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3. Suppose, for example, the gauge sides of the nearest rails of the main and side tracks are 6 feet 6 inches asunder; gauge of track, 4 feet 84 inches; frog, a No. 9. Reducing inches to decimals, we have then the distance between tracks 6.5 feet, less the gauge, 4.7 feet, 1.8 feet; and 1.8 multiplied by 9, the number of the frog, gives 16.2 feet for the distance D E. The proper spring will be given to rail D E on the ground; and curve E G, from frog to toe of side-track switch, will be staked off as directed in the section on turnouts.
ELEVATION OF THE OUTER RAIL ON CURVES.
1. Great precision in this adjustment is unattainable, owing to differences in the speed of trains and to the cost of trackmaintenance, if it were attempted. The annexed table will be found convenient in practice. It has been calculated by the following simple rule: –
2. Divide the speed in miles per hour by 10; multiply the square of the quotient by the degree of curve. The product is the elevation in sixteenths of an inch for full gauge of 4 feet 81 inches. Take two-thirds of it for 3-feet narrow gauge.
3. Molesworth gives the following formula for determining the elevation of the outer rail with any gauge:
V=greatest velocity of trains in feet per second.
gauge of railway in feet. С length of chord whose middle ordinate will give the required elevation.
Then C=1 VNG.
A modification of this formula gives the following approximate rules:
To fix the elevation of the outer rail on the standard gauge of 4 feet 81 inches,
the product by 3. This will give the length of tape, C, to stretch on the gauge side of the outer rail; and the distance, e, from the middle of the tape to the gauge side of the rail, will be the proper elevation.
For gauge of one metre, 3.28 feet, make C equal to one and one-third times the speed of trains in miles per hour.
For 3-feet gauge, make C equal to one and one-fourth times the speed of trains in miles per hour.
TRACKMEN'S TABLE OF CURVES AND SPRING OF RAILS.
MIDDLE ORDINATES IN INCHES AND FRACTIONS, THE
LENGTH OF CHORD BEING
LENGTH OF CHORD IN FEET AND
INCHES, WITH A MIDDLE
DEGREE OF CURVE.
DEGREE OF CURVE.
Full Gauge, Narrow Gauge, 4 feet 82 inches. 3 feet.
EXPLANATION OF THE FOREGOING TABLE.
Columns 1 and 10 give the degree of curve.
The use of column 2, containing the deflection distances, may be illustrated thus: Suppose stakes 4, 5, and 6 to be missing from a 3-degree curve, and that stakes 2 and 3 are still standing 100 feet apart. To replace the missing stakes, proceed as follows: Measure 100 feet from 3 to A, and make a mark at A exactly in range with 2 and 3. Find, in column 2 of the table, the deflection distance for a 3-degree curve, which is seen to be 5 feet 3 inches. Hold one end of the tape at A,
and, stretching 5 feet 3 inches towards 4, nearly square to the range A-3, make a scratch on the ground three or four feet long, swinging the tape around A as a centre. Next lay off 100 feet from stake 3 to the scratch; where the end of that measurement strikes it, is the place for stake 4. By measuring 100 feet out to B on the range 3-4, and proceeding in like manner, stake 5 may be set; and so on.
3. If the centre line is already staked for track at points 100 feet asunder, and the degree of curve is wanted, range out the straight line between stakes, as above, to A or B, and measure across from those marks to the neighboring location-stake. Suppose the distance B-5, for example, to be 8 feet 9 inches. Referring, then, to column 2 of the table, we find that deflecproved to be 4 feet 4 inches, we should soon discover that that distance was about half-way between 3 feet 6 inches and 5 feet 3 inches, the nearest numbers in the table corresponding respectively to a 2-degree and a 3-degree curve, and showing the located line to be a 23-degree curve.
4. Let A C B in the figure, which is drawn very much out of proportion in order to make the subject clear, represent the centre line of a curve. Suppose G H to be a chord 100 feet long, and G C or C H to be a chord 50 feet long. Then column 3 in the table gives the distance, CD, from the middle of the 100-feet chord to the rail, and columu 4 gives the distance, EF, from the middle of the 50-feet chord to the rail, for the different degrees of curve. By the aid of these columns, pins can be set 25 feet apart on a curve where the location-stakes are 100 feet apart. Thus, for a 3-degree curve, C D is 8 inches,
and EF 2 inches. If pins were wanted at the half-way marks, N, their distance from the dotted short chords would be onequarter of EF. It must be an uncommon case, however, that calls for stakes closer together than 25 feet.
5. Columns 5, 6, and 7 give the spring of rails of different lengths for the various degrees of curve.
6. Columns 8 and 9 give figures for finding the degree of curve, by simple measurement of a straight line on the track, as follows: Suppose A C B and KIL to represent the rails of a curving track. From any point A, on the outer rail, sight across to a point B, on the same rail, along a line just touching the inner rail at I. Measure from A to B, and seek the distance in column 8 or 9, according to the gauge of track. If the distance, for example, measured 232 feet on the full gauge, then the curve would be a 4-degree curve; if 249 feet, then it