Skating on Thin Ice. 21 



Equating these values in (5) and (9), 



[(1-0)C +,S\]|^[(l H 3)0,+/3\i^ = 0, . (10) 



a differential relation, leading on integration to 



[(l-/3)a+/3\] tog. P + [(l-jS)(V+/SX] log(*-«) 



= a constant, . . . (11) 



reducing to the ordinary adiabatic equation when a,/3 = 0. 

 In the experiments of Noble and Abel, they found 



^=0-57, ^ZL a ==0 -43r T J ^=^- = 1, 3256, (13) 

 v v ' 1—/3 v —a K J 



taking the solid and gaseous products of the same density 

 when fired ; 



\ = 0-45, C p = 0-2324, C„ = 0*1762, . (14) 



making p 



m = 1-074, against y = ^P - 1«33. . . (15) 



Thus 57 per cent of this gunpowder would issue as smoke 

 from the muzzle of a gun. But with modern powder, such as 

 cordite, the solid part of explosion or smoke is insensible, and 

 the index m regains the full value of y. 



The raindrops in the air are the equivalent of the non- 

 gaseous part of the powder gas, and their effect is to reduce 

 the value of 7, and diminish the velocity of sound. 



16. Next treat the air in an unsaturated state as a 

 mechanical mixture of dry air and aqueous vapour, each 

 obeying the laws of the Gas Equation. 



The question has been considered by Professor C. Niven 

 for a mixture of any number of gases, and he gives the 

 formula (Solutions of the Senate House Problems, 1878, 

 p. 66) 



U2 = |^ k_ 



for U the sound-velocity in the mixture, where m denotes 

 the density of a gas, c the S.H. at constant volume, k at 

 constant pressure, and u the velocity of sound in that gas. 



