3-20 



JOURNAL OF THE ROYAL HORTICULTURAL SOCIETY. 



As these ray florets are developed at the ends of the spirals, into which 

 the head can be divided (compare Church) and of which the number is a 

 term in the Fibonacci series and distinctly affected by external conditions, 

 it is clear that the number of ray florets is useless as a systematic 

 character.— G. F. S.-E. 



Variation, Mathematics of. By Dr. G. Bitter (Beih. Bot. 

 Gentralbl. vol. xxv. Abth. 1, Heft 1, pp. 1-29 ; August 1909).— The author 

 gives numerous measurements (number of flowers in heads of Sanguisorba. 

 breadth of leaves, length of leaves and leaflets, width of fruits, &c.) which 

 show that the variations are not evenly distributed about a mean, and do 

 not agree with expectation according to the mathematical formulae of 

 probability. Larger numbers are found to occur at certain figures than 

 would be expected according to the above law. These maxima belong to 

 the Fibonacci series (3, 5, 8, 13, 21, &6., or 1, 3, 4, 7, 11, 18, 29, &c, or the 

 doubles and trebles of these). 



When ordinary linear growth or growth in surface (two dimensional 

 growth) is measured, it is found that there are maxima at the figures 

 10, 13-14, 17-18, 22, 28, 36, 45, and also at 20, 24-25, 31-32, 40, 50-51, 

 30, 38, 49, 26-27, 33, 42. In the author's tables one finds, for instance, 

 that there are maxima at 14 in fifteen series, and at 17 in sixteen series. 

 The author shows, however, that these particular figures correspond with 

 10 s/ 'i\ 10 s/2, 10 s/3, 10 n/5, 10 n/8, &c, 10 10 s/ 6, 10 s/ 10, &c, 

 10 n/9, 10 \ 7 15, &c, 10 n/7, 10n/11, &c, or ten times the square root in 

 the Fibonacci series. 



Similarly the maxima in measurements of nuts and fruits are 10, that 

 is 10 x %/l, 13-14, or 10 x 1/2 or \/3, 17 or 10 x s/5, 20 or 10 x ^8, 

 23 or 10 x s/13, and so on. 



These results are of great interest and importance. The season of 

 gathering and degree of nutrition alter the distribution of the figures, but 

 there are always maxima at figures in one or other of the forms of this 

 series. For the suggested explanation, on the ultra mikron (r^'of oooo 

 of a millimetre) theory, reference must be made to the original. 



G. F. S.-E. 



Variegated Leaves, Investigations on. By H. Kranzlin (Zcit.f. 

 Pflanzkr. vol. xviii. No. 4, 1908, p. 193). — An investigation of the colouring 

 matters in variegated leaves, based on the adsorption method of Tswett. 

 As a result it is found that in all leaves, even in the pure yellow ones, 

 green colouring matter (chlorophylline) is present. The colouring matters 

 in a variegated leaf differ only quantitatively, not qualitatively, from 

 thpse in a healthy green leaf. 



There is no difference in the composition of the colouring matters in 

 infectious variegation and non-infectious variegation. The amount of the 

 different colouring matters is always less in the yellow parts of the leaf 

 fchan in the green, the colouring matters diminishing in relatively different 

 degrees. There is a striking parallelism between the diminution of the 

 green colouring matters (chlorophylline) and of carotin. — G. H. P. 



