1858.] On Jlypsometrical Measurements. 343 



both which depend on t, the half sum of the temperatures at the 

 two stations, so that we may write t = \ ( t -f t') — 32°, t and 

 t' being the temperatures of the air at the lower and upper stations 

 respectively in degrees Faht. The values of log A and log C are 

 tabulated in the first table at the end of this with the argument 



i (t + to 



The whole factor dependant on the humidity of the air may be 



written — 



1 

 C = — — . 



a + a' 



1 — c. 



</(BB') 



and its logarithm is given in Table II with the argument- 



C (a + a') 



Los: 



For the term giving the correction for latitude we may write— 

 1 1 



(g) 1 — 0.0026257 cos. 2 X 

 and tabulate log G for the different values of A, as in Table III. 

 Then :— 

 Log {Ji — li) = log (log B — log B') + log A + log C + log G. 



And lastly from Table IV a small correction due to the decrease 



h ,% 



of gravity above the sea-level is found, and the quantity there 



r — li* 

 li 



given, is to be added to li f — h, and the value of is to be sub- 



r — h 

 tracted, giving 



Ji' 2 W 



IV — H = h' — h + , 



r — n' r — li 

 for the true difference of altitude of the two stations in feet. 



In using the tables, it must be observed that t and t' being the 

 temperatures of the mercury at the two stations and b, V the 

 observed heights of the barometer, 



Log B — log B' = log b — log V — 0.0000435 (r — r) 



2x2 



