C. Davison—Creeping of Soil-cap by Frost. 207 
distance of the particle from the surface to which freezing extends. 
The more intense and lasting the frost, the thicker will be the frozen 
layer, and the greater the displacement of the surface particles. 
On the recurrence of warmer weather, the interstitial ice will be 
melted, and in melting will contract, and the particles will return, 
not, as they came, along the normal to the surface, but in a direction 
nearly vertically downwards owing to their weight; not quite 
vertically, however, because the adherence of each particle to its 
neighbours, by reason of the water between them, tends to bring it 
back towards its old position. The particles will thus after every 
frost and thaw occupy a lower position down the slope than they 
did before; and the whole outer layer of the soilcap will in this 
way creep slightly downwards, the creeping being greatest at the 
surface, and diminishing downwards to zero at the greatest depth 
to which freezing extended. 
3. If all the particles descend vertically during the thaw, or at 
any rate in the same direction, it may be shown that a series of 
particles lying in a straight line will, after a single frost and thaw, 
continue to lie in a straight line, inclined, however, at a different 
angle to the horizon. Let a 3B (Fig. 2) represent the surface of the 
soil, cp the surface to which freezing extends. Let p be any 
particle of soil on the straight line qr. Its normal displacement, 
and therefore also its creep, PP’, will be proportional to the distance 
of pe from cD, and therefore to pr. Hence, the series of particles 
originally lying along the straight line qr, will, after the frost and 
thaw, lie along the straight line Q’k; and the effect of the creeping 
will be to bend the line qR 58 into the form QRS. 
4, But, since during any winter or series of winters, there must 
be numerous frosts of different degrees of intensity and duration, 
and therefore penetrating to different depths, and since the surface 
layers of soil are affected by every frost, however slight, and in any 
one frost are more displaced than those below them, it follows that 
after any given time (including many changes of temperature across 
the freezing-point), particles lying originally on a straight line will 
in the end lie on a curved line with its concavity facing downwards. 
DECADE III.—VOL. VI.—NO. VI. 17 
