by Flemming to the whole phenomenon. Kollmann (_Biol. Centralbl._
II, p. 107, 1882) called it _divisio per fila_, or _divisio laqueis
implicata_. Many of the earlier students, such as Van Beneden (Rech.
sur la maturation de l’œuf, _Arch. de Biol._ IV, 1883), and Hermann
(Zur Lehre v. d. Entstehung d. karyokinetischen Spindel, _Arch. f.
mikrosk. Anat._ XXXVII, 1891) thought they recognised actual muscular
threads, drawing the nuclear material asunder towards the respective
foci or poles; and some such view was long maintained by other writers,
Boveri, Heidenhain, Flemming, R. Hertwig, and many more. In fact, the
existence of contractile threads, or the ascription to the spindle
rather than to the poles or centrosomes of the active forces concerned
in nuclear division, formed the main tenet of all those who declined to
go beyond the “contractile properties of protoplasm” for an explanation
of the phenomenon. (Cf. also J. W. Jenkinson, _Q. J. M. S._ XLVIII, p.
471, 1904.)
[226] Cf. Bütschli, O., Ueber die künstliche Nachahmung der
karyokinetischen Figur, _Verh. Med. Nat. Ver. Heidelberg_, V, pp. 28–41
(1892), 1897.
[227] Arrhenius, in describing a typical colloid precipitate, does so
in terms that are very closely applicable to the ordinary microscopic
appearance of the protoplasm of the cell. The precipitate consists, he
says, “en un réseau d’une substance solide contenant peu d’eau, dans
les mailles duquel est inclus un fluide contenant un peu de colloide
dans beaucoup d’eau ... Evidemment cette structure se forme à cause
de la petite différence de poids spécifique des deux phases, et de la
consistance gluante des particules séparées, qui s’attachent en forme
de réseau.” _Rev. Scientifique_, Feb. 1911.
[228] F. Schwartz, in Cohn’s _Beitr. z. Biologie der Pflanzen_, V, p.
1, 1887.
[229] Fischer, _Anat. Anzeiger_, IX, p. 678, 1894, X, p. 769, 1895.
[230] See, in particular, W. B. Hardy, On the structure of Cell
Protoplasm, _Journ. of Physiol._ XXIV, pp. 158–207, 1889; also Höber,
_Physikalische Chemie der Zelle und der Gewebe_, 1902. Cf. (_int. al._)
Flemming, _Zellsubstanz, Kern und Zelltheilung_ 1882, p. 51, etc.
[231] My description and diagrams (Figs 42–51) are based on those of
Professor E. B. Wilson.
[232] If the word _permeability_ be deemed too directly suggestive of
the phenomena of _magnetism_ we may replace it by the more general
term of _specific inductive capacity_. This would cover the particular
case, which is by no means an improbable one, of our phenomena being
due to a “surface charge” borne by the nucleus itself and also by
the chromosomes: this surface charge being in turn the result of a
difference in inductive capacity between the body or particle and its
surrounding medium. (Cf. footnote, p. 187.)
[233] On the effect of electrical influences in altering the
surface-tensions of the colloid particles, see Bredig, _Anorganische
Fermente_, pp. 15, 16, 1901.
[234] _The Cell_, etc. p. 66.
[235] Lillie, R. S., _Amer. J. of Physiol._ VIII, p. 282, 1903.
[236] We have not taken account in the above paragraphs of the obvious
fact that the supposed symmetrical field of force is distorted by
the presence in it of the more or less permeable bodies; nor is it
necessary for us to do so, for to that distorted field the above
argument continues to apply, word for word.
[237] M. Foster, _Lectures on the History of Physiology_, 1901, p. 62.
[238] _Op. cit._ pp. 110 and 91.
[239] Lamb, A. B., A new Explanation of the Mechanism of Mitosis,
_Journ. Exp. Zool._ V, pp. 27–33, 1908.
[240] _Amer. J. of Physiol._ VIII, pp. 273–283, 1903 (_vide supra_, p.
181); cf. _ibid._ XV, pp. 46–84, 1905. Cf. also _Biological Bulletin_,
IV, p. 175. 1903.
[241] In like manner Hardy has shewn that colloid particles migrate
with the negative stream if the reaction of the surrounding fluid
be alkaline, and _vice versa_. The whole subject is much wider than
these brief allusions suggest, and is essentially part of Quincke’s
theory of Electrical Diffusion or Endosmosis: according to which the
particles and the fluid in which they float (or the fluid and the
capillary walls through which it flows) each carry a charge, there
being a discontinuity of potential at the surface of contact, and hence
a field of force leading to powerful tangential or shearing stresses,
communicating to the particles a velocity which varies with the
density per unit area of the surface charge. See W. B. Hardy’s paper
on Coagulation by Electricity, _Journ. of Physiol._ XXIV, p. 288–304,
1899, also Hardy and H. W. Harvey, Surface Electric Charges of Living
Cells, _Proc. R. S._ LXXXIV (B), pp. 217–226, 1911, and papers quoted
therein. Cf. also E. N. Harvey’s observations on the convection of
unicellular organisms in an electric field (Studies on the Permeability
of Cells, _Journ. of Exper. Zool._ X, pp. 508–556, 1911).
[242] On Differences in Electrical Potential in Developing Eggs, _Amer.
Journ. of Physiol._ XII, pp. 241–275, 1905. This paper contains an
excellent summary of various physical theories of the segmentation of
the cell.
[243] Gray has recently demonstrated a temporary increase of electrical
conductivity in sea-urchin eggs during the process of fertilisation
(The Electrical Conductivity of fertilised and unfertilised Eggs,
_Journ. Mar. Biol. Assoc._ X, pp. 50–59, 1913).
[244] Schewiakoff, Ueber die karyokinetische Kerntheilung der _Euglypha
alveolata, Morph. Jahrb._ XIII, pp. 193–258, 1888 (see p. 216).
[245] Coe, W. R., Maturation and Fertilization of the Egg of
Cerebratulus, _Zool. Jahrbücher_ (_Anat. Abth._), XII, pp. 425–476,
1899.
[246] Thus, for example, Farmer and Digby (On Dimensions of Chromosomes
considered in relation to Phylogeny, _Phil. Trans._ (B), CCV, pp. 1–23,
1914) have been at pains to shew, in confutation of Meek (_ibid._
CCIII, pp. 1–74, 1912), that the width of the chromosomes cannot be
correlated with the order of phylogeny.
[247] Cf. also _Arch. f. Entw. Mech._ X, p. 52, 1900.
[248] Cf. Loeb, _Am. J. of Physiol._ VI, p. 32, 1902; Erlanger, _Biol.
Centralbl._ XVII, pp. 152, 339, 1897; Conklin, _Biol. Lectures_, _Woods
Holl_, p. 69, etc. 1898–9.
[249] Robertson, T. B., Note on the Chemical Mechanics of Cell
Division, _Arch. f. Entw. Mech._ XXVII, p. 29, 1909, XXXV, p. 692.
1913. Cf. R. S. Lillie, _J. Exp. Zool._ XXI, pp. 369–402, 1916.
[250] Cf. D’Arsonval, _Arch. de Physiol._ p. 460, 1889; Ida H. Hyde,
_op. cit._ p. 242.
[251] Cf. Plateau’s remarks (_Statique des liquides_, II, p. 154) on
the _tendency_ towards equilibrium, rather than actual equilibrium, in
many of his systems of soap-films.
[252] But under artificial conditions, “polyspermy” may take place,
e.g. under the action of dilute poisons, or of an abnormally high
temperature, these being all, doubtless, conditions under which the
surface-tension is diminished.
[253] Fol, H., _Recherches sur la fécondation_, 1879. Roux, W.,
Beiträge zur Entwickelungsmechanik des Embryo, _Arch. f. Mikr. Anat._
XIX, 1887. Whitman, C. O., Oökinesis, _Journ. of Morph._ I, 1887.
[254] Wilson. _The Cell_, p. 77.
[255] Eight and twelve are by much the commonest numbers, six and
sixteen coming next in order. If we may judge by the list given by E.
B. Wilson (_The Cell_, p. 206), over 80 % of the observed cases lie
between 6 and 16, and nearly 60 % between 8 and 12.
[256] _Theory of Cells_, p. 191.
[257] _The Cell in Development_, etc. p. 59; cf. pp. 388, 413.
[258] E.g. Brücke, _Elementarorganismen_, p. 387: “Wir müssen in der
Zelle einen kleinen Thierleib sehen, und dürfen die Analogien, welche
zwischen ihr und den kleinsten Thierformen existiren, niemals aus den
Augen lassen.”
[259] Whitman, C. O., The Inadequacy of the Cell-theory, _Journ. of
Morphol._ VIII, pp. 639–658, 1893; Sedgwick, A., On the Inadequacy of
the Cellular Theory of Development, _Q.J.M.S._ XXXVII, pp. 87–101,
1895, XXXVIII, pp. 331–337, 1896. Cf. Bourne, G. C., A Criticism of the
Cell-theory; being an answer to Mr Sedgwick’s article, etc., _ibid._
XXXVIII, pp. 137–174, 1896.
[260] Cf. Hertwig, O., _Die Zelle und die Gewebe_, 1893, p. 1;
“Die Zellen, in welche der Anatom die pflanzlichen und thierischen
Organismen zerlegt, sind die Träger der Lebensfunktionen; sie sind,
wie Virchow sich ausgedrückt hat, die ‘Lebenseinheiten.’ Von diesem
Gesichtspunkt aus betrachtet, erscheint der Gesammtlebensprocess eines
zusammengesetzten Organismus nichts Anderes zu sein als das höchst
verwickelte Resultat der einzelnen Lebensprocesse seiner zahlreichen,
verschieden functionirenden Zellen.”
[261] _Journ. of Morph._ VIII, p. 653, 1893.
[262] Neue Grundlegungen zur Kenntniss der Zelle, _Morph. Jahrb._ VIII,
pp. 272, 313, 333, 1883.
[263] _Journ. of Morph._ II, p. 49, 1889.
[264] _Phil. Trans._ CLI, p. 183, 1861; _Researches_, ed. Angus Smith,
1877, p. 553.
[265] Cf. Kelvin, On the Molecular Tactics of a Crystal, _The Boyle
Lecture_, Oxford, 1893, _Baltimore Lectures_, 1904, pp. 612–642. Here
Kelvin was mainly following Bravais’s (and Frankenheim’s) theory
of “space-lattices,” but he had been largely anticipated by the
crystallographers. For an account of the development of the subject in
modern crystallography, by Sohncke, von Fedorow, Schönfliess, Barlow
and others, see Tutton’s _Crystallography_, chap. ix, pp. 118–134, 1911.
[266] In a homogeneous crystalline arrangement, _symmetry_ compels a
locus of one property to be a plane or set of planes; the locus in this
case being that of least surface potential energy.
[267] This is what Graham called the _water of gelatination_, on the
analogy of _water of crystallisation_; _Chem. and Phys. Researches_, p.
597.
[268] Here, in a non-crystalline or random arrangement of particles,
symmetry ensures that the potential energy shall be the same per unit
area of all surfaces; and it follows from geometrical considerations
that the total surface energy will be least if the surface be spherical.
[269] Lehmann, O., _Flüssige Krystalle, sowie Plasticität von
Krystallen im allgemeinen_, etc., 264 pp. 39 pll., Leipsig, 1904. For a
semi-popular, illustrated account, see Tutton’s _Crystals_ (Int. Sci.
Series), 1911.
[270] As Graham said of an allied phenomenon (the so-called
blood-crystals of Funke), it “illustrates the maxim that in nature
there are no abrupt transitions, and that distinctions of class are
never absolute.”
[271] Cf. Przibram, H., Kristall-analogien zur Entwickelungsmechanik
der Organismen, _Arch. f. Entw. Mech._ XXII, p. 207, 1906 (with copious
bibliography); Lehmann, Scheinbar lebende Kristalle und Myelinformen,
_ibid._ XXVI, p. 483, 1908.
[272] The idea of a “surface-tension” in liquids was first enunciated
by Segner, _De figuris superficierum fluidarum_, in _Comment. Soc. Roy.
Göttingen_, 1751, p. 301. Hooke, in the _Micrographia_ (1665, Obs.
VIII, etc.), had called attention to the globular or spherical form of
the little morsels of steel struck off by a flint, and had shewn how
to make a powder of such spherical grains, by heating fine filings to
melting point. “This Phaenomenon” he said “proceeds from a propriety
which belongs to all kinds of fluid Bodies more or less, and is caused
by the Incongruity of the Ambient and included Fluid, which so acts
and modulates each other, that they acquire, as neer as is possible, a
_spherical_ or _globular_ form....”
[273] _Science of Mechanics_, 1902, p. 395; see also Mach’s article
Ueber die physikalische Bedeutung der Gesetze der Symmetrie, _Lotos_,
XXI, pp. 139–147, 1871.
[274] Similarly, Sir David Brewster and others made powerful lenses
by simply dropping small drops of Canada balsam, castor oil, or other
strongly refractive liquids, on to a glass plate: _On New Philosophical
Instruments_ (Description of a new Fluid Microscope), Edinburgh, 1813,
p. 413.
[275] Beiträge z. Physiologie d. Protoplasma, _Pflüger’s Archiv_, II,
p. 307, 1869.
[276] _Poggend. Annalen_, XCIV, pp. 447–459, 1855. Cf. Strethill
Wright, _Phil. Mag._ Feb. 1860.
[277] Haycraft and Carlier pointed out (_Proc. R.S.E._ XV, pp.
220–224, 1888) that the amoeboid movements of a white blood-corpuscle
are only manifested when the corpuscle is in contact with some solid
substance: while floating freely in the plasma or serum of the blood,
these corpuscles are spherical, that is to say they are at rest and in
equilibrium. The same fact has recently been recorded anew by Ledingham
(On Phagocytosis from an adsorptive point of view, _Journ. of Hygiene_,
XII, p. 324, 1912). On the emission of pseudopodia as brought about
by changes in surface tension, see also (_int. al._) Jensen, Ueber
den Geotropismus niederer Organismen, _Pflüger’s Archiv_, LIII, 1893.
Jensen remarks that in Orbitolites, the pseudopodia issuing through
the pores of the shell first float freely, then as they grow longer
bend over till they touch the ground, whereupon they begin to display
amoeboid and streaming motions. Verworn indicates (_Allg. Physiol._
1895, p. 429), and Davenport says (_Experim. Morphology_, II, p. 376)
that “this persistent clinging to the substratum is a ‘thigmotropic’
reaction, and one which belongs clearly to the category of
‘response.’ ” (Cf. Pütter, Thigmotaxis bei Protisten, _A. f. Physiol._
1900, Suppl. p. 247.) But it is not clear to my mind that to account
for this simple phenomenon we need invoke other factors than gravity
and surface-action.
[278] Cf. Pauli, _Allgemeine physikalische Chemie d. Zellen u. Gewebe_,
in Asher-Spiro’s _Ergebnisse der Physiologie_, 1912; Przibram,
_Vitalität_, 1913, p. 6.
[279] The surface-tension theory of protoplasmic movement has been
denied by many. Cf. (e.g.), Jennings, H. S., Contributions to the Study
of the Behaviour of the Lower Organisms, _Carnegie Inst._ 1904, pp.
130–230; Dellinger, O. P., Locomotion of Amoebae, etc. _Journ. Exp.
Zool._ III, pp. 337–357, 1906; also various papers by Max Heidenhain,
in _Anatom. Hefte_ (Merkel und Bonnet), etc.
[280] These various movements of a liquid surface, and other still more
striking movements such as those of a piece of camphor floating on
water, were at one time ascribed by certain physicists to a peculiar
force, _sui generis_, the _force épipolique_ of Dutrochet: until
van der Mensbrugghe shewed that differences of surface tension were
enough to account for this whole series of phenomena (Sur la tension
superficielle des liquides considérée au point de vue de certains
mouvements observés à leur surface, _Mém. Cour. Acad. de Belgique_,
XXXIV, 1869; cf. Plateau, p. 283).
[281] Cf. _infra_, p. 306.
[282] Cf. p. 32.
[283] Or, more strictly speaking, unless its thickness be less than
twice the range of the molecular forces.
[284] It follows that the tension, depending only on the
surface-conditions, is independent of the thickness of the film.
[285] This simple but immensely important formula is due to Laplace
(_Mécanique Céleste_, Bk. x. suppl. _Théorie de l’action capillaire_,
1806).
[286] Sur la surface de révolution dont la courbure moyenne est
constante, _Journ. de M. Liouville_, VI, p. 309, 1841.
[287] See _Liquid Drops and Globules_, 1914, p. 11. Robert Boyle used
turpentine in much the same way. For other methods see Plateau, _op.
cit._ p. 154.
[288] Felix Plateau recommends the use of a weighted thread, or
plumb-line, drawn up out of a jar of water or oil; _Phil. Mag._ XXXIV,
p. 246, 1867.
[289] Cf. Boys, C. V., On Quartz Fibres, _Nature_, July 11, 1889;
Warburton, C., The Spinning Apparatus of Geometric Spiders, _Q.J.M.S._
XXXI, pp. 29–39, 1890.
[290] J. Blackwall, _Spiders of Great Britain_ (Ray Society), 1859, p.
10; _Trans. Linn. Soc._ XVI, p. 477, 1833.
[291] The intermediate spherules appear, with great regularity
and beauty, whenever a liquid jet breaks up into drops; see the
instantaneous photographs in Poynting and Thomson’s _Properties of
Matter_, pp. 151, 152, (ed. 1907).
[292] Kühne, _Untersuchungen über das Protoplasma_, 1864, p. 75, etc.
[293] _A Study of Splashes_, 1908, p. 38, etc.; Segmentation of a
Liquid Annulus, _Proc. Roy. Soc._ XXX, pp. 49–60, 1880.
[294] Cf. _ibid._ pp. 17, 77. The same phenomenon is beautifully and
continuously evident when a strong jet of water from a tap impinges on
a curved surface and then shoots off it.
[295] See a _Study of Splashes_, p. 54.
[296] A case which we have not specially considered, but which may be
found to deserve consideration in biology, is that of a cell or drop
suspended in a liquid of _varying_ density, for instance in the upper
layers of a fluid (e.g. sea-water) at whose surface condensation is
going on, so as to produce a steady density-gradient. In this case the
normally spherical drop will be flattened into an oval form, with its
maximum surface-curvature lying at the level where the densities of the
drop and the surrounding liquid are just equal. The sectional outline
of the drop has been shewn to be not a true oval or ellipse, but a
somewhat complicated quartic curve. (Rice, _Phil. Mag._ Jan. 1915.)
[297] Indeed any non-isotropic _stiffness_, even though _T_ remained
uniform, would simulate, and be indistinguishable from, a condition of
non-stiffness and non-isotropic _T_.
[298] A non-symmetry of _T_ and _T′_ might also be capable of
explanation as a result of “liquid crystallisation.” This hypothesis is
referred to, in connection with the blood-corpuscles, on p. 272.
[299] The case of the snow-crystals is a particularly interesting one;
for their “distribution” is in some ways analogous to what we find, for
instance, among our microscopic skeletons of Radiolarians. That is to
say, we may one day meet with myriads of some one particular form or
species only, and another day with myriads of another; while at another
time and place we may find species intermingled in inexhaustible
variety. (Cf. e.g. J. Glaisher, _Ill. London News_, Feb. 17, 1855;
_Q.J.M.S._ III, pp. 179–185, 1855).
[300] Cf. Bergson, _Creative Evolution_, p. 107: “Certain Foraminifera
have not varied since the Silurian epoch. Unmoved witnesses of the
innumerable revolutions that have upheaved our planet, the Lingulae are
today what they were at the remotest times of the palaeozoic era.”
[301] Ray Lankester, _A.M.N.H._ (4), XI, p. 321, 1873.
[302] Leidy, Parasites of the Termites, _J. Nat. Sci., Philadelphia_,
VIII, pp. 425–447, 1874–81; cf. Saville Kent’s _Infusoria_, II, p. 551.
[303] _Op. cit._ p. 79.
[304] Brady, _Challenger Monograph_, pl. XX, p. 233.
[305] That the Foraminifera not only can but do hang from the surface
of the water is confirmed by the following apt quotation which I owe
to Mr E. Heron-Allen: “Quand on place, comme il a été dit, le dépôt
provenant du lavage des fucus dans un flacon que l’on remplit de
nouvelle eau, on voit au bout d’une heure environ les animaux [_Gromia
dujardinii_] se mettre en mouvement et commencer à grimper. Six heures
après ils tapissent l’extérieur du flacon, de sorte que les plus élevés
sont à trente-six ou quarante-deux millimetres du fond; le lendemain
beaucoup d’entre eux, _après avoir atteint le niveau du liquide, ont
continué à ramper à sa surface, en se laissant pendre au-dessous_
comme certains mollusques gastéropodes.” (Dujardin, F., Observations
nouvelles sur les prétendus céphalopodes microscopiques, _Ann. des Sci.
Nat._ (2), III, p. 312, 1835.)
[306] Cf. Boas, _Spolia Atlantica_, 1886, pl. 6.
[307] This cellular pattern would seem to be related to the “cohesion
figures” described by Tomlinson in various surface-films (_Phil. Mag._
1861 to 1870); to the “tesselated structure” in liquids described by
Professor James Thomson in 1882 (_Collected Papers_, p. 136); and to
the _tourbillons cellulaires_ of Prof. H. Bénard (_Ann. de Chimie_
(7), XXIII, pp. 62–144, 1901, (8), XXIV, pp. 563–566, 1911), _Rev.
génér. des Sci._ XI, p. 1268, 1900; cf. also E. H. Weber. (_Poggend.
Ann._ XCIV, p. 452, 1855, etc.). The phenomenon is of great interest
and various appearances have been referred to it, in biology, geology,
metallurgy and even astronomy: for the flocculent clouds in the solar
photosphere shew an analogous configuration. (See letters by Kerr
Grant, Larmor, Wager and others, in _Nature_, April 16 to June 11,
1914.) In many instances, marked by strict symmetry or regularity, it
is very possible that the interference of waves or ripples may play
its part in the phenomenon. But in the majority of cases, it is fairly
certain that localised centres of action, or of diminished tension, are
present, such as might be provided by dust-particles in the case of
Darling’s experiment (cf. _infra_, p. 590).
[308] Ueber physikalischen Eigenschaften dünner, fester Lamellen, _S.B.
Berlin. Akad._ 1888, pp. 789, 790.
[309] Certain palaeontologists (e.g. Haeusler and Spandel) have
maintained that in each family or genus the plain smooth-shelled
forms are the primitive and ancient ones, and that the ribbed and
otherwise ornamented shells make their appearance at later dates in
the course of a definite evolution (cf. Rhumbler, _Foraminiferen der
Plankton-Expedition_, 1911, i, p. 21). If this were true it would be of
fundamental importance: but this book of mine would not deserve to be
written.
[310] _A Study of Splashes_, p. 116.
[311] See _Silliman’s Journal_, II, p. 179, 1820; and cf. Plateau, _op.
cit._ II, pp. 134, 461.
[312] The presence or absence of the contractile vacuole or vacuoles
is one of the chief distinctions, in systematic zoology, between the
Heliozoa and the Radiolaria. As we have seen on p. 165 (footnote),
it is probably no more than a physical consequence of the different
conditions of existence in fresh water and in salt.
[313] Cf. Doflein, _Lehrbuch der Protozoenkunde_, 1911, p. 422.
[314] Cf. Minchin, _Introduction to the Study of the Protozoa_, 1914 p.
293, Fig. 127.
[315] Cf. C. A. Kofoid and Olive Swezy, On Trichomonad Flagellates,
etc. _Pr. Amer. Acad. of Arts and Sci._ LI, pp. 289–378, 1915.
[316] D. L. Mackinnon, Herpetomonads from the Alimentary Tract of
certain Dungflies, _Parasitology_, III, p. 268, 1910.
[317] _Proc. Roy. Soc._ XII, pp. 251–257, 1862–3.
[318] Cf. (_int. al._) Lehmann, Ueber scheinbar lebende Kristalle und
Myelinformen, _Arch. f. Entw. Mech._ XXVI, p. 483, 1908; _Ann. d.
Physik_, XLIV, p. 969, 1914.
[319] Cf. B. Moore and H. C. Roaf, On the Osmotic Equilibrium of the
Red Blood Corpuscle, _Biochem. Journal_, III, p. 55, 1908.
[320] For an attempt to explain the form of a blood-corpuscle by
surface-tension alone, see Rice, _Phil. Mag._ Nov. 1914; but cf.
Shorter, _ibid._ Jan. 1915.
[321] Koltzoff, N. K., Studien über die Gestalt der Zelle, _Arch. f.
mikrosk. Anat._ LXVII, pp. 364–571, 1905; _Biol. Centralbl._ XXIII,
pp. 680–696, 1903, XXVI, pp. 854–863, 1906; _Arch. f. Zellforschung_,
II, pp. 1–65, 1908, VII, pp. 344–423, 1911; _Anat. Anzeiger_, XLI, pp.
183–206, 1912.
[322] Cf. _supra_, p. 129.
[323] As Bethe points out (Zellgestalt, Plateausche Flüssigkeitstigur
und Neurofibrille, _Anat. Anz._ XL. p. 209, 1911), the spiral fibres
of which Koltzoff speaks must lie _in the surface_, and not within the
substance, of the cell whose conformation is affected by them.
[324] See for a further but still elementary account, Michaelis,
_Dynamics of Surfaces_, 1914, p. 22 _seq._; Macallum,
_Oberflächenspannung und Lebenserscheinungen_, in Asher-Spiro’s
_Ergebnisse der Physiologie_, XI, pp. 598–658, 1911; see also W.
W. Taylor’s _Chemistry of Colloids_, 1915, p. 221 _seq._, Wolfgang
Ostwald, _Grundriss der Kolloidchemie_, 1909, and other text-books of
physical chemistry; and Bayliss’s _Principles of General Physiology_,
pp. 54–73, 1915.
[325] The first instance of what we now call an adsorptive phenomenon
was observed in soap-bubbles. Leidenfrost, in 1756, was aware that the
outer layer of the bubble was covered by an “oily” layer. A hundred
years later Dupré shewed that in a soap-solution the soap tends to
concentrate at the surface, so that the surface-tension of a very weak
solution is very little different from that of a strong one (_Théorie
mécanique de la chaleur_, 1869, p. 376; cf. Plateau, II, p. 100).
[326] This identical phenomenon was the basis of Quincke’s
theory of amoeboid movement (Ueber periodische Ausbreitung von
Flüssigkeitsoberflächen, etc., _SB. Berlin. Akad._ 1888, pp. 791–806;
cf. _Pflüger’s Archiv_, 1879, p. 136).
[327] J. Willard Gibbs, Equilibrium of Heterogeneous Substances, _Tr.
Conn. Acad._ III, pp. 380–400, 1876, also in _Collected Papers_, I,
pp. 185–218, London, 1906; J. J. Thomson, _Applications of Dynamics
to Physics and Chemistry_, 1888 (Surface tension of solutions), p.
190. See also (_int. al._) the various papers by C. M. Lewis, _Phil.
Mag._ (6), XV, p. 499, 1908, XVII, p. 466, 1909, _Zeitschr. f. physik.
Chemie_, LXX, p. 129, 1910; Milner, _Phil. Mag._ (6), XIII, p. 96,
1907, etc.
[328] G. F. FitzGerald, On the Theory of Muscular Contraction, _Brit.
Ass. Rep._ 1878; also in _Scientific Writings_, ed. Larmor, 1902, pp.
34, 75. A. d’Arsonval, Relations entre l’électricité animale et la
tension superficielle, _C. R._ CVI, p. 1740. 1888; cf. A. Imbert, Le
mécanisme de la contraction musculaire, déduit de la considération des
forces de tension superficielle, _Arch. de Phys._ (5), IX, pp. 289–301,
1897.
[329] Ueber die Natur der Bindung der Gase im Blut und in seinen
Bestandtheilen, _Kolloid. Zeitschr._ II, pp. 264–272, 294–301, 1908;
cf. Loewy, Dissociationsspannung des Oxyhaemoglobin im Blut, _Arch. f.
Anat. und Physiol._ 1904, p. 231.
[330] We may trace the first steps in the study of this phenomenon
to Melsens, who found that thin films of white of egg become firm
and insoluble (Sur les modifications apportées à l’albumine ... par
l’action purement mécanique, _C. R. Acad. Sci._ XXXIII, p. 247, 1851);
and Harting made similar observations about the same time. Ramsden has
investigated the same subject, and also the more general phenomenon
of the formation of albuminoid and fatty membranes by adsorption: cf.
Koagulierung der Eiweisskörper auf mechanischer Wege, _Arch. f. Anat.
u. Phys._ (_Phys. Abth._) 1894, p. 517; Abscheidung fester Körper in
Oberflächenschichten _Z. f. phys. Chem._ XLVII, p. 341, 1902; _Proc.
R. S._ LXXII, p. 156, 1904. For a general review of the whole subject
see H. Zangger, Ueber Membranen und Membranfunktionen, in Asher-Spiro’s
_Ergebnisse der Physiologie_, VII, pp. 99–160, 1908.
[331] Cf. Taylor, _Chemistry of Colloids_, p. 252.
[332] Strasbürger, Ueber Cytoplasmastrukturen, etc. _Jahrb. f. wiss.
Bot._ XXX, 1897; R. A. Harper, Kerntheilung und freie Zellbildung im
Ascus, _ibid._; cf. Wilson, _The Cell in Development, etc._ pp. 53–55.
[333] Cf. A. Gurwitsch, _Morphologie und Biologie der Zelle_, 1904,
pp. 169–185; Meves, Die Chondriosomen als Träger erblicher Anlagen,
_Arch. f. mikrosk. Anat._ 1908, p. 72; J. O. W. Barratt, Changes in
Chondriosomes, etc. _Q.J.M.S._ LVIII, pp. 553–566, 1913, etc.; A.
Mathews, Changes in Structure of the Pancreas Cell, etc., _J. of
Morph._ XV (Suppl.), pp. 171–222, 1899.
[334] The question whether chromosomes, chondriosomes or chromidia
be the true vehicles or transmitters of “heredity” is not without
its analogy to the older problem of whether the pineal gland or the
pituitary body were the actual seat and domicile of the soul.
[335] Cf. C. C. Dobell, Chromidia and the Binuclearity Hypotheses; a
review and a criticism, _Q.J.M.S._ LIII, 279–326, 1909; Prenant, A.,
Les Mitochondries et l’Ergastoplasme, _Journ. de l’Anat. et de la
Physiol._ XLVI, pp. 217–285, 1910 (both with copious bibliography).
[336] Traube in particular has maintained that in differences of
surface-tension we have the origin of the active force productive
of osmotic currents, and that herein we find an explanation, or an
approach to an explanation, of many phenomena which were formerly
deemed peculiarly “vital” in their character. “Die Differenz der
Oberflächenspannungen oder der Oberflächendruck eine Kraft darstellt,
welche als treibende Kraft der Osmose, an die Stelle des nicht mit
dem Oberflächendruck identischen osmotischen Druckes, zu setzen ist,
etc.” (Oberflächendruck und seine Bedeutung im Organismus, _Pflüger’s
Archiv_, CV, p. 559, 1904.) Cf. also Hardy (_Pr. Phys. Soc._ XXVIII, p.
116, 1916), “If the surface film of a colloid membrane separating two
masses of fluid were to change in such a way as to lower the potential
of the water in it, water would enter the region from both sides at
once. But if the change of state were to be propagated as a wave of
change, starting at one face and dying out at the other face, water
would be carried along from one side of the membrane to the other. A
succession of such waves would maintain a flow of fluid.”
[337] On the Distribution of Potassium in animal and vegetable Cells;
_Journ. of Physiol._ XXXII, p. 95, 1905.
[338] The reader will recognise that there is a fundamental difference,
and contrast, between such experiments as these of Professor Macallum’s
and the ordinary staining processes of the histologist. The latter
are (as a general rule) purely empirical, while the former endeavour
to reveal the true microchemistry of the cell. “On peut dire que la
microchimie n’est encore qu’à la période d’essai, et que l’avenir de
l’histologie et spécialement de la cytologie est tout entier dans la
microchimie” (Prenant, A., Méthodes et résultats de la Microchimie,
_Journ. de l’Anat. et de la Physiol._ XLVI, pp. 343–404, 1910).
[339] Cf. Macallum, Presidential Address, Section I, _Brit. Ass. Rep._
(Sheffield), 1910, p. 744.
[340] In accordance with a simple _corollary_ to the Gibbs-Thomson law.
[341] It can easily be proved (by equating the increase of energy
stored in an increased surface to the work done in increasing that
surface), that the tension measured per unit breadth, _T__{_ab_}, is
equal to the energy per unit area, _E__{_ab_}.
[342] The presence of this little liquid “bourrelet,” drawn from the
material of which the partition-walls themselves are composed, is
obviously tending to a reduction of the internal surface-area. And it
may be that it is as well, or better, accounted for on this ground than
on Plateau’s assumption that it represents a “surface of continuity.”
[343] A similar “bourrelet” is admirably seen at the line of junction
between a floating bubble and the liquid on which it floats; in which
case it constitutes a “masse annulaire,” whose mathematical properties
and relation to the form of the _nearly_ hemispherical bubble, have
been investigated by van der Mensbrugghe (cf. Plateau, _op. cit._,
p. 386). The form of the superficial vacuoles in Actinophrys or
Actinosphaerium involves an identical problem.
[344] In an actual calculation we must of course always take account of
the tensions on _both sides_ of each film or membrane.
[345] Hofmeister, _Pringsheim’s Jahrb._ III, p. 272, 1863; _Hdb. d.
physiol. Bot._ I, 1867, p. 129.
[346] Sachs, Ueber die Anordnung der Zellen in jüngsten
Pflanzentheilen, _Verh. phys. med. Ges. Würzburg_, XI, pp. 219–242,
1877; Ueber Zellenanordnung und Wachsthum, _ibid._ XII, 1878; Ueber
die durch Wachsthum bedingte Verschiebung kleinster Theilchen in
trajectorischen Curven, _Monatsber. k. Akad. Wiss. Berlin_, 1880;
_Physiology of Plants_, chap. xxvii, pp. 431–459, Oxford, 1887.
[347] Schwendener, Ueber den Bau und das Wachsthum des Flechtenthallus,
_Naturf. Ges. Zürich_, Febr. 1860, pp. 272–296.
[348] Reinke, _Lehrbuch der Botanik_, 1880, p. 519.
[349] Cf. Leitgeb, _Unters. über die Lebermoose_, II, p. 4, Graz, 1881.
[350] Rauber, Neue Grundlegungen zur Kenntniss der Zelle, _Morph.
Jahrb._ VIII, pp. 279, 334, 1882.
[351] _C. R. Acad. Sc._ XXXIII, p. 247, 1851; _Ann. de chimie et de
phys._ (3), XXXIII, p. 170, 1851; _Bull. R. Acad. Belg._ XXIV, p. 531,
1857.
[352] Klebs, _Biolog. Centralbl._ VII, pp. 193–201, 1887.
[353] L. Errera, Sur une condition fondamentale d’équilibre des
cellules vivantes, _C. R._, CIII, p. 822, 1886; _Bull. Soc. Belge
de Microscopie_, XIII, Oct. 1886; _Recueil d’œuvres_ (_Physiologie
générale_), 1910, pp. 201–205.
[354] L. Chabry, Embryologie des Ascidiens, _J. Anat. et Physiol._
XXIII, p. 266, 1887.
[355] Robert, Embryologie des Troques, _Arch. de Zool. exp. et gén._
(3), X, 1892.
[356] “Dass der Furchungsmodus etwas für das Zukünftige unwesentliches
ist,” _Z. f. w. Z._ LV, 1893, p. 37. With this statement compare,
or contrast, that of Conklin, quoted on p. 4; cf. also pp. 157, 348
(footnotes).
[357] de Wildeman, Etudes sur l’attache des cloisons cellulaires, _Mém.
Couronn. de l’Acad. R. de Belgique_, LIII, 84 pp., 1893–4.
[358] It was so termed by Conklin in 1897, in his paper on Crepidula
(_J. of Morph._ XIII, 1897). It is the _Querfurche_ of Rabl (_Morph.
Jahrb._ V, 1879); the _Polarfurche_ of O. Hertwig (_Jen. Zeitschr._
XIV, 1880); the _Brechungslinie_ of Rauber (Neue Grundlage zur K. der
Zelle, _M. Jb._ VIII, 1882). It is carefully discussed by Robert, Dév.
des Troques, _Arch. de Zool. Exp. et Gén._ (3), X, 1892, p. 307 seq.
[359] Thus Wilson (_J. of Morph._ VIII, 1895) declared that in
Amphioxus the polar furrow was occasionally absent, and Driesch took
occasion to criticise and to throw doubt upon the statement (_Arch. f.
Entw. Mech._ I, 1895, p. 418).
[360] Precisely the same remark was made long ago by Driesch: “Das so
oft sehematisch gezeichnete Vierzellenstadium mit zwei sich in zwei
Punkten scheidende Medianen kann man wohl getrost aus der Reihe des
Existierenden streichen,” _Entw. mech. Studien, Z. f. w. Z._ LIII, p.
166, 1892. Cf. also his _Math. mechanische Bedeutung morphologischer
Probleme der Biologie_, Jena, 59 pp. 1891.
[361] Compare, however, p. 299.
[362] _Ricreatione dell’ occhio e della mente, nell’ Osservatione delle
Chiocciole_, Roma, 1681.
[363] Cf. some of J. H. Vincent’s photographs of ripples, in _Phil.
Mag._ 1897–1899; or those of F. R. Watson, in _Phys. Review_, 1897,
1901, 1916. The appearance will depend on the rate of the wave, and in
turn on the surface-tension; with a low tension one would probably see
only a moving “jabble.” FitzGerald thought diatom-patterns might be due
to electromagnetic vibrations (_Works_, p. 503, 1902).
[364] Cushman, J. A. and Henderson, W. P., _Amer. Nat._ XL, pp.
797–802, 1906.
[365] This does not merely neglect the _broken_ ones but _all_ whose
centres lie between this circle and a hexagon inscribed in it.
[366] For more detailed calculations see a paper by “H.M.” [? H.
Munro], in _Q. J. M. S._ VI, p. 83, 1858.
[367] Cf. Hartog, The Dual Force of the Dividing Cell, _Science
Progress_ (n.s.), I, Oct. 1907, and other papers. Also Baltzer, _Ueber
mehrpolige Mitosen bei Seeigeleiern_, Inaug. Diss. 1908.
[368] Observations sur les Abeilles, _Mém. Acad. Sc. Paris_, 1712, p.
299.
[369] As explained by Leslie Ellis, in his essay “On the Form of Bees’
Cells,” in _Mathematical and other Writings_, 1853, p. 353; cf. O.
Terquem, _Nouv. Ann. Math._ 1856, p. 178.
[370] _Phil. Trans._ XLII, 1743, pp. 565–571.
[371] _Mém. de l’Acad. de Berlin_, 1781.
[372] Cf. Gregory, _Examples_, p. 106, Wood’s _Homes without Hands_,
1865, p. 428, Mach, _Science of Mechanics_, 1902, p. 453, etc., etc.
[373] _Origin of Species_, ch. VIII (6th ed., p. 221). The cells of
various bees, humble-bees and social wasps have been described and
mathematically investigated by K. Müllenhoff, _Pflüger’s Archiv_
XXXII, p. 589, 1883; but his many interesting results are too complex
to epitomise. For figures of various nests and combs see (e.g.) von
Büttel-Reepen, _Biol. Centralbl._ XXXIII, pp. 4, 89, 129, 183, 1903.
[374] Darwin had a somewhat similar idea, though he allowed more play
to the bee’s instinct or conscious intention. Thus, when he noticed
certain half-completed cell-walls to be concave on one side and convex
on the other, but to become perfectly flat when restored for a short
time to the hive, he says: “It was absolutely impossible, from the
extreme thinness of the little plate, that they could have effected
this by gnawing away the convex side; and I suspect that the bees
in such cases stand on opposite sides and push and bend the ductile
and warm wax (which as I have tried is easily done) into its proper
intermediate plane, and thus flatten it.”
[375] Since writing the above, I see that Müllenhoff gives the
same explanation, and declares that the waxen wall is actually a
_Flüssigkeitshäutchen_, or liquid film.
[376] Bonnet criticised Buffon’s explanation, on the ground that his
description was incomplete; for Buffon took no account of the Maraldi
pyramids.
[377] Buffon, _Histoire Naturelle_, IV, p. 99. Among many other papers
on the Bee’s cell, see Barclay, _Mem. Wernerian Soc._ II, p. 259
(1812), 1818; Sharpe, _Phil. Mag._ IV, 1828, pp. 19–21; L. Lalanne,
_Ann. Sci. Nat._ (2) Zool. XIII, pp. 358–374, 1840; Haughton, _Ann.
Mag. Nat. Hist._ (3), XI, pp. 415–429, 1863; A. R. Wallace, _ibid._
XII, p. 303, 1863; Jeffries Wyman. _Pr. Amer. Acad. of Arts and Sc._
VII, pp. 68–83, 1868; Chauncey Wright, _ibid._ IV, p. 432, 1860.
[378] Sir W. Thomson, On the Division of Space with Minimum Partitional
Area, _Phil. Mag._ (5), XXIV, pp. 503–514, Dec. 1887; cf. _Baltimore
Lectures_, 1904, p. 615.
[379] Also discovered independently by Sir David Brewster, _Trans.
R.S.E._ XXIV, p. 505, 1867, XXV, p. 115, 1869.
[380] Von Fedorow had already described (in Russian) the same figure,
under the name of cubo-octahedron, or hepta-parallelohedron, limited
however to the case where all the faces are plane. This figure,
together with the cube, the hexagonal prism, the rhombic dodecahedron
and the “elongated dodecahedron,” constituted the five plane-faced,
parallel-sided figures by which space is capable of being completely
filled and symmetrically partitioned; the series so forming the
foundation of Von Fedorow’s theory of crystalline structure. The
elongated dodecahedron is, essentially, the figure of the bee’s cell.
[381] F. R. Lillie, Embryology of the Unionidae, _Journ. of
Morphology_, X, p. 12, 1895.
[382] E. B. Wilson, The Cell-lineage of Nereis, _Journ. of Morphology_,
VI, p. 452, 1892.
[383] It is highly probable, and we may reasonably assume, that the two
little triangles do not actually meet at an apical _point_, but merge
into one another by a twist, or minute surface of complex curvature, so
as not to contravene the normal conditions of equilibrium.
[384] Professor Peddie has given me this interesting and important
result, but the mathematical reasoning is too lengthy to be set forth
here.
[385] Cf. Rhumbler, _Arch. f. Entw. Mech._ XIV, p. 401, 1902; Assheton,
_ibid._ XXXI, pp. 46–78, 1910.
[386] M. Robert (_l. c._ p. 305) has compiled a long list of cases
among the molluscs and the worms, where the initial segmentation of
the egg proceeds by equal or unequal division. The two cases are about
equally numerous. But like many other writers, he would ascribe this
equality or inequality rather to a provision for the future than to
a direct effect of immediate physical causation: “Il semble assez
probable, comme on l’a dit souvent, que la plus grande taille d’un
blastomère est liée à l’importance et au développement précoce des
parties du corps qui doivent en naître: il y aurait là une sorte de
reflet des stades postérieures du développement sur les premières
phénomènes, ce que M. Ray Lankester appelle _precocious segregation_.
Il faut avouer pourtant qu’on est parfois assez embarrassé pour
assigner une cause à pareilles différences.”
[387] The principle is well illustrated in an experiment of Sir David
Brewster’s (_Trans. R.S.E._ XXV, p. 111, 1869). A soap-film is drawn
over the rim of a wine-glass, and then covered by a watch-glass. The
film is inclined or shaken till it becomes attached to the glass
covering, and it then immediately changes place, leaving its transverse
position to take up that of a spherical segment extending from one side
of the wine-glass to its cover, and so enclosing the same volume of air
as formerly but with a great economy of surface, precisely as in the
case of our spherical partition cutting off one corner of a cube.
[388] Cf. Wildeman, _Attache des Cloisons_, etc., pls. 1, 2.
[389] _Nova Acta K. Leop. Akad._ XI, 1, pl. IV.
[390] Cf. _Protoplasmamechanik_, p. 229: “Insofern liegen also die
Verhältnisse hier wesentlich anders als bei der Zertheilung hohler
Körperformen durch flüssige Lamellen. Wenn die Membran bei der
Zelltheilung die von dem Prinzip der kleinsten Flächen geforderte Lage
und Krümmung annimmt, so werden wir den Grund dafür in andrer Weise
abzuleiten haben.”
[391] There is, I think, some ambiguity or disagreement among botanists
as to the use of this latter term: the sense in which I am using it,
viz. for any partition which meets the outer or peripheral wall at
right angles (the strictly _radial_ partition being for the present
excluded), is, however, clear.
[392] _Cit._ Plateau, _Statique des Liquides_, i, p. 358.
[393] Even in a Protozoon (_Euglena viridis_), when kept alive under
artificial compression, Ryder found a process of cell-division to occur
which he compares to the segmenting blastoderm of a fish’s egg, and
which corresponds in its essential features with that here described.
_Contrib. Zool. Lab. Univ. Pennsylvania_, I, pp. 37–50, 1893.
[394] This, like many similar figures, is manifestly drawn under the
influence of Sachs’s theoretical views, or assumptions, regarding
orthogonal trajectories, coaxial circles, confocal ellipses, etc.
[395] Such preconceptions as Rauber entertained were all in a direction
likely to lead him away from such phenomena as he has faithfully
depicted. Rauber had no idea whatsoever of the principles by which we
are guided in this discussion, nor does he introduce at all the analogy
of surface-tension, or any other purely physical concept. But he was
deeply under the influence of Sachs’s rule of rectangular intersection;
and he was accordingly disposed to look upon the configuration
represented above in Fig. 168, 6, as the most typical or most primitive.
[396] Cf. Rauber, Neue Grundlage z. K. der Zelle, _Morph. Jahrb._ VIII,
1883, pp. 273, 274:
“Ich betone noch, dass unter meinen Figuren diejenige gar nicht
enthalten ist, welche zum Typus der Batrachierfurchung gehörig am
meisten bekannt ist .... Es haben so ausgezeichnete Beobachter sie als
vorhanden beschrieben, dass es mir nicht einfallen kann, sie überhaupt
nicht anzuerkennen.”
[397] Roux’s experiments were performed with drops of paraffin
suspended in dilute alcohol, to which a little calcium acetate was
added to form a soapy pellicle over the drops and prevent them from
reuniting with one another.
[398] Cf. (e.g.) Clerk Maxwell, On Reciprocal Figures, etc., _Trans. R.
S. E._ XXVI, p. 9, 1870.
[399] See Greville, K. R., Monograph of the Genus Asterolampra,
_Q.J.M.S._ VIII, (Trans.), pp. 102–124, 1860; cf. IBID. (n.s.), II, pp.
41–55, 1862.
[400] The same is true of the insect’s wing; but in this case I do not
hazard a conjectural explanation.
[401] _Ann. Mag. N. H._ (2), III, p. 126, 1849.
[402] _Phil. Trans._ CLVII, pp. 643–656, 1867.
[403] Sachs, _Pflanzenphysiologie_ (_Vorlesung_ XXIV), 1882; cf.
Rauber, Neue Grundlage zur Kenntniss der Zelle, _Morphol. Jahrb._ VIII,
p. 303 _seq._, 1883; E. B. Wilson, Cell-lineage of Nereis, _Journ. of
Morphology_, VI, p. 448, 1892, etc.
[404] In the following account I follow closely on the lines laid down
by Berthold; _Protoplasmamechanik_, cap. vii. Many botanical phenomena
identical and similar to those here dealt with, are elaborately
discussed by Sachs in his _Physiology of Plants_ (chap. xxvii, pp.
431–459, Oxford, 1887); and in his earlier papers, Ueber die Anordnung
der Zellen in jüngsten Pflanzentheilen, and Ueber Zellenanordnung und
Wachsthum (_Arb. d. botan. Inst. Würzburg_, 1878, 1879). But Sachs’s
treatment differs entirely from that which I adopt and advocate here:
his explanations being based on his “law” of rectangular succession,
and involving complicated systems of confocal conics, with their
orthogonally intersecting ellipses and hyperbolas.
[405] Cf. p. 369.
[406] There is much information regarding the chemical composition and
mineralogical structure of shells and other organic products in H. C.
Sorby’s Presidential Address to the Geological Society (_Proc. Geol.
Soc._ 1879, pp. 56–93); but Sorby failed to recognise that association
with “organic” matter, or with colloid matter whether living or dead,
introduced a new series of purely physical phenomena.
[407] Vesque, _Ann. des Sc. Nat._ (_Bot._) (5), XIX, p. 310, 1874.
[408] Cf. Kölliker, _Icones Histiologicae_, 1864, pp. 119, etc.
[409] In an interesting paper by Irvine and Sims Woodhead on the
“Secretion of Carbonate of Lime by Animals” (_Proc. R. S. E._ XVI,
1889, p. 351) it is asserted that “lime salts, of whatever form, are
deposited _only_ in vitally inactive tissue.”
[410] The tube of Teredo shews no trace of organic matter, but consists
of irregular prismatic crystals: the whole structure “being identical
with that of small veins of calcite, such as are seen in thin sections
of rocks” (Sorby, _Proc. Geol. Soc._ 1879, p. 58). This, then, would
seem to be a somewhat exceptional case of a shell laid down completely
outside of the animal’s external layer of organic or colloid substance.
[411] _C. R. Soc. Biol. Paris_ (9), I, pp. 17–20, 1889; _C. R. Ac. Sc._
CVIII, pp. 196–8, 1889.
[412] Cf. Heron-Allen, _Phil. Trans._ (B), vol. CCVI, p. 262, 1915.
[413] See Leduc, _Mechanism of Life_ (1911), ch. X, for copious
references to other works on the artificial production of “organic”
forms.
[414] Lectures on the Molecular Asymmetry of Natural Organic Compounds,
_Chemical Soc. of Paris_, 1860, and also in Ostwald’s _Klassiker d. ex.
Wiss._ No. 28, and in _Alembic Club Reprints_, No. 14, Edinburgh, 1897;
cf. Richardson, G. M., _Foundations of Stereochemistry_, N. Y. 1901.
[415] Japp, Stereometry and Vitalism, _Brit. Ass. Rep._ (Bristol), p.
813, 1898; cf. also a voluminous discussion in _Nature_, 1898–9.
[416] They represent the general theorem of which particular cases are
found, for instance, in the asymmetry of the ferments (or _enzymes_)
which act upon asymmetrical bodies, the one fitting the other,
according to Emil Fischer’s well-known phrase, as lock and key. Cf.
his Bedeutung der Stereochemie für die Physiologie, _Z. f. physiol.
Chemie_, V, p. 60, 1899, and various papers in the _Ber. d. d. chem.
Ges._ from 1894.
[417] In accordance with Emil Fischer’s conception of “asymmetric
synthesis,” it is now held to be more likely that the process is
synthetic than analytic: more likely, that is to say, that the plant
builds up from the first one asymmetric body to the exclusion of the
other, than that it “selects” or “picks out” (as Japp supposed) the
right-handed or the left-handed molecules from an original, optically
inactive, mixture of the two; cf. A. McKenzie, Studies in Asymmetric
Synthesis, _Journ. Chem. Soc._ (Trans.), LXXXV, p. 1249, 1904.
[418] See for a fuller discussion, Hans Przibram, _Vitalität_, 1913,
Kap. iv, Stoffwechsel (Assimilation und Katalyse).
[419] Cf. Cotton, _Ann. de Chim. et de Phys._ (7), VIII, pp. 347–432
(cf. p. 373), 1896.
[420] Byk, A., Zur Frage der Spaltbarkeit von Razemverbindungen durch
Zirkularpolarisiertes Licht, ein Beitrag zur primären Entstehung
optisch-activer Substanzen, _Zeitsch. f. physikal. Chemie_, XLIX, p.
641, 1904. It must be admitted that further positive evidence on these
lines is still awanting.
[421] Cf. (_int. al._) Emil Fischer, _Untersuchungen über Aminosäuren,
Proteine_, etc. Berlin, 1906.
[422] Japp, _l. c._ p. 828.
[423] Rainey, G., On the Elementary Formation of the Skeletons of
Animals, and other Hard Structures formed in connection with Living
Tissue, _Brit. For. Med. Ch. Rev._ XX, pp. 451–476, 1857; published
separately with additions, 8vo. London, 1858. For other papers by
Rainey on kindred subjects see _Q. J. M. S._ VI (_Tr. Microsc. Soc._),
pp. 41–50, 1858, VII, pp. 212–225, 1859, VIII, pp. 1–10, 1860, I (n.
s.), pp. 23–32, 1861. Cf. also Ord, W. M., On Molecular Coalescence,
and on the influence exercised by Colloids upon the Forms of Inorganic
Matter, _Q. J. M. S._ XII, pp. 219–239, 1872; and also the early
but still interesting observations of Mr Charles Hatchett, Chemical
Experiments on Zoophytes; with some observations on the component parts
of Membrane, _Phil. Trans._ 1800. pp. 327–402.
[424] Cf. Quincke, Ueber unsichtbare Flüssigkeitsschichten, _Ann. der
Physik_, 1902.
[425] See for instance other excellent illustrations in Carpenter’s
article “Shell,” in Todd’s _Cyclopædia_, vol. IV. pp. 550–571,
1847–49. According to Carpenter, the shells of the mollusca (and also
of the crustacea) are “essentially composed of _cells_, consolidated
by a deposit of carbonate of lime in their interior.” That is to
say, Carpenter supposed that the spherulites, or calcospherites
of Harting, were, to begin with, just so many living protoplasmic
cells. Soon afterwards however, Huxley pointed out that the mode of
formation, while at first sight “irresistibly suggesting a cellular
structure, ... is in reality nothing of the kind,” but “is simply the
result of the concretionary manner in which the calcareous matter is
deposited”; _ibid._ art. “Tegumentary Organs,” vol. V, p. 487, 1859.
Quekett (_Lectures on Histology_, vol. II, p. 393, 1854, and _Q. J.
M. S._ XI, pp. 95–104, 1863) supported Carpenter; but Williamson
(Histological Features in the Shells of the Crustacea, _Q. J. M. S._
VIII, pp. 35–47, 1860) amply confirmed Huxley’s view, which in the
end Carpenter himself adopted (_The Microscope_, 1862, p. 604). A
like controversy arose later in regard to corals. Mrs Gordon (M. M.
Ogilvie) asserted that the coral was built up “of successive layers
of calcified cells, which hang together at first by their cell-walls,
and ultimately, as crystalline changes continue, form the individual
laminae of the skeletal structures” (_Phil. Trans._ CLXXXVII, p. 102,
1896): whereas v. Koch had figured the coral as formed out of a mass
of “Kalkconcremente” or “crystalline spheroids,” laid down outside
the ectoderm, and precisely similar both in their early rounded and
later polygonal stages (though von Koch was not aware of the fact) to
the calcospherites of Harting (Entw. d. Kalkskelettes von Asteroides,
_Mitth. Zool. St. Neapel_, III, pp. 284–290, pl. XX, 1882). Lastly
Duerden shewed that external to, and apparently secreted by the
ectoderm lies a homogeneous organic matrix or membrane, “in which the
minute calcareous crystals forming the skeleton are laid down” (The
Coral _Siderastraea radians_, etc., _Carnegie Inst. Washington_, 1904,
p. 34). Cf. also M. M. Ogilvie-Gordon, _Q. J. M. S._ XLIX, p. 203,
1905, etc.
[426] Cf. Claparède, _Z. f. w. Z._ XIX, p. 604, 1869.
[427] Spicules extremely like those of the Alcyonaria occur also in a
few sponges; cf. (e.g.), Vaughan Jennings, _Journ. Linn. Soc._ XXIII,
p. 531, pl. 13, fig. 8, 1891.
[428] _Mem. Manchester Lit. and Phil. Soc._ LX, p. 11, 1916.
[429] Mummery, J. H., On Calcification in Enamel and Dentine, _Phil.
Trans._ CCV (B), pp. 95–111, 1914.
[430] The artificial concretion represented in Fig. 202 is identical
in appearance with the concretions found in the kidney of Nautilus, as
figured by Willey (_Zoological Results_, p. lxxvi, Fig. 2, 1902).
[431] Cf. Taylor’s _Chemistry of Colloids_, p. 18, etc., 1915.
[432] This rule, undreamed of by Errera, supports and justifies the
cardinal assumption (of which we have had so much to say in discussing
the forms of cells and tissues) that the _incipient_ cell-wall behaves
as, and indeed actually is, a liquid film (cf. p. 306).
[433] Cf. p. 254.
[434] Cf. Harting, _op. cit._, pp. 22, 50: “J’avais cru d’abord que ces
couches concentriques étaient produites par l’alternance de la chaleur
ou de la lumière, pendant le jour et la nuit. Mais l’expérience,
expressément instituée pour examiner cette question, y a répondu
négativement.”
[435] Liesegang, R. E., _Ueber die Schichtungen bei Diffusionen_,
Leipzig, 1907, and other earlier papers.
[436] Cf. Taylor’s _Chemistry of Colloids_, pp. 146–148, 1915.
[437] Cf. S. C. Bradford, The Liesegang Phenomenon and Concretionary
Structure in Rocks, _Nature_, XCVII, p. 80, 1916; cf. _Sci. Progress_,
X, p. 369, 1916.
[438] Cf. Faraday, On Ice of Irregular Fusibility, _Phil. Trans._,
1858, p. 228; _Researches in Chemistry, etc._, 1859, p. 374; Tyndall,
_Forms of Water_, p. 178, 1872; Tomlinson, C., On some effects of small
Quantities of Foreign Matter on Crystallisation, _Phil. Mag._ (5) XXXI,
p. 393, 1891, and other papers.
[439] A Study in Crystallisation, _J. of Soc. of Chem. Industry_, XXV,
p. 143, 1906.
[440] _Ueber Zonenbildung in kolloidalen Medien_, Jena, 1913.
[441] _Verh. d. d. Zool. Gesellsch._ p. 179, 1912.
[442] _Descent of Man_, II, pp. 132–153, 1871.
[443] As a matter of fact, the phenomena associated with the
development of an “ocellus” are or may be of great complexity, inasmuch
as they involve not only a graded distribution of pigment, but also,
in “optical” coloration, a symmetrical distribution of structure or
form. The subject therefore deserves very careful discussion, such
as Bateson gives to it (_Variation_, chap. xii). This, by the way,
is one of the very rare cases in which Bateson appears inclined to
suggest a purely physical explanation of an organic phenomenon: “The
suggestion is strong that the whole series of rings (in _Morpho_) may
have been formed by some one central disturbance, somewhat as a series
of concentric waves may be formed by the splash of a stone thrown into
a pool, etc.”
[444] Cf. also Sir D. Brewster, On optical properties of Mother of
Pearl, _Phil. Trans._ 1814, p. 397.
[445] Biedermann, W., Ueber die Bedeutung von Kristallisationsprozessen
der Skelette wirbelloser Thiere, namentlich der Molluskenschalen,
_Z. f. allg. Physiol._ I, p. 154, 1902; Ueber Bau und Entstehung der
Molluskenschale, _Jen. Zeitschr._ XXXVI, pp. 1–164, 1902. Cf. also
Steinmann, Ueber Schale und Kalksteinbildungen, _Ber. Naturf. Ges.
Freiburg i. Br_ IV, 1889; Liesegang, _Naturw. Wochenschr._ p. 641, 1910.
[446] Cf. Bütschli, Ueber die Herstellung künstlicher Stärkekörner oder
von Sphärokrystallen der Stärke, _Verh. nat. med. Ver. Heidelberg_, V,
pp. 457–472, 1896.
[447] _Untersuchungen über die Stärkekörner_, Jena, 1905.
[448] Cf. Winge, _Meddel. fra Komm. for Havundersögelse_ (_Fiskeri_),
IV, p. 20, Copenhagen, 1915.
[449] The anhydrite is sulphate of lime (CaSO_{4}); the polyhalite is
a triple sulphate of lime, magnesia and potash (2 CaSO_{4}. MgSO_{4}.
K_{2}SO_{4} + 2 H_{2}O).
[450] Cf. van’t Hoff, _Physical Chemistry in the Service of the
Sciences_, p. 99 seq. Chicago, 1903.
[451] Sphärocrystalle von Kalkoxalat bei Kakteen, _Ber. d. d. Bot.
Gesellsch._ p. 178, 1885.
[452] Pauli, W. u. Samec, M., Ueber Löslichkeitsbeeinflüssung von
Elektrolyten durch Eiweisskörper, _Biochem. Zeitschr._ XVII, p. 235,
1910. Some of these results were known much earlier; cf. Fokker in
_Pflüger’s Archiv_, VII, p. 274, 1873; also Irvine and Sims Woodhead,
_op. cit._ p. 347.
[453] Which, in 1000 parts of ash, contains about 840 parts of
phosphate and 76 parts of calcium carbonate.
[454] Cf. Dreyer, Fr., Die Principien der Gerüstbildung bei Rhizopoden,
Spongien und Echinodermen, _Jen. Zeitschr._ XXVI, pp. 204–468, 1892.
[455] In an anomalous and very remarkable Australian sponge, just
described by Professor Dendy (_Nature_, May 18, 1916, p. 253) under the
name of _Collosclerophora_, the spicules are “gelatinous,” consisting
of a gel of colloid silica with a high percentage of water. It is not
stated whether an organic colloid is present together with the silica.
These gelatinous spicules arise as exudations on the outer surface of
cells, and come to lie in intercellular spaces or vesicles.
[456] Lister, in Willey’s _Zoological Results_, pt IV, p. 459, 1900.
[457] The peculiar spicules of Astrosclera are now said to consist of
spherules, or calcospherites, of aragonite, spores of a certain red
seaweed forming the nuclei, or starting-points, of the concretions (R.
Kirkpatrick, _Proc. R. S._ LXXXIV (B), p. 579, 1911).
[458] See for instance the plates in Théel’s Monograph of the
Challenger Holothuroidea; also Sollas’s Tetractinellida, p. lxi.
[459] For very numerous illustrations of the triradiate and
quadriradiate spicules of the calcareous sponges, see (_int. al._),
papers by Dendy (_Q. J. M. S._ XXXV, 1893), Minchin (_P. Z. S._ 1904),
Jenkin (_P. Z. S._ 1908), etc.
[460] Cf. again Bénard’s _Tourbillons cellulaires_, _Ann. de Chimie_,
1901, p. 84.
[461] Léger, Stolc and others, in Doflein’s _Lehrbuch d.
Protozoenkunde_, 1911, p. 912.
[462] See, for instance, the figures of the segmenting egg of
Synapta (after Selenka), in Korschelt and Heider’s _Vergleichende
Entwicklungsgeschichte_ (Allgem. Th., 3^{te} Lief.), p. 19, 1909. On
the spiral type of segmentation as a secondary derivative, due to
mechanical causes, of the “radial” type of segmentation, see E. B.
Wilson, Cell-lineage of Nereis, _Journ. of Morphology_, VI, p. 450,
1892.
[463] Korschelt and Heider, p. 16.
[464] _Chall. Rep. Hexactinellida_, pls. xvi, liii, lxxvi, lxxxviii.
[465] “Hierbei nahm der kohlensaure Kalk eine halb-krystallinische
Beschaffenheit an, und gestaltete sich unter Aufnahme von
Krystallwasser und in Verbindung mit einer geringen Quantität von
organischer Substanz zu jenen individuellen, festen Körpern, welche
durch die natürliche Züchtung als _Spicula_ zur Skeletbildung benützt,
und späterhin durch die Wechselwirkung von Anpassung und Vererbung im
Kampfe ums Dasein auf das Vielfältigste umgebildet und differenziert
wurden.” _Die Kalkschwämme_, I, p. 377, 1872; cf. also pp. 482, 483.
[466] _Op. cit._ p. 483. “Die geordnete, oft so sehr regelmässige und
zierliche Zusammensetzung des Skeletsystems ist zum grössten Theile
unmittelbares Product der Wasserströmung; die characteristische
Lagerung der Spicula ist von der constanten Richtung des Wasserstroms
hervorgebracht; zum kleinsten Theile ist sie die Folge von Anpassungen
an untergeordnete äussere Existenzbedingungen.”
[467] Materials for a Monograph of the Ascones, _Q. J. M. S._ XL. pp.
469–587, 1898.
[468] Haeckel, in his _Challenger Monograph_, p. clxxxviii (1887)
estimated the number of known forms at 4314 species, included in 739
genera. Of these, 3508 species were described for the first time in
that work.
[469] Cf. Gamble, _Radiolaria_ (Lankester’s _Treatise on Zoology_),
vol. I, p. 131, 1909. Cf. also papers by V. Häcker, in _Jen. Zeitschr._
XXXIX, p. 581, 1905, _Z. f. wiss. Zool._ LXXXIII, p. 336, 1905, _Arch.
f. Protistenkunde_, IX, p. 139, 1907, etc.
[470] Bütschli, Ueber die chemische Natur der Skeletsubstanz der
Acantharia, _Zool. Anz._ XXX, p. 784, 1906.
[471] For figures of these crystals see Brandt, _F. u. Fl. d. Golfes
von Neapel_, XIII, _Radiolaria_, 1885, pl. v. Cf. J. Müller, Ueber die
Thalassicollen, etc. _Abh. K. Akad. Wiss. Berlin_, 1858.
[472] Celestine, or celestite, is SrSO_{4} with some BaO replacing SrO.
[473] With the colloid chemists, we may adopt (as Rhumbler has done)
the terms _spumoid_ or _emulsoid_ to denote an agglomeration of
fluid-filled vesicles, restricting the name _froth_ to such vesicles
when filled with air or some other gas.
[474] Cf. Koltzoff, Zur Frage der Zellgestalt, _Anat. Anzeiger_, XLI,
p. 190, 1912.
[475] _Mém. de l’Acad. des Sci., St. Pétersbourg_, XII, Nr. 10, 1902.
[476] The manner in which the minute spicules of Raphidiophrys arrange
themselves round the bases of the pseudopodial rays is a similar
phenomenon.
[477] Rhumbler, Physikalische Analyse von Lebenserscheinungen der
Zelle, _Arch. f. Entw. Mech._ VII, p. 103, 1898.
[478] The whole phenomenon is described by biologists as a “surprising
exhibition of constructive and selective activity,” and is ascribed,
in varying phraseology, to intelligence, skill, purpose, psychical
activity, or “microscopic mentality”: that is to say, to Galen’s
τεχνικὴ φύσις, or “artistic creativeness” (cf. Brock’s _Galen_, 1916,
p. xxix). Cf. Carpenter, _Mental Physiology_, 1874, p. 41; Norman,
Architectural achievements of Little Masons, etc., _Ann. Mag. Nat.
Hist._ (5), I, p. 284, 1878; Heron-Allen, Contributions ... to the
Study of the Foraminifera, _Phil. Trans._ (B), CCVI, pp. 227–279,
1915; Theory and Phenomena of Purpose and Intelligence exhibited
by the Protozoa, as illustrated by selection and behaviour in the
Foraminifera, _Journ. R. Microscop. Soc._ pp. 547–557, 1915; _ibid._,
pp. 137–140, 1916. Prof. J. A. Thomson (_New Statesman_, Oct. 23,
1915) describes a certain little foraminifer, whose protoplasmic body
is overlaid by a crust of sponge-spicules, as “a psycho-physical
individuality whose experiments in self-expression include a masterly
treatment of sponge-spicules, and illustrate that organic skill which
came before the dawn of Art.” Sir Ray Lankester finds it “not difficult
to conceive of the existence of a mechanism in the protoplasm of the
Protozoa which selects and rejects building-material, and determines
the shapes of the structures built, comparable to that mechanism
which is assumed to exist in the nervous system of insects and other
animals which ‘automatically’ go through wonderfully elaborate series
of complicated actions.” And he agrees with “Darwin and others [who]
have attributed the building up of these inherited mechanisms to
the age-long action of Natural Selection, and the survival of those
individuals possessing qualities or ‘tricks’ of life-saving value,” _J.
R. Microsc. Soc._ April, 1916, p. 136.
[479] Rhumbler, _Das Protoplasma als physikalisches System_, Jena, p.
591, 1914; also in _Arch. f. Entwickelungsmech._ VII, pp. 279–335, 1898.
[480] Verworn, _Psycho-physiologische Protisten-Studien_, Jena, 1889
(219 pp.).
[481] Leidy, J., _Fresh-water Rhizopods of N. America_, 1879, p. 262,
pl. xli, figs. 11, 12.
[482] Carnoy, _Biologie Cellulaire_, p. 244, fig. 108; cf. Dreyer, _op.
cit._ 1892, fig. 185.
[483] In all these latter cases we recognise a relation to, or
extension of, the principle of Plateau’s _bourrelet_, or van der
Mensbrugghe’s _masse annulaire_, of which we have already spoken (p.
297).
[484] Apart from the fact that the apex of each pyramid is interrupted,
or truncated, by the presence of the little central cell, it is also
possible that the solid angles are not precisely equivalent to those of
Maraldi’s pyramids, owing to the fact that there is a certain amount of
distortion, or axial asymmetry, in the Nassellarian system. In other
words (to judge from Haeckel’s figures), the tetrahedral symmetry in
Nassellaria is not absolutely regular, but has a main axis about which
three of the trihedral pyramids are symmetrical, the fourth having its
solid angle somewhat diminished.
[485] Cf. Faraday’s beautiful experiments, On the Moving Groups of
Particles found on Vibrating Elastic Surfaces, etc., _Phil. Trans._
1831, p. 299; _Researches in Chem. and Phys._ 1859, pp. 314–358.
[486] We need not go so far as to suppose that the external layer
of cells wholly lacked the power of secreting a skeleton. In many
of the Nassellariae figured by Haeckel (for there are many variant
forms or species besides that represented here), the skeleton of the
partition-walls is very slightly and scantily developed. In such a
case, if we imagine its few and scanty strands to be broken away, the
central tetrahedral figure would be set free, and would have all the
appearance of a complete and independent structure.
[487] The “bourrelet” is not only, as Plateau expresses it, a “surface
of continuity,” but we also recognise that it tends (so far as
material is available for its production) to further lessen the free
surface-area. On its relation to vapour-pressure and to the stability
of foam, see FitzGerald’s interesting note in _Nature_, Feb. 1, 1894
(_Works_, p. 309).
[488] Of the many thousand figures in the hundred and forty plates of
this beautifully illustrated book, there is scarcely one which does
not depict, now patently, now in pregnant suggestion, some subtle and
elegant geometrical configuration.
[489] They were known (of course) long before Plato: Πλάτων δὲ καὶ ἐν
τούτοις πυθαγορίζει.
[490] If the equation of any plane face of a crystal be written in
the form _h_ _x_ + _k_ _y_ + _l_ _z_ = 1, then _h_, _k_, _l_ are
the indices of which we are speaking. They are the reciprocals of
the parameters, or reciprocals of the distances from the origin
at which the plane meets the several axes. In the case of the
regular or pentagonal dodecahedron these indices are 2, 1 + √5, 0.
Kepler described as follows, briefly but adequately, the common
characteristics of the dodecahedron and icosahedron: “Duo sunt corpora
regularia, dodecaedron et icosaedron, quorum illud quinquangulis
figuratur expresse, hoc triangulis quidem sed in quinquanguli formam
coaptatis. Utriusque horum corporum ipsiusque adeo quinquanguli
_structura perfici non potest sine proportione illa, quam hodierni
geometrae divinam appellant_” (_De nive sexangula_ (1611), Opera,
ed. Frisch, VII, p. 723). Here Kepler was dealing, somewhat after
the manner of Sir Thomas Browne, with the mysteries of the quincunx,
and also of the hexagon; and was seeking for an explanation of the
mysterious or even mystical beauty of the 5-petalled or 3-petalled
flower,—_pulchritudinis aut proprietatis figurae, quae animam harum
plantarum characterisavit_.
[491] Cf. Tutton, _Crystallography_, p. 932, 1911.
[492] However, we can often recognise, in a small artery for instance,
that the so-called “circular” fibres tend to take a slightly oblique,
or spiral, course.
[493] The spiral fibres, or a large portion of them, constitute what
Searle called “the rope of the heart” (Todd’s _Cyclopaedia_, II, p.
621, 1836). The “twisted sinews of the heart” were known to early
anatomists, and have been frequently and elaborately studied: for
instance, by Gerdy (_Bull. Fac. Med. Paris_, 1820, pp. 40–148), and by
Pettigrew (_Phil. Trans._ 1864), and of late by J. B. Macallum (_Johns
Hopkins Hospital Report_, IX, 1900) and by Franklin P. Mall (_Amer. J.
of Anat._ XI, 1911).
[494] Cf. Bütschli, “Protozoa,” in Bronn’s _Thierreich_, II, p. 848,
III, p. 1785, etc., 1883–87; Jennings, _Amer. Nat._ XXXV, p. 369, 1901;
Pütter, Thigmotaxie bei Protisten, _Arch. f. Anat. u. Phys._ (_Phys.
Abth. Suppl._), pp. 243–302, 1900.
[495] A great number of spiral forms, both organic and artificial, are
described and beautifully illustrated in Sir T. A. Cook’s _Curves of
Life_, 1914, and _Spirals in Nature and Art_, 1903.
[496] Cf. Vines, The History of the Scorpioid Cyme, _Journ. of Botany_
(n.s.), X, pp. 3–9, 1881.
[497] Leslie’s _Geometry of Curved Lines_, p. 417, 1821. This is
practically identical with Archimedes’ own definition (ed. Torelli, p.
219); cf. Cantor, _Geschichte der Mathematik_, I, p. 262, 1880.
[498] See an interesting paper by Whitworth, W. A., “The Equiangular
Spiral, its chief properties proved geometrically,” in the _Messenger
of Mathematics_ (1), I, p. 5, 1862.
[499] I am well aware that the debt of Greek science to Egypt and the
East is vigorously denied by many scholars, some of whom go so far as
to believe that the Egyptians never had any science, save only some
“rough rules of thumb for measuring fields and pyramids” (Burnet’s
_Greek Philosophy_, 1914, p. 5).
[500] Euclid (II, def. 2).
[501] Cf. Treutlein, _Z. f. Math. u. Phys._ (_Hist. litt. Abth._),
XXVIII, p. 209, 1883.
[502] This is the so-called _Dreifachgleichschenkelige Dreieck_; cf.
Naber, _op. infra cit._ The ratio 1 : 0·618 is again not hard to find
in this construction.
[503] See, on the mathematical history of the Gnomon, Heath’s _Euclid_,
I, _passim_, 1908; Zeuthen, _Theorème de Pythagore_, Genève, 1904; also
a curious and interesting book, _Das Theorem des Pythagoras_, by Dr. H.
A. Naber, Haarlem, 1908.
[504] For many beautiful geometrical constructions based on the
molluscan shell, see Colman, S. and Coan, C. A., _Nature’s Harmonic
Unity_ (ch. ix, Conchology), New York, 1912.
[505] The Rev. H. Moseley, On the Geometrical Forms of Turbinated and
Discoid Shells, _Phil. Trans._ pp. 351–370. 1838.
[506] It will be observed that here Moseley, speaking as a
mathematician and considering the _linear_ spiral, speaks of _whorls_
when he means the linear boundaries, or lines traced by the revolving
radius vector; while the conchologist usually applies the term _whorl_
to the whole space between the two boundaries. As conchologists,
therefore, we call the _breadth of a whorl_ what Moseley looked upon
as the _distance between two consecutive whorls_. But this latter
nomenclature Moseley himself often uses.
[507] In the case of Turbo, and all other “turbinate” shells, we are
dealing not with a plane logarithmic spiral, as in Nautilus, but with
a “gauche” spiral, such that the radius vector no longer revolves
in a plane perpendicular to the axis of the system, but is inclined
to that axis at some constant angle (θ). The figure still preserves
its continued similarity, and may with strict accuracy be called a
logarithmic spiral in space. It is evident that its envelope will
be a right circular cone; and indeed it is commonly spoken of as a
logarithmic spiral _wrapped upon a cone_, its pole coinciding with the
apex of the cone. It follows that the distances of successive whorls
of the spiral measured on the same straight line passing through the
apex of the cone, are in geometrical progression, and conversely just
as in the former case. But the ratio between any two consecutive
interspaces (i.e. _R__{3} − _R__{2}/_R__{2} − _R__{1}) is now equal to
ε^{2π sin θ cot α}, θ being the semi-angle of the enveloping cone. (Cf.
Moseley, _Phil. Mag._ XXI, p. 300, 1842.)
[508] As the successive increments evidently constitute similar
figures, similarly related to the pole (_P_), it follows that their
linear dimensions are to one another as the radii vectores drawn to
similar points in them: for instance as _P_ _P__{1}, _P_ _P__{2}, which
(in Fig. 264, 1) are radii vectores drawn to the points where they meet
the common boundary.
[509] The equation to the surface of a turbinate shell is discussed
by Moseley (_Phil. Trans._ tom. cit. p. 370), both in terms of polar
coordinates and of the rectangular coordinates _x_, _y_, _z_. A more
elegant representation can be given in vector notation, by the method
of quaternions.
[510] J. C. M. Reinecke, _Maris protogaei Nautilos, etc._, Coburg,
1818. Leopold von Buch, Ueber die Ammoniten in den älteren
Gebirgsschichten, _Abh. Berlin. Akad., Phys. Kl._ pp. 135–158, 1830;
_Ann. Sc. Nat._ XXVIII, pp. 5–43, 1833; cf. Elie de Beaumont, Sur
l’enroulement des Ammonites, _Soc. Philom., Pr. verb._ pp. 45–48, 1841.
[511] _Biblia Naturae sive Historia Insectorum_, Leydae, 1737, p. 152.
[512] Alcide D’Orbigny, _Bull. de la soc. géol. Fr._ XIII, p. 200,
1842; _Cours élém. de Paléontologie_, II, p. 5, 1851. A somewhat
similar instrument was described by Boubée. in _Bull. soc. géol._ I,
p. 232, 1831. Naumann’s Conchyliometer (_Poggend. Ann._ LIV, p. 544,
1845) was an application of the screw-micrometer; it was provided also
with a rotating stage, for angular measurement. It was adapted for the
Study of a discoid or ammonitoid shell, while D’Orbigny’s instrument
was meant for the study of a turbinate shell.
[513] It is obvious that the ratios of opposite whorls, or of radii
180° apart, are represented by the square roots of these values; and
the ratios of whorls or radii 90° apart, by the square roots of these
again.
[514] For the correction to be applied in the case of the helicoid, or
“turbinate” shells, see p. 557.
[515] On the Measurement of the Curves formed by Cephalopods and other
Mollusks. _Phil. Mag._ (5), VI, pp. 241–263, 1878.
[516] For an example of this method, see Blake, _l.c._ p. 251.
[517] Naumann, C. F., Ueber die Spiralen von Conchylien, _Abh. k.
sächs_. Ges. pp. 153–196, 1846; Ueber die cyclocentrische Conchospirale
u. über das Windungsgesetz von _Planorbis corneus_, _ibid._ I, pp.
171–195, 1849; Spirale von Nautilus u. _Ammonites galeatus_, _Ber. k.
sächs. Ges._ II, p. 26, 1848; Spirale von _Amm. Ramsaueri_, _ibid._
XVI, p. 21, 1864; see also _Poggendorff’s Annalen_, L, p. 223, 1840;
LI, p. 245, 1841; LIV, p. 541, 1845, etc.
[518] Sandberger, G., Spiralen des _Ammonites Amaltheus_, _A. Gaytani_,
und _Goniatites intumescens_, _Zeitschr. d. d. Geol. Gesellsch._ X, pp.
446–449, 1858.
[519] Grabau, A. H., _Ueber die Naumannsche Conchospirale_, etc.
Inauguraldiss. Leipzig, 1872; _Die Spiralen von Conchylien_, etc.
Programm, Nr. 502, Leipzig, 1882.
[520] It has been pointed out to me that it does not follow at once
and obviously that, because the interspace _AB_ is a mean proportional
between the breadths of the adjacent whorls, therefore the whole
distance _OB_ is a mean proportional between _OA_ and _OC_. This is a
corollary which requires to be proved; but the proof is easy.
[521] A beautiful construction: _stupendum Naturae artificium_,
Linnaeus.
[522] English edition, p. 537, 1900. The chapter is revised by
Prof. Alpheus Hyatt, to whom the nomenclature is largely due. For
a more copious terminology, see Hyatt, _Phylogeny of an Acquired
Characteristic_, p. 422 _seq._, 1894.
[523] This latter conclusion is adopted by Willey, _Zoological
Results_, p. 747, 1902.
[524] See Moseley, _op. cit._ pp. 361 _seq._
[525] In Nautilus, the “hood” has somewhat different dimensions in the
two sexes, and these differences are impressed upon the shell, that is
to say upon its “generating curve.” The latter constitutes a somewhat
broader ellipse in the male than in the female. But this difference
is not to be detected in the young; in other words, the form of the
generating curve perceptibly alters with advancing age. Somewhat
similar differences in the shells of Ammonites were long ago suspected,
by D’Orbigny, to be due to sexual differences. (Cf. Willey, _Natural
Science_, VI, p. 411, 1895; _Zoological Results_, p. 742, 1902.)
[526] Macalister, Alex., Observations on the Mode of Growth of Discoid
and Turbinated Shells, _P. R. S._ XVIII, pp. 529–532, 1870.
[527] See figures in Arnold Lang’s _Comparative Anatomy_ (English
translation), II, p. 161, 1902.
[528] Kappers, C. U. A., Die Bildung künstlicher Molluskenschalen,
_Zeitschr. f. allg. Physiol._ VII, p. 166, 1908.
[529] We need not assume a _close_ relationship, nor indeed any more
than such a one as permits us to compare the shell of a Nautilus with
that of a Gastropod.
[530] Cf. Owen, “These shells [Nautilus and Ammonites] are revolutely
spiral or coiled over the back of the animal, not involute like
Spirula”: _Palaeontology_, 1861, p. 97; cf. _Mem. on the Pearly
Nautilus_, 1832; also _P.Z.S._ 1878, p. 955.
[531] The case of Terebratula or of Gryphaea would be closely
analogous, if the smaller valve were less closely connected and
co-articulated with the larger.
[532] “It has been suggested, and I think in some quarters adopted
as a dogma, that the formation of successive septa [in Nautilus] is
correlated with the recurrence of reproductive periods. This is not the
case, since, according to my observations, propagation only takes place
after the last septum is formed;” Willey, _Zoological Results_, p. 746,
1902.
[533] Cf. Woodward, Henry, On the Structure of Camerated Shells, _Pop.
Sci. Rev._ XI, pp. 113–120, 1872.
[534] See Willey, Contributions to the Natural History of the Pearly
Nautilus, _Zoological Results_, etc. p. 749, 1902. Cf. also Bather,
Shell-growth in Cephalopoda, _Ann. Mag. N. H._ (6), I, pp 298–310,
1888; _ibid._ pp. 421–427, and other papers by Blake, Riefstahl, etc.
quoted therein.
[535] It was this that led James Bernoulli, in imitation of Archimedes,
to have the logarithmic spiral graven on his tomb, with the pious
motto, _Eadem mutata resurgam_. On Goodsir’s grave the same symbol is
reinscribed.
[536] The “lobes” and “saddles” which arise in this manner, and on
whose arrangement the modern classification of the nautiloid and
ammonitoid shells largely depends, were first recognised and named by
Leopold von Buch, _Ann. Sci. Nat._ XXVII, XXVIII, 1829.
[537] Blake has remarked upon the fact (_op. cit._ p. 248) that in
some Cyrtocerata we may have a curved shell in which the ornaments
approximately run at a constant angular distance from the pole, while
the septa approximate to a radial direction; and that “thus one law
of growth is illustrated by the inside, and another by the outside.”
In this there is nothing at which we need wonder. It is merely a
case where the generating curve is set very obliquely to the axis of
the shell; but where the septa, which have no necessary relation to
the _mouth_ of the shell, take their places, as usual, at a certain
definite angle to the _walls_ of the tube. This relation of the septa
to the walls of the tube arises after the tube itself is fully formed,
and the obliquity of growth of the open end of the tube has no relation
to the matter.
[538] Cf. pp. 255, 463, etc.
[539] In a few cases, according to Awerinzew and Rhumbler, where the
chambers are added on in concentric series, as in Orbitolites, we have
the crystalline structure arranged radially in the radial walls but
tangentially in the concentric ones: whereby we tend to obtain, on a
minute scale, a system of orthogonal trajectories, comparable to that
which we shall presently study in connection with the structure of
bone. Cf. S. Awerinzew, Kalkschale der Rhizopoden, _Z. f. w. Z._ LXXIV,
pp. 478–490, 1903.
[540] Rhumbler, L., Die Doppelschalen von Orbitolites und anderer
Foraminiferen, etc., _Arch. f. Protistenkunde_, I, pp. 193–296, 1902;
and other papers. Also _Die Foraminiferen der Planktonexpedition_, I,
1911, pp. 50–56.
[541] Bénard, H, Les tourbillons cellulaires, _Ann. de Chimie_ (8),
XXIV, 1901. Cf. also the pattern of cilia on an Infusorian, as figured
by Bütschli in Bronn’s _Protozoa_, III, p. 1281, 1887.
[542] A similar hexagonal pattern is obtained by the mutual repulsion
of floating magnets in Mr R. W. Wood’s experiments, _Phil. Mag._ XLVI,
pp. 162–164, 1898.
[543] Cf. D’Orbigny, Alc., Tableau méthodique de la classe des
Céphalopodes, _Ann. des Sci. Nat._ (1), VII, pp. 245–315, 1826;
Dujardin. Félix, Observations nouvelles sur les prétendus Céphalopodes
microscopiques, _ibid._ (2), III, pp. 108, 109, 312–315, 1835;
Recherches sur les organismes inférieurs, _ibid._ IV, pp. 343–377,
1835, etc.
[544] It is obvious that the actual _outline_ of a foraminiferal, just
as of a molluscan shell, may depart widely from a logarithmic spiral.
When we say here, for short, that the shell _is_ a logarithmic spiral,
we merely mean that it is essentially related to one: that it can be
inscribed in such a spiral, or that corresponding points (such, for
instance, as the centres of gravity of successive chambers, or the
extremities of successive septa) wall always be found to lie upon such
a spiral.
[545] von Möller, V., Die spiral-gewundenen Foraminifera des russischen
Kohlenkalks, _Mém. de l’Acad. Imp. Sci., St Pétersbourg_ (7), XXV, 1878.
[546] As von Möller is careful to explain, Naumann’s formula for the
“cyclocentric conchospiral” is appropriate to this and other spiral
Foraminifera, since we have in all these cases a central or initial
chamber, approximately spherical, about which the logarithmic spiral
is coiled (cf. Fig. 309). In species where the central chamber is
especially large, Naumann’s formula is all the more advantageous.
But it is plain that it is only required when we are dealing with
diameters, or with radii; so long as we are merely comparing the
breadths of _successive whorls_, the two formulae come to the same
thing.
[547] Van Iterson, G., _Mathem. u. mikrosk.-anat. Studien über
Blattstellungen, nebst Betrachtungen über den Schalenbau der
Miliolinen_, 331 pp., Jena, 1907.
[548] Hans Przibram asserts that the linear ratio of successive
chambers tends in many Foraminifera to approximate to 1·26, which = ∛2;
in other words, that the volumes of successive chambers tend to double.
This Przibram would bring into relation with another law, viz. that
insects and other arthropods tend to moult, or to metamorphose, just
when they double their weights, or increase their linear dimensions
in the ratio of 1 : ∛2. (Die Kammerprogression der Foraminiferen als
Parallele zur Häutungsprogression der Mantiden, _Arch. f. Entw. Mech._
XXXIV p. 680, 1813.) Neither rule seems to me to be well grounded.
[549] Cf. Schacko, G., Ueber Globigerina-Einschluss bei Orbulina,
_Wiegmann’s Archiv_, XLIX, p. 428, 1883; Brady, _Chall. Rep._, p. 607,
1884.
[550] Cf. Brady, H. B., _Challenger Rep._, _Foraminifera_, 1884, p.
203, pl. XIII.
[551] Brady, _op. cit._, p. 206; Batsch, one of the earliest writers
on Foraminifera, had already noticed that this whole series of
ear-shaped and crozier-shaped shells was filled in by gradational
forms; _Conchylien des Seesandes_, 1791, p. 4, pl. VI, fig. 15_a_–_f_.
See also, in particular, Dreyer, _Peneroplis_; _eine Studie zur
biologischen Morphologie und zur Speciesfrage_, Leipzig, 1898; also
Eimer und Fickert, Artbildung und Verwandschaft bei den Foraminiferen,
_Tübinger zool. Arbeiten_, III, p. 35, 1899.
[552] Doflein, _Protozoenkunde_, 1911, p. 263; “Was diese Art
veranlässt in dieser Weise gelegentlich zu varüren, ist vorläufig noch
ganz räthselhaft.”
[553] In the case of Globigerina, some fourteen species (out of a very
much larger number of described forms) were allowed by Brady (in 1884)
to be distinct; and this list has been, I believe, rather added to than
diminished. But these so-called species depend for the most part on
slight differences of degree, differences in the angle of the spiral,
in the ratio of magnitude of the segments, or in their area of contact
one with another. Moreover with the exception of one or two “dwarf”
forms, said to be limited to Arctic and Antarctic waters, there is no
principle of geographical distribution to be discerned amongst them.
A species found fossil in New Britain turns up in the North Atlantic:
a species described from the West Indies is rediscovered at the
ice-barrier of the Antarctic.
[554] Dreyer, F., Principien der Gerüstbildung bei Rhizopoden, etc.,
_Jen. Zeitschr._ XXVI, pp. 204–468, 1892.
[555] A difficulty arises in the case of forms (like Peneroplis) where
the young shell appears to be more complex than the old, the first
formed portion being closely coiled while the later additions become
straight and simple: “die biformen Arten verhalten sich, kurz gesagt.
gerade umgekehrt als man nach dem biogenetischen Grundgesetz erwarten
sollte,” Rhumbler, _op. cit._, p. 33 etc.
[556] “Das Festigkeitsprinzip als Movens der Weiterentwicklung ist zu
interessant und für die Aufstellung meines Systems zu wichtig um die
Frage unerörtert zu lassen, warum diese Bevorzügung der Festigkeit
stattgefunden hat. Meiner Ansicht nach lautet die Antwort auf diese
Frage einfach, weil die Foraminiferen meistens unter Verhältnissen
leben, die ihre Schalen in hohem Grade der Gefahr des Zerbrechens
aussetzen; es muss also eine fortwahrende Auslese des Festeren
stattfinden,” Rhumbler, _op. cit._, p. 22.
[557] “Die Foraminiferen kiesige oder grobsandige Gebiete des
Meeresbodens _nicht lieben_, u.s.w.”: where the last two words have no
particular meaning, save only that (as M. Aurelius says) “of things
that use to be, we say commonly that they love to be.”
[558] In regard to the Foraminifera, “die Palaeontologie lässt uns
leider an Anfang der Stammesgeschichte fast gänzlich im Stiche,”
Rhumbler, _op. cit._, p. 14.
[559] The evolutionist theory, as Bergson puts it, “consists above all
in establishing relations of ideal kinship, and in maintaining that
wherever there is this relation of, so to speak, _logical_ affiliation
between forms, _there is also a relation of chronological succession
between the species in which these forms are materialised_”: _Creative
Evolution_, 1911, p. 26. Cf. _supra_, p. 251.
[560] In the case of the ram’s horn, the assumption that the rings are
annual is probably justified. In cattle they are much less conspicuous,
but are sometimes well-marked in the cow; and in Sweden they are then
called “calf-rings,” from a belief that they record the number of
offspring. That is to say, the growth of the horn is supposed to be
retarded during gestation, and to be accelerated after parturition,
when superfluous nourishment seeks a new outlet. (Cf. Lönnberg,
_P.Z.S._, p. 689, 1900.)
[561] Cf. Sir V. Brooke, On the Large Sheep of the Thian Shan,
_P.Z.S._, p. 511, 1875.
[562] Cf. Lönnberg, E., On the Structure of the Musk Ox, _P.Z.S._, pp.
686–718, 1900.
[563] St Venant, De la torsion des prismes, avec des considérations
sur leur flexion, etc., _Mém. des Savants Étrangers_, Paris, XIV, pp.
233–560, 1856.
[564] This is not difficult to do, with considerable accuracy, if the
clay be kept well wetted, or semi-fluid, and the smoothing be done with
a large wet brush.
[565] The curves are well shewn in most of Sir V. Brooke’s figures of
the various species of Argali, in the paper quoted on p. 614.
[566] _Climbing Plants_, 1865 (2nd edit. 1875); _Power of Movement in
Plants_, 1880.
[567] Palm, _Ueber das Winden der Pflanzen_, 1827; von Mohl, _Bau
und Winden der Ranken_, etc., 1827; Dutrochet, Mouvements révolutifs
spontanés, _C.R._ 1843, etc.
[568] Cf. (e.g.) Lepeschkin, Zur Kenntnis des Mechanismus der
Variationsbewegungen, _Ber. d. d. Bot. Gesellsch._ XXVI A, pp. 724–735,
1908; also A. Tröndle, Der Einfluss des Lichtes auf die Permeabilität
des Plasmahaut, _Jahrb. wiss. Bot._ XLVIII, pp. 171–282, 1910.
[569] For an elaborate study of antlers, see Rörig, A., _Arch. f.
Entw. Mech._ X, pp. 525–644, 1900, XI, pp. 65–148, 225–309, 1901;
Hoffmann, C., _Zur Morphologie der rezenten Hirschen_, 75 pp., 23 pls.,
1901: also Sir Victor Brooke, On the Classification of the Cervidae,
_P.Z.S._, pp. 883–928, 1878. For a discussion of the development of
horns and antlers, see Gadow, H., _P.Z.S._, pp. 206–222, 1902, and
works quoted therein.
[570] Cf. Rhumbler, L., Ueber die Abhängigkeit des Geweihwachstums der
Hirsche, speziell des Edelhirsches, vom Verlauf der Blutgefässe im
Kolbengeweih, _Zeitschr. f. Forst. und Jagdwesen_, 1911, pp. 295–314.
[571] The fact that in one very small deer, the little South American
Coassus, the antler is reduced to a simple short spike, does not
preclude the general distinction which I have drawn. In Coassus we have
the beginnings of an antler, which has not yet manifested its tendency
to expand; and in the many allied species of the American genus
Cariacus, we find the expansion manifested in various simple modes of
ramification or bifurcation. (Cf. Sir V. Brooke, Classification of the
Cervidae, p. 897.)
[572] Cf. also the immense range of variation in elks’ horns, as
described by Lönnberg, _P.Z.S._ II, pp. 352–360, 1902.
[573] Besides papers referred to below, and many others quoted in
Sach’s _Botany_ and elsewhere, the following are important: Braun,
Alex., Vergl. Untersuchung über die Ordnung der Schuppen an den
Tannenzapfen, etc., _Verh. Car. Leop. Akad._ XV, pp. 199–401, 1831; Dr
C. Schimper’s Vorträge über die Möglichkeit eines wissenschaftlichen
Verständnisses der Blattstellung, etc., _Flora_, XVIII, pp. 145–191,
737–756, 1835; Schimper, C. F., Geometrische Anordnung der um eine Axe
peripherische Blattgebilde, _Verhandl. Schweiz. Ges._, pp. 113–117,
1836; Bravais, L. and A., Essai sur la disposition des feuilles
curvisériées, _Ann. Sci. Nat._ (2), VII, pp. 42–110, 1837; Sur la
disposition symmétrique des inflorescences, _ibid._, pp. 193–221,
291–348, VIII, pp. 11–42, 1838; Sur la disposition générale des
feuilles rectisériées, _ibid._ XII, pp. 5–41, 65–77, 1839; Zeising,
_Normalverhältniss der chemischen und morphologischen Proportionen_,
Leipzig, 1856; Naumann, C. F., Ueber den Quincunx als Gesetz der
Blattstellung bei Sigillaria, etc., _Neues Jahrb. f. Miner._ 1842,
pp. 410–417; Lestiboudois, T., _Phyllotaxie anatomique_, Paris, 1848;
Henslow, G., _Phyllotaxis_, London, 1871; Wiesner, Bemerkungen über
rationale und irrationale Divergenzen, _Flora_, LVIII, pp. 113–115,
139–143, 1875; Airy, H., On Leaf Arrangement, _Proc. R. S._ XXI, p.
176, 1873; Schwendener, S., _Mechanische Theorie der Blattstellungen_,
Leipzig, 1878; Delpino, F., _Causa meccanica della filotassi
quincunciale_, Genova, 1880; de Candolle, C., _Étude de Phyllotaxie_,
Genève, 1881.
[574] _Allgemeine Morphologie der Gewächse_, p. 442, etc. 1868.
[575] _Relation of Phyllotaxis to Mechanical Laws_, Oxford, 1901–1903;
cf. _Ann. of Botany_, XV, p. 481, 1901.
[576] “The proposition is that the genetic spiral is a logarithmic
spiral, homologous with the line of current-flow in a spiral vortex;
and that in such a system the action of orthogonal forces will be
mapped out by other orthogonally intersecting logarithmic spirals—the
‘parastichies’ ”; Church, _op. cit._ I, p. 42.
[577] Mr Church’s whole theory, if it be not based upon, is interwoven
with, Sachs’s theory of the orthogonal intersection of cell-walls, and
the elaborate theories of the symmetry of a growing point or apical
cell which are connected therewith. According to Mr Church, “the law
of the orthogonal intersection of cell-walls at a growing apex may be
taken as generally accepted” (p. 32); but I have taken a very different
view of Sachs’s law, in the eighth chapter of the present book. With
regard to his own and Sachs’s hypotheses, Mr Church makes the following
curious remark (p. 42): “Nor are the hypotheses here put forward more
imaginative than that of the paraboloid apex of Sachs which remains
incapable of proof, or his construction for the apical cell of Pteris
which does not satisfy the evidence of his own drawings.”
[578] _Amer. Naturalist_, VII, p. 449, 1873.
[579] This celebrated series, which appears in the continued fraction
(1/1) + (1/(1 + )) etc. and is closely connected with the _Sectio
aurea_ or Golden Mean, is commonly called the Fibonacci series, after a
very learned twelfth century arithmetician (known also as Leonardo of
Pisa), who has some claims to be considered the introducer of Arabic
numerals into christian Europe. It is called Lami’s series by some,
after Father Bernard Lami, a contemporary of Newton’s, and one of
the co-discoverers of the parallelogram of forces. It was well-known
to Kepler, who, in his paper _De nive sexangula_ (cf. _supra_, p.
480), discussed it in connection with the form of the dodecahedron
and icosahedron, and with the ternary or quinary symmetry of the
flower. (Cf. Ludwig, F., Kepler über das Vorkommen der Fibonaccireihe
im Pflanzenreich, _Bot. Centralbl._ LXVIII, p. 7, 1896). Professor
William Allman, Professor of Botany in Dublin (father of the historian
of Greek geometry), speculating on the same facts, put forward the
curious suggestion that the cellular tissue of the dicotyledons,
or exogens, would be found to consist of dodecahedra. and that of
the monocotyledons or endogens of icosahedra (_On the mathematical
connexion between the parts of Vegetables_: abstract of a Memoir read
before the Royal Society in the year 1811 (privately printed, _n.d._).
Cf. De Candolle, _Organogénie végétale_, I, p. 534).
[580] _Proc. Roy. Soc. Edin._ VII, p. 391, 1872.
[581] The necessary existence of these recurring spirals is also
proved, in a somewhat different way, by Leslie Ellis, On the Theory
of Vegetable Spirals, in _Mathematical and other Writings_, 1853, pp.
358–372.
[582] _Proc. Roy. Soc. Edin._ VII, p. 397, 1872; _Trans. Roy. Soc.
Edin._ XXVI, p. 505, 1870–71.
[583] A common form of pail-shaped waste-paper basket, with wide
rhomboidal meshes of cane, is well-nigh as good a model as is required.
[584] _Deutsche Vierteljahrsschrift_, p. 261, 1868.
[585] _Memoirs of Amer. Acad._ IX, p. 389.
[586] _De avibus circa aquas Danubii vagantibus et de ipsarum Nidis_
(Vol. V of the _Danubius Pannonico-mysicus_), Hagae Com., 1726.
[587] Sir Thomas Browne had a collection of eggs at Norwich, according
to Evelyn, in 1671.
[588] Cf. Lapierre, in Buffon’s _Histoire Naturelle_, ed. Sonnini, 1800.
[589] _Eier der Vögel Deutschlands_, 1818–28 (_cit._ des Murs, p. 36).
[590] _Traité d’Oologie_, 1860.
[591] Lafresnaye, F. de, Comparaison des œufs des Oiseaux avec
leurs squelettes, comme seul moven de reconnaître la cause de leurs
différentes formes, _Rev. Zool._, 1845, pp. 180–187, 239–244.
[592] Cf. Des Murs, p. 67: “Elle devait encore penser au moment où ce
germe aurait besoin de l’espace nécessaire à son accroissement, à ce
moment où ... il devra remplir exactement l’intervalle circonscrit par
sa fragile prison, etc.”
[593] Thienemann, F. A. L., _Syst. Darstellung der Fortpflanzung der
Vögel Europas_. Leipzig, 1825–38.
[594] Cf. Newton’s _Dictionary of Birds_, 1893, p. 191; Szielasko,
Gestalt der Vogeleier, _J. f. Ornith._ LIII, pp. 273–297, 1905.
[595] Jacob Steiner suggested a Cartesian oval, _r_ + _mr′_ = _c_, as a
general formula for all eggs (cf. Fechner, _Ber. sächs. Ges._, 1849, p.
57); but this formula (which fails in such a case as the guillemot), is
purely empirical, and has no mechanical foundation.
[596] Günther, F. C., _Sammlung von Nestern und Eyern verschiedener
Vögel_, Nürnb. 1772. Cf. also Raymond Pearl, Morphogenetic Activity of
the Oviduct, _J. Exp. Zool._ VI, pp. 339–359, 1909.
[597] The following account is in part reprinted from _Nature_, June 4,
1908.
[598] In so far as our explanation involves a shaping or moulding of
the egg by the uterus or “oviduct” (an agency supplemented by the
proper tensions of the egg), it is curious to note that this is very
much the same as that old view of Telesius regarding the formation
of the embryo (_De rerum natura_, VI, cc. 4 and 10), which he had
inherited from Galen, and of which Bacon speaks (_Nov. Org._ cap. 50;
cf. Ellis’s note). Bacon expressly remarks that “Telesius should have
been able to shew the like formation in the shells of eggs.” This old
theory of embryonic modelling survives only in our usage of the term
“matrix” for a “mould.”
[599] _Journal of Tropical Medicine_, 15th June, 1911. I leave this
paragraph as it was written, though it is now once more asserted that
the terminal and lateral-spined eggs belong to separate and distinct
species of Bilharzia (Leiper, _Brit. Med. Journ._, 18th March, 1916, p.
411).
[600] Cf. Bashforth and Adams, _Theoretical Forms of Drops, etc._,
Cambridge, 1883.
[601] Woods, R. H., On a Physical Theorem applied to tense Membranes,
_Journ. of Anat. and Phys._ XXVI, pp. 362–371, 1892. A similar
investigation of the tensions in the uterine wall, and of the varying
thickness of its muscles, was attempted by Haughton in his _Animal
Mechanics_, pp. 151–158, 1873.
[602] This corresponds with a determination of the normal pressures (in
systole) by Krohl, as being in the ratio of 1 : 6·8.
[603] Cf. Schwalbe, G., Ueber Wechselbeziehungen und ihr Einfluss
auf die Gestaltung des Arteriensystem, _Jen. Zeitschr._ XII, p. 267,
1878, Roux, Ueber die Verzweigungen der Blutgefässen des Menschen,
_ibid._ XII, p. 205, 1878; Ueber die Bedeutung der Ablenkung des
Arterienstämmen bei der Astaufgabe, _ibid._ XIII, p. 301, 1879;
Hess, Walter, Eine mechanisch bedingte Gesetzmässigkeit im Bau des
Blutgefässsystems, _A. f. Entw. Mech._ XVI, p. 632, 1903; Thoma, R.,
_Ueber die Histogenese und Histomechanik des Blutgefässsystems_, 1893.
[604] _Essays_, etc., edited by Owen, I, p. 134, 1861.
[605] On the Functions of the Heart and Arteries, _Phil. Trans._ 1809,
pp. 1–31, cf. 1808, pp. 164–186; _Collected Works_, I, pp. 511–534,
1855. The same lesson is conveyed by all such work as that of Volkmann,
E. H. Weber and Poiseuille. Cf. Stephen Hales’ _Statical Essays_, II,
_Introduction_: “Especially considering that they [i.e. animal Bodies]
are in a manner framed of one continued Maze of innumerable Canals,
in which Fluids are incessantly circulating, some with great Force
and Rapidity, others with very different Degrees of rebated Velocity:
Hence, _etc._”
[606] “Sizes” is Owen’s editorial emendation, which seems amply
justified.
[607] For a more elaborate classification, into colours cryptic,
procryptic, anticryptic, apatetic, epigamic, sematic, episematic,
aposematic, etc., see Poulton’s _Colours of Animals_ (Int. Scientific
Series, LXVIII), 1890; cf. also Meldola, R., Variable Protective
Colouring in Insects, _P.Z.S._ 1873, pp. 153–162, etc.
[608] Dendy, _Evolutionary Biology_, p. 336, 1912.
[609] Delight in beauty is one of the pleasures of the imagination;
there is no limit to its indulgence, and no end to the results which
we may ascribe to its exercise. But as for the particular “standard of
beauty” which the bird (for instance) admires and selects (as Darwin
says in the _Origin_, p. 70, edit. 1884), we are very much in the
dark, and we run the risk of arguing in a circle: for wellnigh all we
can safely say is what Addison says (in the 412th _Spectator_)—that
each different species “is most affected with the beauties of its own
kind .... Hinc merula in nigro se oblectat nigra marito; ... hinc
noctua tetram Canitiem alarum et glaucos miratur ocellos.”
[610] Cf. Bridge, T. W., _Cambridge Natural History_ (Fishes), VII,
p. 173, 1904; also Frisch, K. v., Ueber farbige Anpassung bei Fische,
_Zool. Jahrb._ (_Abt. Allg. Zool._), XXXII, pp. 171–230, 1914.
[611] _Nature_, L, p. 572; LI, pp. 33, 57, 533, 1894–95.
[612] They are “wonderfully fitted for ‘vanishment’ against the
flushed, rich-coloured skies of early morning and evening .... their
chief feeding-times”; and “look like a real sunset or dawn, repeated on
the opposite side of the heavens,—either east or west as the case may
be”: Thayer, _Concealing-coloration in the Animal Kingdom_, New York,
1909, pp. 154–155. This hypothesis, like the rest, is not free from
difficulty. Twilight is apt to be short in the homes of the flamingo:
and moreover, Mr Abel Chapman, who watched them on the Guadalquivir,
tells us that they _feed by day_.
[613] Principal Galloway, _Philosophy of Religion_, p. 344, 1914.
[614] Cf. Professor Flint, in his Preface to Affleck’s translation
of Janet’s _Causes finales_: “We are, no doubt, still a long way
from a mechanical theory of organic growth, but it may be said to be
the _quaesitum_ of modern science, and no one can say that it is a
chimaera.”
[615] Cf. Sir Donald MacAlister, How a Bone is Built, _Engl. Ill. Mag._
1884.
[616] Professor Claxton Fidler, _On Bridge Construction_, p. 22 (4th
ed.), 1909; cf. (_int. al._) Love’s _Elasticity_, p. 20 (_Historical
Introduction_), 2nd ed., 1906.
[617] In preparing or “macerating” a skeleton, the naturalist nowadays
carries on the process till nothing is left but the whitened bones. But
the old anatomists, whose object was not the study of “comparative”
morphology but the wider theme of comparative physiology, were wont
to macerate by easy stages; and in many of their most instructive
preparations, the ligaments were intentionally left in connection with
the bones, and as part of the “skeleton.”
[618] In a few anatomical diagrams, for instance in some of the
drawings in Schmaltz’s _Atlas der Anatomie des Pferdes_, we may see
the system of “ties” diagrammatically inserted in the figure of the
skeleton. Cf. Gregory, On the principles of Quadrupedal Locomotion,
_Ann. N. Y. Acad. of Sciences_, XXII, p. 289, 1912.
[619] Galileo, _Dialogues concerning Two New Sciences_ (1638), Crew
and Salvio’s translation, New York, 1914, p. 150; _Opere_, ed. Favaro,
VIII, p. 186. Cf. Borelli, _De Motu Animalium_, I, prop. CLXXX, 1685.
Cf. also Camper, P., La structure des os dans les oiseaux, _Opp._ III,
p. 459, ed. 1803; Rauber, A., Galileo über Knochenformen, _Morphol.
Jahrb._ VII, pp. 327, 328, 1881; Paolo Enriques, Della economia di
sostanza nelle osse cave, _Arch. f. Ent. Mech._ XX, pp. 427–465, 1906.
[620] _Das mechanische Prinzip. im anatomischen Bau der Monocotylen_,
Leipzig, 1874.
[621] For further botanical illustrations, see (_int. al._) Hegler,
Einfluss der Zugkraften auf die Festigkeit und die Ausbildung
mechanischer Gewebe in Pflanzen, _SB. sächs. Ges. d. Wiss._ p.
638, 1891; Kny, L., Einfluss von Zug und Druck auf die Richtung
der Scheidewande in sich teilenden Pflanzenzellen, _Ber. d. bot.
Gesellsch._ XIV, 1896; Sachs, Mechanomorphose und Phylogenie, _Flora_,
LXXVIII, 1894; cf. also Pflüger, Einwirkung der Schwerkraft, etc., über
die Richtung der Zelltheilung, _Archiv_, XXXIV, 1884.
[622] Among other works on the mechanical construction of bone
see: Bourgery, _Traité de l’anatomie_ (_I. Ostéologie_), 1832
(with admirable illustrations of trabecular structure); Fick, L.,
_Die Ursachen der Knochenformen_, Göttingen, 1857; Meyer, H., Die
Architektur der Spongiosa, _Archiv f. Anat. und Physiol._ XLVII, pp.
615–628, 1867; _Statik u. Mechanik des menschlichen Knochengerüstes_,
Leipzig, 1873; Wolff, J., Die innere Architektur der Knochen, _Arch.
f. Anat, und Phys._ L, 1870; _Das Gesetz der Transformation bei
Knochen_, 1892; von Ebner, V., Der feinere Bau der Knochensubstanz,
_Wiener Bericht_, LXXII, 1875; Rauber, Anton, _Elastizität und
Festigkeit der Knochen_, Leipzig, 1876; O. Meserer, _Elast, u.
Festigk. d. menschlichen Knochen_, Stuttgart, 1880; MacAlister, Sir
Donald, How a Bone is Built, _English Illustr. Mag._ pp. 640–649,
1884; Rasumowsky, Architektonik des Fussskelets, _Int. Monatsschr. f.
Anat._ p. 197, 1889; Zschokke, _Weitere Unters. über das Verhältniss
der Knochenbildung zur Statik und Mechanik des Vertebratenskelets_,
Zürich, 1892; Roux, W., _Ges. Abhandlungen über Entwicklungsmechanik
der Organismen, Bd. I, Funktionelle Anpassung_, Leipzig, 1895; Triepel,
H., Die Stossfestigkeit der Knochen, _Arch. f. Anat. u. Phys._ 1900;
Gebhardt, Funktionell wichtige Anordnungsweisen der feineren und
gröberen Bauelemente des Wirbelthierknochens, etc., _Arch. f. Entw.
Mech._ 1900–1910; Kirchner. A., Architektur der Metatarsalien, _A.
f. E. M._ XXIV, 1907; Triepel, Herm., Die trajectorielle Structuren
(in _Einf. in die Physikalische Anatomie_, 1908); Dixon, A. F.,
Architecture of the Cancellous Tissue forming the Upper End of the
Femur, _Journ. of Anat. and Phys._ (3) XLIV, pp. 223–230, 1910.
[623] Sédillot, De l’influence des fonctions sur la structure et la
forme des organes; _C. R._ LIX, p. 539, 1864; cf. LX, p. 97, 1865,
LXVIII. p. 1444. 1869.
[624] E.g. (1) the head, nodding backwards and forwards on a fulcrum,
represented by the atlas vertebra, lying between the weight and the
power; (2) the foot, raising on tip-toe the weight of the body against
the fulcrum of the ground, where the weight is between the fulcrum and
the power, the latter being represented by the _tendo Achillis_; (3)
the arm, lifting a weight in the hand, with the power (i.e. the biceps
muscle) between the fulcrum and the weight. (The second case, by the
way, has been much disputed; cf. Haycraft in Schäfer’s _Textbook of
Physiology_, p. 251, 1900.)
[625] Our problem is analogous to Dr Thomas Young’s problem of the best
disposition of the timbers in a wooden ship (_Phil. Trans._ 1814, p.
303). He was not long of finding that the forces which may act upon the
fabric are very numerous and very variable, and that the best mode of
resisting them, or best structural arrangement for ultimate strength,
becomes an immensely complicated problem.
[626] In like manner, Clerk Maxwell could not help employing the term
“skeleton” in defining the mathematical conception of a “frame,”
constituted by points and their interconnecting lines: in studying the
equilibrium of which, we consider its different points as mutually
acting on each other with forces whose directions are those of the
lines joining each pair of points. Hence (says Maxwell), “in order
to exhibit the mechanical action of the frame in the most elementary
manner, we may draw it as a _skeleton_, in which the different points
are joined by straight lines, and we may indicate by numbers attached
to these lines the tensions or compressions in the corresponding
pieces of the frame” (_Trans. R. S. E._ XXVI, p. 1, 1870). It follows
that the diagram so constructed represents a “diagram of forces,” in
this limited sense that it is geometrical as regards the position and
direction of the forces, but arithmetical as regards their magnitude.
It is to just such a diagram that the animal’s skeleton tends to
approximate.
[627] When the jockey crouches over the neck of his race-horse, and
when Tod Sloan introduced the “American seat,” the object in both cases
is to relieve the hind-legs of weight, and so leave them free for the
work of propulsion. Nevertheless, we must not exaggerate the share
taken by the hind-limbs in this latter duty; cf. Stillman, _The Horse
in Motion_, p. 69, 1882.
[628] This and the following diagrams are borrowed and adapted from
Professor Fidler’s _Bridge Construction_.
[629] The method of constructing _reciprocal diagrams_, in which one
should represent the outlines of a frame, and the other the system of
forces necessary to keep it in equilibrium, was first indicated in
Culmann’s _Graphische Statik_; it was greatly developed soon afterwards
by Macquorn Rankine (_Phil. Mag._ Feb. 1864, and _Applied Mechanics_,
passim), to whom is mainly due the general application of the principle
to engineering practice.
[630] _Dialogues concerning Two New Sciences_ (1638): Crew and Salvio’s
translation, p. 140 _seq._
[631] The form and direction of the vertebral spines have been
frequently and elaborately described; cf. (e.g.) Gottlieb, H., Die
Anticlinie der Wirbelsäule der Säugethiere, _Morphol. Jahrb._ LXIX,
pp. 179–220, 1915, and many works quoted therein. According to
Morita, Ueber die Ursachen der Richtung und Gestalt der thoracalen
Dornfortsätze der Säugethierwirbelsäule (_ibi cit._ p. 201), various
changes take place in the direction or inclination of these processes
in rabbits, after section of the interspinous ligaments and muscles.
These changes seem to be very much what we should expect, on simple
mechanical grounds. See also Fischer, O., _Theoretische Grundlagen für
eine Mechanik der lebenden Körper_, Leipzig, pp. 3, 372, 1906.
[632] I owe the first four of these determinations to the kindness
of Dr Chalmers Mitchell, who had them made for me at the Zoological
Society’s Gardens; while the great Clydesdale carthorse was weighed for
me by a friend in Dundee.
[633] This pose of Diplodocus, and of other Sauropodous reptiles, has
been much discussed. Cf. (_int. al._) Abel, O., _Abh. k. k. zool.
bot. Ges. Wien_, V. 1909–10 (60 pp.); Tornier, _SB. Ges. Naturf.
Fr. Berlin_, pp. 193–209, 1909; Hay, O. P., _Amer. Nat._ Oct. 1908;
_Tr. Wash. Acad. Sci._ XLII, pp. 1–25, 1910; Holland, _Amer. Nat._
May, 1910, pp. 259–283; Matthew, _ibid._ pp. 547–560; Gilmore, C. W.
(_Restoration of Stegosaurus_). _Pr. U.S. Nat. Museum_, 1915.
[634] The form of the cantilever is much less typical in the small
flying birds, where the strength of the pelvic region is insured in
another way, with which we need not here stop to deal.
[635] The motto was Macquorn Rankine’s.
[636] John Hunter was seldom wrong; but I cannot believe that he was
right when he said (_Scientific Works_, ed. Owen, I, p. 371), “The
bones, in a mechanical view, appear to be the first that are to be
considered. We can study their shape, connexions, number, uses, etc.,
_without considering any other part of the body_.”
[637] _Origin of Species_, 6th ed. p. 118.
[638] _Amer. Naturalist_, April, 1915, p. 198, etc. Cf. _infra_, p. 727.
[639] Driesch sees in “Entelechy” that something which differentiates
the whole from the sum of its parts in the case of the organism: “The
organism, we know, is a system the single constituents of which are
inorganic in themselves; only the whole constituted by them in their
typical order or arrangement owes its specificity to ‘Entelechy’ ”
(_Gifford Lectures_, p. 229, 1908): and I think it could be shewn that
many other philosophers have said precisely the same thing. So far
as the argument goes, I fail to see how _this_ Entelechy is shewn to
be peculiarly or specifically related to the _living_ organism. The
conception that the whole is _always_ something very different from its
parts is a very ancient doctrine. The reader will perhaps remember how,
in another vein, the theme is treated by Martinus Scriblerus: “In every
Jack there is a _meat-roasting_ Quality, which neither resides in the
fly, nor in the weight, nor in any particular wheel of the Jack, but is
the result of the whole composition; etc., etc.”
[640] “There can be no doubt that Fraas is correct in regarding this
type (_Procetus_) as an annectant form between the Zeuglodonts and
the Creodonta, but, although the origin of the Zeuglodonts is thus
made clear, it still seems to be by no means so certain as that author
believes, that they may not themselves be the ancestral forms of the
Odontoceti”; Andrews, _Tertiary Vertebrata of the Fayum_, 1906, p. 235.
[641] Reprinted, with some changes and additions, from a paper in the
_Trans. Roy. Soc. Edin._ L, pp. 857–95, 1915.
[642] M. Bergson repudiates, with peculiar confidence, the
application of mathematics to biology. Cf. _Creative Evolution_,
p. 21, “Calculation touches, at most, certain phenomena of organic
destruction. Organic creation, on the contrary, the evolutionary
phenomena which properly constitute life, we cannot in any way subject
to a mathematical treatment.”
[643] In this there lies a certain justification for a saying of
Minot’s, of the greater part of which, nevertheless, I am heartily
inclined to disapprove. “We biologists,” he says, “cannot deplore
too frequently or too emphatically the great mathematical delusion
by which men often of great if limited ability have been misled into
becoming advocates of an erroneous conception of accuracy. The delusion
is that no science is accurate until its results can be expressed
mathematically. The error comes from the assumption that mathematics
can express complex relations. Unfortunately mathematics have a
very limited scope, and are based upon a few extremely rudimentary
experiences, which we make as very little children and of which no
adult has any recollection. The fact that from this basis men of
genius have evolved wonderful methods of dealing with numerical
relations should not blind us to another fact, namely, that the
observational basis of mathematics is, psychologically speaking, very
minute compared with the observational basis of even a single minor
branch of biology .... While therefore here and there the mathematical
methods may aid us, _we need a kind and degree of accuracy of which
mathematics is absolutely incapable_ .... With human minds constituted
as they actually are, we cannot anticipate that there will ever be a
mathematical expression for any organ or even a single cell, although
formulae will continue to be useful for dealing now and then with
isolated details...” (_op. cit._, p. 19, 1911). It were easy to discuss
and criticise these sweeping assertions, which perhaps had their
origin and parentage in an _obiter dictum_ of Huxley’s, to the effect
that “Mathematics is that study which knows nothing of observation,
nothing of experiment, nothing of induction, nothing of causation”
(_cit._ Cajori, _Hist of Elem. Mathematics_, p. 283). But Gauss called
mathematics “a science of the eye”; and Sylvester assures us that
“most, if not all, of the great ideas of modern mathematics have had
their origin in observation” (_Brit. Ass. Address_, 1869, and _Laws of
Verse_, p. 120, 1870).
[644] _Historia Animalium_ I, 1.
[645] Cf. _supra_, p. 714.
[646] Cf. Osborn, H. F., On the Origin of Single Characters, as
observed in fossil and living Animals and Plants, _Amer. Nat._ XLIX,
pp. 193–239, 1915 (and other papers); _ibid._ p. 194, “Each individual
is composed of a vast number of somewhat similar new or old characters,
each character has its independent and separate history, each character
is in a certain stage of evolution, each character is correlated with
the other characters of the individual .... The real problem has
always been that of the origin and development of characters. Since
the _Origin of Species_ appeared, the terms variation and variability
have always referred to single characters; if a species is said to be
variable, we mean that a considerable number of the single characters
or groups of characters of which it is composed are variable,” etc.
[647] Cf. Sorby, _Quart. Journ. Geol. Soc._ (_Proc._), 1879, p. 88.
[648] Cf. D’Orbigny, Alc., _Cours élém. de Paléontologie_, etc., I, pp.
144–148, 1849; see also Sharpe, Daniel, On Slaty Cleavage, _Q.J.G.S._
III, p. 74, 1847.
[649] Thus _Ammonites erugatus_, when compressed, has been described as
_A. planorbis_: cf. Blake, J. F., _Phil. Mag._ (5), VI, p. 260, 1878.
Wettstein has shewn that several species of the fish-genus _Lepidopus_
have been based on specimens artificially deformed in various ways:
Ueber die Fischfauna des Tertiären Glarnerschiefers, _Abh. Schw.
Palaeont. Gesellsch._ XIII, 1886 (see especially pp. 23–38, pl. I).
The whole subject, interesting as it is, has been little studied: both
Blake and Wettstein deal with it mathematically.
[650] Cf. Sir Thomas Browne, in _The Garden of Cyrus_: “But why
ofttimes one side of the leaf is unequall unto the other, as in
Hazell and Oaks, why on either side the master vein the lesser and
derivative channels stand not directly opposite, nor at equall angles,
respectively unto the adverse side, but those of one side do often
exceed the other, as the Wallnut and many more, deserves another
enquiry.”
[651] Where gourds are common, the glass-blower is still apt to take
them for a prototype, as the prehistoric potter also did. For instance,
a tall, annulated Florence oil-flask is an exact but no longer a
conscious imitation of a gourd which has been converted into a bottle
in the manner described.
[652] Cf. _Elsie Venner_, chap. ii.
[653] This significance is particularly remarkable in connection with
the development of speed, for the metacarpal region is the seat of very
important leverage in the propulsion of the body. In the Museum of
the Royal College of Surgeons in Edinburgh, there stand side by side
the skeleton of an immense carthorse (celebrated for having drawn all
the stones of the Bell Rock Lighthouse to the shore), and a beautiful
skeleton of a racehorse, which (though the fact is disputed) there is
good reason to believe is the actual skeleton of Eclipse. When I was a
boy my grandfather used to point out to me that the cannon-bone of the
little racer is not only relatively, but actually, longer than that of
the great Clydesdale.
[654] Cf. Vitruvius, III, 1.
[655] _Les quatres livres d’Albert Dürer de la proportion des parties
et pourtraicts des corps humains_, Arnheim, 1613, folio (and earlier
editions). Cf. also Lavater, _Essays on Physiognomy_, III, p. 271, 1799.
[656] It was these very drawings of Dürer’s that gave to Peter Camper
his notion of the “facial angle.” Camper’s method of comparison was the
very same as ours, save that he only drew the axes, without filling in
the network, of his coordinate system; he saw clearly the essential
fact, that the skull _varies as a whole_, and that the “facial angle”
is the index to a general deformation. “The great object was to shew
that natural differences might be reduced to rules, of which the
direction of the facial line forms the _norma_ or canon; and that these
directions and inclinations are always accompanied by correspondent
form, size and position of the other parts of the cranium,” etc.; from
Dr T. Cogan’s preface to Camper’s work _On the Connexion between the
Science of Anatomy and the Arts of Drawing, Painting and Sculpture_
(1768?), quoted in Dr R. Hamilton’s Memoir of Camper, in _Lives of
Eminent Naturalists_ (_Nat. Libr._), Edin. 1840.
[657] The co-ordinate system of Fig. 382 is somewhat different from
that which I drew and published in my former paper. It is not unlikely
that further investigation will further simplify the comparison, and
shew it to involve a still more symmetrical system.
[658] _Dinosaurs of North America_, pl. LXXXI, etc. 1896.
[659] _Mem. Amer. Mus. of Nat. Hist._ I, III, 1898.
[660] These and also other coordinate diagrams will be found in Mr G.
Heilmann’s book _Fuglenes Afstamning_, 398 pp., Copenhagen, 1916; see
especially pp. 368–380.
[661] Cf. W. B. Scott (_Amer. Journ. of Science_, XLVIII, pp. 335–374,
1894), “We find that any mammalian series at all complete, such as
that of the horses, is remarkably continuous, and that the progress
of discovery is steadily filling up what few gaps remain. So closely
do successive stages follow upon one another that it is sometimes
extremely difficult to arrange them all in order, and to distinguish
clearly those members which belong in the main line of descent, and
those which represent incipient branches. Some phylogenies actually
suffer from an embarrassment of riches.”
[662] Cf. Dwight, T., The Range of Variation of the Human Scapula,
_Amer. Nat._ XXI, pp. 627–638, 1887. Cf. also Turner, _Challenger Rep._
XLVII, on Human Skeletons, p. 86, 1886: “I gather both from my own
measurements, and those of other observers, that the range of variation
in the relative length and breadth of the scapula is very considerable
in the same race, so that it needs a large number of bones to enable
one to obtain an accurate idea of the mean of the race.”
[663] There is a paper on the mathematical study of organic forms
and organic processes by the learned and celebrated Gustav Theodor
Fechner, which I have only lately read, but which would have been of
no little use and help to our argument had I known it before. (Ueber
die mathematische Behandlung organischer Gestalten und Processe,
_Berichte d. k. sächs. Gesellsch._, _Math.-phys. Cl._, Leipzig,
1849, pp. 50–64.) Fechner’s treatment is more purely mathematical
and less physical in its scope and bearing than ours, and his paper
is but a short one; but the conclusions to which he is led differ
little from our own. Let me quote a single sentence which, together
with its context, runs precisely on the lines of the discussion with
which this chapter of ours began. “So ist also die mathematische
Bestimmbarkeit im Gebiete des Organischen ganz eben so gut vorhanden
als in dem des Unorganischen, und in letzterem eben solchen oder
äquivalenten Beschränkungen unterworfen als in ersterem; und nur sofern
die unorganischen Formen und das unorganische Geschehen sich einer
einfacheren Gesetzlichkeit mehr nähern als die organischen, kann die
Approximation im unorganischen Gebiet leichter und weiter getrieben
werden als im organischen. Dies wäre der ganze, sonach rein relative,
Unterschied.” Here in a nutshell, in words written some seventy years
ago, is the gist of the whole matter.
An interesting little book of Schiaparelli’s (which I ought to have
known long ago)—_Forme organiche naturali e forme geometriche pure_,
Milano, Hoepli, 1898—has likewise come into my hands too late for
discussion.
{780}
INDEX.
Abbe’s diffraction plates, 323
Abel, O., 706
Abonyi, A., 127
Acantharia, spicules of, 458
Acanthometridae, 462
Acceleration, 64
Aceratherium, 761
Achlya, 244
Acromegaly, 135
Actinomma, 469
Actinomyxidia, 452
Actinophrys, 165, 197, 264, 298
Actinosphaerium, 197, 266, 298, 468
Adams, J. C., 663
Adaptation, 670
Addison, Joseph, 671
Adiantum, 408
Adsorption, 192, 208, 241, 277, 357;
orientirte, 440, 590;
pseudo, 282
Agglutination, 201
Aglaophenia, 748
Airy, H., 636
Albumin molecule, 41
Alcyonaria, 387, 413, 424, 459
Alexeieff, A., 157, 165
Allmann, W., 643
Alpheus, claws of, 150
Alpine plants, 124
Altmann’s granules, 285
Alveolar meshwork, 170
Ammonites, 526, 530, 537, 539, 550, 552, 576, 583, 584, 728
Amoeba, 12, 165, 209, 212, 245, 255, 288, 463, 605
Amphidiscs, 440
Amphioxus, 311
Ampullaria, 560
Anabaena, 300
Anaxagoras, 8
Ancyloceras, 550
Andrews, G. F., 164;
C. W., 716
Anhydrite, 433
Anikin, W. P., 130
Anisonema, 126
Anisotropy, 241, 357
Anomia, 565, 567
Antelopes, horns of, 614, 671
Antheridia, 303, 403, 405, 409
Anthoceros, spore of, 397
Anthogorgia, spicules of, 413
Anthropometry, 51
Anticline, 360
Antigonia, 750, 775
Antlers, 628
Apatornis, 757
Apocynum, pollen of, 396
Aptychus, 576
Arachnoidiscus, 387
Arachnophyllum, 325
Arcella, 323
Arcestes, 539, 540
Archaeopteryx, 757
Archimedes, 580;
spiral of, 503, 524, 552
Argali, horns of, 617
Argiope, 561
Argonauta, 546, 561
Argus pheasant, 431, 631
Argyropelecus, 748
Aristotle, 3, 4, 5, 8, 15, 138, 149, 158, 509, 653, 714, 725, 726
Arizona trees, 121
Arrhenius, Sv., 28, 48, 171
Artemia, 127
Artemis, 561
Ascaris megalocephala, 180, 195
Aschemonella, 255
Assheton, R., 344
Asterina, 342
Asteroides, 423
Asterolampra, 386
Asters, 167, 174
Asthenosoma, 664
Astrorhiza, 255, 463, 587, 607
Astrosclera, 436
Asymmetric substances, 416
Asymmetry, 241
Atrypa, 569
Auerbach, F., 9
Aulacantha, 460
Aulastrum, 471
Aulonia, 468
Auricular height, 93
Autocatalysis, 131
Auximones, 135
Awerinzew, S., 589
Babak, E., 32
Babirussa, teeth of, 634
Baboon, skull of, 771
Bacillus, 39;
B. ramosus, 133
Bacon, Lord, 4, 5, 51, 53, 131, 656, 716
Bacteria, 245, 250
Baer, K. E., von, 3, 55, 57, 155
Balancement, 714, 776
Balfour, F. M., 57, 348
Baltzer, Fr., 327
Bamboo, growth of, 77
Barclay, J., 334
Barfurth, D., 85
Barlow, W., 202
Barratt, J. O. W., 285
Bartholinus, E., 329
Bashforth, Fr., 663
Bast-fibres, strength of, 679
Baster, Job, 138
Bateson, W., 104, 431
Bather, F. A., 578
Batsch, A. J. G. K., 606
Baudrimont, A., and St Ange, 124
Baumann and Roos, 136
Bayliss, W. M., 135, 277
Beads or globules, 234
Beak, shape of, 632
Beal, W. J., 643
Beam, loaded, 674
Bee’s cell, 327, 779
Begonia, 412, 733
Beisa antelope, horns of, 616, 621
Bellerophon, 550
Bénard, H., 259, 319, 448, 590
Bending moments, 19, 677, 696
Beneden, Ed. van, 153, 170, 198
Bergson, H., 7, 103, 251, 611, 721
Bernard, Claude, 2, 13, 127
Bernoulli, James, 580;
John, 30, 54
Berthold, G., 8, 234, 298, 306, 322, 346, 351, 357, 358, 372, 399
Bethe, A., 276
Bialaszewicz, K., 114, 125
Biedermann, W., 431
Bilharzia, egg of, 656
Binuclearity, 286
Biocrystallisation, 454
Biogenetisches Grundgesetz, 608
Biometrics, 78
Bird, flight of, 24;
form of, 673
Bisection of solids, 352, etc.
Bishop, John 31
Bivalve shells, 561
Bjerknes, V. 186
Blackman, F. F. 108, 110, 114, 124, 131, 132
Blackwall, J. 234
Blake, J. F. 536, 547, 553, 578, 583, 728
Blastosphere, 56, 344
Blood-corpuscles, form of, 270;
size of, 36
Blood-vessels, 665
Boas, Fr., 79
Bodo, 230, 269
Boerhaave, Hermann, 380
Bonanni, F., 318
Bone, 425, 435;
repair of, 687;
structure of, 673, 680
Bonnet, Ch., 108, 138, 334, 635
Borelli, J. A., 8, 27, 29, 318, 677, 690
Bosanquet, B., 5
Boscovich, Father R. J., S.J., 8
Bose, J. C., 87
Bostryx, 502
Bottazzi, F., 127
Bottomley, J. T., 135
Boubée, N., 529
Bourgery, J. M., 683
Bourne, G. C., 199
Bourrelet, Plateau’s, 297, 339, 446, 470, 477
Boveri, Th., 38, 147, 170, 198
Bowditch, H. P., 61, 79
Bower, F. O., 406
Bowman, J. H., 428
Boyd, R., 61
Boys, C. V., 233
Brachiopods, 561, 568, 577
Bradford, S. C., 428
Brady, H. B., 255, 606
Brain, growth of, 89;
weight of, 90
Branchipus, 128, 342
Brandt, K., 459, 482
Brauer, A., 180
Braun, A., 636
Bravais, L. and A., 202, 502, 636
Bredig, G., 178
Brewster, Sir D., 209, 337, 350, 431
Bridge, T. W., 671
Bridge construction, 18, 691
Brine shrimps, 127
Brooke, Sir V., 614, 624, 628, 631
Browne, Sir T., 324, 329, 480, 650, 652, 733
Brownian movement, 45, 279, 421
Brücke, C., 160, 199
Buccinum, 520, 527
Buch, Leopold von, 528, 583
Buchner, Hans, 133
Budding, 213, 399
Buffon, on the bee’s cell, 333
Bühle, C. A., 653
Bulimus, 549, 556
Burnet, J., 509
Bütschli, O., 165, 170, 171, 204, 432, 434, 458, 492
Büttel-Reepen, H. von, 332
Byk, A., 419
Cactus, sphaerocrystals, in 434
Cadets, growth of German, 119
Calandrini, G. L., 636