Ai-Gi'ST, 1912. 



kno\vli:dgk. 



./>i^ 



one of the ancestors of our buttercups and daisies 

 and other phanerogams, and it occurred to me that 

 it might be worth while to see if any conclusions 

 could he drawn from counting the discal florets. In 

 picking the flowers to pieces it was observed that 

 there were some dwarfed and aborted discal florets, 

 hut not nearly so many as in the case of the thirteen- 

 ra\ed ox-eve daisy, no doubt because the number of 

 discal florets (range about fifty to one hundred and 

 tifty-hvc) was much smaller and consequently they 

 were less crowdeil. Tliis would, howe\-er. mean a 

 certain negative error : again, 

 owing to the greater number of 

 the florets, the errors in countin.i; 

 w ould also be greater than 

 in the case of the calen- 

 dulas, and such errors are 

 generalK' negative oni'S. 

 A floret is passed o\er 

 uncoimted. It is to be 

 observed, however, tliat 

 these errors do not tend 

 to false conclusions, but 

 onl\- to diminish the 

 evidence for a maximum, 

 if one exist ; for example. 

 sup[)ose a plant \\kv 

 Sciiecio jiicohocii has 

 generally thirteen rays : 

 in counting the rays we 

 are much more likely to 

 make a mistake in the 

 case of a thirteen-ra}ed flower. 

 than in a twelve or fourteen-raved 

 one, because there are hardly anv 

 of the latter, and the same is true 

 to a less extent in the case of 

 flower-heads with a smaller 





Figure 330. 



The primitive form of Senccio as deduced 



from Senccio jacohoca. 



that the discal florets tend not to be produced in 

 groups or multiples of five. 



We have, therefore, only to consider phyllotaxis 

 numbers, concentric ring numbers and their doubles. 

 Referring to the diagram we see that there is a 

 shadowy, very shadowy, tendenc)' for maxima to 

 coincide with numbers representing concentric rings 

 of circles. It is possible that the maxima at one 

 less than these numbers, of which there are four, may 

 realK- l)elong to these numbers, errors of counting or 

 the abortion of discal florets having reduced them 

 by one. The most important of 

 such maxima is at one hundred 

 and twenty representing six con- 

 centric rings of florets 

 in-ginning \sitli a ring of 

 live. 



The three really impor- 

 tant maxima are, howe\ei, 

 at c'iglit\--nin(\ one h\m- 

 (liiil and t<ii, and one 

 hundred anil twehe. The 

 eighty-nine maximum is 

 explained at once, eight\'- 

 iiine being the next phyllo- 

 taxis number above fifty- 

 li\e. The absence of a 

 maxinumi at fifty-fi\-e is 

 due to the fact that there 

 are hardly any flower- 

 heads of Senccio jacobocn 

 w ith less than sixtv discal 

 florets. How are the two principal 

 maxima at one hundred and ten 

 and one hundred and twelve to 

 be explained? Evidently they are 

 due to the doubling of the two 

 numbers, fifty-five the phyllotaxis 



maximum or maxima. On the other hand, if there number, and fifty-six w hich represents four concentric 

 be no sensible maxima, and there is pretty nearly the rings of the ring system beginning w ith a ring of five 



same number of flower-heads with one number of 

 discal florets as w ith another within the whole range, 

 we are as likely to count one number wrong as 

 another, so that the errors will not build up a 

 tictitious maximum, but, if we go on long enough, 

 more or less completely cancel one another out 



(5, 11, 17, 23 = 56). I am afraid those who have no 

 practical knowledge of the working of the phyllotaxis 

 and concentric circle law in the evolution of com- 

 posite flowers will hesitate to accept the inference, 

 which, however, I believe to be valid, viz., that 

 Senccio jacoboca has been developed from a more 



,llot;i 



The di.scal florets of three hundred flower heads primitive form, which flourished on poor or rocky sod 

 were counted. The subjoined diagram summarizes by straggling on to a more fertile habitat. All 

 the result, which, considering the small number of organic life develops by dichotomy (cell division) 

 flower-heads counted and the sources of error above giving numbers 2\ 2^, 2' — 2". At the beginnmg of 

 alluded to, is sufficiently striking and complete, this series eight and sixteen gave a ring of three sur- 

 rounded by a ring of five (imperfect five instead of 

 nine, but corresponding to vast numbers of 

 phanerogam flowers) and the perfect s\stem of five 

 surrounded by a ring of eleven, giving 2* or 16, and 

 considering the maximum at one himdred and twenty, 

 six concentric rings beginning with one of five, it is 

 not wonderful if the primitive form had a closeh- 

 similar arrangement, viz., four concentric rings begin- 

 ning with a ring of five. If to the phyllotaxis 

 number, fiftv-five, we add the other, thirteen, the 

 number of 'the raved florets, we get the number 



Three possibilities occur to one. 



1. — The discal florets mav represent 

 numbers or their doubles. 



2. — Concentric rings and their doubles. 



3. — Or they may be multiples of five. 



In one hundred and five consecutive numbers, the 

 number of multiples of five to the whole number is 

 roughly six to twenty-one, or about eighty-eight to 

 three hundred ; and it was found that in the countings 

 the number of multiples of five was considerably 

 below this average that chance would have given, so 



