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XIX.— On some Abnormal Cones of Pinus Pinaster. By Alexander Dickson, 

 M.D., Eclin. & Dublin. ; Regius Professor of Botany in the University 

 of Glasgow. (Plates XIX.-XXII.) 



(Paper read 1st May 1871. Given in for publication 23d October 1871.) 



It is well known that although the overwhelming majority of specimens of fir 



cones exhibit one or other of the simple spiral arrangements represented by the 



112 3 5 



terms of the ordinary series ^, „, -^, =, j^, &c, whose generating and successive 



secondary spirals are indicated by the numbers 1, 2, 3, 5, 8, 13, &c, yet excep- 

 tional 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, 



112 3 5 



6, 10, 16, 26, &c, and simple spirals belonging to the system^, j, -, — , — , &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 



112 3 5 8 

 system -^ ^ ^, ^, ^, gf> &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 communi- 

 cation. 



The occurrence of exceptional arrangements in structures exhibiting so much 

 general uniformity as fir cones, naturally raises the question as to whether these 

 deviations may not be deduced from the simple spiral of the ordinary system, or 

 from some fundamental form, affording a common basis for both. 



In his great work on the Arrangement of the Scales on Fir Cones, Alex- 

 ander Braun, in speaking of the occasional occurrence of cones where the 

 most apparent secondary spirals, instead of being, as usual, 5 and 8 in number, 

 are 4 and 7, refers to the temptation to explain away the anomaly by assum- 

 ing the abortion of the fifth and eighth secondary spirals respectively, only, 

 however, to reject such an assumption as an absurdity of the same kind, as 

 if 2-nary, 4-nary, and 7-nary flowers were considered respectively as 3-nary, 

 5-nary, and 8-nary ones reduced by abortion ; adding, that " it will be better 



VOL. XXVI. PART II. 6 Q 



