ON A GLOBULAR BODY OF CONDENSIBLE AND ELASTIC MATTER. 173 



RULE. To the given depth of the sea, add the height of a 

 column of sea water, which is equal to the weight or pressure 

 of the atmosphere ; divide the sum by the height of the atmo- 

 spheric column, and multiply the radius of the body at the 

 bottom of the sea by the cube root of the quotient, and the 

 product will give the radius at the surface. 



174. EXAMPLE. The radius of a globe of elastic arid condensible 

 matter, when placed at the depth of 75 fathoms in sea water, is equal 

 to 4 inches ; what will be the radius on ascending to the surface, the 

 atmospheric column being equal to 33 feet ? 



Here we have given d~ 75 fathoms, or 75 x 6 m 450 feet ; h zz 33 

 feet; fizz 4 inches; consequently, by the rule, we have 



=v 



- izz 9. 785 inches nearly. 



33 



175. From this it appears, that if a globe of condensible matter, 

 whose radius is 9.785 inches, be immersed in the sea to the depth of 

 450 feet, its radius will be decreased to 4 inches ; this circumstance 

 may suggest some easy and accurate methods of determining the depth 

 of the ocean, when it is so great as to preclude the application of 

 other methods. 



176. In order, however, to adapt our equation to the determination 

 of the depth, we must consider the radii at the surface and at the 

 bottom, together with the height of the atmospheric column, to be 

 accurately known at the time of trial ; then, by a very obvious trans- 

 formation, the depth of descent may be ascertained ; for let R be 

 substituted instead of y in the foregoing equation, to denote the radius 

 at the surface, and we shall have 



R r V ~T~~' 



in which equation, d is the unknown quantity. 

 Let both sides of the equation be divided by r, the radius of the 

 globe at the bottom of the sea, and we shall obtain 



(d+h), 

 ~T~~' 

 and cubing both sides, it becomes 



multiply by h, and we obtain 



