tion level above datum is 269.20, from which point the gradient descends at the rate of 20 feet per mile, or 0.25 feet per chain, towards No. 1083; the distance from 1064 to 1083 is 19 chains, which multiplied by 0.25, gives 4.75 for the fall of the railway in the interval between the two points; consequently the height of the railway above datum at No. 10.83 is 269.20, minus 4.75 264.45; this sum, subtracted from the whole height of the surface, gives 344.78-264.45 — 80.33, for the depth of the cutting at that point, and so of all the remaining numbers. After giving the above particulars nothing need be added upon this subject. It may be worth observing, that in laying down the gradients care should be had so to dispose them as to produce the minimum quantity of work in the execution, and that the cuttings should equalize the embankments, or, if anything otherwise, they should be a little in excess, to allow for subsidence or slips in the embankments. The facilities for working the excavations and carrying the earth to bank should also be considered; a down-hill gradient in that direction is most suitable, provided it can be obtained without interfering with other and often more important considerations; the drainage of the works during the formation and after the line is completed should also be considered at the time of determining the gradients. We have inserted (Table I. at the end of the work) a very extensive and useful Table of Gradients, which is sufficiently self-explanatory as not to require further notice. When a surveyor is required to level through a country in a perfectly straight line, and has not the advan tage of its being picketed or poled out, his only means to keep a rectilineal course is by ascertaining, as accurately as possible, the magnetic bearing of one extremity from the other, and work in that direction by means of a compass. We once had business of this kind, and determined the bearing of our intended line from the map of the Ordnance survey (allowing for the variation of the needle), and after pursuing the route thus determined, we were surprised and delighted at finding how exactly we came to our required point, convincing us (if a proof had been required) how justly the public confidence has been placed in our national survey. It is seldom the case in practice that the instrument can be placed precisely equi-distant from the back and forward staves, on account of the inequalities of the ground, &c. It would appear, therefore, to be necessary, to make our results perfectly correct, to apply to each observation the correction for curvature and refraction, as explained in the early pages of our book; this, however, we believe, is seldom done unless in particular cases, where the utmost possible accuracy is necessary, on account of the smallness of such correction, as may be seen by referring to our Table, page 13, where the correction for eleven chains is shown to amount to no more than of a foot; and as the difference in the distances of the instrument from the 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. 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. By 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 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) ....... 287.6 on the road from Godstone to East Grinstead........ River Medway (tributary stream) meadows, west side of turnpike road, at Blundley Heath.... Broadham Green, near Oxted, foot of pointing post...... 268.2 151.2 COUNTY OF SUSSEX. Honey-pot Lane, South Chailley Common.... 122.5 Gullage Farm, source of the Medway, near the barn..... 324.6 Waste weir canal (east side of Lindfield)... Summit of South Downs at Plumpton Plains... 82.1 682.5 Turnpike road, Brighton to Lewes, near the barracks... 851 535.2 LEVELLING WITH THE THEODOLITE. The application of the theodolite to the practice of levelling is an operation of great simplicity. We must |