readings should then be identical in any case; if not, as before, first correct half the error by the plate screws and then the remainder by the capstan-headed screw.

2nd. The error from unadjusted attachment to the vertical axis. The former adjustment being carried out, the instrument should reverse well, that is, when levelled the bubble should remain steady in the centre of its run, however the telescope may be turned. If it does not do so, set the telescope in such a position as to show the utmost amount of error in position of the bubble; correct half the error by the plate screws, and then correct the remaining half by the special screws that affect the attachment.

In testing the correctness of levels by sighting on pairs of staves, the latter should be held in the same amount of light, that is the direction from one to the other should be at right angles to the direction of the

sun.

Levels of other patterns.-Troughton's level is a variation on Gravatt's; the principal difference being that the level is permanently fixed to the telescope, and cannot be adjusted, but the horizontal crosswire can be moved by screws until the line of collimation is set parallel to the level; this adjustment therefore in this. instrument takes the place of that for level error just described, and can be tested in the same way.

The Y level, on the contrary, is an older pattern and is now generally used of small size, having a small telescope and short spirit-level; it admits of every sort of adjustment, and frequently requires it. In this instrument the level hangs below the telescope, which rests on Y's or forks, one of which is moveable by a large screw. The adjustment for level error can be tested by lifting

the telescope out of its forks and reversing it end for end; the adjustment of attachment to the vertical axis is easily effected by a movement of the large screw attached to one fork; and the adjustment of the crosswires can be effected by screws, while the coincidence of the line of collimation with the axis of the telescope can be tested by rolling the telescope round in its forks between two observations on a distant object; as previously explained for the Y theodolite.

The larger levels made on this pattern were sufficiently good for the times when people seemed indifferent whether their drains ran uphill or downhill, but they are now used in small sizes only for rough work, such as foundations of buildings. The inherent defect of the pattern being the shortness of its spirit-level, similar large instruments would be heavy.

An improvement on Gravatt's level is sometimes used, which has a moveable inner telescope-tube and admits of testing and adjustment of the line of collimation.

The theodolite can be used, with its vertical arc clamped, in the same way as a level; but it is heavy. Some Austrian universal instruments are very light theodolites intended also for use as levels in this manner; they mostly suffer from the defect of having the telescopes too small for levelling operations of an extended nature; but their lightness of make and portability present an advantage that might well be partially imitated by English instrument-makers.

There is also a type of level distinct from the above, that admits of taking sights on inclinations; in some, the telescope turns in a vertical plane about its middle, to which an index is attached at right angles reading

on a graduated vertical arc; in others the telescope turns in a vertical arc on a hinge near one extremity, the index at the other extremity reading on a vertical arc of larger radius. They are useful in moderately hilly country or for rather rapid inclinations, but necessarily lack the steadiness and simplicity of instruments of the former type, and are not so well suited for work in level country.

There is also a combination of the level with a reflecting circle invented by Professor Piazzi Smyth, that has some special advantages.

6. Reflecting Levels.-These are generally very small instruments without telescopes, intended for rough use in short distances, and generally used in very steep country for interpolating between contour lines, and setting out gradients of hill-roads and paths.

The simplest form of such instruments consists of a half-silvered small mirror attached to a ring and weighted below to keep it vertical in windy weather; it is used either suspended on the finger or on a light staff of known length; the horizontal edge of the silvering acts as the horizontal wire of a diaphragm for sighting on a graduated level-staff, or on a vane staff, the reflection of half the eye being seen in the mirror when the sight is correctly taken.

Another form is the tube reflecting-level; this consists of a small brass tube having a small spirit-level attached, and having a small mirror covering half of one end of the tube; on taking a horizontal sight on a levelstaff the round bubble of the level is reflected in the mirror, or appears to pass the horizontal edge of the silvering. The attachment of the level to the tube admits of adjustment by screws.

Each of these instruments should be tested before use, especially the latter, which has not the advantage that the former possesses, of affording a steady sight. The principle adopted in the tube reflecting-level has been applied in larger telescopic levels, and is more satisfactory in instruments with stands; the size of the bubble in a spirit-level may be increased or diminished as required from air in a reserve chamber at one end of its tube specially constructed for the purpose; this is a great advantage in hot countries where the bubble's length may contract to one-half in an hour.

7. The Barometer is used for taking flying levels, more especially in hilly country; a pair of tolerably large aneroids, reading clearly to hundredths of an inch, are best for the purpose. The correction for temperature can be either calculated in accordance with the indications of a thermometer, and by comparison with a standard mercurial barometer, or the instruments may be self-compensating for change of temperature; the former method is preferable unless the self-compensation has been thoroughly verified by the observer. The testing and verification should be made both before and after any series of observations, and the correction for temperature suited to each instrument recorded for future reference. Two barometers are necessary for practical work in determining heights; after comparison one is kept at a fixed spot throughout the day and its variations recorded every quarter of an hour during the time that the other is in use at neighbouring points where its readings are recorded. Another method is to take simultaneous observations with two aneroids along a series of stations within signal of each other; thus obtaining a series of relative elevations.

The difference of barometric reading due to increase of height is nearly oor inch less for every 10 feet of increased elevation above mean sea-level, at a permanent standard temperature of 55° Fahrenheit. The following scale is calculated according to the formula

where b is the barometrical reading at the upper station in inches, and h is the elevation in feet; the values are arranged to admit of interpolation.

For any other permanent temperature (t) at any two stations, where the barometric readings are B and b, the Schuklburgh scale for thermometric variation of the height of a column of air, gives the formula,

if B is the barometrical reading at the lower station, b is the barometrical reading at the upper station, T the temperature at the lower, t at the upper, the ordinary formula is

B b

h=60360xlog x1+0·001014(T+t−64°)}