Of BAROMETRICAL MEASUREMENTS. 115 



fathoms, which muft be nearly true ; and, if we call A 

 the height, or the value of z, computed from the formula 



z P\ l + m ( r ))%--jr, the correction to be applied on 



account of , will be Alog.bfi. 



2 



30. IT is not, however, now a matter of indifference in what 

 meafure the lengths of the columns of mercury in the baro- 

 meters are exprefled, as it was, when only the ratios of thefe co- 

 lumns entered into the computation. They muft be exprefled 

 in terms of the fame meafure, wherein the height of the moun- 

 tain is required, and wherein q has been already determined. 

 For, if we take the exact expreflion for the height, 



I 



t 



MS r-^-A or that to which it may be re- 



H r hr ' * 



(l rri) (i ffz) 



duced, z = 



- ~ h is evident > 



n 



that can have no definite fignification, unlefs ^, (3, 



n n 



(3 nb 



and q be all exprefled in terms of the fame meafure. As the 



i+n 



conveniency of computation requires that p or q fhould be ex- 

 prefled in fathoms, fo b and P muft alfo be exprefled in parts 

 of a fathom. The fame is true of the logarithmic expreflion, 



log.b$, to which the preceding one is reduced. Thus, if 



b 30 inches, and (3 = 20 inches, we muft make b , 



P a. and 



