26 Land Magnetic Observations, 1914-20 



REVISIONS OF FIELD COMPUTATIONS. 



Astronomical Work. 



The astronomical observations necessary for determination of geographic position 

 and of the true azimuth of a line of reference at a magnetic station are computed 

 in the field by the observers of the Department before the records are transmitted. These 

 field computations are later revised at the office in Washington, where corrections de- 

 manded by any obvious error in the original work are applied, and also refinements are 

 made arising from considerations such as a better determination of atmospheric refraction 

 or of chronometer rate. Changes in latitude are frequently made in these revisions, and it 

 is desirable to correct for the effects of such changes in azimuth of the reference lines or 

 in the chronometer corrections on local mean time and consequent longitude determina- 

 tions, without making an entire recomputation. This may be done with sufficient ac- 

 curacy for the purpose by using differential formulae involving azimuth, A, latitude, <p, 

 and hour-angle, t, thus 1 : 



= sec<pcott (1) 



dip 



= sec <pcotA (2) 



d<p 



Since the changes in latitude for which corrections must be made are relatively 

 small, usually not more than one minute of arc, and since the accuracy demanded in 

 the resulting true azimuth is on the order of one-tenth of a minute of arc with a larger 

 permissible range in hour-angle, the requirements of the problem may be sufficiently met 

 by using graphs of the values of the quantities, given by the formulae. The formulae (1) 

 and (2) being identical but for the interchange of the symbols representing azimuth 

 and hour-angle, one system of curves will serve for both quantities. 



The derivatives in the form adopted above are functions of two variables, and a 

 family of curves is required to fully represent the series. The loci for like values of the 

 correction-factors when dtp = 1 minute of arc for different values of <p and A or of <p and t 

 may be readily determined from the above equations. By suitably selecting the factors 

 to be plotted a graphical chart of correction-curves is obtained from which corrections 

 of requisite accuracy may be easily noted. Figure 1 gives such a chart. 



To determine the change in the azimuth arising from a given change in latitude, the 

 computer has only to locate the point on the graph corresponding to the approximate 

 latitude of the station for the approximate hour-angle of the celestial body as shown by 

 the original computation, to estimate from the adjacent curves the value of the correction- 

 factor, and to multiply the given change in latitude expressed in minutes by this factor. 

 The change in the chronometer correction on local mean time is obtained in the same 

 way, but by using the azimuth of the body instead of the hour-angle. The change in the 

 coefficient from one locus to the following is not linear, but within the limits laid down 

 no appreciable error will arise from so regarding it. 



To apply properly the corrections obtained by use of the graph, it is necessary to 

 give attention to the sign. It is convenient to modify the usual convention in this case, 

 and instead of counting continuously around through 360 from the meridian, to regard 

 the azimuth or hour-angle of a body west of the meridian as positive, and when east of 

 the meridian as negative, thus avoiding the danger of confusion of sign arising from using 

 angles greater than 180. The factor sec <p is always positive since latitude cannot ex- 

 ceed 90, and consequently the sign of the correction factor will depend upon that of 

 cot t or of cot A. 



1 Cf. Comatock, G. C, Astronomy for Engineers, p. 207. 



