IN THE EARTH’S CRUST RESULTING FROM SECULAR COOLING. 
247 
Hence, for the upper layers, we have approximately 
K=e( Y-v) . (11) 
Thus it appears that the integral effect is always a stretching, and that it is the 
same in amount at whatever speed the globe cools. The fact that, if the globe cools 
suddenly, the integral effect must be stretching has been pointed out by Mr. Davison. 
If we differentiate (10), we have 
But 
and, near the surface, 
Hence 
dK _ j" dv 3 k ' 
dt p dt c ( 7 r/cty 
dv x dv 
dt 21 dx ’ 
dv V 
dx ( 7 TKt)* 
dK 
dt 
dv I x "6k\ 
C dx \2 1 c ) 
e dv fx 6/et\ 
2t ° dx\c J 
and thus we find equation 
written— 
(8) again, as ought to be 
dK _ e_ V / 6*A 
dt 2 1 ( 7 r/ctf)* \ c ) ' 
the case. This may also be 
We must now see whether the amount of crumpling of the surface strata can be 
such as to explain the contortions of geological strata. 
It must be borne in mind that, from a geological point of view, contraction is not 
the negative of stretching. When a stratum is stretched it may perhaps be ruptured, 
and rock may be squeezed up into the crack, at least for the strata which are very 
near the surface, and therefore not under great pressure ; but when compressed the 
stratum is no doubt crumpled. Hence it is insufficient to know that the integral 
effect from the time of consolidation is a stretching; for that stretching may be merely 
the excess of a stretching over a crumpling. Now we have found above that the 
depth of the stratum of no strain is given by 
§Kt 
x — — • 
c 
Hence, at the time t', given by t f — cx/Gk, the surface of no strain was at depth x ; 
and at all later times than t' the surface of no strain lies deeper. Therefore, to find 
