62 
HAYFORD. 
probably has many spots of weakness in it which will tend 
to cause failure long before the stronger material gives way. 
The stress-differences at which failure will commence there- 
fore depend upon the strength at the exceptionally weak 
spots in the material rather than upon the average strength 
of the material. 
4. The materials composing the earth’s crust, except those 
near the surface, are subjected to high temperatures, which 
tend to reduce their strength. The temperature at 70 miles 
below the surface probably exceeds 1,900° centigrade — above 
the melting point of iron and many other materials, under 
surface conditions. 
5. It is stated in Darwin’s paper that one at least of the 
assumptions is such as probably to make the computed 
stresses smaller than the fact.* The speaker believes that 
there are other implicit assumptions, to which no attention 
is clearly called in the paper, which also tend to make the 
stresses computed by Darwin too small. For example, Dar- 
win has dealt with a hypothetical continent represented by 
a regular mathematical form. His hypothetical continent 
resembles, as he states, an actual continent after its irregu- 
larities have been supposed smoothed out by leveling down 
the mountains and filling in the valleys. The stresses due 
to such a hypothetical smoothed-out continent are less than 
those due to an actual irregular continent. He has also com- 
puted the stress-differences due to ranges of mountains not 
much greater than some of the actual ranges which exist on 
the continents and has found the stress-differences nearly 
two-thirds as large as those due to the smoothed-out conti- 
nents. In nature the two sets of stresses, those due to 
smoothed-out continents as a whole and those due to 
separate mountain ranges, exist at the same time in com- 
bination. The stresses are not in general combined by a 
mere algebraic addition. Nevertheless the combined stress- 
difference due to both at any one point is in general larger 
than the stress-difference due to either one alone. 
* See, especially, the statement in regard to the figure of equi- 
librium, on page 225 of the paper. 
