The author s object in this paper is principally to form a correct estimate of the absolute and relative degrees of accuracy of the instruments at Dublin and at Greenwich. He first , considers the difference of parallax between γ Draconis and α Lyrse, and secondly, the absolute parallax of a Lyræ. He exhibits, in a table, the whole of the results of 337 observations of Mr. Pond for the intercepted arc, reduced to the 1st of January 1815, chiefly by Mr. Pond’s own computations. From 46 observations made in the year 1812, he deduces 0"·28 for the coefficient of the effect of parallax; and from such of his observations as were made in the same day, the number deduced is 0"·54.