3. Next lay off the proposed line of the near rail of the side track, X D. Mark the point G on that line where the range of the proper gauge side of frog C strikes it. Measure CG. Set off G D, equal to CG, along the side-track line, and drive a pin at D. Stretch the cord from C to D. Mark the middle point of it at K, and drive a pin at N, half-way between K and G. Stretch the cord from C to N, and from N to D. Stick pins outside the middle points, M and O, of those stretches at a distance from those points, M and O, equal to one-quarter of KN.

4. These three sets of pins will fix the line of one rail of the turnout. The corresponding rail of a double turnout can be laid off from them, if required, by symmetrical measurements.

5. In the case of a singie turnout, stretch the cord from the toe of switch, as above, to the point of frog, located by the foregoing tables; catch it at the middle, and pull it outwards to a point in range with the line of the switch-rail in one direction, and the gauge side of frog in the other direction. Half-way between that point and the middle of the cord, when straight, stick a pin. Measure that half-way distance, and divide it by 4; call the quotient the " quarter-distance." Stretch the cord from the pin just set to the toe of switch in one direction, and to the point of frog in the other. Outside the middle points of these short stretches, lay off the "quarterdistance," as above found, and stick two other pins. These three pins will sufficiently mark the line of the outer rail of the turnout.

6. The same methods will apply in practice to turnouts from curves. In the latter case, the distance C G is to be calculated as follows:

Multiply the distance Y D, between the nearest rails of the parallel tracks, by the number of the frog, taken from the foregoing table. Thus, on the full gauge, with a space between tracks of 7 feet and a No. 6 frog, the distance CG would be 7 × 642 feet. Lay off CG, in range of the gauge side of the frog, and stick a pin at G. Measure out GD, equal to C G, and set another pin at D, making DY the proper distance between tracks. Then stretch the cord from D to C, and proceed to stake off the curve CND, as above directed.

XLVIII.

CROSSINGS ON STRAIGHT LINES.

1. Having located frogs B and C by the preceding methods, stretch the cord any convenient distance, CD, in the range of

G

B

E

G

the outer gauge side of the frog C. Set off EF parallel to CD, and distant the gauge-width from it. The intersection of said parallel at F with the near rail of the side track marks the spot for point of side-track frog; the curve F G, thence to toe of switch, corresponds to AC on the main track, and may be staked out in like manner.

XLIX.

CROSSINGS ON CURVES.

1. Having located frogs B and C by the preceding methods, set off the width of gauge, CD, from point of frog C, and square to its outer gauge side. Stick a pin at D.

2. Next calculate the distance D E to the point of side-track

tance, HI, between the gauge sides of the nearest rails of the main and side tracks; multiply the remainder by the number

3. Suppose, for example, the gauge sides of the nearest rails of the main and side tracks are feet 6 inches asunder; gauge of track, 4 feet 8 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 DE on the ground; and curve EG, from frog to toe of side-track switch, will be staked off as directed in the section on turnouts.

=

L.

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 8 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

G

C

=

=

greatest velocity of trains in feet per second.
gauge of railway in feet.

length of chord whose middle ordinate will give the required elevation.

Then CVG.

A modification of this formula gives the following approximate rules:

To fix the elevation

Tan.

Curve

of the outer rail on the standard gauge of 4 feet 8 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.