the Trigonometrical Operation. 2 39 
contained arc of diftance nearly, one-half of which, or %' 34".?, 
is equal to the angle ODL. 
At the flat ion D, the ground at T was, by obfervation, 
elevated 8" 37" equal to the angle TDO, to which adding 
ODL=2 7 34 /7 .7, we have for the angle TDL n / n / 7 .j . 
Now, if the diftance of the ftations be taken as radius, the 
lines TO, TL, &c. will be nearly as the tangents of their op* 
pofite angles; therefore the angle TDL, with the diftance 
3 r 554*6 give TL= 102.7 fe el b or what the ground at the fta- 
tion T would have been higher than the axis of the telefcope 
at D, if there had been no refra&ion. 
But the axis of the telefcope, when at the ftation T, was 
5.5 feet above the ground ; therefore 102.74-5.5= 108.2 feet 
would be the height of the axis at T above the axis at D. 
Now, let T (fig. 12..) be the place of the axis of the tele- 
fcope, when the inftrument flood at Folkftone Turnpike ; D 
the top of the parapet of the north turret in the Keep of Do- 
ver Caftle ; TO the ho rizontal line ; and CL=ST. 
At the ftation T, the parapet of the turret was by obferva- 
tion deprefled 14' 17T 5 = OTD, from which fubtrading half 
the arc of diftance 34L7, there remains for the angle LTD 
1 1' 42 // .S. This laft angle, with the former known diftance, 
give LD = 107.5 feet, or what the parapet was lower than the 
axis at T, if there had been no refraction. 
But the axis of the telefcope when at D was 3.2 feet above 
the parapet; hence 107.5-3.2=: 104.3 * s w ^ at the axis at D 
would be lower than the axis at T. 
In this cafe it is evident, that half the fum of 108.2 and 
104.3, or 106.25 feet, is the difference of the relative heights 
of the axis at the two ftations by a mean refraflion ; and that 
this mean refraClion is fubtended by half the difference, or 
ic8.2 
