60 



ANGULAR SURVEYING 



to the right for positive longitudes, and to the left for negative 

 longitudes. The polygon ABCDEFA formed by joining the 

 points, A, B, C, etc., is the required plat of the field. 



Determination of Areas by Longitudes and Latitudes. The 

 longitude of a course is the longitude of its middle point. The 

 double longitude of a course is twice its longitude, and is equal to 

 the sum of the longitudes of the extremities of the course. 



In Fig. 4, SN is the refer- 

 ence meridian, K, L, and Q 

 are the middle points, and 

 KiK, LiL, and QiQ are the 

 longitudes of the courses 

 AB, EC, and FA. 



The calculation of the 

 area of a closed field re- 

 quires that all the double 

 longitudes be determined. 

 This can be done by apply- 

 ing the following principle: 

 Principle. The double 

 longitude of any course is 

 equal to the algebraic sum of 

 the double longitude of the 

 preceding course, the longi- 

 tude range of the preceding 

 course, and the longitude range of the course considered. 



To apply this principle, note that the double longitude of the 

 first course AB is equal to BiB which is the longitude range 

 of that course. As a check on the accuracy of the work, it 

 should be noted that the double longitude of the last course is 

 equal to its longitude range, but has the opposite algebraic 

 sign. 



After the double longitudes of all the courses have been 

 calculated, the area of the field may be found by the following 

 rule: 



Rule. Multiply the latitude range of each course by the double 

 longitude of the course, giving to the product its proper sign accord- 

 ing to the signs of the factors. Add these products algebraically 

 and divide the sum by 2. 



FIG. 4 



