34 Jackson . — Anatomical Structure of the Roots of Barley. 
a given time a plant with superphosphate would have more and older 
‘ unbranched 5 roots than an unmanured plant of the same age. Hence it 
is obvious that in such a plant there would be more chance of preserving 
as branched roots those which were originally of the ‘ unbranched ’ type. 
Considering only the figures in Table I, there is quite a marked 
difference between the sizes of the roots of the two types, the range for 
the diameters of the branched roots being 0*26 mm. -0*40 mm. against 
0-38 mm-071 mm. for the ‘ unbranched 5 roots. The stelar diameters also 
show a corresponding difference in size, the range being 0-15 mm.-o-i6 mm. 
for the branched root against 0-19 mm.-o-29 mm. for the £ unbranched ’ roots. 
It may be observed that for the branched and ‘ unbranched ’ types re- 
spectively, the size of the stele is remarkably uniform in the roots taken 
from all the different types of manuring. 
An attempt was made to get some estimate of the ratio of {a) the 
area of the stele (in cross-section) to the area of the whole root ; ( b ) the 
area of the central ducts to the area of the whole root ; and (c) the area 
of the central ducts to the area of the stele. Since the different areas to 
be measured were neither true circles nor true ellipses, it was impossible 
to secure actual figures. The ratios, however, can be obtained fairly 
accurately by taking as area the product of the two diameters, since the 
area of an ellipse is proportional to that of its escribed rectangle. In cases 
where there are several central ducts, the sum of the products of their 
several diameters is taken as representing the total central space. The 
ratios of stele to whole and of central space to whole did not seem to 
follow any definite rule. This may possibly be explained by the fact that 
all the cortical tissues had shrunk considerably owing to their lengthy 
immersion in alcohol. Of course this shrinkage also affects the total 
diameter measurements, but as these figures can only be very preliminary, 
it was thought justifiable to include them as a slight indication of the 
differences existing between the two root types. The material was all 
treated in exactly the same way, so that presumably the shrinkage of the 
different sets of material would be approximately the same, and the figures 
are therefore comparable, though not true measures of the diameter of the 
fresh roots. This shrinkage, however, did not affect the stele — except 
perhaps in the case of the very thin-walled cells of the £ unbranched ’ roots 
in the unmanured series. There is a fairly well marked difference between 
the ratios of stele to central space in the branched and in the £ unbranched * 
roots, the ratio being persistently higher in the former than in the latter, as 
would be expected from the large amount of central space in the £ unbranched 5 
roots. 
Summary of the chief points of difference in the morphology and anatomy 
of the branched and ‘ unbranched' roots. 1. The £ unbranched 5 roots are 
thick and very white. They grow to a length of several inches without any 
