COMPUTATION AND OFFICE WORK 39 



the three trapezoids b B C c, c C D d, and d D E e. 

 The area of these trapezoids and triangles is easily com- 

 puted from their dimensions. All that is necessary is to 

 express those dimensions clearly in terms of latitude and 

 departure. 



One dimension of these figures, the altitude, is the lati- 

 tude of the course in question. Thus for the triangle A B b, 

 the altitude A b is the latitude of the course A B, and in 

 the same way e A, the altitude of the triangle A E e, is the 

 latitude of E A. These latitudes, it is to be noted, are 

 negative and, to correspond, the areas of A B b and of 

 E A e are to be deducted from b B C D E e to give the area 

 of A B C D E which we are after. B m, the altitude of 

 the trapezoid b B C c, is the latitude of the course B C and 

 is positive. D n and E o have the same relation to the two 

 succeeding courses. 



The bases of these triangles and trapezoids are clearly 

 related to departure, b B is the departure of the course 

 A B, and A b Xb B = twice the area of A B b. b B + 

 c C, the two bases of the trapezoid b B C c, = twice the 

 departure of A B + the departure of B C. c C + d D 

 = the same expression as the last + the departure of B C 

 + the departure of C D, which last, however, being west- 

 erly, is reckoned negatively. Now a general expression 

 for these values is double meridian distance, meridian dis- 

 tance being perpendicular distance from the meridian. 

 The D. M. D. of a course is the sum of the meridian dis- 

 tances of its two ends. For a course starting on the me- 

 ridian it equals the departure of the course. For any 

 succeeding course it equals the D. M. D. of the preceding 

 course plus the departure of that course plus the departure 

 of the new course, easterly departures being reckoned as 

 positive and westerly departures as negative. 



A check on the reckoning of the D. M. D.'s is in the 

 last one, which should be numerically equal to the de- 

 parture of the last course. 



These elements for convenient working out of the area 

 surrounded by a closed survey are embodied in the follow- 

 ing rule : Twice the area of the figure enclosed by a sur- 

 vey is equal to the algebraic sum of the products of the 



