sary to determine the azimuth error separately, both before and after reversal. A comparison of the clock error, determined from observations upon north and south stars, will furnish the data necessary for the determination of azimuth. Practically, it is determined by elimination from equations involving the mean of all these stars observed in each of the two positions of the instrument, after correcting for level, and as it is slightly complicated with collimation it must be reached by two or more approximations. The errror is essentially positive when the telescope points east of south, and negative when west of south. The correction applicable to any star is expressed (see formula (130)) in the following. equation: aA = a sin ( - d) sec d. (165) It must be understood that the declination when north is positive for upper and negative for lower culmination, and that with south declination it is negative. The right ascension of stars, as taken from the Star Catalogue, must be corrected for diurnal aberration, which equals 0.021 cos sec 8. This correction is positive for upper and negative for lower culmination. The foregoing corrections are summarized (see formula (135)) in the following equation: A, B, C are constants, depending upon the latitude of the place of observation and the declination of the star. Tables for these quantities will be found in an appendix to Annual Report U. S. Coast and Geodetic Survey for 1880. (Extract reprinted herewith, Table LXX.) 333. Record of Time Observations.-On pages 755 to 757 is an example of the form for record of observation and reduction of time observations, taken from a series made for the determination of position of Rapid, South Dakota. EXAMPLE OF RECORD OF TIME OBSERVATIONS. (Rapid, South Dakota, November 20, 1890. Fauth transit, No. 534. Sidereal chronometer: Bond & Sons, No. 187. 1 division of level = 0.118. Hourly rate of chronometer = 0.133.) (From Gannett's Manual.) 334. Longitude Computation. EXAMPLE OF REDUCTION. (Rapid, South Dakota, November 20, 1890. After exchange of clock signals.) Subtracting (2) from (1), ignoring azimuth terms wh ich are small, we have: Aw+.415 36.09 = 0 36.93 = 0 0.84 = 0 Ae=+.285. Forming equations to determine c' from columns 4 and 9: + 1.73c' — 368.786 = 3.68 -36.736 36.762 + 2.95 A'c + 0.038 = 0 A'e .013 Ae.285 Adopted..Ac = +*.272 5 Normal equation, formed from columns 1, 3, 4, and a - T= .028 X.436 = +.049 X + .272 = +.039 X .004 = AT= TABLE LXX. FACTORS FOR REDUCTION OF TRANSIT OBSERVATIONS. (Extracted from Appendix 14, U. S. Coast and Geodetic Survey Report for 1880.) To find A enter left-hand column with the zenith distance; its intersection with declination column given azimuth factor. To find Benter right-hand column with the zenith distance; its intersection with declination column gives level factor. Cis given on last line of each section of the table. Azimuth factor A = sin sec 8. Star's declination ± 8. Inclination factor B = cos sec 8. .39 .40 .40 43 .68 .69 .71 44 .69 .71 72 73 45 .71 72 58 59 59 .58 .59 .60 .64 .65 58 .67 .69 .70 .71 .73 .77 .79 .86 45 .74 .79 29 .45 .46 .47 .48 .48 .49 30 .50 .51 31 .52 .52 32 .53 .54 33 .54 .55 34 .56 .57 69 .45 .46 68 •44 .44 45 .46 .47 .48 67 .45.46 .47 .48 .49 .50 .47 .48 .49 .50 .51 .52 65 .45 .47 .47 .48 .49 .50 .51 .52 .53 .54 .47 .48 .49 .50 .51 .51 .52 154 -55 .56 .49.50 .51 .51 .52.53 .54 -55 -57 .58 .50 .52 .52 .53 .54 .55 .56 .57 .58 .60 .52 53 .54 .55 .56 .57 .58 .59 .60 .62 60 .53 .56 .57 .61 .62 .64 .61 .63 55.56 .55.56.57 .56 .58.59 .58 .59 .60 55555 976 in |
