PROFESSOR DICKSON ON SOME ABNORMAL CONES OF PINUS PINASTER. 511 



Table E. — Cone of Pinus Lambertiana, in Museum, Edinburgh Botanic Garden. 





S 



D 



S 



D 



S 



V 



Top, 



1 



4 



5 



9 



14 



23 = — 

 23 



Middle, 



— 



2 



4 



10 



14 



24= 5 



12x2 



Bottom, 



1 



4 



5 



9 



14 



23 - - 



Having submitted the foregoing facts, I shall now proceed to consider : — 



1st, in what the so-called convergence of secondary spirals really consists ; 



2d, what constitutes affinity of different spiral systems as regards their 

 possible or actual derivation one from another ; and 



3d, whether it is possible to conceive of the varying spirals in fir cones, or 

 in other plants, being mediately or immediately derived from some one funda- 

 mental arrangement in a given set of cases. 



1st, As to the nature of "convergence" of secondary spirals. It cannot 

 fail to strike the attentive observer that a certain absurdity is involved 

 in the idea of coalescence, or fusion of two secondary spirals into one. 

 Secondary spirals, it is to be remembered, have only a relative existence. For 



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example, in a cone with an — spiral the very same scales which constitute the 



eight secondary spirals running to the one hand, make up the thirteen 

 running to the other. The same objection applies to " convergence " considered 

 as the result of an abortion or suppression of a secondary spiral ; for it is as 

 difficult to conceive of the abortion of one spiral, which has only a relative 

 existence, as of the fusion of two similarly circumstanced. To take a special 

 case. About the middle of Cone III., described above, an ordinary trijugate 



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changes by " convergence " into an ^= spiral; but it would be quite as correct 



to say that coalescence (or abortion) occurred among the spirals by 15, or 

 by 24, as among those by 6, &c. (see Plate XXII. fig. 1). MM. Bravais 

 appear to have felt this difficulty, but content themselves with arguing for the 

 probability of the abortion occurring among the more apparent secondary 

 spirals, where the successive insertions are in contact, as contrasted with the 

 improbability of its occurrence among the less apparent secondary spirals 

 whose insertions are not contiguous. 



Having disposed of the hypotheses of abortion and fusion of secondary 

 spirals, respectively, — hypotheses which are, in fact, little more than different 

 attempts to express what is simply one of the results of a certain disturbance, 

 viz., diminution in the number of secondary spirals, — we proceed to inquire if 

 there are any facts to guide us in ascertaining the proximate cause of the disturb- 



