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 seer at once, without calcuis tion, to be a 41-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 means (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 1889. DATE. E. ELONG. UPPER CULM. W. ELONG. LOWER CULM. Jan. 1 15 Feb. 1 15 March 1 15 April 1 15 May 1 15 June 1 15 July 1 15 Aug. 1 15 h. m. 0 36.2 23 37.0 22 29.9 21 31.6 20 39.4 1944.4 18 37.4 17 42.4 16 39.5 15 44.6 14 37.9 13 43.0 12 40.4 11 45.5 10 39.0 9 44.1 8 37.5 7 42.6 6 39.7 5 44.7 4 37.9 3 42.7 2 39.7 1 44.4 h. m. 6 31.0 5 35.7 4 28.6 3 33.3 2 38.1 1 43.1 0 36.0 23 37.1 22 34.2 21 39.3 20 32.7 1937.8 18 35.2 17 40.3 16 33.8 15 38.9 14 32.3 13 37.4 12 34.5 11 39.5 10 32.7 9 37.5 8 34.5 7 39.2 h. m. 12 25.7 11 30.4 10 23.3 9 28.1 8 32.8 7 37 7 6 30.7 5 35.7 4 32.9 3 38.0 2 31.3 1 36.4 0 83.8 23 35.0 22 28.4 21 33.5 20 26.9 19 32.0 18 29.1 17 34.1 16 27.3 15 32.2 14 29.2 13 34.0 h. m. 18 29.1 17 33.8 16 26.7 15 31.4 14 36.2 13 41.1 12 34.1 11 39.0 10 36.1 9 41.2 8 34.6 ñ 39.7 6 37.1 5 42.2 4 35.7 3 40.8 2 34.2 1 39.3 0 36.4 23 37.6 22 30.8 21 35.6 20 32.6 19 37.3 Sept. 1 Oct. Nov. 15 1 15 1 15 1 15 To refer the tabular times to any year subsequent to the tabular year (1889) add om 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 om 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 To refer to any calendar day other than the 1st and 15th of each month, subtract 3m.94 for every day between it and the preceding tabular day, or add 3m 94 for every day between it and the succeeding tabular day. The longitude correction will amount to Om 16 for each hour. To refer to any other than the tabular latitude, and between the limits of 25° and 50° North, add to the time of west elongal tion Om. 13 for every degree South of 40° and subtract from the time of west elongation Om 18 for every degree North of 40°. Reverse these signs for corrections to times of east elongation. Observe that the year 1900 is not a leap year, and this must be kept in view when dealing with dates from and after March 1 of that year. The 20th century begius after the expiration of Dec. 31, 1900. The deduced tabular times may be relied on to have no greater error than + Om.3. Table II. below Låt. 24° is abridged from a table for each degree of latitude between 25° and 50° North, computed for this book by Mr. C. A. Schott, Asst. Supt. of the U. S. C. and G. Survey, with the mean declination of Polaris for each year. A closer result will be had by applying to the tabular values the following correction, which depends on the difference of the mean and the apparent places of the star : FOR FOR LAT 250 LAT 40° LAT. 50° MIDDLE OF MIDDLE OF The deduced tabular azimuth, counted from the North, may generally be depended upon with no greater error than 0.2. In making the computation the mean places of Polaris were first accurately deduced from Newcomb’s Catalogue of 1098 standard clock and zodiacal stars, Washington, 1881, for five equidistapt epochs. From these fundamental places those for each year were readily found by interpolation. Azimuth for latitudes less than 25 was reckoned by the TABLE II. AZIMUTH OF POLARIS WHEN AT ELONGATION FOR THE YEARS 1890 TO 1910 INCLUSIVE. To avoid crowding and needless repetition the minutes and their decimals only are given in this Table. LAT. 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 Lat. 4 16.9 16.6 16.2 15.9 15.6 15.3 15.0 14.7 14.4 14.0 13.7 13.4 13.1 12.8 12.5 12.1 11.8 11.5 11.2 10.9 10.6 31. 29.0 28.6 28.2 33.3 33. 36.8 36 36.0) 40.3 39. 15.3 44. 44. .6 43. 49.5 49.0 48.6 48.2 47. .3 46.8 45.91 53.7 53.2 52.8 52.3 51.9 51.4 50.9 49.9 45.3 58.4 57.9 57.4 56.9 56.4 55.9 55.4 54 54.5 54. 52.0 51. 51.0 50.1 49.6 |