104 Mr. Toppings Account of the Measurement 
Besides this linear measurement , seven essential angles were 
taken (each angle several times over, for security) with an 
excellent theodolite by Ramsden. These were the angles 
formed, at each extremity of the base, by the nearest interme- 
diate flag, and the remote signal ; and those formed at each 
intermediate flag, by the nearest flag to it, on each hand. 
The nature and purport of all this will be easily understood, 
by inspecting the accompanying figure, Tab. III. fig. 1. and 
attending to the following explanation and 
DEMONSTRATION. 
Let N and S represent the northern and southern signals, 
placed at each extremity of the base line NS. 
Let ABCDE represent the positions of the five intermediate 
flags, between each of which, including the two signals, the 
six right lines, before mentioned, were measured. 
At each of these points the angle formed by the flag, or 
signal, on each side of it, was taken with the theodolite: for in- 
stance, at A, the angle formed at that point by the northern 
signal N, and flag B ( 177 0 24' 40") ; at B, the angle formed 
by the flags A and C ( 176 0 23') ; and so on. At each end of 
the base line, the angle formed by the nearest flag and the dis- 
tant signal was also taken ; e. g. at N, the angle SNA, and at 
S, the angle NSE. 
These things being premised, to find the angles the other 
four lines make with the base line, proceed in the following 
manner : — Produce the line NA to K ; also the line BA to H ; 
and, through the point A, draw FG parallel to NS, the base 
line. From the points ABCDE let fall perpendiculars upon 
the base line, meeting it at OPQR and T. 
