PAPER BY PROF. HELMHOLTZ. 83 



aud if we consider a steady mode of motion, in which il, p, P, and e are 

 functions of x and p only, then the equations (1) become 



yP_yP^O (3a) 



,lf € JX 



^p' p £'?p'p 'p* 



dp'p e'dp'p "'/>*' 

 The two last equations combine into the one following^: 



'l+lj£=% (3&) 



,)/j 6 :\p p^ ^ ' 



Equation 1,, is satisfied by the above adopted values of u, v, w. There- 

 fore the only equations to be satisfied are (3«) and {3b). 



As concerns the value of the density e, this depends upon the pressure 

 p and the temperature 6. Since appreciable eifective conduction of 

 heat is excluded, therefore we must here retain the law of adiabatic 

 variations between p and € ; therefore we have 



P \^ ^ 



Po/^ • 



wherein ;/ again represents the ratio of the specific heats. If we indi- 

 cate by the temperature that the mass of air under consideration 

 would acquire adiabatically under the pressure jh (wherefore 6 indi- 

 cates the constant quantity of heat contained in the air while its tem- 

 perature is varying with the pressure), and if we put 



then we have 





^ * c)P \P J^ ' Po ' ^P^ 



or if, for further abbreviation, we put 



r 



2i^.sR.^'f^=(Z ...... (3c) 



-1 



V— 1 



j)-y=7r (Sd) 



we shall have 



€ dp~'- " dp 



^P=q.d.^, 



