— 21 — 



This arrangement of the bracts is what is called in a newer term (Church, 

 V. Iterson, Schoute) the 3 + 5-position. 



The 4th bract being inserted between the second and first, it indicates 

 with the first bract one of the 3-curves (the other two are determined by 

 the second and 5th and by the third and 6th bract) but in the same time it 

 forms with the second the beginning of a 2-curve (zweier - Zeile) which, 

 of course, runs opposite to the 3-curve and thus runs in the same direction 

 with the 5-curve but forms a much lowerspiral ; the other 2-curve is determined 

 by the first and third bract. Mostly these are also contact-parastichies ; so 

 that we have in most cases a (2 + 3 + 5)-position. Following tlien the 

 genetic spiral it appears that also tlie 9th leaf forms with the 1st a parastichy, 

 the 10th with the second etc. and also the 14th with the first; these are 

 the 8 and 13-curves, of which there are of course resp. 8 and 13. Often 

 the 14th bract is quite perpendicular above the first the 15th above the 

 second so as to form orthostichous lines. So we have substantially a divergency 

 of 5/8, but the line is very seldom really an orthostichous one but is more 

 or less curved. In very dense spikes the 21-curves and sometimes the 34- 

 curves are easily to be seen and thus both nearly perpendicular lines. 



A general scheme of a leaf-positon of the divergency 13/21 (3 + 5- 

 position with a rectangular parastichous angle) stretched out on a flat plane 

 is to be found in Schwendener's Mechanische Biattstellungs-theorie (1878 

 fig. 1.) copied in Schneider's Handwörterbuch (1905, 93) and the leaf- 

 position in a spike of Curcuma brog agreed perfectly with this; also in 

 C. purpurascens this occurs sometimes in spikes of 40— 50 bracts. Our PI. IV 

 fig. 1 of the young spike of a middle-sized C. purpurascens, is almost built accord- 

 ing^ to this scheme. Taking here an indifferent bract we see that it is surrounded 

 by 8 other leaves and thus the centre of 4 parastichies. So No. 9 is the 

 point of contact of the 5-curve: 4, 9, 14, which takes to the left — of the 

 three-curve: 6, 9, 12, which takes to the right, and is most conspicuous, 

 of the two-curve: 7, 9, 11, which does not form a complete contact and of 

 the 8-curve (1, 9, 17) which does not form a contact at all. When we 

 think these figures placed on the "Dachstuhl" of Schwendener (1, c. 13) 

 and we move these figures in such a way that the first and 9th separate a little 

 farther, then the 7th and 1 1th will approach the 9th and the two-curve will become 

 a contact parastichy. Then we get the 2 -f- 3 + 5-system usually occurring 

 in the mesantha-oi purpurascens-group. When we continue this stretching 

 still farther, then the 4th, 9th and 14th also separate and the five-curve is 

 no more a contact-line, and we have the system 2 -|- 3. This occurs often 

 in very feeble spikes of the C. aurantiaca. It is thus the form of the paras- 

 tichous angle, which determines the shape of the spikes, and this depends 

 again on the number of the bracts, and the thickness of the axis. Of course 

 such movings in- and outwards do not happen in natura. 



