34° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 



but for adiabatic change 



or 



o = c p dt — Avdp 

 c p dt = Avdp (1) 



But the diminution of atmospheric pressure with altitude, or the 

 baro-hypsometric formula follows from the equation 



dp = - pdh (2) 



where p is the weight of the air contained in a unit volume, and h 

 is the altitude, and where we assume that at the point under con- 

 sideration the force of gravity has its normal value or that the column 

 of air is located at latitude 45 and that the change of gravity with 

 altitude may be neglected. 



Since now according to the definition here adopted the unit of 

 weight is the weight of the unit mass, therefore p is the mass of the 

 air contained in the unit of volume, hence 



1 



v = 



P 



Hence Ave can write the equation (2) in the form 



dh = '- v d p . (2a) 



and now by combination with equation (1) we obtain for the diminu- 

 tion of temperature with altitude the well-known formula 



dt = - A dh (3) 



c p 



or after substituting the numerical values 



dt - - 1 dh = - 0.0099 dh. 



424 X 0.2375 



If now, on the other hand, we ask as to the work necessary to lift 

 the unit mass, then under the assumption above made, that the 

 weight of the unit mass is the unit of weight, 8 we have the equation ■ 



L = h or d L = dh 



5 In the metric system, the mass of a kilogram is the unit of mass, its 

 weight under normal conditions is the unit of weight and the kilogram- 

 meter is the unit of work. 



