56 ANGULAR SURVEYING 



Thus, the latitude and the longitude range of PQ are, respect- 

 ively, +PD and +DQ; those of QP are QE and EP. 

 Likewise, the latitude range of PiQi is PiDi, because the 

 end of the line is south of the beginning. The longitude range 



_ is +DiQi, because the end of the line is 



east of the beginning. These values may 

 be verified by observing that the latitudes 

 of Pi and Qi are, respectively, HiPi 

 and HiDi, whose algebraic difference is 

 -HiDi-(-HiPi) = -HiDi+HiPi= -Pi 

 Di; and that the longitudes of Pi and 

 Qi are, respectively, -\-Hi'Pi and -\-Ki'Qi, 

 whose difference is equal to DiQ\. 



General Formulas. Let AB, Fig. 2, 

 be a course whose length is I and whose 

 bearing is G. In the right triangle A MB, 

 FIG. 2 j n w hich AM is the direction of the 



meridian through A, the latitude range AM and the longitude 

 range MB are denoted by t and g, respectively. According to 

 trigonometry, 



t = lcosG ' (1) 

 g = /sinG (2) 



These formulas serve to compute the ranges when the length 

 and bearing of the course have been measured. Special care 

 should be taken to give t and g their proper signs, t being 

 positive when G is north (that is, either northeast or north- 

 west), and g being positive when G is east (that is, either 

 northeast or southeast). When G is south (that is, either 

 southeast or southwest), t is negative; and when G is west 

 (that is, either northwest or southwest), g is negative. 

 If t and g are given, G is found by the formula 



tanG = - (3) 



and I by either of the formulas following- 



(4) 

 /= VP+* (5) 



