G. F. Becker — Current Theories of Slaty Cleavage. 17 



are mutually perpendicular." This is true only for a case of 

 static equilibrium. In any authoritative text-book on dynamics 

 will be found Poinsot's theorem, that the forces acting on any 

 point are reducible to a resultant and a couple* If Mr. Leith's 

 statement were correct, it would be possible to reduce a couple 

 to a single force. It is, of course, the couple which when resisted 

 gives rise to the rotational strain, just as it is an unresisted or 

 partially resisted couple which gives the rotation of a planet 

 or a rifle ball. 



All the arguments which Mr. Leith offers in favor of his 

 views of slaty cleavage and against my theory have now been 

 passed in review ; while to his denial of my accuracy in report- 

 ing the orientation of bubbles in cakes of ceresin and in stating 

 the directions of cleavage,f I have no reply to make. Messrs. 

 Van Hise and Leith do not seem to me to have improved upon 

 Sharpe's theory, and, so far as I can see, geologists must choose 

 between the pure strain theory of the able Englishman and my 

 rotational strain theory. Sharpe's theory is consistent but 

 leaves much to be explained, both from a molecular and a 

 molar standpoint. When the prevalence of rotational strains is 

 admitted, so that a slate belt becomes tectonically equivalent to 

 a distributed fault, this theory does not apply and cannot be 

 adapted. 



It appears to me that Mr. Leith is in duty bound to make 

 public exact reasons for his assertions, to give precise methods 

 for determining the position of the strain ellipsoid or the equi- 

 potentials in a slate, to show why there is no cleavage on planes 

 of maximum slide, and to explain thermodynamically how it 

 happens that the planes on which the entire energy of defor- 

 mation is expended are not those on which feldspar is converted 

 into mica. We are past the stage in which mere opinions or 

 general impressions should be allowed decisive weight. 



The distinction which Mr. Leith draws between flow cleavage 

 and fracture cleavage is substantially a real one, which I pointed 

 out 14 years ago. u Flow will tend to take place," I stated, 

 " along one set of planes of maximum slide " because of the 

 inferior viscous resistance." The other set of planes of maximum 

 slide, it was inferred, would be marked by ruptures such as 

 joints. I did not perhaps sufficiently consider that the scale of 

 the whole structure might be microscopic, yet the magnified 

 reproduction of Mr. Dale's slide precisely resembles a reduced 

 photograph of the structure which I had in mind. 



Washington, D. C, April, 1907. 



*Cf. e. g., Thomson and Tait, Nat. Phil., section 559 g. 

 \Op. cit, p. 129. 



Am. Jour. Sci. — Fourth Series, Vol. XXIV, No. 139. — July, 1907. 

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