Of HA ROME TRICAL MEASUR EMENDS. 1 23 



the different corrections that have been inveftigated. We muft, 

 therefore, recollect, that the coefficient p is the length of a co- 

 lumn of mercury, which, preffing on air of the temperature r, 

 would give to it the denfity of mercury, (which is denoted by 

 unity), fuppofing, at the fame time, that the denfity of air is as the 

 force comprefling it. Hence p is likewife the height of a homoge- 

 neous column of air, of any denfity whatever, which, by its pref- 

 fure, would make air of the fame denfity with itfelf ; or it is 

 the height to which the atmofphere would extend above the 

 furface of the earth, if it were reduced to the fame denfity 

 throughout, which it has at the furface of the earth, when it is 

 of the temperature r. It has been" found by experiment, that, 

 when r = 32, p is nearly equal to 4342.94 8 fathoms, which 

 number is the modulus of the tabular logarithms multiplied by 

 10000. This determination, however, is only to be confidered 

 as approaching to the truth, if we are to have regard to the fol- 

 lowing corrections. Inftead of />, in fome of thefe inveftigations, 

 we have ufed q to denote the height of a column of mercury, 

 which, fuppofing the condenfation of air to be as the power 

 i + of the comprefling force, would, by its preflure, give to 



air the denfity of mercury, or the denfity i; q cannot differ 

 much from/>, but its precife length is to be determined only by 

 experiment. In what follows, p is put for the numeral coeffi- 

 cient, whatever it may be, by which the formula muft be mul- 

 tiplied to give the height in fathoms, or in any known mea- 

 fure. 



THE expansion of air for one degree of heat, the temperature 

 being 32, and the height of the barometer 29.5 inches, is 



m .00245 nearly, f* is the exponent of a power fuch that 



& 



39.5 being denoted by y, x m =. the expanfion for one 



^ 

 y 



degree of heat, when the mercury in the barometer (lands at 

 (3. The value of /* is not certainly known ; it is probably be- 



tween 



