The rule “to ‘swing’ the azimuths to the adjacent quadrants” as stated on page 485, and to reverse the columns of the traverse tables as required in the last paragraph of page 486, may be a “ rule of thumb ” to obtain the result, but it does not show the “ reason why.”
From the figure given above, the deductions of the same formulae are clearer and simpler and at the same time the reasons for the operations are apparent.
After having found the azimuths and then the directions (α1 and α2) of the altitude differences, and their values (h1 and h2) ; and after having plotted them and their lines of position—draw through the assumed point (B), the lines BM and BN, parallel to the lines of position—thus forming the parallelogram BMZN.
The quadralateral BCZE is formed by the altitude differences (h1 and h2) and their lines of position.
In the quadralateral BCZE
angle CBE = difference in direction of h2 and h1
= α2— α1 = Α