686 Col. Roy s Experiments for 
to 20; the 15th inch being half of the obferved expan- 
llon. The five next columns towards the right, compre- 
hend the additive equation for condenfations, anl'wering 
to o°, 12 0 , and 22 0 , with their intermediate differences; 
thofe that are progreffive, as aiiiing from difference of 
tempei'ature, being ranged horizontally; and thofe that 
are arithmetical, as depending on the height of the ba- 
rometer, being placed vertically. The temperature of 
3 2 0 requires no equation, and the thirteen columns from 
thence towards the right hand, contain the lubtradfive 
equations for expanfion, correfponding to every io° as 
far as 102°, with their progreffive and arithmetical dif- 
ferences ranged as before. By means of thefe differences, 
the equation for intermediate temperatures may readily 
be taken out by infpedtion. Hence is deduced the firft 
part of the rule for meafuring heights by the barometer. 
When the temperature of the quickfilver is below 32 0 of 
Fahrenheit, add the correfponding equation for con- 
denfation to the obferved heights of the columns reflec- 
tively; when above 32 0 , fubtradt the equation for expan- 
fion from the obferved heights of the columns refpec- 
tively; with which equated heights of quickfilver, ex- 
preffed in 1 oooth parts of an inch, the tables of loga- 
rithms are to be entered. 
Table 
