﻿132 Rev. 0. Fisher on the Level of 



could be demonstrable at so insignificant a depth, and a poste- 

 riori, considering the magnitude of the actually observed 

 features of the earth's surface/' 



As regards the a priori objection, that it is improbable that 

 any critical change in condition should be demonstrable at 

 the small depth of from two to four miles, it may be replied 

 that no claim is made that such a change in condition exists 

 at that depth in the actual earth. But what has been demon- 

 strated is, that, if the earth had cooled as a solid globe, a level 

 of no strain would be found in that position. In that case, 

 however, the surface-features would not have resembled in 

 size and arrangement those which we see. Consequently we 

 do regard the improbability of a critical change at so small a 

 depth to be a reductio ad absurdum, and conclude that one 

 of the premisses, viz. that of solidity, is wrong. The a poste- 

 riori objection involves a petitio principii ; for it assumes that 

 the observed features are due to contraction through cooling, 

 which is the very question that is being brought to the 

 proof. 



But it is in the method of investigation rather than in the 

 premisses that Mr. Blake appears to think a mistake has been 

 made; for he contends that the use of the "linear"* equa- 

 tions for the conduction of heat in the calculation of the 

 position of the level of no strain, as was done by Mr. Davison 

 and Professor Darwin f, and also by me, is inconsistent with 

 the introduction of the radius of the earth already assumed 

 infinite. The objection is prima facie plausible, and it had 

 occurred to me ; but seeing that the changes of temperature 

 involved occurred only near the surface, I did not think it 

 necessary to take sphericity into account as regarded the 

 temperature gradient ; and what follows will show that I was 

 justified. Using for convenience of reference the same 

 symbols as in my book J : — 



r = the radius of the earth considered spherical, 20,902,404 

 feet, 3958*78 miles ; 



t = the time since the globe solidified ; 



V= the temperature of solidification ; 



x = the distance of a spherical shell from the surface ; 



z = distance of the same from the centre ; 



v = the temperature of that shell when sphericity is 

 neglected — as was done in the work referred to ; 



* Mr. Blake thus refers to the equation for the conduction of heat in 

 one dimension. 



f Phil. Trans. Roy. Soc. vol. clxxviii., 1887. 



% l Physics of the Earth's Crust,' chap, viii., " On the Cooling of a Solid 

 Earth," 2nd ed., 1889, p. 94. 



