PAPER BY DR. HERTZ. 205 



from one to the next the value of the constant (which is the entropy) 

 increases by the quantity 



0.0025 Cal0rie 



Cels. degree x kilogram' 



These lines therefore appear at equal distances apart from each other. 

 One of them is drawn to the point 0° Cels., and the pressure 760 milli- 

 metres. 



The curves of the adiabatics in the second stage must satisfy the 

 equation* — 



c p \og T-AR log p + j|.r.i = constant .... (/?) 



R 



In this equation -n- is the density of aqueous vapor in reference to the 



air, and therefore is equal to 0.6219. According to Clausius, 



r = 607 - 0.708 ( T - 273) . C . al ° rie . 

 v ' kilogram 



I have taken the value of e for the different temperatures from the 

 table computed by Broch (Travaux. du Bur. Intemat. des Poids et Mes- 

 ures, tome i). The curves run along with feeble curvature from the 

 right hand above to the left hand below. One of these is distinguished 

 by the letter beta (/?). They also are so drawn that the entropy in- 

 creases from one to the next by a constant value of— 



0.0025, Cal0ri6 



Cels. degree x kilogram' 



or the same as before for the alpha system, and so that one of them 

 passes through the point 0° C, 760 millimetres. 



The curves that correspond to the third stage coincide with the iso- 

 therm of 0° C. 



Finally the curves of the fourth stage are entirely similar to those 

 of the second stage, but are not exactly the same, for their formula is 

 derived from that belonging to the second system by substituting r + q 

 for r where q is equal to 80 calories per kilogram. They are distin- 

 guished by the letter gamma (y), and are drawn according to the same 

 rules as alpha (a) and beta (/3) curves. In general the gamma curves 

 are not precise prolongations of the /? system. 



We have now to find some means by which the points of transition 



* Although jx is neglected in comparison with X, still it is questionable whether cp 

 is negligible in comparison with c p X, since c is four times larger than c p . Even al- 

 though within the limits of the diagram ju. does not exceed -fo A, yet the cp, is -fa c v*~ 

 But in meteorologic applications we recall that in these extreme cases the liquid water 

 is not generally wholly carried up with the air. Frequently so large a fraction of it 

 falls from this air as rain that we keep nearer the truth when we entirely neglect the 

 specific heat of the liquid water, rather than to introduce it with full value into the 

 computation. 



