Extracts from Field Reports 135 



Each observation will give a similar equation, and the most probable values of x, y, z, 

 and w may be found from all the observations by the method of least squares. 



In the case of the "aUdade method," the number of unknowns may be reduced by 

 methods given below, where each imknown is separately considered. 



X, its significance and value. — x in this discussion, represents the combined results of — 



(1) Non-coincidence of the axis of the magnetic system with the zeros of the card; 



(2) The vertical plane containing the optical ray, peep-sight and vertical thread, not 



passing through center of card ; 



(3) Lack of horizontaUty of reading prism (that is, the optical ray from peep-sight to 



reading thread of prism may not be reflected perpendicularly on to the plane of the 

 card graduations) ; 



(4) The vertical thread and the reading thread of reading prism may not he in the same 



vertical plane; 



(5) Errors of graduation (in some instnmients errors have been found amounting to aa 



much as 0?3); 



(6) Eccentric mounting of the pivot; 



n) Altered balance of compass card owing to extreme values of the vertical intensity of 

 the magnetic field. 



The value of x may be determined from declination observations at land stations 

 where simultaneous standard values are available for comparison, and where it is possible 

 to have azimuth marks fairly well distributed around the horizon. If the compass bowl is 

 turned or oriented during observations on these marks, so as to set the forward lubber-line 

 at any 3 or more equidistant points, e. g., the cardinal points, the mean result of the dec- 

 lination from the pointings on any one mark in the equidistant orientations will be free 

 from errors of eccentricity of pivot. A comparison of these mean results with the corre- 

 sponding standard values of the decUnation wiU give a value of x for the bearing of each 

 mark. A graph may be constructed or a table calculated from these results, by which any 

 compass-bearing of an object in the horizon may be corrected. The difTerences between 

 the individual values of x and the mean of all are the periodic and graduation errors. 

 The non-coincidence of the axis of the magnetic system with the zeros of the card, lack of 

 horizontality of the reading prism, and any error in the assembling of vertical thread and 

 reading thread of the prism may be considered constant for aU practical purposes, and 

 this combined effect is assumed to be the mean of all observations made for the purpose 

 of determining x. Therefore, during the remainder of this discussion, x may be considered 

 as determined or known, and represented by x^. Equation (1) may then be written 



y tan h + z tan h tan ^ + w tan h &ec,^ = Do — D — x^ (2) 



which contains but three unknowns. 



In the following demonstrations it is assumed that the azimuth circle revolves about an 

 axis which is perpendicular to the compass-bowl glass, since the instrument is leveled by a 

 circular level resting on this surface. This condition may be verified by placing the instru- 

 ment on a solid pier or otherwise making it immovable and then observing two circular 

 levels while the azimuth circle is being rotated, one resting on the bowl-glass surface, the 

 other on the circle. 



a = y tan h. — If the dark mirror is in perfect adjustment, as it rotates about its axis 

 a normal to its surface will move in a vertical plane (EZH, Fig. 5), which contains the 

 line "peep-sight and vertical thread," and hence also the object sighted. The intersection of 

 this plane with the horizon plane is the apparent and also the true azimuthal direction. 

 Figure 5 is an orthographic projection upon the plane of the horizon. If the mirror axis 

 is inclined to the horizon plane by a small angle, y, the plane EOHPS, now described by 

 a normal to the mirror surface as it rotates about its incUned axis, no longer passes through 



