766 Mr. hutton’s Calculations to af certain 
fore be found by barely dividing the given perpendicular 
by the bafe; and if we find this number in its proper 
column in a table of fines and tangents, on the fame line 
with it, in the column of lines will be found the fine of 
the angle required. This feems to be the eafieft way of 
refolving all the triangles when computed feparately. 
But as the labour would be very great in performing fo 
many hundreds of arithmetical divifions, &c. either by 
logarithms, or by the natural numbers, inftead of it, the 
following method, propofed by the Hon. Mr. cavendish, 
was adopted, as being a much more expeditious way of 
obtaining the fum of the fines required. This method 
conlifts in finding, in a very eafy manner, the difference 
between each tangent and its correfponding fine, from 
the given bafe and perpendicular, and then, fubtradting 
the fum of all the differences from the fum of the tan- 
gents, there remains the fum of the lines. Several ad- 
vantages attend this method of proceeding : for, to find 
the tangents we need not divide every perpendicular fe- 
parately by its correfponding bafe, but add together all 
the perpendiculars that are on the fame line, and divide 
their fum by their common bafe, which is the radius of 
the middle of the ring, and is placed on the fame line 
with them towards the right-hand; for thus we fhall 
have little more than a twelfth part of the number of 
divifions 
