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Proceedings of the Royal Society 
water under tire ice in Linlithgow Loch had only a temperature of 
about 37°, while in Loch Lomond the mean temperature was as low 
as 34°. 
The object of the present communication is to offer an explanation 
of this unexpected condition of the water — to show how theory has 
failed correctly to predict the thermal conditions of a frozen lake. 
Mr Buchanan in the papers already referred to, and also in 
“ Nature ” of 6th March 1879, gives an explanation of how water in 
lakes becomes cooled below its temperature of maximum density. 
As this theory is at variance with many well-known results of ex- 
periment, and does not seem satisfactorily to explain the facts, it 
will be necessary first to show wherein this explanation fails. Mr 
Buchanan’s theory is simply this: — The water in the lake gets gradu- 
ally cooled to the temperature of its maximum density, namely 39*2°. 
Some time after all the water has acquired nearly this temperature, 
freezing begins at the edge first, while there is open water in the middle 
of the lake. The effect of this freezing would be expressed graphi- 
cally by the dipping of the isothermal of 39-2° at the edge. This 
alteration of the temperature will be accompanied by an alteration in 
density; and if we consider a vertical section in the middle of the lake 
and another section at the edge, we will find the mean density at the 
middle greater than at the edge, the result of which is convection 
currents, flowing on the surface from the ice, and under currents 
from the middle towards the sides. This appears to be a perfectly 
correct statement of the condition of the water under the circum- 
stances, but it does not seem capable of giving an explanation of the 
temperature of the water all through the lake being below 39*2°. 
The colder and lighter water near the edge, where freezing first 
begins, will certainly tend to spread itself towards the middle of the 
lake — but it will tend to keep the surface, and will not sink and 
produce a vertical circulation. And unless this cold surface water 
sinks how is the lower temperature to be carried downwards? We 
have here a precisely corresponding condition of matters to what 
exists in the lake on the return of summer, when the water is being 
heated. At first the temperature of the lake is below 39 *2°, and 
the warmer water brought in by the rivers and that heated by 
the sun, sinks to the bottom and raises the mean temperature of 
the lake to the temperature of its maximum density. After it 
