70 Proceedings of the Royal Society 
where it terminated towards the upper and deeper reaches of the 
loch. 
It results, from the discussion of these results, that the pheno- 
mena attending the freezing of a fresh-water lake may he stated as 
follows : — 
First. Cooling down of the whole water to an approximately uni- 
form temperature of 39 -2° F. 
Second. Local formation of ice generally as a shore fringe. 
Third. Convection currents flowing at the surface from the ice to 
the middle of the loch, and at the bottom from the middle to the 
edge, caused by the disturbance of the equilibrium in consequence 
of the local occurrence of ice. 
Fourth. Continuance of these currents for some time without 
appreciable diminution of strength, then gradual slackening of these 
currents as the temperature of the open water becomes lower, and 
the consequent difference of density on which their existence de- 
pends becomes less. 
Fifth. The velocity of the water leaving the ice fringe and the 
facilities for losing heat at the surface, by radiation or convection, 
are so related that a portion of water leaving the ice fringe freezes 
before it can mix with the warmer water off shore. 
Sixth. When condition fifth has been attained, rapid propagation of 
ice over the surface, and complete covering of the water with ice. 
Seventh. Existence of the water under the exceptional condition 
of a uniform surface temperature, and consequent rapid equalising 
of differences of density in different parts. Did the loch consist of 
a mass of water enclosed in a basin which neither supplied nor re- 
moved heat, the condition of the water would alter only very slowly, 
owing to variation in thickness of the ice covering, and the gradual 
alteration of temperature of the water by conduction from the lower 
ice surface. 
Hence the temperature of the bulk of the water under the ice of 
a frozen lake will tend to be uniform, and the uniform temperature 
to which it approximates will be determined by a number of local 
circumstances. It will lie between 39*2° and 32° F., and will 
depend on the shape and position of the loch as well as the geo- 
graphical features of the surrounding land, and especially on the 
severity of the weather. The body of a loch will be cooled more 
