[ *59 ] 
the repulfion of the quickfilver by the glafs 
tube, from air and moifture admitted into the 
tube, and from the variations of the denfity of 
quickfilver by heat and cold ; another very con- 
fiderable error arofe, in calculating heights from 
the barometer, by not allowing for the changes 
of the denfity of the air, whole gravity affords 
us this meafure of heights, owing to heat and 
cold. The firft caufe of error, that of the repul- 
fion of the tubes, he remedied, by fubftituting a 
fyphon-barometer infiead of the fimple upright 
tube, the repulfion of the two legs of the fyphon, 
counteracting itfelf;' the error arifing from air and 
moifture in the tube he cured by boiling the quick- 
filver, after it was put into the' tube, and other 
precautions; the errors, in the eftimatton of the 
heights, arifing from the changes of the denfity 
of the quickfilver, and denfity of the air by heat 
and cold, he fliews how to correct by allowances 
depending on two thermometers, one attached 
to the frame of the barometer itfelf, and the other 
made to be expofed to the open air, to Ihew its 
degree of heat ; which thermometers are to be 
noted both at the top and bottom of the hill. 
Laftly, by a great number of experiments made 
with accurate barometers and thermometers of h s 
own conftrudtion, he has deduced a rule for cal- 
culating heights of places ; the exaCtnefs of which 
he has fufficiently proved by a large table of ex- 
periments. But this rule is exprefled in French 
meafure, and is adapted either to a thermometer, 
whofe f reezing point is o, and that of boiling water 
80, or to thermometers of particular fcales. It 
may 
