THE EARTH, A FAILING STRUCTURE. 
59 
loads are to be applied. On the other hand, the yielding of 
a failing structure increases with the lapse of time; it is very 
slow if the stresses are but little in excess of the elastic limit, 
and is faster the greater the excess of stress beyond the elastic 
limit. To predict the behavior of a failing structure, it is 
necessary to know how much the stresses exceed the elastic 
limit of the material and how long they continue to be 
beyond that point. 
Second, in a competent structure the distribution of the 
yielding or distortion does not change with increase of load 
or lapse of time. With double the load applied at a given 
point, every part of a competent bridge yields by a double 
amount. On the other hand, the distribution of the perma- 
nent yielding or distortion in a failing structure is con- 
tinually changing. The damage tends more and more 
strongly to concentrate at the weakest point or points as 
failure progresses. 
G.H. Darwin, in his classic paper entitled “On the Stresses 
Caused in the Interior of the Earth by the Weight of Conti- 
nents and Mountains,”* has furnished a very good way of 
approaching the question, “Is the earth a failing structure?” 
He assumes that the earth is a competent elastic structure, 
and upon that assumption proceeds to compute the stresses 
which must exist in it, due to the weight of the continents 
and mountains. He assumes the earth to be homogeneous 
in its elastic properties from surface to center. The material 
forming and underlying the continents is assumed to be of 
the same density as the material beneath the oceans. The 
computation is made under a sufficiently complete theory 
of elastic deformation to take account of the support which 
each portion of the material in the earth obtains from all 
the surrounding material. It takes into account the trans- 
mission of stress, by compression and shear, through the 
solid sphere in every direction from the points of application 
of the forces. 
* Philosophical Transactions of the Royal Society of London, vol. 
173, 1882, pp. 187-230. 
