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J. Small and M. W. Rea. 
decrease with the growth in length of the main axis on the apical 
side of the point of junction, because the strength of the leak of the 
normal polarity current at the point of junction will decrease, and 
therefore a smaller angle, giving a smaller action current, will be 
required to balance that leak. These deductions are made with the 
additional hypotheses that the meristems of the lateral organs are 
more or less the same size in all the secondary roots or stem 
branches or leaves of the same species, and that the apical meristems 
of the main roots or stems are likewise constant within limits. 
The angle of the lateral organ with the main axis would then 
vary directly as the length of the lateral and inversely as the 
distance of the point of junction from the apex of the main axis. 
If L be the length and D the distance, then the fraction L/D should 
vary as the sine of the angle. 
Measurements have accordingly been made of the root-system 
of the pea, of the branch systems of the privet, cherry-laurel, 
Rumex , yellow cress and Equisetum, and of the leaves of Pelargonium , 
Chrysanthemum , Rumex , hazel and mint. The branches and roots 
have yielded curves which are similar within ten degrees either way 
to the sine curves for the angles found. The leaves have yielded 
similar curves which are, however, different in direction although 
not in kind. Superficial observations of many other herbs, shrubs 
and trees readily show that the same relations hold in them for 
both stem and leaf angles and lengths. This investigation is being 
continued and the detailed results will be given later. 
III.—A Theory of the Origin of Leaves. 
By J. Small. 
In a recent account of the elements of phyllotaxis Church, 
referring to “the initiation of primary ramuli” says “One may not 
see exactly how it is done, as a more intimate plasmic or even 
‘ molecular ’ function ” (6, p. 56). The present contribution is an 
attempt to explain the missing point “ how it is done ” in so far as 
the higher plants are concerned, and the theory might be extended 
with certain modifications to the marine algae of the phytobenthon. 
In the above-mentioned paper (2) it is shown that the apical 
meristem of the shoot may be considered to be surrounded by 
circular zones of potential differences. The lateral organs, such 
as growing leaves, can be considered as possessing similar but 
excentric zones of potential differences. If the E.M.F. of the stem 
is small compared with that of the lateral organ we may compare 
