Handbook of Railroad Construction; For the use of American engineers

Published by Good Press, 2019

goodpress@okpublishing.info

EAN 4064066199364

Table of Contents

CHAPTER I. RECONNOISSANCE.

GENERAL TOPOGRAPHY.

BAROMETRICAL LEVELLING.

CHAPTER II. SURVEY.

TOPOGRAPHICAL SKETCHING.

GENERAL ESTABLISHMENT OF GRADES.

EQUATING FOR GRADES.

COMPARISON OF SURVEYED LINES.

CHAPTER III. LOCATION.

ALIGNMENT.

FINAL ADJUSTING OF GRADES.

COMPARISON OF LOCATED LINES.

CHAPTER IV. PRELIMINARY OPERATIONS.

SPECIFICATION.

THE CONTRACT.

SOLICIT FOR BIDS.

FORM FOR A BID.

COMPARISON OF BIDS.

CHAPTER V. LAYING OUT WORK.

SLOPES.

CULVERTS.

MASONRY.

TUNNELS.

CHAPTER VI. EARTHWORK.

FORM OF RAILROAD SECTIONS.

EXCAVATION AND EMBANKMENT.

TRANSPORT OF MATERIAL.

OF THE AVERAGE HAUL.

DRAINING.

METHOD OF CONDUCTING OPERATIONS.

CHAPTER VII. ROCKWORK.

ROCK EXCAVATION.

BLASTING AND QUARRYING.

TUNNELLING.

CHAPTER VIII. WOODEN BRIDGES.

OF THE FORCES AT WORK IN BRIDGES.

TENSION.

COMPRESSION.

CROSS STRAIN.

DETRUSION.

ACTUAL STRENGTH OF MATERIALS.

RULES FOR PRACTICE.

OF THE TRUSS.

THE ARCH.

OF THE ROAD-WAY.

LATERAL BRACING.

PILE BRIDGING.

TRESTLING.

DRAWBRIDGES.

CENTRES.

CHAPTER IX. IRON BRIDGES.

NATURE AND STRENGTH OF IRON.

CLASSIFICATION OF IRON BRIDGES.

COMBINATIONS OF CAST AND WROUGHT IRON.

SUSPENSION BRIDGES.

BOILER PLATE BRIDGES.

CHAPTER X. STONE BRIDGES.

CONTRACTION OF THE WATER-WAY.

OF THE FORM OF THE ARCH.

THICKNESS OF VOUSSOIRS, (RING STONES) .

THICKNESS AND FORM OF ABUTMENTS.

PIERS.

CHAPTER XI. MASONRY.

STONES.

LIMES, CEMENTS, MORTARS, AND CONCRETES.

CONSTRUCTION OF ARCHES.

CULVERTS AND DRAINS.

RETAINING WALLS.

CHAPTER XII. FOUNDATIONS.

PILE DRIVING.

MITCHELL’S SCREW PILE.

DR. POTTS’S ATMOSPHERIC SYSTEM.

COFFER-DAM.

FOUNDATION BY CAISSON.

CHAPTER XIII. SUPERSTRUCTURE.

TIMBERWORK.

SECTION OF THE RAIL.

CHAIRS AND JOINTS.

FROGS.

SWITCHES.

SIDINGS AND CROSSINGS.

ELEVATION OF THE EXTERIOR RAIL.

CHAPTER XIV. EQUIPMENT.

PART I. LOCOMOTIVES.

PART II. CARS.

CHAPTER XV. STATIONS.

CLASSIFICATION OF BUILDINGS.

LOCATION OF BUILDINGS.

TERMINAL PASSENGER HOUSE.

TERMINAL FREIGHT HOUSE.

ENGINE HOUSE AND APPURTENANCES.

WOOD SHED AND TANK.

OF THE WATER SUPPLY.

CHAPTER XVI. MANAGEMENT.

ORGANIZATION OF EMPLOYEES.

DUTIES OF EMPLOYEES.

NUMBER OF TRAINS TO BE USED.

AMOUNT OF SERVICE OF ENGINES.

EXPENSES, RECEIPTS, PROFITS.

EXPRESS TRAINS.

COMPARATIVE COST OF WORKING HEAVY AND LIGHT TRAINS.

BRANCH ROADS.

REPRODUCTION OF ROAD AND STOCK.

WORKING RAILROADS BY CONTRACT.

CLASSIFICATION OF FREIGHT.

TIME TABLES.

LOCOMOTIVE REGISTERS.

TELEGRAPH.

NEW YORK AND ERIE RAILROAD.

APPENDIX.

A. DECIMAL ARITHMETIC.

B. ALGEBRAIC FORMULÆ.

C. WEIGHTS AND MEASURES.

D. VALUE OF THE BIRMINGHAM GAUGES.

E. LOCOMOTIVE BOILERS.

F. EFFECT OF GRADES ON THE COST OF WORKING RAILROADS.

G. SPECIFICATION FOR A PASSENGER LOCOMOTIVE ENGINE FOR THE A. AND B. RAILROAD.

H. RELATIVE COST OF TRANSPORT BY RAILROAD AND BY STAGE.

I. FORM FOR RECORDING THE RESULTS OF EXPERIMENTAL TRIPS WITH LOCOMOTIVES.

K. PROPER WEIGHT OF LOCOMOTIVES.

CHAPTER I.
RECONNOISSANCE.

Table of Contents

26. The object of the reconnoitre is to find approximately the place for the road, (i.e. within half of a mile,) to find the general form of the country, and to choose that part which with reference to the expected traffic, shall give the best gradients; to determine the elevations of summits upon competing routes; and, in fine, to prepare the way for the survey.

GENERAL TOPOGRAPHY.

Table of Contents

27. The general topography of a country may be ascertained by reference to State maps, where such exist, and when not, by riding over the district. The direction and size of watercourses, will show at once the position of summits.

Fig. 1.

28. Water flowing as in fig. 1, indicates a fall from B to E; and also traverse slopes from a a and c c to d d.

Fig. 2.

29. Fig. 2 shows a broken ridge a a a from which the water flows in both directions; and in general, the sources of streams point towards the higher lands.

Fig. 3.

30. If it be required to join the points A and D by railroad, (fig. 3.) it may be better to pass at once from A through B and C, than to go by the streams F E, F′ E′. By the latter route the road would ascend all of the way from A to E; and descend from E′ to D. By the first if it requires steep gradients to rise from A to B, and to fall from C to D, still if the section B C is a plateau, and if the rise between A and B and A and E is the same, by grouping the grades at B and C we may so adapt the motive power, as to take the same train from A to D without breaking. The general arrangement of grades by the line A B C D is then as fig. 4; and A F E E′ F′ D, as in fig. 5. The saving in this case is by length, as the same amount of power is required to overcome a given ascent.

Fig. 4.

Fig. 5.

31. Valleys generally rise much faster near their source, than at any point lower down; also the width increases as we approach the debouch. Fig. 6 shows the cross sections of a valley from its source to the mouth.

Fig. 6.

32. In the case of parallel valleys running in the same direction, the form will be as in fig 7. Let 1 2, 1 2, etc., represent a datum level, or a horizontal plane passing through the lowest point. The line a b, shows the height of the bottom at B; c d that at D, e f that at E, and g h that at C. The broken lines i, k, l, m, n, show the general form of the land. Now by the route m m m m, from A to F, we have the profile m m m m, fig. 8, by n n n n, the profile n n n n, and by o o o, the profile o o o.

Fig. 7.

Fig. 8.

Fig. 9.

33. In the case of parallel valleys running in opposite directions, as in fig. 9, we have the form there shown; and the profiles corresponding to the several lines are shown in fig. 10. As we should always adopt the line giving the least rise and fall, other things being equal, it is plain which line on the plan we must follow.

Fig. 10.

34. In passing from A to B, figs. 11 and 12, by the several lines c, d, e, f, we have the profiles shown at c, d, e, f, from which it appears, that the nearer we cross to the heads of streams, the less is the difference of heights.

Fig. 11.

Fig. 12.

Fig. 12 (a).

35. If we wish to go from A to B, fig. 12 (a), we should of course take first the straight line; but being obliged to avoid the hill C, on arriving at d, we should not try to recover that line at e, but proceed at once to B. Also as we are obliged to pass through d, we ought to go directly to d and not by the way of c; and the same idea is repeated between A and d; the last line being A b d B. Few rules can be given in the choice of routes. Practice only will enable the engineer to find the best location for a railroad.

BAROMETRICAL LEVELLING.

Table of Contents

36. The relative height of summits, the rate of fall of streams, and absolute elevation, within a few feet, may be easily, rapidly, and cheaply found by the barometer. This also affords an excellent check upon subsequent levelling operations. The results thus obtained depend upon the physical property, that the density of the air decreases as the square of the height.

37. The barometer is a glass tube, partly filled with mercury, having a vacuum in the upper part. By it the exact density of the air at any point is determined. Accompanying are two thermometers; one attached, showing the temperature of the barometer; the other detached, showing the atmospheric temperature.

38. Knowing now the manner of finding the density of the air at any two points, and also the relation between density and height, the operation of levelling by the barometer is very simple.

The modus operandi is as follows, (see tables A, B, C, and D):—

Let us have the notes.

	Barom.	Attached Therm.	Detached Therm.
Upper Station,	29.75	28.5	27.9
Lower Station,	26.80	36.8	36.3
	Latitude 46° N.

We have by table A, against the bar. point,	29.75,	6108.6
also by table A, against the bar. point,	26.80,	5276.6
The difference		832.0
Diff. of attached therm. 36.8°- 28.5° = 8.3°	(table B)	−12.2
		819.8
Double the sum of detached thermometers multiplied by 1 1000 of 819.8 is
2(27.9 + 36.3) × .8198 =		+ 105.3
		925.1
Correction (see table C) for lat. 46° N. and approximate height 925.1		+ 3.1
		928.2

Final correction by table D. The barometer at the lower station being 26.80, and the tabular number against 27.56 being 0.22, that for 26.80 will be 0.31, and we have

1000 to .31 as 928.2 to 0.287, or 0.3,

which add to 928.2 and we have as the final height

928.5 metres, or 928.5 × 3.28 = 3045.48 feet.

The tables above referred to, are those of Mr. Oltman, and are considered as the most convenient and reliable of any published.

TABLE A.
English Inches.	Metres.
14.56	418.5
14.61	440.0
14.65	461.5
14.68	482.9
14.72	504.2
14.76	525.4
14.80	546.6
14.84	567.8
14.88	588.9
14.92	609.9
14.96	630.9
15.00	651.8
15.04	672.7
15.08	693.5
15.12	714.3
15.16	735.0
15.20	755.6
15.24	776.2
15.28	796.8
15.31	817.3
15.35	837.8
15.39	858.2
15.43	878.5
15.47	898.8
15.51	919.0
15.55	939.2
15.59	959.3
15.63	979.4
15.67	999.5
15.71	1019.5
15.75	1039.4
15.79	1059.3
15.83	1079.1
15.87	1098.9
15.91	1118.6
15.95	1138.3
15.98	1157.9
16.02	1177.5
16.06	1197.1
16.10	1216.6
16.14	1236.0
16.18	1255.4
16.22	1274.8
16.26	1294.1
16.30	1313.3
16.34	1332.5
16.38	1351.7
16.42	1370.8
16.46	1389.9
16.50	1408.9
16.54	1427.9
16.57	1446.8
16.61	1465.7
16.65	1484.7
16.69	1503.4
16.73	1522.2
16.77	1540.8
16.81	1559.5
16.85	1578.2
16.89	1596.8
16.93	1615.3
16.97	1633.8
17.01	1652.2
17.05	1670.6
17.09	1689.0
17.13	1707.3
17.17	1725.6
17.20	1743.8
17.24	1762.1
17.28	1780.3
17.32	1798.4
17.36	1816.5
17.40	1834.5
17.44	1852.5
17.48	1870.4
17.52	1888.3
17.56	1906.2
17.60	1924.0
17.64	1941.8
17.68	1959.6
17.72	1977.3
17.76	1994.9
17.79	2012.6
17.83	2030.2
17.87	2047.8
17.91	2065.3
17.95	2082.8
17.99	2100.2
18.03	2117.6
18.07	2135.0
18.11	2152.3
18.15	2169.6
18.19	2186.9
18.23	2204.1
18.27	2221.3
18.31	2238.4
18.35	2255.5
18.39	2272.6
18.42	2289.6
18.46	2306.6
18.50	2323.6
18.54	2340.5
18.58	2357.4
18.62	2374.2
18.66	2391.1
18.70	2407.9
18.74	2424.6
18.78	2441.3
18.82	2458.0
18.86	2474.6
18.90	2491.3
18.94	2507.9
18.98	2524.3
19.02	2540.8
19.05	2557.3
19.09	2573.7
19.13	2590.2
19.17	2506.6
19.21	2622.9
19.25	2639.2
19.29	2655.4
19.33	2671.6
19.37	2687.9
19.41	2704.1
19.45	2720.2
19.49	2736.3
19.53	2752.3
19.57	2768.3
19.61	2784.4
19.65	2800.4
19.68	2816.3
19.72	2832.2
19.76	2848.1
19.80	2864.0
19.84	2879.8
19.88	2895.6
19.92	2911.3
19.96	2927.0
20.00	2942.7
20.04	2958.4
20.08	2974.0
20.12	2989.6
20.16	3005.2
20.20	3020.7
20.24	3036.2
20.28	3051.7
20.31	3067.2
20.35	3082.6
20.39	3097.9
20.43	3113.3
20.47	3128.6
20.51	3143.9
20.55	3159.2
20.59	3174.4
20.63	3189.7
20.67	3204.9
20.71	3220.0
20.75	3235.1
20.79	3250.2
20.83	3265.3
20.87	3280.3
20.90	3295.3
20.94	3310.3
20.98	3325.3
21.02	3340.2
21.06	3355.1
21.10	3370.0
21.14	3384.8
21.18	3399.6
21.22	3414.4
21.26	3429.2
21.30	3443.9
21.34	3458.6
21.38	3473.3
21.42	3487.9
21.46	3502.5
21.50	3517.2
21.54	3531.8
21.57	3546.3
21.61	3560.8
21.65	3575.3
21.69	3589.8
21.73	3604.2
21.77	3618.6
21.81	3633.0
21.85	3647.4
21.89	3661.7
21.93	3676.0
21.97	3690.3
22.01	3704.6
22.05	3718.8
22.09	3733.0
22.13	3747.2
22.17	3761.3
22.20	3775.4
22.24	3789.5
22.28	3803.6
22.32	3817.7
22.36	3831.7
22.40	3845.7
22.44	3859.7
22.48	3873.7
22.52	3887.6
22.56	3901.5
22.60	3915.4
22.64	3929.3
22.68	3943.1
22.72	3956.9
22.76	3970.7
22.80	3984.5
22.83	3998.2
22.87	4011.9
22.91	4025.6
22.95	4039.3
22.99	4052.9
23.03	4066.6
23.07	4080.2
23.11	4093.8
23.15	4107.3
23.19	4120.8
23.23	4134.3
23.27	4147.8
23.31	4161.3
23.35	4174.7
23.39	4188.1
23.43	4201.5
23.46	4214.9
23.50	4228.2
23.54	4241.6
23.58	4254.9
23.62	4268.2
23.66	4281.4
23.70	4294.7
23.74	4307.9
23.78	4321.1
23.82	4334.3
23.86	4347.4
23.90	4360.5
23.94	4373.7
23.98	4386.7
24.02	4399.8
24.06	4412.8
24.09	4425.9
24.13	4438.9
24.17	4451.9
24.21	4464.8
24.25	4477.7
24.29	4490.7
24.33	4503.6
24.37	4516.4
24.41	4529.3
24.45	4542.1
24.49	4554.9
24.53	4567.7
24.57	4580.5
24.61	4593.2
24.65	4606.0
24.68	4618.7
24.72	4631.4
24.76	4644.0
24.80	4656.7
24.84	4669.3
24.88	4682.0
24.92	4694.5
24.96	4707.1
25.00	4719.7
25.04	4732.2
25.08	4744.7
25.12	4757.2
25.16	4769.7
25.20	4782.1
25.24	4794.6
25.28	4807.0
25.31	4819.4
25.35	4831.7
25.39	4844.1
25.43	4856.4
25.47	4868.7
25.51	4881.0
25.55	4893.3
25.59	4905.6
25.63	4917.8
25.67	4930.0
25.71	4942.2
25.75	4954.4
25.79	4966.6
25.83	4978.7
25.87	4990.9
25.91	5003.0
25.94	5015.1
25.98	5027.2
26.02	5039.3
26.06	5051.2
26.10	5063.2
26.14	5075.3
26.18	5087.2
26.22	5099.2
26.26	5111.2
26.30	5123.1
26.34	5135.0
26.38	5146.9
26.42	5158.8
26.46	5170.6
26.50	5182.5
26.54	5194.3
26.57	5206.1
26.61	5217.9
26.65	5229.7
26.69	5241.4
26.73	5253.2
26.77	5264.9
26.81	5276.6
26.85	5288.3
26.89	5300.0
26.93	5311.6
26.97	5323.2
27.01	5334.8
27.05	5346.4
27.09	5358.0
27.13	5369.6
27.17	5381.1
27.21	5392.7
27.25	5404.2
27.28	5415.6
27.32	5427.2
27.36	5438.7
27.40	5450.1
27.44	5461.5
27.48	5472.9
27.52	5484.3
27.56	5495.7
27.60	5507.1
27.64	5518.4
27.68	5529.8
27.72	5541.1
27.76	5552.4
27.80	5563.7
27.84	5575.0
27.87	5586.2
27.91	5597.5
27.95	5608.7
27.99	5619.6
28.03	5631.1
28.07	5642.2
28.11	5653.4
28.15	5664.6
28.19	5675.7
28.23	5686.8
28.27	5697.9
28.31	5709.0
28.35	5720.1
28.39	5731.1
28.43	5742.1
28.46	5753.1
28.50	5764.2
28.54	5775.1
28.58	5786.1
28.62	5797.1
28.66	5808.0
28.70	5819.0
28.74	5829.9
28.78	5840.8
28.82	5851.7
28.86	5862.5
28.90	5873.4
28.94	5884.2
28.98	5894.9
29.02	5905.8
29.06	5916.7
29.09	5927.5
29.13	5938.2
29.17	5949.0
29.21	5959.7
29.25	5970.4
29.29	5981.2
29.33	5991.9
29.37	6002.5
29.41	6013.2
29.45	6023.8
29.49	6034.4
29.53	6045.1
29.57	6055.7
29.61	6066.3
29.65	6076.9
29.69	6087.5
29.72	6098.0
29.76	6108.6
29.80	6119.1
29.84	6129.6
29.88	6140.1
29.92	6150.6
29.96	6161.1
30.00	6171.5
30.04	6182.0
30.08	6192.4
30.12	6202.8
30.16	6213.2
30.20	6223.6
30.24	6234.0
30.28	6244.4
30.32	6254.7
30.35	6265.0
30.39	6275.4
30.43	6285.7
30.47	6296.0
30.51	6306.2
30.55	6316.5
30.59	6326.7
30.63	6337.0
30.67	6347.2
30.71	6357.4
30.75	6367.6
30.79	6377.8
30.83	6388.0
30.87	6398.2
30.91	6408.3
30.94	6418.5
30.98	6428.6
31.02	6438.7
31.06	6448.8

TABLE B.
Deg.[4]	Met.
0.2	0.3
0.4	0.6
0.6	0.9
0.8	1.2
1.0	1.5
1.2	1.8
1.4	2.1
1.6	2.3
1.8	2.6
2.0	2.9
2.2	3.2
2.4	3.5
2.6	3.8
2.8	4.1
3.0	4.4
3.2	4.7
3.4	5.0
3.6	5.3
3.8	5.6
4.0	5.9
4.2	6.2
4.4	6.5
4.6	6.8
4.8	7.1
5.0	7.4
5.2	7.6
5.4	7.9
5.6	8.2
5.8	8.5
6.0	8.8
6.2	9.1
6.4	9.4
6.6	9.7
6.8	10.0
7.0	10.3
7.2	10.6
7.4	10.9
7.6	11.2
7.8	11.5
8.0	11.8
8.2	12.1
8.4	12.4
8.6	12.6
8.8	12.9
9.0	13.2
9.2	13.5
9.4	13.8
9.6	14.1
9.8	14.4
10.0	14.7
10.2	15.0
10.4	15.3
10.6	15.6
10.8	15.9
11.0	16.2
11.2	16.5
11.4	16.8
11.6	17.1
11.8	17.4
12.0	17.6
12.2	17.9
12.4	18.2
12.6	18.5
12.8	18.8
13.0	19.1
13.2	19.4
13.4	19.7
13.6	20.0
13.8	20.3
14.0	20.6
14.2	20.9
14.4	21.2
14.6	21.5
14.8	21.8
15.0	22.1
15.2	22.4
15.4	22.7
15.6	22.9
15.8	23.2
16.0	23.5
16.2	23.8
16.4	24.1
16.6	24.4
16.8	24.7
17.0	25.0
17.2	25.3
17.4	25.6
17.6	25.9
17.8	26.2
18.0	26.5
18.2	26.8
18.4	27.1
18.6	27.4
18.8	27.7
19.0	28.0
19.2	28.2
19.4	28.5
19.6	28.8
19.8	29.1
20.0	29.4

4. The degrees refer to the centigrade thermometer.

TABLE C.
Approximate Height.	0°	15°	40°	55°
200	1.2	1.0	0.6	0.4
400	2.4	2.2	1.4	0.8
600	3.4	3.2	2.0	1.2
800	4.5	4.3	2.8	1.7
1000	5.7	5.3	3.4	2.2
1200	7.0	6.4	4.2	2.6
1400	8.2	7.6	4.8	3.0
1600	9.2	8.8	5.6	3.4
1800	10.4	9.8	6.3	3.8
2000	11.6	11.0	7.0	4.2
2200	12.8	12.1	7.6	4.6
2400	14.0	13.3	8.4	5.1
2600	15.2	14.4	9.2	5.6
2800	16.5	15.6	10.0	6.2
3000	17.7	16.8	10.8	6.6
3200	10.1	18.0	11.5	7.0
3400	20.5	19.3	12.4	7.7
3600	21.8	20.4	13.4	8.2
3800	23.1	21.6	14.3	8.7
4000	24.6	22.9	15.1	9.4
4200	25.9	24.3	15.9	10.1
4400	27.5	25.8	16.9	10.8
4600	28.9	27.1	18.0	11.5
4800	30.4	28.4	19.0	12.1
5000	31.8	29.8	19.9	12.7
5200	33.0	31.0	20.8	13.3
5400	34.3	32.4	21.7	13.9
5600	35.7	33.7	22.6	14.5
5800	37.1	35.0	23.6	15.1
6000	38.5	36.3	24.6	15.7

TABLE D.
Barometrical Height	Metres
15.75	1.71
17.72	1.39
19.68	1.11
21.65	0.86
23.62	0.63
25.59	0.42
27.56	0.22
29.53	0.03

CHAPTER II.
SURVEY.

Table of Contents

TOPOGRAPHICAL SKETCHING.

Table of Contents

39. Topographical drawing includes every thing relating to an accurate representation upon paper, of any piece of ground. The state of cultivation, roads, town, county, and state boundaries, and all else that occurs in nature. The sketching necessary in railroad surveying, however, does not embrace all of this, but only the delineation of streams and the undulations of ground within that limit which affects the road, perhaps 500 feet on each side of the line. The making of such sketches consists in tracing the irregular lines formed by the intersection of the natural surface, by a system of horizontal planes, at a vertical distance of five, ten, fifteen, or twenty feet, according to the accuracy required.

Fig. 13.

40. Suppose that we wish to represent upon a horizontal surface a right cone. The base m m, fig. 13, is shown by the circle of which the diameter is m, m. If the elevation is cut by the horizontal planes a a, b b, c c, the intersection of these planes with the conical surface is shown by the circles a, b, c, in plan. The less we make the horizontal distances, on plan, between the circles, the less also will be the vertical distance between the planes.

Wishing to find the elevation of any line which exists on plan, as 1, 2, 3, 3, 2, 1, we have only to find the intersection of the verticals drawn through the points 1, 2, 3, 3, 2, 1, and the elevation lines a a, b b, c c; this gives us the curve 4, 5, 6, 7, 6, 5, 4.

Fig. 14.

41. Again, in fig. 14, the cone is oblique, which causes the circles on plan to become eccentric and elliptic. Having given the line 1, 2, 3, as before, we find it upon the elevation in the same manner.

42. In the section of regular and full lined figures, the horizontal and vertical projections are also regular and full lined; but in a broken surface like the ground, the lines become quite irregular.

Suppose we wish to show on plan the hill of which we have the plan, fig. 15, and the sections figs. 16, 17, and 18. Let AD be the profile (made with the level) of the line AD on plan, fig. 15. B E that of B E, and C F that of CF.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18.

To form the plan from the profiles proceed as follows:—

Intersect each of the profiles by the horizontal planes a a, b b, c c, d d, equidistant vertically. In the profile A D, fig. 18, drop a vertical on to the base line from each of the intersections a, b, c, d, d, c, b, a. Make now A 1,1 2, 2 3, 3 4, etc., on the plan equal to the same on the profile. Next draw, on the plan, the line B E, at the right place and at the proper angle with A D; and having found the distances B 1, 1 2, 2 3, etc., as before, transfer them to the line B E on plan. Proceed in the same manner with the line C F.

The points a a a, b b b, c c c, are evidently at the same height above the base upon the profiles, whence the intersections of these lines with the surface line or 1 1 1, 2 2 2, 3 3 3, etc., on the plan, are also at the same height above the base; and an irregular line traced through the points 1 1 1, or 2 2 2, will show the intersection of a horizontal plane, with the natural surface.

When as at A we observe the contour lines near to each other, we conclude that the ground is steep. And when the distances are large, as at 6, 7, 8, we know that the ground falls gently. This is plainly seen both on plan and profile.

Fig. 15.

Having now the topographical sketch, fig. 15, we may easily deduce therefrom at any point a profile. If we would have a profile of G E, on plan, upon an indefinite line G E, fig. 19, we set off G 1, 1 2, 2 3, 3 4, etc., equal to the same distances on the plan. From these points draw verticals intersecting the horizontals a a, b b, c c; and lastly, through the intersections draw the broken line (surface line or profile) a, b, c, d, d, c, b, a. Thus we see how complete a knowledge of the ground a correct topographical sketch gives.

Fig. 19.

43. Field sketches for railroad work are generally made by the eye. The field book being ruled in squares representing one hundred feet each. When we need a more accurate sketch than this method gives, we may cross section the ground either by rods or with the level.

By making a very detailed map of a survey, and filling in with sketches of this kind, the location may be made upon paper and afterwards transferred to the ground.

So far we have dealt with but one summit; but the mode of proceeding is precisely the same when applied to a group or range of hills, or indeed to any piece of ground.

44. As a general thing, the intersection of the horizontal planes with the natural surface (contour lines) are concave to the lower land in depressions, and convex to the lower land on spurs and elevations. Thus at B B B b b, fig. 20, upon the spurs, we have the lines convex to the stream; and in the hollows c c c, the lines are concave to the bottom.

45. Having by reconnoissance found approximately the place for the road, we proceed to run a trial line by compass. In doing this we choose the apparent best place, stake out the centre line, make a profile of it, and sketch in the topography right and left.

Fig. 20.

Fig. 21.

Fig. 22.

Suppose that by doing so we have obtained the plan and profile shown in figs. 21 and 22, where A a a B is the profile of A C D B, on the plan. The lowest line of the valley though quite moderately inclined at first, from A to C, rises quite fast from C to the summit; and as the inclination becomes greater, the contour lines become nearer to each other.

Now that the line may ascend uniformly from A to the summit, the horizontal distances between the contour lines must be equal; this equality is effected by causing the surveyed line to cut the contours square at 1, 2, 3, 4, and obliquely at 5, 8, 10. Thus we obtain the profile A 5 5 B.

Figs. 23 and 24.

46. Having given the plan and profile, figs. 23 and 24, where A C D B represents the bed of the stream, in profile, if it were required to put the uniformly inclined line A m m B, upon the plan, we should proceed as follows. Take the horizontal distance A m from the profile, and with A (on plan) as a centre, describe the arc 1, 3. The point m on the profile is evidently three fourths of a division above the bed of the stream. So on the plan we must trace the arc 1, 3, until we come to a, which is three fourths of b c, from b. Again, m′ is nine and one half divisions above m. From a, with a radius m n on profile, describe the arc 4, 5, 6. Now, as on the profile, in going from m to m′, we cross nine contour lines, and come upon the tenth at m′, so on the plan we must cross nine contour lines and come upon the tenth, and at the same time upon the arc 4, 5, 6.

Proceeding in this way, we find A, a, b, B, on the plan, as corresponding to A m m′ B on the profile.

To establish in this manner any particular grade, we have first to place it upon the profile, and next to transfer it to the plan.

47. It may be remembered as a general thing, that the steepest line is that which cuts the contour line at right angles; the contour line itself is level, and as we vary between these limits we vary the incline.

GENERAL ESTABLISHMENT OF GRADES.

Table of Contents

48. Considerable has been written upon the relation which ought to exist between the maximum grade, and the direction of the traffic. Some have given formulæ for obtaining the rate and direction of inclines as depending upon the capacity of power. This seems going quite too far, as the nature of the ground and of the traffic generally fix these in advance.

49. Between two places which are at the same absolute elevation, there should be as little rise and fall as possible.

50. Between points at different elevations, we should if possible have no rise while descending, and consequently no fall while on the ascent.

51. Some engineers express themselves very much in favor of long levels and short but steep inclines. There are cases where the momentum acquired upon one grade, or upon a level, assists the train up the next incline. The distance on the rise during which momentum lasts, is not very great. A train in descending a plane does not receive a constant increase of available momentum, but arrives at a certain speed, where by increased resistance and by added effect of gravity, the motion becomes nearly regular. Up to this point the momentum acquired is useful, but not beyond.

Any road being divided into locomotive sections, the section given to any one engine should be such as to require a constant expenditure of power as nearly as possible; i.e., one section, or the run of one engine, should not embrace long levels and steep grades. If an engine can carry a load over a sixty feet grade, it will be too heavy to work the same load upon a level economically. It is best to group all of the necessarily steep grades in one place, and also the easy portions of the road; then by properly adapting the locomotives the cost of power may be reduced to a minimum.

As to long levels and short inclines the same power is required to overcome a given rise, but quite a difference may be made in the means used to surmount that ascent.

Fig. 25.

52. Suppose we have the profiles A E D and A B D, fig. 25. The resistance from A to D by the continuous twenty feet grade is the same as the whole resistance from A to B and from B to D. The reason for preferring A E D is, that an engine to take a given load from B to D would be unnecessarily heavy for the section A B; while the same power must be exerted at each point, of A E D. Also the return by A E D is made by a small and constant expenditure of power, being all of the way aided by gravity; while in descending by B, we have more aid from gravity than we require from D to B, after which we have none.

When the distances A B, B C, are sixty and twenty miles in place of six and two, we may consider the grades grouped at B D, and use a heavier engine at that point, as we should hardly find eighty miles admitting of a continuous and uniform grade.

EQUATING FOR GRADES.

Table of Contents

53. In comparing the relative advantages of several lines having different systems of grades, it is customary to reduce them all to the level line involving an equal expenditure of power.

The question is to find the vertical rise, consuming an amount of power equal to that expended upon the horizontal unit of length. This has been estimated by engineers all the way from twenty to seventy feet. For simple comparison it does not matter much what number is used if it is the same in all cases; but to find the equivalent horizontal length to any location, regard must be had to the nature of the expected traffic.

The elements of the problem are, the length, the inclination or the total rise and fall, and the resistance to the motion of the train upon a level, which latter depends upon the speed and the state of the rails and machinery.

From chapter XIV. we have the following resistances to the motion of trains upon a level:—

Velocity, in miles, per hour.	Resistance, in lbs. per ton.
10	8.6
15	9.3
20	10.3
25	11.6
30	13.3
40	17.3
50	22.6
60	27.1
100	66.5

The power expended upon any road is of course the product of the resistance per unit of length, by the number of units. Calling R the resistance per unit upon a level, and R′ the resistance per unit on any grade, and designating the lengths by L and L′, that there shall be in both cases an equal expenditure of power, we must have

RL = R′L′,

whence the level length must be

L = L′R′
R.

Thus assuming the resistance on a level as twenty lbs. per ton, that on a fifty feet grade is

20 + 50
5280 of 2240, or 20 + 21.2 or 41.2,

and if the length of the inclined line is ten miles, the equivalent level length is

L = 41.2 × 52800
20 = 108768 feet, or 20.6 miles.

Also 10 miles × 41.2 lbs. = 412,

and 20.6 miles × 20 lbs. = 412.

54. The above may be somewhat abridged as follows: Let R be the resistance on a level. The resistance due to any grade is expressed by

W × 1
a,

where 1
a is the fraction showing the grade, and W the weight of the load.

The vertical height in feet, to overcome which we must expend an amount of power sufficient to move the train one mile on a level, must be such that

W × 1
a = R,

or

1
a = R
W;

and to find the number by which to equate, we have only to place the values of R and W in the formula. For example, let the speed be twenty miles per hour, the corresponding resistance is 10.3 lbs. per ton. W being one ton, or 2240 lbs., we have

1
a = R
W = 10.3
2240 = 1
218 of 5280, (the number of feet in one mile,)

1
218 of 5280 = 24 feet.

In the same manner we have

Speed, in miles, per hour.	Equating number.
15	22
20	24
30	32
40	41
50	53
60	67
100	155

Thus when we take the speed as thirty miles per hour, for each thirty-two feet rise we shall consume an amount of power sufficient to move the train one mile on a level. In descending, the grade instead of being an obstacle, becomes an aid; indeed the incline may be such as to move the trains independently of the steam power. Thus if on account of ascending grades we increase the equated length, so also in descending we must reduce the length. The amount of reduction is not, however, the reverse of the increase in ascending, as after thirty or forty feet any additional fall per mile instead of being an advantage is an evil; as too much gravity obliges us to run down grades with brakes on. Twenty-five feet per mile is sufficient to allow the train to roll down, and any more than this is of very little use. Therefore for every mile of grade descending at the rate of twenty-five feet per mile we may deduct one mile in equating, and for every mile of grade descending twelve and one half feet per mile deduct a proportional amount; but for any more fall per mile than twenty-five feet, no allowance should be made; i.e., if we descend at the rate of forty feet per mile, we may deduct one mile in equating for the twenty-five feet of fall, and throw aside the remaining fifteen feet.

55. This is a common method of equating for grades, and represents a length which is proportional to the power expended, but not proportional to the cost of working, as the ratios of power expended and cost of working under different conditions are very different, double power requiring only twenty per cent. more working capital. The above rules, therefore, require a correction.

The cost of working a power represented by unity being expressed by	100;
That of working a power 2 is expressed by	125;
That of working a power 3 is expressed by	150;
That of working a power 4 is expressed by	175;
That of working a power 5 is expressed by	200.
(See Appendix F.)

Now the resistance on a level being at a velocity of twenty miles per hour, 10.3 lbs. per ton by the formula

1
a = R
W,

the vertical height in feet causing a double expenditure of power is twenty-four; but as above, the whole expense of a double power is increased by only twenty-five per cent.; we should not add one mile for twenty-four feet rise, but one fourth of a mile only, or one mile for each ninety-six feet; and by correcting our former table in this manner, we have the following table:—

Speed, in miles, per hour.	Equating number.
15	88
20	96
25	110
30	128
40	164
50	212
60	268
100	620

So much for equating for the ascents. In descending, we have allowed one mile reduction for each mile of twenty-five feet of descending grade; but as in ascending we correct the first made table, so in descending we must also correct as follows. If we needed no steam power either while descending or afterwards, we should only save wood and water; as a general thing the fire must be kept up while descending, and the only gain is a small part of the expense of fuel; so small, in fine, that with the exception of roads which incline for the whole or a great part of their length, no reduction should be made.

COMPARISON OF SURVEYED LINES.

Table of Contents

56. The requisite data for an approximate comparison of lines are, the measured length, total rise, total fall.

Let the length of line A be	100	miles,
Let the length of line B be	90	miles,
Whole rise on A	2000	feet,
Whole rise on B	5100	feet,
Whole fall on A	1200	feet,
Whole fall on B	4300	feet.

Assume the number by which to equate, as ninety-six, and we shall have

Line A.
Ascending, 100 + 2000 96 =	120.83
Descending, 100 + 1200 96 =	112.50
Sum	233.33
Mean	116.66
Line B.
Ascending, 90 + 5100 96 =	143.13
Descending, 90 + 4300 96 =	134.80
Sum	276.93
Mean	138.46
The mean equated length of A is	116.66
The measured length of A is	100.00
The difference	16.66
The mean equated length of B is	138.46
The measured length of B is	90.00
The difference	48.46.

The cost of construction being assumed as the actual length, and that of working as the equated length, we have the final approximate comparison thus:—

Assume the construction cost as $25,000 per mile, and the cost of maintenance $4,000 per mile, and we have

The line A to the line B as

100 × 25000 + 116.66 × 4000 × 100
6 = 10,277,333, is to

90 × 25000 + 138.46 × 4000 × 100
6 = 11,480,667;

or A is to B as 10.3 to 11.5 nearly, although the line A is ten miles longer than B.

CHAPTER III.
LOCATION.

Table of Contents

ALIGNMENT.

Table of Contents

57. The broken line furnished by the survey is of course unfit for the centre line of a railroad. The angles require to be rounded off to render the passage from one straight portion to the other easy.

Fig. 26.

58. Let A X B, fig. 26, represent the angle formed by any two tangents which it is required to connect by a circular curve. It is plain that knowing the angle of deflection of the lines A X, B X, we obtain also the angles A C X, X C B. The manner of laying these curves upon the ground is by placing an angular instrument at any point of the curve, as at A, and laying off the partial angles E A a, E A M, E A G, etc., which combined with the corresponding distances A a, a M, M G, fix points in the curve.

These small chords are generally assumed at one hundred feet, except in curves of small radius (five hundred feet) when they are taken less.

The only calculation necessary in laying out curves, is, knowing the partial deflection to find the corresponding chord, or knowing the chord, to get the partial angle.

As the radius of that curve of which the angle of deflection is 1° is 5730 feet, the degree of curvature for any other radius is easily found. Thus the radius 2865 has a degree of curvature per one hundred feet of

5730
2865 = 2°;

again,

5730
2000 = 2°.86 or 2° 51.6.

The radius corresponding to any angle is found by reversing the operation. If the angle is 3° 30′, or 210′, we have

5730 × 60
210 = 1637 feet radius.

The following figures show the angle of deflection for chords one hundred feet long, corresponding to different radii:—

Angle of deflection.		Radius, in feet.
¼°	or 15′	22920.0
½°	or 30′	11460.0
¾°	or 45′	7640.0
1°	or 60′	5730.0
1¼°		4585.0
1½°		3820.0
1¾°		3274.0
2°		2865.0
2½°		2292.0
3°		1910.0
3½°		1637.0
4°		1433.0
4½°		1274.0
5°		1146.0
5½°		1042.0
6°		955.4
6½°		822.0
7°		819.0
7½°		764.5
8°		716.8
10°		573.7

Points in any curve may also be fixed by ordinates, as a b, M D′, G F, or by E a, K M, etc.

For the details of locating, of running simple and compound curves, and of the calculations therefor, the reader is referred to the works of Trautwine, and of Henck.

Fig. 27.

59. Suppose now that we have the surveyed lines m m, and n n, fig. 27, one of which is to be finally adjusted to the ground. The shortest line is the straight one, which is generally impracticable. The most level line is the contour line, which is also impracticable. Between these two lies the right line, which is to be found by an instrumental location. The line A n n n n B, on the plan, gives the profile A n n n n B. The line A m m m m B gives the profile A m m m m B, while the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6 B.

Fig. 28.

60. Again, in fig. 28, the straight line A n n n B gives the profile A n n n B, requiring either steep grades or a great deal of work. By fitting the line to the ground, as by the line A a b c d … m n o B, we obtain the profile A a b c … m n o B.

FINAL ADJUSTING OF GRADES.

Table of Contents

Fig. 29.

61. The general arrangement of inclines must not be interfered with to save work, but a large part of the excavation and embankment may be saved by breaking up long grades so as not to affect materially the character of the road. Upon some lines the grades must necessarily undulate, as in fig. 29. The difference in the amount of work is plainly seen. The steepest grades thus applied must not be greater than the ruling grade upon the travel of one engine.

62. In long and shallow cuts and fills, the best plan is to place the grade line quite high, avoiding much cutting, and to make the embankments from side cuttings, (ditching). Banks must at least be placed two or three feet above the natural surface, first to prevent the snow from lodging too much upon the rails, second, to insure draining.

63. Snow fences are much used in the northern parts of the United States. These are high pieces of lattice-work, made roughly, but well braced; from eight to twelve feet high, and standing from sixty to one hundred feet from the road. The object of the fence is to break the current of the wind, and cause it to precipitate its snow. Close fences effect the object no better than the open ones, are more liable to blow down, and cost more.

64. In locating a road which is to have a double track eventually, regard must be paid to this fact in side-hill work. The first track should, if possible, be so placed as not to require moving when the double line is put on.

COMPARISON OF LOCATED LINES.

Table of Contents

65. In this comparison there is an element which does not enter the approximate comparison of surveyed lines, curvature. The resistance arising from this cause has never been accurately determined. Mr. McCallum estimates the resistance at one half pound per degree of curvature per one hundred feet; i.e., the resistance due to curvature on a 4° curve, would be two lbs. per ton, (see report of September 30, 1855). Mr. Clark estimates the resistance due to curves of one mile radius and under, as 6.3 lbs. per ton, or twenty per cent. of the whole resistance. The average radius encountered, therefore, by Mr. Clark, would be, at Mr. McCallum’s estimate,

6.3
0.5 = 12° nearly, or 477.5 feet.

So small a radius is by no means allowable upon English roads; thus the estimate of Mr. Clark and of Mr. McCallum differ considerably. Experiments might easily be made with the dynamometer upon different curves, by which we might find very nearly the correct resistance caused by curves.

The curvature on any road cannot be adjusted to trains moving at different speeds.

66. The tractive power acts always tangent to the curve at the point where the engine is, and thus tends to pull the cars against the inner rail. The tangential force, generated by the motion of the cars, tends to keep the flanges of the wheels against the outer rail; and only when a just balance is made between the tractive and tangential forces, the wheel will run without impinging on either rail, (the wheel being properly coned). For these forces to balance, there must be a fixed ratio between the weight of a car and the speed, (not the weight of a train, as the shackling allows the cars to act nearly independently, some indeed rubbing hard for a moment against the rail, while the next car is working at ease). Whenever the right proportion is departed from, as it nearly always is, (and perhaps necessarily in some cases,) upon railroads, the wheels will rub against one rail or the other. Thus on any road where the speed on the same curve, or the radii of curvature under the same speed, differ, there must be loss of power, and dragging or pushing against the rails.

67. We are obliged to elevate the outer rail (see chapter XIII.), for the fastest trains, and the slower trains on such roads will therefore always drag against the inner rails. Thus in practice we generally find the inside of the outer rail most worn on passenger roads, and the inside of the inner rail upon chiefly freight roads.

68. It has been the practice of some engineers in equating for curvature, to add one fourth of a mile to the measured length for each 360° of curvature, disregarding the radius, as the length of circumference increases inversely as the degree of curvature.

69. Now in equating for grades, in doubling the power we do not double the expense of working. We however increase it more by curvature than we do by grades, because besides requiring double power, the wear and tear of cars and rails and all machinery is increased upon curves, which is not the case upon grades.

70. The analysis of expense (in Appendix F.) upon the New York system of roads, gives the following:—

Locomotives,	40	per cent.
Cars,	20	per cent.
Way and works,	15	per cent.
or in all,	75	per cent.

Now each 360° will be equal to 75
100 of one quarter of a mile, or 75
400 of a mile; whence the number of degrees which shall cause an expense equal to one straight and level mile, will be 1920°.

71. The number of degrees by Mr. McCallum’s estimate would be thus:—

The resistance upon a level being ten lbs. per ton, and that due to curves one half pound per ton, per degree per one hundred feet; the length of a 2° curve to equal one mile will be

10 lbs.
1 lb.,

or ten miles. Also ten miles, or 530 hundred feet by 2° is 1060°.

72. Again, by Mr. Clark’s resistance of twenty per cent. of the level resistance, upon curves averaging 2°, we have as the length of 2° curve

10
2 = 5 miles,

or 265 hundred feet, which by 2° gives 530°.

73. Averaging the first and last, we have as the number of degrees which should be considered as causing an amount of expense equal to one straight and level mile, 1225°, which averaging with the estimated resistance by Mr. McCallum, gives finally 1142½° as causing an expense equal to one straight and level mile, or, in round numbers, 1140°.

74. Suppose now that we would know which of the lines below to choose.

Line A.	Line B.	Description.
100 miles,	110 miles,	Actual length,
5000 feet,	3000 feet,	Rise,
3500 feet,	1500 feet,	Fall,
3600°	9000°	Degrees of curvature.

Assuming the speed as twenty miles per hour, the number by which to equate for grades, see chapter II., is ninety-six, also the number of degrees for curvature 1140, whence,

Line A ascending 100 + 52.1 + 3.16 = 155.26	147.46
Line A descending 100 + 36.5 + 3.16 = 139.66
Line B ascending 110 + 31.25 + 7.89 = 149.14	141.31,
Line B descending 110 + 15.62 + 7.89 = 133.49

and if the cost of construction is as the actual, and the cost of maintaining and working as the mean equated length, we have, as a final comparison,

A to B as 100 + 147.46 to 110 + 141.31,

or as

247.46 to 251.31.

Here the extra grades on the one hand nearly equal the curvature and the extra length on the other hand.

75. As a further example in the comparison of competing lines, let us take the actual case of the location of the eastern part of the New York and Erie Railroad.

It was questioned which of the two lines between Binghampton and Deposit should be adopted, and also between the mouth of Callicoon Creek and Port Jervis.

Fig. 30.

Between A and c, fig. 30, were located the lines shown in the sketch, one following the Susquehanna river from A to B, thence crossing the dividing ridge between that river and the Delaware to Deposit (c). The other passing up the Chenango river to a, thence crossing first the summit M to the Susquehanna at L, and second the summit K, to Deposit (c). The elements of the two lines are as follows:—

	A route, A B c.	B route, A M K c.
Length,	39.29	43.58
Rise A to c,	540.00	1087.00
Rise c to A,	395.00	936.00
Whole rise and fall,	935.00	2023.00
Degrees of curvature,	2371°.00	3253°.00
Estimated cost,	$746,900.00	$628,600.00

Assuming the number by which to equate for grades, as 96, and the equating number of degrees of curvature as 1140°; equating for grades and curvature in both directions, we have,

Route A. A to c.			Mean, 46.25.
39.29 +	540 96 + 2371 1140 = 39.29 +	5.63 + 2.08 = 47.00
Route A. c to A.
39.29 +	395 96 + 2371 1140 = 39.29 +	4.12 + 2.08 = 45.49
Route B. A to c.			Mean, 56.96.
43.58 +	1087 96 + 3253 1140 = 43.58 +	11.32 + 2.85 = 57.75
Route B. c to A.
43.58 +	936 96 + 3253 1140 = 43.58 +	9.75 + 2.85 = 56.18

Assuming the cost of working and of maintaining as $4,000 per mile, we have

The cost of building A to B as $746,900 to $628,600

The cost of operating A to B as (46.25 × 4000) × 100
6 to (56.96 × 4000) × 100
6,

or as	$3,083,334	to	$3,797,334
and the sum as	$3,830,234		$4,425,934

giving the preference of $595,700 to the route A B c, notwithstanding that the estimate thereon exceeds that on B by $118,300. The route A B c was adopted.

Again, it was doubtful whether to adopt the route E F, in going from D to G, or the line I H. The following are the elements of the two lines:—

	I H.	E F.
Measured length,	61.14	58.53
Rise D to G,	1187	454
Rise G to D,	1049	316
Degrees curve,	7609°	4588°
Estimated cost,	$1,094,950	$1,496,430

The mean equated lengths are as follows:—

Line I H. D to G.			Mean, 79.46,
61.14 +	1187 96 + 7609 1140 = 61.14 +	12.36 + 6.68 = 80.18
Line I H. G to D.
61.14 +	1049 96 + 7609 1140 = 61.14 +	10.93 + 6.68 = 78.75
Line E F. D to G.			Mean, 66.56.
58.53 +	454 96 + 4588 1140 = 58.53 +	4.73 + 4.02 = 67.28
Line E F. G to D.
58.53 +	316 96 + 4588 1140 = 58.53 +	3.29 + 4.02 = 65.84

The comparison as to cost is

I H to E F as $1,094,950 to $1,496,430,

and as to working,

I H to E F as (79.46 × 4000) × 100
6 to (66.56 × 4000) × 100
6,

and the sum as

	1,094,950	to	1,496,430
	+ 5,297,334		+ 4,437,334
or	$6,392,284	to	$5,933,764

Although the cost of E F is $401,480 more than that of I H, the line E F was adopted.

CHAPTER IV.
PRELIMINARY OPERATIONS.

Table of Contents

SPECIFICATION.

Table of Contents

76. The object of this paper is to define exactly the terms of the contract as regards execution of work. Every thing therein should be expressed in a manner so plain as to leave no room for misunderstanding.

A AND B RAILROAD.

77. Specification for Graduation.

LINE.

The centre of the road-bed to conform correctly to the centre line of the railroad, as staked out or otherwise indicated on the ground, and to its appropriate curvatures and grades as defined and described by the engineer; and the contractor shall make such deviations from these lines or grades at any time, as the said engineer may require. The road-bed to conform to the cross section which shall be given or described, or to such other instructions as may be given as hereinafter limited; and the same of the ditches and slopes of the work, and of all operations pertinent to the satisfactory performance of the graduation or masonry on the part or parts of the line contracted for.

CLEARING.