V] THE MEANING OF SYMMETRY 209 



111 all cases where the principle of maxima and minima comes 

 into play, as it conspicuously does in the systems of liquid films 

 which are governed by the laws of surface-tension, the figures and 

 conformations produced are characterised by obvious and remark- 

 able symmetry. Such symmetry is in a high degree characteristic 

 of organic forms, and is rarely absent in living things, — save in such 

 cases as amoeba, where the equilibrium on which symmetry depends 

 is likewise lacking. And if we ask what physical equilibrium has 

 to do with formal symmetry and regularity, the reason is not far 

 to seek ; nor can it be putbetter than in the following words of 

 Mach's*. "In every symmetrical system every deformation that 

 tends to destroy the symmetry is complemented by an equal and 

 opposite deformation that tends to restore it. In each deformation 

 positive and negative work is done. One condition, therefore, 

 though not an absolutely sufficient one, that a maximum or 

 minimum of work corresponds to the form of equilibrium, is thus 

 supplied by symmetry. Regularity is successive symmetry. 

 There is no reason, therefore, to be astonished that the forms of 

 equilibrium are often symmetrical and regular." 



As we proceed in our enquiry, and especially when we approach 

 the subject of tissues, or agglomerations of cells, we shall have 

 from time to time to call in the help of elementary mathematics. 

 But already, with very little mathematical help, we find ourselves 

 in a position to deal with some simple examples of organic forms. 



When we melt a stick of sealing-wax in the flame, surface 

 tension (which was ineffectively present in the solid but finds play 

 in the now fluid mass), rounds off its sharp edges into curves, so 

 striving towards a surface of minimal area ; and in like manner, 

 by melting the tip of a thin rod of glass, Leeuwenhoek made the 

 little spherical beads which served him for a microscope "j". When 

 any drop of protoplasm, either over all its surface or at some free 

 end, as at the extremity of the pseudopodium of an amoeba, is 



* Science of Mechanics, 1902, p. 395 ; see also Mach's article Ueber die physika- 

 lische Bedeutung der Gesetze der Symnietrie, Lotos, xxi, pp. 139-147, 1871. 



t Similarly, Sir David Brewster and others made powerful lenses by simply 

 dropping small drops of Canada balsam, castor oil, or other strongly refractive 

 liquids, on to a glass plate: On New Philosophical Instruments (Description of a 

 new Fluid Microscope), Edinburgh, 1813, p. 413. 



T. G. 14 



