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 ABODE 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 By and A b X b B — twice the area of A B b. b B + 
c Cy 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 
