508 PROFESSOR DICKSON ON SOME ABNORMAL CONES OF PINUS PINASTER. 



spiral (series -, -, -, ^, ^, —-, &c), with secondary spirals 9 S, 14 D, 23 S. 



A little above the base, however, two of the nine spirals to the left " converge " 

 into one, leaving, from that point up to about the middle of the cone, an 



arrangement with secondary spirals 8 S, 14 D, 22 S, = a left-handed bijugate 



112 3 5 



of the series -, -, -, — , — -, &c, whose two fundamental spirals have each the 

 3 4 7 11 18 l 



5 

 divergence — — -., About the middle of the cone, two of the fourteen spirals 

 18 x 2 ' 



to the right converge into one, leaving from thence to the top of the cone an 



13 



arrangement of secondary spirals 8 S, 13 D, 21 S, = a left-handed — spiral of 



1 1 2 3 5 8 13 

 the ordinary series -, -, -, -, — , ^-, ^-, &c. The following table (where the 



three regions are roughly termed " top," " middle," and " bottom ") will 

 render the arrangement intelligible : — 







Table A .*- 



-Cone 



of Pinus Pinaster. 









S 



D 



S 



D 



S 



D 



S 



V 



13 

 34 



Top, 



1 



2 



3 



5 



8 



13 



21 



34 = 



Middle, 



— 



— 



2 



6 



8 



14 



22 



36 = 



5 

 18x2 



Bottom, 



— 



1 



4 



5 



9 



14 



23 



37 = 



8 



37 



II. P. Pinaster— Mr Smyth— (Plate XIX. fig. 1 ; Plate XX. fig. 3 ; Plate 



XXI. fig. 2). Length of cone 5§ inches. From the base to near the top there 



5 112 3 5 



is a right-handed — spiral (series -, -, >-, — , — , &c), with secondary spirals, 

 18 o 4 7 11 18 



4 D, 7 S, 11 D. Near the top of the cone, however, two consecutive scales in 



one of the spirals by 4 to the right (adjacent scales of two of the spirals by 7 to 



the left) have partially coalesced, giving beyond that point an arrangement of 



secondary spirals 4 D, 6 S, 10 D, = a left-handed bijugate of the ordinary series, 



3 

 whose two fundamental spirals have each the divergence - — -. The following 



8x2 



table represents the arrangement : — 



Table B. — Cone of P. Pinaster. 





D 



S 



D 



S 



D 



V 



Top, 



— 



2 



4 



6 



10 



16 -8x 2 



Bottom, 



1 



3 



4 



7 



11 



- = 4 



* 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. 



