PAPER BY PROF. HELMHOLTZ. 83 



and if we consider a steady mode of motion, in which £1, p, P, and s are 

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



.£-M*-0 (3.) 



dX £ JX v ' 



-^l y.-^^u =-y f^L 



dp' p e'dp'p V 



_dP z__l dp z_ £X 

 dp'p e'dp'p ' p^ 



The two last equations combine into the one following : 



Jt + ?Tp-l? {b) 



Equation 1, ( is satisfied by the above adopted values of u, v, u: There- 

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



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

 p and the temperature 8. Since appreciable effective conduction of 

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

 variations between p and e ; therefore we have 



a> 



p \ I _ e 



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

 cate by 8 the temperature that the mass of air uuder consideration 

 would acquire adiabatically under the pressure p (wherefore 8 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 



e'dp\pJ r 'Po 'dp' 

 or if, for further abbreviation, we put 



X - y =a ( 3c ) 



JL^.&.p r =q 



' — 1 



Y 



P y =7t 



we shall have 



. . • (3d) 



1 dP a 1* 



6 dp l dp 



