G8 
Prof. J. Milne — On tlie Flotation of Icebergs. 
Now if the specific gravity of ice = l - 028 and that of sea-water '918, 
then p for sea-water and ice= ’893 
whence r > a '196 
Case II. 1 — As in Oase I. let r=thc radius of the base of the cone, 
a = the height ofthe cone, and p as before. 
Yolume of Cone ACMivol. of BCÜ ”1:1 — p AC:BC= 
radius of plane of flotation=r (1 — p) :> and k the radius of 
V — 
gyration of plane of flotation =-2 (1 — p) 3 (1) 
Area A of plane of flotation=7rr ä (l — p) 3 (2) 
1 3 
The distance between G and E which are as before, or h — (— — l) 4 " 
a (1— V 7 J— p) 
Y the volume of displaced water= 
üow substituting in A k 2 >Yh 
( 3 ) 
( 4 ) 
-rrr\l-pY^(l-pf>^p~‘ (y- 1 ) 4 - « (l-V 7 ! -p) 
or r > a 
(1 -pf 
or r > a 1'05 
Approximation s to these two limiting cones are represented in 
the woodcuts given on page 69. Fig. 1 represents a cone of ice 
floating witli 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 y- 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.Gr. 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). 
