;-NRLF D E 551 773 m M E T H O D S FOR THE COMPUTATION FROM DIAGRAMS OF PKELIMINAKY AND FINAL ESTIMATES OF KAILWAY EAKTHWORK, WITH DIAGRAMS GIVING QUANTITIES ON INSPECTION TO THE NEAREST CUBIC YARD, FOR BOTH REGULAR AND IRREGULAR SECTIONS, DIRECT FROM ORDINARY FIELD-NOTES. BY ARTHUR M. WELLINGTON, CIVIL ENGINEER. PART IL PLATES. NEW YORK: D. APPLETON AND COMPANY, 549 & 551 BROADWAY. 1874. ENTERED, according to Act of Congress, in the year 1874, by D. APPLETON & COMPANY, In the Office of the Librarian of Congress, at Washington. LIST OF PLATES. I. DIAGRAM OF CROSS-SECTIONS, ROAD-BED 14, SLOPES If TO 1. II. " III. " * IV. 15j 1* TO 1. 18, n TO 1. 20, u TO 1. 18, " ii TO 1. 18, i TO 1. VI. " VII. DIAGRAM OF SIDE-HILL CROSS-SECTIONS, ROAD-BEDS 12, 14, 15, 16, 18, 20, SLOPES If TO 1, ROAD-BED 18, SLOPES 1J TO 1 AND 1 TO 1. VIII. DIAGRAM OF TRIANGULAR PRISMS. t DIAGRAM OF PRISMOIDAL CORRECTION. IX. ) " CORRECTION ON CURVES. ' " SLOPE-STAKES, ROAD-BED 12, SLOPES 1^ TO 1. X. DIAGRAM FOR COMPUTATION BY HENCK'S FORMULA, ROAD-BED 18, SLOPES 1 TO 1. XL DIAGRAMS FOR PRELIMINARY ESTIMATES^ SLOPES If TO 1. XII. " " " " 1 TO 1 AND li TO 1. TABLE OF REFERENCE. THE table below is added to facilitate reference to the text, or to render frequent reference unnecessary. The third, fourth, and fifth columns give the quantities on each of the plates which are represented by the vertical, inclined, and horizontal lines respectively, and, by interpolating the words in parentheses below, may be made substantially equivalent to the rule for use given in the text. Thus, for the Diagram of Cross-Sections, read as follows : " (Take the) vertical line representing width of section on top, (and follow up to the) inclined line representing the centre-height. The horizontal lines give quantity sought in cubic yards." The general rule for the use of every one of the diagrams in the table may be similarly read oft' by the interpolation of the same words. The remaining columns of the table give references to the text for the formulae, and a few of the rules, etc., which it may be most frequently necessary to consult. For more detailed references, the table of contents in the text must be consulted. PLATE. DIAGRAM OF VERTICAL LINKS represent INCLINED LINES represent HORIZONTAL LINES give Quantity sought in- FORMULA. GENERAL KULE FOR Usu. Indirect Applica'ns to other road-beds. When given Dimensions exceed limits of Diagram. MISCELLANEOUS RULES. equa. pa e par. page par. page par. page par. page. I. to VI. Cross-Sections. Width of Sec- tion on top. Centre-Height. Cubic Yards. (5), 16 21, 20 105, 99 22, 23 23, 25 To reduce to Level Section. 24, 26 VII. Side - Hill Cross-Sec- tions. it it tt tt ti tt (7) to (9), 29 30, 32 107, 102 VIII. Triangular Prisms. Horizontal di- mension.* Vertical dimen- sion.* tt ti (19), 46 61, 40 (General) 62, 47 Special Rules for Computation. 62, 47 IX. Prismoidal Correc- tion. Width of Sec- tion on top. Centre-Height. u It (16), 38 43, 43 108, 102 46, 46 Method of Centre- ( Heights. \ 41, 42 46, 44 it Correction on Curves it ii Differ'nce of dis- tances out. Feet and tenths. (29), 77 82, 79 (General) For Sidings and Bor- row-Pits. 84-87, 81 " ti it Solidity for Section. u ii Cubic Yards. (32), 78 83, 80 ( General) H Slope-Stakes. Centre-heig'tg Surface-Slope. Feet and tenths. (34), (86), 85 91, 86 110, 104 Side-Hill Sections. 132, 138 X. Compt'n by Henck's Formula. Width of Sec- tion on top. Centre-Height. Cubic Yards. (22)to(24),66 71, 67 109, 103 72, 69 73, 70 Side-Hill and Irregu- lar Earthwork. 74-76,71 XI. & XII. Prelim. Est., No. 1. Centre-h'ts.f Surface-Slope. it it (38), 90 96, 90 ( Gen'oTj^ 94, 89 Use of Odometer. 97, 92 " " No. 2. ti tt i ti it it u (36), (37), 88 93, 88 (GerSalft 94, 89 it tt it 94, 89 " " No. 3. C u u Coefficient. (89), 96 104, 97 (General) " No. 4. Cubic Yards. Coefficient. Cubic Yards. (40), 96 104, 98 ' General) Or nice verta. t To intersection of side-slopes. Roles for application to other side-slopes, par. Ill, page 104. S See par. 103, p. 96. PLATE I. OF 5B > K o X o 01 w M O M 6 2 w TJ r PLATE II. PIAGRAM OF CROSS SECTIONS. TO 1, O X X o co ._ w TJ -w r w > H H o PI g s PLATE III. PIAGRAM OF CROSS SECTIONS. 18; i ^ TO i, o JD o w M 13 r m r H n o Z I-H 00 PLATE IV. plAGRAM OF jDROSS ^ECTIONS. 2O; 1 ^ TO 1 . O ' o w tn 2 H to o PLATE V. DIAGRAM OF CROSS SECTIONS. 18; i^ TO i. o X so o en w "TO B n H O 2 w TJ r > H n PLATE VI. DIAGRAM OF CROSS SECTIONS. 18; i TO i. "73 - > O 5D > * O o in *Tfl m n r H P] g r 00 H C o u cd z o I LJ _l Q. O. < O iff CC O ^ UJ O o h- o . m UJ Q PLATE VII. DIAGRAMS OF SIDE HILL CROSS SECTIONS. D 33 CD o M r r 53 O CO CO n n j o 2 r > H tn o o h- CD CD O UJ Z CD CO UJ Q PLATE VIII. DIAGRAM. OF TRIANGULAR PRISMS. m 2 H > PI 1 < r E > 0) i PLATE VIII DIAGRAM OF TRIANGULAR PRISMS. Mr\A/ vnoi/ n ADDI rrn\i a PLATE IX. DIAGRAMS OF PRISMOIDAL CORRECTION, ETC. JO s co *) w O 3 r o m n o z n H n PLATE IX. DIAGRAMS OF PRISMOIDAL CORRECTION, ac. MFW vnRk n APPI FTDN r.r PLATE X. JDlAGRAM FOR COMPUTATION BY HENCK'S FORMULA. l8| I ^ TO o a o X o V c o 2 n 2 n O 5) c: r TJ r H O PLATE XI. DIAGRAMS FCR PRELIMINARY ESTIMATES. i ^ TO i. fO g CO a a w r 5 r 5 > CO H - J rn n n PLATE XI, : M rn HV A M \A/FI i i MCITONI r r DIAGRAMS FOR PRELIMINARY ESTIMATES, NFW YORK n. APPI FTflN ft T.n PLATE XII. DIAGRAMS FOR PRELIMINARY ESTIMATES. i TO i , AND 1-4 TO i. o 73 > X H i I W HH c 1: 3 PLATE .XII. DESIGNED BY A. M. WELLI NGTON, C. E. DIAGRAMS FOR PRELIMINARY ESTIMATES. 1 to 1, andV4tol M r\A/ VfiDi/ n A nn i U.C.BERKELEY LIBRARIES CDM71S13SM >;;i r ssy Pgsj< ''>'- '.;v:/..', : , -:;'?: ;;;-.. .'-c;:'*^;-. "