426 TERENCE T. QUIRKE 



of the proportions of the crustal units, the abandonment of any 

 idea of those members being unsupported arches, the recognition 

 that they are probably relatively temporary phenomena coming 

 into being only upon occasion, and the limitation of this discussion 

 to those members subject to fracture put this conception of strata- 

 plate members in an entirely different class from the old theory of 

 crustal members which Chamberlin and Salisbury^ emphatically 

 discarded long ago. 



A comparison of the crustal members with sheets and long columns. 

 — Euler's formula^ has been used in comparing the deformation of 

 sheetlike members of the earth's crust to the yielding and failure 

 of long columns because the failure of sheets is similar to that of 

 long columns and because analyses of the deformation of sheets 

 under lateral thrust are rare or wanting. Euler's formula applies 

 strictly only to columns having lengths many times greater than 

 their least diameter. Of course this formula is used merely as an 

 illustration of the order of magnitude of the strength of a sheet. 

 It is not accurate to apply it even to every long column; yet it 

 applies with appropriate empirical modifications to all long columns. 



W. H. Burr^ says: ''Pieces of material subjected to compression 

 are divided into two general classes — 'short blocks' and 'long 

 columns'; the first of these only, afford phenomena of pure com- 

 pression. A 'short column' is such a piece of material, that if it 

 be subjected to compressive load it will fail by pure compression. 

 On the other hand, a long column (as has been indicated in Art. 25) 



fails by combined compression and bending The length of a 



short block is usually about three times its least lateral dimension." 



Therefore it is concluded that the earth's crust in major defor- 

 mation follows closely the behavior of long columns because it 



^T. C. Chamberlin and R. D. Salisbury, Geology, I (1904), 554-62. 



= T. T. Quirke, Geol. Survey, Canada, Mem. No. 102, " Espanola District, Ontario" 

 (191 7), p. 71, and Chamberlin and Miller, op.cit., p. 19. According to Euler's formula 

 the strength of a column equals 



in which E equals the coefficient of elasticity of the material involved, I equals the 

 moment of inertia, and L equals the length of the column. 



3 W. H. Burr, The Elasticity and Resistance of the Materials of Engineering (1890), 

 P- 371- 



