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 miss ing 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,

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 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 CB 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 CH 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 column 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, CD 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 E F. 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

measured distance falls half-way between the distances corresponding 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 different 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 8 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 calcuiation, to be a 44-degree curve.

TABLES

TABLES OF THE TIMES OF CULMINATION AND OF ELONGATION OF THE POLE-STAR AND

OF ITS AZIMUTH AT ELONGATION.

These tables are designed to facilitate the determination of a meridian line and of the magnetic declination (variation of the compass) by simple instrumental meaus (p. 44). For this purpose the tables are sufficiently accurate. They will also be found useful when preparing for or laying out work for a more refined determination of the astronomical azimuth and for the measures of the value of an eye-piece micrometer.

148

TABLE I.

MEAN LOCAL (ASTRONOMICAL) TIME, COUNTED FROM NOON AND FROM ZERO TO TWENTY-FOUR HOURS, OF THE CULMINATIONS AND ELONGATIONS OF POLARIS IN THE YEAR 1889. COMPUTED FOR LATITUDE 40° NORTH AND LONGITUDE 6 HOURS WEST FROM GREENWICH.

1889.

DATE.

E. ELONG. UPPER CULM. W. ELONG. LOWER CULM.

To refer the tabular times to any year subsequent to the tabular year (1889) add 0m.33 for every year.

To refer the tabular times, corrected as above, to any year in a quadrennium, observe the following rules:

For the first year after a leap-year the table is correct.

For the second year after a leap-year add 0m.9 to the tabular value.

For the third year after a leap-year add 1m.7 to the tabular value.

For leap-year and before March 1 add 2m.6 to the tabular value.

For leap-year from and after March 1 subtract 1m.2 from the