70 
Prof. J. Mihie — On the Flotation of Icebergs. 
deptli of 2400 feet would be under a pressure of about 73 atmo- 
spheres. Altbough tkis lowering of temperature, wliich 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 deptks, more especially so when we consider tbat the 
actiou 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., 
wkere 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 regulär 
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 greatest height of ice above the surface of the 
water relatively to that which is below we must imagine a sheet of 
ice, from the Tipper 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 parallelopipeds 
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 regulär 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 
V 
v 
H = 8 h 
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 will 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. 
