668 Lieutenant Renny on the Constants of the Barometric Formulce, ^-c. 



Whereas the hygrometric element, £= |(\// ')> acts a very important part in 

 my new correct formulas, I think it advisable to give the means of calculating 

 it. I have given already in the Appendix, page 661, Bessel's excellent and 

 extremely simple equation for calculating the elastic forces (or tensions) of 

 vapour of water, corresponding to temperatures Centigrade, as also Fahrenheit 

 thermometers. I will now give Dr. Apjohn's formula for calculating the elastic 

 forces or tensions of aqueous vapours of the atmosphere, from observations 

 made with the wet and dry bulb hygrometers : — 



Dr. Apjohn's Formula for calculating the Elastic Force or Tension of the Vapour 

 of Water of the Deiv-point of the Atmosphere, from Observations made with the 

 Wet and Dry Bulb Hygrometers. 



Let t be the observed temperature (Fahrenheit) of the dry thermometer. 



Let t' be the observed temperature (Fahrenheit) of the wet thermometer. 



Lety be the elastic force (or tension) of the vapour of water, correspond- 

 ing to the observed temperature t' of the wet thermometer, as ascertained from a 

 sound table of elastic forces (or tensions) of aqueous vapour, or calculated by 

 means of Bessel's equation, or otherwise correctly obtained. 



Let i*^be the elastic force (or tension) of aqueous vapour, corresponding to 

 the dew-point of the atmosphere, being extremely nearly equal to the actual 

 elastic force (or tension) of the aqueous vapour of the atmosphere, and being 

 the unknown quantity to be determined by the formula. 



We have — 



n -f 

 F = f - 0'01135 {t — t') X ^ for temperatures above the freezing-point. 



p - f 



F —f — 0-01014 {t — t') X ' ' for temperatures below the freezing-point. 



N. B. — The character p indicates the weight or pressure of the atmosphere 

 in inches (as determined by a barometer, or otherwise determined accurately) ; 



P -f 

 the value of F is given in inches ; and whereas ■ ^ is seldom much different 



from unity, this quantity may always be omitted, when calculating the value of 

 the hygrometric element {£ = %'/{ff')\- 



