meafuring Heights with the Barometer. 741; 
may take at 40°, the Englifh meafure being ufed, the 
common error in the refult will be equal to the fum of 
the two equations, 2.1 + 2.45 = 4.55 for each degree; 
which amounts to ^ pai+s for the 8° that the zero is too 
high. Above 40°,the former error ^ will be augmented 
by the difference of the equations for each degree that 
the temperature is above his zero, viz. 2.45- 2.1 =^l.. 
In either cafe it is to be obferved, that the progreflive 
rate of equation for the heat of the quickfilver is not 
here taken into the account; becaufe it will not produce 
any material difference, unlefs one barometer is much 
hotter than the other, at the fame time that their verti- 
cal diftance is very great. Thus the gad degree of Fah- 
renheit, or freezing temperature, which is fundamen- 
tal in all thermometers, happens, fomewhat remarkably, 
to be the zero of the fcale, when the Englifh fathom 
bears fuch proportion to the modulus of the common lo- 
garithms, as that their difference, in computing heights 
by the barometer, brings out the refult in fathoms. No 
other proportion of a meafure will do it: for if we fup- 
pofe twenty-four of different lengths, between ours 
and the French toife, each furpafling the othei by riSho 
of that toife, the zero of the fcale, in computing heights 
by thefe meafures refpedtively, will afcend a ffngle de- 
