ON A GLOBULAR BODY OF CONDENSIBLE AND ELASTIC MATTER. 171 



Here we have given, RZH 8 inches, H m 20 inches, and 0m 48 

 degrees, of which the natural cotangent is 0.9004 very nearly; con- 

 sequently, by the rule, we have 



x = $ {8X0.9004 + 20} =18.1355 inches. 



If therefore, 18.1355 inches be set off from the vertex, a straight 

 line drawn through that point parallel to the base, will be the diameter 

 of the section on which the pressure is a maximum. 



171. In any fluid the particles towards its base support those that 

 are immediately above ; these again bear the load above them, and 

 so on to the surface, where the whole mass supports the super- 

 incumbent atmosphere. There is therefore a pressure among the 

 successive strata of an homogeneous fluid increasing in exact propor- 

 tion to the perpendicular depth. Hence a bubble of air or of steam, 

 set at liberty far below the surface of water, is small at first, and 

 gradually enlarges as it rises. This phenomenon shows that the 

 compressive power of the fluid slackens by ascent. Experiment and 

 calculation most readily demonstrate the compressibility of water : 

 and the next problem exhibits the striking effects from the increase of 

 pressure at great depths of the sea. 



PROBLEM XXVIII. 



172. A globular body of condensible and elastic matter, is 

 suffered to ascend vertically from the bottom to the surface 

 of the sea : 



It is required to determine its diameter at the surface, the 

 depth of the sea, and the diameter at the bottom being given. 



Let AB be the surface of the sea, ab its bottom, and ecf, ECF, two 

 positions of the globular body in its ascent 

 from the bottom to the surface, and A sea, 

 B vfb the curves described by the extremities 

 of the diameter. 



Through G and g, the centre of the globe 

 in the two positions, draw the vertical line 

 cc, which is manifestly the abscisse to the 

 curve, the radii ge and GE, as well as ca and 

 CA, being ordinates. 



Produce the abscisse cc to D, and make CD equal to the height of 

 a column of sea water, which would be in equilibrio with the pressure 



