﻿70 Prof. J. Milne — On the Flotation of Icebergs. 



depth of 2400 feet would be under a pressure of about 73 atmo- 

 spheres. Although this lowering of temperature, which can be 

 easily calculated, is very small, it must nevertheless have some 

 influence in the destruction of masses of ice should they extend to 

 considerable depths, more especially so when we consider that the 

 action is not merely a surface one, but one that extends throughout 

 the mass. 



The more probable form in which the generality of icebergs 

 exist are those which have their limit represented by Case II., 

 where we have a series of stable forms, more or less conical in their 

 shape. Here the depth below the surface of the water never 

 exceeds the height which is above, but is probably always less. 



Of course many other forms of ice also approximating to regular 

 solids might be supposed, in which the ratio of the depth of ice 

 below water to that which is above would be greater than that 

 of the inverted cone, and which would be less than that of the 

 upright cone. Thus, for instance, such a solid as would be described 

 by an equilateral hyperbola, revolving round one of its asymptotes, 

 might be taken as pointing downwards or upwards. In the former 

 case the ratio of the depth below the surface of the water to the 

 height which is above might be infinitely greater than in the case of 

 the inverted cone of ice, and in the latter case or pointing upwards 

 the ratio of the depth below the surface of the water to the height 

 which is above infinitely less than in the case of the upright cone. 



To obtain the gi-eatest height of ice above the surface of the 

 water relatively to that which is below we must imagine a sheet of 

 ice, from the upper surface of which a needle or pencil extends 

 vertically upwards. The same figure reversed would give us the 

 greatest depth to which ice could descend below the surface of the 

 water. Such a case is however purely theoretical. In cubes which 

 are in stable equilibrium with a face upwards, and in parallelepipeds 

 which are in stable equilibrium with one of their largest faces 

 upwards, the depth of ice below the surface of the water would be 

 about eight times the height which is exposed above. 



Combinations of regular solids might also be considered. Thus 

 two cones might be supposed placed base to base, and floating one 

 with its apex upwards and the other with its apex downwards. 



First — let the volume of the lower cone V, whose height is H, be 

 eight times the volume of the small cone v, whose height is h. 



In this case we have 



I = S = i.-.H = 8* 



V h 1 



or the depth below the surface of the water is eight times the 

 height which is above. 



Secondly — let the upper or smaller cone be less than ^ the 

 volume of the lower one, then the depth below water wiU be 

 greater than eight times the height above. 



Thirdly — let the upper or smaller cone be greater than ^ the 

 volume of the lower one, then the depth below water will be less 

 than eight times the height which is above. 



