132 EXAMPLES. 



face within below the surface without, and IT, TT', the press- 

 ures of the atmospheric air and of the compressed air. 

 Then (Art. 48) we have 



TT' : TT :: a : b + x; (1) 



also, TT' = pressure on the water within = n 4 gpx = 

 gph + 9P X > if h be the height of the water barometer. 



Substituting these values of n and TT' in (1), we have 



7/4-ft _ a 

 h ~ b + x' 



(h b) 2 (h + b) 

 ~~ 



5. A cylinder, 20 ft. long, is half filled with water, and 

 inverted with the open end just dipping into a vessel of 

 water. Find the altitude of the water in the cylinder, the 

 height of the water barometer being 33 feet. 



Ans. 7.21 feet. 



6. When the mercurial barometer stands at 30 inches, 

 what is the height of the barometer formed of a liquid 

 whose specific gravity is 5.6 ? Ans. 72.7 inches nearly. 



7. The air contained in a cubical vessel, the edge of 

 which is one foot, is compressed into a cubical vessel of 

 which the edge is one inch. Compare the pressures on a 

 side of each vessel. Ans. 1 : 12. 



8. If the elastic force of a mass of gas whose volume is 

 100 cubic inches be 30.275 inches of mercury, find its elastic 

 force if it be allowed to expand to a volume of 387 cubic 

 inches. Ans. 7.823 inches. 



9. If Fahrenheit's Thermometer mark 40, what are the 

 corresponding marks of Reaumur's and the Centigrade ? 



Ans. 4$; 3f 



