earth and would pass through the observer were he anywhere 

 between the topics at a latitude equal to the sun's declination. 

 Otherwise there is a slight error of parallax increasing from 0" at 

 the equator to less than 9" at the pole, so that it is usually neglected. 

 Having found the altitude, h, the declination, d, and the latitude, 

 1, the complements of these three angular values constitute the 

 spherical triangle PZS, which can be solved by the formula: 



//;/ co-alt X sin co-tat 

 in which s sum of 90 h, 90 d, and 90 1. Also we have, 



/ ,. 



StH , 2 / 7.. 



(sin '2 s co-lat) (sin %. s co alt) 



\ ~ ~~ - - 



> nn co-alt X //// co-lat 



Mr. Ross developed and used the following simplified formula: 

 (sin h sin 1) sin d 



cos Az. 



cos h X cos 



In Johnson-Smtth, p. 99, attention is directed to the fact that in 

 spherical trigonometry, 



cos (90 d) = [cos (90 h) X cos (90 1)] -}- [sin (90 h) X 

 sin (90 D] cos Az. from whence another simplified formula: 



cos Az. 



cos h x cos 1 



(tan h x tan 1) 



The sign of the first term in the second half of the equation 

 will be minus if the declination is south, and the second term will 

 be plus if the latitude is south. If the cos Az. is plus, the azimuth 

 is between and 90 as measured from the north; if minus, it is 

 between 90 and 180. For observations in the southern hemisphere, 

 use minus signs for north declination and refer azimuth to the south 

 pole. 



The application of the theory can be understood by following 

 a specific case, using the second formula given above. Let it be 

 supposed that we are measuring azimuth to a line that was thought 

 to be a true meridian. The example suggests the practice of 

 observing the sun in the diagonally opposite corners of the diaphragm 

 on the assumption that it is easier to point to the edge than the center 

 of the sun's disc; but Mr, Ross reports that, in actual practice, the 

 center of the sun can be determined by an average of four or six 

 pointingrwithina probable error of 1'. 



EM 



