# Function Sentence Examples

But that, too, is a

**function**of present technology.In the sense he can

**function**but the memory is probably gone for good.Exportable technology can

**function**around the world.She didn't understand how humans could feel so much and still

**function**when she was overwhelmed.Tests revealed normal brain

**function**, and there was no indication of any permanent damage.Her mind was beginning to

**function**somewhere near normal.And yes, everything and everyone in my life has a

**function**and purpose.The first is " the law that thought is a

**function**of the brain."Their

**function**is not quite clear.To this high conception of a preacher's

**function**the prophet was faithful throughout his career.AdvertisementIt was then that my slowly reacting brain, flowing like cold molasses began to

**function**, more than a gerbil driven wheel.In many sees there were no vidames, their

**function**being exercised by viscounts or chatelains.Depending on

**function**, robots can come in all shapes and sizes, and I see no compelling reason to make them like humans.Unable to

**function**from shock, he sat down on a rock overlooking the lake.He was performing the same

**function**, but meeting him didn't darken Dean's mood appreciably.AdvertisementFree and peaceful societies

**function**best when government is transparent and open.Based on her medical records, the tumor didn't grow until she hit puberty and didn't interfere with her ability to

**function**before a few years ago, Wynn started.Simspon concluded that for a given wind velocity dissipation is practically a linear

**function**of ionization.The polyps are all non-sexual individuals whose

**function**is purely nutritive.Its

**function**is to examine criminal cases and to decide whether they shall be referred for trial to the lower courts or the cours dassises.AdvertisementThe most important change introduced by the new law has been the creation in every province of a provincial administrative junta entrusted with the supervision of communal administrations, a

**function**previously discharged by the provincial deputation.Early in the 19th century the venue of the dinner, which had now become a ministerial

**function**, was transferred to Greenwich, and though at first not always held here, was later celebrated regularly at the "Ship," an hotel of ancient foundation, closed in 1908.If Ritschl had clearly shown that judgments of value enfold and transform other types of knowledge, just as the "spiritual man" includes and transfigures but does not annihilate the "natural man," then within the compass of this spiritually conditioned knowledge all other knowledge would be seen to have a

**function**and a home.When Ethel did the inviting, the

**function**was nearly always out of town.Accepting the law he distinguishes productive from permissive or transmissive

**function**(p. 32), and, rejecting the view that brain produces thought, he recognizes that in our present condition brain transmits thought, thought needs brain for its organ of expression; but this does not exclude the possibility of a condition in which thought will be no longer so dependent on brain.AdvertisementOne of the chief names for the priest was baru - literally the "inspector" - which was given to him because of the prominence of his

**function**as an inspector of livers for the purpose of divining the intention of the gods.As it is with mechanical improvements, so is it to a still greater degree with changes in the

**function**of timbre in art.An instance of this characteristic

**function**, specially remarkable because the composer has taken exceptional measures for it, is Beethoven's overture to Fidelio.Bach's conception of the

**function**of an instrument is that it holds a regular part in a polyphonic scheme; and his blending of tones is like the blending of colours in a purely decorative design.Laplace is due the theoretical proof that this

**function**is independent of temperature and pressure, and apparent experimental confirmation was provided by Biot and Arago's, and by Dulong's observations on gases and vapours.Finally the theory defined is opposed to all forms of realism, whether in the older form which sought to reduce mind to a

**function**of matter, or in any of the newer forms which seek for the ultimate essence of both mind and matter in some unknown force or energy which, while in itself it is neither, yet contains the potentiality of both.Perhaps the earliest of such specializations is connected with the reproductive

**function**.Their chief

**function**is to ordain, and to act as "intercessors."Mention may also be made of the Tribunal des Conflits, a special court whose

**function**it is to decide which is the competent tribunal when an administration and a judicial court both claim or refuse to deal with a given case.The principal

**function**of these courts is the hearing of appeals both civil and criminal from the courts of first instance; only in.All access to the Deity is restricted to the one priesthood and to the one sanctuary at Jerusalem; the worshipping subject is the nation of Israel as a unity, and the

**function**of worship is discharged on its behalf by divinely chosen priests.The formation of a massive body naturally involves the localization of the absorptive region, and the

**function**of absorption (which in the simpler forms is carried out by the whole of the vegetative part of the mycelium penetrating a solid or immersed in a liquid substratum) is subserved by the outgrowth of the hyphae of the surface-layer of that region into rhizoids, which, like those of the Algae living on soil, resemble the root-hairs of the higher plants.Besides absorption, assimilation, conduction and protection there is another very important

**function**for which provision has to be made in any plant-body of considerable size, especially when raised into the air, that of support.As a secondary

**function**we may recognize, in certain cases, the power of closing wounds, which results from the rapid coagulation of exuded latex in contact with the air.The requirements of the several protoplasts must be met by supplies from without, and, as many of them are deep seated, varieties of need arise, so that various members of the colony are set apart for special duties, masses of them being devoted to the discharge of one

**function**, others to that of another, and so on.The latter

**function**has been found to be of extreme importance in the case of plants exposed to the direct access of the suns rays, the heat of which would rapidly cause the death of the protoplasts were it not employed in the evaporation of the water.Another enzyme, rennet, which in the animal body is proteolytic, is frequently met with in plants, but its

**function**has not been ascertained.Every plant is constrained to carry Out its functions of germination, growth, nutrition, reproduction, &c., between certain limits of temperature, and somewhere between the extremes of these limits each

**function**finds ao optimum temperature at which the working of the living machinery is at its best, and, other things being equal, any great departure from this may induce pathological conditions; and many disasters are due to the failure to provide such suitable temperaturese.g.The special

**function**of the so-called "Socratic dialectic" was to show the inadequacy of popular beliefs.As your husband, what will he consider his most important

**function**?Nevertheless, the

**function**of reproduction is occasionally exercised by larvae.Chladni's experiment of strewing a vibrating bell with flour, investigated the nature of sound and the

**function**of the air in respiration and combustion, and originated the idea of using the pendulum as a measure of gravity.The

**function**of this pair of muscles is the closing of the valves.A similar expression for the variation of the specific heat S at constant pressure is obtained from the second expression in (8), by taking p and 0 as independent variables; but it follows more directly from a consideration of the variation of the

**function**(E+pv).This latter

**function**, however, is one unknown to the English common law.Besides the distinctions of human and nonhuman, hostile and friendly, the demons in which the lower races believe are classified by them according to

**function**, each class with a distinctive name, with extraordinary minuteness, the list in the case of the Malays running to several score.Their monotheism remains Semitic - even in their conception of the cosmogonic and illuminating

**function**of Wisdom they regard God as standing outside the world of physical nature and man, and do not grasp or accept the idea of the identity of the human and the divine; there is thus a sharp distinction between their general theistic position and that of Greek philosophy.The collar-pores are remarkable for their constancy; this is probably owing to the fact that they have become adapted to a special

**function**, the inhalation of water to render the collar turgid during progression.The respiratory current of water is therefore conducted to the exterior by different means from that adopted by Amphioxus, and this difference is so great that the theory which seeks to explain it has to postulate radical changes of structure,

**function**and topography.It seems likely that the coelomic pore-canals were originally excretory organs, but in the existing Enteropneusta the pore-canals (especially the collar canals) have, as we have seen, acquired new functions or become vestigial, and the

**function**of excretion is now mainly accomplished by a structure peculiar to the Enteropneusta called the glomerulus, a vascular complex placed on either side of the anterior portion of the stomochord, projecting into the proboscis-coelom.Interchanges must be supposed to go on whether a current passes or not, the

**function**of the electric forces in electrolysis being merely to determine in what direction the parts of the molecules shall work their way through the liquid and to effect actual separation of these parts (or their secondary products) at the electrodes.This result again indicates that the parts of the molecules are effectively separate from each other, the

**function**of the electric forces being merely directive.Clausius extended to electrolysis the chemical ideas which looked on the opposite parts of the molecule as always changing partners independently of any electric force, and regarded the

**function**of the current as merely directive.Its exact

**function**is not fully understood.Two other pairs have been termed divaricators by Hancock, or cardinal muscles (" muscles diducteurs " of Gratiolet), and have for

**function**the opening of the valves.The

**function**of these muscles, according to the same authority, is not only that of erecting the shell; they serve also to attach the peduncle to the shell, and thus effect the steadying of it upon the peduncle.Those who have not seen the animal in life, or who did not believe in the possibility of the valves crossing each other with a slight obliquity, would not consent to appropriating any of its muscles to that purpose, and consequently attributed to all the lateral muscles the simple

**function**of keeping the valves in an opposite position, or holding them adjusted.R is a

**function**of the coefficients which is called the " resultant " or " eliminant " of the k equations, and the process by which it is obtained is termed " elimination."Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a

**function**which vanishes if any one system of values, common to the first two equations, also satisfies the third.The

**function**Zap 1 a 2 P2 ...an n being as above denoted by a partition of the weight, viz.Theorem.- The

**function**symbolized by (n), viz.The general monomial symmetric

**function**is a P1 a P2 a P3.The weight of the

**function**is the sum of the numbers in the bracket, and the degree the highest of those numbers.The sum of the monomial functions of a given weight is called the homogeneous-product-sum or complete symmetric

**function**of that weight; it is denoted by h.; it is connected with the elementary functions by the formula 1 7r1l7r2!7r3!Application to Symmetric

**Function**Multiplication.-An example will explain this.It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric

**function**a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a

**function**which does not involve the variables, viz.From these formulae we derive two important relations, dp4 = or the

**function**F, on the right which multiplies r, is said to be a simultaneous invariant or covariant of the system of quantics.We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a

**function**of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.Evidently the idea of the great Yokoya experts, the originators of the style, was to break away from the somewhat formal monotony of ordinary engraving, where each line performs exactly the same

**function**, and to convert the chisel into an artists i It is first boiled in a lye obtained by lixiviating wood ashes; it is next polished with charcoal powder; then immersed in plum vinegar and salt; then washed with weak lye and placed in a, tub of water to remove all traces of alkali, the final step being to digest in a boiling solution of copper sulphate, verdigris and water.It is apparent that a vitrified enamel may be made to perform, in part at any rate, the

**function**of a porcelain glaze.Spencer welcomed the Darwinian theory, and enriched it with the phrase" survival of the fittest "; but he did not give up the (Lamarckian) belief in the hereditary transmission of the modifications of organisms by the exercise of

**function**.On the other hand, he advances too easily from the maxim that

**function**is prior to, and makes, structure to the conclusion that the results of use and disuse are therefore immediately incarnated in structural adaptations capable of hereditary transmission.The result was the formation of a cabinet belonging, in Fox's own words, partly to the king and partly to the country - that is to say, partly of Whigs who wished to restrain the king, and partly of the king's friends, represented by Lord Shelburne, whose real

**function**was to baffle the Whigs.The Word of God alone is there to do it."Nevertheless Luther assigned to the state, which he assumes to be Christian, the

**function**of maintaining the Gospel and the Word of God in public life.One or more reserve teeth, in various stages of development, lie between the folds of the gum and are ready to take the place of the one in

**function**whenever it is lost by accident, or shed.In the last ten years of his life Horace resumed his lyrical

**function**for a time, under pressure of the imperial command, and produced some of the most exquisite and mature products of his art.This capacity is then a

**function**of the geometrical dimensions of the conductor, and can be mathematically determined in certain cases.The mathematical importance of this

**function**called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.This is mathematically expressed by the statement that dE is an exact differential of a

**function**of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.He therefore employed the corresponding expression for a cycle of infinitesimal range dt at the temperature t in which the work dW obtainable from a quantity of heat H would be represented by the equation dW =HF'(t)dt, where F'(t) is the derived

**function**of F(t), or dF(t)/dt, and represents the work obtainable per unit of heat per degree fall of temperature at a temperature t.It simply asserts that the efficiency

**function**F'(t), which is known as Carnot's**function**, is the same for all substances at the same temperature.Holtzmann (1845) by the same assumption deduced the value J/T for the

**function**F'(t), but obtained erroneous results by combining this assumption with the caloric theory.Kelvin had previously proposed to define an absolute scale of temperature independent of the properties of any particular substance in terms of Carnot's

**function**by making F'(t) constant.He now proposed to define absolute temperature as proportional to the reciprocal of Carnot's

**function**, so as to agree as closely as possible with the scale of the gas thermometer.Since the two expressions (9) are the partial differential-coefficients of a single

**function**E of the independent variables v and 0, we shall obtain the same result, namely d 2 E/d0dv, if we differentiate the first with respect to v and the second with respect to 0.Observing that F is a

**function**of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.The specific heats may be any

**function**of the temperature consistently with the characteristic equation provided that their difference is constant.If we assume that s is a linear

**function**of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =oIt is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a

**function**of the temperature only.But this procedure in itself is not sufficient, because, although it would be highly probable that a gas obeying Boyle's law at all temperatures was practically an ideal gas, it is evident that Boyle's law would be satisfied by any substance having the characteristic equation pv = f (0), where f (0) is any arbitrary

**function**of 0, and that the scale of temperatures given by such a substance would not necessarily coincide with the absolute scale.This gives by equation (9) the condition Odp/d0 =p, which is satisfied by any substance possessing the characteristic equation p/0=f(v), where f(v) is any arbitrary

**function**of v.The characteristic equation of the fluid must then be of the form v/0=f(p), where f(p) is any arbitrary

**function**of p. If the fluid is a gas also obeying Boyle's law, pv = f (0), then it must be an ideal gas.Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =f(p) - SA /30 3, in which f(p) is an arbitrary

**function**of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put f(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .The advantage of this type of equation is that c is a

**function**of the temperature only.Other favourite types' of equation for approximate work are (I) p=RO/v±f(v), which makes p a linear

**function**of 0 at constant volume, as in van der Waal's equation; (2) v=RO/p+f(p), which makes v a linear**function**of 0 at constant pressure.At higher densities it is probable that more complex aggregates would be formed, so that as the effect of the collisions became more important c would cease to be a

**function**of the temperature only; experiment, indeed, shows this to be the case.The

**function**J = E-94,, has been called the " free energy " of the substance by Helmholtz, and 90 the " bound energy."This

**function**is also called the " thermodynamic potential at constant volume " from the analogy with the condition of minimum potential energy as the criterion of stable equilibrium in statics.If J', J" represent the values of the

**function**for unit mass of the substance of specific volumes v' and v" in the two states at temperature 0 and pressure and if a mass m is in the state v', and 1-m in the.The

**function**G is represented by the negative area D"DM under the isothermal, bounded by the isopiestic DM and the axis of pressure.The increment of 00 is always greater than that of the total heat F=E+pv, except in the special case of an equilibrium change at constant temperature and pressure, in which case both are equal to the heat absorbed in the change, and the

**function**G remains constant.This is geometrically obvious from the form of the area representing the

**function**on the indicator diagram, and also follows directly from the first law.If G' and G" are the values of the

**function**G for the two states in equilibrium at the same pressure and temperature, we must have G' =G".Assuming the

**function**G to be expressed in terms of p and 0, this condition represents the relation between p and 0 corresponding to equilibrium between the two states, which is the solution of the relation (v" - v')dp/dO=L/D, (5).To find the border curve of equilibrium between the two states, giving the saturation pressure as a

**function**of the temperature, we have merely to equate the values of G and G".This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a

**function**of the temperature only.Finally, the

**function**of the archbishop as judge in a court of appeal, though it still subsists, is of little practical importance now that the clergy, in civil matters, are universally subject to the secular courts.The "powers" (numina, not dei), which thus become the objects of worship, are spirits specialized in

**function**and limited in sphere.Migration in general may be described as a natural

**function**of social development.The development of a true insect society among the Hymenoptera is dependent on a differentiation among the females between individuals with well-developed ovaries (" queens ") whose special

**function**is reproduction; and individuals with reduced or aborted ovaries (" workers ") whose duty is to build the nest, to gather food and to tend and feed the larvae.In the hive-bee and among ants, on the other hand, there are constant structural distinctions between queen and worker, and the

**function**of the queen bee in a hive is confined to egg-laying, the labour, of the community being entirely done by the workers.The hinder abdominal segments in the male show a curious asymmetrical arrangement, the sixth segment bearing on its upper side a small stalked plate (strigil) of unknown

**function**, furnished with rows of teeth.The

**function**of such an agency is performed in the United States of America by the express companies (see Express).Its highest

**function**is the contemplation of the divine unity, discoverable under the manifold of objects.The former contrivances consist essentially of levers or cams with toothed surfaces or gripping shoes mounted upon transverse axes attached to the sides of the cage, whose

**function**is to take hold of the guides and support the cage in the event of its becoming detached from the rope.By inference only, increasing complication of stomach with ruminating

**function**superadded.The corresponding solid figure, in its most general form, is such as would be constructed to represent the relation of a magnitude E to two magnitudes F and G of which it is a

**function**; it would stand on a plane base, and be comprised within a cylindrical boundary whose cross-section might be of any shape.The area of the trapezette, measured from the lower bounding ordinate up to the ordinate corresponding to any value of x, is some

**function**of x.The statement that the ordinate u of a trapezette is a

**function**of the abscissa x, or that u=f(x), must be distinguished from u =f(x) as the equation to the top of the trapezette.The simplest case is that in which u is constant or is a linear

**function**of x, i.e.The next case is that in which u is a quadratic

**function**of x, i.e.Generally, if the area of a trapezette for which u is an algebraical

**function**of x of degree 2n is given correctly by an expression which is a linear**function**of values of u representing ordinates placed symmetrically about the mid-ordinate of the trapezette (with or without this mid-ordinate), the same expression will give the area of a trapezette for which u is an algebraical**function**of x of degree 2n + 1.In the case, therefore, of any solid whose cross-section at distance x from one end is a quadratic

**function**of x, the position of the crosssection through the centroid is to be found by determining the position of the centre of gravity of particles of masses proportional to So, S2, and 4S 1, placed at the extremities and the middle of a line drawn from one end of the solid to the other.If u is an algebraical

**function**of x of degree not exceeding p, and if the area of a trapezette, for which the ordinate v is of degree not exceeding p+q, may be expressed by a formula Aovo-1--yivi+..This ordinate will be an algebraical

**function**of x, and we can again apply a suitable formula.The area of the section by a plane at distance x from the edge 0 is a

**function**of x whose degree is the same as that of u.The volume of the briquette for which u is a

**function**of x and y is found by the operation of double integration, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order.If, as is usually the case, the ordinate throughout each strip of the trapezette can be expressed approximately as an algebraical

**function**of the abscissa, the application of the integral calculus gives the area of the figure.These results may be extended to the calculation of an expression of the form fxo u4(x)dx, where 0(x) is a definite

**function**of x, and the conditions with regard to u are the same as in § 82.It is also clearly impossible to express u as an algebraical

**function**of x and y if some value of du/dx or duldy is to be infinite.Even where u is an explicit

**function**of x, so that f x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.Its

**function**is to deliberate on subjects of common concern to the entire denomination, and to publish such opinions and counsels as a majority may see fit to send forth to the churches.There is a tendency, moreover, to accord to the conferences the

**function**of determining the tests of ministerial standing in the Congregational denomination.In some of the states the licensing of preachers, which was formerly left to the voluntary associations of ministers in the different localities, has been made a

**function**of the state conferences.The

**function**of the angels is that of the supernatural servants of God, His agents and representatives; the Angel of Yahweh, as we have seen, is a manifestation of God.In Scripture the

**function**of the angel overshadows his personality; the stress is on their ministry; they appear in order to perform specific acts.In some of them the hind toe, which has already ceased to have any

**function**in the lapwing, is wholly wanting.C. Burkitt's The Gospel History (1906) vigorously sketches the book's dominant characteristics and true

**function**.He established the Federal Department of Commerce and Labor, the secretary of which has a seat in the cabinet, and in which there exists a bureau of corporations possessing the specific

**function**of inspecting and supervising interstate corporations - an entirely new feature in American government.Its colour varies with the liturgical colour of the day, or of the

**function**at which it is worn.This

**function**is named the "power" of the two spheres, and it is important in the investigation of systems of spheres.As to those of the first description, it is from the British charters that they derive a capacity by which they are considered as a public body, or at all capable of any public

**function**....In the modern metal bridge every member has a definite

**function**and is subjected to a calculated straining action.The

**function**of the flanges is to resist a horizontal tension and compression distributed practically uniformly on their cross sections.Her letter to the emperor, pervaded with he religious and almost mystic sentiments which predominate in the queen's mind, particularly since the death of Prince Albert, seems to have made a deep impression on the sovereign who, amid the struggles of politics, had never completely repudiated the philanthropic theories of his youth, and who, on the battlefield of Solferino, covered with the dead and wounded, was seized with an unspeakable horror of war."Moreover, Disraeli's two premierships (1868, 1874-80) did a good deal to give new encouragement to a right idea of the constitutional

**function**of the crown.The laws of the Day of Atonement belong to the Priestly Code.4 There is no trace of this

**function**before the exile; the earliest reference to any such special time of atonement being the proposal of Ezek.In later Judaism, especially from about ioo B.C., great stress was laid on the Day of Atonement, and it is now the most important religious

**function**of the Jews.Mexican acquaintance with the signs related only to their secondary

**function**as dies (so to speak) with which to stamp recurring intervals of time.Religious or semi-religious ceremonies, however, play a great part in the life of the Siamese, and few weeks pass without some great

**function**or procession.But on the modern theory, which includes the play of electrical phenomena as a

**function**of the aether, there are other considerations which show that this number io 2 is really an enormous overestimate; and it is not impossible that the co-efficient of ultimate inertia of the aether is greater than the co-efficient of inertia (of different kind) of any existing material substance.Returning now to the aether, on our present point of view no such complications there arise; it must be regarded as a continuous uniform medium free from any complexities of atomic aggregation, whose

**function**is confined to the transmission of the various types of physical effect between the portions of matter.Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(VX-1)/dX-', the value of K occurring in V being a

**function**of X determined by the law of optical dispersion of the medium.In his train also are found Enyo, the goddess of war who delights in bloodshed and the destruction of cities; his sister, Eris, goddess of fighting and strife; and the Keres, goddesses of death, whose

**function**it is especially to roam the battle-field, carrying off the dead to Hades.It is consistent with this circle of ideas that initiation into the profound mysteries of the liturgy was regarded, together with the preservation of dogma, as the most exalted

**function**of theology.On the other hand the seer, diviner and prophet is a minister whose

**function**it is to communicate God's will or word to man.There was also a third kind of priest called the zammaru, whose

**function**it was to sing hymns.There remains, indeed, one other sacred

**function**of great importance in the ancient world in which the Greek priests had a share.Thus for the

**function**= 1 I -x.Introducing another letter z, and considering the

**function**I+xz.And similarly, considering the

**function**I +z(x+x2+..)...+Nxnzk-..Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 Daniel Bernoulli obtained the

**function**of zero order as a solution to the problem of the oscillations of a chain suspended at one end.Mehler, who proved that a simple relation existed between the

**function**of zero order and the zonal harmonic of order n.The mandibles are normally five-jointed, with remnants of an outer branch on the second joint, the biting edge varying from strong development to evanescence, the terminal joints or " palp " giving the organ a leg-like appearance and

**function**, which disappears in suctorial genera such as Paracytherois.The variable first maxillae are seldom pediform, their

**function**being concerned chiefly with nutrition, sensation and respiration.In 1892 he distinguished the former as those in which the first antennae of the male have both members modified for holding the female, and the genital openings of the female have a ventral position, sometimes in close proximity, sometimes strongly lateral; the latter as those in which the first antennae of the male are similar to those of the female, the

**function**of holding her being transferred to the male maxillipeds, while the genital openings of the female are dorsal, though at times strongly lateral.He has observed that in young specimens of Siren lacertina (the larva is still unknown) the gills are rudimentary and functionless, and that it is only in large adult specimens that they are fully developed in structure and

**function**; he therefore concludes that the sirens are the descendants of a terrestrial type of batrachians, which passed through a metamorphosis like the other members of their class, but that more recently they have adopted a permanently aquatic life, and have resumed their branchiae by reversion.It is in this way that the

**function**of the seer is closely connected (as in the case of Balaam) with sacrifices.The rise of this

**function**of the prophets is plainly parallel with the change which took place under the kings in the position of the priestly oracle; the Torah of the priests now dealt rather with permanent sacred ordinances than with the giving of new divine counsel for special occasions.But in point of fact the

**function**of the new prophecy was not to preserve but to destroy Israel, if Israel still meant the actual Hebrew nation, with its traditional national life.The current theological formula for this two-sided position is that the prophets are at once preachers of the law and forerunners of the gospel; and, as it is generally assumed that they found the law already written, their originality and real importance is made to lie wholly in their evangelical

**function**.So long as the great problems of religion could be envisaged as problems of the relation of Yahweh to Israel as a nation the prophets continued to speak and to bring forth new truths; but the ultimate result was that it became apparent that the idea of moral government involved the destruction of Israel, and then the

**function**of prophecy was gone because it was essentiall y national in its objects.It had therefore to find out a new world and a new spiritual

**function**, in order first to establish the existence of what it desiderated, and then to realize and describe what it had proved to exist.Money, however, is in men's actual transactions the measure of value, as well as the vehicle of exchange; and the precious metals are best suited for this

**function**, as varying little in their own value for periods of moderate length; for distant times, corn is a better standard of comparison.The mathematical

**function**log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.The notation log x is generally employed in English and American works, but on the continent of Europe writers usually denote the

**function**by lx or lg x.The logarithmic

**function**is most naturally introduced into analysis by the equation log x= x ?Thus log x is the integral

**function**of 1/x, and it can be shown that log x is a genuinely new transcendent, not expressible in finite terms by means of functions such as algebraical or circular functions.A relation which is of historical interest connects the logarithmic

**function**with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.The

**function**log x as x increases from o towards w steadily increases from - co towards +co.The exponential

**function**possesses the properties (i.) exp (x+y) =exp x X exp y.It is customary, therefore, to denote the exponential

**function**by e x, and the result ex = I +x+x2/2 !It follows from this property of the

**function**that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform**function**, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.The exponential

**function**, which may still be defined as the inverse of the logarithmic**function**, is, on the other hand, a uniform**function**of x, and its fundamental properties may be stated in the same form as for real values of x.An alternative method of developing the theory of the exponential

**function**is to start from the definition exp x = I +x+x2/2 !The progress of navigation and the association of divinities of the sky with maritime affairs probably also assisted to bring about the change, although the memory of her earlier

**function**as a goddess of childbirth survived till imperial times.The ordinary pleasures of festivals were mingled with all this, such as dances in beast-masks, sham fights and children's games, but the type of a religious

**function**was a sickening butchery followed by a cannibal feast.Only what falls under the first and second of the divisions so indicated can be said to have discharged a

**function**in developing philosophy; only so much constitutes Schelling's philosophy proper.The

**function**of Naturphilosophie is to exhibit the ideal as springing from the real, not to deduce the real from the ideal.The absolute was left with no other

**function**than that of removing all the differences on which thought turns.Each of these limbs was twobranched, the external branch consisting of a slender fringed flagellum possibly respiratory in

**function**, and the inner of a normal jointed ambulatory leg.It is probable that the first of these forms is the primary one and the second in most cases a development from it due to (i.) the influence of other individual cults, (ii.) anthropomorphic tendencies, (iii.) the influence of chieftainship, hereditary and otherwise, (iv.) annual sacrifice of the sacred animal and mystical ideas connected therewith, (v.) syncretism, due either to unity of

**function**or to a philosophic unification, (vi.) the desire to do honour to the species in the person of one of its members, and possibly other less easily traceable causes.Its main

**function**was that of passing the lex curiata which was necessary for the ratification both of the imperium of the higher magistracies of the people, and of the potestas of those of lower rank.After the peace of Villafranca he was sent to organize the army of the Central Italian League (composed of the provisional governments of Tuscany, Modena, Parma and Romagna), and converted it in a few months into a well-drilled body of 45, 000 men, whose

**function**was to be ready to intervene in the papal states on the outbreak of a revolution.The Senates act as courts for the trial of state officers impeached by the house (in imitation of the British House of Lords and the Federal Senate), and have in some states Powers and the

**function**of confirming or refusing appointments Funcons made by the governor.He has also the almost mechanical

**function**of representing the state for various formal purposes, such as demanding from other states the extradition of offenders, the issuing of writs for the election of members of the legislature and of members of the Federal House of Representatives, and the receiving of reports from various state officials or boards.The vice-president of the United States is ex officio presiding officer of the Senate, and this is his only active

**function**in the government.The judicial

**function**of the Senate is to sit as a high court for the trial of persons impeached by the House of Representatives, a vote of two-thirds of those present being needed for conviction.This latter

**function**is discharged by written messages addressed by the president to Congress, the message sent at the beginning of each session being usually the most important; but the suggestions made in these messages do not necessarily or directly induce legislation, although it is open to him to submit a bill or have one drafted by a minister presented to Congress through a member.Nevertheless, the distribution of offices under the so-called spoils system remains the most important ordinary

**function**of the president, and the influence he exerts over Congress and legislation is due mainly to his patronage.In ordinary times the president may be almost compared to the managing clerk in a large business establishment, whose chief

**function**is to select his subordinates, the policy of the concern being in the hands of the board of directors.There is, of course, a committee for every state, and at the head of the whole stands .a national committee for the whole Union, whose special

**function**it is to make arrangements for the conduct of party work at a presidential election.The other and parallel branch of the party organization consists of the bodies whose

**function**it is to nominate party candidates for elective posts, whether legislative or Pa,aty Noni.The paired ctenidia are very greatly developed right and left of the elongated body, and form the most prominent organ of the group. Their

**function**is chiefly not respiratory but nutritive, since it is by the currents produced by their ciliated surface that food-particles are brought to the feebly-developed mouth and buccal cavity.Septibranchia Gills have lost their respiratory

**function**, and are transformed into a muscular septum on each side between mantle and foot.On the whole, then, the most probable conclusion is that the original ancestral form of the Mollusca was unsegmented, possessed one pair of true nephridia, and one pair of coelomic ducts whose

**function**was to conduct the generative products to the exterior.Near the base of the ctenidium is a patch of sensory epithelium innervated from the branchial nerve, forming a sense-organ called the osphradium, whose

**function**is to test the water entering the branchial cavity.Two days later he showed that he intended to exercise the right of the President to address Parliament direct - a right which had fallen into desuetude - by sending a message to the Chambers, in which he stated that it was his

**function**as President "to be a guide and adviser for public opinion in times of crisis" and "to seek to make a rational choice between conflicting interests."He does, however, lay much stress upon the naturally social character of man; and this points forward to that treatment of morality as a

**function**of the social organism which characterizes modern ethical theory.They were parish ministers and subject like their brethren to church courts; their added

**function**was to plant churches, and place ministers, elders and deacons where required.Elders are rulers; their

**function**also is spiritual, though practical and disciplinary.These investigations led him to the announcement of the fundamental law of action between elements of current, or currents in infinitely short lengths of linear conductors, upon one another at a distance; summed up in compact expression this law states that the action is proportional to the product of the current strengths of the two elements, and the lengths of the two elements, and inversely proportional to the square of the distance between the two elements, and also directly proportional to a

**function**of the angles which the line joining the elements makes with the directions of the two elements respectively.He discovered a

**function**, which has been called the potential of one circuit on another, from which he deduced a theory of induction, completely in accordance with experiment.After he had educated himself by the study of the phenomena of lines of magnetic force in his discoveries on electromagnetic induction, he applied the same conception to electrostatic phenomena, and thus created the notion of lines of electrostatic force and of the important

**function**of the dielectric or non-conductor in sustaining them.In the Isopoda the respiratory

**function**has been taken over by the abdominal appendages, both rami or only the inner becoming thin or flattened.Although the excretory

**function**of these has been demonstrated by physiological methods, however, their morphological relations are not clear.When feathered or provided with secondary barbs the setae will respond to movements or vibrations in the surrounding water, and have been supposed to have an auditory

**function**.Recent observations, however, make it very doubtful whether aquatic Crustacea can hear at all, in the proper sense of the term, and it has been shown that one

**function**, at least, of the so-called otocysts is connected with the equilibration of the body.In certain Copepoda and Ostracoda glands of the same type produce a phosphorescent substance, and others, in certain Amphipoda and Branchiura, are believed to have a poisonous

**function**.It should be noticed that the real

**function**denoted by (ab) 2 is not the square of a real**function**denoted by (ab).For a single quantic of the first order (ab) is the symbol of a

**function**of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.If the forms be all linear and different, the

**function**is an invariant, viz.For these only will the symbolic product be replaceable by a linear

**function**of products of real coefficients.Similarly regarding 1 x 2 as additional parameters, we see that every covariant is expressible as a rational

**function**of n fixed covariants.To exhibit any covariant as a

**function**of uo, ul, a n = (aiy1+a2y2) n and transform it by the substitution fi y 1+f2 y where f l = aay 1, f2 = a2ay -1, x y - x y = X x thence f .The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral

**function**of the fundamental invariants it is expressible as a linear**function**of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.Two of these show that the leading coefficient of any covariant is an isobaric and homogeneous

**function**of the coefficients of the form; the remaining two may be regarded as operators which cause the vanishing of the covariant.Every symmetric

**function**denoted by partitions, not involving the figure unity (say a non-unitary symmetric**function**), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.In order to obtain the seminvari ants we would write down the (w; 0, n) terms each associated with a literal coefficient; if we now operate with 52 we obtain a linear

**function**of (w - I; 8, n) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0, n) linear equations; hence (w; 8, n)-(w-I; 0, n) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8, n) - (w - I; 0, n).Putting n equal to co, in a generating

**function**obtained above, we find that the**function**, which enumerates the asyzvgetic seminvariants of degree 0, is 1 1-z2.1-z3.1-z4....1-z0 that is to say, of the weight w, we have one form corresponding to each non-unitary partition of w into the parts 2, 3, 4,...0.The existence of such a relation, as 0-1+0-2+.,.+cr2=0, necessitates the vanishing of a certain

**function**of the coefficients A2, A 3, ...A 9, and as a consequence one product of these coefficients can be eliminated from the expanding form and no seminvariant, which appears as a coefficient to such a product (which may be the whole or only a part of the complete product, with which the seminvariant is associated), will be capable of reduction.The generating

**function**is I - z2' 52 For 0 =3, (alai +a2a2+a3a3) 10; the condition is clearly a1a2a3 = A3 = 0, and since every seminvariant, of proper degree 3, is associated, as coefficient, with a product containing A3, all such are perpetuants.The generating

**function**is thus z2e-1 - 1 (1 -z 2) (1 -z 3) (1 -z 4)...Q 1 The Unreduced Generating

**Function**Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.Their Number For Any Weight W Is The Number Of Ways Of Composing W 3 With The Parts I, 2, And Thus The Generating

**Function**Is Verified.By the rules adopted we take A?B 2 B 3, which gives (12)a(32)b - (1)a(321)b+ao(3212)b, the simplest perpetuant of weight 7; and thence the general form enumerated by the generating

**function**1 -z.1-z2.1 - z3 ?Every other concomitant is a rational integral

**function**of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.In general any pencil of lines, connected with the line a x by descriptive or metrical properties, has for its equation a rational integral

**function**of the four forms equated to zero.Moreover, it is not constant, being an apparently arbitrary

**function**of H or of B; in the same specimen its value may, under different conditions, vary from less than 2 to upwards of 5000.If a coil of insulated wire is suspended so that it is in stable equilibrium when its plane is parallel to the direction of a magnetic field, the transmission of a known electric current through the coil will cause it to be deflected through an angle which is a

**function**of the field intensity.But they have lost their respiratory

**function**.Their present

**function**in scorpions is not ascertained.The coxal glands do not establish any special connexion between Limulus and Scorpio, since thay also occur in the same somite in the lower Crustacea, but it is to be noted that the coxal glands of Limulus are in minute structure and probably in

**function**more like those of Arachnids than those of Crustacea.Appendages of 1st pair.tri-segmented, chelate; of 2nd pair chelate, with their basal segments subserving mastication; of 3rd, 4th, 5th and 6th pairs similar in form and

**function**, except that in recent and Carboniferous forms the basal segments of the 3rd and 4th are provided with sterno-coxal (maxillary) lobes, those of the 4th pair meeting in the middle line and underlying the mouth.Remaining pairs of appendages similar in form and

**function**, each tipped with two or three claws.Appendages of the 3rd, 4th, 5th and 6th pairs similar in form and

**function**, tipped with two claws, their basal segments in contact in the median ventral line.Hitherto, in order to prove the equality of two expressions for the same

**function**, it was necessary to transform the one into the other, i.e.The subject he had chosen for his Habilitationsschrift was the "Representation of a

**Function**by Means of a Trigonometrical Series," a subject which Dirichlet had made his own by a now well-known series of researches.Most of the Scottish kings were crowned at Scone, the last

**function**being held on the 1st of January 1651, when Charles II.It has frequently been confused with determinism, which, however, differs from it categorically in assigning a certain

**function**to the will.These researches derive additional importance from having introduced two powerful engines of analysis for the treatment of physical problems, Laplace's coefficients and the potential

**function**.By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single

**function**, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism.Laplace published in 1779 the method of generating functions, the foundation of his theory of probabilities, and the first part of his Theorie analytique is devoted to the exposition of its principles, which in their simplest form consist in treating the successive values of any

**function**as the coefficients in the expansion of another**function**with reference to a different variable.The latter is therefore called the generating

**function**of the former.A direct and an inverse calculus is thus created, the object of the former being to determine the coefficients from the generating

**function**, of the latter to discover the generating**function**from the coefficients.The first formal proof of Lagrange's theorem for the development in a series of an implicit

**function**was furnished by Laplace, who gave to it an extended generality.It is important to begin the study of graphics with concrete cases rather than with tracing values of an algebraic

**function**.In the first class come equations in a single unknown; here the

**function**which is equated to zero is the Y whose values for different values of X are traced, and the solution of the equation is the determination of the points where the ordinates of the graph are zero.Then, since nr rl is also a rational integral

**function**of n of degree r, we can find a coefficient c r, not containing n, and such as to make N-c r nr ri contain no power of n higher than n r - 1.From this point of view, the

**function**which, by algebraical operations on i+o.x+o.x2+..., produces the series, is called its generating**function**.In the same way, the generating

**function**of the series I+2x+x 2 +0.x 3 +o.x 4 +...Other cases arise when we consider the continuity of a

**function**.Indeed, the historical and present importance of this aspect or branch of zoological science is so great that the name " zoology " has until recently been associated entirely with it, to the exclusion of the study of minute anatomical structure and

**function**which have been distinguished as anatomy and physiology.We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a

**function**of r, the distance from the origin.The second and third factors of (3) being each of the form sin 2u/u2, we have to examine the character of this

**function**.The (8), A

**function**of the telescope is in fact to allow the use of a wider, and therefore more easily measurable, aperture.The

**function**of a lens in forming an image is to compensate by its variable thickness the differences of phase which would otherwise exist between secondary waves arriving at the focal point from various parts of the aperture.If we put for shortness 7 for the quantity under the last circular

**function**in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .If we write p = 27rR/A (6), we must regard p as a

**function**of f, and we may take with sufficient approximation under any ordinary circumstances where p' denotes the value of p at 0, and is a constant, which is positive when the retarding plate is held at the side on which the blue of the spectrum is seen.In the former case the

**function**of the telescope is simply to increase the dispersion, and the formation of the bands is of course independent of the particular manner in which the dispersion arises.In the limiting case in which the medium is regarded as absolutely incompressible S vanishes; but, in order that equations (2) may preserve their generality, we must suppose a at the same time to become infinite, and replace a 2 3 by a new

**function**of the co-ordinates.The name " South African Republic " was adopted as the title of the state, and the new constitution made provision for a volksraad to which members were to be elected by the people for a period of two years, and in which the legislative

**function**was vested.Naturally, as the temperature became lower, a new

**function**was gradually acquired by his clothing, that of protecting the body of the wearer.Such objects might be imitated in other materials and by successive copying lose their identity, or their first meaning might be otherwise forgotten, and they would ultimately exercise a purely decorative

**function**.No writer in any literature, who has contented himself with so limited a

**function**, has gained so great a reputation as Terence.The localization of

**function**in the cerebral and in the cerebellar cortex has doubtless been the main cause of this progress, and has proceeded poi passu with an extended insight into the structure and connexions of the parts concerned.Health is simply that condition of structure and

**function**which, on examination of a sufficient number of examples, we find to be commonest.Disease we may define, accordingly, as any departure from the normal standard of structure or

**function**of a tissue or organ.If, for instance, we find that instead of the natural number of Malpighian bodies in the kidney there are only half that number, then we are entitled to say that this defect represents disease of structure; and if we find that the organ is excreting a new substance, such as albumen, we can affirm logically that its

**function**is abnormal.Once grant the above definition of disease, and even the most trivial aberrations from the normal must be regarded as diseased conditions, quite irrespective of whether, when structural, they interfere with the

**function**of the part or not.It is much more likely, as Verworn alleges, that the nerves which influence the characteristic

**function**of any tissue regulate thereby the metabolism of the cells in question - in other words, that every nerve serves as a trophic nerve for the tissues it supplies.Atrophy may follow primary arrest of

**function**- disuse atrophy.Increased work thrown on to a tissue may produce hypertrophy, but, if this excessive

**function**be kept up, atrophy will follow; even the blacksmith's arm breaks down owing to the hypertrophic muscle fibres becoming markedly atrophied.According to our present knowledge of physiological and pathological processes, we must regard the cell as the ultimate biological unit - a unit of structure and a unit of

**function**; this was first put forward by Schleiden in 1838, and by Schwann in 1839, but we owe to Virchow the full recognition of the fundamental importance of the living cell in all the processes of life, whether in health or disease.On reaching the vicinity they leave the blood stream and join in the warfare - many performing their

**function**of phagocytosis (q.v.), others falling victims to the toxins.Their principal

**function**is to bring about the removal of foreign, dead or degenerating material.The vessels are only temporary channels by which is brought forward the food supply that is needed by the advancing army if it is suc-, cessfully to carry on its

**function**; they probably also drain off the deleterious fluid substances formed by the cellular disintegration that has taken place in the part.Although we have not reached a stage of certainty regarding their origin,

**function**and destiny, recent investigations have brought forward evidence to elucidate the importance of the part played by the different cells in the various types of the inflammatory process.Their

**function**being at an end they give way to these cells which carry on the process of absorption.Oertel finds an explanation of this want of complete celldifferentiation, loss of

**function**, and acquired vegetative activity in the non-homogeneous character of the nuclear chromatin elements of the cell, and maintains that the different properties of the cell are carried and handed down by the different orders of chromatin loops.But their disintegration is more commonly brought about by " phagocytosis " on the part of the phagocytic cells in the different organs concerned with the

**function**of haemolysis, i.e.Heidenhain, on the other hand, rejected entirely the filtration view of lymph-formation, believing that the passage of lymph across the capillary wall is a true secretion brought about by the secretory

**function**of the endothelial plates.It is clear that the knowledge of

**function**(physiology) did not by any means keep pace with the knowledge of structure, and this was probably the reason why the important sect of the empirics were able entirely to dispense with anatomical knowledge.Discovery in these various directions then led physicians to regard fever and inflammation not as separable entities, but as fluctuating symptomgroups, due to swervings of

**function**from the normal balance under contingent forces.Thus the digestive

**function**, in its largest sense, is now seen to consist, not only in preparation and supply, but in no small measure also of protective and antidotal conversions of the matters submitted to it; coincidently with agents of digestion proper are found in the circuit of normal digestion "anti-substances" which neutralize or convert peptones in their poisonous phases; an autochthonous ferment, such as rennet for instance, calling forth an anti-rennet, and so on.The discoveries of the separate paths of sensory and motor impulses in the spinal cord, and consequently of the laws of reflex action, by Charles Bell and Marshall Hall respectively, in their illumination of the phenomena of nervous

**function**, may be compared with the discovery in the region of the vascular system of the circulation of the blood; for therein a key to large classes of normal and aberrant functions and a fertile principle of interpretation were obtained.This law has important ethical and political bearings; but in the province of disease this advance of what may be compared to the interlocking of points and signals has had wide influence not only in altering our conceptions of disease, but also in enlarging our views of all perturbations of

**function**.It is needless to point out how such paths of disease, in their association with characteristic symptoms, have illuminated the clinical features of disease as well as the processes of normal

**function**.Diseases of the latter kind are especially interesting, as in them we see that parts of the nervous structure, separated in space, may nevertheless be associated in

**function**; for instance, wasting of a group of muscles associated in**function**may depend on a set of central degenerations concurring in parts whose connexion, in spite of dissociation in space, we thus perceive.Many other diseases formerly regarded as primarily diseases of the nervous system are not such; but, by means of agents either introduced into the body or modified there, establish themselves after the affinities of these in contiguous associated parts of the structure, as in vascular, membranous or connective elements, or again in distant and peripheral parts; the perturbations of nervous

**function**being secondary and consequential.His "grandeur in social

**function**" was unequalled and his interests were very wide.The

**function**of the academic department is to control the teaching branch, internal examinations, &c., and that of the external department to control external examinations, while the university extension system occupies a third department.**Function**of receive antenna is extraction energy from electromagnetic field.But the Liberalism of his early years was gone for ever, and he had become reconciled to Metternich's view that, in an age of decay, the sole

**function**of a statesman was to "prop up mouldering institutions."His pages abound in symbols representing unknown functions, the form of the

**function**being left to be ascertained by observation of facts, which he does not regard as a part of his task, or only some known properties of the undetermined**function**being used as bases for deduction.This varies in metals from 594 (lithium) to 22.48 (osmium), and in one and the same species is a

**function**of temperature and of previous physical and mechanical treatment.Ignoring temperature effect, and taking the density as a

**function**of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some**function**P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream

**function**being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-

**function**4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream**function**of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-**function**, constant over a solid boundary moving with components U and V of velocity.Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a

**function**' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current**function**," as it is constant along a stream line (Trans.Similarly, with the

**function**(19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?For instance, with n = I in equation (9), the relative stream

**function**is obtained for a sphere of radius a, by making it, y' =1y+2Uy 2 = 2U(r 2 -a 3 /r) sin?Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential

**function**; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.When the liquid is bounded externally by the fixed ellipsoid A = A I, a slight extension will give the velocity

**function**4 of the liquid in the interspace as the ellipsoid A=o is passing with velocity U through the confocal position; 4 must now take the formx(1'+N), and will satisfy the conditions in the shape CM abcdX ¢ = Ux - Ux a b x 2+X)P Bo+CoB I - C 1 (A 1 abcdX, I a1b1cl - J o (a2+ A)P and any'confocal ellipsoid defined by A, internal or external to A=A 1, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along Ox BA+CA-B 1 -C1 W'.Taking Ox along OS, the Stokes'

**function**at P for the source S is p cos PSx, and of the source H and line sink OH is p(a/f) cos PHx and - (p/a) (PO - PH); so that = p (cos PSx+f cos PHx PO a PH), (q) and Ili = -p, a constant, over the surface of the sphere, so that there is no flow across.A distribution of sources and doublets over a moving surface will enable an expression to be obtained for the velocity

**function**of a body moving in the presence of a fixed sphere, or inside it.The method of electrical images will enable the stream

**function**, )' to be inferred from a distribution of doublets, finite in number when the surface is composed of two spheres intersecting at an angle 7r/m, where m is an integer (R.Conversely, if the kinetic energy T is expressed as a quadratic

**function**of x, x x3, y1, y2, y3, the components of momentum, the partial differential coefficient with respect to a momentum component will give the component of velocity to correspond.Thus if T is expressed as a quadratic

**function**of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic**function**of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathematicians; and the general solution requires the double-theta hyperelliptic

**function**.In 1739 the General Assembly, without any application from him, removed the sentence of deposition which had been passed against him, and restored him to the character and

**function**of a minister of the gospel of Christ, but not that of a minister of the Established Church of Scotland, declaring that he was not eligible for a charge until he should have renounced principles inconsistent with the constitution of the church.