7 68 Mr. hutton’s Calculations to afcertain 
correfponding altitude or depreffion in the fixteen fore- 
going tables, without regarding the number of places 
they contain, and bring them to correfpond; then, if 
they confift of the fame number of places, the lower in- 
dex on the Aider or firft column, or that anfwering to 
100 0, points to the true difference between the fine and 
tangent in the laft column; but if the number of places 
in the bafe exceed that in the perpendicular by one, the 
upper index too muft be ufed. And in this manner 
were computed all the differences which were neceffary 
to be found, and placed in their proper fquares formed 
by the meeting of the horizontal and vertical lines, or 
rings and fedloral fpaces, in the following fet of fixteen 
tables, which correfpond to the foregoing fet of fixteen, 
each to each, according to the number of them, and 
marked at the tops with the numbers i, 2, 3 See. to 1 2 
for the fefcoral fpaces, and with the number of the rings 
on the left-hand margin. Alfo, in the column imme- 
diately after the number of the ring are placed the radii 
which formed the laft column in the preceding tables ; 
then, in the third column, are placed the fums of the al- 
titudes and depreffions found in each line of the former 
tables ; and, in the next column, the quotients found by 
dividing the numbers in the third by thofe in the fecond 
column; thefe quotients are the fums of the tangents 
belonging 
