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modes. But there cannot be two substances of the same two infinite attributes, extension and thought. Exten sicti is attribute, since there would be no means of distinguishing visible thought, and thought is invisible extension. The thein except their modes or affections, and every substance, use of the word substance, by which he signifies existence, being prior in order of time to its modes, may be considered the “prima materia' of the schoolmen, has led 10 much misindependently of them; hence two such substances could understanding, and his adversaries have replied as if te not be distinguished at all. One substance therefore cannot meant by substance what we express by matter and body. be the cause of another, for they cannot have the same at- When Spinoza therefore says that God is the infinite subtribute, that is, anything in common with another. Every stance, he does not mean ihe material universe, which is substance is therefore self-caused; that is, its existence is only one attribute of existence, namely, extension ; be implied in its essence. It is also necessarily infinite, for it simply gives the Platonic expression (óv kal Fay), ibe would otherwise be terminated by some other of the same unique conception of the All. When Spinoza asserts nature and necessarily existing; but two substances cannot thought to be the other infinite attribute of substance, he have the same attribute, and therefore cannot both possess follows Parmenides, of whom Ritter says, “Thought appeare necessary existence.

The more existence anything pos- to liim to exhibit merely one aspect of the All.: (Geschickie sesses, the more attributes are to be ascribed to it. This der Philos., vol. i., p. 460.) It should be observed that the follows from the definition of an attribute. The more attri- attribute of thought is not proved. He demonstrates the butes we ascribe to anything therefore, the more we are necessity for extension, by saying that we cannot conceive forced to believe in its existence; and from this is derived substance without conceiving it as extended; but as we can the existence of God. God, or i substance consisting of conceive substance without thought, we may demand a deinfinite attributes, each expressing an eternal and infinite monstration of the necessity of this attribute, which Spinoza power, necessarily exists, for such an essence involves ex- has not given. In other words, from the definition of subistence. If anything does not exist, a cause must be given stance, extension follows as a necessary aitribute; but ia for its non-exisience. If only twenty men exist, an extrinsic the definition of substance, there is no necessity involvei reason must be giren for this number, since the definition of for thought as an attribute. man does not involve it or any number.

God then, according to Spinoza, is the idea immanens.' There can be only one substance, God. Whatever is, is the fundamental fact and reality of all existence, the only in God, and without God nothing can be conceived. For power, the only eternity. What we name the universe is he is the sole substance, and modes cannot be conceived only the visible aspect, the realised form of his existence. without substance; but besides modes and substance no- All concrete things change and perish; they are only modes thing exists. God is not corporeal, but body is a mode of of the infinite Being, who alone remains unchangeable. It God, and therefore uncreated. God is the cause of all is a gross error (the origin of which may be traced to the things, and that immanently, but not transiently. He is misconception of his word “substance') to assert, as it ofici. the efficient cause of their essence as well as their existence, has been, and on which Bayle founds his refutation of since otherwise their essence might be conceived without Spinoza, that this system is paritheistic, in the common acGod, which is absurd. Thus all particular and concrete ceptation of the term, that it identifies all things with God, things are only the accidents or affections of God's attributes, and consequently that every concrete thing is a part of God. or modes in which they are determinately expressed. God's Such a conception is purely material and superfcial. power is the same as his essence; for he is the necessary Schelling has well refuted it: *God is that which exists in cause both of himself and of all things, and it is as impos- itself, and is comprehended from itself alone; the finile is sible for us to conceive him not to act as not to exist. God that which is necessarily in another, and can only be comviewed in the attributes of his infinite substance is the prehended from that other. Things therefore are not only same as nature, that is, to use his fine and subtle expres- in degree, or through their limitations, different from Ged, sion, the natura naturans ;' but in another sense, nature, but toto genere. Whatever their relation to God on other or 'natura naturata,' expresses only the modes under which points, they are absolutely divided from him on this, that the divine attributes appear. And intelligence considered ihey exist in another, and he is self-existent or original. in act, even though infinite, should be referred to 'natura From this difference it is manifest that all individual inte naturata ;' for intelligence in this sense is but a mode of things taken together cannot constitute God; since that thinking, which can only be conceived by means of our con which is in its nature derived cannot be one with its orie ception of thinking in the abstract, that is, by an attribute ginal, any more than the single points of a circumference of God. The faculty of thinking, as distinguished from the taken together can constitute the circumference, wbich as a act, as also those of desiring, loving, and the rest, have no whole is of necessity prior to them in idea.' (Philosophiscke existence. This is an anticipation of Hume's doctrine. Schriften, p. 104.) [SCEPTICISM] There is, says Spinoza, an infinite power of We have not space to go through the ideological and Thinking, which, considered in iis infinity, embraces all na- moral parts of Spinoza's "Ethics,' as we have done the ture as its object, and of which the thoughts proceed ac metaphysical, but a few of the more important propositions cording to the order of nature, being iis correlative ideas. may be usefully quoted. This agrees with Plato, who says a law of nature is an idea The mind does not know itself, except so far as it receives in its objective reality; that is, idea and law (in this sense) ideas of the affections of the body. But these ideas of sen. are correlations. This opinion is indeed as old as philosophy sation do not give an adequate knowledge of an external itself, and is found in every country. The universe is taken body, nor of the human body itself. The mind therefore las as the manifestation of the Deity; not, as many suppose, but an inadequate and confused notion of anything so long as the Deity himself; but, to use the words of Cousin,' the as it judges only by fortuitous perceptions; but it may alDeity passing into activity, but not exhausted by the act. tain it clear and distinct by internal reflection and com(Cours de Phil.. Intro.). It is owing to the abstract and parison. This is the doctrine of Hobbes and Locke er. subtle nature of Spinoza's method that his system has been plicitly stated. No positive idea can be false ; for there can so often misunderstood. The positions, for example, which be no such idea without God, and all ideas in God are true, we have set down, require patient meditation and an ac- that is, correspond with their object. Falsity therefore conquaintance with metaphysical language to be intelligible, sists in that privation of truth which arises from inadequate and some of them are open to the grossest misinterpretations. ideas; an adequate idea being one which contains no inThus Spinoza is usually accused of atheism, while not only compatibility, without regard to the reality of its supposed are his doctrines found in St. Paul, St. Augustin, and the correlative object. Error is imperfect truth. It seizes one Greek writers, but all the modern German philosophy, from aspect of the truth to the neglect of the rest. Kant downwards, owns him as its master.

All bodies agree in some things, and of these all men Spinoza does not confound God with the material uni- have adequate ideas; hence common notions which all verse; his words distinctly absolve him from such a charge: possess, such as extension, duration, number. The human "God is the identity of the natura naturans and the natura mind however can only form a certain number of distinct naturata’ (natura naturans et natura naturata in identitate images at the same time; if this number be exceeded, they Deus est). God and nature are not two distinct entities, become confused: and as the mind perceives distinctly just but one living whole. God is the idea immanens,' the many mages as can be formed in the body; when these true spiritual existence, the living principle which permeates are confused the mind also will perceire them confusedly, and the whole. The material universe is only one phasis of his will comprehend them under one attribute, as man, horse, dog, infinite attributes, vamely, extension; but Spinoza rigidly &c.; the mind perceiving a number of such images, but not and universally teaches that the One Infinite Substance has their differences of stature, colours, &c. Thus are universal

ness.

ideas formed : first, by singulars,which the senses represent, We are acted upon when anything takes place within us which coafusedly and imperfectly; secondly, by signs, that is, by cannot wholly be explained by our own nature. Passions are associating the remembrances of things with words, which the affections of the body, which increase or diminish its power. Spinoza calls imagination ; thirdly, by reason ; and, fourthly, of action, and they are also the ideas of those affections. by intuitive knowledge. Knowledge of the first kind is the Neither the body can determine the mind to thinking, nor source of error; the second and third are necessarily true. can the mind determine the body to rest or motion. For all It is important to distinguish images from words. Those that takes place in body must caused by God, considered who think ideas consist in images which they perceive, under his attribute of extension, and all that takes place in fancy that ideas of which they can form no image are arbi- mind must be caused by God, considered under his attribute trary. They look at ideas as pictures on a tablet, and hence of thought. The mind and the body are but one thing con do not understand that an idea, as such, involves an affirma- stdered under different attributes ; the order of action and tion or negation. And those who confound words with ideas passion in the body being the same in nature with that of fancy they can will something contrary to what they per- action and passion in the mind. But men, though iynorant ceive, because they can aflirm or deny it in words. But how far the natural powers of body reach, ascribe its operations thought does not involve the conception of extension; and to the determination of the mind, veiling their ignorance in therefore an idea, or mode of thought, neither consists in specious words. For if they allege that the body cannot act images nor in words, the essence of which consists in cor without the mind, it may be answered that the mind cannot poreal motions not involving the conception of thought. think till impelled by the body, nor are all the volitions of the

Men can have an adequare knowledge of the eternal and mind anything else than its appetites, which are modified by infinite being of God, but cannot imagine God as they can

the body. bodies; and hence have not that clear perception of his All things endeavour to continue in their actual being, being which they have of that of bodies, and have perplexed this endeavour being nothing else than their essence, which themselves by associating the word Gorl with sensible causes them to be, until some exterior cause destroys their images, which it is hard to avoid. The existence of God being. The mind is conscious of its own endeavour to concan be conceived ; indeed it is a necessary conception from tinue as it is, which is, in other words, the appetite that which no mind can escape; but the manner of his exisience seeks self-preservation; what the mind is thus conscious of can never be conceived. The source of error in this case is seeking, it judges to be good, and not inversely. Many that men do not name things correctly; for they do not err things increase or diminish the power of action in the body, in their own minds, but in this application; as men who cast and all such things have a corresponding effect on the power up wrong see different numbers in their minds from those of thinking in the mind. Thus it undergoes many changes, in the true result.

and passes through different stages of more or less perfect The inind has no free will, but is determined by a cause, power of thinking. Joy is the name of a passion, in which which itself is determined by some other cause, and so on the mind passes to a greater perfection or power of thinkfor crer. For the mind is only a mode of thinking, and ing; grief, one in which it passes to a less. From these two therefore cannot be the free cause of its actions. Will and passions, and from desire, Spinoza deduces all the rest of understanding are one and the same thing; and volitions the passions in a curious but questionable manner. 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 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 ship.' (Rede über die Religion, p. 47.) Göthe thus speaks which they proceed, are in reality but links in the series, The mind that wrought so powerfully on mine, and had so and proceed in harmony with the common laws of universal great an influence on the whole frame of my opinions, was nature. Men finding many things in themselves and in Spinoza's. After I had looked round the world in vain for nature, serving as means to a certain good, which things means of shaping my strange moral being, I fell at length on they know to have not been provided by themselves, have the Ethics' of this man. What I read in this work — what I believed that some one has provided them, arguing by ana- thought I read in it, I can give no account of; enough that logy of the means which they in other instances employ I found there a calm to my passions; it seemed to open to themselves. Hence they have imagined a variety of gods, me a wide and free view over the sensuous and moral world and these gods they suppose to consult the good of men in But what particularly riveted me was the boundless disin: order to be worshipped by them, and have devised every terestedness that beamed forth from every sentence. Thu means of superstitious devotion to ensure the favour of these all-equalizing serenity of Spinoza contrasted with my alldivinities. Finding also in the midst of so many beneficial agitating vehemence; his mathematical precision, with my things in nature not a few of an opposite effect, they have poetical way of feeling and representing.' (Dichtung und ascribed them to the anger of the gods on account of Wahrheit, xiv.) 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 Breslau, 1789; and from Hallam’s History of the Literafor the sake of things created.

ture of Europe, vol. iv., pp. 213-263.) Men having thought that all things were created for them, SPIRÆA, a genus of plants of the natural family have invented names to distinguish that as good which tends Rosaceæ, tribe Špiraceæ. The name occurs in antient to their benefit; and believing themselves free, have got authors, and is supposed to be derived from otelpa, a cord, the notions of right and wrong, praise and dispraise. And in allusion to the fitness of the plants for twisting into when they can easily apprehend the relations of things, they garlands. The genus is diffused through the temperate call them well ordered, if not, ill ordered ; as if order were parts of the northern hemisphere, and is characterised by anything except in regard to our imagination of it.

having a 5-cleft permanent calyx; stamens 10 to 50, in We are said to act when anything takes place within us, serted in a torus with the 5 petals, which are inserted into the or without us, for which we are an adequate cause; that is, calyx; carpels sessile, solitary or several, rarely connected when it may be explained by means of our own nature alone. into a capsule; seeds 2-15, pendulous, very rarely ascend PC, No. 1403.

VOL. XXII.-27

ing. The species, upwards of 50 in number, form small there is one succession of convolutions beginning with unarmed shrubs or perennial herbs; leaves usually simple, OABCD, and another beginning with OABCd. But the sometimes pinnately cut. Flowers whiie or reddish. They second equation, which is only the first in a different form, are found in Europe, North America, Siberia, China, and the does not yield any of the second set of convolutions, unless Aliai and Himalayan Mouniains. Several form ornamental by means of the negative values of the radius vector anshrubs and herbs, which are found in our gardens, and are swering to negative values of 0. of easy cultivation. S. Ulmaria, or Meadow-Sweet, is found The manner in which the negative value of r is to be in our meadows, and S. Filependula on our downs, &c. Pigs treated, is as follows:-Every line passing through the are said to be fund of the tubers of the roots. Several of origin, as POQ, makes two angles with the positive side of the species are astringent, and might be used in tanning. the axis of x, POD, less than a right angle in the diagram, S. trifoliata is sometimes called Ipecacuanha de Virginia, and QOD, between two and three right angles: the second of being employed as an emetic.

which may be considered as the common angle QOD, taken SPIRAL, a name belonging properly to curves which negatively. The bounding directions of these angles are difwind round a point in successive convolutions. The easiest ferent, OP and OQ: the rule is, whichever angle the straight mode of representing such curves algebraically is by means line QOP is supposed to make with OD, let the bounding of polar COORDINATES: hence, in many of the older English direction of that angle be the positive direction, and the oiber works, any curve referred to such coordinates is said to be direction negative. Thus, when POD is the angle, OP is posiconsidered as a spiral. Thus we have the circle considered tive and OQ negative: when QOD is the angle, OQ is posias a spiral; the ellipse considered as a spiral, and so on. tive and OP negative. In this manner it will be found that The rest of this article is intended only for those who have the first three of the four spirals above enumerated have never some knowledge of the mathematical part of the subject. been completely drawn. There is little need to iusist much

If qo be the radius vector of a curve, O the angle which it on the necessity of the extension here described: one mote makes with a given line, and r= 0 (0) the equation of the instance may suffice. Let the reader trace the curve whose curve, it is obvious that if po be a common trigonometrical equation isfunction of sin 0, cos 0, &c., the curve will not have an unlimited number of convolutions. The whole of the curve

2y = 1 4x - 2x ENĪ - 8x, from @ = "7 to 0 = 47, will be merely a repetition of that derived from r = 1 2 cose. The rectangular equation from 0 = 0 to 0 = 27. Thus, r = sin o is the equation gives a curve of two loops, of which the polar equation will of a circle of a unit diameter, tangent at the origin to the only yield one, unless negative values of r be employed, in line from which r sets out; the fifteenth half-revolution of the manner above described. Nevertheless, if the process the radius vector is only the fifteenth description of this had been inverted, and the polar equation deduced from the circle. It is only then when the angle o occurs indepen- rectangular, we should have found r=1 - 2 cos o for dently of trigonometrical quantities, that any curve is repre- the former; and the effect of the double sign is that the sented which can properly be called a spiral. Thus, the positive values of r only, in the the two equations r=1-? spiral of Archimedes, or Conon, of ivhich the equation is cos 0, and r = - 1 - 2 cos 0, will give ihe complete curre n = ao, has a convolution in which r changes from 0 to deduced from the rectangular equation. As far as this in272, while e changes from 0 to 21; another, in which r | stance goes, it might seem as if the complete polar equation, changes from 2aa to 4 a, while o changes from 27 to 47, ! as deduced from the rectangular, would give the whole curre and so on.

The principal spirals to which distinct names by means of positive radii; ihough at the same time a single have been given, are

instance bardly proves anything. But even granting that Equation.

the passage from the rectangular to the polar equation will 1. Spiral of Archimedes

que = a0

always give forms enough to the latter to trace the whole 2. Reciprocal Spiral

r0 =

curve from positive radii, it remains indisputable that the 3. Lituus

po = a

other transition, from the polar to the rectangular, requires 4. Logarithmic or Equiangular

the negative radii to be taken into account. Spiral .

SPIRAL of ARCHIMEDES. (SPIRAL.] with some others of less note. The figures of these spirals SPIRAL STRUCTURE IN PLANTS. In the deveare given in all books on the application of algebra to geo- lopment of the tissuer of plauts iwo tendencies are obserred, metry.

the one simply that of extension in a vertical direction, the It has hitherto been universal to consider spirals in a other is that of curvation, mostly resulting in the produe-manner which has deprived these curves of half their con tion of a spire. The tendency to develop parts in a spiral volutions: this has been done by refusing to entertain ne- direction, though much more prominent in the vegelable gative values of the radius. For example, in the spiral of than the animal kingdom, is by no means confined to it. Archimedes r = ut, a being a positive quantity, the curve In a recent paper in the ninth volume of the Annales des is supposed to have no convolutions when e is negative, or Sciences Naturelles, Mandl has shown that all the teguwhen ihe radius revolves negatively. The consequence is, mentary appendages of animals, as the scales, feathers, hair, that the curve begins abrupily at ihe origin. It would be &c., have a spiral arrangement, and that many of the ina maiter of liitle importance 10 insist on the existence of ternal organs are subject to the same law. The lendeney the additional branches which belong to the negative radii, to develop structures in a spiral form appears to be depenif it were not that the other mode of representing curves, dent on some of the higher laws regulating organic lile; by means of rectangular coordinates, always gives ihe addi- and in this view the subject has been investigated by receat tional branches : so ihat, if we refuse to receive the latter as botanists. Goethe, the German poet and philosopher, to coming from the polar equation, we have only the alternative whom botanists are indebted for the development of those of supposing that the mere transformation of coordinates theoretical views of the structure of plants on which is destroys a part of the curve. In the spiral of Archimedes, based the science of morphology, hus investigated this subfor example, the rectangular and polar equations are - ject. In his Essay on the Spiral Tendency of Vegetation, ♡ (.ro + y)

published in 1831, he gives the following view. He supy = x tan

1 = a.

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 facis. 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

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flower, have normally a spiral arrangement. Von Martius, Mohl has pointed out an essential difference. The cirrhi Mohl, and others, have also written on the general theory of are frst developed longitudinally, and the spiral tendency spiral structure. We shall confine ourselves to pointing out proceeds from the point to the base; but in siems the first those plants and parts of plants that exhibit this struc ure. three or four internodes grow straight, and the next inter

Cellular tissue was at one time supposed to consist of nude is developed very rapidly; and from this lower inierplain simple cells, but the researches of later botanists have node the spiral tendency is developed upwards. Sometimes proved that the cells of this tissue are often furnished with a spiral direction is seen in the direction of trees that ordiibres, which are twisted in a spiral manner. This spiral narily grow straight; and Göthe records several instances fibrous tissue is abundant in the roots of orchidaceous of twisted trunks in the chesnut, the whitethorn, beech, plants, in the seed-coats of many plants, and in the linings and others. A remarkable instance of spiral structure con

of the valves of almost all anihers. Spiral fibres, inde nected with function is seen in the peduncle of the female Martine pendent of any cells, and apparently surrounded by vege. Howers of Valisneria, which is a waier-plant. The female De table mucus, hare been found in the testa of the seeds of towers spring to the surface of the water in the summer.

Collomia linearis. In the seed-coats of the seeds of spe at the time ihe male flowers have perfected their pollen is cies of Blepharis and Acanthodium spiral fibres enclosed in and scattered it upon the surface of the water. As soon as

membranous tubes are found in very great abundance. The the pollen is conveyed to the female flower, its spiral stem
organs called elaters, which are contained with the sporules becoines contracted, and its fruit is perfected at the bottom
in the conceptacles of Jungermannia, consist of spiral fibres of the water.
surrounded by a tube. A structure also of this kind has Many theories have been proposed to account for the

been described as existing in a species of Trichia, but it mere winding of the stem. Dutrochet supposes that it dedi general the fungi do not present any spiral structure in pends on the different relations of cellular ind fibrous tissue

The elaters are analogous in structure to to each other in plants during the action of endosmose. Mohl the vascular tissue, which is almost entirely composed thinks that it arises from the irritability of the tissues of of a tissue, which on account of its spiral structure these plants, which, on the plant being placed in contact with has been called 'spiral vessels.' These vessels appear certain external objects, is called into action, producing the to be little more than fibrous cellular tissue elongated, the peculiar development observed. This irritability is supposed parietes of the cell forming an elongated tube, which is only to exist on the sides and under surface of the twining iapering at each extremity, and contains within it one, part, and when called into action contracts and produces the two, three, or more spiral fibres. This tissue is exceedingly twisting of the unaffected part. These explanations are not abundant in exogenous and endogenous plants, but is not satisfactory. The spiral structure is too intimately confound in the lower families of Cryptogamia. It exists how nected with the essential existence of plants to be explained ever in ferns, Lycopodiaceæ, and Equisetaceæ. It is only in all cases by a reference to immediate agents. sparingly found in Coniferæ. These spiral fibres possess the. The most remarkable and important exhibition, in a pracpower of moving when touched, which was attributed by tical point of view, of the spiral tendency in plants is the Malpighi to irritability, but De Candolle attributes this to arrangement of the leaves upon the axis of the plant. If their hygrometrical properties.

we take a branch of the willow, oak, pear, apple, or many From the tissues we pass on to the entire plant, where others, and examine the leaves, we shall find they are we frequently see the spir tendency developed in the arranged in such a manner, that if we were to draw a line structure of stein and leaves. The part of the latter from leaf to leaf up the stem, we should produce upon it a which exhibits this structure is the petiole, and in this spiral which would in the case of any of these trees be of organ all forms of the spire may be seen, from a single a different character from any of the oihers. In theoretical twist to the complicated spires observed in the organs called botany the spiral arrangement of the leaves which makes them cirrhi. In most plants iliese cirrhi assist them in climb- alternate upon the stem is looked upon as their normal form, ing, their structure adapting them to this purpose. The and those leaves which are opposite or verticillate are supspires of the cirrhi twist in some from right to left, in others posed to be produced by the suppression of an interr.odium. from left to right; and in the cirrhi of the genera Passiflora The spiral arrangement of the leaves on the stem has been and Bryonia the direction changes several times in the made a matter of mathematical investigation by Braun and course of the spire from right to left and from left to right. Schimper, and it is found that this arrangement is possessed

In the structure of many of the Confervæ a spiral ar of certain fixed maihematical properties. Of course the same rangement of the tissues is observed, especially of those observations are applicable to all those parts of the plant, as which approach the animal kingdom in their noiements, the bracts, sepals, petals, scales of the fruit, &c., which are as the Oscillatoriæ. The setæ which support the concep- considered modifications of the leaf. The fruit of the common tacle of Jungermannia, and which contain the spiral ela- pine may be taken as an illustration of these prope: ties. If ters before mentioned, possess in many instances a spiral the cone of a pine or a spruce-fir be broken through the structure. This is also occasionally developed in the same middle, thrpe scales will be observed, which, at first sight, organ in mosses, a remarkable instance of which occurs in

appear to be upon the same plane; but a more attentive Punaria hygrometrica. In this moss the seta are quite examination shows that they really originate at different straight when young, but assume the spiral structure as heighis, and moreover, that they are not placed at equal they increase in age. In these seld the spire turns in two distances from each other ; so that we cannot consider thu.n directions ; from the base about two-thirds up the stem it as a whorl, but only a portion of a very close spiral. But congoes from right to left; it then becomes quite straight, and sidering the external surface of the cone viewed as a whole, turns in the opposite direction from left to right. A curious we find that the scales are disposed in oblique lines, which property is possessed by these setæ when the capsules are may be studied -1, As to their composition or the number ripe. If the upper part of the spiral is moistened, the cap- of scales requisite to form one complete turn of the spire; sule commences turning from right to left; but if the lower 2, as to their inclination, or the angle, more or less open, part only is moistened, it turns from left to right.

which they form with their axis ; 3, as to their total numThe entire stems of plants are frequently spiral, as is seen ber, and their arrangement round the common axis, which in the plants which are called climbers. These plants, by constitutes their co-ordination. Finally, we may endeavour reason of the spiral arrangement of their tissues, twine to ascertain whether the spires turn from right to left or around the nearest objects, whether organic or inorganic. vice versa.' (Lindley.) In most of them the winding of the spire is to the left In the arrangement of the leaves several series of spires side, but in a few the turning is to the right. Amongst the are discoverable, and between these there constantly exists former are the genera Cuscuta. Phaseolus, Dolichos, Passi a certain arithmetical relation which may be expressed by fora, Banisteria, &c.; amongst the latter are the genera figures, and which results from the combination of the eleHumulus, Dioscorea, Lonicera, Polygonum, &c. This

ments of which they are composed. All the spires depend winding in a particular direction is not only confined to the

upon the position of a fundamental series, fruin which the species of a genus, but to the genera of an order ; and others are deviations. The nature of this series is expressed Mohl, who has paid great attention to this subject, states by a fraction, of which the numerator expresses the number that he knows of but one exception to this rule, which is of turns which make up one spire, whilst the denominator the genus Abras in the family of Leguminosa, which expresses the number of leaves, scales. &c. upon the spire. twines to the left, whilst all the others twine 10 the right. So that suppose we mark the seat of one leaf at the boitom The direction of the spires of the cirrhi is not so consant. 0, and go on following the leaves, we shall come at one Between the twining of the cirrhi and the stems of plans directly over the first, and this completes the spire; of this

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leaf occurs after ten turns of the spiral, and there should be up into the slender tapering spire. According to such sup eighteen leaves upon the spire, the expression for this series position, we would refer to ihe tower of Than church is would be to By applying this rule very different figures Normandy, as an example exhibiting the rudiments of the may be obiained for various plants. The following are spire, it being no more than a steep peaked roof or low results obtained by Braun :

pyramid, whose height does not exceed three-fourths of its is the expression for the leaves of Woad, Plantago lan- base. A peak of this kind differs also from the spire both ceolata, and the bracts of Digitalis lanata. 1 in Sempervi- in being the same in plan as the tower on which it is placed, vum arboreum, and the bracts of Plantago media. I is a and in being immediately set upon it, whereas the spire is common form; it exists in the bay.tree, the holly, and almost invariably an octagon or other polygon, and is surAconite. } is the most common, representing the quincunx. rounded at its base with a parapet. In Italy, where camIt is seen in Mezereum, Lapsana communis, the potato, &c. paniles are usually detached square towers of very slender 1 is seen in the spikes of all grasses, in Asraum, the lime- or lofty proportions, the spire is almost unknown, for such tree, the veteli, and pea.

towers have seldom more than a mere pyramidal roof or No application of this doctrine has at present been made, peak, which, though it may be considered as the germ from and these researches are only in their infancy. It seems in which the Gothic spire was afterwards developed, is in some genera to be a mode of distinguishing species. Thus itself of quite different character; yet, at the same time, the expressions for the following species of Pinus are P. that of each is best adapted to the respective style. There pinaster 3); P. sylvestris ji; P. cembra zi; P. Tarix &; P. | are some few instances of square spires; among them a micro carpa .

very singular one at Egeln in Germany, where two such For further information on the subject of this article the spires are set immediately together upon the same tower. reader may consult Göthe, Veber die Spiral-Tendenz der But however slender in their proportions such spires may Vegetation; Meyen, Pflanzen-Physiologie, Band iii.; otherwise be, they have a certain heavy massiveness of Lindley, Introduction to Botany; Henslow's Botany, in Cab. form. When therefore greater loftiness and lightness were Cyc.; Virey, Philosophie de l'Histoire Naturelle.

aimed at in this feature, ihe adoption of a polygonal plan SPIRATELLA. (HYALIDÆ, vol. xii., p. 372.] for it became almost matter of course; for although in a SPIRAL VESSELS. [TISSUES, VEGETABLE.] geometrical drawing the general outline and proportions of SPIRE (in German, Spitze, or Thurm-spitze; in French, a spire are the same wheiher it be square or octangular in Flèche, from its resemblance to the pointed tip of an ar- plan, the perspective or actual appearance is widely difrow; but the Latin spira signifies a coil, or spiral line, ferent; because in the latter case the diagonal breadth of the and not an upright cone or pyramid). The term belongs to square tower below is cut off, and each side or plane of Gothic architecture, and is used to designate ihe tapering which the spire is composed becomes a much more pointed pyramidal mass erected on a tower by way of finish and or- triangle. Besides which, the polygonal spire produces a

That so little relative to spires is said in works on degree of contrast and variety highly favourable to general Gothic architecture is the more remarkable, because, in effect in the Pointed style. proportion to the number of examples, they exhibit more A gradual and progressive transition from the mere peak variety than almost any other separate feature in edifices or pyramidal roof io the slender tapering spire, cannot hos in that style. Though the spire is a very striking feature ever be clearly traced. On the contrary, some of the earliest in a building, it has nothing to recommend it on the score deviations from the simple pyramidal form appear to bave of direct utility. It is a mere external appendage to an produced uncouthness rather than lightness; for although edifice, since it does not, like the dome, contribute to any much greater loftiness upon the whole was so occasioned, the kind of effect whatever internally, a circumstance that appearance of it was reduced by the sides of the tower beseems to have been overlooked by Mr. A. W. Pugin, for ing made to terminate in gables cutting into, and therefore else he would hardly have made it a reproach against the partly cutting off, the base of the pyramid or spire itself. architect of St. Paul's, that the exterior done of that fabric Many of the earlier German edifices contain examples of is merely for effect. Though the same objection might be this peculiarity-one almost confined to them; among made to the spire, we are far from urging it: mere utility is a others the cathedrals of Worms and Gelnhausen, the chure low test of merit in architecture, and although this merit at Andernach, and that of the Apostles at Cologne, exbibit cannot be claimed for this feature in Gothic architecture, many varieties of spires, or rather spire-roofs, springing we hold the spire to be one of paramount value in it, inas- up from gables at their base; and in some the gables are much as that pyramidal figure concentrates all its principles so large and rise up so high, that the appearance of spire and characteristics, rendering it most eminently the Pointed is almost entirely lost. Such is the case with the pyramidal style. So considered, the spire may be said to be the key covering of the square tower at the west end of the church stone of the whole idea of such style; that which visibly at Gelnhausen, of which the portion above the gable forms completes it. It serves, moreover, to impart an air of grace- a mere capping. The same claurch offers other specimens ful lightness to the whole of a building, and to correct--if of the kind, there being, besides the one mentioned, a spire we may so express it—what might else be excess of length over the intersection of the transept, one over the apsis at as compared with the general height of a structure, by giving the cast end, and two others over the towers adjoining it a corresponding degree of loftiness to one portion of it. All these are polygonal, but otherwise differ-except that

The origin of the spire, like that of the pointed arch, is those to the towers are similar to each other-both is merely matter of conjecture. The probability is that it dimensions and proportions; that over the apsis being not arose out of the peaked roof usually given to campaniles and quite so high as it is broad, while that over the transept is towers of a preceding period, which form was afterwards one diameter and a half, and the two others three diameters gradually improved upon and refined, till it eventually grew 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; wbieb last circumstance is almost peculiar to the earliest Germaa spires. Another distinction belonging to them is, that er: cept gables or pediments, they have nothing at their base, neither parapet nor pinnacles of any kind, which woux 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 immediateis upon a tower without any parapel, &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 sug. gest 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

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