THE THEORY OF TERRESTRIAL MAGNETISM. 445 



Hence the equations for finding x and y are 



= - 2762-4 + 10506-3x + 8033'2y, 



0=- 1338-1+ 7916-8z-1949-9y, 

 giving x = 0-19190 and y= '092895; 



hence Long. = 261^9 and Lat. = 10'45, 



which agree very well with the chart. 



Also we have 



X= 1030-3 - 9-55z - 26'35?/ - S'Soar 1 - 8'65f - 3'4xy, 

 and Y=- 154'4 - l'25a;+ 2'65?/ + 6-35x J + 0'357/ 2 + 8'25xy. 



From the equation tan 8 = ^, we get 8= -8 32''4. 



According to Erman's chart, 8= 8" 33''2. 



The equation which gives the tangent to the two branches of the 

 line of equal declination at their common point is 



10506-3 (Sec) 2 + 7975-0 x ZoxSy - 1949'9 (Sy)' - 0, 



hence ^= -0-6128 or +87928. 



ox 



On a Mercator's chart this must be divided by sin 6, which gives 

 the values -31 55''7 and 83 37'' 1 for the directions of the lines. 



