Motion of Gases. 377 



fall the perpendicular FH, and take HG equal to HC, the dis- 

 tance CG will be the horizontal range of the jet. But 

 CG '= 2 CH - 2 CF X cos FCH = 2 O# X sin 2 EOF. 



Therefore, when the angle of elevation is 45, the focus of the 

 parabola falls on the horizontal line at F', and the range CK is 

 then the greatest possible, being double the altitude CB. 



Of the Motion of Gases. 



488. To determine with what velocity the air or any other gas 

 will rush into a void space, when urged by its own weight, we 

 proceed according to a method analogous to that by which the 

 moiion of liquids is determined. When the moving force and the 

 mass or matter to be moved vary in the same proportion, the 



velocity will continue the same, since v . 28. 



Thus, if there be similar vessels of air and water, extending 

 to the top of the atmosphere, on the supposition of a uniform 

 density throughout, they will be discharged through equal and 

 similar apertures with the same velocity; for in whatever pro- 

 portion the quantity of matter moving through the aperture be 

 varied by a change of density, the pressure which forces it out 

 acting in circumstances perfectly similar will vary in the same 

 proportion. Hence it follows that the air rushes into a void with 

 the velocity which a heavy body would acquire by falling from the 

 top of the atmosphere, this fluid being supposed to be of a uniform 

 density throughout. 



The height of a uniformly dense or homogeneous atmosphere 

 being 27807 feet, according to article 467, and g = 32,2, we 

 shall have for the velocity in question 



v = \S2gh = V 2 X 32,2 X 27807 = 1338. m 



489. But as the space into which the air rushes becomes more 

 and more filled with air the velocity must be diminished contin- 

 ually. Indeed whatever be the density of this rarer air, its elas- 

 ticity varying with its density, will balance a proportional part 



Mech. 48 



