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A divided by B = 1,530 divided by 23.6 = distance; say, 65 feet.

64,8 feet, the frog

19. If the switch-rail be curved, the formula would stand thus:

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Which may be made a written rule as follows:

Multiply the length of switch-rail in feet by the number of the frog, and their product by 84; call the result A. Add together the length of switch-rail in feet and four-fifths of the frog number; call the sum B. Then divide A by B, and the quotient will be the distance from toe of outer switch-rail to point of frog in feet.

20. The foregoing rules are applicable to turnouts from curves, as well as from straight lines.

21. To find the radius of outer rail of a turnout curve from straight track. Data same as in previous rules for frogs; R the required radius in feet.

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22. To find the radius of the outer rail of a turnout curve from curved track, proceed thus:

:

First find the radius as for a turnout from straight track by the preceding rule; call it, as before, R. Call the radius of the main track R2, and the required radius of turnout curve r. Then, if the turnout be towards the concave side of main track,

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R2 X R
R2+R

If the turnout be towards the convex side of main track, –

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More explicitly, in the first case, r is equal to the product of the other radii divided by their sum; and, in the second case, r is equal to the product of the other radii divided by their

23. The angle of a frog is equal to 3,440' divided by the frog number.

24. To find the frog distances and radii for a three-foot gauge, find them by the preceding rules for standard gauge, and take five-eighths of the result, using a switch-rail reduced in like measure.

For a metre gauge, take seven-tenths of the result, using a switch-rail reduced in like measure.

Or these radii and distances may be found from the appended tables for standard gauge by pro-rating as above.

25. Three frog patterns are enough for general service. They should be so proportioned, that, taken in couples, the less may fit as middle frogs on double turnouts. Numbers 51, 71, and 10 make an excellent suit; numbers 5, 7, and 9 also answer very well.

26. At the terminal stations, and about the shops of busy roads, patterns necessarily multiply. The better way in such cases is to plot the situation to a large scale, and to take the required distances and angles from the drawing.

TURNOUT TABLE. SWITCH-RAILS, STRAIGHT; GAUGE OF TRACK, 4 FEET 8 INCHES; THROW OF SWITCHRAIL, 5 INCHES.

MAIN FROG NUMBERS AND ANGLES.

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Main frog dist.

4

14° 20 12 14

4

5

51

6

61

14° 20/ 12° 44/ 11° 28/10° 21′ 9° 33′ 8° 52′

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8

81

9

91

10

10

11

11

12

7° 10′ 6° 46′ 6° 22′ 6° 03′ 5° 44′ 5° 28′ 5° 13′ 5° 00′ 4° 47′

30.2 33.5 36.6 39.9 42.7 45.3 48.4 50.9 53.7 56.1 58.8 61.3 63.6 65.9 68.3 70.3 72.7 140.6 178.9 221.8 274.9 325.0 378.4 450.2 515.0 595.8 675.0 772.0 870.0 976.7 1,089 1,224 1,342 1,506 19.0 20.9 22.6 24.4 25.8 27.3 28.9 30.1 31.6 32.8 34.0 35.1 36.2 37.2 35.3 39.2 40.1 19° 28′ 17° 20/ 15° 41′ 14° 14/13° 12′ 12° 16/11° 24′ 10° 46′ 10° 04/9° 34′ 9° 03′ 8° 40′ 8° 15/ 7° 55′ 7° 38′ 7° 21′ 7° 05′|

31.2 34.6 38.0 41.6 44.6 47.5 50.9 53.7 56.8 59.5 62.6 65.3 68.0 70.0 73.4 75.7 78.5 139.4 176.9 218.8 270.3 318.6 369.7 438.0 499.2 575.0 648.0 737.0 826.0 921.0 1,020 1,137 1,263 1,377 19.9 22.0 24.0 26.0 27.8 29.4 31.3 32.8 34.5 35.9 37.4 38.7 40.4 41.6 43.0 43.8 45.3 19° 22′ 17° 14/15° 34/ 14° 06′ 13° 02/ 12° 06/ 11° 14/10° 34′ 9° 54′ 9° 22′ 8° 51/8° 27/ 8° 01/ 7° 40/7° 22/7° 09′ 6° 49/

31.8 35.4 38.9 42.7 45.9 48.9 52.6 55.5 58.8 61.8 65.0 68.0 71.0 73.8 76.9 79.4 82.5 138.8 176.0 217.4 268.2 315.7 365.8 432.6 492.1 565.0 636.0 721.0 807.0 897.0 992.0 1,102 1,196 1.325 20.5 22.7 24.8 27.1 28.9 30.8 32.8 34.5 36.5 38.1 39.9 41.4 43.1 44.4 45.9 47.6 49.0 19° 19′ 17° 10/15° 30/14° 02/ 12° 58/ 12° 02/ 11° 10/10° 30/ 9°47′ 9° 16′ 8° 44′ 8° 21/7° 54/ 7° 34/ 7° 15′ 6° 57′ 6° 41′

32.2 35.9 39.5 43.5 46.8 49.9 53.7 56.8 60.3 63.4 66 8 70.0 73.1 76.1 79-4 82.0 85.3 138.5 175.6 216.6 267.1 314.2 363.7 429.6 488.4 560.2 630.0 713.5 796.5 885.0 976.2 1,083 1,175, 1,298 20.9 23.2 25.5 27.8 29.8 31.7 33.9 35.6 37.9 39.7 41.6 43.3 45.2 46.8 48.3 49.9 51.4 19° 17′ 17° 09/ 15° 28′ 14° 00/12° 56′ 12° 00/ 11° 06/10° 28′ 9° 44′ 9° 14/8° 41/8° 17/7° 50/7° 30/7° 12′ 6° 54′ 6° 37′

32.6 36.4 40.1 44.2 47.7 50.9 54.9 58.1 61.8 65.0 68.7 72.0 75.3 78.5 82.0 84.8 88.4 Switch-rail,30 ft Rad. outer rail. 138.3 175.2 215.6 266.2 312.9 362.0 427.3 485.3 556.2 624.8 707.0 788.5 875.0 964.2 1,068 1,157, 1,276 Do.angle,0° 48′ Mid. frog dist. 21.3 23.7 26.1 28.6 30.6 32.8 34.2 37.0 39.3 41.3 43.3 45.2 47.3 49.0 50.9 52.9 54.2 Mid. frog angle. 19° 16' 17° 08′ 15° 25′ 13° 58′ 12° 54′ 11° 58/11° 04/10° 25′ 9° 42′ 9° 10/ 8° 39′ 8° 14/7° 47′ 7° 27/ 7° 09′ 6° 50′ 6° 34/

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TURNOUT TABLE.-SWITCH-RAILS, CURVED; GAUGE OF TRACK, 4 FEET 8 INCHES; THROW OF SWITCHRAIL, 5 INCHES.

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XLVII.

TO LOCATE A TURNOUT.

1. Let the heavy parallels in the figure represent the rails of the main track.

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2. Stick a pin or drive a spike at A, the toe of switch, at a distance from the gauge side of the main-track rail equal to the throw of the switch-rail. Lay off the distances AC and AB (if a double turnout), taken from the foregoing tables, and place the frogs C and B, or mark those points. Stretch the cord from A to B, and from B to C. Mark the middle points of those stretches at H and P. Catch the cord at H with your forefinger, and pull it outwards until your finger, at E, lines with the switch-rail, and also with the right gauge side of frog B. Stick a pin at L, half-way between H and E. Let the cord spring in against L, so that it shall stretch straight from A to L, and from L to B. Opposite the middle points, V, of those stretches, stick pins on the outside at a distance from the cord equal to one-quarter of HL. In like manner, catch the cord at P, the point midway between B and C; stretch it to F, in line with the gauge sides of the frogs; and stick a pin

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