to the reflecting type of telescope, whose advantages were so clearly demonstrated by Director J. E. Keeler of the Lick Observatory some thirty-five years ago. Many large reflecting telescopes had been constructed and actively employed long before the work of Keeler, but their advantages were nullified to a great extent by crudities in mounting and by poor climatic conditions. The importance of proper seeing conditions has been emphasized by the work of Keeler. At present there appears to be no limit in size to which the reflecting telescope may be pushed. The California Institute of Technology, in co-operation with the Mount Wilson Observatory, is now engaged in constructing a reflecting telescope having a mirror 200 inches in diameter, or twice that of the largest now in existence. The construction of such a telescope calls for the highest degree of optical and mechanical skill that this generation can produce. The present paper is concerned with the optical requirements, and examines recent advances in the design of mirror systems to see to what extent if any they may be useful, keeping in mind the important problems confronting the present-day astronomer. In planning a telescope, the F number, or ratio of focal length to aperture, is of primary importance. Three considerations govern the choice: (a) mechanical, (b) optical, (c) program of work. The large reflecting telescopes of the present day nearly all operate at a focal ratio of 5, with very satisfactory results. But with an increase in the size of the mirror beyond that of the 100-inch now in operation, many considerations point