HELICES AND SPIRALS OP ARCHIMEDES. 65 



for the same reason as the curves become helices on a cylindrical 

 stem. As soon as the section of the actually growing primordia is 

 observed, the resemblance to spirals of Archimedes vanishes. 



AVhether the log. spiral system is so far satisfactory or not, 

 it is thus quite evident that helices and spirals of Archimedes will 

 not satisfy the requirements of ontogenetic observation ; the ultimate 

 approximation to such curves is a secondary phenomenon; and 

 with the rejection of helices and Archimedean spirals, as implying 

 anything more than a subjective effect, must disappear all prejudices 

 in favour of the application of hypothetical torsion-agencies. 



