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XXII. Torsion- Structure in the Alps. 

 B\j John Buchanan, B.Sc* 



IN an article with the above title (' Nature/ Sept. 7, 1899), 

 Dr. Maria M. Ogilvie has given an outline of some of 

 the results to which her observations in the field have led her. 



I have here attempted to examine the application of some 

 of the ideas there set forth to the case of a plastic, or quasi- 

 plastic sheet. Let us imagine such a sheet to be subjected to 

 forces of compression parallel to its surface. For our present 

 purpose we may treat the sheet as incompressible. The 

 resulting deformation of the sheet will be a series of corruga- 

 tions, each corrugation consisting of an arch and a trough. 

 The axes of these corrugations will on the average be, at 

 each point, perpendicular to the direction of the force at that 

 point. What will be the result if the sheet be now acted on 

 by another set of compressive forces again parallel to the 

 surface, but in a different direction from the first set ? 



Evidently, this second set of forces would tend to give rise 

 to a new series of corrugations, which in turn would tend to 

 have their axes everywhere at right angles to the direction of 

 these forces. The actual result obtained at any point will be 

 that due to the combination of the displacements which each 

 set of forces would separately produce, the combination being 

 effected by the parallelogram rule. 



We will now proceed to consider the result of superposing 

 a regular series of corrugations on another regular series, the 

 two series being combined according to the method just 

 indicated. In order to show the bearings of the method, two 

 comparatively simple cases are here dealt with. 



Case 1. — Let us assume the original corrugations of the 

 sheet to be parallel to one another, and equally spaced, with 

 their axes lying say east and west. Let now the second 

 system of compressive forces act inwards towards a centre, so 

 that, if alone, they will be assumed to give rise to a series 

 of equally spaced concentric circular corrugations. The 

 resultant curves are what Dr. M. M. Ogilvie has called 

 " torsion-curves/' Those figured in fig. 1 are confocal para- 

 bolas ; the focus is the centre of the circular corrugations. 



t ■ 



So long, however, as the spacings are regular in the two sets 

 of corrugations, the torsion-curves in case 1 are always con- 

 focal conies. Fig. 1 shows also how it is possible for the 

 superposed system to cross the original corrugations at all 

 angles from 0° to 90°. 



In the more general case where the spacing of the circles 

 and of the parallel lines is irregular, it would appear that each 



* Communicated bv the Author. 

 Phil Mag. S. 5. Vol, 50. No. 303. Aug. 1900. T 



