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XIX.—On some Abnormal Cones of Pinus Pinaster

Published online by Cambridge University Press:  17 January 2013

Alexander Dickson
Alexander Dickson
Affiliation:
Regius Professor of Botany in theUniversity of Glasgow
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Extract

It is well known that although the overwhelming majority of specimens of fircones exhibit one or other of the simple spiral arrangements represented by the terms of the ordinary series ½, ⅓, ⅖, ⅜, , &c., whose generating and successive secondary spirals are indicated by the numbers 1, 2, 3, 5, 8, 13, &c., yet exceptional cases occur now and again, where we find either conjugate spirals of the ordinary system, or arrangements (usually simple, but sometimes conjugate) belonging to other systems of spirals. Of these exceptional arrangements, perhaps the most common are bijugates of the ordinary system, giving the numbers 2, 4, 6, 10, 16, 26, &c., and simple spirals belonging to the system ⅓, , &c., giving the numbers 1, 3, 4,7,11, 18, &c. More rarely, trijugates of the ordinary system occur, giving the numbers 3, 6, 9, 15, 24, 39, &c.; or spirals of the system , ⅕, , &c., giving the numbers 1, 4, 5, 9, 14, 23, 37, &c.; not to speak of various other arrangements, some of which will fall to be considered in the special cases which form the subject of the present communication.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 26 , Issue 2 , 1871 , pp. 505 - 520
Copyright
Copyright © Royal Society of Edinburgh 1871

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References

page 506 note * Braun, , Vergleichende Untersuchungen über die Ordnung der Schuppen an den Tannenzapfen; Nova Acta Acad. C.L. xv. 1, p. 316Google Scholar.

page 506 note † L. et A. Bravais, Sur la disposition des feuilles curviseriées. Ann. des Sc. Nat. 2me sér. vii. p. 100.

page 506 note ‡ L. c. pp. 106, 107.

page 506 note § L. c. p. 93.

page 506 note ∥ L. c. p. 103.

page 507 note * L. c. p. 103.

page 507 note † See Proceedings R. S. Edin., vii. pp. 398, 399.

page 508 note * In this and the following tables, under S, are indicated the numbers of spirals, generating as well as secondary, running to the left; under D, the numbers of those running to the right; while under V, are indicated the numbers of vertical rows.

page 514 note * It might, perhaps, be possible for a mathematician to furnish a formula, whereby, from two spiral systems given, to deduce the number of ambiguous scales, and the value in the upper system of the scale of convergence, thus saving the trouble of a preliminary geometrical construction.

page 516 note * It will be remembered that in Cone III. the system 1, 2, 5, 7, 12, &c., is derived from the ordinary system by coalescence of consecutive scales in one of the secondary spirals by 5. Here, the system 1, 3, 4, 7, 11, &c., would be derived from the same by coalescence of consecutive scales in one of the secondary spirals by 3.

page 517 note * This view I published (under reserve) in the abstract of this communication in the Society's Proceedings, vol. vii. p. 453.