[60] This statement is *not strictly* correct for *Tubularia*. I found
(*Archiv f. Entwickelungsmechanik*, ix. 1899), that a reduction of the
length of the stem is always followed by a reduction of the size of the
hydranth-primordium, but there is no real proportionality between them.
It is only for theoretical simplification that a strict proportionality
is assumed here, both in the text and the diagram. But there is an
almost strict proportionality in all cases of “closed forms.”
[Illustration: Fig. 12.--Tubularia.
*a.* Diagram of the “Hydranth,” with its short and long tentacles.
*b.* Restitution of a new hydranth inside the perisarc (*p*).
*c.* The same--later stage; the tentacles are complete; the whole
hydranth will be driven out of the perisarc by a process of growth that
occurs at the locality marked ⬆.
*d.* A stem of *Tubularia* cut either at *a_1 b_1* or at *a_2 b_2*,
or at *a_1 c*.
*e.* Position of tentacles in the piece cut at *a_1 b_1*.
*f.* Position of tentacles in the piece cut at *a_2 b_2*,
which is equal in length to *a_1 b_1*.
*g.* Position of tentacles in the piece cut at *a_1 c*,
which is half as long as *a_1 b_1*.]
So we find our formula *p.v. (X) = f(s, l, E)* very well
illustrated in *Tubularia*. The formula indeed may help us to predict,
in any case, where a certain part of the polyp’s organisation is
to originate, at least if we know all that is included under our
letter *E*, *i.e.* the normal proportion of our form. Of course such
prediction would not have much practical importance in all our cases of
morphogenesis, but nevertheless I should like to state here that it is
possible; for many scientific authors of recent times have urged the
opinion that prediction of, and domination over, what will happen, can
be the only true aims of sciences at all. I myself judge these aims to
be of second or third-rate importance only, but, if they may be reached
by what our purely theoretical study teaches, so much the better.
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