Meafuremmt of a Bfe on Ho un flow -Heath. 421 
The computed numbers in the feventh column are the 
reductions * depending on the aforefaid heights, or the dif- 
ferences between the hypothenufal diitances of 600 feet each 
and the reduced bale diftances. With regard to the remaining 
columns of the table, or thofe towards the right-hand, they 
will be feverally fpoken to hereafter,- in taking into confidera- 
tion the expanlion of metals, as determined with great accu- 
racy by the experiments with the pyrometer. 
Hitherto no ufe had been made of the tranfit inftrument : 
for, in order that it might be applied to advantage, there was 
a neceliity for laying the wheel into the ground at the lower 
end of the bafe, and fo to modify the St. George’s flag-ftafF 
that, being placed in the pipe, it might be headily fupported 
by braces in a true vertical pofition ; which we found, from 
experience, could not be effeCted by ropes only. 
The wheel being accordingly laid in its place, and the other 
precautions taken for fecuring the flag-ftaff, which was like- 
wife painted white, that it might be more diftin&ly feen from 
The reduction in the feventh column, I have computed by the difference 
between the fquare of the hypothenufe, adhialiy meafured, and the fquare of 
the height found by the level ; and Lieut. Colonel Calderwood has done the fame 
thing by a much fhorter method. Thus, in the annexed 
figure, CE being the hypothenufe of 600 feet, DE the 
perpendicular height obtained by levelling, DB the re- 
duction required, or the difference between the hypothe-J 
nufe and true bafe; then, fubftituting the chord BE in-A 
ftead of DE, the following analogy is obtained; AB : BE:: 
BE 2 
BE : DB ; confequently, ~ DB : that is, the fquare of the perpendicular 
height being divided by double the diftance, or 1200 feet, the quotient is equal to 
DB the reduction, without fenfible error. For if DE were four feet, the greateft 
perpendicular height in the bafe, BE the chord would only exceed it which 
would not be more than 4^^ part of an inch. The difference between the refults, 
by the two modes of computation, is fo trifling as not to deferve notice. 
the 
