728 THE THEORY OF TRANSFORMATIONS [ch. 



comprehension is, in many cases, capable of very simple graphic 

 expression. This, after many trials, I believe to be in general 

 the case, bearing always in mind that the occurrence of indepen- 

 dent or localised variations must often be considered. 



We are dealing in this chapter with the forms of related organisms, in order 

 to shew that the differences between them are as a genera' rule simple and 

 symmetrical, and just such a.s might have been brought about by a slight and 

 simple change in the system of forces to which the living and growing organism 

 was exposed. Mathematically speaking, the phenomenon is identical with one 

 met with by the geologist, when h3 finds a bed of fossils squeezed flat or other- 

 wise symmetrically deformed by the pressures to which they, and the strata 

 which contain them, have been subjected. In the first step towards fossilisation, 

 when the body of a fish or shellfish is silted over and buried, we may take it 

 that the wet sand or mud exercises, approximately, a hydrostatic pressure — 

 that is to say a pressure which is un form in aU dii'ections, and by which the 

 form of the buried object will not be appreciably changed. As the strata 

 consolidate and accumulate, the fossil organisms which they contain will 

 tend to be flattened by the vast superincumbent load, just as the stratum 

 which contains them will also be compressed and will have its molecular 

 arrangement more or less modified*. But the deformation due to direct 

 vertical pressure in a horizohtal stratum is not nearly so striking as are the 

 deformations produced by the ob ique or shearing stresses to which mc'ined 

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

 have been brought about. And espec"ally 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 t-" A great number of described species, and here and 

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

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



If we begin by drawing a net of rectangular equidistant 

 co-ordinates (about the axes x and y), we may alter or deform this 



* Cf. Sorby, Quart. Journ. Geol. Soc. {Proc), 1879, p. 88. 



t Cf. D'Orbigny, Ale, Cours elem. de Paleon.tologie, etc., i, pp. 144-148, 1849: 

 see also Sharpe, Daniel, On Slaty Cleavage, Q.J.G.S. in, p. 74, 1847. 



X Thus Ammonites erugatus, when compressed, has been described as A. 

 ■planorhis: cf. Blake, J. F., Phil. Mag. (5), vi, p. 260, 1878. Wettstein has shewn 

 that several species of the fish-genus Lejyidopris have been based on specimens 

 .artificially deformed in various ways: Ueber die Fischfauna des Tertiaren 

 Glarnerschiefers, Abh. Schw. Palaeont. Geselhch. xni, 1886 (see especially pp. 

 2.3-38, pi. I). The whole subject, interesting as it is, has been little studied: both 

 Blake and Wettstein deal with it mathematically. 



