THE DIVING BELL. 



207 



entirely emptied of water by the air forced in by the pump. 

 There are also contrivances for the expulsion of the air when 

 it becomes impure. 



The force tending to lift the bell is the weight of the 

 water displaced by the bell and the enclosed air. Hence 

 the tension on the suspending chain, being equal to the 

 weight of the bell diminished by the weight of water dis- 

 placed by the bell and the air within, will increase as the 

 bell descends, in virtue of the diminution of air space due 

 to the increased pressure, unless fresh air is forced in from 

 above. 



Let ABCD be the bell, let EF = 

 a, the depth of its top below the 

 surface of the water, FK = b, the 

 height of the cylinder, FH = x, the 

 length occupied by air, n and n' the 

 pressures of the atmospheric air and 

 of the compressed air within the bell, 

 and h the height of the water ba- 

 rometer. Then we have (Art. 48) 



Fig. 72 



But, 

 which in (1) gives 



= * - = w + ffp (a + z). 

 TT = gph, 



x 2 + (a + h) x = hb, 



(1) 



-(a + A) + V ( + A) 2 4- 



& - "" ^ 



(2) 



the positive value only being the one which belongs to the 

 problem. 



COR. If A be the area of the top of the bell, and its 

 thickness be neglected, the volume of displaced water is Ar, 

 and the tension of the chain 



^= weight of bell ypAz, (3) 



