96 BOYLE AND MARIOTTE'S LAW. 



the open branch, and is therefore equal to one atmosphere 

 (Art. 47). 



Take DH = DE, and pour mercury slowly into the 

 tube AB till it stands at H in the shorter branch ; in the 

 longer branch it will be found to stand at the height LK = 

 30 inches above HK, i. e., the mercury, rising in the shorter 

 branch, compresses the air which it drives before it, and 

 when the air in the shorter branch is reduced to half its 

 volume, its elastic force or pressure is two atmospheres, 

 since it now sustains not only the atmospheric pressure 

 which is exerted on the surface of the mercury in the open 

 branch, but also the weight of a column of mercury 30 

 inches high. When mercury is poured into the tube till it 

 rises in the shorter branch to M, where DM = ^DE, it will 

 be found to stand in the longer branch at the height AN = 

 60 inches above MN, i. e., when the air in the shorter 

 branch is reduced to one-third of its volume, its elastic 

 force or pressure is three atmospheres, since it now sustains 

 the atmospheric pressure and the weight of a column of 

 mercury 60 inches in height. In the same way, it may be 

 shown that if the air occupy one-fourth of its original vol- 

 ume DE, it will sustain a pressure of four atmospheres, and 

 so on for any number. Hence, generally, the pressure of a 

 quantity of air varies inversely as its volume. 



When the volume is reduced to one-half, the density is 

 doubled ; when reduced to one-third, the density is trebled, 

 and so on ; that is, the volume varies inversely as the density. 

 Hence, the pressure varies directly as the density. 



Let v and v' be the volumes of a given mass of air, p and 

 p' the corresponding pressures, and p and p' the correspond- 

 ing densities. Then we have 



P ._ v> _ P m 



7-vp" w 



P = *P, (2) 



where k is a constant to be determined by experiment. 



