VARYING GROWTH IN LATERAL MEMBERS. 317 



as Newton's first law of motion comes before the second : granted 

 the conditions for uniform growth are known, any variations from 

 these must imply the existence of secondary agencies ; and thus, 

 if primordia are once started in a certain direction, and continue 

 to expand at a uniform rate of growth, very nearly uniform also 

 with that of the main axis, the transverse section of the bud at 

 any time would be marked out along orthogonally intersecting 

 log. spirals ; and conversely, if the construction observed does not 

 consist of true log. spirals, or the intersections are not orthogonal, 

 it must follow that some secondary change in the rate or direc- 

 tion of growth must have taken place subsequent to the time 

 at which the primordia were laid down, or perhaps became visible. 

 As already noted, a deep-seated faith in this very fact, that a 

 primordium which has been set growing in any given direction 

 will, in the absence of any secondary disturbing force, continue 

 to do so, and so retain its relative station with perfect accuracy, 

 has led to the utilisation of such structures as the Pine-cone, the 

 Aroid spadix, and bractless capitula of Composites as the most 

 typical examples of phyllotaxis. 



While a log. spiral construction thus possibly represents the 

 arrangement of certain " lines of force '' which are intimately 

 connected with the primary cause of phyllotaxis, the most usual 

 •disturbing factor will be the capacity for variation in the rate of 

 growth in the members themselves ; while alterations in the 

 direction of growth will be less marked, but may follow pressure 

 changes as the members become adult, and the action of external 

 conditions of environment, as in the case of the light-induced 

 eccentricity of certain spirally constructed leafy shoots {Abies), 

 or still better, a Pine-cone which grows unequally as a whole 

 as it bends down after pollination. 



It is so far evident that the original phyllotaxis construction 

 along the log. spiral paths conceivably laid down in the protoplasm 

 at the actual growing-point, will be exactly maintained so long, 

 and so long only, as growth remains uniform in the system, and 

 the members retain the same general shape as that of the apex 

 on which they are borne, or tend by mutual pressure to take 

 the form of quasi-squares as seen in section. Such an ideal 



