453 
Trigonometrical Survey. 
between the chords, the spheric angle will be represented by a , 
and the angle between the chords by A = a -j- da\ and d a 
= i't>k a • H ~ h — \t,\a .vs, H + h—vs, da.'t,a (if D,d 
represent the arcs to the chords) = \ 't,\a .vs, ^ (D ~ 
— \t, \ a . vs, \ (D d) — vs,d a .'t,a\ 
A — a — [\t,\ a .v i,{D + d — \ 't,\a .vs \ D ~ d) —vs, 
da .'t, a; where the last term will change its sign to affir- 
mative, if a is greater than go°. If the answer is required in 
seconds, the correction must be multiplied by 206265, the 
number of seconds in an arc = radius. The calculation will 
be easily made by logarithms. 
Practical Rule. 
The practical rule deduced from the above conclusions is 
the following, and given in the words of the Astronomer 
Royal. 
“ To the constant logarithm 5,0134 add L . t, \a and L . 
“ v s D -fi d ; the sum diminished by 20 in the index is the 
“ logarithm of the first part of the value of d a in seconds, 
“ which is always negative. To the constant logarithm 5,0134 
“ add L .t',\ a, and the sum diminished by 20 
“ in the index, is the logarithm of the second part in seconds, 
“ which is always affirmative. These two joined together, ac- 
“ cording to their proper signs, will give the approximate value 
“of da. To its logarithmic versed sine, add L .t', a and con- 
“ stant logarithm 5,3144, the sum, diminished by 20 in the 
“ index, will be the logarithm of the third part in seconds, 
“ which will be negative or affirmative, according as a is less 
“ or more than 90°. This applied according to its sign, to the 
3 N 2 
