Of BAROMETRICAL MEASUREMENTS. 99 



D = - ;r^j j and, for a like reafon, A = - ^y There- 



(i m) (i ni) 



fore, log.D = log.b (r H}g, and /o^.A = log.$+(r h}g. 

 Hence log.D /C^.A = log.b log.$+(Hh}g, and fubftituting for 

 log. D log. A in the formula of the laft feclion, 



_ 



H-r h-r 



(i m) (i m) 



1 6. THIS is the exacT: value of z, or of the whole height to 

 be meafured, on the fuppofition that the heat of the atmofphere 

 decreafes uniformly as the height increafes ; and that the con- 

 tradlion for a given difference of heat decreafes according to the 

 law defcribed in 5. But, in order that it may be more con- 

 venient for computation, and may be more eafily compared 



with the formula now in ufe, the quantity - jj 



muft be reduced into a feries. Now 



(i TW) (i m) 

 rr - r 



Hr a r 



TO) (i m) 



(im) - ^ g u( . f rom ^g nature O f logarithms, (g being, 



H h 



(i m) (i m) 



as before, the logarithm of i m) 



H H*g* #V 



~ - + - + &c- And 



(i = ! bj feff. Therefore 



H 



N 2 and 



