the Trigonometrical Operation. 197 
Now, by proceeding as directed above, we get GK =r 
460423 2. 9, AK= 2980006.3, and AH = 2841 2.2fathoms. Hence 
the angle AHK = 1-3.5° 4 $' 20". od, and KH = 2979745.4 
fathoms; whence HT= 141.37 fathoms, This, with AH, 
and the included angle AHT = 44 ° * 4 ' 39" - 9 2 (the comple- 
ment of AHK.) give the angle TAH- 1 T 58". 9 , the difference 
between the horizontal angles on the fphere and fpheroid. 
Hence the obferved angles at A and B would be 43° 5 T 48". 2 
+ ii' 58 // .9 = 44° 3 ' 47 "- and *35 45 ' 1^.2-iT 58A9 
=1 35 ° 33 ' i 7 " 3 - — 
If the figure is an ellipfoid having the fame axes, the angle 
TAH will be found = 8 / 4T4. 
It may be remarked, that the angle TAH, or the horizon^ 
tal angle TAK, diminifhes or augments as the point obferved 
in TB is elevated or depreffed ; this variation is however too 
fmall to be worth attending to in practice, as may be (hewn in 
the following manner. 
Let the fpheroid be M. Bouguer’s (becaufe the difference 
will be greater than on an ellipfoid) ; and let the points A, B, 
fig. 3. have the fame latitudes and difference of longitude as 
above ; alfo, let BT be the flag-ftaff, and through B draw 
GBn. 
Now, if we fuppofe B to be in the horizontal line nearly* 
the horizontal angle at A, taken between the north part of the 
meridian AP and the flag-ftaff at B, will be the angle BAP, 
the telefcope in this cafe being pointed to B, and the vertical 
plane which it would then move in is the plane nBGA ; but if 
the telefcope is directed to fome pointT in the flag-ftaff above B, 
the angle TAP in this cafe will evidently be lefs than it was 
in the former by the angle n AT nearly; and.confequently.it 
diminifhes as the obferved point T is elevated ; and it is alfo 
a evident. 
