1038 THE THEORY OF TRANSFORMATIONS [ch. 



and folded strata have been exposed, and by which their various "dislocations " 

 have been brought about. And especially in mountain regions, where "these 

 dislocations are especially numerous and complicated, the contained fossils 

 are apt to be so curiously and yet so symmetrically deformed (usually by a 

 simple shear) that they may easily be interpreted as so many distinct and 

 separate "species*." A great number of described species, and here and 

 there a new genus (as the genus Ellipsolithes for an obliquely deformed 

 Goniatite or Nautilus), are said to rest on no other foundation f. 



If we begin by drawing a net of rectangular equidistant coordinates 

 (about tlie axes x and y), we may alter or deform; this network in 

 various ways, several of which are very simple indeed. Thus (1) we 

 may alter the dimensions of our system, extending it along one or 





Fig. 491. 



Fig. 492. 



other axis, and so converting each little square into a corresponding 

 and proportionate oblong (Figs. 491, 492). It follows that any 

 figure which we may have inscribed in the original net, and which 

 we transfer to the new, will thereby be deformed in strict proportion 

 to the deformation of the entire configuration, being still defined 

 by corresponding points in the network and being throughout in 

 conformity with the original figure. For instance, a circle inscribed 



* Cf. Ale. D'Orbigny, Cmirs dim. de PaUontologie, etc., i, pp. 144-148, 1849; 

 see also Daniel Sharpe, On slaty cleavage, Q.J.G.S. m, p. 74, 1847. 



t Thus Ammonites erugatus, when compressed, has been described &a A . planorbis : 

 cf. J. F. Blake, Phil. Mag. (5), vi, p. 260, 1878. Wettstein has shewn that^several 

 species of the fish-genus Lepidopus have been based on specimens artificially 

 deformed in various ways: Ueber die Fischfauna des Tertiaren Glarnerschiefers, 

 Abh. Schw. Palaeont. Gesellsch. xiii, 1886 (see especially pp. 23-38, pi. i). The 

 whole subject, interesting as it is, has been httle studied ; both Blake and Wettstein 

 deal with it mathematically. 



