Extracts from Field Reports 139 



In the spherical triangle SHZ, sin SZH = sin c = '-. — ^^ sin SHZ, hence, 



sm oZf 



sin SH 1 OTT ■ sin SH i „,. 



sm c = sm w -. — jr^ sec - SH = sm w r- sec - SH 



sm SZ 2 cos /i 2 



When to is small, c is also small, and SH does not differ appreciably from h, hence this 

 equation may be written 



c = w tan h sec „ 



If /i is reckoned through the zenith, the formula becomes general, so for h = 180° 

 there results, when evaluated, c = —2w, which agrees with the physical fact. 



Let the mirror be turned on its axis until its surface is vertical, or so nearly so that 

 the reflected image of the peep-sight may be observed through the peep-sight. Then, if 

 this image does not coincide with the vertical thread, the displacement may be measured 

 by reading a white scale held against the peep-sight. This displacement is equal to the 

 combined effects of z and w and may be represented by the equation 



2 n = 2 (z -h w) 



The ratio of this displacement to the distance between the mirror surface and peep-sight 

 is tan 2 n. 



Since n may be determined from direct Unear measurements, z = n — w may be sub- 

 stituted in equation (3), which gives 



Do— D— Xo — m tan h — n tan h tan j; 



"=- k IT (^) 



tan h + tan h tan ^ — tan h sec ^ 



The equation now contains but one unknown, w, which varies with the altitude and which 

 may be determined from solar observations. It is evident that the best determination of 

 w will result from those observations which give a large numerical value to the denominator; 

 hence only high Sun observations should be used to determine w from this equation. 



Application of Preceding Theory to Measures Made at Honolulu, 

 September 6 and 7, 1907. 



m = y -\- w iov standard compass R3C was measured at the Honolulu Magnetic 

 Observatory, and its value was found to be — 0?10. The sign was determined by 

 considering the relative size of the angles between the distant object and its images in 

 the compass-bowl glass and mirror. It was found that the normal was deflected to the 

 left when looking in the direction "peep-sight and vertical thread" {i. e., the direction 

 used in observing). Therefore, any observed compass-bearing of a high Sun was too great 

 (clockwise). If a„ be the observed bearing, always clockwise from the south point, and a 

 the true azimuth, then 



Do = a — a„ 



In this equation, if a^ is too great, Z)« is small as compared with D, so in the equation 



if Do is smaller than D, because the normal is deflected to the left, then that part of Aa, 

 which is due to this deflection is negative. 



