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Tribune Extras Lecture and Letter Scries. 



explain the operation of forces beneath the earth's 

 surface in producing its characteristic features are here 

 referred to two types : (1) those attributing the surface 

 features to contraction from loss of heat, which may he 

 failed the contractions! hypothesis, and (2) the argu- 

 ments winch attribute them more or less to disturbances 

 produced by external changes, which may be called the 

 fractional hypothesis. 



The contractioual hypothesis assumes that the earth 

 may be regarded as of two portions a cooled exterior 

 and ;\ hot nucleus. The secular loss of heat is supposed 

 to bo greater from the latter than from the former, ami 

 by a consequent contraction of the nucleus it is assumed 

 that the shell would tend to collapse. Owing to the 

 unequal ability of certain portions of the shell to bear 

 the tangential strains thus occasioned, the yielding 

 taking place along the lines of least resistance would be 

 manifested in the production of table lands, or moun- 

 tains, or disturbed stratification. The smaller con- 

 ductivity of materials underlying the land is held to 

 account for the primary division into land and water, 

 the land having been left behind in a general con- 

 vergence of material toward the center. 



There can be no reasonable doubt that the earth mass 

 consists of a cooled exterior inclosing a hot nucleus, 

 and secular cooling and contraction are necessary corol- 

 laries. As the process was of immense duration, we 

 nrny take sonic starting point, and assuming the loss of 

 temperature to have been continuous, may arrive at a 

 period when the whole mass was lluid. As was pointed 

 out by Sir William Thompson, this was a period of homo- 

 geneity, both as to material and heat. The first result 

 of loss of heat would apparently be consolidation, and 

 the argument of Hopkins is here accepted that consoli- 

 dation would begin at the center, where pressure would 

 enable congelation to be effected at high temperatures. 

 Materials solidifying at the surface would sink by their 

 Increased density, until the surface was so far reached 

 l>y solidification proceeding from the interior as to leave 

 only an imperfectly liquid mass, where such movements, 

 gradually retarded, at length ceased. The result would 

 be a solid globe with perhaps isolated reservoirs of 

 liquid tint might consist of matter having a higher 

 melting point. 



MATHEMATICAL BASIS OF THE ARGUMENT. 

 Here follows in Capt. Dutton's memoir a summary of 

 Fourier's solution of the problem of secular cooling. It 

 is based upon certain factors, which are represented 

 thus: 



V, denotes half the difference of the two initial 

 temperatures. 



r, halt their sum. 



t, the, time. 



x. the iliit. mce of any point from tho plnne. 



T, the temperature of the point x at the time t. 



k. the conduct i vity of the material in terms of its own 

 thermal capacity. 



With these, data a formula is computed. To obtain tho 

 coefficient of k, Messrs. Thompson and Forbes made 

 experiments on rock material with thermometers im- 

 bedded at dUtance^ of from three to 25 feet during a 

 period of 14 years. V, representing the, maximum tem- 

 p'-rature of the interior ot the, earth at the beginning of 

 cooling, mint bo hypothetical; for our purposes we may 

 take it as the melting point of tho more refractory 

 material forming the chief bulk of the nucleus, and as- 

 sume it to be that of the anhydrous silicates and that 

 they are 600 to 800 miles in depth. Allowing for tho 

 effect of pressure upon the congealing point \ve may ac- 

 cept Sir William Thompson's estimate of this tempera- 

 ture as, at a maximum, 7,00') F. A course of mathemati- 



cal reasoning then is put forwar.1 by C:ipt. Button, 

 which shows that if it be possible to determine a true 

 mean rate of increase of temperature per foot of descent 

 at any point near the surfac >, the time required to elapse 

 from tho epoch of the establishment of the cooling to 

 the present time can bo deduced. This moan is placed 

 by some investigators at 1-50 of a degree of Fahrenheit 

 per foot, by others at 1-60 ; the formar would give about 

 100.090,000, and the latter about 130,000,030 years. 



The correctness of the mathematical deductions can- 

 not be questioned, but the data on which they proceed 

 are open to doubt. The coefficient of k may not bo an 

 invariable constant, as it seems probable from experi- 

 ment that the conductivity of material incn>as3.s as 

 fluidity is approached. The time required to establish 

 an increase which may be represented by 1 Fab., 

 divided by 50.6, would thus probably bo largely aug- 

 mented. Tais would also reduce the basis of the con- 

 tractional hypothesis by reducing the total dissipation 

 of heat and the contraction inferred from it. Again, as 

 to k, if porous roclrs are saturated with water they are 

 much worse conductors than those on which Sir William 

 Thompson experimented : this value, now represented 

 at 400, might theu be put at 259. The effect of this would 

 be to extend the duration of the cooling. Another factor 

 open to question is the rate of increase of temperature 

 per foot of descent. Its value, varying widely with lo- 

 cality, is found in some places one-fifteenth and la 

 others one one-huudred-and-tenth. Proximity to igne- 

 ous masses may vitiate any average based on such 

 observations, as these case* may be extreme, and 

 aqueous circulation below the surface may equally 

 vitiate other observations. 



KKSUL.TS AS TO THE AGE OF THE EAIITIT. 

 (1.) Lot us assume that tue earth, wuon first ceasing 



to be fluid, had a temperature of 7,000 F.. and now ex- 

 hibits an increase of oue one-hundredth of a degree for 

 each foot of descent near thn surface. Tho period be- 

 tween would then be about 625,000,000 years. At a depth 

 of 300 miles the Increase of temperature would bo about 

 a fifty-six hundred and fortieth of a degree per foot of 

 descent; thence inward the total amount of coolinsr 

 would bu inconsiderable ; outward it would augment at 

 an increasing rate to the mean temperature at the 

 surface. 



(2.) Tike the present surface rate of increase of tem- 

 perature at, per foot, one degre3 Fall, divided by 60.6. 

 The epoch would be about 160,003,030 years, and bo- 

 low 140 miles the rate of increase of heat would be 

 inconsiderable. 



(3.) Take the valuation of k at 400 instead of 250, and of 

 tin' surface rate at 1 divided by 50.0, tho epoch becomes 

 about 98,000,000 years, and bolow 150 miles the rate of 

 increase would bo less than 1 divided by 2,700. 



(4.) Take k at 250 and the surface rate at 1 divided 

 by 230, the epoch would be 2,503,000.003 years, and at a 

 depth of 600 miles tho cooling might bo disregarded. 



Hut in general the application of this theorem is fatal 

 to (he contraction hypothesis, as it shows that after 200 

 or 300 miles tho cooling has been comparatively little; 

 \\ ere it otherwise tin- present rate of increase of hoat per 

 foot would be lower than the lowest reasonable estimate 

 with our present knowledge. Our acquaintance with 

 the laws of plutonio action is insulli /lent to take it 

 into account, but as an element in the problem it may 

 be regarded as of Inconsiderable moment. Chemical 

 changes could scarcely take place at the limits of sensible 

 cooling, and cannot bo regarded as operative at greater 

 depths than 200 or 1100 miles. The contraction of this 

 portion cannot bo more than one-tenth, if we assume the 



