In the 12th vol. of the Asiatick Researches, there are detailed accounts of two complete sections of an arc on the meridian, measured by me at different times, in prosecuting the trigonometrical survey of the Peninsula of India. The first is comprehended between the parallels of Punnæ, a station near Cape Comorin, in latitude 8° 9' 38",39, and Patchipolliam in Coimbetoor, in latitude 10° 59'48'',93; being an amplitude of 2° 50' 10",54. The second is comprehended between the parallels of Patchipolliam and Namthabad, a station near Gooty, in the ceded districts ; and lying in latitude 15° 6' 0",21, gives an amplitude of 4° 6'11",28. Since these measurements were made, I have had the good fortune to get another section, extending from Namthabad to Daumergidda, in the Nizam's dominions, which being in latitude 18° 3' 23",6, gives an increase of 2° 37' 23",32; making in the whole an arc of 9° 53' 45", 14 in amplitude; the longest single arc that has ever been measured on the surface of this globe. The detailed accounts of this last arc, with various conclusions concerning the three sections, have been presented to the Asiatick Society by the Marquess of Hastings, the present Governor General, and will be published in the 13th volume of the Asiatick Researches. But as it may be three or four years before that volume makes its appearance, I have been induced to draw out this abstract of the results, thinking that the conclusions herein contained may be interesting to the Royal Society, and to the astronomers of Europe. As a reference may be made to the volumes above mentioned, I have simply given the lengths of the sides of the triangles from which the arcs are deduced, together with the lengths of the terrestrial and celestial arcs, without including either the tables of triangles, or the particulars of the astronomical observations, farther than the names of the stars, and the mean lengths of the celestial arcs, and, consequently, the mean degrees deduced therefrom. The first of these sections gives the degree due to latitude 9° 34' 44", the middle point of that arc, equal 60472,83 fathoms. The second section, whose middle point is in latitude 13° 2'55", gives the mean degree equal 60487,56' fathoms. The last section gives the degree equal 60512,78 fathoms, due to the latitude of 16° 34' 42", the middle point of that section.