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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 5inches. 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 41-degree curve.

TABLES.

TABLES.

TABLE I.

TIME OF MERIDIAN PASSAGE OF NORTH STAR ABOVE THE

POLE, FOR THE YEAR 1870.

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For the year 1880, add three minutes to the time; for 1890, add 7 minutes; for 1900, add 11 minutes.

149

TABLE II.

TIME OF EXTREME ELONGATIONS OF NORTH STAR FOR THE

YEAR 1870, - LAT. 40°.

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66

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9.38 " 7.48 " 5.46 " 3.48 "

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Jan. Feb. Mar. April. May. June. July. Aug. Sept. Oct. Nov. Dec.

H. M. H. M.

H. M.

H. M. H. M. H. M. 0.32 P.M. 0.24 A.M. 11.52 A.M. 11.40 P.M.11.13 A.M. 11.01 P.M. 10.29 A.M. 10.18 P.M. 9.50

9.11
8.27

7.20 7.09
6.37
5.58

5.19 5.07
4.39
4.27 4.00

3.21 3.09
2.38
2.26
1.58
1.47 1.19

1.07
0.39

11.57 P.M. 11.49 A.M. 11.18 P.M. 11.09 A.M. 10.35 P.M. 10.27 A.M.

9.08
7.54

7.14
6.27
5.56

5.17

5.09
4.33
4.26
3.54

3.15 3.07
2.27 1.56 1.48

0.28 "

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9.56

9.16 "

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9.48 " 7.46 « 5.48 "

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For the year 1880, add 3 minutes to the time; for 1890, add 7 minutes ; for 1900, add 11 minutes. Change of latitude affects the tabular time very slightly.

TABLE III.

AZIMUTHS OF THE NORTH STAR, AND THEIR NATURAL

TANGENTS.

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