Mar. 27, 1873] 
Fossil Cryptogams * 
T Do not propose at present to controvert in deiail all the posi- 
tions taken up by my friend Prof. McNab in his brief com- 
Munication to your pages on ‘Fossil Cryptogams” (vol. vii. 
p. 267), because the time has not yet arrived for doing so. 
Much more detailed information respecting the subject which 
yet awaits publication must be had befure it can be discussed 
in a satisfactory manner. I merely wish to avoid: leaving 
the impression, by my silence, that I either admit his supposed 
facts or accept his infer-nces. When his paper, to which he 
refers, was read in Edinburgh, specimens of sections of Calamites 
of various ages were sent down by me for the purpose of being 
exhibited to the Botanical Society. This was done by Prof. 
Dickson, who at the same time expressed his preference for my 
views over those of Dr. McNab, as is stated in the officially 
published notice of the meeting in question. Since then I have 
received a kind letter from Dr. Balfour, who has carefully 
examined the specimens referred to, and who also expresses a 
similar conviction. I think that I have unmistakeable proof of 
the circumferential growth of Calamites, which Dr. Macnab 
denies, in specimens of large size, andin which the exozenous 
zone is of great thickness. 
Prof. McNab speaks of “the moist nature of the soil in which 
the Calamites must have grown,” as probably causing a different 
mode of growth in them, to that ‘circumferential? one which 
he admits has probably taken place in Lepidodendra, Sigillarize, 
and Dictyoxylons ;-but I beg to suggest that we have no reasons for 
thinking otherwise than that these plants grew side by side, and 
under precisely the same physical conditions, hence the ‘‘ moist 
soil” of my friend is an assumption. This close association of 
Calamites with Sigillarize was demonstrated and commented upon 
by Mr. Binney many years ago. Dr. McNab further separates 
Lepidodendron from Sigillaria and Stigmaria, placing them in 
different groups. When he receives my third memoir ia the 
Philosophical Transactions (which is printed but not yet circu- 
lated), he will see how utterly this plan of procedure is opposed 
to the facts. I contend that Sigillarie are virtually Lepido- 
dendra, and that Stigmaria is equally the root of both. As to 
the location of my old, but now abandoned genus, Dictyoxylon, 
the more I study it the less I feel competent to fix its true place 
amongst the Cryptogams. But notwithstanding Dr. McNab’s 
idea as to its coniferous affinities, I venture to affirm, froma pro- 
longed study of a cabinet full of specimens, that its woody axis 
is not one bit more exogenous than those of Calamites and of 
matured Lepidodendra. The fact is that whatever the vessels of 
these various exogenous woody zones signify, they must stand or 
fall together. They are either all ligneous or they are all cortical. 
I think that my forthcoming illustrations of the dark-structures 
amongst the Burntisland Lepidodendra, as well as of our Lanca- 
shire specimens, will show that all the elements which Dr. McNab 
finds in Lycopodium Chamzcyparissus arepresent, in their proper 
places, the schlerenchyma of the hypoderm being especially well 
represented, yet it is precisely this hypoderm with which Dr. 
McNab believes my exogenous layer to correspond, There is 
one if not two distinct layers of cortical parenchyma between 
this schlerenchymatous layer and my ligneous zone, which latter 
is so magnificently represented in these plants. 
The intimate structure of these latier layers, whether we re- 
gard the forms and arrangements of the entire woody wedges or 
that of their component tissues, is so identical in the two cases of 
Calamites and Lepidodendra, that an active imagination alone 
can make the one axial and ligneous, and the other cortical. 
Dr. McNab draws a distinction between vessels representing 
(*‘feebly ”) the fibro-vascular bundles of the living Equisetums, 
in the Calamites, and the more external portions of each woody 
wedge, which he regards as representing the hypodermal 
schlerenchyma of Mettenius. I unhesitatingly avow that there 
is no ground whatever for this arbitrary separation. He is 
putting asunder things which-have been joined together from the 
beginning of time. The tissues in question are as identical in 
their structure as they are uninterruptedly coutinuous in their 
arrangement, S 
Whils: I am thus opposed to Dr. McNab both on questions of 
fact and of inference, I feel obliged to him for calling my 
attention to this possible explanation of the facts, even though 
after a careful study of his views I fecl constrained to reject 
them so far as the interpretation of Calamites are concerned. 
On the questions relating to Meristem growths, we are much 
~* We regret that the insertion of this letter has 
been so long delayed in 
consequence of the great pressure upon our space, 
NATURE 
"SiS a ||| «(oe Jat Seance eee 
403 
nearer to mutual agreement, and I accept thankfully his admis- 
son of the coniferous affinities of Dictyoxylon, not because I 
am prepared to recognise any specially close coniferous relation- 
ships, bat because Dr. McNab’s idea necessirily involves an 
admission of the existence of exogenous features in these plants ; 
yet I contend that the Dictyoxylons are neither more coniferous 
nor more exogenvus than most of the other Cryptogamic 
carboniferous stems which exhibit equally strong proofs of 
a similar exogenous growth; But I again repeat that we 
shall not be in a positioa to grapple philosophically with 
these problems until all the results of my pro'onged researches 
are publisied. This is being accomplished as rapidly as my 
limited leisure admits of. When completed, T shall be quite 
prepared to enter, if necessary, and in a friendly spirit, upon the 
entire controversy. W. C. WILLIAMSON 
Owens College : 
Leaf Arrangement 
AFTER reading Dr. Airy’s paper on Phyllotaxis (NaTuRE, 
vol. vii. p. 343), I cannot see that we are at all nearer than 
before, any satisfactory explanation as to the inherent cause of 
it. Let the question be put thus:—If we can conceive, as all 
will admit, the possibility of leaves being scattered anyhow along 
a branch, why are they not so, but in some strictly mathematical 
order? Any disturbance in that order is usually so slight and 
trivial (due apparently in part to the comical nature of the axis, 
and unequal growth or slight twists; and which thereby cause 
certain leaves to assume slightly wrong positions), that it does 
not destroy the fact that they absolutely are arranged, and can be 
represented, mathematically. 
Ia my paper on the angular divergences of the Jerusalem 
artichoke (Linnean Trans. vol. xxvi. p. 647), I pointed out that 
two questions might represent all that is required to be solved. 
(t) That if a leat be selected as No. 1, then No. 2 lies within 
a certain arc, viz. :—120°—180° from No. 1, for the ordinary 
series of fractions, and which it does not transgress—why is this ? 
(2) If we allow that arc—why does the second leaf not assume 
any spot, but is rigidly confined to a certain angular distance 
from the first ? 
I cannot think with Dr. Airy that ‘the way in which all the 
spiral orders may have been derived from one original order 
[was] by means of different degrees of twist in the axis,” 
For if we take a piece of round elastic as he describes, with balls 
fixed according to some spiral arrangement—say 2—then the 
successive balls will lie at an angular distance of 144°; and if 
No. 1 be fixed and we twist the indiarubber at No. 2, we may 
cause it to make a complet rotation if we choose. 
If, now, his idea of ‘‘twist” be admitted as a vera causa of 
phyllotaxis, we may ask, what causes the twist to be just so 
much and no more as to make No. 2 pass through 9° (the 
angular divergence of $ being 135), so as to pass into the next 4 
arrangement? To say that som2 such point is a ** position of 
maximum stability” seems to me to give a fictitious importance 
to the idea of twist, for the expression conveys no really ex- 
planatory meaning at all. 
Again, to admit that it does not accurately hit the right place, 
and is in consequence more like Nature, is equally delusive, for 
Nature is quite accurate enough to be represented mathe- 
matically, whereas the positions taken up by the balls 
must be arbitrary, or at least in proportion to the twist 
given by the hand —a perfectly arbitrary force ? Moreover he 
appears to overlook the fact that if an axis becomes twisted the 
fibres will be twisted also, but they are not so ; the elastic band 
he adopts would, if it were a pliant shoot, contort the vessels and 
wood fibres, a condition not obtaining in nature. 
Nor can Lagree with him in deducing all the members of the 
series from 4, My experience leads me to infer they are derived 
from offosite leaves, such as one finds in the cotyledons. In 
the Jerusalem artichoke opposite leaves are frequently succeeded 
by ¢3 and this is obtained by the pair of leaves, next above 
the strictly opposite pair, converging to one side, the next pair 
do so still more, when it will be found that the 2 arrangement 
will be henceforth established ; the internodes having become 
more and more developed at the same time. 
I strongly suspect the original arrangement to have been 
whorled and quincuncial. This is at least very abundant, if not 
universal, in coal plants. The whorls may have subsequently 
become reduced to fours, threes, and twos or decussate. We 
see this tendency to symmetrical reduction in many existing 
plants, ¢.2, stamens and carpels of Crucifere ; Circea as coms 
