Chapter CV: Act 1890: was passed and the reconstruction commenced in (11)

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.