SECT. I. ORGANOGRAPHY AND GLOSSOLOGY. 



127 



of a fir-cone (fig. 137.) ; and we shall endeavour to 

 show, how the real dispos- 137 



ition of the scales on the 

 " generating" spiral may be 

 readily ascertained, from 

 merely inspecting the ap- 

 pearances presented by these 

 secondary spirals. Thus, in 

 the spruce fir (Pinus abies*), 

 it is easy to trace several sets 

 of spirals, running parallel to 

 1, 9, 17, 25, &c.; and other 

 sets parallel to 1, 6, 11, 

 16, &c. ; and others to 1, 4, 

 7, &c., and so on. In the 

 present example, there are twenty-one lines which may 

 be drawn through those scales which are ranged ver- 

 tically over the others, as 1, 22, 43, &c., 14, 35, 56', 

 &c. and so on. This number, as was before shown of 

 the seven verticals, inland B (fig. 136'.), indicates the 

 number of scales that are ranged upon one length of the 

 spiral. But the course of the generating spiral is not 

 apparent, and, consequently, the numerator of the frac- 

 tion which expresses the divergence is unknown. 



(124.) To fix Numbers to the Scales. We may 

 easily observe, that the numbers on the scales which 

 form the different secondary spirals, are in arithmetical 

 progression ; and we shall presently show, in the next 

 article, that the common differences in these progressions, 

 also indicate the number of similar secondary spirals 

 which range parallel to each other. Thus, there are 

 eight parallel spirals, 1, 9, 17, &c., 6, 14, 22, &c., 

 where the arithmetical progressions have all the same 

 common difference eight. Hence we see a ready means 

 of numbering the scales on the cone, without the necessity 

 of previously ascertaining the course of the generating 

 spiral. Fixing on scale (l) for a beginning, and count- 

 ing the number of parallel spirals (viz. eight) which 

 run in one direction, as above, we can fix the numbers 



