420 Proceedings of Royal Society of Edinburgh. [sess. 
take an incalculably long time to escape by conduction and 
radiation. This contraction must have been going on during the 
whole period of the earth’s existence, and it is impossible to say 
when the heating effect ceased to balance the loss of heat by 
conduction and radiation ; or, in other words, when the earth 
ceased to grow hotter because it was contracting, and began 
-contracting chiefly because it was growing colder. 
NOTES ON MR ROMANES’ PAPER BY PROFESSORS 
A. GRAY AND C. G. KNOTT. 
In communicating the paper Professor Knott pointed out that 
Mr Romanes’ problem was a particular case of the general theory 
first enunciated by Helmholtz that gravitational contraction is 
necessarily accompanied by evolution of heat sufficient to account 
for the high temperatures of cosmic bodies. Mr Romanes worked 
by a process of averages; but with the same assumed law of 
density the problem could be worked out rigorously. The most 
-direct way of doing this was to find an expression for the potential 
of the whole mass of the earth in the given state. For this pur- 
pose it is not necessary to estimate the pressures at the different 
-depths ; but when this is done the results are of the same order of 
-quantity as those obtained by Mr Romanes by his tentative 
.process. 
The problem attacked by Mr Romanes suggested another 
problem which could be easily solved along the same lines — namely, 
the rate of gravitational contraction necessary in the present state 
of the earth to produce a given amount of heat. The earth is 
known to be losing heat annually at a definite rate. What rate 
of contraction is required to generate an amount of heat equal to 
the amount that is being lost by radiation 1 It was found that a 
very slight contraction indeed was sufficient to restrain the cooling 
■of the earth due to loss of heat, a contraction which was the 
fraction of a foot in a thousand years. 
Subsequently in reporting on the paper Professor Gray carried 
-out independently calculations which led to results similar to 
