the Trigonometrical Operation. , . 3 ^_ 
Hence It follows, that fuppofing the refradion to have been 
the fame at, each of the ftations when the obfervations were 
made, half the difference of thefe heights, or - 3 i,8 ~ i8 ' 3 - (, - 
feet, would be the difference between the relative heights of 
the axis at the two ftations ; and that the quantity of refrac- 
tion would be fubtended by half the fum, or 31,8+ i8 ~ 3 - 2 ^ Q 
feet ; therefore, to find the mean refradion, as the diftance of 
the ftations : rad. :: 25.05 feet : tang. 1^23"! the mean 
refra&ion. 
For fuppofing t (fig. 1.5.) to be the true place of the top of 
the flag-ftaff, we fhall then have the angle OKT the depreffion 
+ the angle TK/ the refradion, or $1" + T 23"! = 5' l4 " | 
= the angle OK/. Hence the angle OKT - the angle OKL = 
5 *4 i~S 2 •6 = o / 1 1 !/ .<) — the angle LK/. Now, this laft 
angle, with the diftance of the ftations 61775.3, give L/ = 3.6 
feet, or what the top of the flag-ftaff at Tenterden would be lower 
than the axis at the Knoll; and this being added to 3. 1 feet 
(what the axis at Tenterden was lower than the top of the 
flag-ftaff), we get, as before, 6.7 feet for the height of the 
axis at the Knoll above the axis at Tenterden. 
In like manner, fuppofing k (fig. 16 ) to be the place of the 
ground at the Knoll, we have the fum of the depreflion and 
refradion, or OTK -fKT/r—o' 21" + 1' 22"*=*' rS^x* 
0 «; and OtL-OTfej' j8"|=o' 4 "fi = the 
angle £TL» Hence, kt= 1.2 feet is the height of the ground 
at the Knoll above the axis at Tenterden, which being added 
to 5.5 feet the height of the axis at the Knoll above the 
ground, we have as before 6.7 feet for the difference of the 
heights. 
I i 2 
The 
