the Contraction of a Solid Earth. 393 



to it, the shell is about to sink into a position where, being 

 nearer to the centre, it will find less room to occupy. The 

 question then is — Will the horizontal linear contraction of 

 this shell exceed or fall short of that loss of room ? If it 

 exceeds, the shell will tend to be extended. If, on the other 

 hand, the contraction is less than the loss of room due to the 

 sinking through shortening of the radius, the shell will be 

 compressed. Mr. Davison has shown that near the surface 

 the shells are being compressed, and deeper down extended, 

 and that there is a certain level of no strain, where there is 

 neither extension nor compression ; and that this level sinks 

 deeper as time goes on. We see, then, that no compression 

 has ever taken place below the level of no strain, and that, 

 between the surface and it, all the shells have successively 

 passed from a state of extension into one of compression. In 

 calculating the amount of compression in this third case, it 

 will be necessary to have regard to the position of the level 

 of no strain at every successive moment from the commence- 

 ment of the cooling, because it defines at that moment the 

 limit, below which compression does not reach. Any calcu- 

 lation, in which we did not integrate for the time, would 

 therefore give an incorrect result in the case we are now 

 considering. I hope to send shortly a calculation of the mean 

 height of the elevations which might be formed on this 

 hypothesis. 



4. But we may make a fourth hypothesis, impossible no 

 doubt, but still one which, being "too highly favourable " in 

 its impossibility, will give an amount of compression, and 

 therefore of surface- elevations caused by it, greater than 

 would be formed on the third and truer hypothesis. It is 

 that which I made in my paper in this Magazine*, and of 

 which Mr. Davison says that the argument based upon it 

 " loses its force when we consider the natural process of a 

 continuous and gradual cooling." But I submit that any 

 argument derived from the smailness of the elevations cannot 

 lose its force because the hypothesis, on which they have been 

 estimated, errs on the side of making them not small enough. 

 For observing that, upon the more correct hypothesis, the 

 compression, or folding, is the excess of the loss of room due 

 to the sinking of a shell bej'ond the horizontal contraction 

 due to the cooling of that shell, if we neglect altogether 

 the horizontal contraction of the shells, every shell will be 

 compressed, and if, to keep the mass unchanged, we likewise 



* Phil. Mag. vol. xxiii. (1887) pp. 145-149. (In the figure to this 

 paper 6 should be q, and in the explanation of it OQ should be Oq.) 

 Phil. Mag. S. 5. Vol. 24. No. 150. Nov. 1887. 2 D 



