NEW METHOD OF CALCULATING THE CUBIC CONTENTS OF EXCAVATIONS AND EMBANKMENTS, BY THE AID OF DIAGRAMS. BY JOHN CCr~RAUTWINE, CIVIL ENGINEER. SECoND EDITION. -REVISED. PHILADELPHIA: R. W. BARNARD, PRINTER. 1853. Entered, according to the Act of Congress, in the year 1851, by JOHN C. TRAUTWINE, in the Clerk's Office of the District Court of the United States, for the Eastern District of Pennsylvania. NOTICE. Mr. Joseph Hufty, the enterprising Engineers' Stationer, No. 139 Chesnut street, Philadelphia, having proposed to me, that he would prepare a handsome copperplate engraving of figure 5, for sale, on condition that I would secure a copy-right, and transfer it exclusively to him for a limited time, I have done so. Mr. Hufty's engraving will be found more accurate than paper ruled by the stationer's multiple pen; and will moreover exhibit the slopes, &c., which could not be effected by the ruling process. As this engraving will.be required only in cases where the ground-slope cannot be regarded as uniform, throughout the width occupied by the excavation and embankment, it will rarely be necessary to use more sheets of it than there are miles in the length of the road. Its title is "Trautwine's Cross-section Diagram." Mr. Hufty will also print upon transparent paper, a diagram of Transverse Groundslopes, which, being laid upon a sheet of figure 5, will give by inspection, the horizontal distances of the side-stakes from the centre. I have no other interest in these engravings, than the desire to facilitate a thorough testing of the merits of my plan. For merely obtaining Cubic Contents, the division of figure 5 into squares, is not necessary; their use being confined to the determining of the side-distances. J. C. T. ERRATA.- NoNE. PREFACE. Although the usual methods of obtaining correctly the cubic contents of Excavations and Embankments, cannot be said to involve any dificulty, still they are certainly open to the objection of being very tedious. Consequently, any device for diminishing the labor, without affecting the accuracy, of the operation, may justly be regarded as a desideratum of some importance; and, in the belief, that the method by diagrams which I here propose, will conduce to that result, both in the field and in the office, I submit it to the notice of the profession. It originated with myself, several years since; but the want of sufficient leisure to reduce it to its present form, has hitherto prevented me from giving it publicity. Should an objection be made to the admission of the transverse ground-slopes, as an element in the Calculations, I can only reply that, practically, it is at least as accurate as that based upon the usual assumption, that the two outer heights or depths of a crosssection represent the exterior elevation of straight lines, drawn from those points to the centre-stake. Sensible of the necessity of perfect accuracy in the Tables, I have prepared them all with the greatest care; and they have undergone so many revisions, both before and after being stereotyped, as to leave no doubt of their entire reliability. JOHN C. TRAUTWINE. A NEW MET HOD CALCULATING THE CUBIC CONTENTS or EXCAVATIONS AND EMBANKMENTS. There is but one correct principle upon which to calculate the cubic contents of excavations and embankments; and that is, by means of what is known as the Prismoidal Formula, or Rule. This Rule is as follows: AJdd together the areas of the two parallel ends of the prismoid, andfour times the area of a section half way between and parallel to them,; and multiply the sum by one-sixth of the length of the prismoid, measured perpendicularly to its two parallel ends. Since, in railroad measurements, the prismoids are generally 100 feet long, it becomes easier in practice to multiply the sum of the areas by 100, (by merely adding two ciphers,) and to divide the product by 6; which amounts to the same thing as multiplying their sum by ith of 100 feet. The very general application of the prismoidal formula to other solids than such as are commonly understood by the term "prismoids," has been shown by Mr. Ellwood Morris, Civil Engineer, in an able paper published in the Journal of the Franklin Institute. Vol. xxv, 2d Ser. p. 381. It embraces all parallelopipeds, pyramids, prisms, cylinders, cones, wedges, &c., whether regular or irregular, right or oblique; together with their frustra, when cut by planes parallel to their bases; in a word, any solid whatever, which has two parallel ends, connected together by plane or unwarped surfaces. It also applies to spheres, hemispheres, spheroids, paraboloids, &c. In the cylinder and cone, the sides may be considered as consisting of an infinite number of infinitely narrow unwarped planes. In railroad cuttings, it rarely happens that the ground surface lying between two 6 consecutive cross sections 100 feet apart, is absolutely unwarped; yet, for practical purposes, it may very frequently be assumed to be so. When much warped, the cross sections must be taken closer together than 100 feet. There are generally two circumstances under which it is necessary to compute the cubic contents on a public work; viz: first, after a preliminary survey of one or more trial lines, for the purpose of determining approximately their actual, or comparative costs; and, second, after the final adoption and staking out of the determined route, in order to knowprecisely the amount of work to be done. The measurements for the latter are performed with considerably more care, and attention to detail, than those of the former, inasmuch as upon them depend the payments to be made to the person who executes the work. They, moreover, involve considerations which cannot be attended to during a preliminary survey, without incurring an expenditure of time and labor, more than commensurate with the importance of the result. When the ground is level transversely of the line of survey, there is no difficulty whatever in ascertaining the contents from a table of level-cuttings, previously calculated; but when the ground is inclined or irregular transversely, the calculations have hitherto been attended with considerable labor. The following method by diagrams, devised by myself during my probation as an assistant, and now communicated for the first time, will, I trust, be found to render the operations in the last cases nearly as simple and expeditious as in those of level ground; or, at least, infinitely more so than the usual ones. It dispenses with a great deal of calculation, and is, therefore, comparatively free from liability to error arising from that source. METHOD OF USING THE DIAGRAMS. The construction of the diagrams is extremely simple, notwithstanding that, at first sight, they appear somewhat complex. They are but few in number, since any particular road will generally require but three or four, which may be prepared by one person in a day or two. Before proceeding to explain the manner of drawing them, I will give one or two examples of their use, that the reader may see the object aimed at, and to what extent it is attained. Example 1. Suppose that in a roadway of 28 feet wide, and with sideslopes of 1i to 1, the cutting at a. certain station is 20 feet; and that the ground, instead of being level transversely, inclines at an angle of 15~. Turn to the diagram (page 29) for a roadway 28 feet wide, with sideslopes of 1 -to 1: place a finger on the centre line, at the height of 20 feet, and run it along up the curved line which commences at that point, until it strikes the inclined line marked 150. It will be seen at once that the two coincide at the height of 22'8 feet: and this is the depth of the equivalent level cutting, which would have precisely the same area as the section under consideration. 7: All such cases may therefore be instantly, and without any calculation whatever, reduced to others of equivalent level cuttings. This constitutes the main feature of the principle involved in the diagrams. Had the depth been 20'3, or other decimal of a foot, the proceeding would have been the same as with the 20 feet; and the equivalent level cutting would be found on the inclined line 15~, at the distance of 3 of a foot (estimated by eye) above the curved line 20. Example 2. Using the same diagram; let the depth of cutting be 2 feet, and the transverse slope of the ground 20~. Here, placing a finger on the centre line, at the height of 2 feet, and running it along the curved line commencing at that point, it will be found that before reaching the inclined line of 200, it encounters the dotted curved line drawn near the bottom of the diagram. When this occurs, we know that the ground-slope cuts the roadway, forming a cross section, partly in excavation, and partly in embankment, as in fig. 9. This is a most useful check; for in such cases, the contents cannot be obtained by means of the diagram; but recourse must be had to a figure of the section drawn for the purpose; as must also be the case when the garound is irregular transversely. A simple method of proceeding, in all such cases, will be given further on. I trust that what has been already shown, will satisfy the reader that my method partakes of utility, as well as of novelty. On the page opposite each diagram, is a table of cubic yards for level cuttings, and for lengths of 100 feet. By means of this, the cubic contents may at once be taken out, when the equivalent level cuttings at both ends of a station are equal: but if they are not so, the prismoidal rule must be employed, thus: Suppose the equivalent level cutting at one end to be 20 feet, and at the other 25 feet. Then, that at a point half way between them would be 224 feet. Therefore, the cubic content will be equal to one-sixth of the sum of those corresponding to each of the two end depths, and of four times that of the centre depth; that is, Cubic content by table Ix, for 20 feet depth - 4296 cubic yards, (c," " ~' 25 " = 6065 " " Four times " "22, - 584, or 4 times 5146 20584 " " 6 )30945 Cubic yards contained in the station, = 5157'5 It will be perceived that, instead of the areas corresponding to the different depths of cutting, or heights of filling, our tables give the cubic yards corresponding to those areas, for lengths of 100 feet. For the purposes of calculating cubic contents, these solidities may evidently be used instead of the areas; but for such cases as require the areas themselves, a table of such is added. Its use will be shown further on. I will here observe, that for mere comparative estimates of trial lines, the labor may be much reduced by taking from the tables, the cubic con. tent corresponding to the average of the equivalent level cuttings at the two ends. This mode is, of course, by no means mathematically correct, and should never be resorted to for final estimates; but it will frequently be sufficiently approximate (always a little deficient) for such trapezoids as occur in ordinary cuttings and fillings, where the depths at the two ends difer'but afewfeet. For instance, in the foregoing example, the correct contents of the station 20 feet deep at one end, and 25 feet at the other, were found to be 5157'5 cubic yards; while by this approximating mode, the contents of an average equivalent level depth of 22- feet, would be 5146 cubic yards; or but 11- yards less than the truth. In this manner, an entire cut or fill may be approximately estimated at one operation, by merely adding together all the average midway equivalent level cuttings or fillings, and dividing their sum by their number for an average one of them all. Thus, if the average midway equivalent level depths of 6 consecutive stations of cuttings, be respectively 2, 5, 6, 4, 3, 7 feet, an average depth may be taken of 2~5+6 + 4 + 3+7 27 depth may be taken of 6 - -= 45 feet; and thecubic contents taken from'the proper table, for a depth of 4'5 feet, and multiplied by 6, (the number of stations,) would give the contents of the whole 600 feet, but slightly too little. PRINCIPLE ON WHICH THE METHOD IS BASED. To find the sides of a triangle, of which toe have given, the area, and the angles. RULE.-In any plane triangle, as the product of the sines of any two Fig. 1. of the angles, is to the product of radius by the sine of the remaining angle, so is twice q:................P the area of the triangle, to the square of the side lying between the two angles first taken. - - X X Demonstration.-Let a d e be a triangle,,~ —— /|\! in which we have given, its area, and its | / \three angles: it is required to find any side, aa e. a'LO o —-e e By trigonometry we have the two following proportions:Sine of a (d c): Radius (a d):: d c: a d; also Sine of e Sine of dd * ae. theangleopp. a d' theangle opp. a e a By multiplication of these two proportions, we haveSineof a X Sine of e: Rad. X Sine of:: d c X a d: a e X a d; or, 1 leaving out the factor a d, common to the last two terms, Sine of a X Sine of e: Rad XSine of d:: dc: ae. But, asdc: ae:: dcXae: a e2,(becausedc X ae=the rectangle a enm; and a e2 —-a ep o.) Again, d c X a e=twice the area of the triangle a d e. Hence we haveSine of a X Sine of e: Rad X Sine of d 2 area: to a e2, the square root of which=a e, the required side. Q. E. D. Now, let n m c b, fig. 2, be the level cutting equivalent, or equal to the side-hill cutting n mn e d. From the point of intersection at i, draw Fig. 2. ia. / Then, if t ul represent any other side-hill cutting parallel to d e, we. f I have only to draw the horizontal i.. line x w, through s, in order to obtain the equivalent level cutting n s. g.. )...._G m WX..s The demonstration of this, on the principle of similar triangles, is so i simple as not to require insertion. / The point required is to findf i, the distance to be laid off on the'. horizontal linefc, in order to draw z a. To do this, we have the triangle a e d, of which we know the area, (composed of the triangle n m a, and the level cutting n m c b,) and also the three angles, (derived from the side slopes and ground slopes.) First find the side a e, by the rule just given, viz: Sin a X Sin e: Rad X Sin d:: 2 area: a e2. Then find r a, thus: Sine of e r a. Sine ofe.. opp. given side a e. * opp. req'd. side r a. * a e Thenfa-r a=rf. Also, the angle e i c, representing the ground slope, is equal to the anglefi r; and considering fi as a radius, and rf as a tangent to the anglefi r, we haveNat. Tang. off i r, (or ground slope,): Rad, or 1:: rf: fi. Then as af: fi:: 1:: fi when a f is assumed as unity, in preparing a working diagram. To save the reader the trouble of calculating these distancesf i, I have in this edition extended the table to all side slopes likely to occur in practice. 2 10 METHOD OF PREPARING THE DIAGRAMS. I will now proceed to describe the mode of preparing the diagrams, for any width of roadway, and for any side-slope whatever. Draw a vertical line a b, fig. 3, of any given length at pleasure. (One Fig. 3. foot decimally divided; or 12- inches, divided into -ths of an inch, or 10 b a e inches divided into 1 ths of an inch, will generally be found convenient.) Call the length of this line unity, or 6 1. It represents the usual centre-line.15 Iof levels, or of cuttings and fillings. 3 From the upper end of this line draw 2.9',. b c, at right angles to it; and from b e.. 5 towards c, lay off and number the distances b50, b100, b150~, &c., contained in the following table; using as a scale the length a b, as 1 or unity, divided into tenths and hundredths. For example; if the side-slopes h e, gf, of the excavation or embankment, are i_ to 1, lay off (without any regard to the width of roadway,) the distances on the upper column of the table; if 1 to 1, those on the 3d column, &c. This done, the scale of a b, as unity, will be of no further use. Distances on b c, intermediate of those in the table, may be inserted with sufficient accuracy by eye. Those beyond 200 will rarely be required; because, when the transverse ground-slope is great, retaining walls are resorted to as a matter of economy. ITable of Distances from b, to be laid off on the Horizontal Line b c, Fig. 3; the Line a b being assumed as Unity, or 1. Side Slopes. 100 200 250 3oo 350 400 450 5oo 550 600 650 7oo i to 1, ~.005 011 014 017 022'026'032 038 *046 057'073'099 or 750 5810''1 Side Slopes. 50 10 150 200 250 300 350 400 450 500 530 550 i to 1,'011'022 *034'046'058'072'090'110 *132.165 *189'211 or 630 26'._ Side Slopes. 50 100 150 180 200 23~ 25~ 280 300 330 360 390 1 to 1,.044'089'136'167 *188'222 *247'288 |318 *369'431'510 or 450 Side Slopes. ~ 50 100 130 150 18~ 200 230 250 280 300 320 340 a1 to 1,, tor3342 1,097 1.158'201'267 314'390'445'506 574'*652'696'747 Side Slopes. 30 50 80 100 12~0 14~0 160 180 190 20 210 220 or 26134,'106'175'285'363'447'533 629 -*739'798'865 -936 1'017 or to 1,'112'226 340'454 582'719'875 10569 or 210 48' Side Slopes. 20 40 60 80 O 12 14 3 to 1, 20~40 60 8~ 0 120 140 or 18~ 26't 160'322'486'660'858 1'080 1'349 11 From the points 50, 100, 15~, &c., on the line b c, (and from the sub-, divisions of single degrees between them, as shown in the working diagrams,) draw lines to a. From a upwards, set off, by any scale at pleasure, (from / th to 8th inch to a foot will be found convenient,) the distance a o, which is the height of the triangle ef a, formed by the prolongation of the side-slopes gf, and h e to a; ef representing the width of the roadway, whatever it may be, on the same scale. It is not necessary actually to draw h a, g a and ef, as we may set off a o, by recollecting that if the side-slopes are ~ to 1, then a o will be 4 times of, (the half width of roadway.) I- to 1, " " twice of. 1 to l, " C equal to of. 1 tol, "'" ofof 2 to, " " of of. 2, to 1, " " 4 of of: 3 to, ",of of. Beginning at o, divide the vertical or cen'tre line o b, by the same scale into feet; numbering them 1, 2, 3, &c., from o upwards; and from the points of division 1, 2, 3, &c, draw horizontal lines parallel to b c, as shown in fig. 3 From o as a centre, lay off with a protractor, the several angles of transverse ground-slope as shown by the arc in fig. 3. As before remarked, angles higher than 20~ will seldom be required. NoTE.-In fig. 3, the inclined lines, and also the angles on the arc, are, for convenience, numbered only for every 50; but in a working diagram they should be taken nearer together, fbr instance, every 2~ to 3~. Lay a parallel ruler from o to 50 on the arc, and mark with a dot the point of intersection on the inclined line a 5~; then keeping the ruler in the same position, move it upwards along o b, stopping at every division of 1 foot, and making corresponding dots on the inclined line a 5~, as in fig. 3, continuing to such a height on the centre line as will include the greatest cutting or filling to be calculated by the diagram. Then lay the parallel ruler from o to 10~ on the arc, and mark with a dot, the point of intersection on the inclined line a 1~00; then keeping the ruler in the same position, move it upwards along o b, stopping at every division of 1 foot, making corresponding dots on the inclined line a 100~. Then lay the parallel ruler from o to 15~ on the are, and proceeding as before, make corresponding dots on the inclined line a 15~, and so on up to as high an angle as will equal the greatest transverse slope of the ground which occurs on the work to be calculated by means of the diagrains. Finally, connect the corresponding dots on the several inclined lines, forming thereby a series of curves, as shown in fig. 3, and also in our working diagrams. The diagram is now ready for use, for all cases of 12 ground-slope which do not intersect the roadway, thereby forming a section partly in excavation, and partly in embankment, as shown in fig. 9. In order that the diagram itself may inform us when this is the case, the dotted curve shown near the ~Fig. 4~ bottom of the working diagrams d is added. It is prepared as follows: Let a b, fig. 4, represent the width ofroadway, (in excavation, if for a diagram of excavation; or in embankment, if for a diagram of embankment,) and c d the centre line of cuttings and fillings. From d as a centre, lay off with a protractor, the angles 5%, 10~, &c., and draw the lines a e, aj; a g, &c., to the centre line. Now, suppose the height c e, corresponding to 50, to be 2 feet. Mark on the working diagram, the intersection of the curved line of 2 feet with the inclined lineof f50. Suppose the height cf corresponding to 100 to be 4 feet; and mark on the diagram the intersection of the cumved line of 4 feet with the inclined line of 10Q; and so on with the rest. Then join their several marks of intersection, and the dotted curve is formed, and the diagram is finished. The working drawings which I have given, are on a scale of 11,th of an inch to a foot, for convenience of insertion in this volume; yet, although the curved lines are drawn straight across several divisions of the inclined lines, (generally five of them,) they will rarely be found, in operating with them, to differ as much as -i'-th of a foot from the truth. They are adapted to such widths of roadway as I judged most likely to be adopted in ordinary practice, viz: for single and double track embankments, 14 and 24 feet wide on top, and with side-slopes of 1J to 1; and for single and double track excavations, 18 and 28 feet wide at bottom, with side-slopes of from 1 to 1, up to 2 to 1. The widths will rarely differ more than 2 feet from those for which the diagrams have been prepared. The most mistaken economist would hardly venture to make them more than 2 feet less; nor do I conceive that any advantage would attend making them more than 2 feet greater. It is sometimes advisable to increase the quantity of excavation to be taken from a cut, in order to furnish earth for an adjoining embankment. When the value of land is not sufficiently great to constitute an objection, this may generally be most advantageously effected by merely increasing the side-slopes of the cut to 2 or 3 to 1; but, where that would not be sufficient, it becomes necessary to increase the width of the cut at bottom also, and separate calculations must be made for the purpose. No diagrams accompany the tables of level cuttings for side-slopes of 4 to 1, which are used only for rock; because with this side-slope, the transverse inclination of the ground rarely aflects the quantity of material to an important extent. Still, on every work on which much rock cutting 13 occurs, a diagram should be prepared for the purpose; neither are therediagrams, or tables for slopes of i to 1, 21 to 1, or 3 to 1. Should other widths of roadway be adopted, new diagrams must be drawn for them; as also new tables of level cuttings calculated. These new tables may be easily made by merely adding to, or subtracting from the contents corresponding to every consecutive'lth of a foot of depth in the tables of level cuttings, an additional'741 of a cubic yard, for each 2 feet of width added or subtracted. For example, suppose that the roadway, instead of 28 feet, is to be made 30 feet wide, with side slopes of 1j to 1. Here, By the continual ad- Cubic Yards in a 30 ft. The Cubic Yards for a 28 feet Road- dition of'741 of a Roadway; equal to way are by the Table, Cubic Yard, we ob- the sum of the two tain, preceding columns, Depth in Feet. Cubic Yards. ~1.... 104...' 741.. 11'1 -741 *2.. 21.0. 1-482.. 22-5'741 *3.. 31-6.. 2223...33-8'741 -4... 42'4....2964... 45-3'741 *5.... 53-2... 3-705.. 5669 6741 -6... 64-2... 4-446... 68-6 -741 -7... 75-3.. 5187 *.. 80-5 -741 ~8... 86-5....5-928.... 92-4 -741.9... 97-9.. 6669.. 104-6 -741'10 *.. 109-3... 7-410.. 116-7 Had the new roadway been 26 feet wide, instead of 30, the third column would have been subtracted from the second, in order to form the fourth one. For mere approximate, or preliminary estimates, it is not absolutely necessary to calculate new tables of level-cuttings for widths differing 2 feet from those which I have assumed in the working diagrams. The contents of an excavation or embankment may be taken from the nearest table, by means of the equivalent level-cuttings deduced from the diagrams; and an allowance be made afterwards for the 2 feet difference of 14 width, by adding together all the average midway level depths, and dividing their sum by their number, for an average depth of the whole. The number of cubic yards taken from table 14, fbr this average depth, and a width of 2 feet, will, when multiplied by the number of 100 feet stations in the cut or fill, be approximately the amount to be added to, or taken from, the quantity previously obtained from the tables; being more nearly correct in proportion as the ground-slope is slight. While the width of roadway remains the same, a separate diagram is required only for each side-slope; so that when the roadway has the same width in cuttings, and on embankments, with side-slopes of 14 to 1 in both, but one diagram is necessary for the entire road. But, generally, the roadway is wider in the cuts than on the embankments; requiring at least one diagram for embankments, with side-slopes of 14 to 1, and one for excavations, with such side-slopes as may be adopted. Frequently one will be required also for rock-cuttings, of 4 to 1; and if different side-slopes of excavation are employed in different kinds of soil, a diagram must be prepared for each side-slope. An entire set for any particular road, may be completed by a ready draughtsman, in a day or two. CASES OF GROUND WHICH IS IRREGULAR TRANSVERSELY. All cases of irregular transverse ground-slope, (except that in which the ground-slope intersects the roadway, as in fig. 9,) may easily be reduced, by drawings, to such a form that their equivalent level-cuttings may be obtained by means of diagrams, and the corresponding contents taken out from the tables. For this purpose it is very convenient to have paper of about 14 by 24 inches, ruled across in both diFig.,5. rections, with parallel lines about 1*1 A;'' -,I -th of an inch apart, as in fig. 5.....' i..... Every fifth line should be..........stronger than the intermediate _.. ".::::-; —.I!i ones, if drawn or engraved; or of,io...' I,_ a —' — a different color, if ruled by a stat......l.. -,ti..'"...- tioner. By means of the multiple ruling pens used by stationers, _ _ _ _ _;i;; ~ I this paper is ruled to order, at a............... -.... 1...... i very trifling cost. _" i;.......:'............. When this ruled paper is prepared for use at leisure moments, according to the following directions, nothing more will be required in order to obtain the data for the subsequent calculations, than a parallel ruler about 2 feet long. Those flat rulers which move on rollers are preferable to those with hinges, which invariably get out of order in a short time. The ruled paper is prepared by drawing upon some sheets, outlines of 15 the side-slopes of an excavation, with a small piece of embankment below it, as in fig. 5; and upon others, the side-slopes of an embankment, with a small piece of excavation above it. The heights, or depths, should be numbered along the centre line, as in fig. 5. Finally, lay off on both sides of o as a centre, by means of a large protractor, single degrees up to as high as the greatest transverse ground slope for which the paper is to be used; this, as before remarked, will rarely exceed 20~; because, with high transverse ground-slopes, it is generally better to resort to retaining walls. The paper is now ready for use, and all the subsequent operations may be performed by the parallel ruler. One sheet may be made to serve for the calculations of many stations, by merely drawing in the transverse ground-slopes, very lightly, with lead pencil marks, which may be rubbed out as each station is finished. It is advisable, however, in very irregtdar sections, to represent but two consecutive ones on one sheet; and after having drawn them in ink, and added the numbers of the sections or stations to which they belong, as well as the cubic content comprised between them, to lay them aside for future reference, in case of dispute with the contractor, after the work is commenced. The method which I advise for reducing irregular cross-sections to equivalent regular ones, which may be calculated by means of the working diagrams and tables of level-cuttings, is as follows: CASE 1.- When the ground slopes diferently from the centre each way, as e d, e a, inJfigs. 6 and 7. Fig. 6. Fig. 7. 1j/ 1 c my b a I On the prepared paper, fig. 5, from the centre-height or depth e, figs. 6 and 7, and by means of the parallel ruler, and the degrees marked on the sheet, fig. 5, draw the two slopes e d, e a, figs. 6 and 7; the inclinations of which are taken from the field slope-book. Draw ef, parallel to a d, and join af. Then is a b cf equal to a b c d e, figs. 6 and 7. PRooF. —The two triangles a df, a d e, fig. 6, being on the same base a d, and between the sam~e parallels a d and ef, are equal to each other. Leaving out from each, the triangle a d o, which is common to both, we have the triangle df o, equal to the triangle ae o; and consequently a b cf is equal to a b c de. 16 Find by means of the parallel ruler and degrees marked on the paper, the slope of a f; and with that slope, and the new centre-depth m n, (which is had from the figure by inspection,) use the proper diagram for finding the equivalent level-cutting; and take out the cubic yards from the table. Also, in fig. 7, the triangles fe d, and f e a, being on the same base f e, and between the same parallelsf e, d a, are equal to each other; and leaving out from each the triangle f e o, which is common to both, we have the trianglef o d, equal to the triangle e o a, and consequently a b cf abcd e. CASE 2.- When the ground is very irregular transversely, as in fig. 8. Having drawn the figure on the prepared paper, find by trial with a piece of thread, the line a d, which Fig~. 8. equalizes, as nearly as can be judged by eye, the irregularities above and below a it. By means of the parallel ruler, and i! / the degrees on the paper, find the slope of a d; and with that slope, and the new'-ap,- centre-depth m n, (which is had from the figure by inspection,) use the proper diagram for finding the equivalent level-cutting; and take out the cubic yards from the table. CASE 3.- When the ground-slope intersects the roadway, as in fig. 9. Such cases are always detected by the dotted curve line in the working diagrams. Having drawn the figure on the prepared paper, measure the two bases Fig. 9.6, a b'and a o; and also the two,~, perpendiculars to them, c d and ef o, —,f Multiply a b by c d, and half e: the product is the area of the triangle of excavation a b d. If the triangle of excavation at the other end of the 100 feet station has the same area, the number of cubic yards corresponding to this area for a length of 100 feet will be taken from table 15. Also multiply a o by ef, and half the product will be the area of the triangle of embankment a o e. If the triangle of embankment at the other end of the 100 feet station has the same area, the corresponding number of cubic yards will be taken from table 15. But if the triangles of excavation, (or those of embankment,) at the two ends, are not of the same area, the trapezoidal rule must be employed, as in the case of trapezoidal cross sections of unequal areas. See page 7. That is, we must add together the contents corresponding to the two 17 end triangles, and 4 times that corresponding to the triangle half way between them, and divide the sum by 6, for the true content. The base of the centre triangle of excavation, will be the average between the two bases a b, fig. 9, at the ends; and its perpendicular, the average between the two perpendiculars c d, at the ends. In like manner, the base and perpendicular of the centre triangle of embankment, will be averages of the two end bases a o, and of the two end perpendiculars eJ: If from irregularities in the ground, in the direction of the line of the road, it should bec me necessary to take cross-sections nearer together than 100 feet, onlybthe same proportional parts of the cubic yards must be taken from the tables; and on this account, it is better always, when possible, to subdivide the 100 feet station-distances into such parts as will furnish numbers easy to divide by; thus, if the station be divided into 10, 20, 25, or 50 feet distances, they will furnish respectively the numbers 10, 5, 4, or 2, by which to divide the cubic yards in the tables, all of which are calculated for 100 feet distances. TO FIND THE DISTANCES OF THE SIDE-STAKES FROM THE CENTRESTAKE. In all cases in which the cross-sections are drawn, as just described, these distances may be had by measurement on the figures. But they may be obtained much more rapidly thus: prepare a piece of tracing paper, as in fig. 10, of the same size as the ruled paper on which the cross-sections are drawn. From c as a centre, lay off and number the degrees above and below a b, as marked at the ends, to as high as the greatest transverse groundslope in the work. Also, from c as a centre, draw by the same scale as the ruled paper, fig. 5, arcs of a circle one foot apart, and number them with their distances from c in feet. Then, by laying this paper upon a cross-section of the road, fig. 5, with c of fig. 10, placed at the given centre-height or depth on Fig.* 10. the line a a, of figt5, we at once. read off, without any calculation I whatever, the distances of the D's side-stakes from the centre-.' stake, measured along the trans- 5 verse ground-slope. These dis- d tances will be copied into the proper book for field use. If, instead of concentric arcs, vertical straight lines. are drawn -. on the transparent Npper, we shall in like manner obtain, by mere inspection, the horizontal distances of the side-stakes from the centre one. When the horizontal distances 3 18 are employed in preference to those measured along the transverse groundslope, it is necessary to use a plumb at the end of the measuring line, in order to hold it vertically over the centre, or the side-stake, depending upon which is lowest. The tracing paper figure should be pasted to a frame, so as to lie flat on fig. 5. The frame may be of stiffpasteboard. ON THE USUAL METHOD OF CALCULATING EXCAVATIONS AND EMBANKMENTS. Different engineers employ different methods, of which the following is, perhaps, as simple as any: It requires that there shall be given, (beside the width of roadway m n, figs. 11 and 12, and the side-slope,) the extreme horizontal width a b of the cut, or embankment; and the vertical depths f e at the centre; and. c a, d b at the sides. The Rule then is, multiply the extreme horizontal width a b, by half the centre depth f e; also multiply ONE-FOURTH of the width of roadway m n, by the sum of the two side depths c a and d b: the sum of the products will be the area of the cross section m n d f c,Jfig. 11 or fig. 12. This area, thus found, multiplied by 100, (the usual length of the station in feet,) and divided by 27, (the number of cubic feet in a cubic yard,) gives the cubic content of the station, provided the area of the cross-section at the other end of the station be the same; but if not, the prismoidal Rule must be used, as already explained. The trouble of multiplying by 100, and dividing by 27, may be avoided by the use of table 15, which I have prepared for that purpose. The centre-depthsf e, figs. 11 and 12, are given by the level book; but the side-depths c a and d b, have to be found by trial on the ground; thus, USUAL METHOD OF FINDING SIDE-DEPTHS, AND PLACING SIDESTAKES. 1st. For an Excavation. The level is placed conveniently for sighting from the same position uponf, c, and d, figs. 11 and 12. Fig. 11. Fig. 12.,4t c A sightf o, is then taken on the target-rod held atf; this sightf o, being added to the centre-depthfe, gives the height e o, of-tie instrument above a b; or the height of the horizontal plane, (represented by hp,) through which the line of sight passes as the telescope of the level is swept round -on the axis of the instrument. 19 The height of d abovef is then estimated by eye, say at 2 feet; this 2 feet, added to f e, gives the aproximate height of d b. Assuming the approximate height d b as the correct one, we find what would be the horizontal distance from the centre to d, either by calculation, or from a previously prepared table of horizontal distances. Measure off that distance horizontally towards d, and placing the target 2 feet lower on the target rod, hold it at the end of the measured distance. A sight is then taken with the level, and if it strikes the centre of the target, it proves that the assumed height of d, and the corresponding horizontal distance from the centre of the roadway, were correct; and that the proper spot is found for placing the side-stake d. It seldom happens that such a coincidence is found at the first trial; at least two trials are generally required; and frequently three, or even four when the ground is extremely irregular. A very close approximation, however, can always be made by an experienced leveller after the first trial. An error of a4 inch or two in the position of a side.stake is a matter of no practical importance whatever. The same operation is performed at c, except that as c is lower than f, the target is raised on the rod, as far above the sight taken at f as c is estimated to be below f. 2d. For an Embanlcment. When putting in side-stakes for an embankment, fig. 13, the sight taken on the rod at the centre-stake, is subtracted from the centre-height of the embankment, in order to obtain the depth of the instrument below the roadway; and the outer sights, c a, d a, are to be added to this depth, s t, for the side-depths; except when, as in fig. 14, the sight r y, on the rod at the centre-stake, is greater than the height r x of the embankment, in which case the difference x y, between the two, will be the height of' the instrument above the roadway; and this difference, x y, must then be subtracted from the sights a c, a d, for the side-depths, o c, o d; all of which is apparent from the figures. Fig. 13. Fig. 14. It is plain that if the height on the target rod at d, fig. 11, be subtracted from e o, the remainder will be d b; and that taken at c, subtracted from e o, will give c a. These operations give us therefore, at the same time, the heights d b, and c a; and also the horizontal distances from the centre to each sidestake. All these are at once entered into the proper field-book, to be used in estimating the areas and cubic contents in the office. The sum of the two horizontal distances manifestly gives the extreme width of the excavation or embankment. 20 It is evident, that in the time required for a leveller and rodman to ascertain the positions and heights of the side-stakes, at a single station, by this method, those of several stations could be found by one person in the office, by mine. Still, in some rare cases, where the ground-slope is extremely irregular, as among jagged rocks, the mode by the level is the only one proper to be used; as, in that case it would be impossible to take the transverse ground-slopes with any degree of accuracy. Transverse ground-slopes are obtained in the field with great facility, by means of a small slope level, or clinometer, placed upon a rod, 10 or 12 feet long, which, at every station, is laid upon the ground as nearly at right angles to the line of survey, as can be judged by the eye. These clinometers are sold by most of our principal instrument makers. When the ground is regular transversely, but one slope need be taken; at other times, one may be required from the centre each way; and rarely, more than one on each side of the centre-stake. The slopes for estimating the final adopted line, must be taken with much more care than during preliminary surveys of trial lines. They need not, however, extend beyond the widths actually occupied by the cuttings and fillings; while those taken in preliminary surveys should comprise a considerable width, as they are, moreover, used in the office for changing the position of the surveyed line, in order to avoid excavation and embankment. In the following tables of level-cuttings, the left hand vertical column contains the height or depth of the embankment or excavation, in feet; and the upper horizontal column, the intermediate tenths of a foot. Thus in table 1, the cubic yards in a station 100 feet long and 10 feet deep, are 1074; for 10'1 deep, 1090; for 10'2 deep, 1107, &c. Plate I 5 10 15 too 60 55 50 45.2I_ 40 35 30 25 20 di z: 15SIDE-SLOPE S 1~ tol. ROADWAY 14 F? 10 For nzbawknzt,,. 0. a 1z> 21 TABLE 1.-LEVEL CUTTINGS. Roadway 14 feet wide, side-slopes 1j to 1.'ght t. 0 *1 *2 *3 *4 *5 *6'.7.8 *9 " cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds cu. yds. cu. yds. 0 5'24 10.6 16-1 21.6 27.3 33.1 39.0 45'0 51.2 1 57.4 63.8' 70.2 76.8 83:5 90.3 - 97.2 104.2 111.3 118.6 2 125'9 133-4 141.0 148.6 156.4 164.4 172.4 180.5 188*7 197.1 3 205.6 214.1 222.8 231.6 240.5 249.5 258.7 267'9 277.3 286.7 4 296.3 306.0 315.8 325*7 335*7'345.8 356.1 366.4 376.9 387.5 5 3981- 408*9 419.9 430.9 442.0 453.2 464.6 476.1 487.6 499.3 6 511.1 523.0 535.0 547.2 559.4 571.8 584.2 596.8 609*5 622.3 7 635.2 648.2 661.3 674.6 687.9 701.4 714.9 728.6 742.4 756.3 8 770.3 784.5 798.7 813.1 827.5 842.1 856.8 871.6 886.5 901*5 9 916*7 931*9 947*3 962*7 978*3 9940'1010 1026 1042 1058 10 1074 1090 1107 1123'1 140 1157 1174 1191 1208 1226 11 1243 1260 1278 1295 1313 1331 1349 1367 1386 1404 12 1422 1441 1459 1478 1497'1516 1535 1554 1574 1593 13 1613 1638 1652 1672 1i692 1712 1733:1753 1773 1794 14 1815 1835 -1856 1.877 1;898.. 1920 1941, 1962 1984 2006 15 2028 2050 2072 2094 2116 2138 2161 2183. 220d 2229 16 2252 2275 2298' 2321 2344 2368 2391 2415 2439 2463 17 2487'2511 2535':2559 2584 2608' 2633 2658 2683 2708 18 2733 2759 2784 2809' 2835 2861 2886 2912 2938 2964 19 2991 3017 3044 3070 3097 3124' 3151 3178 3205 3232 20 3259 3287 3314 3342 3370 3398 3426 3454 3482 3510 21 3539 3557 3586 3616 3644 3673 3702 3731 3761 3790 22 3820 3849 3879 3909 3939 3969 3999 4030 4060 4091 23 4132'4162 4193 4224 4255 4287- 431'8 4349.. 4381 4413 24 4444 4476 4508 4541 4573 -4605 4638 4670 4703 4736 25 4769 4802 4835 4868'4901 4935 4968 5002 5036 5070 56 5104 5138 5172 5206' 6241 5275 5310 5345 5380 5415 27 5450 5485 5521 5556 5592 5627 5663 5699 5735 5771 28 5807 5844 65880'5917 5953' 5990 6027 6064 610'1 6139 29 6176 6213 6251 6289 6326 6364 6402 6440 6479 6517 30 6556 6594 6633 6672 - 6711 6750 6789 6828 6867 6907 31 6946 6986 7026, 7066 7106 7146 7186 7226 7267 7307 32 7348 7389 7430 17471 7512' 7553 7595' 7636: 7678 7719 33 7761 7803 784-5 7887 7929 7972 8014 8057 8099 8142 34 8185 8228 8271 8315 8358 8401 8445 8489 8532 8576 35 8620 8664 870'9 8753'8798 8842 8887 8932 8976 9022 36 9067 9112 9157 9203 9248. 9294. 9340 9386. 9432 9478 37 9524 9570 9617 9663 9710.'9757 9804 98651 9898 9945 38 9993 10040 10088 10135 10183 10231 10279 10327'10375 10424 39 10472 10521 10569 10618 10667 10716 10765 10816 10864 10913 40 10963 11013 11062 11112 11162 11212 11263' 11313 11364 11414 41 11465 11516 11567 11618 11669 11720 11771' 11823 11874 11926 42 11978 12029 1i081' 12134, 12186 12238 12291 12343 12396 12449 43 12502 12555 12608 12661 12715 12768 12822 12876 12929 12983 44 13037 13091 13145 13200 13254 13309 13363 i13418- 13473 13528 45 13583 13639 13694 13749 13805 13861 13916.13972 14028 14084 46 14141 14197 14254 14310. 14367 14424 14480 14537 14595 14652 47 14709 14767 14824 14882 14940 14998 15056 15114 15172 15230 48 15289 15347 15406 15465'15524 15583 15642 15701 15761 15820 49 15880 15939 15999 16059 16119 16179 16239 16300 16360 16421 50 16481 16542 16603 16664 16725 16787 16848 16909 1'6971 17033 51 17094 17156 17218 17280 17343 17405 17467 17530 17593 17656 52 17719 17782 17845 17908 17971 18035 18098 18162 18226 18290 53 18354 18418 1'8482 18546 18611 18675 18740 18805 18870 18935 54 19000 19065 19131 19196 19262 19327 19393 19459 19525 19591 55 L9657 19724 19790 19857 19923 19990 20067 20124 20191 20259 56 20326 20393 20461 20529 20596 20064 20732 20800 20869 20937 57 21005 21074 2'1143'- 21212 21280 21349 21419 21488 21557 21627 58 21696 21766 218316 21906 21976 22946 22116 22186 22257 22327 59 22398 22469 22540'22611 22682 22753 22825 22896 22968 23039'60 23111 23183 2325'5 23327 23399 23472 23544 23617 23689 23762 For eontinuation to 100 feet Bee Table 13. 22 TABLx 2.-LEVEL CUTTINGS. Roadway 24 feet wide, side-slopes 1~ to 1. H'gbt in ft. -0.1'2 - 3 4.5.6'7'8.9 cu. yd. cu. y yd yd cu yds. cu. ydss. cu. yds. cu. yds cuy u.ds. 0 8,94 18.0 27-2 3.6.4 45,8 55,3 64.9 74.7 84.5 1 94'4 104.5 114,7 124.9i 135.3 145.8 156.4 167.2 178-0 188.9 2 00'0 211'2 222'4 233'8 24853 256'9 268'6 280'5 292'4 304.4 3 316.6 328'9 341.2 353'7 366 3 379'0 391'9 404.8 417'8 431.0 4 444.4 457,8 471'3 4384'9 498'6 512.4 526-4 540-4 554'6 568.8 5 583-3 597'8 612.4 627'1 642'0 656.9 671,9 687.1 702.3 717.7 6 733.3 748,9 764.7 7805 *7964 812'5 828'7 844.9 861'3 877.8 7 894.4 911'2 928.0 944i9 962.0 979.2 996'4 1014 1031 1049 8 1067 1085 1102 1121 1139 11t57 1175 1194! 1212 1231 9 1250 1269 1288 1307 1326 1346 1 1365 1385 1405 1425 10 1444 1465 1485 1605 1525 1546 15666 1587 1608 1629 11 1650 1671 1692 1714 1735 1757 1779 1800 1822 1845 12 1867 1889 1911 1934 1956. 1,979 2002 2025 2048 2071 13 2094 2118 2141 2165 2189 2213 2236 2261 2285 2309 14 2333 2358 2382 4Q07 2432 2457 2482 2507 2532 2558 15 2583 -2609 2635 2661 2686 2713 2739 2765 2791 2818 16 2844 2871 2898 2925 2952 2979 3006 3034 3061 3089 17 3117 3146 3172 3201 3229 3257 3285 3314 3342 3371 18 3400 3429 3458' 3487 3516 3546 3575 3605 3635 3665 19 3694 9725 3755 3785 3815 3846 3876 3907 3938 3969 20 400000 031 4062 4094 4125 4157 4189 4221 4252 4285 21 4317 4349 4381 4414 4446 4479 4512 4545 4578 4611 22 4644 4678 4711 4745 4779 4818 4846 4881 4915 4949 23 4983 5018 5052 5087 5122 5157 5192 5227 5262 5298 $4 5333 5369 6405 5441 5476 5513 5549 5685 5621 6658 25 5694 5731 5768 5805 5842 5879 5916 5954 5991 6029 26 6067 6106 6142 6181 6219 6257 0295 6334 6372 6411 27 6450 6489 6528 6567 6606 6646 6685 6725 6765 6805' 28 6:844 6885 6925 6965 7005 7046 7086 -7127 -7168 7209 29 7250 7291 7382 7374 7415 7457 7499 7541 7582 7625 30 7667 7709 7751 7794 7836 7879 7922 7965 8008 8051 31 8094 8138 8181 8225 8269 8313 8356 8401 8445 8489 32 8533 8578 8622 8667 871 8757 8802 8847 8892 8938 33 8983 9029 9075 9121 9166 9212 9259 9305 9351 9398 34 9444 9491 9538 9585 9632 9679 97P6 9774 9821 9869 35 9917 9965 10012 10061 10109 10157 10205 10254 10302 10351 36 10400 10449 10498 10547 10596 10646 10695 10745 10795 10845 37 10894 10945 10995 11045 11095 11146 11196 11247 112'98 11349 38 11400 11451 11502 11554 11605 11657 11709 11761 11812 11865 39 11917 11969 12021 12074 12126 12179 12232 12285 12338 12391 40 12444 12498 12551 12605 12659 12713 12766 12821 12875 12929 41 12983 13038 13092 13147 13202 13257 13312 13367 13422 13478 42 13533 13589 13645 13701 13756 13813 13869 13925 13981 14038 43 14094 14151 14208 14265' 14322 14379 14436 14494 14551 14609 44 14667 14725 14782 14840 14899 14957 15015 15074 15132 15191 45 15250 15309 15368; 15427 15486 1'5546 15605 1,5665 15725 15785 46 15844 15905 165965 16025 16085 16146 16206- 16267 16328 16389 47 16450 16511 16572 16634' 16695 16757 16819 16881 16942 17005 48 17067 17129 17191 17254 17316 17379 17442 17505 17568 17631 49 17694 17758 17821 17885 17949 18013 18076 18141 18205 18269 50 18333 18398 18462 18527 18592 18657 18722 18787 18852 1.8918 51 18983 19049 19115 19181 19246 19313 t9379 19445 1951 19578 52 19644 19711 19778 19845 19912 19979 20046 20114 20181 20249 53 20317 20385 20452 20521 20589 20657 20725 20794 208.62 20931 54 91000 21069 21138 21207 21276 21346 21415 21485 21555 216265 55 21694 21765 21835 21905 21975 22046 22116 22187 22258 22329 56 22400 22471 22542 22614 22685 22757 22829 22901 22972 23045 57 23117 23189 ]23261 23334 23406 23479 23552 23625 23698 23771 58:3844 23918 23991 24065 24139 24213 24286 24361 24435 24509 69 ~4583 24658 24732 24807 24882 24957 25032. 25107 25182 25568 60 125333 25409 25485 25561 25636 25713 2.5789 25865 25941 26018 For continuation to 100 feet, see table 13. _.. —.. —---------....................................._........ _.. PlateL7. 5o tO~ 1~ sO~~~~~~~~O 6505 I'm t20~ 55 50' 45 -- 40 35 14-F~~~~~~~~~~~~s 30 20 1 5 I...~f-"~ /-SIED.-SLOPES to.. ROADWAYP 24F? 10 -for -Embaidwwwt. 5~~~ -L"Lkb-./////// -— ~ _q-.'.~7-t~-t./'f///~ _Pla tJ.Pa ~~~~~~~~~~~~~~~~~~. _. 5~ l0 is o 25~ 30~' 3~S 3E 60 36j 370 55 36o 50 39~ 45i 40 - 3530 25.. 20 12 SIDE-SLOPES ltol. ROADvWAY 18 Ft 10 -Por Excavat&an. 5 0 23 TA BLr 3. —LE'VEL CUTTINGS. Roadway 18 feet wide, side-slopes 1 to 1. Dep t;h i n ft.'0 *1'2 *3 *4: 5 *6'7'8.9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. Cu. yds. cu. yds. cu. yds. cu. yds 0 6'70 13'5 20'3 27'3 34'3 41'3 48'5 55'7 63,0 1 70.4 77-8 85-3 92 9 100-6 108-3 116-1 124 0 132-0 1400 2 148-1 156.3 164.6 172.9 181.3 189-8 198s4 207.0 215.7 224.5 3 233.3 242'3 251.3 260'3 269'5 278'7 28830 297'4i 306'8 316.3 4 325'9 335'6 345.3 355'1 365'0 375'0 385.0 395- 1 405'3 4-15-( 5 425'9 436'3 446.8 457'4 468'0 478'7 489.5 500,3 511'3 522., G 533'3 544'5 555.7 567.0 578'4 589'8 601.3 612'9 624'6 636.3 7 648 1 660 0) 672.0 684.0 696'1 708'3 720.6 732.9 745'3 757.8 8 770'4 783'0 795.7 808'5[ 821'3 8.34'3 847.3 860'3 873'5 886.7 9 9000G 913.4 926.8 940.3 953.9 967.6 981.3 995.1 1009 1023 10 1037 1 051 1065 1080 1094 1108 1123 1137 1152 1167 11 1181 1196 1211 1226 1241 1256 1272 1287 1302 1318 12 1333 1349 1365 1380 1396 1412 1428 1444 1460 14.76 13 1493 1509 1525 1542 1558 1575 1592 1608 1625 1642 14 1659 1676 1693 1711 1728 1745 1763 1780 1798 1816 15 1833 1851 1869 1887 1905 1923 1941 1960 1978 1996 16 2015 2033 2052 2071 2089 2108 2127 2146 2165 2184 17 2204 2223 2242 2262 2281 230 1 2321 2340 2360 2380 18 2400 2420 2440 2460 2481 2501 i 2521 2542 2562 2583 19 2604 2624 2645 2666 2687 2708 2729 27f51 2772 2793 20 2815 2836 2858 2880 2901 2923 2945 2967 2989 3011 21.3033 3056 3078 3100 3123 3145 3168 3191 3213 3236 22 3259 3282 3305 3328 3352 3375 3398 3422 3445 3469 23 3493 3516 3540 3564 3588 3612 3636 3660 3685 3709 24 3733 3758 3782 3807 3832 3856 3881 3906 3931 3956 25 3981 4007 4032 4057 4083 4108 4134 4160 41835 4211 26 4237 4263 4289 4315 4341 4368 4394 4420 4447 4473 27 4500 4527 4553 4580 4607 4634 4661 4688 4716 4743 28 4770 4798 4825 4853 4881 4908 4936 4964 4992 5020 29 5048 5076 5105 5133 5161 5190 5218 5247 5276 5304 30 5333 5362 5391 5420 5449 5479 5508 5537 5567 5596 31 5626 5656 5685 5715 5745 5775 5805 5835 5865 5896 32 5926 5956 15987 6017 6048 6079 6109 6140 6171 6202 33 6233 6264 6296 6327 6358 6390 6421 6453 6485 6516 34 6548 6580 6612 6644 6676 6708 6741 6773 6805 6838 35 6870 6903 6936 6968 7001 7034 7067 7100 7133 716 7 36 7200 7233 7267 7300 7334 7368 7401 7435 7469 7503 37 7537 7571 7605 7640 7674 7708 7743 7777 7812 7847 38 7881 7916 7951 7986 8021 8056 8092 8127 8162 8198 39 8233 8269 8305 8340 8376 8412 8448 8484 8520 8556 40 8593 8629 8665 8702 8738 8775 8812 8848 8885 8922 41 8959 8996 9033 9071 9108 9145 9183 9220 9258 9296 42 9333 9371 9409 9447 9485 9523 9561 9600 9638 9676 43 9715 9753 9792 9831 9869 9908 9947 9986 10025 10064 44 10104 10143 10182 10222 10261 10301 10341 10380 10420 10460 45 10500 10540 10580 10620 10661 10701 10741 10782 10822 10863 46 10904 10944 10985 11026 11067 11108 11149 11191 11232 11273 47 11315 11356 11398 11440 11481 11523 11565 11607 11649 11691 48 11733 11776 11818 11860 11903 11945 11988 12031 12073 12116 49 12159 12202 12245 12288 12332 12375 12418 12462 12505 12549 50 12593 12636 12680 12724 12768 12812 12856 12900 12945 12989 51 13033 13078 13122 13167 13212 13256 13301 13346 13391 13436 52 13481 13527 13572 13617 13663 13708 13754 13800 13845 13891 53 13937 13983 14029 14075 14121 14168 14214 14260 14307 14353 54 14400 14447 14493 14540 14587 14634 14681 14728 14776 14823 55 14870 14918 14965 15013 15061 15108 15156 15204 15252 15300 56 15348 15396 15445 15493 15541 15590 15638 15687 15736 15784 57 15833 15882 15931 15980 16029 16079 16128 16177 16227 16276 58 16326 16376 16425 16475 16525 16575 16625 16675 16725 16776 59 16826 16876 16927 16977 17028 17079 17129 17180 17231 17282 60 17333 17384 17436 17487 17538 17590 17641 17693 17745 17796 For continuation to 100 feet see table 13 24 TABL, 4.-LEVEL CUTTINGS. Roadway 18 feet wide, side-slopes 1~ to 1. Depth inft. *0.1'2 *3 *4.5'6 *7 *8.9 cu. yds. cu. yds. Cu. yds.lcu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. 0 6'71 13'5 20'4 27'4 34'5 41'6 49'0 5660 64C0 1 71'3 78'9 86'7 94.5 102'4 110*4 118'5 126'7 135'0 143.4 2 15181 160'4 169'1 1778S 186'7 195'6 204'6, 213'8 223'0 232.3 3 241'6 251.1 260'7 270.4 280.2 290'0 300'0 310'1 320'2 330.5 4 340'7 351.2 361'7 372.3 383'0 393'8 404-7 415.7 426'8 437.9 5 449.2 460.6 472.1 483.7 495.3.507.0 518'8 530'8 542'8 554'. 6 56'6.7 579.0 591.3 603.8 616.4 629.0 641.8 654.5 667.5 680.4 7 693'5 706.7 720.0 733.4 746.9 760.4 774'1 787'8 801'7 815.6 8 829.6 843.8 858.0 87231 886.7 901.2 915.8 930.4 945'2 960.1 9 975.0 990.0 1005 1020 1036 1051 1067 1082 1098 1114 10 1130 1146 1162 1178 1194 1210 1227 1243 1260 1277 11 1293 1310 1327 1344 1361 1379 1396 1413 1431 1448 12 1467 1484 1502 1520 1539 1557 1575 1593 1612 1630 13 1649 1668 1687 1706 1725 1744 1763 1782 1802 1821 14 1841 1860 1880 1900 1920 1940 1960 1980 2001 2021 15 2042 2062 2083 2104 2125 2146 2167 2188 2209 2231 16 2252 2273 229.5 2317 2339 2361 2383 2405 2427 2449 17 2471 2494 2516 2539 2562 2585 2608 2631 2654 2677 18 2700 2723 2747 2770' 2794 2818 2842 2866 2890 2914 19 2938 2962 2987 3011 3036 3060 3085 3110 3135 3160 20 3185 321.0 3236 3261 3287 3312 3338 3364 3390 3416 21 3442 3468 3494 3520' 3547 3573 3600 3627 3654 3680 22 3707 3734 3762 3789' 3816 3844 3871 3899 3927 3954 23 3982 4010 4039 4067 4095 4123 4152 4180 4209 4238 24 4267 4296 4325 4354 4383 4412 4442 44.71 4501 4530 25 4560 4590 4620 4650 4680'4710 4741 4771 4802 4832 26 4863 4894 4925 4956 4987 5018 5049 5080 5112 5143 27 5175 5207 5239 5270 5302 5334 5367 5399 5431 5464 28 5496 5529 5562 5594 5627 5660 5693 5727 5760 5793 29 5827 5860 5894 5928 5962 5996 6030 6064 6098 6132 30 6167 6201 6236 6270 6305 6340 I 6375 6410 6445 6480 31 6516 6551 6587' 6622' 6658 6694 6730 6766 6802 6838 32 6874 6910 6947 6983 7020 7057 7093 7130 7167 7204 33 7242 7279 7316 7354 - 7391 7429 7467 7504 7542 7580 34 7618 7656 7695 7733 7772 7810 7849 7887 7926 7965 35 8005 8044 8083 8122 8162 8201 8241 8280 8320 8360 36 8400 8440 8480 8520 - 8561 8601 8642 8682 8723 8764 37 8805 8846 8887 8928 8969 90i0 9052 9093 9135 9177 38 9219 9260 9302 9344 9387 9429 9471 9514 9556 9599 39 9642 9684 9727 9770 9813 9857 9900 9943 9987 10030 40 10074;10118 10162 10206 10250 10294 10338 10382 10427 10471 41 10516 10560 10605 10650 10695 10740 10785 10830 10876 10921 42 10967 11012 11058 11104 11150 11196 11242 11288 11334 11380 43 11427 11473 11520 11567 11614 11660 11707 11754 11802 11849 44 11896 11944 11991 12039 12087 12134 12182 12230 12278 12327 45 12375 12423 12472 12520 12569 12618 12667 12716 12765 12814 46 12863 12912' 12962 13011 13061 13111 13160 13210 13260 13310 47 13360 13410 13461 1'3511 13562 13613 13662 13713 13764 13815 48 13867 13918 13969 1'4020 14072 14123 14175 14227 14279 14330 49 14382 14435 14487 14539 114591 14644 14696 114749 14802 14855 50 14907 14960 15014 15067 15120 15173 1522.7 15280 15334 15388 51 15442 15496 15550 15604 15658 15712 15767 15821 15876 15931 52 15985 16040 16095 16150 1'6205 16280 16316 16371 16427 16482s 53 16538 16594 16650 16706 16761 1681'7 16874 16930 16987 17043 54 17100 17157 17214 17270 17328 17385 17441 17499 17556 17613 55 17671 17729 17787 17845 17903 17961 18019 18077 18135 18193 56 18252 18310 18369 18428 18487 18545 18604 18663 18723 18782 57 18842 18901 18961 19021 19080 19140 19200 19260 19320 19380 58 19441 19501 19562 19622 19683 19744 19804 19865 19926 19988 59 20049 20110 20172 20233 20295 20357 20418 20480 20542 20604 60 20667 20729 20791 20854 20916 20979 21041 121104 21167 21230 For continuation to 100 feet see table 13. 10 15~ 20 25 by ~~~~~~~~~~~~~~~~~~~Z 60 55 5O 503 45 40 a3f 35MO tg//X/;/ /// 3 5 - - -3 30 i l 25 2 ~i 15. >~~.lmf1/z1tSIDE-SLOPES 114tol. ROADWAY 18 FT 10 -for Excvmlb t. 5.x Zl O n 0 L 60 50 - 45 J_< 40 35 28 30 25 20 - SIDE-SLOPES 1.2-tol. ROAI)WAY IB Fr 10 5 0 25 TABLE 5.-LEVEL CUTTINGS. Roadway 18 feet wide, side-slopes 1, to 1.'Depth in ft. *0'.1 *2 *3.4.5 *6.7 8 *9 CU. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. Yds. CU. yds. cu. yds. cu. yds. cu. yds. 0 6.72 13.6 20.5 27.6 34.7 42.0 49.4 56.9/ 64.5 1 7221 80o1 8880 96.1 104.2 112.5 120.9 129.4 1380 146-7 2 155-5 164 5 173'5 182'7 191'9 201'3 210'8 220'4 230'1 24050 3 249'9 260'0 2701 2,80'4 290'8 301'3 311'9 322'6 333'4 344-5 4 3.555 366'7 378'0 389'4 400'9 412'5 424'2 436'0 448.0 460'0 5 472.2 484.5 496-9 509.4 522.0 534.7 547'6 560.5 573[ 6 586-7 6 600'0 613'4 626'9. 640'5 654'2 668'1 682'0 696'1 710O2 724*5 7.738'9 753,4 768.0 782'7 797'6 812'5 827'6 842'7 858'0 873-4 8 888-9 904'5 92021 9361 9520 968'1 984'2 1001 1017 1033 9 1050 1067 1084 1101 1118 1135 1152 1169 1187 1205 10 1222 1240 1258 1276 1294 1313 1331 1349 1368 1387 1 1406 1425 1444 1463 1482 1501 1521 1541 1560 1580 12 1600 1620 1640 1661 1681 1701 1722 1743 1764 1785 13 1806 1827 1848 1869 1891 1913 1934 1956 1978 2000 14 2022 2045 2067 2089 2112 2135 2158 2181 2204 2227 15 2250 2273 2297 2321 2344 2368 2392 2416 2440 2465 16 2489 2513 2538 2563 2588 2613 2638 2663 2688 2713 17 2739 2765 2790 2816 2842 2868 2894 2921 2,947 2973 18 3000 3027 3054 3081 3108 3135 3162 3189 3217 3245 19 3272 3300 3328 3356 3384 3413 3441 3469 3498 3527 20 3556 3585 3614 3643 3672 3701 3731 3761 3790 3820 21 3850 3880 3910 3941 3971 4001 4032 4063 4094 4125 22 4156 4187 4218 4249 4281 4313 4344 4376 4408 4440 23 4472 4505 4537 4569 4602 4635 4668 4701 4734 4767 24 4800 4833 4867 4901 4934 4968 5002 5036 5070 5105 25 5139 5173 5208 5243 5278 5313 5348 5383 6418 5453 26 5489 5525 5560 5596 5632 5668 5704 6741 6777 5813 27 5850 5887 5924 5961 5998 6035 6072 6109 6147 6185 28 6222 6260 6298 6336 6374 6413 6451 6489 6528 6567 29 6606 6645 6684 6723 6762 6801 6841 6881 6920 6960 30 7000 7040 7080 7121 7161 7201 7242 7283 7324 7365 31 7406 7447 7488 7529 7571 7613 7654 7696 7738 7780 32 7822 7865 7907 7949 7992 8035 8078 8121 8164 8207 33 8250 8293 8337 8381 8424 8468 8512 8556 8600 8645 34 8689 8733 8778 8823 8868 8913 8958 9003 9048 9093 35 9139 9185 9230 9276 9322 9368 9414 9461 9507 9553 36 9600 9647 9694 9741 9788 9835 9882 9929 9977 10025,37 10072 10120 10168 10216 10264 10313 10361 10409 10458 10507 38 10556 10605 10654 10703 10752 10801 10851 10901 10950 11000 39 11050 11100 11150 11200 11251 11301 11352 11403 11454 11505 40 11556 11607 11658 11709 11761 11813 11864 11916 11968 12020 41 12072 12125 121.77 12229 12282 12335 12388 12441 12494 12547 42 12600 12653 12707 12761 12814 12868 12922 12976 13030 13085 43 13139 13193 13248 13303 13358 13413 13468 13523 13578 13633 44 13689 1]3745 13800 13856 13912 13968 14024 14081 114137 14193 45 14250 14307 14364 14421 14478 14535 14592 14649 14707 1476546 14822 14880 14938 14996 15054 15113 15171 15229 15288 15347 47 115406 15465 15524 15583 15642 15701 15761 15821 15880 15940 48 116000 16060 16120 16181 16241 16301 16362 16423 16484 16545 49 16606 16667 16728 16789 16851 16913 16974 17036 17098 17160 50 17222 17285 17347 1 7409 17472 17535 17598 17661 17724 17787 51 17850 17913 17977 18041 18104 18168 18232 18296 18360 18425 52 18489 18553 18618 18683 18748 18813 18878 18943 19008 19073 53 19139 19205 19270 19336 19402 19468 19534 19601 19667 19733 54 19800 19867 19934 20000 20068.20135 20202 20269 20337 20405 55 20472 20540 20608 20676 20744 20813 20881 20949 21018 21087 56 21156 21225 21294 i21363 21432 21501 21571 21641 21710 21780 57 121850 21920 21990 22061 22131 22201 22272 22343 22414 22485 58 22556 22627 22698 22769 22841 22913 22984 23056 23128 23200 59 23272 23345 23417 23489 23562 23635 23708 23781 23854 23927 20 24000 24073 24147 124221 24294 24368 2444 24516 24590 24665 For continuation to 1'00 feet see table 13. 4 26 TABLE 6. —LEVEL CUTTINGS. Roadway 18 feet wide, side-slopes 2 to 1. Depth in ft.'0'1 *2'3'4.5 6'7 8'9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. 0 6'74 13'6 20'7 27'9 35'2 42'7 50'3 58.1 66'0 1 74'1 82'3 90.7 99'2 107'9 116,7 125'6 134'7 144.0 153'4 2 163'0 172'7 182'5 192'5 202'7 213'0 223'4 234'0 244.7 255'6 3 266'7 277'9 289'2 300'7 312'3 324'1 336'0 348'1 360.3 372'7 4 385'2 397'9 410'7 423'6 436'7 450'0 463'4 477'0 490.7 504.5 5 518'5 532'7 547 0 561 4 576'0 590'7 605'6 620'7 635.9 651'2 6 666'7 682'3 698'1 714'0 730'1 746'3 762'7 779'2 795'9 812'7 7 829.6 846'7 864'0 881'4 899'0 916'7 934'5 952'5 970'7 989'0 8 1007 1026 1045 1064 1083 1102 1121 1141 1160 1180 9 1200 1220 1240 1261 1281 1302 1323 1344 1365 1386 10 1407 1429 1451 1473 1495 1517 1539 1561 1584 1607 II 1630 1653 1676 1699 1723 1746 1770 1794 1818 1842 12 1867 1891 1916 1941 1966 1991 2016 2041 2067 2093 13 2119 2145 2171 2197 2223 2250 2277 2304 2331 2358 14 2385 2413 2440 2468 2496 2524 2552 2581 2609 2638 15 2667 2696 2725 2754 2783 2813 2843 2873 2903 2933 16 2963 2993 3024 3055 3086 3117 3148 3179 3211 3242 17 3274 3306 3338 3370 3403 3435 3468 3501 3534 3567 18 3600 3633 3667 3701 3735 3769 3803 3837 3871 3906 19 3941 3976 4011 4046 4081 4117 4152 4188 4224 4260 20 4296 4333 4369 4406 4443 4480 4517 4554 4591 4629 21 4667 4705 4743 4781 4819 4857 4896 4935 4974 5013 22 5052 5091 5131 5170 5210 5250 5290 5330 5371 5411 23 5452 5493 5534 5575 5616 5657 5699 5741' 5783 5825 24 5867 5909 5951 5994 6037 6080 6123 6166 6209 6253 25 6296 6340 6384 6428 6472 6517 6561 6606 6651 6696 26 6741 6786 6831 6877 6923 6969 7015 7061 7107 7153 27 7200 7247 7294 7341 7388 7435 7483 7530 7578 7626 28 7674 7722 7771 7819 7868 7917 7966 8015 8064 811:3 29 8163 8213 8263 8313 8363 8413 8463 8514 8565 8616 30 8667 8718 8769 8821 8872 8924 8976 9028 9080 9133 31 9185 9238 9291 9344 9397 9450 9503 9557 9611 9665 32 9719 9773 9827 9881 9936 9991 10046 10101 10156 10211 33 102-67 10322 10378 10434 10490 10546 10603 10659 10716 10773 34 10830 10887 10944 11001 11059 1.1117 11175 11233 11291 11349 35 11407 11466 11525 11584 11643 11702 11761 11821 11880 11940 36 12000 12060 12120 12181 12241 12302 12363 12424 12485 12546 37 12607 12669 12731 12793 12855 1.2917 12979 13041 13104 13167 38 13230 13293 13356 13419 13482 13546 13610 13674 13738 13802 39 13867 13931 13996 14061 14126 14191 14256 14321 14387 14453 40 14519 14585 14651 14717 14783 14850 14917 14984 15051 15118 41 15185 15253 15320 15388 15456 15524 15592 15661 15729 15798 42 15867 15936 16005 16074 16143 16213 16283 16353 16423 16493 43 16563 16633 16704 16775 16846 16917 16988 17059 17131 17202 44 17274 17346 17418 17490 17563 17635 17708 17781 17854 17927 45 18000 18073 18147 18221 18295 18369 18443 18517 18591 18666 46 18741 18816 18891 18966 19041 19117 19192 19268 19344 19420 47 19496 19573 19649 19726 19803 19880 19957 20034 20111 20189 48 20267 20345 20423 20501 20579 20657 20736 208'15 20894 20973 49 21052 21131 21211 21290 21370 21450 21530 21610 21691 21771 50 21852 21933 22014 22095 22176 22257 22339 22421 22503 22585 51 22667 22,749 22831 22914 22997 23080 23163 23246 23329 23413 52 23496 23580 23664 23748 23832 239'17 24001 24086 24171 24256 53 24341 24426 24511 24597 24683 24769 24855 24941 25027 25113 54 25200 25287 25374 25461 25548 25635 25723 25810 25898 25986 55 26074 26162 26251 26339 26428 26517 26606 26695 26784 26873 56 26963 27053 27143 \,27233 27323 27413 27503 27594 27685 27776 57 27867 27958 28049 28141 28232 28324 28416 28508 28600 28693 58 28785 28878 28971 29064 29157 29250 29343 29437 29531 29625 59 29719 29813 29907 30001 30096 30191 30286 30381 30476 30571,60 30667 30762 30858 30954 31050 31146 31242 31339 31436 31533 For continuation to 100 feet, see table 13. o81 81 L>~CI( ~ ZX ol j z Hi ~o. 09 _-.6,> -i= oIo6T~d' -Dmr _plain FE 5~ lo 15~' 206 25~ 30 33 r 60 _3 3S' 55 t-F- 3~,, 50 $ 0337~ 50~~~~~~~~~~~~~~~~~~~~~~~~~~ - iffiffiffi38~~~~~~~~~3~ WS00 4 35 25 - 20. 15. ~ijiifjf~~ji~4g~4~SIDE-SLOPES Itol. ROADWAYV 28 Ft 00 27 TABLE 7.-LEVEL CUTTINGS. Roadway 28 feet wide, side-slopes 1 to 1. Depth in ft.'0 1. *2.3. 4.5 6 *7.8.9 cu. yd cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds c. yds. cu. yds. 0 10 4 20'9 31'4 42 1 528 63,6 74.4 85-3 96'3 1 107-4 118'6 129'8 141'1 152'4 163.9 175'4 187.0 198'7 210'4 2 222'2 234'1 246'1 258'1 270'2 282'4 294.7 307.0 319'4 331'9 3 344*4 357'1 369'8 382'6 395'4 408'3 421'3 434.4 447'6 460'8 4 474'1 487'4 500'9 514'4 528'0 541'7 555'4 569.2 583'1 597'1 5 611'1 625'2 639'4 653'7 668-'0 682'4 696-9 711.4 726'1 740'8 6 755'6 770'4 785'4 800'4 815'5 830'6 845-8 861.1 876'5 891'9 7 907'5 923'0 938'7 954'5 970'3 986'2 1002 1018 1034 1050 8' 1067 1083 1099 1116 1132 1149 1166 1182 1199 1216 9 1233 1250 1267 1285 1302 1319, 1337 1354 1372 1390 10 1407 1425 1443 1461 1479 1497 1515 1534 1552 1570 11 1589' 1607 1626 1645 1664 1682 1701 1720 1739 1759 12 1778 1797 1816 1836 1855 1875 1895 1914 1934 1954 13 1974 1994 2014 2034 2055 2075 2095 2116 2136 2157 14 2178 2199 2219 2240 2261 2282 2304 2325 2346 2367 15 2389 2410 2432 2454 2475 2497 251.9 2541 2563 2585 16 2607 2630 2652 2674 2697 2719 2742 2765 2788 2810 17 2833 2856 2879 2903 2926 2949 2972 2996 3019 3043 18 3067 3090 3114 3138 3162 3186 3210 3234 3259 3283 19 3307 3332 3356 3381 3406 3431 3455 3480 3505 3530 20 3556 3581 3606 3631 3657 3682 3708 3734 3759 3785 21 3811 3837 3863 3889 3915 3942 3968 3994 4021 4047 22 4074 4101 4128 4154 4181 4208 4235. 4263 4290 4317 23 4344 4372 4399 4427 4455 4482 4510 4538 4566 4594 24 4622 4650 4679 4707. 4735, 4764 4792 4821 4850 4879 25 4907 4936 4965 4994 5024 5053 5082 5111 5141 5170 26 5200 5230 5259 5289 5319 5349 5379 5409-'5439 5470 27 5500 5530 5561 5591 5622'5653 5684 5714 5745 5776 28 5807 5839 5870 5901 5932.5964 5995 6027 6059 6090 29 6122 6154 6186 6218 6250 6282 6315 6347 6379 6412 30 6444 6477 6510 6543 6575 6608 6641 6674 6708 6741 31 6774 6807 6841 6874 6908 6942 6975 7009 7043 7077 32 7111 7145 7179 7214 7248 7282 7317 7351 7386 7421 33 7456 7490 7525 7560 7595 7631 7666 7701 7736 7772 34 7807 7843 7879 7914 7950 7986 8022 8058 8094 8130 35- 8167 8203 8239 8276 8312 8349 8386 8423 8459 8496 36 8533 8570 8608 8645 8682 8719 8757 8794 8832 8870 37 8907 8945 8983 9021 9059 9097 9135 9174 9212 9250 38 9289 9327 9366 9405 9444 9482 9521 9560 9599 9639 39 9678 9717 9756 9796 9835 9875 9915 9954 9994 10034 40 10074 10114 10154 10194 10235 110275 10315 10356 10396 10437 41 10478 10519 10559. 10600. 10641 10682 10724 10765 10806 10847 42 10889 10930 10972 11014 11055 11097 11139 11181 11223 11265 43 11307 11350 1'1392 11434 11477 11519 11562 11605 11648 11690 44 11733 11776 11819 11863 11906 11949 11992 12036 12079 12123 45 12167 12210 12254 12298 12342 12386 12430 12474 12519 12563 46 12607 12652 12696 12741 12786 12831 12875 12920 12965 13010 47 13056 131.01 13146 13191 13237 13282 13328 13374 13419 13465 48 13511 13557 13603 13649 13695 13742 13788 13834 13881 13927 49 13974 14021 14068 14114 14161 14208 14255,,' 14303 14350 14397 50 14444 14492 14539 14587 14635 14682 14730 14778 14826 14874 51 14922 14970 15019 15067 15115 15164 15212 15261 15310 15359 52 15407 15456 15505 15554 15604 15653 15702 15751 15801 15850 53 15900 15950 15999 16049.16099 16149 16199 16249 16299 16350 54 16400 16450 16501 16551 16602 16653 16704 16754 16805 16856 55 16907 16959 17010 17061 17112 17164 17215 17267 17319 17370 56 17422 17474 17526 17578 17630 17682 17735 17787- 17839 17892 57 17944 17997 18050 18103 18155 18208 18261 18314 18368 18421 58 18474 18527 18581 18634 18688 18742 18795 18849' 18903 18957 59 19011 19065 19119 19174 19228 19282 19337 19391 19446 19501 60 19556 19610 19665 19720 19775 19831 19886 19941 19996 20052 For continuation to 100 feet see table 13. 28 TABLE 8.-LEVEL CUTTINGS. Roadway 28 feet wide, side-slopes 1+ to 1. _.... _............ Depth in ft. 0 *1 ~2.3.4'5 -6.7'8 9. cu. yds. cu. yds. cuc y ds. cu. yds. cu. yds.. yd. u. ydscu. yds. cu. yds. cu. yds. 0 10-4 20.9 31.5 42'2 53'0 63'9 74.9 85.9 97~1 1 10Q83 119.7 131.1 142.7 154.3 166.0 177.8 189.7 201.7 21338 2 225'9 238.2 250.6 263.0 275.6 288,2 301.0 313-8 326.7 339-8 3 352'8 366'0 379'3 392'7 406'2 419'8 433'4 447'2 461'1 475'0 4 488'9 503'0 517-3 531'6 546'0 560-5 575'1 589'8 604'6 619-5 5 634.4 649'5 664'7 679'9 695.3 710'7 726-2 741'9 757'6 773'4 6 7.88'9 804'9 821'0 837'2 853'4 8.69'8 886'3 902'8 919'5 936-2 7 9528 969-8 986'8 1004 1021 1038 1056 1073 1091 1109 8 1126 1144 1162 1180 1198 1216 1234 1252 1271 1299 9 1308 1327 1346 1365 1384 1403 1422 1442 1461 1481 10 1500 1520 1540 1559 1579 1599 1620 1640 1660 1681 11 1701 1722 1742 1763 1784 1805 1826 1847 1869 1890 12 1911 1933 1954 1976 1998 2020 2042 2064 2086 2109 13 2131 2153 2175 2198 2221 2244 2267 2290 2313 2336 14 2359 2382 2406 2429 2453 2477 2501 2525 254-9 2573 15 2597 2622 2646 2671 2695 2720 2745 2770 2795 2820 16 2844 2870 2,895 2921 2946 2971 2998 3023 3049 3075 17 3101 3127 3153 3180 3206 3233 3259 3286 3313 3340 18 3367 3393 3421 3448 3475 3503 3531 3558 3586 3614 19 3641 3669 3698 3726 3754 3782 3811 3840 3868 3897 20 3925 3954 3984 4013 4042 4071 4101 4130 4160 4189 21 4219 4249 4279 4309 4339 4369 4399 4430 4460 4491 22 4522 4553 4584 4615 4646 4677 4708 4740 4771 4803 23 4834 4866 4898 4930 4962 4994 5026 5058 5091 5123 24 5156 5188 5221 5254 5287 5320 5353 5386 5419 5453 25 5486 5520 5553 5587 5621 5655 &689 5723 5757 5791 26 5826 5860 5895 5930 5964 5999 6034 6069 6104 6140 27 6175 6210 6246 6282 6317 6353 6389 6425 6461 6497 28 6533 6570 6606 6643 6679 6716 6753 6790 6827 6864 29 6901 6938 6976 7013 7051 7088 7126 7164 7202 7240 30 7278 7316 7354 7393 7431 7470 7508 7547 7586 7625 31 7664 7703 7742 7781 7821 7860 7900 7940 7979 8019 32 8059 8099 8139 8180 8220 8260 8301 8341 8382 8423 33 8464 8505 8546 8587 8628 8669 8711 8752 8794 8836 34 8878 8920 8962 9004 9046 9088 9131 9173 9216 9258 35 9301 9344 9387 9430 9473 9516 9559 9603 9646 9689 36 9733 9777 9821 9865 9909 9953 9997 10041 10086 10130 37 10175 10220 10264 10309 10354 10399 10445 10490 10535 10580 38 10626 10672 10717 10763 10809 10855 10901 10947 10993 11040 39 11086 11133 11179 11226 11273 11320 11367 11414 11461 11508 40 11556 11603 11651 11698 11746 11794 11842 11890 11938 11986 41 12035 12083 12131 12180 12228 12277 12326 12375 12424 12473 42 12522 12572 12621 12671 12720 12770 12819 12869 12919 12969 43 13019 13069 13120 13171 13221 13272 13322 13373 13424 13475 44 13526 13577 13628 13680 13731 13782 13834 13886 13938 13990 45 14042 14094 14146 14198 14251 14303 14356 14408 14461 14514 46 14567 14620 14673 14726 14779 14833 14886 14940 14993 15047 47 15101 15155 15209 15263 15317 15372 15426 15480 15535 1559'0 48 15644 15699 15754 15810 15864 15920 15975 16030 16086 16142 49 16197 16253 163.09 16365 16421 16477 16533 16590 16646 16703 50 16759 16816 16873 16930 16987 17044 17101 17158 17216 17273 51 17331 17388 17446 17504 17562 17620 17678 17736 17794 17853 52 17911 17970 18028 18087 18146 18205 18264 18323 18382 18442 53 18500 18560 18620 18680 18739 18799 18859 18919 18980 19040 54 19100 19160 19220 19282 19342 19403 19464 19525 19586 19647 65 19708 19770 19831 19893 19954 20016 20078 20140 20202 20264 56 20326 20388 20451 20513 20576 20639 20701 20764 20827 20890 57 20953 21016 21079 21143 21206 212,70 21333 21397 21461 21525 58 21589 21653 21717 21782 21846 21911 21975 22040 22104 22169 59 22234 22299 22364 22430 22495 22561 22626 22692 22758'22823 60 22889 22955 23021 23087 23153 23220 23286 23353 23419 23486 For continuation to 100 feet see Table 13. 5 10 150 20 60 55 50 45 I ~.h.q,: _ k /I 36/ 40 icky 35, 3ir 30 li m ~ril l d~'TA-2.' DX/L/'..//P/// v, ESl. /,,,k///../ADWY/ / 28 I 10 Clef 11'/f I5q'Yl ~Y~t~t~iiIESOE /4'A/ to.'' ~i Y rt'lW"Y 28 // ~h'~ LhA' ~q>~.h~.k'//FOr'Y'//I/Y.t'.// PlateL-A 50 l"I 60 J- 1r t:~~~~~~o } 2 0 ~~~~2 55 50 45 40 35 )252o 15 ROADWABY 2 8 F 10-For _~v~cavazt qn,.~ 5 0 29 TABLE 9.-LEVEL CUTTINGS. Roadway 28 feet wide, side-slopes 1 to 1. Depth in ft. 0 1 2 3.4.5.6'7 *8.9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. 0 10-4 21'0 31'6 42.4 53'2 64'2 75.3 86'5 97'9 1 109'3 120-8 132 5 144-3 156 1 16i81 180o2 192-4 204-8 217-2 2 229-6 242-3 25501 267-9 280 9 294-0 307.2i 320.5 33401 347 5 3 361'2 374.9 38-88 402 8 416-9 43181 445.4 459.9 474.4 489,1 4 503 7 518*6 533s6 548 6 563 9 579.3 594,7 610-2 625.8 641.6 5 657-5 673'4 689'5 705'7 722'1 738-5 755'0 771'7 788:4 805'3 6 822'2 839*3 856'5 873'8 891'2 908'8 926'4 944'2 962'0 980'0 7 998'1 1016 1035 1053 1072 1090 1109 1128 1147 1166 8 1185 1204 1224 1243 1263 1283 1303 1322 1343 1363 9 1383 1403 1424 1445 1465 1488 1507 1528 1549 1571 10 1592 1614 1635 1657 1679 1701 1723 1745 1767 1790 11 1812 1835 1858 1881 1904 1927 1950 1973 1997 2020 12 2044 2068 2092 2116'2140 2164 2189 2213 2238 2262 13 2287 2312 2337 2362 2387 2413 2438 2464 2489 2515 1t 2541 2567 2593 2619 2645 2672 2698 2725 2752 2779 15 2806 2833 2860 2887 2915 2942 2970 2997 3025 3053 16 3081 3109 3138 3166 2195 3223 3252 3281 3310 3339 17 3368 3397 3427 3456 3486.3516 8546 3576 3606 3636 18 3667 3697 3728 3758 3789 3820 3851 3882 3913 3944 19 3976 4007 4039 4070 4102 4134 4166 4198 4231 4263 20 4296 4328 4361 4394 4427 4460 4493 4527 4560 4594 21 4627 4661 4695 4729 4763 4797 4832 4866 4900 4935 22 4970 5005 5040 5075 5111 5146 5181 5217 5253 5288 23 5324 5360 5396 5432 5469 5505 5542 5578 5615 5652 24 5689 5726 5763 5800 5838 5875 6913 5951 5989 6027 25 6065 6193 6141 6179 6218 6257 6295 6334 6373 6412 26 6451 64191 6530 6570 6609 6649 6689 6729 6769 6809 27 6850 6890 6931 6971 7012 7053 7094 7135 7176 7217 28 7259 7300 7342 7384 7426 7468 7510 7552 7594 7637 29 7680 7722 7765 7808 7851' 7894 7937 7981 8024 8067 30 8111il 8155 8199 8243 8287 8331 8375! 8420 8464 8509 31 8554 8598 8643 8688 8734 8779 8824 8870 8915 8961 32 9007 9053 9099 9145 9191 9238 9284 9331 9378 9425 33 9472 9519 9566 9613 9661 9708 9756 9804 9851 9900 34 9948 9997 10045 10093 10142 10190 10239 10288 10337 10386 35 10435 10484 10534 10583 10633 10683 110732 10782 10832 10882 36 10933 10983 11034 11084 11135 11186 11237 11288 11339 11391 37 11443 11494 11546 11598 11649 11701 11753 1.1806 11858 11910 38 11963 112016 12068 12121 12174 12227 12281 12334 12387 12441 39 12494 12548 12602 12656 12710 12764 12819 12873 12928 12982 40 13037 13092 13147 1'3202 13257 13312 13368 13423 13479 13535 41 13591 13647 13703 13759 13815 13872 13928 13985 14042 14099 42 14156 14213 14270 14327 14385 14442 14500 14558 14615 14673 43 14731 14790 14848 14906 14965 15024 15082 15141 15200 15259 44 15318 15378 15437 15497 15556 15616 15676 15736 15796 15856 45 15917 15977 16038 16098 16159 16220 16281 16342 16403 16465 46 16526 16587 16649 16711 16773 16835 16897 16959 17021 17084 47 17146 17209 17272 17335 - 17398 17461 1-7524 17587 17651 17714 48 17778 17842 17905 17969 18033 18098 18162 18226 18291 18356 49 18420 18485 18550 18615 18680;18746 18811 18877 18942 1'9008 50 19074 19140 19206 19272 19339 19405 19472 19538 19605 19672 51 19739 19806 19873 19940 20008 20075 20143 20211 20279 20347 52 20415 20483 20551 20620 20688 20:757 20826 20894 20963 21032 53 21102 21171 21241 21310 21380 21450 21519'21589 21659 21730 54 21800 21870 21941 22012 22082 22153 122224 22295 22366 L22438 55 22509 22581 22652 22724 22796 22868 22940 23012 23085 23157 56 23230 23302 23375 23448 23521 23594 23667 23741 23814 23888 57 23961 24035 24109 24183 24257 i24331 24405 24480 24554 24629 58 24704 24779 24854 24929 25004 125079 25155 25230 125306 25381 59 25457 25533 25609 25686 25762 25838 25915 25992 26068 26145 60 126222 26299 i26376 26454 26531 26609 26686 26764 26842 26920 For continuation to 100 feet see table 13. 30 TABLE 10.-LEVEL CUTTINGS. Roadway 28 feet wide, side-slopes 2 -to 1. Depth inft..0.1 2.3 4 5. 6.7 *8.9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. 0. 10'4 21'0 31'8 4;2.7 53'7 64'9 76'2 87'7 99'3 1 111.1 123'0 135'1 147'3 159 7 172'2 184 9 197'7 210 7 223'8 2 237.0 2504 264 0 277.7 29146 30.56 319'7 334'0 348 4 363'0 3 377.8 392.7 407.7 422.9 438 2 453.7 469'3 485'1 501 0 517i 1 4 533:3 549.7 566.2 582.9 599.7 616.6 633-7 651 0 668.4 686, 0 5 703'7 721 5 739'5 757'7 776.0 794'4 813[ 0 831'7 850'6 869i 6 6 888.9 908'2 927'7 948.3 968*1 988.1 1008 1028 1049 1069 7 1090 1111 1132 1153 1174 1195 1217 1239 1260 1282 8 1305 1327 1349 1372 1394 1417 1440 1464 1487 1510 9 1533 1557 1581 1605 1629 1654 1678 1703 1728 1753 10 1778 1803 1828 1854 1880 1905 1931 1958 1984 2010 11 2037. 2064 2091 2118 2145 2172 2200 2227 2255 2283 12 2311 2339 2368 2396 2425 2454 2483 2512 2541 2570 13 2600 2630 2659 2689 2720 2750 2780 2811 2842 2873 14 2904 2935 2966 2998 3029 3061 3093 3125 3157 3190 15 3222 3255 3288 3321 3354 3387 3420 3454 3488 3521 16 3555 3590 3624 3658 3693 3728 3763 3798 3833 3868 17 3904 3939 3975 4011 4047 4083 4120 4156 4193 4230 18 4267 4304 4341 4378 14416 4454 4492 4529 4568 4606 19 4644 4683 j 4722 4761 4800 4839 4878 4918 4957 4997 20 5037 5077 5117 5158 5198 5239 [52803 5321 5362 S403 21 5444 5486 5528 5570 5612 5654 5696 5738 5781 5824 22 5867 5910 5953 5996 6040 6083 6127 6171 6215 6259 23 6303 6348 6393 6438 6483 6528 6573 6618 6664 6710 24 6756 6802 { 6848 6894 6941 6987 7034 7081 7128 7175 25 7222 7270 7317 7365 7413 7461 7509 7558 7606 7655 26 7704 7753 7802 7851 7900 7950 8000 8049 8099 8150 27 8200 8250! 8301 8352 8403 8454 8505 8556 8608 8659 28 8711 8763 8815 8867 1 8920 8972 9025 9078 9131 9184 29 9237 9290 9344 9398 9451 9506 9560 9614 9668 9723 30 9778 9833 9888 9943 9998 10054 10109 10165 10221 10277 31 10333 10390 110446 10503 10560 10617 10674 10731 10788 10846 32 10904 10961 11019 11078 11136 1'1194 11253, 11312 11371 11430 33 11489 11548 11608 11667 11727 11787 11847 11907 11968 12028 34 12089 12150 12211 12272 12333 12394 12456 12518 12580 12642 35 12704 12766 12828 12891 12954 13017 13080 113143 13206 13270 36 13333 13397 13461 13525 13589 13654 13718 13783 13848 13913 37 13978 14043 14108 14174 14240 14305 14371 14438 14504 14570 38 14637 14704 [14770 14838 {14905 114972 15040 15107 15175 115243 39 15311 15379 15448 15516 15585 15654 15723 15792 15861 15930 40 16000 16070 16140 162.10 16280 16350 1'6420 16491 16562 16633 41 16704 16775 16846 16918 16989 17061 17133 17205 17277 17350 42 P1422 17495 17568 17641 17714 117787 17860 17934 18008 18081 43 18156 18230 18304 18378 18453 18528 18603 18678 18753 18828 44 18904 18979 19055 19131 19207 19283 19360 19436 19513 19590 45 19667 j19744 19821 19898 19976 20054 20132 20210 20288 20366 46 20444 20523 20602 20681 20760 {20839 20918 20998 21077 21157 47 21237 21317 21397 21478 21558 21639 21720 21'801 21882 21963 48 22044 22126 22208 22290 22372 22454 22t36 22618 22701 22784 49 22867 22950 23033 23116 23200 23283 23367 23451 23535 23619 50 23704 23788 23873 23958 24043 24128 24213 24298 24384 24470 51 24556 24642 24728 24814 24900 24987 25074 25161 25248 25335 52 25422 25510 25597 25865 25773 25861 25949 26038 26126 26215 53 26304 26393 26482 26571 26660 26750 26840 26930 27020 27110 54 27200 27290 27381 27472 27563 27654 27745 27836 27928 28019 55 28111 28203 28295 28387 28480 28572 28665 28758 28851 28944 56 29037 29130 29224 29318 29412 29506 29600 29694 29788 29883 57 29978 30073 30168 30263 30358 30454 30549 30645 30741 30837 58 30933 31030 31126 31223 31320 131417 31514 31611 31708 31806 59 31904 32002 32100 32198 32296 132394 32493 32592 32691 32790 L60 132889 32988 33038 1R 7 J32287 33387 33487 133587 33688 33788 For continuation to 100 feet see table 13. _Plate/BZ 60 -i 5 5 50 515 35 Paz~~~8 30 - 20. 15 10 HffZiit Y I " t IDE -SLOPE S 2 to 1. ROADWAY 2 8 F? I I L L4 c 7- > "' Z 31 TABLE 11.-LEVEL CUTTINGS. Roadway 18 feet wide, side-slopes, ~ to 1. in ft. O 1 *2.3.4.5 *6 7..8'9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. O 6'68 13'4 20'1 26'8 33-6 40'3 47'1 53o9 60 S 1 67'6 74.5 81'3 88'2 95'1 102'1 1090 116'0 123'0 130'O 2 137'0 144'1 151'1 158'2 165'3 172'4 179'5 186'7 1939 201'O 3 208'2 2155 2227 230'0 237.2 244.5 251'9 259'2 266'5 274'0, 4 281-5 288'9 296'3 303'8 311'3 318'8 326'3 333.8 341.3 348.9 5 356-5 364'1 371'7 379.3 387.0 394.7 402'4 410-1 417'8 425'6 6 433.3 441.1 448.9 456'7 464'6 472.5 480'3 48852 496'1 504.11 7 512.0 520-0 528'0 536'0 544'1 552.1 560-2 568-3 576'4 584.0! 8 592.6 600'8 608'9 617'1 625'3 6336 641.8 650.1 658.4 666'7 9 675.0 683.3 691'7 700'1 708.5 716.9 725.3 733.8 742.3 750.7 10 759.3 767'8 776'3 784'9 793'5 802'1 810'7 819'3 828.0 836.7 11 845.4 854'1 862'8 871'6 880'3 889'1 897'9 9067 915'6 924'4 12 933.3 942'2 951'1 960'1 969'0 978.0 987'0 996.0 1005 1014 13 1023 1032 1041 1050 1060 1069 1078.1087 1096 1106 14 1115 1124 1133 1143 1152 1161 1171 1180 1189 1199 15 1208 1218 1227 1237 1246 1256 1265 1275 1284 1294 16 1304 1313 1323 1333 1342 1352 1362 1372 1381 1391 17 1401 1411 1421 1430 1440 1450 1460 1470 1480 1490] 18 1500 1510 1520 1530 1540 1550 1560 1570 1580 1591 19 1601 1611 1621 1631 1642 1652 1662 1672 1683 1693 20 1703 1714 1724 1735 1745 1755 1766 1777 1787 1798 21 1808 1818 1829 1840 1850 1861 1872 1883 1894 1905 22 1916 1926 1937 1947 1958 19'69 1980 1991 2002 2013 23 2024 2035 2046 2057 2068 2079 2090 2101 2111 2122 24 2133 2144 2156 2167 2178 2189 2200 2212 2223 2234 25 2245 2256 2268 2279 2290 2301 2313 2324' 2336 2347 26 2359 2371 2382 2394 2406 2417 2429 2440 2452 2464 27 2475 2486 2498 2510 252J 2533 2545 2557 2569 2581 28 2592 2604 2616 12628 2640 2652 2664 2676 2688 2700 29 2712 2724 2736 2748 2760 2772 2784 2797 2809 2821 30 2833 2845 2858 2870 2882 2894 2907 2919 2931 2944 31 2956 2969 2981 2994 3006 3018 3031 3044 3056 3069 32 3081 3094 3107 3119 3132 3145 3157 3170 3183 3195 33 3208 3221 3234 3247 3260 3272 3285 3298 3311 3324 34 3337 3350 3363' 3376 3389 3402 3415 3428 3441 3454 35 3467 3481 3494 3507 3520 3533 3547 3560 3573 3587 36 3600 3613 3627 3640 3653 3667 13680 3694 3707 3721 37 3734 3748 3761 3775 3788 3802 3816 3829 3843 3857 38 3870 3884 3898 3911 3925 3939 3953 3967 3980 3994 39 4008 4022 4036 4050 4064 4078 4092 4106 4120 4134 40 4148 4162 4176 4190 4205 4219 4233 4247 4261 4275 41 14290 4304 4318 4333 4347 4361 4376 4390 4404 4419 42 4433 4448 4462 4477 4491 4506 4520 4535 4549 456'4 43 4579 4593 4608 4623 4637 4652 4667 4681 4696 4711 44 4726 4741 4756 4770 4785 4800 4815 4830 4845 4860 45 4875 4890 4905 4920 4935 4950 4965 4980 4995 5011 46 5026 5041 5056 5071 5087 5102 5117 5133 5148 5163 47 5179 5194 5209 5225 5240 5256 5271 5287 5302 5318 48 5333 5349 5364 5380 5396 5411 5427 5443 5458 5474 49 5490 5505 5521 5537 5553 5569 5585 5600 5616 5632 50 5648 5664 5680 5696 5712 5728 5744 5760 5776 5792 51 5808 5824 5840 5857 5873 5889 5905 5921 5938 5954 52 5970 5987 6003 6019 6036 6052 6068 6085 6101 6118 53 6134 6151 6167 6184 6200 6217 6233 6250 6267 6283 54 6300 6317 6333 6350 6367 6383 6400 6417 6434 6451 55 6468 6484 6501 6518 6535 6552 6569 6586 6603 6620 56 6637 6654 6671 6688 6705 6722 6739 6757 6774 6791 57 6808 6825 6843 6860 6877 6895 6912 6929 6947 6964 58 16981 6999 7016 7034 7051 7069 7086 7104 7121 7139 59 7156 -7174 7192 7209 7227 7245 7262 7280 7298 7315 60 1 7333 7351 17369 7387 7405 7422 7440 7458 7476 7494 For continuation to 100 feet see Table 13. 32 TABLE 12.-LEVEL CUTTINGS. Roadway 28 feet wide, side-slopes I to 1. in ft. *0 *1.2.3.4.5.6.7.8.9 cu. yds. cu. yds. cu. yds. cu. yds. cu. yds. cu. yd s cu. yds. cu. yds. cu. yds. cu. yds. 0 10.4 20'8 31'2! 41.61 52'1 62'6 73'0 83 6 94'1 1 104 6 115'2 125*8 136'4 147'0 157'6 168'3 179'0 189'7 200'4 2 211*1 221-9 232'6 243'4 254'3 265'1 275'9 286'8 297'7 308'6 3 319 4 330'4 341'3 352'3 363'3 374'3 385'4 396'4 407 5 418'6 4 429'7 440'8 451'9 463'1 474'3 485'5 496'7 508'0 519'2 530'5 5 541'7 55301 564'3 575'6 587'0 598'4 609'7 621'1 632 6 644'0 6 655 6 667'1i 678'7 690'3 7020C 713'6 725'3 737'0 747 7 759'4 7 771 3 783'0 794'7 806'4 818'1 829*9 841'6 853'4 865'3 877'1 8 888 9 900*8 912'6 923'6 935'5 947'4 959'4 971'4 983'4 995:4 9 1007 1019 1032 1044 1056 1068 1080 1092 1105 1117 10 1130 1142 1154 1166 1179 1191 1203 1216 1228 1240 11 1253 1265 1278 1290 1303 1315 1328 1340 1353 1365 12 1378 1390 1403 1416 1428 1441 1454 1466 1479 1492 13 1505 1517 1530 1543 1556 1569 1582 1595 1607 1620 14 1633 1646 1659 1672 1685 1699 1712 1725 1738 1751 15 1764 1777 1790 1803 1817 1830 1843 1856 1870 1883 16 1896 1910 1923 1936 1950 1963 1977 1990 2004 2017 17 2031 2044 2058 2071 2085 2098 2112 2126 2139 2153 18 2167 2180 2194 2208 2222 2235 2249 2263 2277 2291 19 2305 2318 2332 2346 2360 2374 2388 2402 2416 2430 20;; 2444 2459 2473 2487 2501 2515 2529 2543 2558 2572 21 2586 2600 2615 2629 2643 2658 2672 2686 2701 2715 22 2730 2744 2759 2773 2788 2802 2817 2831 2846 2860 23 2875 2890 2904 2919 2934 2948 2963 2978 2993 3007 24 3022 3037 3052 3067 3082 3097 3111 3126 3141 3156 25 3171 3186 3201 3216 3232 3247 3262 3277 3292 3307 26 3322 3337 3353 3368 3383 3398 3414 3429 3444 3460 27 3475 349,0 3506 3521 3537 3552 3568 3583 3599 3614 28 3630 3645 3661 3676 3692 3708 3723 3739 3755 3770 29 3786 3802 3818 3833 3849 3865 3881 3897 3913 3928 30 3944 3960 3976 3992 4008 4024 4040 4056 4072 4088 31 4105 4121 4137 4153 4169 4185 4202 4218 4234 4250 32 4267 4283 4299 4316 4332 4348 4365 4381 4398 4414 33 4431 4447 4464 4480 4497 4513 4530 4.546 4563 4580 34 4596 4613 4630 4646 4663 4680 4697 4713 4730 4747 35 4764 4781 4797 4814 4831 4848 4865 4882 4899 4916 36 4933 4950 4967 4984 5001 5018 5036 5053 5070 5087 37 5104 5121 5138 5155 5173 5190 5207 5225 5242'5259 38 5278 5295 5313 5330 5348 5365 5383 5400 5418 5436 39 5453 5471 5488 5505 5523 5541 5559 5576 5594 5612 40 5630 5647 5665 5683 5701 5719 5737 5755 5772 5790 41 5808 5826 5844 5862 5880 5898 5916 5935 5953 5971 42 5989 6007 6025 6043 6062 6080 6098 6116 6135 6153 43 6171 6190 6208 6226 6245 6263 6282 6300 6319 6337 44 6356 6374 6393 6411 6430 6448 6467 6486 6504 6523 45 6542 6560 6579 6598 6617 6635 6654 6673 6692 6711 46 6730 6749 6767 6786 6805 6824 6843 6862 6881 6900 47 6919 6938 6958 6977 6996 7015 7034 7053 7072 7092 48 7111 7130 7150 7169 7188 7208 7227 7246 7266 7285 49 7305 7324 7343 7363 7382 7402 7422 7441 7461 7480 50 7500 7520 7539 7559 7579 7598 7618 7638 7658 7677 51 7697 7717 7737 7757 7777 7796 7816 7836 7856 7876 52 7896 7916 7936 7956 7976 7997 8017 8037 8057 8Q77 53 8097 8117 8138 8158 8178 8198 82'19 8239 18259 8280 54 8300 8320 8341 8361 8382 8402 8423 8443 8464 8484 55 8505 8525 8546 8566 8587 8608 8628 8649 8670 8690 56 8711 8732 8753 8773 8794 8815 8836 8857 8878 8899 57 8919 8940 8961 8982 9003.9024 9045 9066 9087 9109 58 9130 9151 9172 9193 9214 9235 9257 9278 9299 9320 59 9342 9363 9384 9406 9427 9448 9470 9491 9513 9534 60 9556 9577 9599 9620 9642 9663 1 9685 9706 9.728 9750 33 TABLE 13.-LEVEL CUTTINGS. Continuation of the foregoing Tables of Cubic Contents to 100 feet of height or depth. or Depth TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE T.ABLE TABLE TABL TABLE in feet. 1 2 3 4 5 6 7 8 9 1 0 1 5 1' cu yd. cu yd. cu yd. cu yd. cu yd. cu yd. cu yd. cu yd. cu yd. cu yd. cu. yds. cu. yds. 61 23835 26094 178-18 21294124739 31630 20107 23553 i26998 33889 7512 9771 -5 24201 26479 18108 21610 25113 32117 20386 23888 27390 34394 7602 9880 62 24570 26867 1.8370 21930125489 32607 20667 24226 27785 349014 7693 9989 ~5 24942 27257 18634 22251 25868 33102 20949 245G6 28183 3.5117 7784 10098 63 25317 27650 18900 22575 26250 33600 21233 24908 28583 35933 7875 10208 [ 5'25694128046 19168:22901 26635 341012 21519 25253 28986 16454 7967 10319 64 26074 28444 19437123230 27022 34607 21807 25600 29393 36978 8059 10430.5 26457 28846 19708 23560 27413 35117 22097 25949 29801 37506 8152 10541 65 26843 29250 19981123894!27806 35630 22389 26300 30213 38037 8245 10653'5 27231 29657 20256!24129 28201 36146!22682 26654 130627 38572 8339 10765 66 27622 30067 20533 24567238600 36667 22978 27011 31044 39111 8433 10878.5 28016 30479120812;2490i7 29001 37191123275 27369 31464139654 8528 10991 67 28413 30894 21093 25249 29406 37719t235740 7730 31887 40200 8623 11105.5 28812 31313 2137525594'29813 38250 2387512809332312 40750 8719 11219 68 29215 31733,21659125941130222 38785 24178 28459 32741 41304 8815 11333.5 29620132157121945 26290130635 39324 24482 28827 33172 41861 8911 11448 69 300283258322233'26642'i3105039867 24789 29197 33605 42422 9008 11564 / 5 30438s33013 22523 26996131468 40413125097 29569 341042 42987 9106 11680 70 30852 33444 22814127352131889 40963 25407 29944 34481 43556 9204 11796.5 31268 33879 23108127710 32313i4151725719 30321 34924 44128 9.302 11913 71 31687134317 23404128071 32739142074 26033 30701 35369144704 9401 12031.5 321083475'723701i28434 33168 4263526349 3108335816 45283 9500 12148 72 32533 35200 24000128800133600 4320026667 31467 36267 45867 9600 12267.5 32960 35646 24301129168134035 43769i26986 31853 36720 46454 9700 12385 73 33390 36094 24604129538534472 44341 27307 32241 37176 47044 9801 12505 *5 33823136546 24907 i29910 34913144917127631 132632 37635 47639 9902 12624 74 3425937000 2521430285 35356 45496 27956 33026 38096 48237 10004 12744 I 5 34697 37457 25522130662 35801 46080 28282 33421 38561 48839 10106 12865 75 35139 37917125832 31042136250 146667 28611133819 39028 49444 10208 112986 E 5 35582138379 26144 31423 36701 47257 2894234219 139498 50054 10311 13108 76 36029 38844 26458i31807 37156 47852 29174 34622 39970 50667 10415 13230 ~5 36479139313126774 32194 37613 48450129608 35027 40446 51283 10519 13352 77 36931 39783 27092132582 38072149052 29944 35434140924 51904 10623 13475'5 37386 40257 27411 32973 38.535 49657 30282 35843 41405 52528 10728 1359S 78 37844 40733 27733'33367139000 50267 30622 36256 41889 53156 10833 13'722 I 5 38305 41213 28056133762 39468 50880 3096436669 42375 53787 10939 103846 79 3876814169428381 34160 39939/51496 31307 37086 42865154422 11045 13971 | 5 39235 42179 28708 34560 40413 52117 31653:37504 4335755061 1111152 14096 8() 39704 42667 29037.34963 40889 52741 32000.37926413852 55704 11259 114222 8F 1 40650 43650 29700135775 41850 54000 32700138775 44850 57000 11475,1175 82 41607144644130370136596142822 55274 3340739633 45859 58311 11693 14730 83 42576145650 31048 37427143806 56563 341224050114986 84 43555146667 31733 38267144800 57867 34844!41378147911160978 12133 15244 85 44546 4769432426 3911645806 59185 35574 42264i48954162333{12357 }15505 86 45548 48733133126 39974 46822G 60519 36311143159 50008 63704 12582 15767 87 46561 49783 33833 40842 47850 61867/3705644064151072165089112808 16031 88 47585150844134548.41718 48889 63230 37807144978 521481 66489 13037 16296 89 48620151917 135270142605 49939164607138567i45901 53235 67904 13268 16564 90 49667153000 36000 43500 5100016600013933346833154333169333113500 16833 91 150724 54094 36737}44405 52072 67407 40107147775 55443 70778 13734 17105 92 /517931552001374.8145319153156168830140889 48726/565631722371 13970 17378 93 52872 56317138233 46242 54250 70267 4167849686 57694 73711 14208 17653 94 153963 57444 38993147174155356 71719 42474 50651 58837 75200 14448 17930 95 55065 158583 39759 48116 56472 73185 43278 51634 599901767041 14690 118208 96 [56178/59733140533 49067 57600174667144089 52622 61155 78222114933 118489 97 57302 60894141315 50027 58739 76163144907153619 62331179756 15179 18771 98 58437162067142104150996 59889 77674 45733 54626 63518 81304 15426 19056 99 59583 63250 42900i51975i61050 79200 46567 55642 64716 82867 15675 19342 100 160741 64444143704152963i62222 80741 4740756667[6592618444415926 19630 34 TABLE 14. Of cubic yards in a 100 foot station, to be added to, or subtracted from, the quantities in the preceding thirteen tables, in case the excavations or embankments should be increased or diminished 2 feet in width. The most rapid method of performing this operation would be to add together the average heights, or depths, of the equivalent level cuttings or fillings of several consecutive 100 foot stations, and divide their sum by their number, for an average one of tlIem all. The number of cubic yards corresponding to this average height, or depth, when multiplied by the number of stations, will give the content of the entire length, nearly. It would, however, be better for the assistant, in cases where the width of roadway differs from those in the preceding Tables, to construct at once a new table, and diagram. Cubic Yards in a length of 100 feet; breadth 2 feet; and of different depths. Height Height Height Height Height or Cubic or Cubic or Cubic or Cubic or Cubic Depth Yards. Depth Yards. Depth Yards. Depth Yards. Depth Yards. in in in in ill feet. feet. feet.. feet. feet..5 3'70.5 152.5 300.5 448.5 596 1 7'41 21 156 41 304 61 452 81 600.5 11.1.5 159.5 307.5 456.5 604 2 14'8 22 163 42 311 62 459 82 607.5 18.5.5 167.5 315.5 463.5. 611 3 22'2 23 170 43 319 63 467 83 615.5 25.9.5 174.5 322.5 470.5 619 4 29.6 24 178 44 326 64 474 84 622.5 33.3.5 181.5 330.5 478.5 626 5 37'0 25 185 45 333 65 481 85 630.5 40'7' 5 189.5 337.5 485.5 633 6 44.4 26 193 46 341 66, 489 86 637.5 48.1.5 196.5 344.5 493.5 641 7 51' 9 27 200 47 348 67 496 87 644.5 55.6.5 204.5 352..5 500.5 648 8 59.3 28 207 48 356 68 504 88 652 ~5 63.0.5 211.5 359.5 507.5 65 9 66.7 29 215 49 363 69 511 89 659.5 70.4.5 219.5 367.5 515.5 663 10 741 30 222 50 370 70 519 90 667.5 77.8.5 226.5 374.5 522.5 670 11 81s5 31 230 51 378 71 526 91 674.5 85.2.5 233.5 381.5 530.5 678 12 88.9 32 237 52 385 72 533 92 681.5 92.6.5 241.5 389.5 537.5 685 13 9.63 33 244 53 393 73 541 93 689 ~5 100.5 248.5 396.5 544.5 693 14 104 34 252 54 400 74 548 94 696 ~5 107 *5 256.5 404 *5 552.5 700 15 1X1 35 259 55 407 75 556 95 704 ~5, 115.5 263 *5 411 *5 559.5 707 16 119 36 267 56 415 176, 563 96 711 -5~ 122 5 270. 5, 419.5 567.5 715 17 126 37 274 57 422 77 570 97 719 ~5 130' 5 278:.5 426.5 574.5 722 18 133 38 281 58 430 78 578 98 726 ~5 137.5 285.5 433.5 581 *5 730 19 141 39 289 59 437 79 585 99 733 ~5 144.5 293'5 441'5 589.5 737 20 148 40 296 60 444 80 593 100 741 35 TABLE 15.-CUBIC YARDS IN 100 FEET LENGTH. This Table shows the number of cubic yards of Excavation, or Embankment, corresponding to different areas of cross section, and to a length of 100 feet. The areas are expressed in square feet. This Table may be extended, by mentally changing the place of the decimal point; thus, the cubic yards corresponding to area of 1100 square feet will be 10 times that of 110 square feet, or 4074; those corresponding to an area of 8955 square feet will be 10 times that of 895-5 square feet, or 33167. If the number is not exactly divisible by 10, we may still take out the corresponding cubic yards with sufficient accuracy for practice, by using the nearest tabular number; thus, if we take 33167 for the cubic yards corresponding to an area of 8953 square feet, the error will be but about 8 cubic yards in 33000. A mean can, however, always be estimated in an instant by the eye, which will reduce the error to still less; thus it is seen at a glance, that 33157 is, in this instance, nearer than 33167. Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic sq. ft. Yar is. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. 1 3'70 45 166'7 89 329'6'5 431'5'5 513-0 * 5 594'4 2 7'41 46 170'4 90 333'3 117 433'3 139 514'8 161 596'3 3 11'1 47 174'1 91 337'0'5 435'2'5 516'7.5 598.2 4 148. 48 177'S 92 340'7 118 437'0 140.5 18'5 162 600'0 5 18'5 49 181'5 93 344'4'5 438'9'5 520'4'5 601.9 6 22'2 50 185'2 94 348'2 119 440'7 141 522'2 163 603'7 7 25'9 51 188-9 95 351'9'5 442'6'5 524'1 5 605'6 8 29'6 52 192'6 96 355'6 120 444'4 142 525.9 164 607'4 9 33'3 53 195'3 97 359'3'5 446.3 -5 527'8'5 609'3 10 37'0 54 200'0 98 363'0 121 448'2 143 529'6 165 611'1 11 40'7 55 203'7 99 366'7'.5 450'0 -5 531.5'5 613.0 12 44'4 56 207'4 100 370'4 122 451'9 144 533.3 166 614.8 13 48'1 57 211'1'5 372'2'5 453'7.5 535'2'5 616'7 14 51'9 58 214'8 101 374'1 123 4556' 145 537'0 167 618'5 15 55'6 59 218.5.5 375'9'5 457-4 *5 538'9'5 620.4 16 59'3 60 222'2 102 377'8 124 459'3 146 540'7 168 622'2 17 63'0 61 225.9'5 379'6'5 461'1 -5 542'6'5 624'1 18 66'7 62 229'6 103 381.5 125 463'0 147 544'4 169 625'9 19 70'4 63 233.3'5 383'3'5 464'8 -5 546'3 5 627'8 20 74'1 64 237'0 104 385'2 126 466'7 148 548'2 170 629'6 21 77'8 65 240.7'5 387'0'5 468.5'5,550'0 5 631.5 22 81'5 66 244.4 105 388'9 127 470'4 149 551.9 171 633'3 23 85'2 67 248.2'5 390'7.5'472'2 -5 553.7'5 635'2 24 88'9 68 251'9 106 392'6 128 474'1 150 555'6 172 637'0 25 92'6 69 255.6'5 394'4 5 475.9.5 557.4'5 638.9 26 96'3 70 259.3 107 396'3 129 477'8 151 559'3 173 640'7 27 100'0 71 263'0'5 398'2.5 479'6 -5 561'1'5 642.6 28 103'7 72 266'7 108 400'0 130 481'5 152 563'0 174 644.4 29 107'4 73 270.4'5 401'9 -5 483-3'5 564'8'5 646'3 30 111 1 74 274'1 109 403'7 131 485'2 153 566'7 175 61t82 31 114'8 75 277.8'5 405'6'5 487'0.5 568.5.5 650'0 32 118'5 76 2815 110 407'4 132 488'9 154 570'4 176 651'9 33 122'2 77 285'2.5 409.3.5 490'7.5 572'2'5 653.7 34 125'9 78 288.9 111 411'1 133 492'6 155 574'1 177 655.6 35 129'6 79 292'6.5 413'0'5 494.4.5 575.9'5 657.4 36 133'3 80 296'3 112 414'8 134 496'3 156 577'8 178 659'3 37 137'0 81 300.0.5 416'7' 5 498'2.5 579'6'5 661'1 38 140'7 82 I303.7 113 418'5 135 500'0 157 581'5 179 663'0 39 144'4 83 307'4'5 420'4.5 501'9'5 583'3'5 664'8 40 148'2 84 311'1 114 422'2 136 503-7 158 585'2 180 666'7 41 151'9 85 314'8'5 424'1 *5 505'6'5 587'0'5 668'5 42 155'6 86 318.5 115 425'9 137 507'4 159 588'9 181 670'4 43 159'3 87 322'2'5 427'8 *5 509'3 *5 5)0'7'5 672'2 44 163'0 88 325'9 116 429'6 138 511'1 160 592'6 182 674'1 36 TA.BL 15.-CUBIC YARDS IN 100 FEET LENGTH. Aroa. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic sq. ft. Yards. sq. ft. Yards. sq. ft. Y;ards. sq. f. Yards. sq. ft. Yards. sq. ft. Yards..5 675-9 *5 7833 *5 890-7 -5 998-2 -5 11056 -5 1213-0 183 677-8 212 785-2 241 892'6 270 1000-0 299 1107-4 328 1214-8 -5 6796 *5 7870.5 894-4 *5 1001-9 -5 1109-3 *5 1216-7 184 681-5 213 788-9 242 896-3 271 1003-7 300 1111-1 329 12185.5' 683-3 5 790-7 *5 898-2 *5 1005-6 *5 1113-0 *5 1220-4 185 685'2 214 792-6 243'900-0 272 1007-4 301 1114-8 330 1222-2.5 687-0'5 7944 *5 901-9 *5 1009-3 -5 1116-7 -5 1224-1 186 688-9 215 796-3 244 903-7 273 1011-1 302 11185 3131 1225-9 *5 690-7 *5 798-2 *5 905-6.5 1013-0' 5 1120-4 *5 1227-8 187 692-6 21B 800-0 245 907-4 274 1014-8 303 1122-2 332 1229-6.5 6944.5 801-9 5 909-3.5 1016-7.5 1124-1 *5 1231-5 188 696-3 217 803-7 246 911-1 275 1018-5 304 1125-9 333 1233-3 5' 698-2 *5 805-6.5 913-0 *5 1020-4 -5 1127-8'5 1235-2 189 700-0 218 807-4 247 914-8 276 1022-2 305 1129-6 334 1237-0 -.5 701-9 -5 809-3.5 916-7 -5 1024-1 *5 1131S' 5 1'238-9 190 703-7 219 811-1 248 918-5 277 1025-9 306 1133-3 335 1240-7.5 7r05.6.5 813-0 *5 920-4 *5 1027-8 *5 1135-2.5 1242-6 191 707-4 220 814-8 249 922-2 278 1029-6 307' 1137-0 336 1244-4.5, 709-3.5 816-7 * 465 9241 51 1015 5 1389 5 11'246-3 192 711-1 221 818-5 250 925-9 279 1033-3 308 1140-7 337 1248-2 -5 713-0.5 820-4 *5 927-8 *5 1035-2 -5 1142-6,5 1250-0 193 714-8 222 822-2 251 929-6 280 1037-0 309 11444 338 1251-9 *5 716-7 -5 824-1 *5 931-5 -5 1038-9 -5 1146-3 *5 1253-7 194 718'5 223 825-9 252 933-3 281 1040-7 310 1148-2 339 1255-6 -5'720-4 -5 827-8 -5'935-2 -5 1042-6 -5 1150-0 -5 1257-4 195 722-2 224 829-6 253 937-0 282 1044-4 311 1151-9 340 1259-3 -5 724-1 -5 831-5 -5 938-9 -. 1046-3 -5 1153-7 -5 1261-1 196 725-9 225 833-3 254 940:7 283 1048-2 312 1155-6 341 1263-0 *-5 727-8 -. 835-2 -5 942-6 -5 1050-0 -5 1157-4 -5 1264-8 197'729-6 226 837-0 255 944-4 284 1051-9 313 1159.3 342 1266-7 -5 731-5 -5 838-9 -5 946-3 -5 1053-7 -5 1161-1 -5 1268-5 198 733-3 227 840-7 256 948-2 285 1055-6 314 1163-0 343 1270-4 -5 735-2 -5 842-6 -5 950-0 -5 1057-4 -5 1164-8 -5 1272-2 199 737-0 228 844-4 257 951-9 286 1'059-3 315 1166-7 344 1274-1 -5 738-9 -5 846-3 -5 953-7 -5 1061-1 -5 1168-5 -5 1275-9 200'740-7 229 848-2 258 955-6 287 1063-0 316 1170-4 345 1277-8 -5'7426 -5 850-0 -5'957-4 -5 1004-8 5 1172-2 -5 1279-6 201 744-4 230 851-9 259 959-3 288 1066-7 317 1174-1 346 1281-5 -5 746-3.5 853-7 -5 961-1 -5 1068-5 -5 1175-9 -5 1283-3 202 748-2 231 855-6 260 963-0 289 1070-4 318 1177-8 347 1285-2 -5 750-0 -5 857-4 -5 964-8 -5 1072-2 -5 1179-6 -5 1287-0 203 751-s9 232 859-3 261 966-7 290 1074-1 319 1181-5 348 1288-9 -5 753-7 -5 861-1 -5 968-5 -5 1075-9 -5 1183-3 -5 1290-7 204 755-6 233 863-0 262 970-4 291 1077-8 320 1185-2 349 1292-6.5 757-4 *5 864-8 *5 972-2'5 1079-6 5 1187-0 *5 1294-4 205 759-3 234 866-7 263 974-1 292 1081-5 321 1188-9 350 1296-3 -5 761-1 -5 868-5 -5 975-9 -5 1083-3 -5 1190-7 -5 1298-2 206 763-0 235 870-4 264 977-8 293 1085-2 322 1192-6 351 1300-0 -5 764-8 -5 872-2 -5 979-6 -5 1087-0 -5 1194-4.5 1301-9 207 766-7 236 874-1 265 981-5 294 1088-9 323 1196-3 352 1303-7 -5 768-5 -5 875-9 -5 983-3 -5 1090-7 -5 1198-2 -5 1305-6 208 770-4 237 877-8 266 985-2 295 1092-6 324 1200-0 353 1307-4 -5 772-2 -.5 879-6 -5 987-0 -5 1094-4 -5 1201-9 -5 1309-3 209 774-1 238 881-5 267 988-9 296 1096-3 325 1203-7 354 1311-1 -5 775-9 -5 883-3 -5 990-7 -5 1098-2 -5 1205-6 -5 1313-0 210 777-8 239 885-2 268 992-6 297 1100-0 326. 1.207-4 355 1314-8.5 779-6 -5 887-0 -5 994-4 -5 1101-9 -5 1209-3 -5 -1316-7 2181 781-5 240 888-9 2369 996-31 298 1103-7 327 1211-1 356 1318-6 37 TABLE 15. —CUBIC YARDS IN 100 FEET LENGTH. Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. YardF. sq. ft. Yards..5 13204 -.5 14278s.5 1535.2 *5 1642-6 -5 1750.0'5 1857.4 357 1322'2' 386 1429.6 415 1537.0 444 1644.4 473 1751.9 502 1859.3 *5 1324l I.5 11431'5'5 1538'9.5 1646'3 *5 1753'7.5 1861.1 358 1325.9 387 143331 416 1540.7 445 1648'2 474 1755'6 503 1863.0 *5 1327'8.5 1435'2 -5 1542'6.5 1650'0 -5 1757'4.5 164'8 139 1329'6 388 1437'0 417 1544.4 446 1651'9 475 1759/ 3 504 1866'7 *5 1331. 5.5 1438.9.5 1546.3.5 1653.7.5 1761.1 5 1868.5 360 1333.3 389 1440.7 418 1548'2 447 1655.6 476; 176301 505 1870.4 -5 1335'2 *5 1442.6.5 1550o0.5 1657'4 -5 1764'8'5 18722 361 1337'0 390 144414 419 1551'9 448 1659.3 477 176617 506 1874.1 -5 1338'9 *5 1446'3'5 1553'7'5 1661'1'5 1768'5 *5 1875'9 362 1340'7 391 1448'2 420 1555'6 449 1663.0 478 1770.4 507 11877.8 35 1342'6.5 1450'0 -5 1557'4' 5 1664'8 *5 1772'2 *5 1879'6 363 13444 392 145191 421 11559'3 450 1666'7 479 1774'1 508 1881.5 *5 1348-3.5 14513.7,5 1561'1'5 1668-5'5 1775.9'5 1883.3 34 1348-2 393 145561 422 1563.0 451 1670.4 480 1777.8 509 188,5.2'5 1350'0.5 1457'4,5 156481'5 1672'2 *5 1779'6.5 1887'0 365 1351-9 394 145931 423 1566.7 452 1674'1 481 1781'5 510 1888,9 ~5 1353'7.5 1461'1.,b 156851'5 1675'9 *5 1783'3 *5 1890'7 s36 1355-6 395 1463-01 424 1570.4 453 1677.8 482 1785.2 511 1892.6 *5 1357'4'5 1464'8'5 1572'2 /5 1679'6 *5 1787'0'5 1894'4 367 1359'3 396 1466'7 425 1574'1 454 1681'5 483 1788'9 512 1896,3 L5 1361'1.5 1468.5.5 1575.9.5 1683.3 5 1790.7,5 1898.2 368 1363.0.397 1470.4 426 1577'8 455 1685,2 484 1792.6 513 1900,0.5 1364.8'5 1472.2.5 1579.6'5 1687.0 |5 1794.4.5 1901.9 369 1366!7 398 1474,1 427 1581'51 456 1 688.9 485 1796'3 514 1903'7'5 136851.5 147591'5 1583'3'5 1690'7'5 1798.2'5 1905.6 370 1370'4 399 1477'8 428 1585'2 457 1692.6 486 1800, 0 515 1907'4 *5 1372.2 *5 1479'6'5 1587'0'5 169441.5 1801'9'5 1909'3 371 1374'1 400 148151 429 1588.9 458 1696'3 487 1803'7 516 1911'1 *5 137959'5 1483.3'5 1590'7'5 16'982 *5 18056'5 1913'0 372 1377S8 1401 1485'2 430 1592'6 459 170070 4888 807'4 517 1914'8'5 1379'6.5 148730'5 159404'5 170169'5 1809.3'5 1916'7 373 1381'S 402 1488.91 431 1596.3 460 170371 489 1811'I 518 1918'5'5 1383'3'5 1490'7'5 1598'2'5 1705'6'5 1813'0'5 1920'4 374 1385'2 403 149261 432 160001 461 170741 490 1814'8 519 1922'2'5 1387'0.5 1494.4'5 1601.9.5] 1709.3 1 5 1816.7'5 1924 1 375 1388'9 404 1496'3. 433 1603'7 462 1711'1 491 1818'5 520 1925'9 56 1390'7 *5 1498'2'5 1605'6'5 ]713'0'5 1820'4'5 1927'8 376 13926' -405 1500'0 434 1607'4 463 1714.1 492 1822'2 521 1929'6'5 1394.4.5 1501.9'5 1609.3'5 171-6'7'5 1824'1'5 1931'5 377 1396'3 406 150371 435 11611.1 464 1718.5 493 1825'9 522 1933-3 ~5 1398,2'5 1505'6'5 1613'0'5 1720'4'5 1827'8 ~6 1935'2 378 140001 407 1507-4 436 16148 465 1722'2 494 1829.6 523 1937.0'5 1401'9 *5 1509'3'5 1616'7'5 1724' 1 5 1831 5 5 1938'9 379 1403'7 408 1511'1 437 1618'5 466 1725.9 495 1833'3 524 1940'7'5 1405.6'5 1513'0'5 1620'4'5 172781'5 1835'2'5 1942'6 380 140741 409 15148S 438 162221 467 1729'61 496 1837.0 525 19444'5 1409'3'5 1516'7'5 1624'l'5 1731'5'5 1838'9'5 194643 381 1411.1 410 151855 439 162591 468 1733'3 497 1840'7 526 1948'2 S 1.413'0 -5 1520.4'5 1627'8'5 1735'2'5 1842'6'5 1950'0 382 14148s 411 1522.2 440 1629.6 469 1737'0 498 1844.4 527 1951.9'5 1416.7'5 1524.1'i5 1631'5'5 1738.9'5 1846.3'5 1953.7 3 1418'5 412 1525.9 441 1633.3 470 1740.7 499 1848.2 528 1955.6'5 1420'4'5 1527'8'5 1635'2 *5 1742'6'5 1850'0'5 1957'4 1422.2.413 1529-6 442 1637'0 471 1744'4 500 1851'9 529 1959'3'5 1424'1 5 11531-5'5 1638.9'5 1746.3'5 1853'7'5. 1961'1 385 1425'9 414 1533.3 44.3 1640'7 472 1748'2 501 1855'6 530 1963'0 38 TABLE 15.-CUBIC YARDS IN 100 FEET LENGTH. Area. Cubie Area. Cubic Area. Cubic Area. Cubic Area.- Cubic Area. Cubic'sq. ft. Yards. sq. ft. Yards. sq. f. Yards. sq. ft. Yards. sq. ft. Yards. sq ft. Yards. *5 1964-8 *5 2072-2 *5 2179-6 *5 2287-0.5 2394-4 *5 2501-9 531 1966.7 560 20741 589 2181.51 618 2288s9 647 2396.3 676 2503.7 *5 1968'5'5 2075'9 *5 2183'3'5 2290'7'5 2398'2'5 2505'6 532 1970'4 561 2077'8 590 2185J2 619 2292'6 648 2400{ 0 677 2507-4 *5 1972'2.5 2079'6 *5 2187.0 *5 2294'4 *5 2401'9'5 2509'3 533 1974-1 562 2081-5 591 2188'9 620 2296'3 649 2403'7 678 2511'1 *5 1975'9.5 2083'3 *5 2190'7'5 22982;2'5 2405'6' 5 2513'0 534 1977'8 563 2085'2 592 2192'6 621 230001 650 2407'4 679 2514'8 *5 1979'6 s5 2087'0.5 2194'4 *5 2301'9 *5 2409'7 *5 2516'7 535 1981'5 564 2088.9 593 2196'3 622 2303'7 651 2411'1 680 2518'5 *5 1983'3.5 2090.7 *5 2198'2.5 2305'6 *5 2413'0 *5 2520'4 536 1985'2 565 2092-6 594 2200'0 623 23074 1652 2414'8 681'2522'2 *5 1987.0.5 2094.4 *5 2201.9.5 2309.3.5 2416.7 51 2524.1 537 1988.9 566 209631 595 2203.7 624 2311.1 653 2418'5 682 2525,9 *5 1990'7.5 2098'2 *5 2205'6 *5 2313'0 *5 2420'4.5 2527'8 538 1992.6 567 2100o0 596 2207I4 625 23148 654 2422'2 683 2529'6 *h5 1994'4'5 2101'9 *5 2209'3 5 2316'7'5 2424'1'5 2531'5 539 199631 568 2103.7 597 2211'1 626 2318-5 655 2425.9 684 2533'3.5 1998.2.5 2105'6 *5 2213'0 *5 2320'4 *5 2427.8.5 2535'2 540 2000'0 569 2107'4 598 221418 627 2322.2 656 2429'6 685 2537.0!5 2001.9.5 2109'3 *. 5 2216j 7 *5 2324.1 I5 243165 *5 2538i9 541 2003'71 570 2111.1 599 22185 628 2325-9 657 2433/3 686 2540'7 *5 2005'6.5 2113'0 *5 2220'4.5 2327'8.5 2435'2'5 2542'6 542 2007.4 571 2114/8 600 2222-2 629 2329'6 658 2437.0 687 25444 *5 2009'3.5 2116'7 *5 2224'1 *5 2331'5 *5 2438'9.5 2546'3 543 2011-1 572 2118.6S 601 22259 630 2333'3 659 2440'7 688 2548'2.5 2013'0 *5 2120'4 *5 2227'8 *5 2335'2 *5 2442'6 *5 2550'0 544 20148s 573 2122.2 602 2229.6 631 2337-0 660 244441 689 2551'9 5{ 2016.7.5'2124.1 *5 2231.5.5 2338.9.5 2446.3.5 2553.7 545 20185 574 2125'9 603 2233. 3 632 2340'7 661 2448'2 690 2555/6,5 2020'4.5 2t27.8 *5 2235.2.5 2342'6 /5 2450.0'5 2557,4 546 2022'2 575 2129'6 6-04 2237-0 633 2344-4 662 2451.9 691 2559.3 *5 2024.1.5 213195' 5 2238'9.5 2346'3 *5 2453'7.5 2561'1 547 2025-9 576 2133-3 605 224071 634 2348'2 663 2455.6 692 2563'0'5 2027'8.5 2135.2.5 2242.6.5 2350'0 *5 2457'4.5 2564'8 548 2029'6 577 2137.0 606 2244.4 635 2351.9 664 1459'3 693 2566/7'5 203151.5 2138'9 /5 2246.3.5 2353.7 *5 2461'1'5 2568'5 549 2033'3 578 2140-7 607 2248'2 636 -2355-6 665 2463'0 694 2570'4'5 2035'2.5 2142'6 *5 2250'0'5 2357'4 *5 2464'8 *5 2572'2 550 2037.0 579 214441 608 2251.9 637 2:359-3 666 2466'7 695 " 2574'1'5 2038'9.5 2146'3'5 2253.7.5 2361.1 *5 2468.5'5 2575'9 551 2040o7 580 2148.2 609 2255.6 638 2363.0 667 2470.4 696- 2577.8.5 2042.6.5 2150'01 5 2257.4.5 23648'5 2472'2. 5 2579'6 552 2044'4 581 2151'9 610 2259'3 639 2366'7 668 2474'1 697 2581'5'5 2046'3'5 2153.7'5 2261.1 -5 2:368.5 5 2475.9'5 2583'3 553 12048'2 582 2155.6 611 2263a0 640 2370.4 669 2477'8 698 2585'2'5 2050'0.5 2157'4'5 2264'8.5 2372'2'5 2479'6'5 2587.0 554 2051I9 583 2159'3 612 2266.7 641 2374-1 670 2481'5 699 2588'9'5 2053'7'5 2161f1'5 2268S5.5 2375.9'5 2483'3'5 2590o7 55 2055'6 584 2163'0 613 2270.4 642 2377'8 671 2485.2 700 2592'6'5 2057.4'5 2164.8'5 2272.2 -5 2379'6'5 2487'0'5 2594'4 556 2059.3 585 2166'7 614 2274-1 643 2381.2 672 2488'9 701 2596.3'5 2061.1'5 2168'5 /5 2275'9.5 2383'3'5 2490'7'5 2598'2 557 2063.0 586 2170-4 615 2277'8 644 2385.2 673 2492'6 702 2600'0'5 2064'8'5 2172'2 5 2279'6'5 2387.0'5 2494'4'5 2601.9 558 2066'7 587 2174'1 616 2281'5 645 2388'9 674 2496'3 703 2603'7'5 2068S5 *5 2175'9'5 2283'3.5 2390.7'5 2498'2'5 2605'6 559 2070o41 588 2177'8 617 2285'2 646 2392'6 675 2500'0 704 2607'4 39 TABLE 15.-CUBIC YARDS IN 100 FEET LENGTH. Area.; Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. (lubic sq. ft. Yards. sq. ft- Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. ~5 2609'3.5 2716.7.5 2824.1.5 2931.5.5 3038.9.5 3146.3 705 26111 1734 2718.5 763 2825.9 792 2933.3 821 3040.7 850 3148.2 *5 2613.0.5 2720.4 5 2827.8.5 2935.2.5 3042.6.5 3150-0 706 2614.8 735 2722.2 764 2829.6 793 2937.0 822 3044.4 851 3151.9 ~5 2616.7.5 2724.1 *5 2S31.5.5 2938.9.5 3046.3.5 31.53-7 707 2618'5 736 2725'9 765 2833'3 794 2940'4 823 3048'2 852 3155'6 ~5 26204.5 2727.8.5 2835.2.5 2942.6.5 30500.5 3157.4 708 2622'2 737 2729'6 766 2837'0 795 2944'4 824 3051'9 853 3159'3 *5 2624.1.5 2731.5.5 2838.9 -5 2946.3.5 3053.7.5 3161l1 709 2625.9 738 2733.3 767 2840.7 796 2948s2 825 3055.6 854 3163'0 ~5 2627.8.5 2735'2.5 2842'6'5 2950'0'5 3057'4'5 3164'8 710 2629'6 739 27:37'0 768 2844'4 797 2951'9 826 3059'3 855 3166'7'5 2631'5'5 2738'9.5 2846'3'5 2953'7'5 3061'1'5 3168'5 711 2633'3 740 2740'7 769 2848'2 798 2955'6 827 3063'0 856 3170'4.5 2635.2.5 2742.6.5 2850.0 5fi 2957.4 *5 30648'5 3172.2 712 2637'0 741 2744'4 770 2851'9 799 2959,3 828 3066'7 857 3174'1 ~5 2638'9'5 2746'3 *5 2853'7 *5 2961'1'5 3068.5'5 3175'9 713 2640'7 742 2748-2 771 2855'6 800 2963.0 829 3070'4 858 3177'8'5 2642'6 *5 2750'0'5 2857'4.5 2964.8'5 3072.2.5 3179'6 714 2644'4 743 2751'9 772 2859'3 801 2966.7 830 3074.1 859 3181'5 *5 2646'3 5 2753'7 -5 2861'1 *5 29685 5 3075.9 *5 3183.3 715 2648'2 744 2755'6 773 2863'0 802 2970Q4 831 3077'8 860 3185'2'5 2650.0 -5 2757.4'5 2864'8'5 2972.2'5 3079'6.5 3187'0 716 2651'9 745 2759.3 774 2866'7 803 2974.1 832 3081'5 861 3188'9'5 2653'7'5 2761'1'5 2868'5'5 2975'9'5 3083'3 -5 3190'7 717 2655'6 746 2763'0 775 2870'4 804 2977.8 833 3085'2 862 3192'6 ~5 2657'4 *5 2764'8'5 2872'2'5 2979.6 *5 3087'0.5 3194'4 718 2659.3 747 2766'7 776 2874'1 805 2981.5 834 3088'9 863 3196'3'5 26611'5 2768'5'5 2875'9 *5 2983.3 *5 3090'7 *5 3198'2 719 2663.0 748 2770'4 777 2877'8 806 2985.2 835 3092'6 864 3200'0 ~5 2664.8.5 2772.2 ~5 2879.6.5 2987.0.5 3094.4.5 3201.9 720 2666.7 749 2774.1 778 2881.5 807 2988.9 836 3096.3 865 3203.7 ~5 2668.5.5 2775.9.5 2883.3.5 2990.7.5 3098.2.5 3205.6 721 2670.4 750 2777'8 779 2885'2 808 2992.6 837 3100.0 866 3207'4 ~5 2672.2'5 2779.6 ~5 2887.0.5 2994.4.5 3101.9.5 3209.3 722 2674'1 751 2781.5 780 2888.9 809 2996.3 838 3103.7 867 3211.1 ~5 2675.9.5 2783.3.5 2890.7.5 2998.2'5 3105.6.5 3213.0 723 2677.8 752 2785.2 781 2892.6 810 3000.0 839 3107.4 868 3214.8 ~5 2679'6.5 2787.0 -5 2894.4.5 3001.9.5 3109.3 -.5 3216.7 724 2681.5 753 2788.9 782 2896.3 811 3003.7 840 3111.1 869 3218.5.5 2683.3.5 2790.7'5 2898.2.5 3005.6.5 3113.0.5 3220.4 725 2685'2 754 2792.6 783 2900,0 812 3007.4 841 3114.8 870 3222'2 ~5 2687.0.5 2794.4'5 2901.9.5 3009.3.5 3116.7.5 3224-1 726 2688.9 755 2796'3 784 2903.7 813 3011.1 842 3118.5 871 3225.9 ~5 2690.7.5 2798.2.5 2905.6.5 3013.0.5 3120.4.5 3227.8 727 2692.6 756 2800'0 785 2907.4 814 3014.8 843 3122.2 872 3229.6 *5 2694.4.5 2801.9.5 2909.3.5 3016.7.5 3124.1.5 3231'5 728 2696'3 757 2803'7 786 2911.1 815 3018.5 844 3125.9 873 3233'3 *5 2698'2'5 2805'6'5 2913'0'5 3020.4.5 3127.8.5 3235'2 729 2700'0 758 2807'4 787 2914'8 816 3022.2 845 3129.6 874 3237.0 *5 2701.9.5 2809'3 *5 2916-7'5 3024.1.5 3131.5.5 3238.9 730 2703.7 759 2811'1 788 2918-5 817 3025.9 846 3133.3 875 3240.7 *5 2705.6 *5 2813'0'5 2920-4.5 3027.8'5 3135.2.5 3242'6 731 2707'4 760 2814'8 789 2922'2 818 3029'6 847 3137'0 876 32444 *5 2709'3 *5 2816'7'5 2924'1 -5 3031-5'5 3138-9'5 3245'3 732 2711'1 761 2818'5 790 2925'9 819 3033-3 848 3140'7 877 32482,'5 2713'0'5 2820'4'5 2927'8'5 3035'2'5 3142-6 *5 3250'0 ~733 2714'8 762 2822'2 791 2929'6 820 3037'0 849 3144-4 878 3251'9 40 TABLE 15.-CUBIC YARDS IN 100 FEET LENGTH. Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cubic Area. Cub'c sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Yards. sq. ft. Iards. *5 3253 7 899 3329*6 *5 3405-6 940 3481 5 *5 3557-4 981 3633'3 879 3255-6 5 3331'5 920 3407'4'5 3483'3 961 3559'3 *5 3635'2 *5 3257.4 900 3333.3 1 5 34~0'3 941 3485'2 *5 3561q1 982 3637.0 880 3259.3.5 3335.2 921 3411'1 *5 3487'0 962 3563'0 *5 3638'9'5 3261.1 901 3337.0 9 5 341301 942 344889 *5 3564*8 983 3640-7 881 3263.0'5 3338'9 922 3414-8 -54 5 3490'7 963 3566'7 *5 3642.6.5 3264'8 902 3340'7 *5 341671 943 3492-61 5 i 3568'5 984 3644.4 882 3266'7 *5 3342'6 923 3418'5'5 3494'4 964 3570'4.5 3646.3 *5 32685 903 3344.4 *5 3420-4 944 34963.5 357221 985 3648-2 883 32704.5 3346.3 924 3422-2.5 349832 965 3574'1 *5 3650.0 *5 3272-2 904 33482 *5 3424'1 945 3500-0 *5 3575-9 986 3651*9 884 3274'1 *5 3350'0 925 3425'9 *5 3501'9 966 3577'8 *5 3653'7.5 3275.9 905 3351'9 *5 3427-8 946 3503.7'5 3579.6 987 3655.6 885 3277s8 /5 3353'7 926 3429'6 15 3505'6 967 3581S5 *5 3657'4 *5 3279'6 906 3355'6 *5 3431'5 947 3507'4 *5 3583'3 988 3659'3 886 3281s5.5 3357.4 927 3433a3.5 3509.3 968 3585.2.5 3661 1 *5 3283'3 907 3359.3 *5 3435'2 948 3511'1 *5 35870 989 3663'0 887 3285.2.5 3361-1 928 3437.0.5 3513.0 969 3588'9.5 3664.8 *5 3287'0 908 3363'0 *5 3438'9 949 3514'8 5 3590'7 990 3666'7 888 3288.9.5 3364'8 929 3440.7 *5 3516.7 970 3592.6 *5 3668.5 *5 3290'7 909 3366'7 *5 3442'6 950 3518,5 *5 3.5944 991 3670'4 889 3292'6 *5 3368'5 930 3444'4 *5 35204 971 3596'3 5 3672'2.5 3294'4 910 3370.4 *5 3446'3 951 35222' 6 3598'2 992 3674'1 890 3296'3'5 3372'2 931 3448'2.5 3524.1 972 3600'0.5 3675'9 *5 3298.2 911 3374.1 *5 3450'0 952 352591 5 3601.9 993 3677.8 891 3300'0 *5 3375'9 932 3451*9 *5 3527'8 973 3603'7 *5 3679'6 *5 3301'9 912 3377'8 *5 3453.7 953 3529! 6 *5 3605'6 994 3681.5 892 3303'7 *5 3379'6 933 3455'6 *5 3531'5 974 3607'4 *5 3683'3 *5 3305.6 913 3381.5 *5 3457.4 954 3533-3 5 3609'3 995 3685'2 893 3307'4 *5 3383'3 934 3459.3 *5 3535-2 975 3611.I1 *5 3687.0 *5 3309'3 914 3385'2 *5 3461'1 955 3537'0 *5 3613'0 996 3688'9 894 3311.1.5 3387.0 935 346310'5 3538'9 976 3614'8 -5 3690-'7 *5 3313'0 915 3388'9 *5 3464'8 956 3540'7 *5 3616'7 997 3692'6 895 3314'8.5 3390'7 936 3466.7.5 3542'6 977 361851'5 3694'4 *5 3316'7 916 3392'6 *5 3468'5 957 3544'4 *5 3620~4 998 3696.3 896 3318.5 *5 3394.4 937 3470'4.5 3546'3 978 3622'2 *5 3698'2 *5 3320'4 917 3396'3 *5 3472'2 958 3548'2.5 3624'1 999 3700-0 897 3322'2 *5 3398'2 938 3474'1 *5 3550'0 979 3625'9 *5 3701'9.5 3324'1 918 3400'0 *5 3475.9 959 3551l9 *5 3627s8 1000 3703'7 898 3325'9'5 3401'9 939 3477'S8'5 3553'7 980 3629'6 *5 3327'8 919 3403'7 *5 3479'6 960 13555'6 5 I 3631.5 _