[ 2 4 r J 
The third of the annexed tables, fhews the quantity 
of this correction correfponding to every value of n 
from i° to 70°. The third column, to the right, exhi- 
bits the value of it in Englifh fathom, in that parti- 
cular temperature of the air, in which the difference 
of the tabular logarithms, of the heights of the quick- 
fdver in the barometer, gives the difference of ele- 
vation in iooothsof an Englifh fathom. What that 
temperature is, will be determined in the fequel. 
It is to be obferved, that the value of thefe correc- 
tions, in the fathom of any other country, will be 
the fame, in that particular temperature, in which 
the tabular fyftem meafures the difference of ele- 
vations in ioooths of the fathom of that country. 
The rule, which I have given for applying this 
correction, fuppofes that it is previoufly known, which 
of the two ftations is the higheft ; otherwife it will 
be doubtful, whether it fhould be added or fub- 
traded. This doubtful cafe may actually happen in 
levelling a conliderable trad of country, that is 
pretty even. The table, however, will ftill give the 
quantity of the corredion. Add that quantity to the 
logarithm of the height of the cooler barometer ; and 
the difference between this logarithm, fo augmented, 
and the logarithm of the height of the other, is the 
difference of the logarithms of the obferved heights, 
duly correded : and the ffation of the cooler ba- 
rometer, was the lower of the two, if its augmented 
logarithm exceeds that of the other: in the con- 
trary cafe, the higher. 
It hath been already obferved, that the change 
of the denfity of quicldilver, by an alteration of its 
heat, muff always be proportional to the increafe 
Vol. LXIV. I i or 
