If this quantity is of the same sign as z, the displacement will be increased, and the equilibrium will be unstable. If it is of the opposite sign from z, the equilibrium will be stable. The limiting condition may be found by putting it equal to zero. One form of the solution of the equation, and that which is applicable to the case of a rectangular orifice, is
z = C sin px sin qy.
Substituting in the equation we find the condition
That the surface may coincide with the edge of the orifice, which is a rectangle, whose sides are a and b, we must have
pa = mπ, qb = nπ,
when m and n are integral numbers. Also, if m and n are both unity, the displacement will be entirely positive, and the volume of the liquid will not be constant. That the volume may be constant, either n or m must be an even number. We have, therefore, to consider the conditions under which
cannot be made negative. Under these conditions the equilibrium is stable for all small displacements of the surface. The smallest admissible value of m²/a² + n²/b² is 4/a² + 1/b², where a is the longer side of the rectangle. Hence the condition of stability is that
is a positive quantity. When the breadth b is less than √[π²T/(ρ − σ)g] the length a may be unlimited.
When the orifice is circular of radius a, the limiting value of a is √[(T/gρ)z], where z is the least root of the equation
The least root of this equation is
z = 3.83171.
If h is the height to which the liquid will rise in a capillary tube of unit radius, then the diameter of the largest orifice is
2a = 3.83171 √(2h)= 5.4188 √(h).
Duprez found from his experiments
2a = 5.485√(h).
[The above theory may be well illustrated by a lecture experiment. A thin-walled glass tube of internal diameter equal to 14½ mm. is ground true at the lower end. The upper end is contracted and is fitted with a rubber tube under the control of a pinch-cock. Water is sucked up from a vessel of moderate size, the rubber is nipped, and by a quick motion the tube and vessel are separated, preferably by a downward movement of the latter. The inverted tube, with its suspended water, being held in a clamp, a beaker containing a few drops of ether is brought up from below until the free surface of the water is in contact with ether vapour. The lowering of tension, which follows the condensation of the vapour, is then strikingly shown by the sudden precipitation of the water.]
Effect of Surface-tension on the Velocity of Waves.—When a series of waves is propagated on the surface of a liquid, the surface-tension has the effect of increasing the pressure at the crests of the waves and diminishing it in the troughs. If the wave-length is λ, the equation of the surface is
The pressure due to the surface tension T is
This pressure must be added to the pressure due to gravity gρy. Hence the waves will be propagated as if the intensity of gravity had been
instead of g. Now it is shown in hydrodynamics that the velocity of propagation of waves in deep water is that acquired by a heavy body falling through half the radius of the circle whose circumference is the wave-length, or
This velocity is a minimum when
and the minimum value is
For waves whose length from crest to crest is greater than λ, the principal force concerned in the motion is that of gravitation.For waves whose length is less than λ the principal force concerned is that of surface-tension. Lord Kelvin proposed to distinguish the latter kind of waves by the name of ripples.
When a small body is partly immersed in a liquid originally at rest, and moves horizontally with constant velocity V, waves are propagated through the liquid with various velocities according to their respective wave-lengths. In front of the body the relative velocity of the fluid and the body varies from V where the fluid is at rest, to zero at the cutwater on the front surface of the body. The waves produced by the body will travel forwards faster than the body till they reach a distance from it at which the relative velocity of the body and the fluid is equal to the velocity of propagation corresponding to the wave-length. The waves then travel along with the body at a constant distance in front of it. Hence at a certain distance in front of the body there is a series of waves which are stationary with respect to the body. Of these, the waves of minimum velocity form a stationary wave nearest to the front of the body. Between the body and this first wave the surface is comparatively smooth. Then comes the stationary wave of minimum velocity, which is the most marked of the series. In front of this is a double series of stationary waves, the gravitation waves forming a series increasing in wave-length with their distance in front of the body, and the surface-tension waves or ripples diminishing in wave-length with their distance from the body, and both sets of waves rapidly diminishing in amplitude with their distance from the body.
If the current-function of the water referred to the body considered as origin is ψ, then the equation of the form of the crest of a wave of velocity w, the crest of which travels along with the body, is
dψ = w ds
where ds is an element of the length of the crest. To integrate this equation for a solid of given form is probably difficult, but it is easy to see that at some distance on either side of the body, where the liquid is sensibly at rest, the crest of the wave will approximate to an asymptote inclined to the path of the body at an angle whose sine is w/V, where w is the velocity of the wave and V is that of the body.
The crests of the different kinds of waves will therefore appear to diverge as they get farther from the body, and the waves themselves will be less and less perceptible. But those whose wave-length is near to that of the wave of minimum velocity will diverge less than any of the others, so that the most marked feature at a distance from the body will be the two long lines of ripples of minimum velocity. If the angle between these is 2θ, the velocity of the body is w sec θ, where w for water is about 23 centimetres per second.
[Lord Kelvin’s formula (1) may be applied to find the surface-tension of a clean or contaminated liquid from observations upon the length of waves of known periodic time, travelling over the surface. If v = λ/τ we have
h denoting the depth of the liquid. In observations upon ripples the factor involving h may usually be omitted, and thus in the case of water (ρ = 1)
simply. The method has the advantage of independence of what may occur at places where the liquid is in contact with solid bodies.
The waves may be generated by electrically maintained tuning-forks from which dippers touch the surface; but special arrangements are needed for rendering them visible. The obstacles are (1) the smallness of the waves, and (2) the changes which occur at speeds too rapid for the eye to follow. The second obstacle is surmounted by the aid of the stroboscopic method of observation, the light being intermittent in the period of vibration, so that practically only one phase is seen. In order to render visible the small waves employed, and which we may regard as deviations of a plane surface from its true figure, the method by which Foucault tested reflectors is suitable. The following results have been obtained
(Phil. Mag.November 1890) for the tensions of various water-surfaces at 18° C., reckoned in C.G.S. measure.
The tension for clean water thus found is considerably lower than that (81) adopted by Quincke, but it seems to be entitled to confidence, and at any rate the deficiency is not due to contamination of the surface.
A calculation analogous to that of Lord Kelvin may be applied to find the frequency of small transverse vibrations of a cylinder of liquid under the action of the capillary force. Taking the case where the motion is strictly in two dimensions, we may write as the polar equation of the surface at time t
r = a + αncos nθ cos pt, (4)
where p is given by
If n = 1, the section remains circular, there is no force of restitution, and p = 0. The principal vibration, in which the section becomes elliptical, corresponds to n = 2.
Vibrations of this kind are observed whenever liquid issues from an elliptical or other non-circular hole, or even when it is poured from the lip of an ordinary jug; and they are superposed upon the general progressive motion. Since the phase of vibration depends upon the time elapsed, it is always the same at the same point in space, and thus the motion issteadyin the hydrodynamical sense, and the boundary of the jet is a fixed surface. In so far as the vibrations may be regarded as isochronous, the distance between consecutive corresponding points of the recurrent figure, or, as it may be called, thewave-lengthof the figure, is directly proportional to the velocity of the jet,i.e.to the square root of the head. But as the head increases, so do thelateralvelocities which go to form the transverse vibrations. A departure from the law of isochronism may then be expected to develop itself.
The transverse vibrations of non-circular jets allow us to solve a problem which at first sight would appear to be of great difficulty. According to Marangoni the diminished surface-tension of soapy water is due to the formation of a film. The formation cannot be instantaneous, and if we could measure the tension of a surface not more than1⁄100of a second old, we might expect to find it undisturbed, or nearly so, from that proper to pure water. In order to carry out the experiment the jet is caused to issue from an elliptical orifice in a thin plate, about 2 mm. by 1 mm., under a head of 15 cm. A comparison under similar circumstances shows that there is hardly any difference in the wave-lengths of the patterns obtained with pure and with soapy water, from which we conclude that at this initial stage, the surface-tensions are the same. As early as 1869 Dupré had arrived at a similar conclusion from experiments upon the vertical rise of fine jets.
A formula, similar to (5), may be given for the frequencies of vibration of a spherical mass of liquid under capillary force. If, as before, the frequency be p/2Π, and a the radius of the sphere, we have
n denoting the order of the spherical harmonic by which the deviation from a spherical figure is expressed. To find the radius of the sphere of water which vibrates seconds, put p = 2Π, T = 81, ρ = 1, n = 2. Thus a = 2.54 cms., or one inch very nearly.]
Tables of Surface-tension
In the following tables the units of length, mass and time are the centimetre, the gramme and the second, and the unit of force is that which if it acted on one gramme for one second would communicate to it a velocity of one centimetre per second:—
Table of Surface-Tension at 20° C.(Quincke).
Quincke has determined the surface-tension of a great many substances near their point of fusion or solidification. His method was that of observing the form of a large drop standing on a plane surface. If K is the height of the flat surface of the drop, and k that of the point where its tangent plane is vertical, then
T = ½(K − k)²gρ
Quincke finds that for several series of substances the surface-tension is nearly proportional to the density, so that if we call (K - k)² = 2T/gρ the specific cohesion, we may state the general results of his experiments as follows:—
Surface-Tensions of Liquids at their Point of Solidification. From Quincke.
The bromides and iodides have a specific cohesion about half that of mercury. The nitrates, chlorides, sugars and fats, as also the metals lead, bismuth and antimony, have a specific cohesion nearly equal to that of mercury. Water, the carbonates and sulphates, and probably phosphates, and the metals platinum, gold, silver, cadmium, tin and copper have a specific cohesion double that of mercury. Zinc, iron and palladium, three times that of mercury, and sodium, six times that of mercury.
Relation of Surface-tension to Temperature
It appears from the experiments of Brunner and of Wolf on the ascent of water in tubes that at the temperature t° centigrade
Lord Kelvin has applied the principles of Thermodynamics to determine the thermal effects of increasing or diminishing the area of the free surface of a liquid, and has shown that in order to keep the temperature constant while the area of the surface increases by unity, an amount of heat must be supplied to the liquid which is dynamically equivalent to the product of the absolute temperature into the decrement of the surface-tension per degree of temperature. We may call this thelatent heat of surface-extension.
It appears from the experiments of C. Brunner and C.J.E. Wolf that at ordinary temperatures the latent heat of extension of the surface of water is dynamically equivalent to about half the mechanical work done in producing the surface-extension.
References.—Further information on some of the matters discussed above will be found in Lord Rayleigh’sCollected Scientific Papers(1901). In its full extension the subject of capillarity is very wide. Reference may be made to A.W. Reinold and Sir A.W. Rücker (Phil. Trans.1886, p. 627); Sir W. Ramsay and J. Shields (Zeitschr. physik. Chem.1893, 12, p. 433); and on the theoretical side, see papers by Josiah Willard Gibbs; R. Eötvös (Wied. Ann., 1886, 27, p. 452); J.D. Van der Waals, G. Bakker and other writers of the Dutch school.
References.—Further information on some of the matters discussed above will be found in Lord Rayleigh’sCollected Scientific Papers(1901). In its full extension the subject of capillarity is very wide. Reference may be made to A.W. Reinold and Sir A.W. Rücker (Phil. Trans.1886, p. 627); Sir W. Ramsay and J. Shields (Zeitschr. physik. Chem.1893, 12, p. 433); and on the theoretical side, see papers by Josiah Willard Gibbs; R. Eötvös (Wied. Ann., 1886, 27, p. 452); J.D. Van der Waals, G. Bakker and other writers of the Dutch school.
(J. C. M.; R.)
1In this revision of James Clerk Maxwell’s classical article in the ninth edition of theEncyclopaedia Britannica, additions are marked by square brackets.2See Enrico Betti,Teoria della Capillarità: Nuovo Cimento(1867); a memoir by M. Stahl, “Ueber einige Punckte in der Theorie der Capillarerscheinungen,”Pogg. Ann.cxxxix. p. 239 (1870); and J.D. Van der Waal’sOver de Continuiteit van den Gasen Vloeistoftoestand. A good account of the subject from a mathematical point of view will be found in James Challis’s “Report on the Theory of Capillary Attraction,”Brit. Ass. Report, iv. p. 235 (1834).3Nouvelle théorie de l’action capillaire(1831).4Determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae(Göttingen, 1831).5Leçons de calcul des variations(Paris, 1861).6“Sur la surface de révolution dont la courbure moyenne est constante,”Liouville’s Journal, vi.7“Théorie géometrique des rayons et centres de courbure,”Bullet, de l’Acad. de Belgique, 1857.8Tractatus de Theoria Mathematica Phaenomenorum in Liquidis actioni gravitatis detractis observatorum(Bonn, 1857).9Journal de l’Institut, No. 1260.10Statique expérimental et théorique des liquides, 1873.
1In this revision of James Clerk Maxwell’s classical article in the ninth edition of theEncyclopaedia Britannica, additions are marked by square brackets.
2See Enrico Betti,Teoria della Capillarità: Nuovo Cimento(1867); a memoir by M. Stahl, “Ueber einige Punckte in der Theorie der Capillarerscheinungen,”Pogg. Ann.cxxxix. p. 239 (1870); and J.D. Van der Waal’sOver de Continuiteit van den Gasen Vloeistoftoestand. A good account of the subject from a mathematical point of view will be found in James Challis’s “Report on the Theory of Capillary Attraction,”Brit. Ass. Report, iv. p. 235 (1834).
3Nouvelle théorie de l’action capillaire(1831).
4Determinatio superficiei minimae rotatione curvae data duo puncta jungentis circa datum axem ortae(Göttingen, 1831).
5Leçons de calcul des variations(Paris, 1861).
6“Sur la surface de révolution dont la courbure moyenne est constante,”Liouville’s Journal, vi.
7“Théorie géometrique des rayons et centres de courbure,”Bullet, de l’Acad. de Belgique, 1857.
8Tractatus de Theoria Mathematica Phaenomenorum in Liquidis actioni gravitatis detractis observatorum(Bonn, 1857).
9Journal de l’Institut, No. 1260.
10Statique expérimental et théorique des liquides, 1873.
CAPISTRANO, GIOVANNI DI(1386-1456), Italian friar, theologian and inquisitor, was born in the little village of Capistrano in the Abruzzi, of a family which had come to Italy with the Angevins. He lived at first a wholly secular life, married, and became a successful magistrate; he took part in the continual struggles of the small Italian states in such a way as to compromise himself. During his captivity he was practically ruined and lost his young wife. He then in despair entered the Franciscan order and at once gave himself up to the most rigorous asceticism, violently defending the ideal of strict observance. He was charged with various missions by the popes Eugenius IV. and Nicholas V., in which he acquitted himself with implacable violence. As legate or inquisitor he persecuted the last Fraticelli of Ferrara, the Jesuati of Venice, the Jews of Sicily, Moldavia and Poland, and, above all, the Hussites of Germany, Hungary and Bohemia; his aim in the last case was to make conferences impossible between the representatives of Rome and the Bohemians, for every attempt at conciliation seemed to him to be conniving at heresy. Finally, after the taking of Constantinople, he succeeded in gathering troops together for a crusade against the Turks (1455), which at least helped to raise the siege of Belgrade, which was being blockaded by Mahommed II. He died shortly afterwards (October 23, 1456), and was canonized in 1690. Capistrano, in spite of this restless life, found time to work both in the lifetime of his master St Bernardino of Siena and after, at the reform of the order of the minor Franciscans, and to uphold both in his writings and his speeches the most advanced theories upon the papal supremacy as opposed to that of the councils.
See E. Jacob,Johannes von Capistrano, vol. i.: “Das Leben und Wirken Capistrans;” vol. ii.: “Die handschriftlichen Aufzeichnungen von Reden und Tractaten Capistrans,” (1st series, Breslau, 1903-1905).
See E. Jacob,Johannes von Capistrano, vol. i.: “Das Leben und Wirken Capistrans;” vol. ii.: “Die handschriftlichen Aufzeichnungen von Reden und Tractaten Capistrans,” (1st series, Breslau, 1903-1905).
(P. A.)
CAPITAL(Lat.caput, head), in architecture, the crowning member of the column, which projects on each side as it rises, in order to support the abacus and unite the square form of the latter with the circular shaft. The bulk of the capital may either be convex, as in the Doric capital; concave, as in the bell of the Corinthian capital; or bracketed out, as in the Ionic capital. These are the three principal types on which all capitals are based. The capitals of Greek, Doric, Ionic and Corinthian orders are given in the articleOrder.
From the prominent position it occupies in all monumental buildings, it has always been the favourite feature selected for ornamentation, and consequently it has become the clearest indicator of any style.
The two earliest capitals of importance are those which are based on the lotus (fig. 1) and papyrus (fig. 2) plants respectively, and these, with the palm tree capital, were the chief types employed by the Egyptians down to the 3rd centuryb.c., when,under the Ptolemaic dynasties, various river plants were employed decoratively and the lotus capital goes through various modifications (fig 3) Some kind of volute capital is shown in the Assyrian bas-reliefs, but no Assyrian capital has ever been found, those exhibited as such in the British Museum are bases.
The Persian capital belongs to the third class above mentioned, the brackets are carved with the lion (fig. 4) or the griffin projecting right and left to support and lessen the bearing of the architrave, and on their backs carry other brackets at right angles to support the cross timbers. The profuse decoration underneath the bracket capital in the palace of Xerxes and elsewhere, serves no structural function, but gives some variety to the extenuated shaft.
The earliest Greek capital is that shown in the Temple-fresco at Cnossus in Crete (1600b.c.); it was of the first type—convex, and was probably moulded in stucco: the second is represented by the richly carved example of the columns (fig 5) flanking the tomb of Agamemnon in Mycenae (c. 1100b.c.), also convex, carved with the chevron device, and with an apophyge on which the buds of some flowers are sculptured. The Doric capital of the temple of Apollo at Syracuse (c. 700b.c.) follows, in which the echinus moulding has become a more definite form: this in the Parthenon reaches its culmination, where the convexity is at the top and bottom with a delicate uniting curve The sloping side of the echinus becomes flatter in the later examples, and in the Colosseum at Rome forms a quarter round.
In the Ionic capital of the Archaic temple of Diana at Ephesus (560b.c.) the width of the abacus is twice that of its depth, consequently the earliest Ionic capital known was virtually a bracket capital. A century later, in the temple on the Ilissus, published in Stuart and Revett, the abacus has become square. One of the most beautiful Corinthian capitals is that from the Tholos of Epidaurus (400b.c.) (fig. 6); it illustrates the transition between the earlier Greek capital of Bassae and the Roman version of the temple of Mars Ultor (fig. 7).
The foliage of the Greek Corinthian capital was based on the Acanthus spinosus, that of the Roman on the Acanthus mollis; the capital of the temple of Vesta and other examples at Pompeii are carved with foliage of a different type.
Byzantine capitals are of endless variety; the Roman composite capital would seem to have been the favourite type they followed at first: subsequently, the block of stone was left rough as it came from the quarry, and the sculptor, set to carve it, evolvednew types of design to his own fancy, so that one rarely meets with many repetitions of the same design. One of the most remarkable is the capital in which the leaves are carved as if blown by the wind; the finest example being in Sta Sophia, Thessalonica; those in St Mark’s, Venice (fig. 8) specially attracted Ruskin’s fancy. Others are found in St Apollinare-in-classe, Ravenna. The Thistle and Pine capital is found in St Mark’s, Venice; St Luke’s, Delphi; the mosques of Kairawan and of Ibn Tūlūn, Cairo, in the two latter cases being taken from Byzantine churches. The illustration of the capital in S. Vitale, Ravenna (figs. 9 and 10) shows above it the dosseret required to carry the arch, the springing of which was much wider than the abacus of the capital.
The Romanesque and Gothic capitals throughout Europe present the same variety as in the Byzantine and for the same reason, that the artist evolved his conception of the design from the block he was carving, but in these styles it goes further on account of the clustering of columns and piers.
The earliest type of capital in Lombardy and Germany is that which is known as the cushion-cap, in which the lower portion of the cube block has been cut away to meet the circular shaft (fig. 11). These early types were generally painted at first with various geometrical designs, afterwards carved.
In Byzantine capitals, the eagle, the lion and the lamb are occasionally carved, but treated conventionally.
In the Romanesque and Gothic styles, in addition to birds and beasts, figures are frequently introduced into capitals, those in the Lombard work being rudely carved and verging on the grotesque; later, the sculpture reaches a higher standard; in the cloisters of Monreale (fig. 12) the birds being wonderfully true to nature. In England and France (figs. 13 and 14), the figures introduced into the capitals are sometimes full of character. These capitals, however, are not equal to those of the Early English school, in which the foliage is conventionally treated as if it had been copied from metal work, and is of infinite variety, being found in small village churches as well as in cathedrals.
Reference has only been made to the leading examples of the Roman capitals; in the Renaissance period (fig. 15) the feature became of the greatest importance and its variety almost as great as in the Byzantine and Gothic styles. The pilaster, whichwas employed so extensively in the Revival, called for new combinations in the designs for its capitals. Most of the ornament can be traced to Roman sources, and although less vigorous, shows much more delicacy and refinement in its carving.
(R. P. S.)
CAPITAL(i.e.capital stock or fund), in economics, generally, the accumulated wealth either of a man or a community, that is available for earning interest and producing fresh wealth. In social discussion it is sometimes treated as antithetical to labour, but it is in reality the accumulated savings of labour and of the profits accruing from the savings of labour. It is that portion of the annual produce reserved from consumption to supply future wants, to extend the sphere of production, to improve industrial instruments and processes, to carry out works of public utility, and, in short, to secure and enlarge the various means of progress necessary to an increasing community. It is the increment of wealth or means of subsistence analogous to the increment of population and of the wants of civilized man. Hence J.S. Mill and other economists, when seeking a graphic expression of the service of capital, have called it “abstinence.” The labourer serves by giving physical and mental effort in order to supply his means of consumption. The capitalist, or labourer-capitalist, serves by abstaining from consumption, by denying himself the present enjoyment of more or less of his means of consumption, in the prospect of a future profit. This quality, apparent enough in the beginnings of capital, applies equally to all its forms and stages; because whether a capitalist stocks his warehouse with goods and produce, improves land, lends on mortgage or other security, builds a factory, opens a mine, or orders the construction of machines or ships, there is the element of self-deprival for the present, with the risk of ultimate loss of what is his own, and what, instead of saving and embodying income productive form, he might choose to consume. On this ground rests the justification of the claims of capital to its industrial rewards, whether in the form of rent, interest or profits of trade and investment.
To any advance in the arts of industry or the comforts of life, a rate of production exceeding the rate of consumption, with consequent accumulation of resources, or in other words, the formation of capital, is indispensable. The primitive cultivators of the soil, whether those of ancient times or the pioneers who formed settlements in the forests of the New World, soon discovered that their labour would be rendered more effective by implements and auxiliary powers of various kinds, and that until the produce from existing means of cultivation exceeded what was necessary for their subsistence, there could be neither labour on their part to produce such implements and auxiliaries, nor means to purchase them. Every branch of industry has thus had a demand for capital within its own circles from the earliest times. The flint arrow-heads, the stone and bronze utensils of fossiliferous origin, and the rude implements of agriculture, war and navigation, of which we read in Homer, were the forerunners of that rich and wonderful display of tools, machines, engines, furnaces and countless ingenious and costly appliances, which represent so large a portion of the capital of civilized countries, and without the pre-existing capital could not have been developed. Nor in the cultivation of land, or the production simply of food, is the need of implements, and of other auxiliary power, whether animal or mechanical, the only need immediately experienced. The demands on the surplus of produce over consumption are various and incessant. Near the space of reclaimed ground, from which the cultivator derives but a bare livelihood, are some marshy acres that, if drained and enclosed, would add considerably in two or three years to the produce; the forest and other natural obstructions might also be driven farther back with the result, in a few more years, of profit; fences are necessary to allow of pasture and field crops, roads have to be made and farm buildings to be erected; as the work proceeds more artificial investments follow, and by these successive outlays of past savings in improvements, renewed and enhanced from generation to generation, the land, of little value in its natural state either to the owner and cultivator or the community, is at length brought into a highly productive condition. The history of capital in the soil is substantially the history of capital in all other spheres. No progress can be made in any sphere, small or large, without reserved funds possessed by few or more persons, in small or large amounts, and the progress in all cases is adventured under self-deprival in the meanwhile of acquired value, and more or less risk as to the final result.
Capital is necessarily to be distinguished from money, with which in ordinary nomenclature it is almost identical. Wealth may be in other things than money; oxen, wives, tools, have at different stages of civilization represented the recognized form of capital; and modern usage only treats capital as meaning the command of money because money is the ordinary form of it nowadays. The capital of a country can scarce be said to be less than the whole sum of its investments in a productive form, and possessing a recognized productive value.
Adam Smith’s distinction of “fixed” and “circulating” capital in theWealth of Nations(book ii. c. i.) cannot fail to be always useful in exhibiting the various forms and conditions under which capital is employed. Yet the principal phenomena of capital are found to be the same, whether the form of investment be more or less permanent or circulable. The machinery in which capital is “fixed,” and which yields a profit without apparently changing hands, is in reality passing away day by day, until it is worn out, and has to be replaced. So also of drainage and other land improvements. When the natural forests have been consumed and the landowners begin to plant trees on the bare places, the plantations while growing are a source of health, shelter and embellishment—they are not without a material profit throughout their various stages to maturity—and when, at the lapse of twenty or more years, they are ready to be cut down, and the timber is sold for useful purposes, there is a harvest of the original capital expended as essentially as in the case of the more rapid yearly crops of wheat or oats. The chief distinction would appear to rest in the element of time elapsing between the outlay of capital and its return. Capital may be employed in short loans or bills of exchange at two or three months, in paying wages of labour for which there may be return in a day or not in less than a year or more, or in operations involving within themselves every form of capital expenditure, and requiring a few years or ninety-nine years for the promised fructification on which they proceed. But the common characteristic of capital is that of a fund yielding a return and reproducing itself whether the time to this end be long or short. The division of expenditure or labour (all expenditure having a destination to labour of one kind or another) into “productive” and “unproductive” by the same authority (book ii. c. 3) is also apposite both for purposes of political economy and practical guidance, though economists have found it difficult to define where “productive expenditure” ends and “unproductive expenditure” begins. Adam Smith includes in his enumeration of the “fixed capital” of a country “the acquired and useful abilities of all the inhabitants”; and in this sense expenditure on education, arts and sciences might be deemed expenditure of the most productive value, and yet be wanting in strict commercial account of the profit and loss. It must be admitted that there is a personal expenditure among all ranks of society, which, though not in any sense a capital expenditure, may become capital and receive a productive application, always to be preferred to the grossly unproductive form, in the interest both of the possessors and of the community.