EXAMPLES. 297 



21. In one of the Bramah presses used in raising the 

 Britannia tube over the Menai Straits, the diameter of the 

 piston (7 was 1 inch, that of A 20 inches; the force applied 

 to C at each stroke was 2 tons ; find the lifting force pro- 

 duced by the upward motion of A. Ans. 1000 tons. 



22. If the receiver be 4 times as large as the barrel of an 

 air-pump, find after how many strokes the density of the 

 air is diminished one-half. 



Ans. Early in the 4th stroke. 



23. After a very great number of strokes of the piston of 

 an air-pump the mercury stands at 30 inches in the 

 barometer-gauge, the capacity of the barrel being one-third 

 that of the receiver, prove that after 3 strokes the height of 

 the mercury is very nearly 12|- inches. 



24. A fine tube of glass, closed at the upper end, is 

 inverted, and its open end is immersed in a basin of mer- 

 cury, within the receiver of a condenser; the length of the 

 tube is 15 inches, and it is observed that after 3 descents of 

 the piston the mercury has risen 5 inches; how far will it 

 have risen after 4 descents ? 



Ans. The ascent x is given by the equation - -f- r 



lo 'jc n 



20 

 = | + 5T If h = 30, x =6.1 nearly. 



Oil 



25. If A = 35 (Art 151), find the elastic force of the 

 air in the receiver after the 5th, 10th, 15th, and 20th 

 strokes, the height of the barometer being 30 inches. 



Ans. 7.119 ins.; 1.689 ins.; 0.401 ins.; 0.095 ins. 



26. In the same pump, the barometer standing at 30, 

 find the number of strokes, (1) when the mercury in the 

 gauge rises to 25 inches, and (2) when the rarefaction is 

 1-^100. Ans. (1) 6.2; (2) 16. 



27. If a hemispherical diving bell be sunk in water until 

 the surface of the water inside the bell bisects its vertical 



