a a at a) 
1897] THE CURVATURE OF ROOTS 311 
It may be due to the actual increase in the surface of the 
membranes, following and caused by the intussusception of new 
material, and the elongation of the convex side may be an actual 
growth, as maintained by Pfeffer (18) and others, and which, 
so faras growth was understood in 1865, is identical with the 
original explanation proposed by Sachs. On the other hand, 
the curvature may be due to an elastic and plastic extensibility 
of these membranes brought about by the induced action of the 
ectoplasm. Hofmeister’s (g) theory of curvature agrees with 
this in the main, though purely mechanical causes were given 
for the increased extension of the membranes of the convex 
side. Sachs admitted the probability of changes in the elas- 
ticity of membranes, but he nowhere makes use of the idea in 
his researches upon the subject. Wiesner held the view that 
increased ductility of the membranes of the convex side, together 
with an increased osmotic coefficient, were the causes of curva- 
ture (30). 
Strasburger also upheld the view that “‘growth” curvatures 
are due to increased ductility of the membranes of the convex 
side, and called attention to instances of changes of ductility in 
the walls of Oedogonium, the branching of Cladophora, and 
similar occurrences (29). Noll has recently brought some strik- 
ing experimental results which, in connection with his previous 
work, go far to establish variations in plastic and elastic exten- 
sibility of the membranes as primary factors in the mechanism 
of curvature (16). 
II], THE CURVATURES OF ROOTS. 
I have indicated above that the constantly increasing mass 
: of facts shows many differences between the phenomena attend- 
ant upon curvatures of roots and shoots, and it will be neces- 
Sary therefore to recall the principal researches directed toward 
eek the mechanism of curvatures of roots, but it will not be profitable 
a to go back of the work of Hofmeister. In the earlier researches, 
ss which reference has been made above, Hofmeister sought to 
Se saa in eer ces such as Fonts, —— oe 
