386 NEWTON S PRTNCIPIA. 



Suppose we reject the effect of changes of temperature, 

 we have, by Boyle s law, p = x p, whence the expression 

 (1.) easily gives 



log 6 - - - (3.) 



MM. Barre de Saint Venant and Wantzel * have under 

 taken the task of testing these expressions by actual experi 

 ment. They have pointed out that the formula (3.) could not 

 possibly be accurate, for it gives the velocity of efflux a 



P 

 maximum when p- = 60653, so that the velocity would 



actually be less the smaller the quantity of air in the vessel 

 A , provided it be less than a certain quantity. The velo 

 city would vanish when P = 0, which leads to the ex 

 traordinary result that a gas cannot rush into a vacuum. 

 If in order not to neglect the changes of temperature, we 

 put p = K f, we get the expression 



;. AS;. 



\f \ 



V m \ -- 



V //* I T~^ 



^ 



If we knew the values of p and y this would no doubt give 

 accurate results. But when we substitute p P , we 

 are led to results as absurd as those we have just mentioned. 

 The truth is, that, other things being the same, the velocity 

 of efflux of air by an orifice is always greater the more 

 the pressure in one vessel exceeds that in the other. So 



P 



long as p- is not greater than -3 or *4, the efflux or the 



quantity of air that has flowed out in a unit of time is 

 sensibly the same ; that efflux diminishes slowly at first, 

 more quickly afterwards, as the pressures approach 

 equality, and it becomes nothing after a finite time, when 



* Comptes Rendus, vol. ix. and xvii. 



