It is beyond the limits of the paper to enter into the theory or practice of surveying, or to say more than a few words of the delicate and refined operations necessary in carrying out the geodetic or trigonometrical work of a national survey which binds together the many parts to make a complete whole. The principal triangulation of the British Isles was begun in 1784 and finished in 1852. Two magnificent 3-feet theodolites made by Ramsden, one for the Royal Society, the other for the Master General of the Ordnance, an 18-inch theodolite also by Ramsden, and 2-feet theodolite by Troughton and Simms were used in these observations. In the principal triangulation of Great Britain and Ireland there are 218 stations, at 16 of which there are no observations, the number of observed bearings is 1554--and the number of equations of condition, 920. In order to avoid the solution of this enormous number of equations, containing 920 unknown quantities, the network covering the kingdom was divided into a number of blocks, each presenting a not unmanageable number of equations of condition. These calculations, all in duplicate, were completed in two years and a half, an average of eight computers being employed. Many of the sides of the principal or primary triangulation are of great length, 66 of them exceeding 80 miles, while 11 measure more than 100 miles, the longest being 111 miles, that from Sea Fell to Sheir Donard. So great, however, had been the accuracy of the observers' work, that the average amount of correction of the observed angles was no more than 0".6, and the measured length of the Salisbury base differed from its length as computed from the Irish Base, 350 miles distant, by a difference of only five inches. The secondary triangulation interpolates points at shorter distances apart ranging down to five miles, the observations being made with theodolites of 12-inch circle. These triangles again are broken up into smaller ones of sides from one to two miles in length, for the use of the surveyor who is to follow and measure between the stations with the chain; and a further subdivision of the trigonal spaces is made in towns to points about 10 chains apart, where the survey is to be made on the very large special scale. In the two last cases, 7 inch instruments suffice for the measurement of the angles. LEVELLING. From 1839 to 1855, lines of initial levelling extending all over England, Scotland and Ireland were run, and the observed altitudes of the bench marks were reduced by the method of least squares. In England and Scotland, these levels are based on the Ordnance Datum at Liverpool, which is approximately the mean tide level of that place; in Ireland, they are based on the low water level at Dublin, which is about 8 feet below the mean level round the coast of Ireland.