188 On the Flow of Elastic Fluids through Orifices. 



we npw remove the stopper from the orifice at C, the column of 

 mercury in the tube m will instantly subside to a point which 

 indicates the difference between the density of the atmosphere 

 and the density in the chamber when an equal quantity of air 

 flows through the two orifices; while at the same time the col- 

 umn of mercury in the tube n will only have began to subside 

 very slowly as the density in the receiver increases. Having 

 noted the height of the barometer at the time of the experiment, 

 if we note the simuhaneous heights of these two cohimns of 

 mercury, and deduct them respectively from the height of the 

 barometer, we shall have the density in the chamber necessary 

 to an equal flow through the two orifices under the relation 

 which subsists at the moment of notation between the density in 

 the receiver and the density of the atmosphere. And if we note 

 the simultaneous heights of these columns at various times during 

 the filling of the receiver, so many densities in the chamber shall 

 we find corresponding to different relations of the other two 

 densities. 



At the time of the experiment the height of the barometer, or 

 density of the atmosphere was thirty inches. In consequence of 

 leaks in the receiver, I was unable to exhaust it so as to raise the 

 column in the tube n higher than twenty-six inches. I noted 

 the simultaneous altitudes of the two columns at the moment 

 when the column 7i coincided with each successive inch-mark 

 upon the graduated rod, and thence ascertained the densities in 

 the chamber under twenty-six different relations between the 

 density in the receiver and that of the atmosphere. These re- 

 sults I have placed in the table beyond, in which the first col- 

 umn shows the densities in the receiver at the times of nota- 

 tion, and the second the densities in the chamber corresponding 

 thereto. 



In order to ascertain what these densities should have been ac- 

 cording to the old theory, I constructed a formula as follows. 

 Let ^ be the height of the barometer at the time of the experi- 

 ment, D the density in the receiver, d the density in the cham- 

 ber, Y the velocity through the first orifice, v the velocity through 

 the second orifice. Then according to the old theory the force 

 which drives the air through the first orifice is^—d and that 

 which drives it through the second orifice is d-U. But since 

 an equal quantity flows through both, these forces are as the ve- 

 locities, that is d - d : d -Dy.V : V. 



Again, according to the old theory the density with which the 

 air passes the first orifice is Jj and that with which it passes the 

 second orifice is d. But since the orifices are equal and the quan- 

 tities which pass through them are also equal, the products of the 



dv 

 velocities by the densities are equal, that is ^Y=dv and Y=^- 



\ 



r 



_J_,i -I_i4:.'^l' 



