Fluid Pressure 103 



short limb. If we assume the bore of the tube to 

 be uniform, the volume of the contained air will be 

 proportional to the length of the portion of the tube 

 containing it. The enclosed volume of air in the short 

 limb is then under a pressure equal to that of the 

 surrounding atmosphere and has a volume proportional 

 to the length of tube measured. 



Wewill now alter the pressure of this air. Pour 

 a little more mercury into the long limb. When the 

 mercury in both limbs is at rest, it will be noticed 

 that the level of that in the longer limb is higher than 

 that in the other. (See Pig. 31.) Let us now consider 

 the pressures acting at the level shown by the dotted 

 line AB in the figure. The only pressure acting 

 downwards at this level in the closed limb is that of 

 the contained air. At the same level in the other 

 limb we have the pressure of the atmosphere acting 

 downwards upon the free surface of the mercury, and 

 transmitted through that liquid in all directions, 

 together with the pressure of the column of mercury 

 in the tube above the level AB. These two pressures 

 combined must be equivalent to the pressure of the 

 air in the other limb, since the pressures of the two 

 columns of mercury below AB balance one another, and 

 hence need not be considered. The pressure of the air 

 in the closed limb is therefore the sum of the atmo- 

 spheric pressure and the height of the mercury surface 

 in the long tube above AB. Measure this height and 

 also the length of the air column in the short tube 

 under the new pressure. 



Add more mercury, and again measure the length 

 of the contained air column and the height of the 

 mercury surface in the long tube above that in the 

 shorter. Continue the addition of mercury in small 



