INTERPEETATTOTf OF PHENOMET^A QF PHTLLOTAXTS. 229 



tlio eminent Swiss matlieinatician, James Bernoulli, that he usually 

 tienominated it f^pira mirahilis ; and in a paper published in the 

 Leipsic Acts in 1G92 he concluded his article on this curve Avith a 

 quaint ])aragrapli, adding the ejngraph, eadcm numero mvfaia resu)-(/o. 

 He directed that an Equiangular Spiral should be engraved on his 

 tomb, as an image of Immortality. 



As to the general principles of plndlotaxis, Mr. Church asserts 

 that modern botany has but little to do merely Avith the effects which 

 appeal to the eye on an adult plant-shoot. It seeks to determine 

 how these phenomena originated, what is the mechanism of their 

 production, what factors lie behind the mechanism, and how it was 

 originally called into operation ; that is to say, for what original 

 function, or by what response to conditions of external environment. 

 A short historical account of earlier writings on the matter is given ; 

 and illustrations expressing some of the more important features of 

 construction are produced in the figures. 



Numerous examples of })hyllotaxis are instanced, including plants 

 belonging to the following thirty-four natural orders of phanerogams : 

 Coniferai {Finns Pinea L., fig. vi. ; Araucaria excelsa K. Br., figs, x., 

 xi), Cj'peraceie, C3^cadace3e, Palmse, Pandanacese, Araceae, Liliacea3, 

 Fagacea3, Casuarinacese, Nymplijeaceae, Banunculaceaj, Calycanthaceae, 

 Berberidaceie, Papaveraceae, Crassulacese {Semjjervivum calcaration 

 Hort., fig. xii.), Bosacea3, Geraniace*, Euphorbiaceae (Uif2)J/o)'hia 

 Wff If enii Ho-ppe, fig. vii.), Sapindaceae, Onagracea?, Myrtaceae, Passi- 

 fioraceie, Cactaceae, Ficoideae, Haloragaceae, Araliaceae, Oleaccie, 

 GentianaceaB, Apocynaceae, Polemoniacea3 {Colcea scandens Cav., 

 fig. xiv.), Libiatae, Dipsaceae {DijysacKS fidlonum L., fig. viii.), Cam- 

 pan ulaceii3, and Composita3. 



Pig. i. exhibits the geometrical construction for uniform centric 

 growth-expansion, showing method of obtaining orthogonally inter- 

 secting pairs of log-spirals for any required ratio, symmetrical or 

 asynmietrical, to be used as curve-rules for drawing any required 

 construction as a standard of reference. Fig. xviii. exhibits retarda- 

 tion-effects in the distichous (1-j-l) system. 



A separate chapter deals with Phyllotaxis-phenomena in ciyptogams 

 and Thallophyta : Pteridophyta, Bryophyta, and Alga?, incfuding the 

 fossil, Lepidostrohus (sp.), fig. xv. Another chapter is devoted to 

 zoological and geological examples, such as, in Foraminifera, Quinque- 

 Joculina vulgaris, Q. semimdum (fig. xiii.), etc. 



The following note (p. 5Q) is interesting : *' Analogies are not 

 wanting in other departments of biology ; for example, a man's nose, 

 with distinctly heritable minor details, is derived from the pointed 

 end of the body of a benthic fish ; the latter expresses the pointed 

 end of a flagellate, overhanging the primary oral aperture (cytostome), 

 in turn the consequence of a phase of elementary polarity beyond the 

 original surface-tension sphere of aqueous plasma, and so far tracing 

 back to phenomena associated with surface-tension. Yet few would 

 saggest that the nose is modelled in the human embryo, at the present 

 time, solel}^ as a result of surface-tension. As the organism becomes 

 more complex, so the mechanism producing it may be elaborated 

 beyond recognition, or new mechanism may replace the old; such 



