346 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



" sliding-growth " is essentially nothing more than the appearance 

 of these circular paths in the spiral asymmetrical diagram. That 

 this appearance of sliding-growth effect tends to change the 

 " spiral of dorsiventrality " into a circular path has already 

 been shown, but this is not a " biological adaptation " ; it is not 

 the direct result of any external conditions of environment ; it is 

 simply the expression in the free primordium of those fundamental 

 properties of a quasi-circle which become masked so long as the 

 primordium tends under pressure to take the properties of a 

 quasi-square. 



The -primary sliding effect is thus defined as the result of the 

 free portion of all appendages produced in contact-systems 

 attempting as they become free to return to their original 

 position of symmetry along radial and circular paths. The occur- 

 rence of oblique spiral symmetry in a contact-system is a 

 phenomenon of distortion, and all such effects are increased by any 

 secondary growth-relations of the appendage, either as it becomes 

 larger above its insertion, or as it tends to tangential extension, as 

 in the differentiation of the leaf-lamina from the midrib. 



It is of interest, therefore, to compare these deductions from the 

 mathematical equation with the facts observed in the plant when 

 plotted into a large drawing under the camera lucida ; it must, 

 however, be remembered that in the section at the level of the 

 growing-point transitional stages will be found, but if the members 

 make contact from the first, the amount of " sliding-growth " is 

 fairly constant (c/. figs. 101, 106), and may be put into the' 

 theoretical diagram with a log. spiral, as in fig. 100 ; the amount 

 of sliding-growth which may be regarded as normal for a given 

 asymmetrical construction being the amount which will make 

 the tangential diagonal of any appendage a circular path. 



