( 461 ) 
This is obvious for cavities which are in the piece rising above the 
surface, as these cavities have no influence on the upward pressure. 
If the inrmerged piece has a cavity of A em, the upward pressure 
is equally large as for a solid piece of ice of the same weight, but 
there are A grammes of ice more above the water. When melting, 
these A grammes of ice form A grammes of water, just sufficient 
for filling up this cavity. 
The law of the permanent level holds also when the ice contains 
air bubbles, at least by the same degree of approximation, with 
which we may neglect the weight of the air. 
§ 8. When fresh water ice floats and melts in salt water, the 
level does rise, though slightly, the immerged part now being smaller 
than before, and so the melted ice cannot be contained in the volume 
of the immerged part. 
Here and in what follows the change of volume, caused by the 
mixing of salt water and fresh water, is neglected, which is certainly 
permissible when the proportion of the salt is slight. 
For A liters of ice, which weigh 917 A grammes and float in 
salt water of 1,03 specific gravity, the volume of the immerged piece 
is 890 A cm.; the available space can therefore hold 890 A em. of 
the melted water, but the remaining 27 A em. raise the level. 
This remaining part is about one fourth of the piece which rises 
above the surface of the water (110 A em). 
§ 9. If in salt water a piece of one liter of ice floats, which has 
a cavity under water of B em, then there are (1000-B) em. of solid 
ice of a weight of 0,917(1000-4) grammes. 
The upward pressure is therefore 0,917 (1000-8) gramme, and 
with a specific gravity of the salt water of 1.03, the immerged 
volume is 0,89(1000-B) em. When melting, we get 0,917(1000-B) em. 
and so there is a surplus of 0,027(1000-B) em. of water to the 
volume yielded by the immerged piece, which raises the level. 
The piece of ice rising above the surface was 1000-0,89(1000-B) em. 
or (110 + 0,894) cm, and the ratio of the remaining piece mentioned 
27—0,027 B 
The smaller B is, the more this relation approaches to about 
a fourth. 
B 
to this volume is as one to (41 + ure 
§ 10. History. A remark made two years ago by a pupil of the 
third year of the “Gymnasium Willem III” at Batavia to the writer 
