ANGULAR SURVEYING 57 



In applying formulas 3 and 5, the signs of t and g should 

 be disregarded, both t and g being treated as positive. 



EXAMPLE 1. The length of a course is 896.7 ft. and its 

 bearing is N 39 15' W; what are the ranges of the course? 



SOLUTION. Here 1 = 896.7 ft. and G = 39 15'. Since the 

 bearing is northwest, its latitude range is positive and its 

 longitude range is negative. Applying formulas 1 and 2, 

 t = 896.7 cos 39 15' = 694.4 ft. 

 g= -S96.7 sin 39 15'= -567.4 ft. 



EXAMPLE 2. The latitude range and the longitude range 

 of a course are, respectively, 13.71 and 9.38 ch.; find the 

 bearing and length of the course. 



SOLUTION. Since both ranges are negative, the course bears 

 southwest. Applying formulas 3 and 4, 



9.38 



tan G = -, whence G = 34 23', and 

 13.71 



9.38 



l = = 16.61 ch. 

 sin 34 23' 



When, instead of bearings, azimuths are measured, the same 

 formulas hold good, only care must be taken to give the func- 

 tions correct algebraic signs. When the azimuths are reckoned 

 from the north, these formulas give both the numerical value 

 and the algebraic sign of each range. This, however, is not the 

 case when azimuths are reckoned from the south. 



Platting by Latitudes and Longitudes. To plat a traverse 

 by latitudes and longitudes, pass reference lines through a 

 convenient corner and figure the latitudes and longitudes of 

 all the corners of the traverse. The courses are taken in the 

 order in which they were run, the start being made at the 

 initial point. The latitude or longitude of the end of the 

 first course is equal to the corresponding range of that course; 

 the latitude or longitude of the end of the second course is 

 equal, respectively, to the latitude or the longitude of the end 

 of the first plus the corresponding range of the second course; 

 and, in general, the latitude or the longitude of the end of any 

 course is equal, respectively, to the algebraic sum of the lati- 

 tude or the longitude of the beginning of the course and the 

 corresponding range of the course. 



