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back and fore staves can in no case equal that sum, it is evident that such correction may be safely disregard

ed in practice.

Several machines have been constructed or designed for the purpose of describing a section of any ground passed over by the instrument, which at the same time would register the distance passed over, as well as the undulations: perhaps the best of this kind was the one designed and constructed by George Edwards, Esq., Civil Engineer, of Lowestoff, which is fully described and illustrated in the forty-fourth volume of the "Transactions of the Society of Arts," page 123, to which we refer. The use of such machines, however, must, from the nature of the work to be performed, be of a very limited character.

We have now described the leading principles and practice of levelling as employed in engineering operations; and although our observations may appear to be confined to its applicability to railroad purposes, yet the intelligent student will find no difficulty in applying to practice the same principles to every other branch of the profession where levelling operations may be required. We might indeed have multiplied instances and examples which would in reality have had no other effect than to swell our volume, as it must have been, to a great extent, but simply a repetition of the details already given.

Before closing this subject we cannot refrain from stating, that it has long been our opinion that if a

register could be kept by some public body (as the Institution of Civil Engineers) of the height of particular spots throughout the kingdom, above some given datum, as Trinity high-water mark, London Bridge, or any other that might be agreed upon, such a record would be invaluable both in a particular and national point of view; to the engineer and geologist it would be most important, and the whole register could be prepared from time to time at a trifling cost, if each engineer and surveyor would but contribute to the common stock by sending to head-quarters the level of any particular spots as he, in the course of his professional engagements, may have opportunity of determining them. We consider that no time is likely to be so favourable for the purpose as the present, as nearly the whole country has been levelled over for railway purposes within the last few years; and no doubt the field notes of the greater part are still in existence from which a great many such standard levels could be extracted by the parties who took the levels, and which in a few years it will be impossible to eliminate. By way of showing more fully our meaning, we have extracted from our own levelling books a few such standard levels, and arranged them after the manner we have above alluded to.

COUNTY OF KENT.

Height in feet above Trinity high-water mark, London Bridge. Upper edge of tablet over door of No. 1 Martello Tower,

near Folkstone....

256.4

Top of first milestone on the road from Folkstone turnpike to Dover....

402.9

Top of second milestone, do...

510.7

Surface of ground at Folkstone turnpike gate..

534.6

Dock wall at Dover, opposite Railway Office...,

7.4

COUNTY OF SURREY.

Surface of ground at New Chapel Turnpike gate..

188.0

Waste board of Godstone Ponds, back of White Hart Inn 319.2 Top of twentieth milestone (from Westminster Bridge)

on the road from Godstone to East Grinstead......... 287.6

151.2

River Medway (tributary stream) meadows, west side of turnpike road, at Blundley Heath....

Broadham Green, near Oxted, foot of pointing post...... 268.2

COUNTY OF SUSSEX.

Honey-pot Lane, South Chailley Common.....

Gullage Farm, source of the Medway, near the barn.....

Waste weir canal (east side of Lindfield)...

Summit of South Downs at Plumpton Plains..

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Turnpike road, Brighton to Lewes, near the barracks...
Cross roads, at Turner's Hill turnpike gate.....

122.5

324.6

82.1

682.5

573.3

85 1

535.2

LEVELLING WITH THE THEODOLITE.

The application of the theodolite to the practice of levelling is an operation of great simplicity. We must

suppose the reader to be already acquainted with the construction and method of measuring angles with that valuable instrument; and those who have no such knowledge, we refer to the Treatise on Mathematical Drawing Instruments spoken of, where every particular respecting it may be found. The ordinary 5-inch theodolite, of the best construction, is the one we recommend to the use of the surveyor, it being sufficiently accurate for most purposes that fall within his province, and is convenient to use on account of its portability. A larger theodolite is seldom employed, except on surveys of great extent upon trigonometrical principles, as those of the United Kingdom under the direction of the Board of Ordnance, where theodolites of 3 feet diameter have been employed to obtain the requisite degree of accuracy.

To use the theodolite in the common purposes of levelling, it is only necessary to set the instrument up at every spot on the line of country to be levelled, where the inclination changes, without regard to the minor inequalities of the surface, taking care that the adjustments have been carefully examined and rectified, as explained in the book above alluded to, especially those adjustments which set the line of collimation, and the spirit-level attached to the telescope, parallel to each other. Then set the instrument level by means of the parallel plate screws, and direct an assistant to go forward with a staff, having a vane, or cross piece, fixed to it exactly at the same height from the

ground as the centre of the axis of the telescope. Having gone to the forward station, the assistant must hold the staff upright, whilst the observer measures the vertical angle, which an imaginary line connecting the instrument and staff makes with the horizon; the instrument and staff should then change places, or, to save time, another staff should take the place of the instrument, and the instrument be removed to the former staff, and from thence the same angle should be taken back again, and the mean taken as the correct

result.

The distance must then be measured, which will furnish all the data required to find the difference of level between the places of the instrument and staff; this, it will appear evident, is a matter of trigonometrical calculation,* the measured distance being considered as the hypothenuse of a right-angled triangle, of which the perpendicular is the difference of level. It scarcely appears necessary to give the rule for the calculation, but for the sake of uniformity we shall do so.†

Add together the logarithm of the measured distance, and the log. sine of the observed angle; the sum, rejecting 10 from the index, will be the log. of the difference of level, in feet or links, &c., the same as the distance was measured in.

If the distance be measured with Gunter s chain, the result (in chains) can at once be obtained in feet, by

* Capt. Frome's Work, in 8vo, published 1840.

† See Appendix I.

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