The Author proposes the construction of a new sidereal catalogue, accompanied with a graphic representation of all the stars visible within the field of view at each observation, by means of the meridian transit of the most conspicuous stars across the field of a telescope of four inches aperture, attached to a three-feet circle. He directs this telescope to any elevation of the heavens that happens to be clear; and bringing any conspicuous star to the horizontal wire, he watches its transit over the two first vertical threads; then, suddenly intercepting the light, makes a diagram of all the stars in the field down to the 12th magnitude; and this he performs with sufficient expedition to enable him, on restoring the light, to observe the transit of his principal star over the fourth and fifth threads. The author has appended to the description of his method explanatory drawings, displaying 600 fields, of which the principal star in each, has its right ascension and declination determined. He subjoins some remarks on the rate of clocks, as influencing the observations on the upper, lower, and opposite passages; and proposes a plan for a system of symbols expressive of the relative magnitude of the stars recorded in his catalogue. The author farther states as one of the most important results of his researches the probable existence of a general and curious law of position in the stars, namely, that they are distributed in pairs ; each star having a corresponding one in the opposite meridian, very nearly of she same declination and magnitude; a coincidence which he considers as extremely favourable to the execution of his project for the accurate determination of the position in the heavens of every star.