114 



Miscellanea 



the fovir sets of results gives a reniarkatile and instnictive demonstration of the change which 

 may occur in individiial i>lant cliaractcrs withiii a .short sjiace of time. The following table, 

 abridged froin tlie fuller tables given by Mr ShuU, shows some fejvtures of the change. 



TABLE I. 

 Yariatiun in Nuinber und S. 1). of Flural Uiyuiin on four different Days. 



The change in mean and -Standard deviation of all the organs studied during the short 

 interval between Scjitoinlxir 27 and September 30 is of especial intcrest in connection with 

 the asserted miiltimodal distribiitions so often describcd in tloral organs. 



Mr Shull lays little stre.ss on the peaks of his frequency curves, but it i.s worth notice 

 that in this carefully collected inaterial there is not a Single c<ise of a niany-jwaked cnrve 

 in which the "uiodes" coincide with the niuubers of the Fibonacci series, and the author 

 criticises the process by which previously recorded "modes" are brought into accord with this 

 series. He sjvys "The niembors of the series, along with Ludwig's 'Unterzahlen,' which are 

 "niade up from the Fibonacci niuubers by nmltiplication or addition, — e.g., 10 = (2x5), 

 "29 = (8 + 21) etc., — include so large a proportion of all the sniallor nunil)ei-s that niany modes 

 " muat fall on or near one of them, even if there l)e no fundanientid relation existing between 

 "this complex series and the number of floral part-s or other organs under consideration. 

 "To account for modes which do not fall on any of theso, Ludwig creatcs the ' Scheingipfel,' 

 "which is formed by the overlapping of curves having their n)odes on adjacent numbcrs of 

 "the Fibonacci-Ludwig complex. Thus, if the maximum fall on 9, it is a ' Sclieingipfel' 

 "formed by the Union of curves having maxima uiwn 8 and 10; if it fall upon 11, it is 

 " made up of curves having maxima lipon 10 and 13, etc. It is evident that such a scheme 

 "will furnish an explanation of alniost any condition which might arise." 



It is to be hoped that Mr ShuU's admirable es.say will induce future investigators to 

 consider niorc carefully the sourcos of error in their proce-ss of collection before they jjssert 

 that even statistically signiticant "multimodality " is an indication of actual polymorphism in 

 plants, and to realise the importance of prolonged study before the difterences between local 

 races can be usefully insisted upon. 



AV. V. W. W. 



