ORIGIN OF SPIRAL STRUCTURES 



19 



and spectroscope, conclusively proved the correctness of Laplace's hypothesis." (For additional information on 

 this subject, see the beginning of the present section — " Prevalence of spiral arrangements on a grand scale in the 

 physical universe," p. 10.) 



While the vast systems of spiral nebulae, spiral cyclones, spiral sand-storms, spiral water-spouts, whirlpools, &c., 

 are on a scale of unexampled magnificence and splendour, there yet exist microscopic spiral arrangements in great 

 plenty which are quite as interesting in a way bo the chemist and physiologist as the others are to the astronomer 

 and physicist. Examples of the nainute spirals are to be found in crystals, plants, and animals ; especially the 

 two latter. 



Fio. 7. — Proelilorite. Shows 

 elegant siriral with transverse 

 markings. (From "System 

 of Mineralogy," by D. T. 

 Dana, 1892.) 



§ 4. Origin of Spiral Structures. 



Stereo-chemistry has shown that " optically active substances may be divided into two classes. Some, like 

 quartz, sodium chlorate, and benzil, produce rotation only when in the crystalline states ; the dissolved (or fused) 

 substances are inactive. Others, like oil of turpentine, camphor, and sugar, are optically active when in the liquid 

 state or in solution. In the former case the molecules of the substance have no twisted 

 structure, hiit they unite to form crystals having such a strudwe. As M. Pasteur expressed 

 it, we may build up a spiral staircase — an asymmetric figure — from symmetric bricks ; 

 when the staircase is again resolved into its component bricks, the asymmetry disappears. 

 In the case of compounds which are optically active in the liquid state, the twisted 

 structure must be predicated of the molecides themselves, that is, there must he a twisted 

 arrangement of the atoms which form these molecules." 



Pasteiir, in discussing the molecular constitution of tartaric acids, says that " the 

 molecular structures of the two tartaric acids are asymmetric, and, on the other hand, 

 that they are rigorously the same, with the sole difference of showing asymmetry in 

 opposite senses. Are the atoms of the right acid grouped on the spirals of a right-handed heUx, or placed on 

 the soUd angles of an irregular tetrahedron, or disposed according to some particular asymmetric group- 

 ing or other 1 We cannot answer these questions. But it cannot be 

 a subject of doubt that there exists an arrangement of the atoms in 

 an asymmetric order having a nonsuperposable image. It is not less 

 certain that the atoms of the left acid reahse precisely the asymmetric 

 grouping which is the inverse of this." Pasteur regarded the 

 formation of asymmetric organic compounds as the special prerogative 

 of the living organism. " Most of the substances of which the animal 

 and vegetable tissues are built up — the proteids, cellulose — are asym- 

 metric organic compounds, displaying optical activity. . . Meso- 

 tartaric acid contains two equal and opposite asymmetric groups of 

 atoms within its molecule." Pasteur was of opinion that compounds 

 exhibiting optical activity were never obtained without the intervention 

 of hfe. He also says : " Artificial products have no molecular asym- 

 metry ; and I could not point out the existence of any more profound 

 distinction between the products formed under the influence of life, 

 and all others." And, again, he refers to the molecular asymmetry of 

 natural organic products as the great characteristic which estabhshes, 

 perhaps, the only well-marked hne of demarcation that can at present 

 be drawn between the chemistry of dead matter and the chemistry of 

 living matter. " Non-hving, symmetric forces, therefore, acting on symmetric atoms or molecules, cannot produce 

 asymmetry, since the simultaneous production of two opposite asymmetric halves is equivalent to the production 

 of a symmetric whole, whether the two asymmetric halves be actually united in the same molecule, as in the case of 

 meso-tartaric acid, or whether they exist as separate molecules, as in the left and right constituents of racemic 

 acid. In any case, the symmetry of the whole is proved by its optical inactivity." ^ 



§ 5. Examples of Spiral Arrangements in Crystals. 



Subjoined the reader will find a striking example of a spiral crystalline formation (Fig. 7) which greatly 

 resembles a ram's horn (Fig. 8). Other examples of spiral crystals will be found at Plate ii., Fig. 23, p. 5. 



1 "Stereo-Chemistry and Vitalism," by Professor F. R. Japp, as given in the "Report of the British Association for the Advancement of 

 Science," 1898. 



Fic. 8.— Photogi-aplis of ram's horns l.iy the 

 Author ; drawn on wood by C. Berjean. A, front 

 view ; B, three quarter- view. Show Hne right and 

 left-handed spirals with transverse markings. 



