SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 417 



of heat consumed in the expansion (a r) of the air for an elevation of 1° of temperature ; 

 that is, 



whence 



or 



whence 



Since, however, 



^ _ ^ _ 1 i'oPo _ -R 



- =c„ 



(iQ = Cpdt— - V dp. 



BT 



and for Cp generally c is written, there results the important equation given in the 

 text. 



No. 3, p. 23. So far as the change of the intensity of gravity with altitude can be 

 neglected, J is, indeed, an absolute constant ; but the unit of weight, the kilogram 

 with which we measure J, needs a correction for gravity. 



No. 4, p. 24. The weight P of dry air in a cubic meter is 



w:here So is the specific gravity of the air, i is the barometric pressure, e is the tension 

 of vapor. The weight of the aqueous vapor is 



P = 0.623 — ^ . ' . 

 1 -\- a t /60 



The sum of both weights gives the weight of a cubic meter of moist air : 



^o h- 0.377 e 



P + p 



760 1 + a *. 



The volume of the unit's weight (kilogram) of this air is therefore — — And since 



o \ a / P+p 



in the unit of volume (a cubic meter) there are contained p kilograms of aqueous vapor, 



therefore in the volume occupied by a kilogram of moist air there is contained 



— -^ — = 0.623 = ^ kilograms of aqueous vapor. 



P-\-p h - 0.377 e ^ ^ 



No. 5, p. 29. Zeuner, in the second edition of his " Grundziige der mechanischea 

 Warmetheorie," gives a table of the values of ^ . — (Table I a, column 5) for each 5°, 



and computed by Regnault's formula. For the temperatures that we here have to do 

 with, the formula of Magnus agrees com^iletely with that of Regnault, but the latter 

 gives a complicated and inconvenient expression for our quotient. 



No. 6, p. 30. I have given a slightly different form to this equation, and have 

 introduced the constants used throughout this essay. I consider it unnecessary to 

 give the process of deduction of this formula, since the work of Reye, "Ueber die Wir- 

 belstiirme," is easily accessible to every reader, which is not true of the treatises of 

 William Thomson and Peslin. 



No. 7, p. 32. This conclusion is limited by the limit of applicability of the Mariotte 

 law at high and low pressures. Since by the recent investigatious of Liljestriim and 

 others it is made probable that the Mariotte law loses its rigid exactness at low press- 

 ures, it follows that we ought not to apply to very low pressures any formula that is 

 founded upon it. All theoretical conclusions as to the height of the atmosphere and 

 27 S 



