386 Royal Society : — 



occurs in many, previously boiled fluids when exposed to the air 

 is not due to a contamination by germs derived from the atmo- 

 sphere, we have also the same right to conclude (2) that in many 

 cases the first organisms which appear hi such fluids have arisen 

 de twvo, rather than by any process of reproduction from pre- 

 existing forms of life. 



Admitting, therefore, that Bacteria are ferments capable of 

 initiating putrefactive changes, I am a firm believer also in the 

 existence of not-hving ferments under the influence of which 

 putrefactive changes mar be initiated in certain fluids — changes 

 which are almost invai'i^bly accompanied by a new birth of Hving 

 particles capable of rapidly developing into Bcuteria. 



Feb. 27, 1873. — William Spottiswoode, M.A., Treasurer and Vice- 

 President, in the Chair. 



" On Leaf -Arrangement." By Hubeet Aiet, M.A., M.D. 



Assuming as generally kno\^-n the main facts of leaf-arrange- 

 ment, the di^dsion into the whorled and spiral types, and in 

 the latter more especially the establishment of the convergent 

 series of _ fractions |, i, f , s, y\, ^, i|, f ^, |^, -^\-, &c. as re- 

 presentatives of a corresponding series of spiral leaf -orders among 

 plants, we have to ask, what is the meaning that hes hidden in 

 this law ? 



Mr. Darwin has taught us to regard the different species of 

 plants as descended from some common ancestor ; and therefore 

 we must suppose that the different leaf-orders now existing have 

 been derived by different degrees of modification from some com- 

 mon ancestral leaf-order. 



One spiral order may be made to pass into another by a twist 

 of the axis that carries the leaves. This fact indicates the way ia 

 which all the spiral orders may have been derived from one 

 original order, namely by means of different degrees of twist ia 

 the axis. 



We naturally look to the simplest of existing leaf-orders, the 

 two-ranked alternate order |, as standing nearest to the original ; 

 for it is manifest that the orders at the other extreme of the 

 series (the condensed arrangement of scales on fir-cones, of florets 

 in heads of Compositce, of leaves in close-l^dng plantains, &c.) 

 are special and highly developed instances, to meet special needs 

 of protection and congregation : they are, -ndthout doubt, the 

 latest feat of phyllotactic development ; and we may be sure that 

 the course of change has been from the simple to the complex, 

 not the reverse. This point will be illustrated by experiment 

 below. 



But first, what are the uses of these orders ? and at w-hat period 

 of the leaf's Hfe does the advantage of leaf-order operate ? The 

 period must be that at which the leaf-order is most perfect — 

 not, therefore, when the twig is mature, with long internodes 

 between the leaves, but while the twig and its leaves are yet in 

 the bud ; for it is in the bud (and similar crowded forms) that 



