rneafuring Heights with the Barometer . 683 
ConJiruBion and application of the table of equation, for 
the expanfton of the quickfilver in the tubes of baro- 
meters. 
Ia the introduction to this paper there was occafion to 
remark, that in the application of the barometer to the 
meafurement of heights, various modes of calculation 
had been adopted. The eafiefl and bell method feems 
however to be, by means of the tables of common loga- 
rithms, which were firft thought of by Mr. mariotte, 
and afterwards applied by Dr. halley, Mr. bouguer, 
Mr. de luc, and others. They have all proceeded on 
the fuppolition, that air is a truly homogeneous and elas- 
tic fluid, whofe condenfations being proportionable to 
the weights with which it is loaded, its dilatations are in 
the inverfe of the weights; and in confequence of this 
law, that the heights of the atmofphere afeended, are in 
geometrical progreflion, while the correfponding fuc- 
ceffive defeents of the quickfilver in the tube of the 
barometer, are in arithmetical progreflion. 
Mr. de luc makes ufe of an arithmetical or uniform 
equation for the heat of the quickfilver in his barome- 
ters, whereby their relative heights are reduced to what 
they would have been in the fixed temperature of 54°^ 
4 T 2 of 
