of conjugation of what are literally aplanospores. Among
those Desmidiaceae which live a free life, two plants
become surrounded by a common mucilage, in which they lie
either parallel (Closterium) or crosswise (Cosmarium.)
Gaps then appear in the apposed surfaces, usually at the
isthmus; the entire protoplasts either pass out to melt into
one another clear of the old walls, or partly pass out and
fuse without complete detachment from the old walls. Among
colonial Desmidiaceae, the break-up of the filament is a
preliminary to this conjugation; otherwise the process is the
same. The zygospore becomes surrounded with its own wall,
consisting finally of three layers, the outer of which is
furnished with spicular prominences of various forms. In
Zygnemaceae there is no dissolution of the filaments, but
the whole contents of one cell pass over by means of a
conjugation-tube into the cavity of a cell of a neighbouring
filament, where the zygospore is formed by the fusion of the two
Fig. 3.--Chlorophyceae, variously magnified.
A. Spirogyra sp., in conjugation.
B. Zoospore of Pandorina. B234, stages of conjugation.
C. Ulothrix sp., zoospores escaping. C23, stages of conjugation.
D1. Oedogonium sp., oogonium at moment
of fertilization with dwarf male attached.
D2. Oedogonium sp., zoospore with crown of cilia.
E1. Coleochaete sp., with antheridia and an oogonium.
E2. Coleochaete sp., fertilized egg with investment of filaments.
E3. Coleochaete sp., zoospore.
F123. Protosiphon, conjugation of zoogametes.
G. Derbesia sp., zoospore with chaplet of cilia.
H1. Chara sp., oogonium and antheridium at a node on a lateral appendage.
H2. Chara sp., antherozoid.
K1. Vaucheria sp., oogonium and antheridium before fertilization.
K2. Vaucheria sp., after fertilization.
(A from Cooke, British Freshwater Algae, by permission
of Kegan Paul, Trench Trubner and Co.; C, E, F. G. H. K
from Engler and Prantl, by permission of Wilheim Engelmann;
B1 from Vines, by permission of Swan Sonnenschein and Co.;
B2, D from Oltmanns, by permission of Gustav Fischer.)
protoplasts. In these cases the activity of one of the
gametes, and the passivity of the other, is regarded
as evidence of incipient sex. In Strogonium there is
cell-division in the parent-cell prior to conjugation; and
as two segments are cut off in the case of the active gamete,
and only one in the case of the passive gamete, there is a
corresponding difference of size, marking another step in
the sexual differentiation. In Zygogonium, although no
cell-division takes place, the gametes consist of a portion
only of the contents of a cell, and this is regularly the
case in Mesocarpaceae, which occupy the highest grade among
Conjugatae. Some Zygnemaceae and Mesocarpaceae form either
a short conjugating tube, or none at all, but the filaments
approach each other by a knee-like bend, and the zygospore is
formed at the point of contact, often being partially contained
within the walls of the parent-cell. It would seem that in
some cases the nuclei of the gametes remain distinct in the
zygospore for a considerable time after conjugation. It is
probable that in all cases nuclear fusion takes place sooner or
later. In Zygnemaceae and Mesocarpaceae the zygospore,
after a period of rest, germinates, to form a new filamentous
colony; in Desmidiaceae its contents divide on germination,
and thus give rise to two or more Desmids. Gametes which fail
to conjugate sometimes assume the appearance of zygospores
and germinate in due course. They are known as azygospores.
The reproduction of Characeae is characterized by a pronounced
oogamy, the reproductive organs being the most highly
differentiated among Chlorophyceae. The antheridia and oogonia
are formed at the nodes of the appendages. The oogonium,
seated on a stalk cell, is surrounded by an investment
consisting of five spirally-wound cells, from the projecting
ends of which segments are cut off, constituting the so-called
stigma. The oosphere is not differentiated within the wall of
the oogonium, but certain cells known as wendungszellen, the
significance of which has given rise to much speculation, are
cut off from the basal portion of the parent-cell during its
development. The antheridia are spherical orange-coloured
bodies of very complex structure. The antherozoid is a
spirally-coiled thread of protoplasm, furnished at one
end with a pair of cilia. It much more resembles the
antherozoids of Bryophyta and certain Pteridophyta than any
known among other algae. The fertilized egg charged with
food reserves rests for a considerable period, surrounded
by its cortex, the whole having assumed a reddish-brown
colour. On germination it gives rise to a row of cells in
which short (nodal) and long (internodal) cells alternate.
From the first node arise rhizoids; from the second a lateral
bud, which becomes the new plant. This peculiar product of
germination, which intervenes between the oospore and the
adult form, is the proembryo. It will be remembered that in
Musci, the asexual spore somewhat similarly gives rise to a
protonema, from which the adult plant is produced as a lateral
bud. The proembryonic branches of Characeae, one of the
means of vegetative reproduction already referred to, are so
called because they repeat the characters of the proembryo.
Before leaving the Chlorophyceae, it should be mentioned
that the genus Volvox has been included by some zoologists
(Butschli, for example) among Flagellata; on the other hand,
certain green Flagellata, such as Euglena, are included by
some botanists (for example, van Tieghem) among unicellular
plants. A similar uncertainty exists with reference to certain
groups of Phaeophyceae, and the matter will thus arise again.
A census of the Chlorophyceae is furnished below:--
1. Confervoideae---12 families, 77 genera, 1021 species.
2. Siphoneae--9 families, 26 genera, 271 species.
3. Protococcoideae--2 families, 90 genera, 342 species.
4. Conjugateae--2 families, 33 genera, 1296
species. (De Toni's Sylloge Algarum, 1889.)
5. Characeae--2 families, 6 genera, 181 species.
(Engler and Prantl's Pflanzenfamilien, 1897)
III. PHAEOPHYCEAE.--The Phaeophyceae are distinguished
by the possession of a brown colouring matter, phycophaein,
in addition to chlorophyll. They consist of the following
groups:--Fucaceae, Phaeosporeae; Dictyotaceae, Cryptomonadaceae,
Peridiniaceae and Diatomaceae. Of these the first three
include multicellular plants, some of them of great size; the
last three are unicellular organisms, with little in common
with the rest excepting the possession of a brown colouring
matter. Fucaceae and Phaeosporeae are doubtless closely
allied, and to these Dictyotaceae may be joined, though
the relationship is less close. They constitute the
Euphaeophyceae, and will be dealt with in the first place.
Euphaeophyceae are almost exclusively marine, growing on
rocks and stones on the coast, or epiphytic upon other
algae. In tidal seas they range from the limits of high water
to some distance beyond the low-water line. On the British
coasts zones are observable in passing from high to low water
mark, characterized by the prevalence of different species,
thus:---Pelvetia canaliculata, Fucus platycarpus, Fucus
vesiculosus, Ascophyllum nodosum, Fucus serratus, Laminaria
digitata. Some species are minute filamentous plants, requiring
the microscope for their detection; others, like Lessonia,
are of considerable bulk, or, like Macrocystis, of enormous
length. In Fucaceae, Dictyotacea, and in Laminariaceae and
Sphacelariaceae, among Phaeosporeae, the thallus consists of
a true parenchyma; elsewhere it consists of free filaments,
or filaments so compacted together, as in Cutleriaceae and
Desmarestiaceae, as to form a false parenchyma. In Fucaceae
and Laminariaceae the inner tissue is differentiated into
a conducting system. In Laminariaceae the inflation of
the ends of conducting cells gives rise to the so-called
trumpet-hyphae. In Nereocystis and Macrocystis a zone
of tubes occurs, which present the appearance of sieve-tubes
even to the eventual obliteration of the perforations by a
callus. While there is a general tendency in the group to
mucilaginous degeneration of the cell-wall, in Laminaria
digitata there are also glands secreting a plentiful
mucilage. Secondary growth in thickness is effected by
the tangential division of superficial cells. The most
fundamental external differentiation is into holdfast and
shoot. In Laminariaceae secondary cylindrical props arise
obliquely from the base of the thallus. In epiphytic forms
the rhizoids of the epiphyte often penetrate into the tissue
of the host, and certain epiphytes are not known to occur
excepting in connexion with a certain host; but to what
extent, if any, there is a partial parasitism in these cases
has not been ascertained. In filamentous forms there is
a differentiation into branches of limited and branches of
unlimited growth (Sphacelaria.) In Laminariaceae there is a
distinction of stipe and blade. The blade is centrally-ribbed
in Alaria and laterally-ribbed in Macrocystis. It is
among the Sargassaceae that the greatest amount of external
differentiation, rivalling that of the higher leafy plants, is
reached. A characteristic feature of the more massive
species is the occurrence of air-vesicles in their tissues.
In Fucus vesiculosus they arise in lateral pairs; in
Ascophyllum they are single and median; in Macrocystis
one vesicle arises at the base of each thallus segment; in
Sargassum and Halidrys the vesicles arise on special
branches. They serve to buoy up the plant when attached to the
sea-bottom, and thus light is admitted into the forest-like
growths of the gregarious species. When such plants are
detached they are enabled to float for great distances, and
the great Sargasso Sea of the North Atlantic Ocean is probably
only renewed by the constant addition of plants detached
from the shores of the Caribbean Sea and Gulf of Mexico.
Growth in length is effected in a variety of ways. In Dictyota
Sphacelariaceae and Fucaceae there is a definite apical
cell. In the first it is a biconvex lens, from which segments
are continually cut off parallel to the posterior surface;
and in the second an elongated dome, from which segments are
cut off by a transverse wall. While, however, in Dictyota
the product of the subsequent division in the segment enlarges
with each subdivision, the divisions in the cylindrical
segment of Sphacelariaceae are such that the whole product
after subdivision, however many cells it may consist of, does
not exceed in bulk the segment as cut off from the apical
cell. In Dictyotaceae the apical cell occasionally divides
longitudinally, and thus the dichotomous branching is provided
for. In some Sphacelariaceae branches may appear at their
inception as lateral protuberances of the apical cell itself.
In Fucaceae an apical cell is situate at the surface of the
thallus in a slit-like depression at the apex. From this cell
segments are cut off in three or four lateral oblique planes.
A peculiar manner of growth in length is that to which the term
trichothallic has been applied. It may readily be observed
that in the hair-like branches of Ectocarpaceae, the point at
which most rapid division occurs is situate near the base of the
hair. In Desmarestia and Arthrocladia, for example, it is
found that the thallus ends in a tuft of such hairs, each of
them growing by means of an intercalated growing point. In these
cases, however, the portions of the hairs behind the growing
region become agglutinated together into a solid cylindrical
pseudo-parenchymatous axis. In Cutleria the laminated thallus
is formed in the same way. The intercalated growing region of
Laminaria affords an example of another variety of growth in
Phaeophyceae. While the laminated portion of the thallus is
being gradually worn off in our latitudes during the autumnal
storms, a vigorous new growth appears at the junction of
the stipe and the blade, as the result of which a new piece
is added to the stipe and the lamina entirely renovated.
Both asexual and sexual reproduction occur among Euphaeophyceae.
Fucaceae are marked by an entire absence of the asexual
method. The sexual organs--oogonia and antheridia---are
borne on special portions of the thallus in cavities known as
conceptacles. Both organs may occur in one conceptacle, as
in Pelvetia, or each may be confined to one conceptacle
or even one plant, as in Fucus vesiculosus. The oogonia
arise on a stalk cell from the lining layer of the cavity, the
contents dividing to form eight oospheres as in Fucus, four
as in Ascophyllum, two as in Pelvetia, or one only as in
Hallidrys. It would seem that eight nuclei primarily arise
in all Fucaceae, and that a number corresponding to the number
of oospheres subsequently formed is reserved, the rest being
discharged to the periphery, where they may be detected at a late
stage. On the maturation of the oospheres the outer layer of
the oogonial wall ruptures, and the oospheres, still surrounded
by a middle and inner layer, pass out through the mouth of the
conceptacle. Then usually these layers successively give
way, and the spherical naked oospheres float free in the
water. The antheridia, which arise in the conceptacular cavity
as special cells of branched filaments, are similarly discharged
whole, the antherozoids only escaping when the antheridia
are clear of the conceptacle. The antherozoids are attracted
to the oospheres, round each of which they swarm in great
numbers. Suddenly the attraction ceases, and the oosphere is
fertilized, probably at that moment, by the entry of a single
antherozoid into the substance of the oosphere; a cell-wall
is formed thereupon, in some cases in so short an interval
as five minutes. Remarkable changes of size and outline of
the oosphere have recently been described as accompanying
fertilization in Hallidrys. Probably the act of fertilization
in plants has nowhere been observed in such detail as in
Fucaceae. Dictyotaceae resemble Fucaceae in their pronounced
oogamy. They differ, however, in being also asexually
reproduced. The asexual cells are immotile spores arising in
fours in sporangia from superficial cells of the thallus. In
Dictyota the oospheres arise singly in oogonia, crowded together
in sori on the surface of the female plant. The antheridia
have a similar origin and grouping on the male plant. Until the
recent discovery by Williams of motility, by means of a single
cilium, of the antherozoids of Dictyota and Taonia, they
were believed to be immotile bodies, like the male cells of
red seaweeds. in Dictyota the unfertilized oosphere is found
to be capable of undergoing a limited number of divisions,
but the body thus formed appears to atrophy sooner or later.
Of the small family of the Tilopteridaceae our knowledge is
as yet inadequate, but they probably present the only case of
pronounced oogamy among Phaeosporeae. They are filamentous
forms, exhibiting, however, a tendency to division in more
than one plane, even in the vegetative parts. The discovery
by Brebner of the specific identity of Haplospora globosa and
Scaphospora speciosa marks an important step in the advance of
our knowledge of the group. Three kinds of reproductive organs
are known: first, sporangia, which each give rise to a single
tetra-, or multi-nucleate non-motile, probably asexual spore;
second, plurilocular sporangia, which are probably antheridia,
generating antherozoids; and third, sporangia, which are
probably oogonia, giving rise to single uni- nucleate non-motile
oospheres. No process of fertilization has as yet been observed.
The Cutleriaceae exhibit a heterogamy in which the female sexual
cell is not highly specialized, as is in the groups already
described. From each locule of a plurilocular sporangium there
is set free an oosphere, which, being furnished with a pair
of cilia, swarms for a time. In similar organs on separate
plants the much smaller antherozoids arise. Fertilization has
been observed at Naples; but it apparently depends on climatic
conditions, as at Plymouth the oospheres have been observed to
germinate parthenogenetically. The asexual organs in the case
of Cutleria multifida arise on a crustaceous form, Aglaozonia
reptans, formerly considered to be a distinct species. They
are unilocular, each producing a small number of zoospores.
The possession of two kinds of reproductive organs, unilocular
and plurilocular sporangia, is general among the rest of the
Phaeosporeae. Bornet, however, called attention in 1871 to
the fact that two kinds of plurilocular sporangia occurred in
certain species of the genus Ectocarpus--somewhat transparent
organs of an orange tint producing small zoospores, and also
more opaque organs of a darker colour producing relatively larger
zoospores. On the discovery of another such species by F.
H. Buffham, Batters in 1892 separated the three species,
Ectocarpus secundus, E. fenestratus, E. Lebelii, together
with the new species, into a genus, Giffordia, characterized
by the possession of two kinds of plurilocular sporangia.
The suspicion that a distinction of sex accompanied this
difference of structure has been justified by the discovery
by Sauvageau of undoubted fertilization in Gidordia secunda
and G. fenestrata. The conjugation of similar gametes,
arising from distinct plurilocular sporangia, was observed
by Berthold in Ectocarpus siliculosus and Scytosiphon
lomentarius in 1880; and these observations have been recently
confirmed in the case of the former species by Sauvageau,
and in the case of the latter by Kuckuck. In these cases,
however, the potential gametes may, failing conjugation,
germinate directly, like the zoospores derived from unilocular
sporangia. The assertion of Areschoug that conjugation
occurs among zoospores derived from unilocular sporangia,
in the case of Dictyosiphon hippuroides, is no doubt to be
ascribed to error of observation. It would thus seem that
the explanation of the existence of two kinds of sporangia,
unilocular and plurilocular, among Phaeosporeae, lies in the
fact that unilocular sporangia are for asexual reproduction,
and that plurilocular sporangia are gametangia--potential or
actual. It must, however, be remembered that so important
a generalization is as yet supported upon a somewhat narrow
base of observation. Moreover, for the important family
of the Laminariaceae only unilocular sporangia are known to
occur; and for many species of other families, only one or
other kind, and in some cases neither kind, has hitherto been
observed. The four species--Ectocarpus siliculosus,
Giffordia secunda, Cutleria multifida and Haplospora
globosa--may be taken to represent, within the phaeosporeae,
successive steps in the advance from isogamy to oogamy.
The Peridiniaceae have been included among Flagellata under
the title of Dinoflagellata. The majority of the species
belong to the sea, but many are found in fresh water. The
thallus is somewhat spherical and unicellular, exhibiting
a distinction between anterior and posterior extremities,
and dorsal and ventral surfaces. The wall consists of a
basis of cellulose, and in some cases readily breaks up into
a definite number of plates, fitting into one another like
the plates of the carapace of a tortoise; it is, moreover,
often finely sculptured or coarsely ridged and flanged. Two
grooves are a constant feature of the family, one running
transversely and anoiher longitudinally. In these grooves
lie two c;lia, attached at the point of meeting on the dorsal
surface. The protoplast is uninucleate and vacuolate,
and contains chromatophores of a brownish colour. It is
not clear that FIG. 4.--Phaeophyceae, variously magnified.
A. Halopteris, apical region.
B. Chordaria sp., apical region showing so-called trichothallic growth.
C. Dictyota sp., apical cells immediately after dichotomy.
D. Cutleria sp., margin of thallus showing trichothallic growth.
E. Halidrys, apical depression with leading cell.
F. Macrocystis sp., tubular elements from the
medulla, with sieve-like transverse walls.
G. Laminaria sp., hyphae with trumpet-like ends also from medulla.
H. Elachistea sp., Plurilocular sporanges.
K. Ectocarpus sp., unilocular sporange.
L. Ectocarpus siliculosus, female gamete surrounded
by male gametes a, b, c, d, e, stages of conjugation.
M. Cutleria multifida. a, antherozoids, b, a female gamete.
N1. Fucus vesiculosus, young oogonium.
N2. Fucus vesiculosus, discharge of eight oospheres from oogonium
O. Laminaria sp., sporanges among paraphyses.
P. Dictyota dichotoma, a sorus of oogonia.
Q. Dictyota dichotoma, part of a sorus of antheridia.
(A, B, C, D, E, H, L, M, P, from Engler and Prantl, by
permission of Wilhelm Engelmann; F, G, K, O, from Oltmanns,
by permission of Gustav Fischer; Q. from The Annals of
Botany, by permission of the Clarendon Press; N1, N2,
from Hauck, Meeresalgen, by permission of Eduard Kummer.)
the brown colouring matter which is added to chlorophyll
is identical with phycophaein: two varieties of it have
been termed phycopyrrin and peridinine. Certain species,
such as Gymnodinium spirale, are colourless and therefore
saprophytic in their method of nutrition. Multiplication
takes place in some cases by the endogenous formation of
zoospores, the organism having come to rest; in others by
longitudinal division, when the organism is still motile.
No method of sexual reproduction is known with certainty.
The Cryptomonadaceae also are unicellular, and live free or in
colonies. Each cell contains a flattened chromatophore of a
brown or yellow colour. Hydrurus forms a branched gelatinous
colony attached to stones in mountain streams. Chromophyton
forms an eight-celled colony. Both plants multiply solely by
means of zoospores. The Cryptomonadeae and Chromulineae are
motile through the greater part of their life. Cryptomonas,
when dividing in a mucilage after encystment, recalls the
condition in Gloeocystis. In Synura and Chromulina the
cells form a spherical motile colony, recalling Volvocaceae.
Chromulina is uniciliate, and is contained in a hyaline
capsule. Like the Peridiniaceae, the Cryptomonadaceae have
been included among Flagellata. They have no close affinity
with Euphaeophyceae. Such colonial forms as Hydrurus
and Phaeocystis are supposed, however, to indicate
a stage in the passage to the multicellular condition.
Diatomaceae have long been recognized as plants. Together
with Peridiniaceae they constitute the bulk of marine plankton,
and thus play an important part in the support of marine
animal life. They exhibit striking adaptations in these
circumstances to the floating habit. (See DIATOMACEAE.)
A census of Phaeophyceae is given below:--
(1) Cyclosporinae (Fucaceae)--4 families, 32 genera, 347 species.
(2) Tetrasporinae (Dictyotaceae)-- 1 family, 17 genera, 130 species.
(3) Phaeozoosporineae (Phaeosporeae)--24 families, 143
genera, 571 species. (De Toni's Sylloge ALgarum.)
(4) Peridiniales---3 families, 32 genera, 167 species.
(5) Cryptomonadaceae (including Chrysomonadaceae)
--2 families, 28 genera, 50-60 species.
(6) Bacillariales (Diatomaceae)--about 150
genera and 5000 species, fossil and recent.
(Engler and Prantl's Pflanzenfamilien)
IV. RHODOPHYCEAE, or FLORIDEAE.--The members of this
group are characterized by the possession of a red colouring
matter, phycoerythrin, in addition to chlorophyll. There is,
however, a considerable amount of difference in the shades
of red which mark different species. The brightest belongs
to those species which grow near low-water mark, or under
the shade of larger algae at higher levels; species which
grow near high-water mark are usually of so dark a hue that
they are easily mistaken for brown seaweeds. Rhodophyceae
are mostly marine, but not exclusively so. Thorea,
Lemanea, Tuomeya, Stenocladia, Batrachospermum, Balbiania
are genera belonging entirely to fresh water; and Bangia,
Chanitransia, Caloglossa, Bostrychia and Delesseria
contain each one or more freshwater species. Most of the
larger species of marine Rhodophyceae are attached by means
of a disc to rocks, stones or shells. Many are epiphytic
on other algae, more especially the larger Phaeophyceae and
Rhodophyceae. As in the case of epiphytic brown seaweeds,
the rhizoids of the epiphyte often penetrate the substance
of the supporting alga. Some Red Algae find a home in the
gelatinous substance of Flustra, Alcyonidium and other
polyzoa, only emerging for the formation of the reproductive
organs. Some are perforating algae and burrow into the
substance of molluscan shells, in company with certain Green
and Blue-green Algae. Some species belonging to the families
Squamariaceae nnd Corallinaceae grow attached through their
whole length and breadth, and are often encrusted with
lime. The forms which grow away from the substratum vary
greatly in external configuration. In point of size the
largest cannot rival the larger Brown Algae, while the majority
require the aid of the microscope for their investigation.
No unicellular Rhodophyceae are known, although a flagellate
organism, Rhodomonas, has recently been described as possessed
of the same red colouring matter. If the sub-group, Bangiaceae,
be excluded, they may be said to consist exclusively of branched
filaments. Growth in these cases takes place by means of an
apical cell, from which successive segments are cut off by means
of a transverse wall. The segment so cut off does not usually
divide again by means of a transverse wall, nor indeed by a
longitudinal wall which passes through the organic axis of the
cell. New cells may be cut off laterally, which become
the apical cells of branches. When the new cells grow no
further, but constitute a palisading round the central cell
covering its whole length, the condition is reached which
characterizes the species of Polysiphonia, the "siphons" of
which may be regarded as one-celled branches. To the law that
no subsequent transverse division takes place in segments cut
off from the apical cell, there seem to be two exceptions:
first, the calcareous genus Corallinia, in the pliable
joints of which intercalated division occurs; and, second,
the Nitophylleae, in which, moreover, median longitudinal
division of axial cells is said to occur. Like the Fungi,
therefore, the Red Algae consist for the most part of branched
filaments, even where the thallus appears massive to the eye,
and, as in the case of Fungi, this fact is not inconsistent
with a great variery of external morphology. In the great
majority the thallus is obviously filamentous, as in some
species of Cillithamnion. In other species of that genus
an apparent cortication arises by the downward growth of
rhizoids, which are retained within the gelatinous wall of the
axial cells. in Batrachospermum the whole system of branches
are retained within a diffluent gelatinous substance derived
from the outer layers of the cell-walls. In other cases the
mucilage is denser and the branches more closely compacted
Helminthora.) In such cases as Lemanea, the terminal
cells of the lateral branches form a superficial layer which
has all the appearance of a parenchyma when viewed from the
surface. In Champia and allied genera, the cylindrical axis
is due not to the derivatives of one axial filament, but of
several, the growth of which is co-ordinated to form a septated
tube. The branching of the thallus, which meets the eye
in all these cases, is due to the unlimited growth of a few
branches. When such a lateral branch overtops the main axis
whose growth has become limited, as in Plocamium and Dasya,
a sympodium is formed. For the most part the branching is
monopodial. Besides the differentiation into holdfast and
shoot, and into branches of limited and branches of unlimited
growth, there appear superficial structures of the nature of
hairs. These are for the most part long, thin-walled,
unicellular and colourless, and arise from the outer cells
of the pseudo-cortex, or from the terminal cells of branches
when the filaments are free. Among Rhodomelaceae, hair-like
structures of a higher order are known. These arise from
the axial cell, and are multicellular and branched. They
soon fall off, and it is from the persistent basal cell that
the branches of unlimited growth arise. Upon them also the
reproductive organs arise in this family. It is not surprising,
therefore, that they have been regarded as the rudiments of
leaves. In Iridaea the thallus is an entire lamina; in
Callophyllis a lobed lamina; in Delesseria it is provided
with midrib and veins, simulating the appearance of a leaf
of the higher plants; in Constantinea the axis remains
cylindrical, and the lateral branches assume the form of
leaves. In the compact thalli a secondary development
often takes place by the growth of rhizoid-like internal
filaments. They present a hypha-like appearance, running
longitudinally for considerable distances. It is not difficult
in such compact species to distinguish between superficial
cells, whose chief function is assimilation, subjacent cells
charged with reserve material, and a core of tissue engaged
in the convection of elaborated material from part to part.
An interesting feature of the minute anatomy of Euflorideae,
as the Red Algae, exclusive of the Bangiaceae, have been
termed, is the existence of the so-called Floridean pit.
When a cell divides it is found that there remains in the
middle of the new wall a single large circular pit, which
persists throughout the life of the cells, becoming more and
more conspicuous with the progress of the thickening of the
wall. These pits serve to indicate the genetic relationship
of adjacent cells, when they form a compact pseudo-parenchyma,
notwithstanding the fact that somewhat smaller secondary pits
appear later between any contiguous cells. Protoplasmic continuity
has been observed in the delicate membrane closing the pit.
Vegetative multiplication occurs only sparingly in Rhodophyceae.
Melobesia callithamnioides gives rise to multicellular
propagula; (Griffithsia corallina is said to give rise
to new individuals, by detaching portions of the thallus
from the base of which new attachment organs have already
arisen. The spores of Monospora are by some regarded as
unicellular propagula. Reproduction is both asexual and
sexual. It is noteworthy that although all the members of
the group are aquatic no zoospores are produced, a negative
character common to them and the Blue-green Algae. As a rule
the asexual cells, and the male and female sexual cells arise
upon different plants, so that the species may be said to be
trioecious. Numerous exceptions, however, occur. Thus in
Lemaneaceae asexual spores are unknown; in Batracho-spermum,
Bonnemaisonia and Polysiphonia byssoides both kinds of
sexual cells appear on the same plant; and in some cases the
asexual cells may occur in conjunction with either the male or
female sexual cells. The asexual cells are termed tetraspores
on account of the usual occurrence of four in each sporangium.
What may be termed monospores, bispores and octospores,
however, are not unknown. The sporangia may be terminal or
intercalated. When they are confined to special branches
such branches are spoken of as stichidia. The tetrasrores
may arise by the simultaneous division of the contents of a
sporangium, when they are arranged tetrahedrally, or they may
arise by two successive divisions, in which case the arrangement
may be zonate when the spores are in a row, or cruciate when
the second divisions are at right angles to the first, or
tetrahedral when the second divisions are at right angles to
the first and also to one another. Tetraspores are at first
naked, but soon acquire a cell-wall and germinate without a
period of rest. The male sexual cells are produced singly
in the terminal cells of branches. They are spoken of as
spermaria. Great numbers of antheridia are usually crowded
together, when the part is distinguishable by the absence
of the usual red colour. In Polysiphonia they cover the
joints of the so-called leaves; in Chondria they arise
on flattened dishs; in the more massive forms they arise in
patches on the ordinary surface; in a few cases (Gracilaria,
Corallina, Galaxaura) they line the walls of conceptacle-like
depressions. The female sexual cell is represented by the
contents of a cell which is terminal on ordinary or specialized
branches. This is the carpogonium: it consists of a neutral
portion which contains a nucleus, but in which no oosphere is
differentiated, and an elongated tubular portion known as the
trichogyne, into which the cytoplasm extends. Fertilization
is effected by the passive convection of a spermatium from
the antheridium to the trichogyne, to which it adheres,
and to which it passes over its nucleus through an open
communication set up at the point of contact. The nucleus
then passes down the trichogyne and fuses with that of the
eeg. This fusion has been observed by Wille in Nemalion
multifidim, and by Schmidle in Batrachospermum. It is
singular that in the last-named species two nuclei occur
regularly in the spermatium. The ventral portion of the
carpogonium may be imbedded deep in the thallus in the
massive species; the trichogyne, however, always reaches the
surface. The first effect of fertilization is the occlusion
of the trichogyne from the fertilized carpogonium. The
subsequent course of development is characteristic of the
Florideae. The carpogonium germinates forthwith, drawing
its nourishment almost wholly from the parent plant. The
ultimate product in all cases is a number of carpospores, but
before this stage is reached the development is different in
different subgroups. In Batrachospermum filaments arise
from the carpogonium on all sides; in Chantransia and
Scinaia on one side only; in Helminthora the filaments
are enclosed in a dense mucilage; in Nemalion, prior to
the formation of the filaments, a sterile segment is cut off
below. In all these cases, however, the end-cells of the
filaments each give rise to a carpospore, and the aggregate
of such sporiferous filaments is a cystocarp. Again, in the
family of the Gelidiaceae, the single filament arising from
the carpogonium grows back into the tissue and preys upon
the cells of the axis and larger branches, after which the
end-cells give rise to carpospores and a diffused cystocarp is
formed. In the whole group of the Cryptonemiales the
parasitism becomes more marked still. The filaments arising
from the carpogonia grow into long thin tubes, which fuse
with special cells rich in protoplasm contents; and from
these points issue isolated tufts of sporogenous filaments,
several of which may form the product of one fertilized female
cell. In Naccaria, one of the Gelidiaceae, it is observable
that the ooblastema filament, as the tube arising from the
fertilized carpogonium has been called, fuses completely with
a cell contiguous to the carpogonium before giving rise to
the foraging filaments already referred to. This is also
the case among Cryptonemiales. In a whole series of Red
Algae, the existence or a highly specialized auxiliary cell
in the neighbourhood of the carpogonium is a characteristic
feature. In the Gigartinales it is already differentiated
previous to fertilization; in Rhodymeniales it arises
subsequent to fertilization. In the Gigartinales, the
filaments which arise from the auxiliary cell may spread and
give rise to isolated tufts of sporogenous filaments, as in the
Cryptonemiales. In the Rhodymeniales a single tuft arises
directly from the auxiliary cell. The carpospores are in
all cases bright red naked masses of protoplasm when first
discharged. They soon acquire a cell-wall, and germinate
without a period of rest. When the cystocarps or segments
of cystocarps are formed in the substance of a thallus, the
site is marked merely by a swelling of the substance. When
the cystocarp is produced externally, it may form a berry-like
mass without an envelope, in which case it it known as a
favella. In Rhodomelaceae there is a special urn-shaped envelope
surrounding the sporogenous filaments. This is a ceramidium.
The attachment of the cell of an ooblastema filament to a
cell of the thallus may be effected by means of a minute
pore, or the two cells may fuse their contents into one
protoplasmic mass. In the latter case, and especially
where the union is with a special auxiliary cell, it is of
importance to know what happens to the nuclei of the fusing
cells. Schmitz was of opinion that in the cases of open
union there occurred a fusion of nuclei similar to that
which occurs in the sexual union of two cells. He founded
his generalization to a large extent upon the observation
that in Gloeosiphonia capillaris two cells completely
fuse, and that only one nucleus can be detecteo in the fused
mass. Oltmanns has recently re-investigated the phenomena in
this plant, among others, and has shown that the nucleus of
the cell which is being preyed upon recedes to the wall and
gradually atrophies. The nucleus of the ooblastema filament
dominates the FIG. 5.--Rhodophyceae, variously magnified.
A. Polysiphonia sp., apical region showing
leading cell and cutting off of pericentral cell.
B. Polysiphonia sp., transverse section through
a branch, and at a, mother-cell of tetraspores.
C. Lomeittaria sp., apex showing growth in length
through coordinated growth of many filaments.
D. Delesseria sp., showing apical region with leading cell.
E. Chrysymenia uvaria, axis with swollen leaf-like appendages.
F. Polyzonia sp., branch with leaf-like branches of limited growth.
G. Collithamnson sp., tetrasporangium with spores arranged in a tetrad.
H. Corallina sp., tetrasporangia with zonate arrangement of tetraspores.
K. Nemalion sp., carpogonial and antheridial branches.
L. Batrachospermum sp., trichogyne with spermatia
attached; carpospores arising from fertilized carpogonium.
M. Polysiphonia sp., antheridium.
N. Constantinea sp., with flattened leaf-like appendages.
O. Dudresnaya coccinea, fusion of ooblastema filaments with auxiliary
cells; a is an axial cell in transverse section with four appendages.
P. Callithamnion corymbosum, a joint cell with
carpogonial branch and a, b, two auxiliary cells.
Q. Callithamnion corymbosum, fusion of products of fertilization with
auxiliary cells, the nuclei of which a and b retire to the wall.
R. Polysiphonia sp., section through young cystocarp.
(A, C, D, E, F, G, H, K, L, M, P, Q, from Oltmanns,
by permission of Gustav Fischer; B, N, O, R, from
Engler and Prantl, by permission of Wilhelm Engelmann.)
mass and from it all the nuclei of the carpospores are thus
derived. There thus seems to be no justification for
believing, as Schmitz taught, that a second sexual
act occurs in the life-cycle of these Florideae.
The Bangiales are a relatively small group of Red Algae,
to which much of the description now given does not apply.
Structurally they are either a plate of cells, as in Porphyra, or
filaments, as in Bangia. There is no exclusive apical growth,
and the cells divide in all directions. The characteristic
pit is also absent. Sexual and asexual reproduction prevail.
The male cell is a spermatium, but the female cell bears no
such receptive trichogyne as occurs in other Rhodophyceae.
After fertilization the equivalent of the oospore divides
directly to form a group of carpospores. There is thus a
certain resemblance to Euflorideae, but sufficient difference
to necessitate their being grouped apart. Fertilization by
means of non-motile spermatia and a trichogyne are known among
the Fungi in the families Collemaceae any Laboulbeniaceae.
A census of Rhodophyceae is furnished below:--
(1) Bangiaceae--4 families, 9 genera, 58 species.
(2) Nemalioninae--4 families, 33 genera, 343 species.
(3) Gigartininae--3 families, 54 genera, 409 species.
(4) Rhodymeninae--4 families, 92 genera, 602
species. (De Toni's Sylloge Algarum, 1897.)
Limits of the algae.
After this survey of the four groups comprised under Algae
it is easier to indicate the variations in the limits of the
class as defined by different authorities. To consider the
Cyanophyceae first, either the marked contrast in the method of
nutrition of the generally colourless Bacteriaceae to that of
the blue-green Cyanophyceae is regarded as sufficient ground for
excluding Bacteriaceae from algae altogether, notwithstanding
their acknowledged morphological affinity with Cyanophyceae,
or, in recognition of the incongruity of effecting such a
separation, the whole group of the Schizophyta --that is to
say, the Cyanophyceae in the narrow sense, together with
Bacteriaceae, is included or excluded together. Again,
while Conjugatae may be shut out from Chlorophyceae as an
independent group co-ordinate with them in rank, the Characeae
constitute so aberrant a group that it has even been proposed
to raise them as Charophyta to the dignity of a main division
co-ordinate with Thallophyta. Similarly, while Diatomaceae
may be excluded from among Phaeophyceae, though retained among
algae, the Cryptomonadaceae and Peridiniaceae, like Euglena
and other Chlorophyceae, may be excluded from Thallophyta
and ranged among the flagellate Protozoa. It is doubtful,
however, whether the conventional distinction between plants
and animals will continue to be urged; and the suggestion of
Haeckel that a class Protista should be established to receive
the forms exhibiting both animal and plant affinities has much
to recommend it on phylogenetic grounds. To adopt a figure,
it is probable that the sources from which the two streams of
life--animal and vegetable--spring may not be separable by a
well-defined watershed at all, but consist of a great level
upland, in which the waterways anastomose. Finally, while
Chlorophyceae and Phaeophyceae exhibit important affinities,
the Rhodophyceae are so distinct that the term ``algae'' cannot
be made to include them, except when used in its widest sense.
Phylogeny.
It has been well said that the attempt to classify plants according
to their natural affinities is an attempt to construct for
them the genealogical tree by which their relationships can be
traced. Algae are, however, so heterogeneous a class, of
which the constituent groups are so inadequately known, that
it is at present futile to endeavour thus to exhibit their
pedigree. A synoptical representation of the present state
of knowledge would be expressed by a network rather than by a
tree. The following table is an adaptation of a scheme
devised by Klebs, and indicates the inter-relationships
PROTOZOA Peridiniaceae......Diatomaceae
| |
Cryptomonadaceae--Hydruraceae--EUPHAEOPHYCEAE
Flagellata
protomastigina......Bacteriaceae--Endosphaeraceae
|
CYANOPHYCEAE........Bangiacaeae--EUFLORIDEAE
Eugleneae
Chloromonadinae Pleurococcaceae--Endosphaeraceae
Volvocaceae Chlorosphaeraceae CONGUGATAE SIPHONALES
Tetrasporaceae----------Ulvaceae----------CONFERVALES......CHARACEAE
FUNGI BRYOPHYTA
of the various constituent groups. The area included in
the thick boundary line represents algae in the widest
sense in which the term is used, and the four included areas
the four main subdivisions. A continuous line indicates a
close affinity, and a dotted line a doubtful relationship.
Alternation of generations.
In comparing algae with the great archegoniate series which
has doubtless sprung from them, it is natural to inquire to
what extent, if any, they present evidence of the existence
of the marked alternation of generations which dominates
the life-history of the higher plants. Turning first to the
Rhodophyceae, both on account of the high place which they
occupy among algae and also the remarkable uniformity in their
reproductive processes, it is clear that, as is the case among
Archegoniatae, the product of the sexual act never germinates
directly into a plant which gives rise to the sexual organs.
Even among Bangiaceae the carpospores arise from the fertilized
cell by division, while in all other Rhodophyceae the oospore,
as it may be called, gives rise to a filamentous structure,
varying greatly in its dimensions, epiphytic, and to a large
extent parasitic upon the egg-bearing parent plant, and in the
end giving rise to carpospores in the terminal cells of certain
branches. There is here obviously a certain parallelism
with the case of Bryophyta, where the sporogonium arising
from the oospore is epiphytic and partially parasitic upon
the female plant, and always culminates in the production of
spores. Not even Riccia, with its rudimentary sporogonium,
has so simple a corresponding stage as Bangia, for, while
there is some amount of sterile tissue in Riccia, in Bangia
the oospore completely divides to form carpospores. Excluding
Bangiaceae, however, from consideration, the Euflorideae
present in the product of the development of the oospore like
Bryophyta a structure partly sterile and partly fertile. There
is, nevertheless, this important difference between the two
cases. While the spore of Bryophyta on germination gives rise
to the sexual plant, the carpospore of the alga may give rise
on germination to a plant bearing a second sort of asexual
cells, viz. the tetraspores, and the sexual plant may only be
reached after a series of such plants have been successively
generated. It is possible, however, that the tetraspore
formation should be regarded as comparable with the prolific
vegetative reproduction of Bryophyta, and in favour of this
view there is the fact that the tetraspores originate on the
thallus in a different way from carpospores with which the
spores of Bryophyta are in the first place to be compared;
moreover, in certain Nemalionales the production of tetraspores
does not occur, and the difficulty referred to does not arise
in such cases. Altogether it is difficult on morphological
grounds to resist the conclusion that Florideae present the
same fundamental phenomenon of alternation of generations
as prevails in the higher plants. It is by means of the
cytological evidence, however, that this problem will finally be
solved. As is well known, the dividing nuclei of the cells
of the sporophyte generation of the higher plants exhibit a
double number of chromosomes, while the dividing nuclei of
the cells of the gametophyte generation exhibit the single
number. In a fern-plant, for example, which is a sporophyte,
every karyokinesis divulges the double number, while in the
prothallium, which is the gametophyte generation, the single
number appears. The doubling process is provided by the
act of fertilization, where an antherozoid with the single
number of chromosomes fuses with an oosphere also with the
single number to provide a fertilized egg with the double
number. The reduction stage, on the other hand, is the
first division of the mother-cell of the spore. From egg to
spore-mother-cell is sporophyte; from spore-mother-cell to
egg is gametophyte. And since this rule has been found to
hold good for all the archegoniate series and also for the
flowering plants where, however, the gametophyte generation
has become so extremely reduced as to be only with difficulty
discerned, it is natural that when alternation of generation
is stated to occur in any group of Thallophyta it should be
required that the cytological evidence should support the
view. The genus Nemalion has been recently investigated by
Wolfe with the object of examining the cytological evidence.
He finds that eight chromosomes appear in karyokinesis in the
ordinary thallus cells, but sixteen in the gonimoblast filaments
derived from the fertilized carpogonium. Eight chromosomes
appear again in the ultimate divisions which give rise to the
carpospores. Upon the evidence it would seem therefore
that so far as Nemalion is concerned an alternation occurs
comparable with that existing in the lower Bryophyta where
the sporophyte is relatively small, being attached to and to
some extent parasitic upon the gametophyte. Nemalion is,
however, one of those Florideae in which tetraspores do not
occur. What is the case with those Florideae which have been
described as trioecious? If the sporophyte generation is confined
to the cystocarp, is the tetrasporiferous plant, as has been
suggested, merely a potential gametophyte reproducing by a
process analogous to the bud- formation of the Bryophyta? In
answer to this question a recent writer, Yamanouchi, states
in a preliminary communication that he has found that in
Polysiphonia violacea the germinating carpospores exhibit
forty chromosomes, and the germinating tetraspores twenty
chromosomes. From this it would seem that in this plant
reduction takes place in the tetraspore mother- cell, and that
the tetrasporiferous plants are sporophytes which alternate with
sexual plants. Novel as this result may seem, the tetraspores
of Florideae become hereby comparable with the tetraspores of
Dictyota, to which reference will be made hereafter. But it
is clear that it becomes on this view increasingly difficult
to explain the occasional occurrence of tetraspores on male,
female and monoecious plants or the role of the carpospores
in the life-cycle of Florideae. The results of future research
on the cytology of the group will be awaited with interest.
Among Phaeophyceae it is well known that the oospore of
Fucaceae germinates directly into the sexual plant, and there
is thus only one generation. Moreover, it is known that
the reduction in the number of chromosomes which occurs at
the initiation of the gametophyte generation in Pteridophyta
occurs in the culminating stage of Fucus, where the oogonium
is separated from the stalk-cell, so that unless it be
contended that the Fucus is really a sporophyte which does
not produce spores, and that the gametophyte is represented
merely by the oogonium and antheridium, there is no semblance
of alternation of generation in this case. The only case
among Phaeophyceae which has been considered to point to the
existence of such a phenomenon is Cutleria. Here the asexual
cells are borne upon the so-called Aglaozonia reptans and the
sexual cells upon the plants known as Cutleria. The spores
of the Aglaozonia form are known to give rise to sexual
plants, and the oospore of Cutleria has been observed to
grow into rudimentary Aglaozonia. Latterly, however, as the
result of the cytological investigations of Mottler and Lloyd
Williams, great advance has been made in our knowledge of the
conditions existing in Dictyota. Mottler first observed that
a reduction in the number takes place in the mother-cells of the
tetraspore. It will be remembered that, as in most Florideae,
the male, female and asexual plants are distinct in this
genus. Mottler's observation has been confirmed by Lloyd
Williams, who has shown, moreover, that the single number
occurs in germlings from the tetraspore, and also in the
adult stages of all sexual plants, while the double number
occurs in germlings from the oospore, and in adult stages of
all asexual plants. It is probable, therefore, that we have
here a sharp alternation of generations, both generations
being, however, precisely similar to the eye up to point of
reproduction. Among Chlorophyceae it is often the case that the
oospore on germination divides up directly to form a brood of
zoospores. In Coleochaete this seems to be preceded by the
formation of a minute parenchymatous mass, in each cell of which
a zoospore is produced. In Sphaeroplea it is only at this
stage that zoospores are formed at all; but in most cases, such
as Oedogogonium, Ulothrix, Coleochaete, similar zoospores
are produced again and again upon the thallus, and the product
of the oospore may be regarded as merely a first brood of a
series. It has been held by some, however, that the first
brood corresponds to the sporophyte generation of the higher
plants, and that the rest of the cycle is the gametophyte
generation. Were the case of Sphaeroplea to stand alone,
the phenomenon might perhaps be regarded as an alternation of
generations, but still only comparable with the case of Bangia,
and not the case of the Florideae. But it is difficult to
apply such a term at all to those cases in which there intervene
between the oospore and the next sexual stage a series of
generations, the zoospores of which are all precisely similar.
Polymorphism.
The difficulty of tracing the relationships of algae is largely
due to the inadequacy of our knowledge of the conditions
under which they pass through the crucial stages of their
life-cycle. Of the thousands of species which have been
distinguished, relatively few have been traced from spore
to spore, as the flowering plants have been observed from
seed to seed. The aquatic habit of most of the species
and the minute size of many of them are difficulties which
do not exist in the case of most seed-plants. From the
analogy of the higher plants observers have justly argued
that when they have seen and marked the characters of the
reproductive organs they have found the plant at the stage
when it exhibits its most noteworthy features, and they have
named and classified the species in accordance with these
observations. While even in such cases it is obvious that
interesting stages in the life of the plant may escape notice
altogether, in the cases of those plants the reproduction of
which is unknown, and which have been named and placed on the
analogy of the vegetative parts alone, there is considerable
danger that a plant may be named as a distinct species which
is only a stage in the life of another distinct and perhaps
already known species. To take an example, Lemanea and
Batrachospermum are Florideae which bear densely-whorled
branches, but which, on the germination of the carpospore,
give rise to a laxly-filamentous, somewhat irregularly-branched
plant, from which the ordinary sexual plants arise at a later
stage. This filamentous structure has been attributed to the
genus Chantransia, which it greatly resembles, especially
when, as is said to be the case in Batrachospermum, it
bears similar monospores. The true Chantransia, however,
bears its own sexual organs as well as monospores. To the
specific identity of Haplospora globosa and Scaphospora
speciosa, and of Cutleria muitifida and Aglaozonia
reptans, reference has already been made. Again, many Green
Algae--some unicellular, like Sphaerella and Chlamydomonas;
some colonial forms, like Volvox and Hormotila; some
even filamentous forms, like Ulothrix and Stigeoclonium--
are known to pass into a condition resembling that of a
Palmella, and might escape identification on this account.
It is, on the other hand, a danger in the opposite sense to
conclude that all Chantransia species are stages in the
life-cycle of other plants, and, similarly, that all irregular
colonial forms, like Palmella, represent phases in the life
of other Green Algae. Long ago Kutzing went so far as to
express the belief that the lower algae were all capable of
transformations into higher forms, even into moss-protonemata.
Later writers have also thought that in all four groups
of algae transformations of a most far-reaching character
occur. Thus Borzi finds that Protoderma viride passes
through a series of changes so varied that at different times
it presents the characters of twelve different genera. Chodat
does not find so general a polymorphism, but nevertheless
holds that Raphidium passes through stages represented by
Protococcus, Characium, Dactylococcus and Sciadium. Klebs
has, however, recently canvassed the conclusions of both
these investigators; and as the result of his own observations
declares that algae, so far from being as polymorphic as
they have been described, vary only within relatively narrow
limits, and present on the whole as great fixity as the higher
plants. It certainly supports his view to discover, on
subjecting to a careful investigation Botrydium granulatum,
a siphonaceous alga whose varied forms had been described
by J. Rostafinski and M. Woronin, that these authors had
included in the life-cycle stages of a second alga described
previously by Kutzing, and now described afresh by Klebs as
Protosiphon bolryoides. In Botrydium the chromatophores
are small, without pyrenoids, and oil-drops are present;
in Protosiphon the chromatophores form a net-work with
pyrenoids, and the contents include starch. Klebs insists
that the only solution of such problems is the subjection of
the algae in question to a rigorous method of pure culture.
It is interesting to learn that G. Senn, pursuing the methods
described by Klebs, has confirmed Chodat's observation of the
passage of Raphidium into a Dactylococcus-stage, although
he was unable to observe further metamorphosis. He has
also seen Pleurococcus viridis dividing so as to form a
filament, but has not succeeded in seeing the formation of
zoospores as described by Chodat. While, therefore, there is
much evidence of a negative character against the existence
of an extensive polymorphism among algae, some amount of
metamorphosis is known to occur. But until the conditions
under which a particular transformation takes place have
been ascertained and described, so that the observation
may be repeated by other investigators, scant credence is
likely to be given to the more extreme polymorphistic views.
Physiology.
In comparison with the higher plants, algae exhibit so much
simplicity of structure, while the conditions under which
they grow are so much more readily controlled, that they have
frequently been the subject of physiological investigation with
a view chiefly to the application of the results to the study
of the higher plants. (See PLANTS: Physiology of.) In the
literature of vegetable physiology there has thus accumulated
a great body of facts relating not only to the phenomena of
reproduction, but also to the nutrition of algae. With
reference to their chemical physiology, the gelatinization
of the cell-wall, which is so marked a feature, is doubtless
attributable to the occurrence along with cellulose of pectic
compounds. There is, however, considerable variation in
the nature of the membrane in different species; thus the
cell-wall of Gedogonium, treated with sulphuric acid and
iodine, turns a bright blue, while the colour is very faint
in the case of Spirogyra, the wall of which is said to
consist for the most part of pectose. While starch occurs
commonly as a cell-content in the majority of the Green
Algae no trace of it occurs in Vaucheria and some of its
allies, nor is it known in the whole of the Phaeophyceae and
Rhodophyceae. In certain Euphaeophyceae bodies built up of
concentric layers, and attached to the chromatophores, were
described by Schmitz as phaeophycean-starch; they do not,
however, give the ordinary starch reaction. Other granules,
easily mistaken for the ``starch'' granules, are also found in
the cells of Phaeophyceae; these possess a power of movement
apart from the protoplasm, and are considered to be vesicles
and to contain phloroglucin. The colourless granules of
Florideae, which are supposed to constitute the carbohydrate
reserve material, have been called floridean-starch. A white
efflorescence which appears on certain Brown Algae (Saccorhiza
bulbosa, Laminaria saccharina), when they are dried in
the air, is found to consist of mannite. Mucin is known in
the cell-sap of Acetabularia. Some Siphonales (Codium)
give rise to proteid crystalloids, and they are of constant
occurrence among Florideae. The presence of tannin has been
established in the case of a great number of freshwater algae.
Colouring matters.
By virtue of the possession of chlorophyll all algae are
capable of utilizing carbonic acid gas as a source of carbon
in the presence of sunlight. The presence of phycocyanin,
phycophaein and phycoerythrin considerably modifies the
absorption spectra for the plants in which they occur. Thus
in the case of phycoerythrin the maximum absorption, apart
from the great absorption at the blue end of the spectrum,
is not, as in the case where chlorophyll occurs alone, near
the Fraunhofer line B, but farther to the right beyond the
line D. By an ingenious method devised by Engelmann, it
may be shown that the greatest liberation of oxygen, and
consequently the greatest assimilation of carbon, occurs in
that region of the spectrum represented by the absorption
bands. In this connexion Pfeffer points out that the penetrating
power of light into a clear sea varies for light of different
colours. Thus red light is reduced to such an extent as
to be insufficient for growth at a depth of 34 metres,
yellow light at a depth of 177 metres and green light at 322
metres. It is thus an obvious advantage to Red Algae, which
flourish at considerable depths, to be able to utilize yellow
light rather than the red, which is extinguished so much
sooner. The experiment of Engelmann referred to deserves
to be mentioned here, if only in illustration of the use
to which algae have been put in the study of physiological
problems. Engelmann observed that certain bacteria were motile
only in the presence of oxygen, and that they retained their
motility in a microscopic preparation in the neighbourhood
of an algal filament when they had come to rest elsewhere
on account of the exhaustion of oxygen. After the bacteria
had all been brought to rest by being placed in the dark,
he threw a spectrum upon the filament, and observed in what
region the bacteria first regained their motility, owing to the
liberation of oxygen in the process of carbon-assimilation.
He found that these places corresponded closely with the
region of the absorption band for the algae under experiment.
Although algae generally are able to use carbonic acid gas
as a source of carbon, some algae, like certain of the higher
plants, are capable of utilizing organic compounds for this
purpose. Thus Spirogyra filaments, which have been
denuded of starch by being placed in the dark, form starch
in one day if they are placed in a 10 to 20% solution of
dextrose. According to T. Bokorny, moreover, it appears
that such filaments will yield starch from formaldehyde
when they are supplied with sodium oxymethyl sulphonate, a
salt which readily decomposes into formaldehyde and hydrogen
sodium sulphite, an observation which has been taken to
mean that formaldehyde is always a stage in the synthesis of
starch. With reference to the assimilation of nitrogen,
it would seem that algae, like other green plants, can
best use it when it is presented to them in the form of a
nitrate. Some algae, however, seem to flourish better
in the presence of organic compounds. In the case of
Scenedesmus acutus it is said that the alga is unable
to take up nitrogen in the form of a nitrate or ammoniacal
salt, and requires some such substance as an amide or a
peptone. On the other hand, it has been held by Bernhard
Frank and other observers that atmospheric nitrogen is fixed
by the agency of Green Algae in the soil: (For the remarkable
symbiotism between algae and fungi see FUNGI and LICHENS.)
Habitat.
Most algae, particularly Phaeophyceae and Rhodophyceae, spend
the whole of the life-cycle immersed in water. In the case of
the freshwater algae, however, belonging to the Chlorophyceae
and Cyanophyceae, although they required to be immersed during
the vegetative period, the reproductive cells are often capable
of resisting a considerable degree of desiccation, and in this
condition are dispersed through great distances by various
agencies. Again, as is well known, many species of marine
algae growing in the region between the limits of high and low
water are so constituted that they are exposed to the air twice
a day without injury. The occurrence of characteristic algae
at different levels constituting the zones to which reference
has already been made, is probably in part an expression of
the fact that different species vary in the capacity to resist
desiccation from exposure. Thus Laminaria digitata, which
characterizes the lowest zone, is only occasionally exposed at
all, and then only for short periods of time. On the other
hand, Pelvetia canaliculata, which marks the upper belt, is
exposed for longer periods, and during neap tides may not be
reached by the water for many days. Algae of more delicate
texture than either Fucaceae or Laminariaceae also occur in
the region exposed by the ebb of the tide, but these secure
their exemption from desiccation either by retaining water
in their meshes by capillary attraction, as in the case of
Pilayella, or by growing among the tangles of the larger
Fucaceae, as in the case of Polysiphonia fastigiata, or by
growing in dense masses on rocks, as in the case of Laurencia
pinnatifida. Such a species as Delesseria sanguinea or
Callophyllis laciniata would on the contrary run great risk
by exposure for even a short period. A few algae approach
the ordinary terrestrial plants in their capacity to live in
a sub-aerial habitat subject only to such occasional supphes
of water as is afforded by the rainfall. Of this nature are
some of the species of Vaucheria. A very few species, like
Chroolepus, which grows on rock surfaces, are comparable
with the land plants which have been termed xerophilous.
Plankton.
The great majority of the aquatic algae, both freshwater and
marine, are attached plants. Some, however, are wanderers,
either swimming actively with the aid of cilia, or floating
inertly as the result of a specific weight closely approaching
that of the medium. To the aggregate of such forms, both
animal and vegetable, the term plankton has been applied, and
the investigation of the vegetable plankton, both freshwater
and marine, has been pursued in recent times with energy and
success. The German Plankton Expedition of 1889 added greatly
to our knowledge of the floating vegetable life of the North
Atlantic Ocean, while many laboratories established on the
shores of inland seas and lakes have rendered a similar
service in the case of our freshwater phyto-plankton.
The quantitative estimate of the amount of this flora has
revealed its enormous aggregate amount and therefore its great
importance in the economy of oceanic and lacustrine animal
life. The organisms constituting this plankton are mostly
unicellular, often aggregated together in colonies, and the
remarkable structure which they exhibit has added a new chapter
to the story of adaptation to environment. The families
Diatomaceae, Peridiniaceae and Protococcaceae are best
represented in the pelagic plankton, while in addition the
Volvocaceae are an important element in freshwater plankton.
Benthos.
The great majority of algae, however, grow like land-plants
attached to a substratum, and to these the term benthos is
now generally applied. While the root of land-plants serves
for the double purpose of attachment and the supply of water,
it is attachment only that is usually sought in the case of
algae. Immersed as they usually are in a medium containing in
solution the inorganic substances which they require for their
nutrition, the absorption of these takes place throughout
their whole extent. The elaborate provision for the conduct
of water from part to part which has played so important
a role in the morphological development of land plants is
entirely wanting in algae, such conducting tissues as do
exist in the larger Phaeophyceae and Rhodophyceae serving
rather for the convection of elaborated organic substance, and
being thus comparable with the phloem of the higher plants.
The attachment organ of algae is thus more properly called
a holdfast, and is found to be of very varied structure.
It generally takes the form of a single flattened disc as
in the Fucaceae, or a group of finger- like processes as in
Laminariaceae, or a tuft of filaments as in many instances.
When the attachment is in sand or mud, it often simulates the
appearance of a true root as in Chara or Caulerpa. It is
clear that where the bottom of a lake or sea consists of oozy
mud or shifting sand, it is impossible for algae to secure a
foothold. Thus a rock emerging from a sandy beach may often
be observed to stand covered with vegetation like an oasis in a
desert. The rapidity with which walls, piles and pontoons--stone,
wood and iron--become covered with marine plants is well known,
while the discovery of some effective means of preventing
the fouling of the bottoms of ships by the growth of algae
would be hailed as a boon by shipowners. While rocks and
boulders are the favoured situation for the growth of marine
algae, those which readily disintegrate, like the coarser
sandstones, are naturally less favoured than the hard and
resistant. A large number of algae again live as epiphytes or
endophytes. In the case of the freshwater species the host-plants
are mostly species of aquatic Graminaceae, Naiadaceae or
Nymphaeaceae. In the case of marine algae, the hosts are
chiefly the larger Phaeophyceae and Rhodophyceae. A bed of
Zostera near the level of low water is, however, on the
British coast a favourite collecting ground for the smaller
red and brown epiphytes. Of endophytes a distinction must be
made between those which occupy the cell-wall only and those
which perforate the cells, bringing about their destruction.
There can be little doubt that in some cases the epiphytism
approaches parasitism. In one case described by Kuckuck the
chromaphores of the infesting algae are absent, a circumstance
which points to a complete parasitism. Allusion has already
been made to the peculiar habit of the shell-boring algae.
Habit.
In many algae certain branches of limited growth bear a remarkable
resemblance to leaves. The Characeae among freshwater algae
and the Sargassaceae among marine algae might be cited as
examples. Surveying the whole range of algae life, Oltmanns
distinguishes bush-forms, whip- forms, net-forms, leaf-forms,
sack-forms, dorsi-ventral forms, and cushions, plates and
crusts. The similarity of outline in many species to that
of trees and shrubs will strike any one who examines algae
mounted for the herbarium. Cladophora and Bryopsis among
monosiphonous forms, Chara, Polysiphonia, Ceramium and
Cystoseira among larger algae, are illustrations of this.
The whip-forms are represented by Spirogyra, Chaetomorpha,
Scytosiphon, Nemalion, Himanthalia and Chorda. Net-forms are
found in Hydrodictyon and Microdictyon. The leaf-forms are
very varied and owe their existence to the advantage accruing
from the exposure of a large surface to the influence of the
light. In some cases such as Delesseria, Neurymenia, Fucus,
Alaria, the leaf-like structure is provided with a strengthening
mid-rib, and when as in Delesseria it is also richly veined
the resemblance to the leaf of a flowering plant is striking.
Laminaria, Padina, Cutleria, Punctaria, Iridaea, Ulva,
Porphyra, are leaf-like with a rigidity varying from a fleshy
lamina to the thin and pliable. Agarum, Claudea and Struvea
are leaf-forms which are perforated like Aldrovanda among
flowering plants. Enteromorpha, Asperococcus and Adenocystis
are sack-forms. Dorsi-ventral algae are rare. Leveillea
jungermanneoides bears a remarkable resemblance to a leafy
liverwort. In the next group of forms the simplest are crusts
attached to the substratum throughout their extent, and growing
at the margin. Such are Myrionema, Ralfsia, Melobesia and
Hildebrandtia. Others are attached throughout their extent,
but also grow vertical filaments so as to form a velvety pile.
Such are Coleochaete, Ochlochaete, Elachistea, Ascocyclus and
Rhododermis. Peysonellia squamaria, Melobesia lichenoides,
Leathesia difformis are forms which are not attached
throughout but grow in plates like the foliaceous lichens.
Ecology.
When it is sought to consider algae with a view to the
correlation of the external form to the conditions of life,
a subject the study of which under the name of ecology has
been latterly pursued with great success among land plants,
it is difficult as yet to arrive at generalizations which are
trustworthy. Among land plants, as is well known, similarity
of environment has often called forth similar adaptations
among plants of widely separated families. The similarity
of certain xerophilous Euphorbiaceae to Cactaceae is a ready
illustration of this phenomenon. From what has been already
said it is evident that among algae also strikingly similar
forms exist in widely different groups. Instances might be
multiplied. Compare, for example, the blue-green Gloeocapsa
with the green Gloeocystis, the red Batrachospermum
with the green Draparnaldia, the red Corallina with the
green Cymopolia, the green Enteromorpha with the brown
Asperococcus, the green Ulva with the red Porphyra, the
red Nemalion with the brown Castagnea, and so on. But on
the one hand similar forms seem to grow often under different
conditions, while on the other hand different forms flourish
under the same conditions. The conceivable variations in the
conditions which would count in algal life are variations in
the chemical character of the water--whether fresh, brackish
or salt; or in the rate of movement of the water, whether
relatively quiet, or a stream or a surf; or in the degree of
illumination with the depth and transparency of the water.
But the laws which determine the associations of various
algae under one environment are as yet little understood. The
occurrence of a plentiful mucilage in many freshwater forms
is, however, doubtless a provision against desiccation on
exposure. The fine subdivision of filamentous and net-forms is
similarly a provision for easy access of water and light to all
parts. The calcareous deposits in Characeae, Corallinaceae
and Siphonaceae are at once a protection against attack and
a means of support. The whip-forms would seem to be designed
to resist injury from surf or current. The vesicles of
Fucaceae and Laminariaceae prevent the sinking of the bulkier
forms. But why certain Fucaceae favour certain zones in
the littoral region, why certain epiphytes are confined
to certain hosts, why Red and Brown Algae are not better
represented in fresh water Or Green Algae in salt,--these
are problems to which it is difficult to find a ready answer.
Uses.
Algae cannot be regarded as directly important in the
industries. On the coasts of Europe marine algae detached
by the autumnal gales are commonly carted on to the land as
a convenient manure. Porphyra laciniata and Rhodymenia
palmata are locally used as food, the latter being known as
dulse. Agar-agar is a gelatinous substance derived from an
eastern species of Gracilaria. The ash of seaweeds, known in
Scotland as kelp, and in Brittany as varec, was formerly used as a
source of iodine to a greater extent than is at present the case.
Occurence in the rocks.
Excepting where the thallus is impregnated with silica, as
in Diatomaceae, or carbonate of lime, as in Corallinaceae,
Characeae and some Siphonales, it is perhaps not surprising that
algae should not have been extensively preserved in the fossil
form. Considering, however, that it is generally believed
that Bryophyta and vascular plants are descended from an
algal ancestry, it is natural to suppose that, prior to the
luxuriant vegetable growths of the Carboniferous period,
there must have existed an age of algae. It was doubtless
this expectation that has led to the description of a number
of Silurian and Devonian remains as algae upon what is now
regarded as inadequate evidence. The geologic record is,
as perhaps is to be expected, exceedingly poor, except as
regards the calcareous Siphonales, which are well represented
at various horizons, from the Silurian to the Tertiary;
even the Diatomaceae, which are found in great quantities in
the Tertiary deposits, do not occur at all earlier than the
chalk. It is believed, however, that the Devonian fossil,
Nematophycus, is a Laminarian alga, but it is not until
the late Secondary and the Tertiary formations that fossil
remains of algae become frequent. (See PALAEOBOTANY.)
The subjoined list includes the larger standard works on
algae, together with a number of papers to which reference is
made in this article. For a detailed catalogue of Algological
literature, see the ``Bibliotheca Phycologica'' in de Tonii's
Syllope Algarum, vo1. i. (1889), with the addendum thereto
in vol. iv. (1897) of the same work. GENERAL.--J. G. Agardh,
Species, genera et ordines Algarum (vols. i-iii., Algernes
Systematik (Lund, 1872-1899); J. E. Areschoug, ``Observationes
Phycologicae,'' Nova Acta reg. soc. sci. Upsaliensis
(Upsala, 1866-1875); F. F. Blackman, ``The Primitive Algae
and the Flagellata,'' Ann. of Botany (vol. xiv., Oxford,
1900); E. Bornet and G. Thuret, Notes agologiques (fasc.
i.-ii., Paris, 1876-1880); P. A. Dangeard, ``Recherches sur
les algues inferieures,'' Ann. des sci. naturelles, Bot.
(vol. vii., Paris, 1888); A. Derbes and A. J. J. Solier,
Momoire de la physiologie des algues (Paris, 1856); J.
B. de Toni, Sylloge Algarum---vol. i. Chlorophyceae,
vol. ii. Bacillariaceae, vol. iii. Fucoideae, vol. iv.
Florideae (Padua, 1889-1900); P. Falkenberg, ``Die Algen
im weitesten Sinne,'' Schenk's Handbuch der Botanik (vol.
ii., 1882); W. G. Farlow, Morine Algae of New England
(Washington, 1881); W. H. Harvey, Phycologia Britannica (4
vols., London, 1846-1855); Nereis Boreali-Americana (3
pts., Washington, 1851-1858); Phycologia Australica (5
vols., London, 1858-1863); F. Hauck, ``Die Meeresalgen
Deutschlands und Osterrichs,'' Rabenhort's Kryptogamen-Flora
(Leipzig, 1885); F. R. Kjellman, The Algae of the Arctic Sea
(Stockholm, 1883); F. T. Kutzing, Tabulae Phycologicae (19
vols., Nordhausen, 1845-1869); P. Kuckuck, Beitrage zur
Kenntniss der Meercsalgen (Kiel and Leipzig, 1897-1899); G.
Murray, Phycological Memoirs (London, 1892-1895) Naegeli,
Die neueren Algensysteme (Zurich, 1847); F. Oltmanns,
Morphologie und Biologie der Algen (Jena, Band i. 1904,
Band ii. 1905); N. Pringsheim, ``Beitrage zur Morphologie
der Meeresalgen,'' Abhand. Konigl. Akad. der Wissensch.
(Berlin, 1862); J. Reinke, Atlas deutscher Meeresalgen
(Berlin, 1889-1892); F. Schutt, Das Pflanzenleben der
Hochsee (Leipzig, 1893); J. Stackhouse, Nereis britannica
(ed. i., Bath, 1801; ed. ii., Oxford, 1816); G. Thuret and E.
Bornet, Etudes phycologiques (Paris, 1878); D. Turner,
Historia Fucorum (4 vols., London, 1808-1819); G. Zanardini,
Iconographia Phycologia Adriatica (Venice, 1860-1876).
1. CYANOPHYCEAE.--E. Bornet and Ch. Flahault, ``Revision
des Nostocacees heterocystees,'' Ann. des sc.
naturelles, Bot.(vols. iii.-vii., Paris, 1887-1888); M.
Gomont, ``Monographic des Oscillariees,'' Ann. des sc.
naturelles, Bot. (vols. xv.-xvi., Paris, 1893); Hegler,
``Uber Kerntheilungserscheinungen,'' Ref. Botan. Centralbl.
(vol. lxiv., Cassel, 1895); O. Kirchner, ``Schizophyceae'',
in Engler and Prantl's Pflanzenfamilien (Leipzig, 1900).
2. CHLOROPHYCEAE.--A. Borzi, ``Studi anamorfici di alcune
alghe verdi,'' Bull. Soc. Bot. Ital. in N. Giorn. Bot.
Ital. (vol. xxii., Pisa, 1890); F. F. Blackman and A. G.
Tansley, A Revision of the Classification of the Green
Algae, reprinted from the New Phytologist (vol. i., London,
1903); K. Bohlin, ``Studier ofver nagra slagten af alggruppen
confervales Borzi,'' Bihang till K. Svenska vel. akad.
Handlinger (Bd. xxiii. afd. 3, 1897);--Ufkasttill, De grona
algernas och arkegomiaternas bylogeni (Upsala, 1901); R.
Chodat, ``On the Polymorphism of the Green Algae,'' Ann.
of Botany (vol. xi., Oxford, 1897); M. C. Cooke, British
Freshwater Algae (2 vols., London, 1884), British Desmids
(London, 1887); G. Klebs, Die Bedingungen der Fortpflanzung
bei einigen Algen und Pilzen (Jena, 1896); A. Luther, ``Uber
Chlorosaccus, n.g.'' Bihang till K. Svenska vel. akad.
Handlinger (Bd. xxiv. afd. 3, 1899); H. Grat zu Solms-Laubach,
``Monograph of the Acetabulariaceae,'' Trans. Linn. Soc.
(Lond.) Bot. (London, 1895); N. Wille, ``Chlorophyceae'',
in Engler and Prantl's Pflanzenfamilien (Leipzig, 1897).
3. PHAEOPHYCEAE.--E. A. L. Batters, ``On Ectocarpus secundus,''
Grevillea (vol. xxi., London, 1893); G. Berthold, ``Die
geschlechliche Fortpflanzung der eigentlichen Phaeosooreen,''
Mitth. Zool. Stat. Neapel (vol. ii., Leipzig, 1881); G.
Brebner, ``On the Classification of the Tilopteridaceae,''
Proc. Bristol Nat. Soc. (vol. viii., Bristol, 1896-1897);
A. H. Church, ``On the Polymorphy of Cutleria multiflda,''
Ann. of Botany (vol. xii., Oxford, 1898); J. B. Farmer
esnd J. Ll. Williams, ``Contributions to our Knowledge
of the Life- history and Cytology of Fucaceae,'' Phil.
Trans. Roy. Soc. (vol. cxc., London, 1898); E. Janczewski,
``Observations sur l'accroissement du thalle des Phaeosporees,''
Mem. soc. nat. de sc. (Cherbourg, 1895); F. R. Kjellmann,
``Phaeophyceae,'' in Engler and Prantl's Pflanzenfamilian
(Leipzig, 1897); F. Oltmanns, ``Beitrage zur Kenntniss der
Fucaceen,'' Bibliotheca botanica, xiv. (Cassel, 1889); C.
Sauvageau, ``Observations relatives a la sexualite des
Phaeosporees,'' Journal de botanique (vol. x., Paris,
1896); E. Strasburger, ``Kerntheilung und Befruchtung bei
Fucus,'' Cytologische Studien (Berlin, 1897); F. Schutt,
Die Peridinien der Plankton-Expedition (Kiel and Leipzig,
1895); R. Valiante, Le Cystoseirae del Golfo di Napoli
(Leipzig, 1883); J. Ll. Williams, ``On the Antherozoids of
Dictyota and Taonia,'' Ann. of Botany (vol. xi., Oxford, 1897).
4. RHODOPHYCEAE.--G. Berthold, ``Die Bangiacen des Golfes
von Neapel,'' Mitth. Zool. Stat. Neapel (Naples, 1882);
F. Oltmanns, ``Zur Entwickelungsgeschichte der Florideen,''
Botanische Zeitung (1898); R. W. Philligs, ``The Development
of the Cystocarp in Rhodymeniales,'' i. and ii., Annals
of Botany (vols. xi. xii., Oxford. 1897-1898); F. Schmitz,
``Untersuchungen uber die Befruchtung der Florideen,''
Sitzungsber. der konigl. Akad.der Wissensch. (Berlin,
1883); ``Kleinere Beitrage zur Kenntniss der Florideen,''
La Nuova Notarisia, 1892-1894; F. Schmitz, P. Falkenberg,
P. Hauptfleisch, ``Rhodophyceae,'' in Engler and Prantl's
Pflanzenfamilien (1897); W. Schmidle, ``Die Befruchtung,
Keimung und Haarinsertion von Batrachospermum,'' Bot.
Zeitung.. (1899); Sirodot, Les Batrachospermes (Paris,
1884); N. Wille, ``Uber die Befruchtung bei Nemalion
multifidum,'' Ber. d. deutschen bot. Gesellsc. Band
xii. (Berlin, 1894); J. J. Wolfe, ``Cytological Studies on
Nemalion,'' Annals of Botany (vol. xviii., Oxford, 1904);
S. Yamanouchi, ``The Life- History of Polysiphonia violacea,''
Botanical Gazette (vol. xli., Chicago, 1906). (R. W. P.)
ALGARDI, ALESSANDRO (1602-1654), Italian sculptor, was born
at Bologna in 1602. While he was attending the school of the
Caracci his preference for the plastic art became evident,
and he placed himself under the instruction of the sculptor
Conventi. At the age of twenty he was brought under the
notice of Duke Ferdinand of Mantua, who gave him several
commissions. He was also much employed about the same period
by jewellers and others in modelling in gold, silver and
ivory. After a short residence in Venice he went to Rome in
1625 with an introduction from the duke of Mantua to the pope's
nephew, Cardinal Ludovisi, who employed him for a time in
the restoration of ancient statues. The death of the duke of
Mantua left him to his own resources, and for several years
he earned a precarious maintenance from these restorations
and the commissions of goldsmiths and jewellers. In 1640 he
executed for Pietro Buoncompagni his first work in marble, a
colossal statue of San Filippo Neri, with kneeling angels.
Immediately after, he produced a similar group, representing
the execution of St Paul, for the church of the Barnabite
Fathers in Bologna. These works, displaying great technical
skill, though with considerable exaggeration of expression
and attitude, at once established Algardi's reputation, and
other commissions followed in rapid succession. The turning
point in Algardi's fortune was the accession of Innocent
X., of the Bolognese house of Panfili, to the papal throne in
1644. He was employed by Camino Panfili, nephew of the pontiff,
to design the Villa Doria Panfili outside the San Pancrazio
gate. The most important of Algardi's other works were the
monument of Leo XI., a bronze statue of Innocent X. for the
capitol, and, above all, La Fuega d'Attila, the largest
alto-relievo in the world, the two principal figures being
about 10 ft. high. In 1650 Algardi met Velasquez, who
obtained some interesting orders for his Italian companion in
Spain. Thus there are four chimneys by Algardi in the palace
of Aranjuez, where also the figures on the fountain of Neptune
were executed by him. The Augustine monastery at Salamanca
contains the tomb of the count and countess de Monterey, which
was also the work of Algardi. From an artistic point of view,
he was most successful in his portrait-statues and groups of
children, where he was obliged to follow nature most closely.
In his later years he became very avaricious and amassed a
great fortune. He died in Rome on the 10th of June 1654.
See Le arti di Bologna disegnate da A. Caracci ed intagliati da
S. Giulini, con' assistenza d' Alessandro A. Algardi (1740).
ALGAROTH, POWDER OF, a basic chloride of antimony. It was
known to Basil Valentine, and was used medicinally by the
Veronese physician Victor Algarotus about the end of the 16th
century. Its composition is probably Sb4O5Cl2, and it may be
prepared by the addition of much water to a solution of antimony
chloride; a bulky amorphous precipitate being formed, which,
on standing, gradually becomes crystalline. It is soluble in
hydrochloric acid and tartaric acid, but insoluble in alcohol.
On its composition and preparation see E. Peligot, Annalen,
1847, lxiv. 280; L. Schaffer, Annalen, 1869, clii. 314;
and R. W. E. MacIvor, Chem. News, 1875, xxxii. 229.
ALGAROTTI, FRANCESCO, COUNT (1712-1764), Italian philosopher
and writer on art, was born on the 11th of December 1712 at
Venice, and died at Pisa in 1764. He studied at Rome and
Bologna, and at the age of twenty went to Paris, where
he enjoyed the friendship of Voltaire and produced his
great work Neutonianismo per le dame, a work on optics.
Voltaire called him his cher cygne de Padoue. Returning
from a journey to Russia, he met Frederick the Great who
made him a count of Prussia (1740) and court chamberlain
(1747). Augustus III. of Poland honoured him with the title of
councillor. In 1754, after seven years' residence partly in
Berlin and partly in Dresden, he returned to Italy, living
at Venice and then at Pisa, where he died on the 3rd of May
1764. Frederick the Great erected to his memory a monument
on the Campo Santo at Pisa. He was a man of wide knowledge,
a connoisseur in art and music, and the friend of most of
the leading authors of his time. His chief work on art
is the Saggi sopra le belle arti (``Essays on the Fine
Arts''). Among his other works may be mentioned Poems,
Travels in Russia, Essay on Painting, Correspondence.
The best complete edition with biography
was published by D. Michelessi (1791-1794).
ALGARVE, or ALGARVES, an ancient kingdom and province
in the extreme S. of Portugal, corresponding with the modern
administrative district of Faro, and bounded on the N. by
Alemtejo, E. by the Spanish province of Huelva, and S. and W.
by the Atlantic Ocean. Pop. (1900) 255,191; area, 1937 sq.
m. The greatest length of the province is about 85 m. from
E. to W.; its average breadth is about 22 m. from N. to S.
The Serra de Malhao and the Serra de Monchique extend in the
form of a crescent across the northern part of the province,
and, sweeping to the south-west, terminate in the lofty
promontory of Cape St Vincent, the south-west extremity of
Europe. This headland is famous as the scene of many
sea-fights, notably the defeat inflicted on the Spanish
fleet in February 1797 by the British under Admiral Jervis,
afterwards Earl St Vincent. Between the mountainous tracts
in the north and the southern coast stretches a narrow
plain, watered by numerous rivers flowing southward from the
hills. The coast is fringed for 30 m. from Quarteira to
Tavira, with long sandy islands, through which there are six
passages, the most important being the Barra Nova, between Faro
and Olinao. The navigable estuary of the Guadiana divides
Algarve from Huelva, and its tributaries water the western
districts. From the Serra de Malhao flow two streams, the
Silves and Odelouca, which unite and enter the Atlantic below
the town of Silves. In the hilly districts the roads are
bad, the soil unsuited for cultivation, and the inhabitants
few. Flocks of goats are reared on the mountain-sides. The
level country along the southern coast is more fertile, and
produces in abundance grapes, figs, oranges, lemons, olives,
almonds, aloes, and even plantains and dates. The land is,
however, not well suited for the production of cereals, which
are mostly imported from Spain. On the coast the people
gain their living in great measure from the fisheries, tunny
and sardines being caught in considerable quantities. Salt
is also made from sea-water. There is no manufacturing or
mining industry of any importance. The harbours are bad, and
almost the whole foreign trade is carried on by ships of other
nations, although the inhabitants of Algarve are reputed to be
the best seamen and fishermen of Portugal. The chief exports
are dried fruit, wine, salt, tunny, sardines and anchovies.
The only railway is the Lisbon-Faro main line, which passes
north-eastward from Faro, between the Monchique and Malhao
ranges. Faro (11,789), Lagos (8291), Loule (22,478),
Monchique (7345), Olhao (10,009), Silves (9687) and Tavira
(12,175), the chief towns, are described in separate articles.
The name of Algarve is derived from the Arabic, and signifies
a land lying to the west. The title ``king of Algarve,''
held by the kings of Portugal, was first assumed by
Alphonso III., who captured Algarve from the Moors in 1253.
ALGAU, or ALLGAU, the name now given to a comparatively
small district forming the south-western corner of Bavaria,
and belonging to the province of Swabia and Neuburg, but
formerly applied to a much larger territory, which extended
as far as the Danube on the N., the Inn on the S. and the Lech
on the W. The Algau Alps contain several lofty peaks, the
highest of which is Madelegabel (8681 ft.). The district
is celebrated for its cattle, milk, butter and cheese.
ALGEBRA (from the Arab. af-jebr wa'l-muqabala, transposition
and removal [of terms of an equation], the name of a treatise by
Mahommed ben Musa al-Khwarizmi), a branch of mathematics which
may be defined as the generalization and extension of arithmetic.
The subject-matter of algebra will be treated in the following
article under three divisions:---A. Principles of ordinary
algebra; B. Special kinds of algebra; C. History. Special
phases of the subject are treated under their own headings,
e.g. ALGEBRAIC FORMS; BINOMIAL; COMBINATORIAL ANALYSIS;
DETERMINANTS; EQUATION; CONTINUED FRACTION; FUNCTION;
GROUPS, THEORY OF; LOGARITHM; NUMBER; PROBABILITY; SERIES.
A. PRINCIPLES OF ORDINARY ALGEBRA
1. The above definition gives only a partial view of the scope of
algebra. It may be regarded as based on arithmetic, or as
dealing in the first instance with formal results of the laws
of arithmetical number; and in this sense Sir Isaac Newton
gave the title Universal Arithmetic to a work on algebra.
Any definition, however, must have reference to the state of
development of the subject at the time when the definition is given.
2. The earliest algebra consists in the solution of equations.
The distinction between algebraical and arithmetical reasoning
then lies mainly in the fact that the former is in a more
condensed form than the latter; an unknown quantity being
represented by a special symbol, and other symbols being
used as a kind of shorthand for verbal expressions. This
form of algebra was extensively studied in ancient Egypt;
but, in accordance with the practical tendency of the
Egyptian mind, the study consisted largely in the treatment
of particular cases, very few general rules being obtained.
3. For many centuries algebra was confined almost entirely
to the solution of equations; one of the most important
steps being the enunciation by Diophantus of Alexandria of
the laws governing the use of the minus sign. The knowledge
of these laws, however, does not imply the existence of a
conception of negative quantities. The development of symbolic
algebra by the use of general symbols to denote numbers is
due to Franciscus Vieta (Francois Viete, 1540-1603).This
led to the idea of algebra as generalized arithmetic.
4. The principal step in the modern development of algebra was
the recognition of the meaning of negative quantities. This
appears to have been due in the first instance to Albert Girard
(1595-1632), who extended Vieta's results in various branches of
mathematics. His work, however, was little known at the time, and
later was overshadowed by the greater work of Descartes (1596-1650).
5. The main work of Descartes, so far as algebra was concerned,
was the establishment of a relation between arithmetical
and geometrical measurement. This involved not only the
geometrical interpretation of negative quantities, but also the
idea of continuity; this latter, which is the basis of modern
analysis, leading to two separate but allied developments,
viz. the theory of the function and the theory of limits.
6. The great development of all branches of mathematics in
the two centuries following Descartes has led to the term
algebra being used to cover a great variety of subjects, many
of which are really only ramifications of arithmetic, dealt
with by algebraical methods, while others, such as the theory
of numbers and the general theory of series, are outgrowths
of the application of algebra to arithmetic, which involve
such special ideas that they must properly be regarded as
distinct subjects. Some writers have attempted unification
by treating algebra as concerned with functions, and Comte
accordingly defined algebra as the calculus of functions,
arithmetic being regarded as the calculus of values.
7. These attempts at the unification of algebra, and its
separation from other branches of mathematics, have usually
been accompanied by an attempt to base it, as a deductive
science, on certain fundamental laws or general rules; and
this has tended to increase its difficulty. In reality, the
variety of algebra corresponds to the variety of phenomena.
Neither mathematics itself, nor any branch or set of branches of
mathematics, can be regarded as an isolated science. While,
therefore, the logical development of algebraic reasoning must
depend on certain fundamental relations, it is important that
in the early study of the subject these relations should be
introduced gradually, and not until there is some empirical
acquaintance with the phenomena with which they are concerned.
8. The extension of the range of subjects to which mathematical
methods can be applied, accompanied as it is by an extension
of the range of study which is useful to the ordinary
worker, has led in the latter part of the 19th century to an
important reaction against the specialization mentioned in
the preceding paragraph. This reaction has taken the form
of a return to the alliance between algebra and geometry
(\S 5), on which modern analytical geometry is based; the
alliance, however, being concerned with the application of
graphical methods to particular cases rather than to general
expressions. These applications are sometimes treated under
arithmetic, sometimes under algebra; but it is more convenient
to regard graphics as a separate subject, closely allied to
arithmetic, algebra, mensuration and analytical geometry.
9. The association of algebra with arithmetic on the one
hand, and with geometry on the other, presents difficulties,
in that geometrical measurement is based essentially on the
idea of continuity, while arithmetical measurement is based
essentially on the idea of discontinuity; both ideas being
equally matters of intuition. The difficulty first arises in
elementary mensuration, where it is partly met by associating
arithmetical and geometrical measurement with the cardinal and
the ordinal aspects of number respectively (see ARITHMETIC.)
Later, the difficulty recurs in an acute form in reference
to the continuous variation of a function. Reference to a
geometrical interpretation seems at first sight to throw light
on the meaning of a differential coefficient; but closer analysis
reveals new difficulties, due to the geometrical interpretation
itself. One of the most recent developments of algebra is
the algebraic theory at number, which is devised with the
view of removing these difficulties. The harmony between
arithmetical and geometrical measurement, which was disturbed
by the Greek geometers on the discovery of irrational numbers,
is restored by an unlimited supply of the causes of disturbance.
10. Two other developments of algebra are of special
importance. The theory of sequences and series is sometimes
treated as a part of elementary algebra; but it is more
convenient to regard the simpler cases as isolated examples,
leading up to the general theory. The treatment of equations
of the second and higher degrees introduces imaginary and
complex numbers, the theory of which is a special subject.
11. One of the most difficult questions for the teacher of
algebra is the stage at which, and the extent to which, the
ideas of a negative number and of continuity may be introduced.
On the one hand, the modern developments of algebra began
with these ideas, and particularly with the idea of a negative
number. On the other hand, the lateness of occurrence of any
particular mathematical idea is usually closely correlated
with its intrinsic difficulty. Moreover, the ideas which
are usually formed on these points at an early stage are
incomplete; and, if the incompleteness of an idea is not
realized, operations in which it is implied are apt to be purely
formal and mechanical. What are called negative numbers in
arithmetic, for instance, are not really negative numbers but
negative quantities (\S 27 (i.)); and the difficulties incident
to the ideas of continuity have already been pointed out.
12. In the present article, therefore, the main portions of
elementary algebra are treated in one section, without reference
to these ideas, which are considered generally in two separate
sections. These three sections may therefore be regarded as to
a certain extent concurrent. They are preceded by two sections
dealing with the introduction to algebra from the arithmetical
and the graphical sides, and are followed by a section dealing
briefly with the developments mentioned in \S \S 9 and 10 above.
[The intermediate portion of this article is typeset in TeX and
is available elsewhere.]
C. HISTORY Various derivations of the word ``algebra,''
which is of Arabian origin, have been given by different
writers. The first mention of the word is to be found in the
title of a work by Mahommed ben Musa al-Khwarizmi (Hovarezmi),
who flourished about the beginning of the 9th century. The
full title is ilm al-jebr wa'l-muqabala, which contains
the ideas of restitution and comparison, or opposition and
comparison, or resolution and equation, jebr being derived
from the verb jabara, to reunite, and muqabala, from
gabala, to make equal. (The root jabara is also met with
in the word algebrista, which means a ``bone-setter,''
and is still in common use in Spain.) The same derivation is
given by Lucas Paciolus (Luca Pacioli), who reproduces the
phrase in the transliterated form alghebra e almucabala,
and ascribes the invention of the art to the Arabians.
Other writers have derived the word from the Arabic
particle al (the definite article), and gerber, meaning
``man.'' Since, however, Geber happened to be the name of
a celebrated Moorish philosopher who flourished in about
the 11th or 12th century, it has been supposed that he was
the founder of algebra, which has since perpetuated his
name. The evidence of Peter Ramus (1515-1572) on this point
is interesting, but he gives no authority for his singular
statements. In the preface to his Arithmeticae libri duo
et totidem Algebrae (1560) he says: ``The name Algebra
is Syriac, signifying the art or doctrine of an excellent
man. For Geber, in Syriac, is a name applied to men, and
is sometimes a term of honour, as master or doctor among
us. There was a certain learned mathematician who sent his
algebra, written in the Syriac language, to Alexander the
Great, and he named it almucabala, that is, the book of
dark or mysterious things, which others would rather call
the doctrine of algebra. To this day the same book is in
great estimation among the learned in the oriental nations,
and by the Indians, who cultivate this art, it is called
aljabra and alboret; though the name of the author
himself is not known.,' The uncertain authority of these
statements, and the plausibility of the preceding explanation,
have caused philologists to accept the derivation from al
and jabara. Robert Recorde in his Whetstone of Witte
(1557) uses the variant algeber, while John Dee (1527-1608)
affirms that algiebar, and not algebra, is the correct
form, and appeals to the authority of the Arabian Avicenna.
Although the term ``algebra'' is now in universal use, various
other appellations were used by the Italian mathematicians
during the Renaissance. Thus we find Paciolus calling it
l'Arte Magiore; ditta dal vulgo la Regula de la Cosa
over Alghebra e Almucabala. The name l'arte magiore,
the greater art, is designed to distinguish it from l'arte
minore, the lesser art, a term which he applied to the
modern arithmetic. His second variant, la regula de la
cosa, the rule of the thing or unknown quantity, appears
to have been in common use in Italy, and the word cosa
was preserved for several centuries in the forms coss or
algebra, cossic or algebraic, cossist or algebraist, &c.
Other Italian writers termed it the Regula rei et census,
the rule of the thing and the product, or the root and the
square. The principle underlying this expression is probably
to be found in the fact that it measured the limits of
their attainments in algebra, for they were unable to solve
equations of a higher degree than the quadratic or square.
Franciscus Vieta (Francois Viete) named it Specious
Arithmetic, on account of the species of the quantities
involved, which he represented symbolically by the various
letters of the alphabet. Sir Isaac Newton introduced the term
Universal Arithmetic, since it is concerned with the doctrine
of operations, not affected on numbers, but on general symbols.
Notwithstanding these and other idiosyncratic appellations,
European mathematicians have adhered to the older
name, by which the subject is now universally known.
It is difficult to assign the invention of any art or science
definitely to any particular age or race. The few fragmentary
records, which have come down to us from past civilizations,
must not be regarded as representing the totality of their
knowledge, and the omission of a science or art does not
necessarily imply that the science or art was unknown. It was
formerly the custom to assign the invention of algebra to the
Greeks, but since the decipherment of the Rhind papyrus
by Eisenlohr this view has changed, for in this work there
are distinct signs of an algebraic analysis. The particular
problem---a heap (hau) and its seventh makes 19---is solved
as we should now solve a simple equation; but Ahmes varies his
methods in other similar problems. This discovery carries the
invention of algebra back to about 1700 B.C., if not earlier.
It is probable that the algebra of the Egyptians was of
a most rudimentary nature, for otherwise we should expect
to find traces of it in the works of the Greek aeometers.
of whom Thales of Miletus (640-546 B.C.) was the first.
Notwithstanding the prolixity of writers and the number of the
writings, all attempts at extracting an algebraic analysis
from their geometrical theorems and problems have been
fruitless, and it is generally conceded that their analysis
was geometrical and had little or no affinity to algebra. The
first extant work which approaches to a treatise on algebra
is by Diophantus (q.v.), an Alexandrian mathematician, who
flourished about A.D. 350. The original, which consisted
of a preface and thirteen books, is now lost, but we have a
Latin translation of the first six books and a fragment of
another on polygonal numbers by Xylander of Augsburg (1575),
and Latin and Greek translations by Gaspar Bachet de Merizac
(1621-1670). Other editions have been published, of which
we may mention Pierre Fermat's (1670), T. L. Heath's (1885)
and P. Tannery's (1893-1895). In the preface to this work,
which is dedicated to one Dionysius, Diophantus explains his
notation, naming the square, cube and fourth powers, dynamis,
cubus, dynamodinimus, and so on, according to the sum in
the indices. The unknown he terms arithmos, the number,
and in solutions he marks it by the final s; he explains
the generation of powers, the rules for multiplication and
division of simple quantities, but he does not treat of the
addition, subtraction, multiplication and division of compound
quantities. He then proceeds to discuss various artifices
for the simplification of equations, giving methods which
are still in common use. In the body of the work he displays
considerable ingenuity in reducing his problems to simple
equations, which admit either of direct solution, or fall
into the class known as indeterminate equations. This latter
class he discussed so assiduously that they are often known as
Diophantine problems, and the methods of resolving them as
the Diophantine analysis (see EQUATION, Indeterminate.)
It is difficult to believe that this work of Diophantus
arose spontaneously in a period of general stagnation. It
is more than likely that he was indebted to earlier writers,
whom he omits to mention, and whose works are now lost;
nevertheless, but for this work, we should be led to assume
that algebra was almost, if not entirely, unknown to the Greeks.
The Romans, who succeeded the Greeks as the chief
civilized power in Europe, failed to set store on their
literary and scientific treasures; mathematics was all but
neglected; and beyond a few improvements in arithmetical
computations, there are no material advances to be recorded.
In the chronological development of our subject we have now to
turn to the Orient. Investigation of the writings of Indian
mathematicians has exhibited a fundamental distinction between
the Greek and Indian mind, the former being pre-eminently
geometrical and speculative, the latter arithmetical and mainly
practical. We find that geometry was neglected except in so far
as it was of service to astronomy; trigonometry was advanced,
and algebra improved far beyond the attainments of Diophantus.
The earliest Indian mathematician of whom we have certain
knowledge is Aryabhatta, who flourished about the beginning
of the 6th century of our era. The fame of this astronomer
and mathematician rests on his work, the Aryabhattiyam, the
third chapter of which is devoted to mathematics. Ganessa, an
eminent astronomer, mathematician and scholiast of Bhaskara,
quotes this work and makes separate mention of the cuttaca
(``pulveriser''), a device for effecting the solution of
indeterminate equations. Henry Thomas Colebrooke, one of the
earliest modern investigators of Hindu science, presumes that
the treatise of Aryabhatta extended to determinate quadratic
equations, indeterminate equations of the first degree, and
probably of the second. An astronomical work, called the
Surya-siddhanta (``knowledge of the Sun''), of uncertain
authorship and probably belonging to the 4th or 5th century,
was considered of great merit by the Hindus, who ranked it
only second to the work of Brahmagupta, who flourished about
a century later. It is of great interest to the historical
student, for it exhibits the influence of Greek science upon
Indian mathematics at a period prior to Aryabhatta. After an
interval of about a century, during which mathematics attained
its highest level, there flourished Brahmagupta (b. A.D. 598),
whose work entitled Brahma-sphuta-siddhanta (``The revised
system of Brahma'') contains several chapters devoted to
mathematics. Of other Indian writers mention may be made of
Cridhara, the author of a Ganita-sara (``Quintessence of
Calculation''), and Padmanabha, the author of an algebra.
A period of mathematical stagnation then appears to have
possessed the Indian mind for an interval of several centuries,
for the works of the next author of any moment stand but little
in advance of Brahmagupta. We refer to Bhaskara Acarya, whose
work the Siddhanta-ciromani (``Diadem of anastronomical
System''), written in 1150, contains two important chapters, the
Lilavati (``the beautiful [science or art]'') and Viga-ganita
(``root-extraction''), which are given up to arithmetic and algebra.
English translations of the mathematical chapters of the
Brahma-siddhanta and Siddhanta-ciromani by H. T. Colebrooke
(1817), and of the Surya-siddhanta by E. Burgess, with
annotations by W. D. Whitney (1860), may be consulted for details.
The question as to whether the Greeks borrowed their algebra
from the Hindus or vice versa has been the subject of much
discussion. There is no doubt that there was a constant traffic
between Greece and India, and it is more than probable that an
exchange of produce would be accompanied by a transference of
ideas. Moritz Cantor suspects the influence of Diophantine
methods, more particularly in the Hindu solutions of indeterminate
equations, where certain technical terms are, in all probability,
of Greek origin. However this may be, it is certain that
the Hindu algebraists were far in advance of Diophantus. The
deficiencies of the Greek symbolism were partially remedied;
subtraction was denoted by placing a dot over the subtrahend;
multiplication, by placing bha (an abbreviation of bhavita,
the ``product'') after the factom; division, by placing the
divisor under the dividend; and square root, by inserting
ka (an abbreviation of karana, irrational) before the
quantity. The unknown was called yavattavat, and if there
were several, the first took this appellation, and the others
were designated by the names of colours; for instance, x
was denoted by ya and y by ka (from kalaka, black).
A notable improvement on the ideas of Diophantus is to be found
in the fact that the Hindus recognized the existence of two roots
of a quadratic equation, but the negative roots were considered
to be inadequate, since no interpretation could be found for
them. It is also supposed that they anticipated discoveries
of the solutions of higher equations. Great advances were
made in the study of indeterminate equations, a branch of
analysis in which Diophantus excelled. But whereas Diophantus
aimed at obtaining a single solution, the Hindus strove for
a general method by which any indeterminate problem could be
resolved. In this they were completely successful, for
they obtained general solutions for the equations ax(+ or -)by=c,
xy=ax+by+c (since rediscovered by Leonhard Euler) and
cy2=ax2+b. A particular case of the last equation,
namely, y2=ax2+1, sorely taxed the resources of modern
algebraists. It was proposed by Pierre de Fermat to Bernhard
Frenicle de Bessy, and in 1657 to all mathematicians. John
Wallis and Lord Brounker jointly obtained a tedious solution
which was published in 1658, and afterwards in 1668 by John
Pell in his Algebra. A solution was also given by Fermat
in his Relation. Although Pell had nothing to do with the
solution, posterity has termed the equation Pell's Equation, or
Problem, when more rightly it should be the Hindu Problem,
in recognition of the mathematical attainments of the Brahmans.
Hermann Hankel has pointed out the readiness with which the
Hindus passed from number to magnitude and vice versa.
Although this transition from the discontinuous to continuous
is not truly scientific, yet it materially augmented the
development of algebra, and Hankel affirms that if we
define algebra as the application of arithmetical operations
to both rational and irrational numbers or magnitudes,
then the Brahmans are the real inventors of algebra.
The integration of the scattered tribes of Arabia in the 7th
century by the stirring religious propaganda of Mahomet was
accompanied by a meteoric rise in the intellectual powers of
a hitherto obscure race. The Arabs became the custodians of
Indian and Greek science, whilst Europe was rent by internal
dissensions. Under the rule of the Abbasids, Bagdad became
the centre of scientific thought; physicians and astronomers
from India and Syria flocked to their court; Greek and Indian
manuscripts were translated (a work commenced by the Caliph
Mamun (813-833) and ably continued by his successors); and
in about a century the Arabs were placed in possession of
the vast stores of Greek and Indian learning. Euclid's
Elements were first translated in the reign of Harun-al-Rashid
(786-809), and revised by the order of Mamun. But these
translations Were regarded as imperfect, and it remained for
Tobit ben Korra (836-901) to produce a satisfactory edition.
Ptolemy's Almagest, the works of Apollonius, Archimedes,
Diophantus and portions of the Brahmasiddhanta, were also
translated. The first notable Arabian mathematician was
Mahommed ben Musa al-Khwarizmi, who flourished in the reign of
Mamun. His treatise on algebra and arithmetic (the latter part
of which is only extant in the form of a Latin translation,
discovered in 1857) contains nothing that was unknown to the
Greeks and Hindus; it exhibits methods allied to those of both
races, with the Greek element predominating. The part devoted
to algebra has the title al-jeur wa'lmuqabala, and the
arithmetic begins with ``Spoken has Algoritmi,'' the name
Khwarizmi or Hovarezmi having passed into the word Algoritmi,
which has been further transformed into the more modern words
algorism and algorithm, signifying a method of computing.