Front Page Titles (by Subject) APPENDIX J.: THE FORM OF THE EARTH NO PROOF OF ORIGINAL FLUIDITY. - An Autobiography, vol. 1
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APPENDIX J.: THE FORM OF THE EARTH NO PROOF OF ORIGINAL FLUIDITY. - Herbert Spencer, An Autobiography, vol. 1 
An Autobiography by Herbert Spencer. Illustrated in Two Volumes. Vol. I (New York: D. Appleton and Company 1904).
Part of: An Autobiography
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THE FORM OF THE EARTH NO PROOF OF ORIGINAL FLUIDITY.
[From the “Philosophical Magazine” for March, 1847.]
It has been generally considered that the spheroidal form of the Earth—indicating as it does obedience to centrifugal force—implies a primary state of fluidity. If, however, it can be shown that, notwithstanding its apparent solidity, the Earth must be at the present moment entirely subject to the influences affecting its general figure, and that so far as the gravitative and centrifugal forces are concerned it is plastic still, the theory of original fluidity, however probable on other grounds, can no longer be inferred from the Earth’s oblateness.
The facts indicative of a varying relationship between the bulk and tenacity of matter are of every-day observation. We constantly see a drop of water maintain its sphericity in spite of opposing forces; increase the mass, and it flows out in complete obedience to them. The mud in our streets stands in ridges behind the passing cart-wheel; when scraped together its appears liquid and assumes a horizontal surface. On the spade of the excavator, clay retains its square figure and its sharp angles; but when made into a bulky embankment, it will, if the slope be insufficient, spread itself out on one or both sides of the base: occasionally continuing to slip until it assumes an inclination of six to one.
A comparison of the physical powers of large and small animals exhibits a series of facts of analogous character. A flea jumps several hundred times its own length, and is uninjured by collision with any obstacle. The greatest mammals, on the other hand, seem to possess no agility whatever; and a concussion borne by the insect with impunity would smash an elephant to a jelly. Between these extremes may be observed a gradation in the ratios of power to bulk; so that commencing with the smaller creatures, every increment of size is, cæteris paribus, accompanied by an under-proportionate increase of strength, until we arrive at that limit (to which the elephant has evidently approximated) where the creature is no longer capable of supporting its own framework.
These, and innumerable like facts, point to the inference that fluidity and solidity are to a great extent qualities of degree; that the cohesive tenacity of any piece of matter bears, as the mass of that matter is increased, a constantly decreasing ratio to the natural forces tending to the fracture of that matter; and that hence any substance, however solid to our perceptions, only requires to have its bulk increased to a certain point, to give way, and become in a sense fluid before the gravitative and other forces.
However repugnant to that “common sense,” for which some have so great a respect, this proposition is capable of a very simple demonstration.
The strength of a bar of iron, timber, or other material subjected to the transverse strain, varies as ; B being the breadth, D the depth, and L the length. Suppose the size of this bar to be changed, while the ratios of its dimensions continue the same; then as the fraction will remain constant, the strength will vary as D2 or (since D bears always the same proportion to B and L) as B2 or L2. Hence in similar masses of matter the resistances to the transverse strain are as the squares of the linear dimensions. The same law still more manifestly applies to the longitudinal strain. Here the strength, depending as it does on the sectional area, must, in similar masses, vary as the square of any side. And in the torsion strain we may readily detect the like general principle, that, other things equal, the resistances to fracture bear a constant ratio to the squares of the dimensions. [This last statement is, I think, erroneous; but the error does not affect the argument.]
No so, however, with the powers tending to the disruption of matter. The effects of gravity, centrifugal force, and all agencies antagonistic to cohesive attraction, vary as the mass, that is, as the cubes of the dimensions.
However great, therefore, in a given portion of matter, may be the excess of the form-preserving force over the form-destroying force, it is clear that if, during augmentation of bulk, the form-preserving force increases only as the squares of the dimensions, whilst the form-destroying force increases as their cubes, the first must in time be overtaken and exceeded by the last; and when this occurs, the matter will be fractured and re-arranged in obedience to the form-destroying force.
Viewed by the light of this principle, the fact that the Earth is an oblate spheroid does not seem to afford any support to the hypothesis of original fluidity as commonly understood. We must consider that, in respect of its obedience to the geodynamic laws, the Earth is fluid now and must always remain so; for the most tenacious substance with which we are acquainted, when subjected to the same forces that are acting upon the Earth’s crust, would exceed the limit of self-support determined by the above law, before it attained th of the Earth’s bulk. [This is an extreme overstatement, since it assumes that the mutual gravitation of the parts of this small mass would expose them to a stress like that to which they would be exposed were the mass placed on the surface of the existing Earth. Still it remains true that a mass of the hardest matter would lose its self-sustaining power long before it approached the size of the Earth.]
Reference to a table of the resistances of various substances to a crushing force will render this manifest.
London, January, 1847.