TRACKMEN'S TABLE OF CURVES AND SPRING OF RAILS.

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,

3

B

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 deflec

proved to be 4 feet 4 inches, we should soon discover that that listance was about half-way between 3 feet 6 inches and 5 feet 3 inches, the nearest numbers in the table corresponding espectively to a 2-degree and a 3-degree curve, and showing he 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 ong, and G C or CH to be a chord 50 feet long. Then column 3 in the table gives the distance, CD, from the middle of the 00-feet chord to the rail, and column 4 gives the distance, EF, from the middle of the 50-feet chord to the rail, for the lifferent 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, CD is 8 inches,

nd E F 2 inches. If pins were wanted at the half-way marks, I, their distance from the dotted short chords would be oneuarter of E F. It must be an uncommon case, however, that alls for stakes closer together than 25 feet.

5. Columns 5, 6, and 7 give the spring of rails of different ngths for the various degrees of curve.

6. Columns 8 and 9 give figures for finding the degree of arve, by simple measurement of a straight line on the track, follows: Suppose A C B and KIL to represent the rails of a rving track. From any point A, on the outer rail, sight ross to a point B, on the same rail, along a line just touching e inner rail at I. Measure from A to B, and seek the disnce in column 8 or 9, according to the gauge of track. e distance, for example, measured 232 feet on the full gauge, en the curve would be a 4-degree curve; if 249 feet, then it

If

*།

measured distance falls half-way between the distances corre sponding to a 3-degree and a 4-degree curve respectively.

7. The rate of curve can be found also very nearly by means of column 3. To do so, stretch a straight line, 100 feet long, between points on either rail; for, though they seem very dif ferent in the figure, the two rails of a track have practically the same curvature. Measure from the middle of the line across to the gauge side of the rail, and seek the measured distance in column 3: opposite to it, in column 1, will be found the degree of curve.

8. If, in any case, the exact figures sought are not found in the table, take out the next figure less and the next greater. Subtract one from the other, and divide the remainder by 4. Add the fourth part of the difference between them, thus determined, to the smaller number, and compare the sum with the number sought. If still too small, add another fourth part; and so on until the distance or the degree is ascertained to within a quarter part.

9. Suppose, for instance, a deflection distance measures 5 feet 7 inches. The nearest tabular numbers are 5 feet 3 inches and 7 feet. Their difference is 21 inches, one-fourth of which is 5 inches. Adding 54 inches to the smaller number, 5 feet 3 inches, gives 5 feet 84 inches, which indicates nearly enough a 34-degree curve. Again: if a measurement of 175 feet is sought in column 9, the track is seen at once, without calculation, to be a 44-degree curve.

TABLES.