236 
tation of the previous analytical investigation, the quantities 
p, ov, 7, or at all events the first two of them, maintain a 
constant proportion. ‘The shape of the curve depends only 
upon the ratio of p to ov’, and the size depends further upon 
the proportional value of tT. 
It is evident, on the other hand, that neither any one curve 
nor the system of curves belonging to any one of the above equa- 
tions nor any portion of it or them can, except im very simple and 
entire leaves, delineate the whole margin of the floating leaf; 
for otherwise there would be no means of explaining the di- 
visions, fissures and incisions which are frequent even in floating 
leaves and which give characters for the definition of species. 
It does not therefore follow as a consequence of this investi- 
gation that all floating leaves grown in a perfectly still 
water (if such a phenomenon were possible to contrive) are 
simply circular in outline, though a circular form might be 
favoured; but it does follow that the several portions of the 
margin would be circular ares. 
It has before been hinted at, that new fissures (in addition 
to any previously existing ones) may be made and accounted 
for by the mechanical action of the current. 
It is a matter of common observation that many floating 
leaves, as for example in Ranunculus, vary considerably in con- 
sequence of, or in association with, the nature of the stream in 
which they grow. 
At all events the theory discusses the forms which floating 
leaves would find mechanically suitable for their growth and 
maintenance, in order that they might dwell free from unne- 
cessary strains and wrenches, and under an equal distribution 
of their power of growth, which as we know is capable of 
exerting considerable force under compulsion, but is in general 
slow and steady. 
