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



IS'ow if the specific gravity of ice = 1-028 and that of sea-water -918, 

 then p for sea-water and iee= '893 



whence r "> a •196 



Case II.^ — As in Case I. let r=the radius of the base of the cone, 

 fl=the height of the cone, and p as before. 



Yolume of Cone A CM: vol. of BCN::1:1— p .*. AC:BC = 



1 : \^i—p X 



/.radius of plane of ilotation=r (1 — pY and k the radius of 



gyration of plane of flotation =^{l — p) ^ ( 1 ) 



Area A of plane of flotation =7rr^(l — p)^ (2) 



1 3. 



The distance between Gr and E which are as before, ov h = ( 1)''* 



a (l-V'i-p) ^^^^ (3) 



Y the volume of displaced water = — o— ^ ^ 



'Now substituting in AF>Yh 

 '^r\l-pf^{l-pf>7rr^p^' (y-l)^- ci (l-V'l-p) 

 or y > « V J — 1 



ox r'> a 1'05 



Approximations to these two limiting cones are represented in 

 the woodcuts given on page 69. Fig. 1 represents a cone of ice 

 floating with its apex downward, which is unstable, and in sea- 

 water might fall on its side, whilst one less acute might float in this 

 position. Any cone, when thus floating, has about 2V of its whole 

 depth above water. If such cones existed in nature, it is evident 

 that they must be much more obtuse in form in order to withstand 

 in such a position the shocks of waves and winds to which they 

 would be subjected. 



Fig. 2 represents a cone of ice floating with its apex upwards, 

 and its base horizontal. Any cone which is more obtuse than this, 

 when floating in sea- water, is stable. In this case '47, or, as before 

 stated, nearly one-half of the height of the cone, is above water. 



To test these results I had several small cones made out of 

 Japanese boxwood (S.G. about -839), which was the most suitable 

 wood for the purpose which I could obtain. The diameter of the base 

 of these cones was in all cases 2 in., whilst their height, which was 

 variable, was made above and below the limits as given by calcula- 

 tion where the specific gravity of the wood I was using took the 

 place of the specific gravity of ice. These cones, when placed 

 in water, behaved in a manner similar to the way I have stated that 

 cones of ice will act. 



1 See Woodcut, Fig. 2, on opposite page (p. 69). 



