modes. But there cannot be two substances of the same attribute, since there would be no means of distinguishing them except their modes or affections; and every substance, being prior in order of time to its modes, may be considered independently of them; hence two such substances could not be distinguished at all. One substance therefore cannot be the cause of another, for they cannot have the same attribute, that is, anything in common with another. Every substance is therefore self-caused; that is, its existence is implied in its essence. It is also necessarily infinite, for it would otherwise be terminated by some other of the same nature and necessarily existing; but two substances cannot have the same attribute, and therefore cannot both possess necessary existence. The more existence anything possesses, the more attributes are to be ascribed to it. This follows from the definition of an attribute. The more attributes we ascribe to anything therefore, the more we are forced to believe in its existence; and from this is derived the existence of God. God, or a substance consisting of infinite attributes, each expressing an eternal and infinite power, necessarily exists, for such an essence involves existence. If anything does not exist, a cause must be given for its non-existence. If only twenty men exist, an extrinsic reason must be given for this number, since the definition of man does not involve it or any number. There can be only one substance, God. Whatever is, is in God, and without God nothing can be conceived. For he is the sole substance, and modes cannot be conceived without substance; but besides modes and substance nothing exists. God is not corporeal, but body is a mode of God, and therefore uncreated. God is the cause of all things, and that immanently, but not transiently. He is the efficient cause of their essence as well as their existence, since otherwise their essence might be conceived without God, which is absurd. Thus all particular and concrete things are only the accidents or affections of God's attributes, or modes in which they are determinately expressed. God's power is the same as his essence; for he is the necessary cause both of himself and of all things, and it is as impossible for us to conceive him not to act as not to exist. God viewed in the attributes of his infinite substance is the same as nature, that is, to use his fine and subtle expression, the natura naturans;' but in another sense, nature, or 'natura naturata,' expresses only the modes under which the divine attributes appear. And intelligence considered in act, even though infinite, should be referred to natura naturata;' for intelligence in this sense is but a mode of thinking, which can only be conceived by means of our conception of thinking in the abstract, that is, by an attribute of God. The faculty of thinking, as distinguished from the act, as also those of desiring, loving, and the rest, have no existence. This is an anticipation of Hume's doctrine. [SCEPTICISM] There is, says Spinoza, an infinite power of thinking, which, considered in its infinity, embraces all nature as its object, and of which the thoughts proceed according to the order of nature, being its correlative ideas. This agrees with Plato, who says a law of nature is an idea in its objective reality; that is, idea and law (in this sense) are correlations. This opinion is indeed as old as philosophy itself, and is found in every country. The universe is taken as the manifestation of the Deity; not, as many suppose, as the Deity himself; but, to use the words of Cousin, the Deity passing into activity, but not exhausted by the act.' (Cours de Phil., Intro.) It is owing to the abstract and subtle nature of Spinoza's method that his system has been so often misunderstood. The positions, for example, which we have set down, require patient meditation and an acquaintance with metaphysical language to be intelligible, and some of them are open to the grossest misinterpretations. Thus Spinoza is usually accused of atheism, while not only are his doctrines found in St. Paul, St. Augustin, and the Greek writers, but all the modern German philosophy, from Kant downwards, owns him as its master. Spinoza does not confound God with the material universe; his words distinctly absolve him from such a charge: 'God is the identity of the natura naturans and the natura naturata' (natura naturans et natura naturata in identitate Deus est). God and nature are not two distinct entities, but one living whole. God is the idea immanens,' the true spiritual existence, the living principle which permeates the whole. The material universe is only one phasis of his infinite attributes, namely, extension; but Spinoza rigidly and universally teaches that the One Infinite Substance has two infinite attributes, extension and thought. Extension is visible thought, and thought is invisible extension. The use of the word substance, by which he signifies existence, the 'prima materia' of the schoolmen, has led to much misunderstanding, and his adversaries have replied as if he meant by substance what we express by matter and body. When Spinoza therefore says that God is the infinite substance, he does not mean the material universe, which is only one attribute of existence, namely, extension; he simply gives the Platonic expression (rò ov Kai Tò nãv), the unique conception of the All. When Spinoza asserts thought to be the other infinite attribute of substance, he follows Parmenides, of whom Ritter says, "Thought appeared to him to exhibit merely one aspect of the All. (Geschichte der Philos., vol. i., p. 460.) It should be observed that the attribute of thought is not proved. He demonstrates the necessity for extension, by saying that we cannot conceive substance without conceiving it as extended; but as we can conceive substance without thought, we may demand a demonstration of the necessity of this attribute, which Spinoza has not given. In other words, from the definition of substance, extension follows as a necessary attribute; but in the definition of substance, there is no necessity involved for thought as an attribute. God then, according to Spinoza, is the 'idea immanens,' the fundamental fact and reality of all existence, the only power, the only eternity. What we name the universe is only the visible aspect, the realised form of his existence. All concrete things change and perish; they are only modes of the infinite Being, who alone remains unchangeable. It is a gross error (the origin of which may be traced to the misconception of his word 'substance') to assert, as it often has been, and on which Bayle founds his refutation of Spinoza, that this system is pantheistic, in the common acceptation of the term, that it identifies all things with God, and consequently that every concrete thing is a part of God. Such a conception is purely material and superficial. Schelling has well refuted it: God is that which exists in itself, and is comprehended from itself alone; the finite is that which is necessarily in another, and can only be comprehended from that other. Things therefore are not only in degree, or through their limitations, different from God, but toto genere. Whatever their relation to God on other points, they are absolutely divided from him on this, that they exist in another, and he is self-existent or original. From this difference it is manifest that all individual finite things taken together cannot constitute God; since that which is in its nature derived cannot be one with its original, any more than the single points of a circumference taken together can constitute the circumference, which as a whole is of necessity prior to them in idea.' (Philosophische Schriften, p. 104.) We have not space to go through the ideological and moral parts of Spinoza's Ethics, as we have done the metaphysical, but a few of the more important propositions may be usefully quoted. The mind does not know itself, except so far as it receives ideas of the affections of the body. But these ideas of sensation do not give an adequate knowledge of an external body, nor of the human body itself. The mind therefore has but an inadequate and confused notion of anything so long as it judges only by fortuitous perceptions; but it may attain it clear and distinct by internal reflection and comparison. This is the doctrine of Hobbes and Locke explicitly stated. No positive idea can be false; for there can be no such idea without God, and all ideas in God are true, that is, correspond with their object. Falsity therefore consists in that privation of truth which arises from inadequate ideas; an adequate idea being one which contains no incompatibility, without regard to the reality of its supposed correlative object. Error is imperfect truth. It seizes one aspect of the truth to the neglect of the rest. All bodies agree in some things; and of these all men have adequate ideas; hence common notions which all possess, such as extension, duration, number. The human mind however can only form a certain number of distinct images at the same time; if this number be exceeded, they become confused: and as the mind perceives distinctly just so many images as can be formed in the body; when these are confused the mind also will perceive them confusedly, and will comprehend them under one attribute, as man, horse, dog, &c.; the mind perceiving a number of such images, but not their differences of stature, colours, &c. Thus are universal ideas formed: first, by singulars, which the senses represent | confusedly and imperfectly; secondly, by signs, that is, by associating the remembrances of things with words, which Spinoza calls imagination; thirdly, by reason; and, fourthly, by intuitive knowledge. Knowledge of the first kind is the source of error; the second and third are necessarily true. It is important to distinguish images from words. Those who think ideas consist in images which they perceive, fancy that ideas of which they can form no image are arbitrary. They look at ideas as pictures on a tablet, and hence do not understand that an idea, as such, involves an affirmation or negation. And those who confound words with ideas fancy they can will something contrary to what they perceive, because they can affirm or deny it in words. But thought does not involve the conception of extension; and therefore an idea, or mode of thought, neither consists in images nor in words, the essence of which consists in corporeal motions not involving the conception of thought. Men can have an adequate knowledge of the eternal and infinite being of God, but cannot imagine God as they can bodies; and hence have not that clear perception of his being which they have of that of bodies, and have perplexed themselves by associating the word God with sensible images, which it is hard to avoid. The existence of God can be conceived; indeed it is a necessary conception from which no mind can escape; but the manner of his existence can never be conceived. The source of error in this case is that men do not name things correctly; for they do not err in their own minds, but in this application; as men who cast up wrong see different numbers in their minds from those in the true result. We are acted upon when anything takes place within us which cannot wholly be explained by our own nature. Passions are the affections of the body, which increase or diminish its power. of action, and they are also the ideas of those affections. Neither the body can determine the mind to thinking, nor can the mind determine the body to rest or motion. For all that takes place in body must be caused by God, considered under his attribute of extension, and all that takes place in mind must be caused by God, considered under his attribute of thought. The mind and the body are but one thing con sidered under different attributes; the order of action and passion in the body being the same in nature with that of action and passion in the mind. But men, though ignorant how far the natural powers of body reach, ascribe its operations to the determination of the mind, veiling their ignorance in specious words. For if they allege that the body cannot act without the mind, it may be answered that the mind cannot think till impelled by the body, nor are all the volitions of the mind anything else than its appetites, which are modified by the body. All things endeavour to continue in their actual being, this endeavour being nothing else than their essence, which causes them to be, until some exterior cause destroys their being. The mind is conscious of its own endeavour to continue as it is, which is, in other words, the appetite that seeks self-preservation; what the mind is thus conscious of seeking, it judges to be good, and not inversely. Many things increase or diminish the power of action in the body, and all such things have a corresponding effect on the power of thinking in the mind. Thus it undergoes many changes, and passes through different stages of more or less perfect power of thinking. Joy is the name of a passion, in which the mind passes to a greater perfection or power of thinking; grief, one in which it passes to a less. From these two passions, and from desire, Spinoza deduces all the rest of the passions in a curious but questionable manner. The mind has no free will, but is determined by a cause, which itself is determined by some other cause, and so on for ever. For the mind is only a mode of thinking, and therefore cannot be the free cause of its actions. Will and understanding are one and the same thing; and volitions are only affirmations or negations, each of which belongs to Such is the substance of Spinoza's celebrated system; a the essence of the idea affirmed or denied. This subtle system which has excited so much odium as to have become opinion is also adopted by Malebranche, Cudworth, and synonymous with atheism. We have pointed out the source Fichte. of this error; but we cannot refrain from adding the testiSpinoza's moral system is as rigidly deduced from pre-mony of the pious Schleiermacher to his religious earnestmises as his metaphysical. Most men who have written on ness. 'Offer up with me,' he exclaims, with reverence a moral subjects, he says, have treated man as something out lock of hair to the manes of the holy but repudiated Spinoza! of nature, as a kind of imperium in imperio,' rather than as The great spirit of the world penetrated him; the Infinite a part of the general order. They have conceived him to was his beginning and his end; the universe his only and enjoy a power of disturbing that order by his own deter- eternal love. He was filled with religion and religious mination, and ascribed his weakness and inconstancy not to feeling; and therefore is it that he stands alone, unapthe necessary laws of the system, but to some strange defect proachable, the master in his art, but elevated above the in himself, which they cease not to lament, deride, or exe-profane world, without adherents, and without even citizen crate. But the acts of mankind, and the passions from which they proceed, are in reality but links in the series, and proceed in harmony with the common laws of universal nature. Men finding many things in themselves and in nature, serving as means to a certain good, which things they know to have not been provided by themselves, have believed that some one has provided them, arguing by analogy of the means which they in other instances employ themselves. Hence they have imagined a variety of gods, and these gods they suppose to consult the good of men in order to be worshipped by them, and have devised every means of superstitious devotion to ensure the favour of these divinities. Finding also in the midst of so many beneficial things in nature not a few of an opposite effect, they have ascribed them to the anger of the gods on account of the neglect of men to worship them. Nor has the expe- These testimonies from such unquestionable sources will rience of calamities falling alike on the pious and impious not be without benefit in directing men to look calmly into cured them of this belief; they choose rather to acknow- Spinoza, and meditate upon him. The student will derive ledge their ignorance why good and evil are thus distributed, great help from Boulainvilliers's Refutation de Spinoza, than give up their favourite theory. But all things occur by Bruxelles, 1731, in which the doctrines are popularized and eternal necessity. Moreover were God to act for an end, he divested of their mathematical precision, which repels many must desire something which he wants; for it is acknow-readers; also from Jacobi's Briefwechsel mit Mendelssohn, ledged by theologians that he acts for his own sake and not for the sake of things created. Men having thought that all things were created for them, have invented names to distinguish that as good which tends to their benefit; and believing themselves free, have got the notions of right and wrong, praise and dispraise. And when they can easily apprehend the relations of things, they call them well ordered, if not, ill ordered; as if order were anything except in regard to our imagination of it. We are said to act when anything takes place within us, or without us, for which we are an adequate cause; that is, when it may be explained by means of our own nature alone. P C, No. 1403. ship.' (Rede über die Religion, p. 47.) Göthe thus speaks The mind that wrought so powerfully on mine, and had so great an influence on the whole frame of my opinions, was Spinoza's. After I had looked round the world in vain for means of shaping my strange moral being, I fell at length on the Ethics' of this man. What I read in this work-what I thought I read in it-I can give no account of; enough that I found there a calm to my passions; it seemed to open to me a wide and free view over the sensuous and moral world But what particularly riveted me was the boundless disin · terestedness that beamed forth from every sentence. The all-equalizing serenity of Spinoza contrasted with my allagitating vehemence; his mathematical precision, with my poetical way of feeling and representing. (Dichtung und Wahrheit, xiv.) Breslau, 1789; and from Hallam's History of the Literature of Europe, vol. iv., pp. 243-263.) SPIREA, a genus of plants of the natural family Rosacea, tribe Spiraceæ. The name occurs in antient authors, and is supposed to be derived from oupa, a cord, in allusion to the fitness of the plants for twisting into garlands. The genus is diffused through the temperate parts of the northern hemisphere, and is characterised by having a 5-cleft permanent calyx; stamens 10 to 50, in serted in a torus with the 5 petals, which are inserted into the calyx; carpels sessile, solitary or several, rarely connected into a capsule; seeds 2-15, pendulous, very rarely ascend VOL. XXII.—2 7 ing. The species, upwards of 50 in number, form small unarmed shrubs or perennial herbs; leaves usually simple, sometimes pinnately cut. Flowers white or reddish. They are found in Europe, North America, Siberia, China, and the Altai and Himalayan Mountains. Several form ornamental shrubs and herbs, which are found in our gardens, and are of easy cultivation. S. Ulmaria, or Meadow-Sweet, is found in our meadows, and S. Filependula on our downs, &c. Pigs are said to be fond of the tubers of the roots. Several of the species are astringent, and might be used in tanning. S. trifoliata is sometimes called Ipecacuanha de Virginia, being employed as an emetic. SPIRAL, a name belonging properly to curves which wind round a point in successive convolutions. The easiest mode of representing such curves algebraically is by means of polar COORDINATES: hence, in many of the older English works, any curve referred to such coordinates is said to be considered as a spiral. Thus we have the circle considered as a spiral; the ellipse considered as a spiral, and so on. The rest of this article is intended only for those who have some knowledge of the mathematical part of the subject. If r be the radius vector of a curve, ✪ the angle which it makes with a given line, and r = (0) the equation of the curve, it is obvious that if pe be a common trigonometrical function of sin e, cos 0, &c., the curve will not have an unlimited number of convolutions. The whole of the curve from 0 to 4, will be merely a repetition of that from 0 1 0 to 02. Thus, r = sin 0 is the equation of a circle of a unit diameter, tangent at the origin to the line from which r sets out; the fifteenth half-revolution of the radius vector is only the fifteenth description of this circle. It is only then when the angle occurs independently of trigonometrical quantities, that any curve is represented which can properly be called a spiral. Thus, the spiral of Archimedes, or Conon, of which the equation is rae, has a convolution in which r changes from 0 to 2a, while changes from 0 to 2; another, in which r changes from 2za to 4a, while changes from 2 to 47, and so on. The principal spirals to which distinct names have been given, are Equation. * = αθ rea g20 = a there is one succession of convolutions beginning with OABCD, and another beginning with OAbCd. But the second equation, which is only the first in a different form, does not yield any of the second set of convolutions, unless by means of the negative values of the radius vector answering to negative values of 0. The manner in which the negative value of r is to be treated, is as follows:-Every line passing through the origin, as POQ, makes two angles with the positive side of the axis of x, POD, less than a right angle in the diagram, and QOD, between two and three right angles: the second of which may be considered as the common angle QOD, taken negatively. The bounding directions of these angles are dif ferent, OP and OQ: the rule is, whichever angle the straight line QOP is supposed to make with OD, let the bounding direction of that angle be the positive direction, and the other direction negative. Thus, when POD is the angle, OP is positive and OQ negative: when QOD is the angle, OQ is positive and OP negative. In this manner it will be found that the first three of the four spirals above enumerated have never been completely drawn. There is little need to insist much on the necessity of the extension here described: one more instance may suffice. Let the reader trace the curve whose equation is 4x SPIRAL of ARCHIMEDES. (SPIRAL.] with some others of less note. The figures of these spirals are given in all books on the application of algebra to geo-lopment of the tissues of plants two tendencies are observed, metry. It has hitherto been universal to consider spirals in a manner which has deprived these curves of half their convolutions: this has been done by refusing to entertain negative values of the radius. For example, in the spiral of Archimedes rao, a being a positive quantity, the curve is supposed to have no convolutions when is negative, or when the radius revolves negatively. The consequence is, that the curve begins abruptly at the origin. It would be a matter of litle importance to insist on the existence of the additional branches which belong to the negative radii, if it were not that the other mode of representing curves, by means of rectangular coordinates, always gives the additional branches: so that, if we refuse to receive the latter as coming from the polar equation, we have only the alternative of supposing that the mere transformation of coordinates destroys a part of the curve. In the spiral of Archimedes, for example, the rectangular and polar equations are — √(x2 + y2) y = tan a r = ae. the one simply that of extension in a vertical direction, the other is that of curvation, mostly resulting in the produc tion of a spire. The tendency to develop parts in a spiral direction, though much more prominent in the vegetable than the animal kingdom, is by no means confined to it. In a recent paper in the ninth volume of the Annales des Sciences Naturelles, Mandl has shown that all the tegumentary appendages of animals, as the scales, feathers, hair, &c., have a spiral arrangement, and that many of the internal organs are subject to the same law. The tendency to develop structures in a spiral form appears to be depen dent on some of the higher laws regulating organic life; and in this view the subject has been investigated by receat botanists. Goethe, the German poet and philosopher, to whom botanists are indebted for the development of those theoretical views of the structure of plants on which is based the science of morphology, has investigated this subject. In his Essay on the Spiral Tendency of Vegetation,' published in 1831, he gives the following view. He sup poses that there is a dependence of those properties which plants possess of resisting external agents, and of enduring The first, treated in the usual way, gives a curve of which for a length of time, upon those parts that are developed vertically, whilst the nutritive and reproductive functions are connected with spirally developed structures. In sup port of this generalization he adduces a number of facts. If a branch of an ash-tree is injured, so that the lower parts become over-nourished, it possesses a tendency to become spiral. When the leaves of the Italian poplar are injured by insects, the petioles become twisted. Spiral vessels exist in greatest numbers in the growing parts of plants, as the alburnum. They also exist in greater numbers in the higher plants, the lowest possessing none. A spiral arrangement of parts is also much less observable in the lower than in the higher groups of plants. The organs of nutrition and reproduction, the leaves and parts of the flower, have normally a spiral arrangement. Von Martius, Mohl, and others, have also written on the general theory of spiral structure. We shall confine ourselves to pointing out those plants and parts of plants that exhibit this structure. Cellular tissue was at one time supposed to consist of plain simple cells, but the researches of later botanists have proved that the cells of this tissue are often furnished with fibres, which are twisted in a spiral manner. This spiral fibrous tissue is abundant in the roots of orchidaceous plants, in the seed-coats of many plants, and in the linings of the valves of almost all anthers. Spiral fibres, inde pendent of any cells, and apparently surrounded by vegetable mucus, have been found in the testa of the seeds of Collomia linearis. In the seed coats of the seeds of species of Blepharis and Acanthodium spiral fibres enclosed in membranous tubes are found in very great abundance. The organs called elaters, which are contained with the sporules in the conceptacles of Jungermannia, consist of spiral fibres surrounded by a tube. A structure also of this kind has been described as existing in a species of Trichia, but in general the fungi do not present any spiral structure in their parts. The elaters are analogous in structure to the vascular tissue, which is almost entirely composed of a tissue, which on account of its spiral structure has been called 'spiral vessels.' These vessels appear to be little more than fibrous cellular tissue elongated, the parietes of the cell forming an elongated tube, which is tapering at each extremity, and contains within it one, two, three, or more spiral fibres. This tissue is exceedingly abundant in exogenous and endogenous plants, but is not found in the lower families of Cryptogamia. It exists however in ferns, Lycopodiacea, and Equisetacea. It is only sparingly found in Coniferæ. These spiral fibres possess the power of moving when touched, which was attributed by Malpighi to irritability, but De Candolle attributes this to their hygrometrical properties. From the tissues we pass on to the entire plant, where we frequently see the spir tendency developed in the structure of stem and leaves. The part of the latter which exhibits this structure is the petiole, and in this organ all forms of the spire may be seen, from a single twist to the complicated spires observed in the organs called cirrhi. In most plants these cirrhi assist them in climbing, their structure adapting them to this purpose. The spires of the cirrhi twist in some from right to left, in others from left to right; and in the cirrhi of the genera Passiflora and Bryonia the direction changes several times in the course of the spire from right to left and from left to right. In the structure of many of the Confervæ a spiral arrangement of the tissues is observed, especially of those which approach the animal kingdom in their no ements, as the Oscillatoris. The set which support the conceptacle of Jungermannia, and which contain the spiral elaters before mentioned, possess in many instances a spiral structure. This is also occasionally developed in the same organ in mosses, a remarkable instance of which occurs in Funaria hygrometrica. In this moss the seta are quite straight when young, but assume the spiral structure as they increase in age. In these set the spire turns in two directions; from the base about two-thirds up the stem it goes from right to left; it then becomes quite straight, and turns in the opposite direction from left to right. A curious property is possessed by these setæ when the capsules are ripe. If the upper part of the spiral is moistened, the capsule commences turning from right to left; but if the lower part only is moistened, it turns from left to right. The entire stems of plants are frequently spiral, as is seen in the plants which are called climbers. These plants, by reason of the spiral arrangement of their tissues, twine around the nearest objects, whether organic or inorganic. In most of them the winding of the spire is to the left side, but in a few the turning is to the right. Amongst the former are the genera Cuscuta, Phaseolus, Dolichos, Passiflora, Banisteria, &c.; amongst the latter are the genera Humulus, Dioscorea, Lonicera, Polygonum, &c. This winding in a particular direction is not only confined to the species of a genus, but to the genera of an order; and Mohl, who has paid great attention to this subject, states that he knows of but one exception to this rule, which is the genus Abrus in the family of Leguminosa, which twines to the left, whilst all the others twine to the right. The direction of the spires of the cirrhi is not so constant. Between the twining of the cirrhi and the stems of plans Mohl has pointed out an essential difference. The cirrhi are first developed longitudinally, and the spiral tendency proceeds from the point to the base; but in stems the first three or four internodes grow straight, and the next internode is developed very rapidly; and from this lower internode the spiral tendency is developed upwards. Sometimes a spiral direction is seen in the direction of trees that ordinarily grow straight; and Göthe records several instances of twisted trunks in the chesnut, the whitethorn, beech, and others. A remarkable instance of spiral structure connected with function is seen in the peduncle of the female flowers of Valisneria, which is a water-plant. The female flowers spring to the surface of the water in the summer. at the time the male flowers have perfected their pollen and scattered it upon the surface of the water. As soon as the pollen is conveyed to the female flower, its spiral stem becoines contracted, and its fruit is perfected at the bottom of the water. Many theories have been proposed to account for the mere winding of the stem. Dutrochet supposes that it depends on the different relations of cellular and fibrous tissue to each other in plants during the action of endosmose. Mohl thinks that it arises from the irritability of the tissues of these plants, which, on the plant being placed in contact with certain external objects, is called into action, producing the peculiar development observed. This irritability is supposed only to exist on the sides and under surface of the twining part, and when called into action contracts and produces the twisting of the unaffected part. These explanations are not satisfactory. The spiral structure is too intimately connected with the essential existence of plants to be explained in all cases by a reference to immediate agents. The most remarkable and important exhibition, in a practical point of view, of the spiral tendency in plants is the arrangement of the leaves upon the axis of the plant. If we take a branch of the willow, oak, pear, apple, or many others, and examine the leaves, we shall find they are arranged in such a manner, that if we were to draw a line from leaf to leaf up the stem, we should produce upon it a spiral which would in the case of any of these trees be of a different character from any of the others. In theoretical botany the spiral arrangement of the leaves which makes them alternate upon the stem is looked upon as their normal form, and those leaves which are opposite or verticillate are supposed to be produced by the suppression of an internodium. The spiral arrangement of the leaves on the stem has been made a matter of mathematical investigation by Braun and Schimper, and it is found that this arrangement is possessed of certain fixed mathematical properties. Of course the same observations are applicable to all those parts of the plant, as the bracts, sepals, petals, scales of the fruit, &c., which are considered modifications of the leaf. The fruit of the common pine may be taken as an illustration of these properties. If the cone of a pine or a spruce-fir be broken through the middle, three scales will be observed, which, at first sight, appear to be upon the same plane; but a more attentive examination shows that they really originate at different heights, and moreover, that they are not placed at equal distances from each other; so that we cannot consider the.n as a whorl, but only a portion of a very close spiral. But considering the external surface of the cone viewed as a whole, we find that the scales are disposed in oblique lines, which may be studied -1, As to their composition or the number of scales requisite to form one complete turn of the spire; 2, as to their inclination, or the angle, more or less open, which they form with their axis; 3, as to their total number, and their arrangement round the common axis, which constitutes their co-ordination. Finally, we may endeavour to ascertain whether the spires turn from right to left or vice versa.' (Lindley.) In the arrangement of the leaves several series of spires are discoverable, and between these there constantly exists a certain arithmetical relation which may be expressed by figures, and which results from the combination of the elements of which they are composed. All the spires depend upon the position of a fundamental series, from which the others are deviations. The nature of this series is expressed by a fraction, of which the numerator expresses the number of turns which make up one spire, whilst the denominator expresses the number of leaves, scales. &c. upon the spire. So that suppose we mark the seat of one leaf at the bottom 0, and go on following the leaves, we shall come at one directly over the first, and this completes the spire; of this leaf occurs after ten turns of the spiral, and there should be eighteen leaves upon the spire, the expression for this series would be. By applying this rule very different figures may be obtained for various plants. The following are results obtained by Braun : is the expression for the leaves of Woad, Plantago lanceolata, and the bracts of Digitalis lanata. in Sempervivum arboreum, and the bracts of Plantago media. is a common form; it exists in the bay tree, the holly, and Aconite. is the most common, representing the quincunx. It is seen in Mezereum, Lapsana communis, the potato, &c. is seen in the spikes of all grasses, in Asraum, the limetree, the vetch, and pea. No application of this doctrine has at present been made, and these researches are only in their infancy. It seems in some genera to be a mode of distinguishing species. Thus the expressions for the following species of Pinus are P. pinaster; P. sylvestris ; P. cembra; P. larix ; P. micro carpa. For further information on the subject of this article the reader may consult Göthe, Ueber die Spiral-Tendenz der Vegetation; Meyen, Pflanzen-Physiologie, Band .; Lindley, Introduction to Botany; Henslow's Botany, in Cab. Cyc.; Virey, Philosophie de l'Histoire Naturelle. SPIRATELLA. [HYALIDE, vol. xii., p. 372.] SPIRAL VESSELS. [TISSUES, VEGETABLE.] SPIRE (in German, Spitze, or Thurm-spitze; in French, Flèche, from its resemblance to the pointed tip of an arrow; but the Latin spira signifies a coil, or spiral line, and not an upright cone or pyramid). The term belongs to Gothic architecture, and is used to designate the tapering pyramidal mass erected on a tower by way of finish and ornament. That so little relative to spires is said in works on Gothic architecture is the more remarkable, because, in proportion to the number of examples, they exhibit more variety than almost any other separate feature in edifices in that style. Though the spire is a very striking feature in a building, it has nothing to recommend it on the score of direct utility. It is a mere external appendage to an edifice, since it does not, like the dome, contribute to any kind of effect whatever internally, a circumstance that seems to have been overlooked by Mr. A. W. Pugin, for else he would hardly have made it a reproach against the architect of St. Paul's, that the exterior dome of that fabric is merely for effect. Though the same objection might be made to the spire, we are far from urging it: mere utility is a low test of merit in architecture, and although this merit cannot be claimed for this feature in Gothic architecture, we hold the spire to be one of paramount value in it, inasmuch as that pyramidal figure concentrates all its principles and characteristics, rendering it most eminently the Pointed style. So considered, the spire may be said to be the keystone of the whole idea of such style; that which visibly completes it. It serves, moreover, to impart an air of graceful lightness to the whole of a building, and to correct-if we may so express it-what might else be excess of length as compared with the general height of a structure, by giving a corresponding degree of loftiness to one portion of it. The origin of the spire, like that of the pointed arch, is merely matter of conjecture. The probability is that it arose out of the peaked roof usually given to campaniles and towers of a preceding period, which form was afterwards gradually improved upon and refined, till it eventually grew up into the slender tapering spire. According to such supposition, we would refer to the tower of Than church in Normandy, as an example exhibiting the rudiments of the spire, it being no more than a steep peaked roof or low pyramid, whose height does not exceed three-fourths of its base. A peak of this kind differs also from the spire both in being the same in plan as the tower on which it is placed, and in being immediately set upon it, whereas the spire is almost invariably an octagon or other polygon, and is surrounded at its base with a parapet. In Italy, where canpaniles are usually detached square towers of very slender or lofty proportions, the spire is almost unknown, for such towers have seldom more than a mere pyramidal roof or peak, which, though it may be considered as the germ from which the Gothic spire was afterwards developed, is in itself of quite different character; yet, at the same time, that of each is best adapted to the respective style. There are some few instances of square spires; among them a very singular one at Egeln in Germany, where two such spires are set immediately together upon the same tower. But however slender in their proportions such spires may otherwise be, they have a certain heavy massiveness of form. When therefore greater loftiness and lightness were aimed at in this feature, the adoption of a polygonal plan for it became almost matter of course; for although in a geometrical drawing the general outline and proportions of a spire are the same whether it be square or octangular in plan, the perspective or actual appearance is widely dif ferent; because in the latter case the diagonal breadth of the square tower below is cut off, and each side or plane of which the spire is composed becomes a much more pointed triangle. Besides which, the polygonal spire produces a degree of contrast and variety highly favourable to general effect in the Pointed style. A gradual and progressive transition from the mere peak or pyramidal roof to the slender tapering spire, cannot however be clearly traced. On the contrary, some of the earliest deviations from the simple pramidal form appear to have produced uncouthness rather than lightness; for although much greater loftiness upon the whole was so occasioned, the appearance of it was reduced by the sides of the tower being made to terminate in gables cutting into, and therefore partly cutting off, the base of the pyramid or spire itself. Many of the earlier German edifices contain examples of this peculiarity-one almost confined to them; among others the cathedrals of Worms and Gelnhausen, the church at Andernach, and that of the Apostles at Cologne, exhibit many varieties of spires, or rather spire-roofs, springing up from gables at their base; and in some the gables are so large and rise up so high, that the appearance of spire is almost entirely lost. Such is the case with the pyramidal covering of the square tower at the west end of the church at Gelnhausen, of which the portion above the gable forms a mere capping. The same church offers other specimens of the kind, there being, besides the one mentioned, a spire over the intersection of the transept, one over the apsis at the east end, and two others over the towers adjoining it. All these are polygonal, but otherwise differ-except that those to the towers are similar to each other-both in dimensions and proportions; that over the apsis being not quite so high as it is broad, while that over the transept is one diameter and a half, and the two others three diameters in height. They are all gabled at the base, and their ridges correspond with the apices of the gables, so that the sides or faces of the spire alternate with those of the tower; which last circumstance is almost peculiar to the earliest German spires. Another distinction belonging to them is, that except gables or pediments, they have nothing at their base, neither parapet nor pinnacles of any kind, which would serve at once as a finish to the tower, and as enrichment to the lower part of the spire. This is so different from the usual mode, that in this country a spire set immediately upon a tower without any parapet, &c. at its base, is techni cally described by the term Broach. Many other distinctions are needed, and if no better can be found, we would suggest that of Stump-spire for one whose height does not exceed two diameters of its base. There are indeed so many peculiarities in spires, that it is highly desirable to have descriptive terms for them. First, as regards its base, a spire may be said to be Cluster-based, when surrounded below with pinnacles connected with it, and from among which it seems to spring up; of which kind St. Mary's, Oxford, is a celebrated example. The |