304 



KNowiJ.Dr.i:. 



August, 1912. 



sixty-eif,'lit.\\lii(h cnrifsixnuls to foiircoiiri'iitrir riii;,'s 

 of ciri-li's of tlic riiiK svsti-in licj,'innin^ with a rinj,' of 

 c-it,'ht (8, 14. JO. i6 = 6S) (soo FiKure 329). Tlif outer- 

 most rill},' contains just t\\onty-si.\ Horcts so that ewrv 

 otlur Horct would lie a rayed one. In tlie analvsis 

 of the calendula there were reasons for believiiif,' that 

 sometimes a certain number of the discal llorets was 

 disposed symmetrically in the outermost, that is. the 

 ring of rayed florets. Let us suppose the cell from 

 which the comjiosite Hower-head sprung submitted 

 to tliree cell divisions and we get eight (2") cells and 

 if these arranged themselves in a ring of eight thev 

 would form the basis of the above-mentioned .system 

 in the ancestral Sciiccio. This may partiv explain 

 the evolution of the phyllotaxis number thirteen, or 

 in certain cases but only partially. The svstem gives 

 an approximately regular thirteen-ra\ed star. 



.\ word of warning is necessary regarding the 

 diagrammatic mode of representing statistics now so 

 much in vogue, at least as regards the present 

 diagram. The two chief maxima appear sufificientlv 

 striking, but making all due allowance for negative 

 errors and aborted florets, they only represent maxima 

 of about five per cent. We need not suppose, there- 

 fore, that the more primitive type had all its flower 

 heads with fifty-five or fifty-six discal florets ; twenty- 

 five per cent, of each would be quite enough to 

 account for the maxiina in the present instance. It 

 so happens that the next lower phyllotaxis number 

 for three concentric rings of circles beginning 

 with a ring of five (thirty-three), and the next 

 low er phyllotaxis number thirty-four, also only differ 

 by unit} , in this case the phyllotaxis number being 

 the greater. 



The next phyllotaxis nunilier twentv-one has no 

 number of the five ring systems at all near it, but the 

 thirteen has sixteen or two concentric rings of circles, 

 beginning with a ring of five corresponding to two 

 maxima in Infyha chicurea. There is another ver\- 

 remarkable case where the phyllotaxis number thirteen 

 occurs invariably in certain of the animal and not 

 vegetable kingdom. 



Leaving this more or less speculative field, the 

 fact remains demonstrated that the four principal 



maxima of the discal raws of Sciiccio Jacohoea 

 represent : — 



(1) The phyllotaxis number .S9. 



(2! The [ihyllotaxis number 55 doubled=110. 



(.i) The sum of four concentric rings beginning 

 with a ring of 5 doubled=112, and 



(4) The sum of five concentric rings beginning 

 with a ring of 5 = 120. 



Those who have hitherto believed that the 

 evolution of symmetrical form can be explained by 

 '■ [irotection " and " survival of the fittest '" in its 

 ordinary sense, at the conclusion of this essay ma\' 

 [lerhaps be less confident in their assertions. The 

 fact is that the fatal gift of symmetry exposes the 

 possessor of it to a host of enemies. The naked 

 eye can detect almost microscopically small 

 snail shells on account of their symmetry, and to 

 protect them " protection " and " natural selection " 

 so far from evolving s\mmetry, have to evolve all 

 sorts of devices to mask it, carried to extreme 

 lengths in certain sea horses and stick-insects. 

 " Protection " and " natural selection " are not 

 invoked to explain the symmetr\- of crystals, and 

 there is not a shred of evidence to prove that they have 

 any more to do with the evolution of organic than 

 with the evolution of crystalline symmetry. I may 

 conclude by saying that the law of the exposure to 

 risk from symmetry is universal, and is found in the 

 moral as well as the organic world. 



Note. — Since writing the above, I took a walk to a 

 spot (above Cimburg) about one thousand metres 

 above sea level. Here, on rocky ground, was 

 grow ing a somewhat viscid plant something between 

 a groundsel and a ragwort. I believe it is classed as 

 a ragwort. I brought home a few heads which gave 

 the following result : — 



13 4n ' 



13 42 '= 55 or 4 rings of 5 -ring system — 1 the 



13 42 I phyllota.\is number. 



13 43) 



13 33 i.e., 13 and 3 rings of the 5-ring system. 



13 39 I.e., 13 and 3 rings of the 7-ring system. 



13 36 



10 31 



VENUS: Till': 



I'LANI'T ()!• MV.sri-.kV 



liv I'KANK r. DLXXl'.TT. 



No other planet shines with such a brilliant light as Venus, 

 either as an evening, or as a morning star ; so briihant even 

 that it will throw a very evident shadow. Although .i little 

 less in size than the Earth, when nearest to us, it attains an 

 apparent diameter greater than that of any other planet. 

 Notwithstanding its closeness, an air of mystery has seemed to 

 hang over its study, making the work of different observers 

 yield most contradictory results. 



Its supposed satellite was observed first by the elder Cassini, 

 who wrote thus: " A.D. 1686, August 2Sth, at fifteen minutes 

 after four in the morning, looking at Veims with a telescope of 

 thirty-four feet, I saw at the distance of one-third of her 

 diameter eastward a luminous appearance of a shape not well 

 defined, that seemed to have the same phase with Venus, 

 which was then gibbous on the western side. The diameter 

 of this phenomenon was nearly equal to a fourth part of the 



diameter of Venus. I observed it attentively for a quarter of 

 an hour, and having left off looking at it for four or five 

 minutes I saw it no more ; but daylight was then advanced. 

 I had seen a like phenomenon which resembled the phase of 

 \'enus, January 25th, .\.D.. 1672. from fifty-two minutes after 

 six in the morning to two minutes after seven, when the 

 brightness of the twilight made it disappear. Venus was then 

 horned ; and this phenomenon, the diameter whereof was 

 nearly a fourth part of the diameter of \'enus. was of the same 

 shape. It was distant from the southern horn of Venus a 

 diameter of the planet on the western side." The ne.xt 

 observations were made by the celebrated reflector-maker, 

 James Short, on the morning of October 23rd, 1740, using a 

 16-5 inch retlector, magnifying between fifty and sixty, when 

 he measured a star 10' distant from the planet. L'sing powers 

 of two hundred and forty and one hundred and forty, the little 



