shown on the vertical arc; and the sixth is left for remarks. Among these remarks, a few horizontal angles to surrounding objects should occasionally be entered.

To "Observe" so as to avoid necessity for Correction in the Vertical Angles.

As before remarked if, from any station the telescope be directed towards the ground, or the top of a signal at the next station, a correction is required in the observed vertical angle. If, for example, the ground be the point observed, the correction is additive if the vertical angle be one of elevation, and negative if the observed angle be one of depression. To avoid the necessity for this correction, the instrument should be set up (as nearly as possible) at a constant height above the ground, and the staff used for the observations should have a cross bar or vane fixed at the same height above the ground as the axis of the telescope, which bar or vane is to be bisected by the cross wires in observing. This precaution cannot always be used in the primary triangulation, and is, of course, inadmissible when the observed objects are permanent structures, such as church steeples, towers, &c.; but it should be universally adopted when levelling for the interior detail of a survey. In this latter case, the reciprocal angles of elevation and

Horizontal Line.

Depr.

Horizontal Line.

depression should be taken in order to ensure accuracy, and when the distances are so short that the effects of curvature

and refraction are not sensible, Elev. the reciprocal angles, if observed correctly, ought to be equal to

one another, the horizontal lines at each station being to

our senses parallel.

Tabular Form for Reduction to Horizontal Base, and for Calculation of Altitudes.

In cases where the distances are short, and the relative altitudes are not required, the reduction of the lines to the horizontal plane, previously to their being used in plotting, may be made by reference to the column for the reduction of the hypotenuse to the horizontal base, as entered in the levelling field-book, by the reading off one side of the vertical arc. But when the distances are long, or the relative altitudes required, logarithmic computation should be used. In an extensive survey, time will be saved, and errors guarded against in this operation, if the entries for the calculation are made according to the following form, thus described in COLONEL COLBY'S Instructions for the Interior Survey of Ireland.

BA 1942 B elev. 2 29 30 9.9996351 1940-3 8-6382280 84.43

spirit-level.

105.93

"In the first column of this register, the designations of the plans and plots in which the points or lines are contained are entered. The second column shows the measured length in feet of the station line, which length is to be written between the letters marking its extremities, thus, A 1942 B. The third column shows the mean or elevation depression of the second object deduced from the reciprocal angles in the levelling field-book, after applying the corrections indicated in the third column of that book, and those for curvature and refraction when very long distances render their effect sensible. The fourth column contains the logarithmic cosine of the angle in the preceding column, and the logarithm of the distance; the natural number answering to the sum of these logarithms is entered in the fifth column. The sixth column contains the logarithmic sine of the angle, and the logarithm of the distance; the number answering to the sum of these two logarithms is entered in the seventh column. The eighth column contains absolute altitudes above the low-water mark. The altitudes in this column are to be proved by always commencing at some point whose altitude is known, either from the trigonometrical survey or by levelling with the spiritlevel, and proceeding in a regular series of additions or subtractions to some other point of which the altitude is also known in like manner. In connexion with these levelling operations, observations should be made for the purpose of ascertaining the heights of the rise and fall of the tide, both at springs and neaps, at various places on the coast, &c., the altitude above low-water (spring tides) of some conspicuous part of each of the points which has been trigonometrically determined; and of a sufficient number of other points, found by levelling, &c., to prevent the accumulation of error in the altitudes given in the register.

"The survey thus performed will furnish a great number

of accurate heights, at short distances from one another, over the district surveyed; it will be easy to render this part of the work complete, and subservient to future local improvements, without devoting much additional time to this object. Not only the heights of hills, but also those of the lowest parts of the necks which connect them should be given; also the heights and depths of lakes, and the altitudes of rivers and streams in various parts of their courses. As churches are usually very prominent objects, the heights of the ground on which their towers or belfries are erected should be given as points for future reference; and a knowledge of the altitudes of mines and mineral deposits, and of manufactories, towns, and villages, will tend to facilitate internal improvements. The heights of canals should be given at all the locks, and the heights of the summit levels of roads; and also, when it can be conveniently done, the height over which a new canal or road must unavoidably pass to connect a valuable mineral deposit, or principal market or manufactory, with some adjacent harbour, navigable river, or existing canal."

144

CHAPTER V.

LEVELLING FOR SECTIONS.

Levelling for Sections with the Theodolite.

WHEN the theodolite is used in levelling for sections along a continued straight line, much time would be lost by placing the instrument at every change of level which it is desired to mark on the section. The following method is adopted to obtain the section required.

The section line having been ranged, and pickets driven at all great changes of inclination of the ground, the theodolite is set up at one extremity of the line, and the intersection of the cross wires made to bisect the vane on a staff erected at the site of the first picket, the vane being as nearly as possible of the same height as the axis of the theodolite. The angle of elevation or depression having been noted, a levelling staff with a sliding vane is taken by an assistant to each irregularity of the ground offering itself in succession between the observer and the second station, and the vane is raised or depressed on the staff according to signs made by the observer, until the centre of the vane is intersected by the cross wires. When the vane is thus fixed, the reading on the staff is noted by the assistant; this mode of levelling being only resorted to when the distances are too great to enable the observer himself to read the divisions on the staff. For example: Let A be the position of the theodolite at the first station, and B that of the staff fixed at the second station. Between A and B, the intermediate positions a, b, c, d, &c., for holding the levelling staff, are determined by the irregula