the object would be just outside the field of view. The method, however, is at best only a very rough one, as the boundary of the field of view in this telescope is unavoidably indistinct. Now let me review the observations made by me during the two months just past, again inviting the attention of all who are eager for true philosophy to the beginnings which led to the sight of most important phenomena. [Sidenote: The Moon. Ruggedness of its surface. Existence of lunar mountains and valleys.]