442 
a time when they undergo such rapid extensions, should 
form the crowning part of chemical studies, and the inter- 
dependence of the two branches of science can only be 
established upon a sound basis when a thorough know- 
ledge of either science has been acquired. 
The main portion of the book comprising the chemistry 
of the non-metallic and metallic elements, arranged under 
the usual headings Preparation and Properties of the 
different elements and their compounds, contains much 
that will highly recommend itself. The more important 
compounds are dealt with in a manner which will help the 
student over most of the difficulties he encounters at first, 
and will enable him to lay a good foundation for more 
extensive chemical studies. The classification of the 
metals according to their atomicity—open to objections 
as it stands—is not always reconcilable with the analytical 
summaries or tests given after each group of metals, nor 
are the analytical explanations always accurate. On p. 
393, &.g. we notice: “ Calcic sulphate cannot produce a 
precipitate in a salt of calcium, because there is more 
than enough of water present to retain dissolved all the 
sulphate that can possibly be formed.” 
There can be little doubt that the new edition of 
Wilson’s Chemistry will be welcomed by all who desire to 
get a general insight into the science, and that it may be 
studied with advantage in preference to many larger and 
more ambitious text-books, 
OUR BOOK SHELF 
Verhandlungen der k, k. geologischen Reichsanstalt. 
Nos. 11 to 18. (Vienna.) 
THESE numbers of the Proceedings of the Geological 
Society contain many useful papers, chiefly, however, of 
local interest. Felix Karrer notes the occurrence of mam- 
moth remains at Vienna. They were obtained during the 
sinking of a well in a “diluvial” (glacial) deposit at a 
depth of 9 fath. 3 ft. from the surface. Dr. Lenz also has 
a short reference to a similar discovery of the teeth of a 
young mammoth in a brown laminated loam near No- 
wakmiihle. Dr. Stur gives an interesting account of his 
own and Baron Petrino’s observations on the superficial 
deposits in the basin of the Dniester in Galicia and Buko- 
wina. A great accumulation of loess covers a wide area in 
that district, the land shells and mammalian remains in 
which enable these geologists to correlate it with the 
loess of the Rhine and other regions. We observe, in No. 
II, an important table showing Dr. C. E, Weis’s sys- 
tematic arrangement of the carboniferous formation and 
the rothliegendes formation of the Saar-Rhine district, 
which is well worth the attention of English geologists. 
The usual admirable literary notices, and other miscel- 
laneous matter, are appended to each number of the 
Proceedings. 
LETTERS TO THE EDITOR 
[ Zhe Editor does not hold himself responsible for opinions expressed 
by his correspondents, No notice is taken of anonymous 
communications. } 
Leaf-Arrangement 
THE chief part of the Rev. G. Henslow’s objections (NATURE, 
vol. vii., p. 403) to my condensation-theory of leaf-arrangement 
are due to a double oversight on his part. First, he has over- 
looked the condition of contact among the balls which I use to 
represent embryo leaves. Second, he has overlooked the funda- 
punia position, that leaf-order exists for, and is determined in, 
the dud, 
NATURE 
[April 10, 1873 
The bud requires economy of space. This involves contact 
among the embryo leaves ; and if we experiment with balls at- 
tached (as described in my paper) in two rows alternately on 
either side of a contractile axis, we shall see that when the axis 
is allowed to contract with a twist, that twist is necessarily 
limited by the conditions of contact which arise, and that we 
cannot ‘‘cause it to make a complete rotation if we choose.” 
Given the size of the balls and their distance from the axis, the 
position which they will assume (under contraction with a twist) 
is necessarily determined by the geometrical conditions of mutual 
contact. This consideration furnishes the answer to Mr, 
Henslow’s italicised query, and also to his two previous ques- 
tions (1) and (2). It also gives back a ‘‘really explanatory 
meaning” to my expression ‘‘#axima of stability,” for if we 
have one sphere standing almost vertically on another and sup- 
ported by a third and a fourth to right and left, we have therein 
some statical conditions which admit of maxima and minima of 
stability. The same consideration also removes the objection 
that ‘‘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.” The twist given by the hand in my experiment 
serves only to determine the direction of the real twist ; the sub- 
sequent real availing twist is insisted upon by the two ranks of 
balls-in-contact as the sole condition of obedience to the contrac- 
tile force of the indiarubber axis ; and this twist is limited by 
the conditions of contact above described. Let the direction of 
the twist be given, and there is nothing arbitrary in the 
result. 
The objection that ‘‘if an axis becomes twisted the fives will 
be twisted also” loses force if we bear in mind that the leaf- 
order is imposed upon the embryo leaves in the very earliest 
stage of their bud-life ; and that the formation of fibres, taking 
place at asubsequent stage, must find itself compromised by an 
already existing arrangement of the embryo leaves. The elastic 
band in my experiment, “if it were a pliant shoot,” would certainly 
“contort the vessels and wood-fibres ;” but it was not meant to 
represent a ‘‘ pliant shoot” except in its earliest embryonic bud- 
stage, and that at some very remote period in the past. 
I must ask Mr. Henslow to bear in mind that he has before 
him only the abstract of my paper, and that necessary brevity 
has left some points too bare, and has wholly suppressed others 
of small importance. Among the latter is some mention of 
the ‘‘secondary series” 4, 3, #, &c., which, though it may be 
found in the abnormal variations exhibited by a cultivated plant 
like the Jerusalem Artichoke, yet cannot be reckoned with 
examples of normal leaf-order. 
Let me take this opportunity of insisting again on the as- 
tonishing agreement between the facts of nature and the results 
which the condensation-theory leads us to expect. Taking one 
member to start from as 0, we find in nature that the members in 
contact with o belong to the following series, 1, 2, 3, 5, 8, 13, 
21, 34, 55, 89, 144, &c., and these are the very same members 
which would necessarily be brought into contact with o under 
Sucoptaive degrees of condensation with twist from an original 
order 4. 
I have lately met with a striking confirmation of the truth of 
the condensation-theory. The simplest order of the whorled 
type is that in which the leaves stand in pairs, decussate. Now 
if we consider what would be the result of condensation with 
twist applied to this arrangement, we can see that it would 
produce a new series of orders, in which the following members 
would successively come into contact with 0,—2, 4, 6, 10, 16, 26, 
2, &c., and would present the phenomenon of 2, 4, 6, 10, &c., 
spirals alternately to right and left. This result is exemplified in 
nature. The teazle ‘Dipsacus silvestris) has the decussate order 
in its leaves ; and in its head (where we might expect to find its 
leaf-order condensed) we count sixteen conspicuous spirals in 
one direction and twenty-six in the other :—that is to say, we 
have 0 in contact with No. 16 on one side and No. 26 on the 
other. No. 42 stands higher between 16 and 26, but inclined 
towards the former. No, to stands next below 26, and No. 6 
next below 16. These numbers belong to the new series above ~ 
mentioned, 
This close parallel between fact and theory appears to me to 
give a value to the latter which it will not lightly lose. 
March 30 HUBERT AIRY 
The Hegelian Calculus 
As Dr. J. H. Stirling has enjoyed the exceptional privilege of 
replying contemporaneously to my paper on Hegel in the 
od 
