the mean Denjity of the Earth. 767 
divisions to perform : alfo a great part of the tangents are 
fo fmall that they do not at all differ from their corref- 
ponding fines in the number of decimals that it is necef- 
fary to continue the computations to, in all which cafes 
the trouble of finding the differences is faved; and thofe 
differences which it is neceffary to compute, are very 
readily found by infpedfion on a peculiar kind of Hiding 
rule, which was conftructed for this purpofe, and of 
which I fhall here give a ihort defcription. 
This rule (the figure of which is reprefented tab. x. 
fig. 2.) confifts of three columns; one marked af or 
bafe, which is moveable by Hiding it up or down by the 
fide of the other two which are fixed ; of thefe two the one 
contains the perpendicular altitudes or depreffions, and 
the other the differences between the fines and tangents 
to the radius 1 . To conftruft the numbers on this rule; 
form a feries of logarithmic tangents in arithmetical pro- 
greflion, of which the firft term is 9*000, and the com- 
mon difference *025; take out from a table the cor- 
refponding natural tangents, and place them in the firft: 
and fecond columns of bafe and perpendicular, and the 
difference between the natural fine and natural tangent 
in the laft column,, marked Diff. To make ufe of this 
fcale ; look out any bafe and its correfponding perpendi- 
cular in their proper columns, that is, any radius and its 
cor? 
