Trigonometrical Survey. 485 
hypotenuses, or the corrections for reducing them 
to the plane of the horizon, is 20,916 feet ; 
and this subtract - — 20,9 16 
3 6 574»9°v 
The sum of the corrections, for the reduction of 
the several horizontal lines from the height of the 
different hypotenuses above the centre of the earth, 
to the height of Beacon Hill above ditto, is 0,521 
feet ; this add - + °> 5 °i 
Therefore the apparent length of the base, as re- — — - — — 
duced to the level of Beacon Hill, is - feet 36575,401 
But it will be hereafter shown, that the height of Beacon 
Hill above the sea is 690 feet nearly, and that of King’s Arbour 
118, and of Hampton Poor House 86 feet ; therefore the height 
of Beacon Hill above the mean point between. King's Arbour 
and Hampton Poor House, is 588 feet, or 98 fathoms. 
Now as the base thus reduced, may be supposed to have been 
measured 98 fathoms farther from the centre of the earth, than 
that on Hounslow Heath, it must be reduced to the same level. 
Therefore if we take 3481794 fathoms for the mean semi-dia- 
meter, and add 98 fathoms to it, we shall get the length by this 
proportion, viz. 3481892 : 3481794 :: 36575,4 : 36574,4, 
the length of the base nearly. 
With respect to that step by which the base is reduced to 
the level of Beacon Hill, or the correction 0,501 foot is ob- 
tained-, it will be proper to show on what principle it is 
founded. 
sR 
MDCCXCV. 
