314 A. Vaughan — Critique on Results of a Shrinking Globe 



la tlie next place it is important to notice the data which, are 

 assumed. Lord Kelvin assumes that, at the epoch of consolidation, 

 the earth, or at least an outer shell of a thickness of 100 or 200 

 miles, was at an uniform temperature, and that the temperature of 

 the surface was subjected to a loss of 7000° F. and then maintained 

 at this lower temperature. 



The temperature at the very start was, in consequence, uniform 

 downwards, not a rise of 1° F. in 10 feet as, by some very curious 

 oversight, is stated by Mr. Reade. This latter temperature gradient, 

 which is given as tliat of first consolidation, was not established, on 

 Lord Kelvin's assumptions, until 4,000,000 years later. 



In this reduction of 7000° F. at the surface we have, at the best, 

 a probable hypothesis with no pretence at exactness. The value 

 is, of course, mainly based upon the heat set free when the earth, 

 or a very thick outer shell, passed from the molten to the solid 

 condition ; in other words, upon the latent heat of fusion for the 

 earth rocks. 



Starting from this datum, and assuming the applicability of 

 Fourier's equations, the temperature which at any given time 

 existed at a given distance below the surface is easily calculated, 

 and it is found that, after 100,000,000 years (not 96,000,000 as 

 quoted by Mr. Eeade), the temperature gradient would be 1° F. in 

 50 feet, which Lord Kelvin assumes as the present temperature 

 gradient very near the surface. Since, also, this gradient varies 

 inversely as the square root of the time from consolidation, it is 

 easy to obtain the number of years which must have elapsed to 

 establish any particular rate of rise of temperatm'e with depth. 

 For example, for a gradient of 1° in 64 feet, the time would be 

 160,000,000 years for the same initial reduction, and the depth to 

 which loss of temperature would have penetrated would be 180 

 miles, as opposed to 150 miles on the assumption of 1° in 50. 



To emphasize how broadly these results must be looked at, it is 

 only necessary to point out that doubling the initial reduction of 

 surface temperature would multiply the number of years before 

 the establishment of any stated gradient by four, and that halving 

 the coefficient of conductivity would double the time. For example, 

 if the initial reduction were 10,000° F. the number of years would 

 amount to about 300,000,000. This is in accordance with the wide 

 general limits assigned by Lord Kelvin in his essay, in which he 

 places the time from first consolidation as somewhere between 

 20,000,000 and 400,000,000 years. 



Again, owing to the partial inapplicability of our equations to 

 surface rocks, it is questionable whether we can, with justice, 

 assume that 1° in 50 feet expresses the surface gradient which 

 would have been established were the whole globe continuous. In 

 short, the efi'ect of discontinuity in surface rocks would seem to 

 point to a retardation in the loss of heat and a consequent increase 

 in time from consolidation. 



To pass on now to consider the value of the assumption of a shell 

 of no-strain : The contraction taking place in one year at any point 



