138 



Ocean Magnetic Observations, 1905-16 



The triangle, SZH, as before, gives 



sin SZH = tan SHZ tan h 

 but SHZ is equal to FEZ, hence when z is small 



h = z tan h tan ^ 



If the altitude is reckoned through the zenith for the Sun behind the observer, the 

 formula is general; so, when /t = 0°, 6 = 0, and when h = 180°, h, evaluated, = -2z, 

 which evidently agrees with the physical fact. 



c= w tan h sec ■^. — If, during Sun observations, the dark mirror is in perfect adjust- 

 ment, a normal to the surface will move in a vertical plane which contains the line "peep- 

 sight and vertical thread," EO, and hence also the Sun. This plane, whose horizontal 

 trace is the Sun's azimuthal direction, intersects the celestial vault in a great chcle EZH 

 (Fig. 7). If the axis of the mirror is horizontal and perpendicular to the line "peep-sight 

 and vertical thread," but does not he in the plane of the mirror surface or parallel to it 



Fig. 7. 



(i. e., "the mirror is not true in the frame"), the normal no longer describes a plane, but the 

 surface of a broad cone, which intersects the celestial vault in a small circle VW, parallel 

 to the great circle EZH, and at an angular distance, w, from it, measured by the arc WZ. 

 The Sun is now found in a plane EPZ' SHO, vihich. contains the hne "peep-sight and vertical 

 thread," the normal, and the Sun. This plane forms an angle SHZ = FEZ with the plane 

 of the apparent azimuth. Since the normal PO bisects the angle between the incident ray 



SO and the reflected ray OE, PZ' = ^SH, or PE = 90° - ]:SH. From the right-angled 

 spherical triangle with PE as hypothenuse, formed by drawing an arc from P perpen- 

 dicular to EZ, equal in length to w, sin PEZ = sin SHZ = sin w sec - SH. 



