414 T. Mellard Reade — Origin of Mountains. 



less be concentrated in one spot ; some of it would go to thicken the 

 earth's ci'iist. 



Mr. Vaughan calls in question the principle adopted by me of 

 ascertaining the radial contraction of the earth under the conditions 

 assumed by me. The method, of course, is only a rough one, but 

 when we are dealing with quantities which cannot be established 

 with great accuracy the rough method is the safest. I take the 

 direct linear radial contraction across the contracting shells, and 

 multiply that by three. A little consideration will show why the 

 linear contraction across the shells is not a true index of the earth's 

 contraction as a whole. The shells are stretching themselves over 

 a nucleus that remains of a nearly constant diameter, therefore they 

 are thinning themselves by stretcliing, as well as by radial con- 

 traction. To put it in other words : A voluminal contraction is 

 a contraction of a given volume along three axes at right angles to 

 one another — this will be expressed roughly by a figure three times 

 the linear contraction. When, however, a shell of rock contracts 

 over an unshrinking sphere below, contraction along two of these 

 axes being impossible, the whole effect is concentrated on the third 

 and becomes a linear contraction — roughly, three times the linear 

 contraction proper for the rock ; of course being accompanied by 

 tensile stresses and deformation of shape. 



Having had considerable difficulty in following Mr. Vaughan's 

 reasoning respecting his own theory, I may possibly have mis- 

 apprehended it as he has mine in the cases just dealt with. 



To put it shortly, his may be called a tensile theory. Before such 

 a theory could be established it would be necessary to show that the 

 tensile strengths of the materials of the earth are sufficient to stand 

 the stresses this theory puts upon them. It appears to be part of 

 Mr. Vaughan's theory that the outer crust has not been able to withstand 

 the tensile stress put upon it by shrinkage through loss of heat, and is 

 consequently full of fractures. How then could the underlayers by 

 shrinking exert such a huge pressure on the interior as to actually 

 compress the materials of the earth into a smaller volume ? Is the 

 tensile strength of any of these underlayers equal to that of steel ? 

 We know that 30 tons to the square inch is about the breaking 

 strength of steel. It would be interesting if Mr. Vaughan or some 

 other mathematician would work out the decrease of volume which 

 would result from a given contraction of a shell of steel, say 

 30 miles thick, acting on a sphere of the size and composition of our 

 earth.^ A theory is of little use wdthout a quantitative basis. When 

 this is worked out it may be found unnecessary to calculate the 

 amount of compression of the interior which a local shrinkage of 

 a given segment of the sphere would be competent to produce, if, 

 indeed, it would produce any, which I very much doubt. 



1 If we look upon this shell as a spherical boiler of steel 30 miles thick and of the 

 diameter of the Earth, dependent only upon its tensile strength, a pressure of steam 

 of half a ton to the square inch would burst it. It is questionable if such a shell 

 of steel could by shrinkage exert an effective pressure of one quarter of a ton per 

 square inch on the materials of the interior of the Globe. 



