At the bottom of the great tube T T T T, (Fig. 280), is placed the large concave mirror D U V F, whose principal focus is at M; and in its middle is a round hole P, opposite to which is placed the small mirror L, concave towards the greater one, and so fixed to a strong wire M, that it may be moved farther from the great mirror or nearer to it, by means of a long screw on the outside of the tube, keeping its axis still in the same line P M N with that of the great one. Now since in viewing a very remote object we can scarcely see a point of it but what is at least as broad as the great mirror, we may consider the rays of each pencil, which flow from every point of the object, to be parallel to each other, [Page 290] and to cover the whole reflecting surface D U V F. But to avoid confusion in the figure, we shall only draw two rays of a pencil flowing from each extremity of the object into the great tube, and trace their progress through all their reflections and refractions to the eye f, at the end of the small tube t t, which is joined to the great one. Let us then suppose the object A B to be at such a distance, that the rays E flow from its lower extremity B, and the rays C from its upper extremity A. Then the rays C falling parallel upon the great mirror at D, will be thence reflected by converging in the direction D G; and by crossing at i in the principal focus of the mirror, they will form the upper extremity i of the inverted image i K, similar to the lower extremity B of the object A B; and passing on the concave mirror L (whose focus is at N) they will fall upon it at g and be thence reflected, converging in the direction N, because g m is longer than g n; and passing through the hole P in the large mirror, they would meet somewhere about r, and form the lower extremity d of the erect image a d, similar to the lower extremity B of the object A B. But by passing through the plano-convex glass R in their way they form that extremity of the image at b. In like manner the rays E which come from the top of the object A B and fall parallel upon the great mirror at F, are thence reflected converging to its focus, where they form the lower extremity K of the inverted image i K, similar to the upper extremity A, of the object A B; and passing on to the smaller mirror L and falling upon it at h, they are thence reflected in the converging state h o; and going on through the hole P of the great mirror, they would meet somewhere about q, and form there the upper extremity a of the erect image a d, similar to the upper extremity A of the object A B; but by passing through the convex glass R, in their way, they meet and cross sooner, as at a, where that point of the erect image is formed. The like being understood of all those rays which flow from the intermediate points of the object, between A and B, and enter the tube T T, all the intermediate points of the image between a and b will be formed; and the