By comparing these results with those obtained by the former process, it will be seen that the cubical quantity of cuttings differs but two yards, and that of the embankments but one yard. The computation by the Tables may be abbreviated by using but one place of decimals, which would be sufficiently accurate for practical purposes. Our object is to show the calculations, by the Tables, in their greatest extent, which even then produce a great saving of labour, and, of course, a much greater probability of accuracy, in consequence of the fewer figures employed, than the former process. It will be seen that the calculation of the embankments by the Tables is a longer process than that of the cuttings, the latter being done by simply multiplying a number taken from the Tables (answering to the height or depth at each end) by the length; whilst, for the embankments, the tabular number is first multiplied by the base (or width of roadway), and to the product is added a second tabular number taken out at the same time as the first. The first series of Sir John Macneill's Tables contain the numbers corresponding to a base of 50, and a slope of 1 to 1 (which is the slope of the cuttings in our example). But for a slope of 2 to 1, reference must be had to the second series of the same tables, which are applicable to every width of base, and from slopes varying from to 1, to 3 to 1. We have adopted this example to show the calculations both by the particular and general Tables, as the first and second series of the valuable work referred to may be called. The following is an extract from Sir John Macneill's preface to his Tables :-"All practical engineers are well aware, by experience, of the inconveniences which arise from the length of time necessary for calculating the cubic quantity of earthwork in the cuttings and embankments of canals, railways, and turnpike roads, especially when the section is of considerable extent, and the ground very uneven. As calculations of this kind are frequently, on a short notice, required to be completed within a limited period, the consequence is, that errors are almost sure to be made, as a multipliplicity of figures is necessary, though the calculations in themselves are so very simple. "To save time in making these calculations, and ensure accuracy in the results, were the principal objects I had in view in constructing the following Tables; how far I have succeeded, must be left to the decision of practical men, for whose use they were intended, and who are best able to judge of their utility. An advantage may rise from the use of these Tables, which I had not at first contemplated. By the common but erroneous method of calculation, the cuttings may appear to be equal to the embankments; yet when the work is carried into effect, a large quantity of earth may be required to make up the embankments, or there may be too much earth in the cuttings for the embankments, according to the shape or figure of the section, as will be shown hereafter. Such a circumstance as this cannot take place if the following Tables be used to ascertain the cubic quantities; for, as they are calculated from the prismoidal formula, they will give the true cubic quantity in any cutting or embankment; and consequently, if the cuttings be laid down on the section to balance the embankments, they will be found in practice to do so, when the work comes to be executed. "Contractors very frequently find that they have more earth to move than they had previously calculated upon from the section, and are, therefore, often great losers. This, in most cases, arises from erroneous calculations; for the common practice is, either to add the two extreme heights together, and to take half the sum for a mean height; or to take half the sum of the areas at each end for a mean area. Both these methods are erroneous; one makes the quantity too much-the other too little." SLOPES, ETC. As connected with the subject of earth-work, we may insert in this place some particulars respecting the arrangement of slopes in cuttings and embankments. They are usually expressed in terms of the height or depth of cutting, as half to one, one to one, two to one, &c., signifying that for every foot perpendicular, the cutting shall batter half a foot, one foot, two feet, &c. The slope adopted must depend upon the nature of the material worked upon. Solid rock may be left perpendicular, whilst loose friable material, or sand, will stand but a very small angle with the horizon. The true criterion to judge of the proper slope to work to, is to observe, if convenient, what slope or angle the materials naturally assume when left to themselves. To determine this by measurement would be troublesome and tedious; but by the aid of a small instrument called a clinometer, the angle which any sloping surface makes with the horizon may be at once measured, and the ratio of the slope to the perpendicular, as one to one, &c., be readily deduced. As this very |