But this formula will not by any means apply correctly to any aneroid barometer; the correction for each instrument should be determined by experiment and comparison with a good standard.

Elevations under 5000 feet can be determined with aneroids within 10 or even 5 feet, if pairs of instruments be used simultaneously: with instruments used independently the errors may be as large as 30 feet.

8. The Hypsometer is a very sensitive thermometer for determining the temperature of pure water when boiling, and thence calculating the elevation of the place above that where the same hypsometer would indicate a boiling point of 212° Fahrenheit; the temperature falls one degree Fahrenheit for about 540 feet of increased elevation.

If D is the depression of temperature of the boiling point in degrees Fahrenheit, h the elevation in feet,

This instrument is suited to determining elevations. above sea-level of spots in mountainous countries in travellers' explorations.

A selection from some hypsometrical observations taken in Thibet will be found in field record No. VII.; they apply to the stations of the route-survey of field record No. VI. shown in reduced plan Plate XI.

Formula and Calculations.

The calculations in connection with levelling are generally of a very simple nature; they mostly consist in the addition of lengthy columns of level-readings by various methods that verify the results; examples of the two more common modes of doing this, the Rise-andFall, and the Collimation-sight method, are given in the

Forms of Record, or patterns of level-book, following. The formulæ required are very few, and are hence given with the account of the instrument and method to which they more specially apply.

Demarcation of level-points. (See Demarcation of Survey-points, Chapter I., pages 67 to 69).--Temporary points may be marked with whites; more permanent level points by single square pegs, to distinguish them from round survey pegs; and specially important level points by two square pegs near each other, so driven that their heads are level. Such pegs should be nearly flush with the ground. Flat-headed iron pins may be used for the same purpose. Bench-marks are generally chiselled on some permanent stone slab, pillar, or wall; the usual form of mark for them is. The upper surfaces of portions of permanent ironwork, rails, flanges of girders, parts of gates, are also made to serve the same purpose, some cross-mark being generally dinted with a chisel to mark the point; in every case a sketch and full description of the position of the bench-mark, both with regard to surrounding objects and the parts of the structure on which it is made, should be recorded. More time has perhaps been wasted on account of want of sufficient precaution in this respect than from any other sort of neglect in operations of this class. It may also be noted that giving insufficient information about bench-marks, or marking them insufficiently or doubtfully for others to work from, has always been a fruitful source of error.

Section 2. CLASSIFICATION OF LEVELLING
OPERATIONS.

The operations of levelling may, like surveying operations, be classified according to the principal instrument chiefly used; such an arrangement would not however be very practical, as the greater portion of levelling operations conducted by Englishmen is now generally carried out with levelling instruments of the Gravatt type; it is more convenient for this as well as other reasons to treat the subject with reference to the various intended objects and the scope of operation; and to classify the modes of operation in accordance with the nature of the ground over which the work proceeds. The more usual objects are:

I. To obtain levels or relative heights of the principal natural features of an extent of country.

2. To obtain sufficient levels over a portion of country for producing a perfectly contoured plan of it, from which the level of any point may be approximately deduced.

3. To obtain a simple chain of distant bench-marks along a line of country for subsequent reference.

4. To take a series of detached or flying levels with a small amount of labour which may serve as a guide in preliminary designs of works of communication.

5. To take such levels in any long strip of country, within previously determined lateral limits, as may sufficiently serve for the purposes of detailed designs of works of communication.

1. The natural features of a country are made up of its distinctive varieties of surface, which are most strongly