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.
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.
A formula of the same type was given by Athenase Dupre (Theorie de chaleur, p. 96, Paris, 1869), on the assumption that the latent heat was a linear function of the temperature, taking the instance of Regnault's formula (io) for steam.
A good many transactions on the Manchester Exchange are intermediate, without fulfilling any useful function, and could be accomplished by the principals if they were brought together.
A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants.
A pair of eyes lie dorsally and behind them is a b closed circlet, often pulled out into various shapes, of modified epidermis, to which an olfactory function has been attributed.
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.
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).
A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved.
A very curious function sometimes discharged by the antennules or antennae of Decapods is that of forming a respiratory siphon in sand-burrowing species.
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.
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.
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.
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.
Alimentary, Respiratory and Excretory Systems. - Although the function of the two latter systems of organs is the purification of the blood, they are not usually considered together, and it is therefore the more remarkable that their close association in Amphioxus renders it necessary to treat them in common.
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.
All, however, perform the same function, viz., combing out the fibres and thus laying them parallel, and in addition drawing out the sliver.
Almost all the institutions of modern states go back to the curia regis, branching off from it at different dates as the growing complexity of business forced differentiation of function and personnel.
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.
Although the cell body or perikaryon of the neuron, with its contained nucleus, is essential for the maintenance of the life of the cell branches, it has become recognized that the actual process and function of "conduction" in many neurons can, and does, go on without the cell body being directly concerned in the conduction.
Although the excretory function of these has been demonstrated by physiological methods, however, their morphological relations are not clear.
Although this Great Being evidently exceeds the utmost strength of any, even of any collective, human force, its necessary constitution and its peculiar function endow it with the truest sympathy towards all its servants.
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.
Among these are papers on The Recurrence of Solar Eclipses, A Transformation of Hansen's Lunar Theory, Development of the Perturbative Function and its Derivatives.
An alternative method of developing the theory of the exponential function is to start from the definition exp x = I +x+x2/2 !
An instance of this characteristic function, specially remarkable because the composer has taken exceptional measures for it, is Beethoven's overture to Fidelio.
And similarly, considering the function I +z(x+x2+..)...+Nxnzk-..
And yes, everything and everyone in my life has a function and purpose.
Another enzyme, rennet, which in the animal body is proteolytic, is frequently met with in plants, but its function has not been ascertained.
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.
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.
Application to Symmetric Function Multiplication.-An example will explain this.
Argand had been led to deny that such an expression as i 2 could be expressed in the form A+Bi, - although, as is well known, Euler showed that one of its values is a real quantity, the exponential function of --7112.
Aristotle's forms had been correlated, though inadequately, with the idea of function.
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.
As it is with mechanical improvements, so is it to a still greater degree with changes in the function of timbre in art.
As Laplace has shown, the values for K and T may also be expressed in terms of the function cs, with which we started.
As the commissioners had no means of enforcing their orders, their function was chiefly advisory, but it was nevertheless of considerable importance on several occasions.
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....
As your husband, what will he consider his most important function?
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).
At first nawabs were only found in important cities, such as Surat and Dacca, with the special function of administering civil justice; criminal justice was in the hands of the kotwdl.
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.
At last, however, no swing into the opposite, with its primarily conflicting, if ultimately complementary function, is any longer possible.
At that moment Hildebert, the bishop of Le Mans, was absent from his episcopal town, and this is one of the reasons why Henry was granted permission to preach (March to July 1loi), a function jealously guarded by the regular clergy.
Atrophy may follow primary arrest of function - disuse atrophy.
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.
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.
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.
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.
Boule and demos long continued to function.
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.
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.
But that, too, is a function of present technology.
But the daily survey of the sun (occasionally also the function of the moon as measurer of time), together with his importance for life, secured him a high moral rank; and Rh, united with the Theban Ammon, became (under the New Empire) the leading god of Egypt for a thousand years, " He who hath made all, the sole One with many hands."
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."
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.
But they have lost their respiratory function.
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.
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.
By inference only, increasing complication of stomach with ruminating function superadded.
By the grant of an immunity to a proprietor the royal officers, the count and his representatives, were forbidden to enter his lands to exercise any public function there.
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 ?
C. Burkitt's The Gospel History (1906) vigorously sketches the book's dominant characteristics and true function.
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.
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.
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.
Darwin and his generation were deeply imbued with the Butlerian tradition, and regarded the organic world as almost a miracle of adaptation, of the minute dovetailing of structure, function and environment.
Depending on function, robots can come in all shapes and sizes, and I see no compelling reason to make them like humans.
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.
Disease we may define, accordingly, as any departure from the normal standard of structure or function of a tissue or organ.
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.
During the early years of the reign of Francis, the emperor kept himself in touch with the various departments by means of a cabinet minister; but he had a passion for detail, and after 1805 he himself undertook the function of keeping the administration together.
During the latter part of this period he was associated with Sir Thomas Smith, whose function was at least partly to watch and check his fellow-ambassador.
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.
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.
Egyptian thought ascribed this function to Thoth, who played somewhat different parts in different systems, but emerges as the representative of the immanent intelligence (1888); Siebeck, Lehrbuch der Religionsphilosophie (1893); Dorner, Grundriss der Religionsphilosophie (1903).
Elders are rulers; their function also is spiritual, though practical and disciplinary.
Even this function is losing its significance.
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.
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.
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.
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.
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.
Exportable technology can function around the world.
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.
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.
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.
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?
For these only will the symbolic product be replaceable by a linear function of products of real coefficients.
Free and peaceful societies function best when government is transparent and open.
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.
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.
Function of receive antenna is extraction energy from electromagnetic field.
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.
Given The Specific Heat As A Function Of The Temperature, Its Variation With Pressure May Be Determined From The Characteristic Equation Of The Gas.
He accepts psychophysical parallelism in the sense that every psychical process has a physical accompaniment, every physiological function has a psychical meaning, but neither external stimulus nor physiological stimulus is cause of a psychical process, nor vice versa.
He also maintained throughout the book that physical and psychical energy do not interfere, but that the psychical is, like a mathematical quantity, a function of the physical, depending upon it, and vice versa, only in the sense that a constant relation according to law exists, such that we may conclude from one to the other, but without one ever being cause of the other.
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.
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.
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.
He filled a similar function in Austria after the battle of Wagram.
He generalized Weber's law in the form that sensation generally increases in intensity as the stimulus increases by a constant function of the previous stimulus; or increases in an arithmetical progression as the stimulus increases in a geometrical ratio; or increases by addition of the same amount as the stimulus increases by the same multiple; or increases as the logarithm of the stimulus.
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.
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.
He is certain, however, that the law of substance somehow proves that conscious soul is a mere function of brain, that soul is a function of all substances, and that God is the force or energy, or soul or spirit, of nature.
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.
He recognized that the fault of the government lay in the fact that it did not govern, and he deplored that his own function, in a decadent age, was but " to prop up mouldering institutions."
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.
He was performing the same function, but meeting him didn't darken Dean's mood appreciably.
Health is simply that condition of structure and function which, on examination of a sufficient number of examples, we find to be commonest.
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.
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.
Henceforth its sole effective function was to endorse and promulgate the decrees of the government of Vienna.
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.
Her mind was beginning to function somewhere near normal.
Her name, the "Unalterable" (a- privative, and Tpbirav, to turn), indicates her function, that of rendering the decisions of her sisters irreversible or immutable.
Heraclitus offers no analogy to the doctrine of four (not three) elements as different grades of tension; to the conception of fire and air as the " form," in Aristotelian terminology, of particulars; nor to the function of organizing fire which works by methodic plan to produce and preserve the world (irup i&w 1 3aSii'ov iri ')4vEru Nor, again, is there any analogy to the peculiar Stoic doctrine of universal intermingling (Kpavms Si iiXov).
His "grandeur in social function" was unequalled and his interests were very wide.
His idealistic scheme of history, which makes religion the keynote of progress, and describes the function of each - Judaism to typify duty, Confucianism order, Mahommedanism justice, Buddhism patience, and Christianity love - does not account for the facts of the history enacted by the devotees.
His main function made him in his early life a preacher even more emphatically than a teacher.
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.
His views on the function of grammar were summarized in a paper on The Spiritual Rights of Minute Research delivered at Bryn Mawr on the 16th of June 1895.
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.
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.
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.
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".
If in its extension to contain the new formations within it the embryo-sac remains narrow, endosperm formation proceeds upon the lines of a cell-division, but in wide embryo-sacs the endosperm is first of all formed as a layer of naked cells around the wall of the sac, and only gradually acquires a pluricellular character, forming a tissue filling the sac. The function of the endosperm is primarily that of nourishing the embryo, and its basal position in the embryo-sac places it favourably for the absorption of food material entering the ovule.
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.
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.
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.
If the forms be all linear and different, the function is an invariant, viz.
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+..
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) =o
If we next introduce a new function of f and write f .f 4(f) d f =Il (f), (23) then m m' II(f) will represent - (I) The work done by the attractive force on the particle m, while it is brought from an infinite distance from m' to the distance f from m'; or (2) The attraction of a particle m on a narrow straight rod resolved in the direction of the length of the rod, one extremity of the rod being at a distance f from m, and the other at an infinite distance, the mass of unit of length of the rod being m'.
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.
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.
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.
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.
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.
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.
In accordance with what is now known to be a very widespread belief, the kingship was a semi-divine function, and the Pharaoh was the incarnation of Amon-Re.
In albuminous Monocotyledons the cotyledon itself, probably in consequence of its terminal position, is commonly the agent by which the embryo is thrust out of the seed, and it may function solely as a feeder, its extremity developing as a sucker through which the endosperm is absorbed, or it may become the first green organ, the terminal sucker dropping off with the seed-coat when the endosperm is exhausted.
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.
In comparative morphology it provides many illustrations of important biological principles (such, for example, as substitution and change of function of organs), and throws new light upon, or at least points the way to new ideas of, the primitive relations of different organic systems in respect of their function and topography.
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.
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.
In its essential nature a set is a linear function of any number of " distinct " units of the same species.
In knowing there are two functions involved, the " organic " or animal function of sensuous experience in virtue of which we are in touch with being, directly in inner perception, mediately in outer experience, and the "intellectual" function of construction.
In later days the same function was performed by the Purim Rabbi, who often indulged in parodies of the ritual.
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.
In Leguminous plants (the pea tribe) the pinnae are frequently modified to form tendrils, as in Lathyrus Aphaca, in which the stipules perform the function of true leaves.
In many plants, as already noticed, phyllodia or stipules perform the function of leaves.
In many questions relating to systems of discrete particles the internal force R55 (which we will reckon positive when attractive) between any two particles m,, m5 is a function only of the distance r55 between them.
In many sees there were no vidames, their function being exercised by viscounts or chatelains.
In mathematics, the term "mean," in its most general sense, is given to some function of two or more quantities which (1) becomes equal to each of the quantities when they themselves are made equal, and (2) is unaffected in value when the quantities suffer any transpositions.
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).
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.
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 short, the function of guarding and supervising the trade monopoly split up into various fragments, the aggregate of the crafts superseding the old general gild merchant.
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.
In some of them the hind toe, which has already ceased to have any function in the lapwing, is wholly wanting.
In the 13th century, however, whatever the civic organization of the townsfolk may have been, it was still strictly subordinate to the archbishop and his Vogt; the council could issue regulations only with the consent of the former, while in the judicial work of the latter, save in small questions of commercial dishonesty, its sole function was advisory.
In the case of the heart muscle this threshold stimulus evokes a beat as extensive as does the strongest stimulus; that is, the intensity of the stimulus, so long as it is above threshold value, is not a function of the amount of the muscular response.
In the cheekteeth the sectorial or scissor-like cutting function is developed at the expense of the tubercular or grinding, there being only one rudimentary tooth of the latter form in the upper jaw, and none in FIG.
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.
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 great majority of Crustacea the antennules are purely sensory in function and carry numerous " olfactory " hairs.
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.
In the Isopoda the respiratory function has been taken over by the abdominal appendages, both rami or only the inner becoming thin or flattened.
In the Koran great prominence is given to his function as the medium of divine revelation, and, according to the Mahommedan interpreters, he it is who is referred to by the appellations "Holy Spirit" and "Spirit of Truth."
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.
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.
In the modern metal bridge every member has a definite function and is subjected to a calculated straining action.
In the Posterior Analytics the syllogism is brought into decisive connexion with the real by being set within a system in which its function is that of material implication Posterior from principles which are primary, immediate and Analytics.
In the same way, the generating function of the series I+2x+x 2 +0.x 3 +o.x 4 +...
In the second case the outer series (calyx of sepals) is generally green and leaf-like, its function being to protect the rest of the flower, especially in the bud; while the inner series (corolla of petals) is generally white or brightly coloured, and more delicate in structure, its function being to attract the particular insect or bird by agency of which pollination is effected.
In the sense he can function but the memory is probably gone for good.
In the solution the value of an elliptic function is found by means of the arithmetico-geometrical mean.
In the steady state, the product kdO/dx must be constant, or the gradient must vary inversely as the conductivity, if the latter is a function of 0 or x.
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.
In those Copepods in which the palps of the mandibles as well as the antennae are biramous and natatory, the first three pairs of appendages retain throughout life, with little modification, the shape and function which they have in the nauplius stage, and must, in all likelihood, be regarded as approximating to those of the primitive Crustacea.
Incidentally, however, they do in some cases partially discharge that function, namely, when what is called a "preheater" is used to warm up the compressed air before it enters in the motor cylinder.
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.
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.
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.
Into this same cloacal chamber open ventrally a pair of ciliated tubes communicating by funnels with the coelom (Nansen and Wheeler); these are possibly nephridia, and excretory in function.
Introducing another letter z, and considering the function I+xz.
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.
It can exercise no organizing or controlling function in knowledge.
It can hardly be doubted that the function of these avicularia is the protection of the tentacles and compensation-sac. The suggestion that they are concerned in feeding does not rest on any definite evidence, and is probably erroneous.
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.
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.
It has frequently been confused with determinism, which, however, differs from it categorically in assigning a certain function to the will.
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.
It is apparent that a vitrified enamel may be made to perform, in part at any rate, the function of a porcelain glaze.
It is assumed further that the absorption is proportional to the incident radiation and (at any rate approximately) independent of the temperature, while the radiation is assumed to be a function of the temperature 6 Phil.
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.
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.
It is customary, therefore, to denote the exponential function by e x, and the result ex = I +x+x2/2 !
It is evident that thought, even as dealt with in pure logic, has an objectifying function.
It 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.
It is highly probable that before it became important merely as a temple, it was the fortified centre uniting the Argive people dwelling in the plain, the citadel which was superseded in this function by Tiryns.
It is important to begin the study of graphics with concrete cases rather than with tracing values of an algebraic function.
It is in this way that the function of the seer is closely connected (as in the case of Balaam) with sacrifices.
It is interesting to remark that the simple result found in equation (25) (according to which the effect of the deviation of the vapour from the ideal state is represented by the addition of the term (c-b)/V to the expression for log p) is independent of the assumption that c varies inversely as the n th power of 9, and is true generally provided that c-b is a function of the temperature only and is independent of the pressure.
It is more probably abeyance of external function during a periodic internal assimilatory phase.
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.
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.
It is not difficult in such compact species to distinguish between superficial cells, whose chief function is assimilation, subjacent cells charged with reserve material, and a core of tissue engaged in the convection of elaborated material from part to part.
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.
It is properly a national function, at least in some of its features.
It is quite a mistake to suppose that, apart from the chlorophyll function, the physiology of the fungus-cell is fundamentally different from that of ordinary plant-cells.
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,...
It is, however, far more probable that it was a general term that gradually became crystallized as applying to that service in which the dismissal represented a more solemn function.
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.
It should be noticed that the real function denoted by (ab) 2 is not the square of a real function denoted by (ab).
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.
It was his function also to display and guard in battle the banner of the baron or banneret or the pennon of the knight he served, to raise him from the ground if he were unhorsed, to supply him with another or his own horse if his was disabled or killed, to receive and keep any prisoners he might take, to fight by his side if he was unequally matched, to rescue him if captured, to bear him to a place of safety if wounded, and to bury him honourably when dead.
It was then that my slowly reacting brain, flowing like cold molasses began to function, more than a gerbil driven wheel.
It would seem, then, that, while he regards rhetoric as the function of normal sophistry, taking indifferently as his types Protagoras, Gorgias and Isocrates, he accounts Euthydemus and Dionysodorus (together with Socrates) as sophists, but as sophists of an abnormal sort, who may therefore be neglected.
Its chief function was to regulate the trade monopoly conveyed to the borough by the royal grant of gilda mercatoria.
Its colour varies with the liturgical colour of the day, or of the function at which it is worn.
Its exact function is not fully understood.
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.
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.
Its highest function is the contemplation of the divine unity, discoverable under the manifold of objects.
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.
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.
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.
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.
Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathematicians; and the general solution requires the double-theta hyperelliptic function.
Lotze's logic then represents the statical aspect of the function of thought in knowledge, while, so far as we go in knowledge thought is always engaged in the unification of a manifold, which remains contradistinguished from it, though not, of course, completely alien to and unadapted to it.
Many of his conclusions have been corrected and extended by later criticism; but he indicated more decisively than any of his predecessors the fruitful principle that each art is subject to definite conditions, and that it can accomplish great results only by limiting itself to its special function.
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.
Many suffered under this law, but the ultimate effect was to invest the press with new popularity, and very soon the newspapers conceived a device which effectually protected their literary staff, for they employed dummy editors whose sole function was to go to prison in lieu of the true editor.
Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order n.
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.
Metaphysical materialism is the view that everything known is body or matter; but while according to ancient materialists soul is only another body, according to modern materialists mind without soul is only an attribute or function of body.
Mexican acquaintance with the signs related only to their secondary function as dies (so to speak) with which to stamp recurring intervals of time.
Migration in general may be described as a natural function of social development.
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.
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.
Moreover, this is precisely the condition for the absence of interference between the component of a split beam; because, the time of passage being to the first order fds/V f(udx+vdy+wdz)V2, the second term will then be independent of the path (43 being a single valued function) and therefore the same for the paths of both the interfering beams. If therefore the aether can be put into motion, we conclude (with Stokes) that such motion, in free space, must be of strictly irrotational type.
Most of the Scottish kings were crowned at Scone, the last function being held on the 1st of January 1651, when Charles II.
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.
Naturally, as the temperature became lower, a new function was gradually acquired by his clothing, that of protecting the body of the wearer.
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.
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.
Nevertheless, the function of reproduction is occasionally exercised by larvae.
No writer in any literature, who has contented himself with so limited a function, has gained so great a reputation as Terence.
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.
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.
Of the carbon dioxide and ammonia no exhaustion can take place, but of the mineral constitutents the supply is limited because the soil cannot afford an indefinite amount of them; hence the chief care of the farmer, and the function of manures, is to restore to the soil those minerals which each crop is found, by the analysis of its ashes, to take up in its growth.
Officers, commonly called wardens in England, were elected by the members, and their chief function was to supervise the quality of the wares produced, so as to secure good and honest workmanship. Therefore, ordinances were made regulating the hours of labour and the terms of admission to the gild, including apprenticeship. Other ordinances required members to make periodical payments to a common fund, and to participate in certain common religious observances, festivities and pageants.
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.
On the approach of winter the males, having no further function to perform for the community, are refused food-supplies by the workers, and are either excluded or banished from the hive to perish.
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.
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.
On the other, he assigned to vas with its insight into rationality too high a function with regard to the concrete in which the surd was present, a power to certify the truth of scientific principles.
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.
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.
One 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.
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.
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.
Other cases arise when we consider the continuity of a function.
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.
Pearson has shown that Galton's function has a value of 0.28 for stature of middle-class Englishmen and their wives.
Perhaps the earliest of such specializations is connected with the reproductive function.
Perry (Steam Engine, p. 580), assuming a characteristic equation similar to Zeuner's (which makes v a linear function of the temperature at constant pressure, and S independent of the pressure), calculates S as a function of the temperature to satisfy Regnault's formula (10) for the total heat.
Peter's function in relation to the Gentiles belongs to the early Palestinian conditions, before Paul's distinctive mission had taken shape.
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 .
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.
Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.
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."
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.
Refusing to take the oaths of allegiance to an "uncovenanted" ruler, or to exercise any civil function, they passed through a period of trial and found some difficulty in maintaining a regular ministry; but in 1706 they were reinforced by some converts from the established church.
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.
Remaining pairs of appendages similar in form and function, each tipped with two or three claws.
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.
Schleiermacher's formula obviously ascribes a function in knowledge to thought as such, and describes in a suggestive manner a duality of the intellectual and organic functions, resting on a parallelism of thought and being whose collapse into identity it is beyond human capacity to grasp. It is rather, however, a statement of a way in which the relations of the terms of the problem may be conceived than a system of necessity.
Septibranchia Gills have lost their respiratory function, and are transformed into a muscular septum on each side between mantle and foot.
She didn't understand how humans could feel so much and still function when she was overwhelmed.
Similarly regarding 1 x 2 as additional parameters, we see that every covariant is expressible as a rational function of n fixed covariants.
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,, ?
Simspon concluded that for a given wind velocity dissipation is practically a linear function of ionization.
Since T is a homogeneous quadratic function.
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.
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.
Some petioles are long, slender and sensitive to contact, and function as tendrils by means of which the plant climbs; as in the l,' nasturtiums (Tropaeolum), clematis and c in others; and in compound leaves the midrib and some of the leaflets may similarly be transformed into tendrils, as in the pea and vetch.
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.
Such machines are not properly described as air-engines since their function is not the conversion of heat into work.
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.
Such philosophies are called rationalist or sensationalist according as they lay emphasis specially on the function of reason or that of the senses.
Syllogism is simply summation of propositions, its function being communication merely.
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.
Tests revealed normal brain function, and there was no indication of any permanent damage.
That this is so appears even more clearly when we examine his general conception of the unity, gradation and function of the sciences.
The "powers" (numina, not dei), which thus become the objects of worship, are spirits specialized in function and limited in sphere.
The (8), A function of the telescope is in fact to allow the use of a wider, and therefore more easily measurable, aperture.
The aberrations can also be expressed by means of the "characteristic function " of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order.
The absolute was left with no other function than that of removing all the differences on which thought turns.
The accumulation of vast masses of snow, which have gradually been converted into permanent glaciers, maintains a gradation of very different climates within the narrow space that intervenes between the foot of the mountains and their upper ridges; it cools the breezes that are wafted to the plains on either side, but its most important function is to regulate the water-supply of that large region which is traversed by the streams of the Alps.
The advantage of this type of equation is that c is a function of the temperature only.
The air-bladder may be so reduced as to lose its hydrostatic function and become subservient to a sensory organ, its outer exposed surface being connected with the skin by a meatus between the bands of muscle, and conveying the thermobarometrical impressions to the auditory nerves.
The apparatus for this function is placed immediately over the II th and 12th rollers of the softening machine and an idea of its construction may be gathered from fig.
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 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 attainment of the higher stage of development is the moral and religious vocation of man; this higher stage is self-determination, the performance of every human function as a voluntary and intelligent agent, or as a person, having as its cosmical effect the subjection of all material to spiritual existences.
The bishops have no political function by reason of their office, although they may, and often do, take a prominent part in politics.
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.
The chief function of the instrument is to measure slow displacements due to distant earthquakes.
The chief incidents and episodes would be deeply graven in the popular memory; and it is the poet's function to make the past live again.
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 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 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.
The cylinder, however, seems to have been generally superseded in Egypt by the engraved scarab, or beetle-shaped object, which, it may be assumed, was used at an early time, as it certainly was in later Egyptian history, for sealing purposes, although its proper function was that of an amulet.
The damage to the cerebellum must, it would seem, occur abruptly or quickly in order to occasion marked derangement of function, and then the derangement falls on the execution of movements.
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.
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.
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.
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 exponential function possesses the properties (i.) exp (x+y) =exp x X exp y.
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.
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.
The first is " the law that thought is a function of the brain."
The flower is a shoot (stem bearing leaves) which has a special form associated with the special function of ensuring the fertilization of the egg and the development of fruit containing seed.
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.
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.
The frontal organ varies in form and apparently in function, and is sometimes absent.
The function 0(z) is insensible for all sensible values of z.
The function F is therefore called by Lord Rayleigh the dissipation function.
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 function II(f) is also insensible for sensible values of f, but for insensible values of f it may become sensible and even very great.
The function J = E-94,, has been called the " free energy " of the substance by Helmholtz, and 90 the " bound energy."
The function log x as x increases from o towards w steadily increases from - co towards +co.
The function of " binding and loosing," here assigned to him, is in identical terms assigned to the disciples generally in a passage in ch.
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.
The function of logic is to exhibit its formal implications and repulsions.
The function of Naturphilosophie is to exhibit the ideal as springing from the real, not to deduce the real from the ideal.
The function of such an agency is performed in the United States of America by the express companies (see Express).
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.
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.
The function of the apron is to prevent the escape of electrification from the glass during its passage from the rubber to the collecting points.
The function of the electrolyte may be to annul such a natural charge and thus allow the non-electric surface energy to produce coagulation.
The function of the ferric oxide present in ordinary cement is little more than that of a flux to aid the union of silica, alumina and lime in the clinker; its role in the setting of the cement is altogether secondary.
The function of the flanges is to resist a horizontal tension and compression distributed practically uniformly on their cross sections.
The function of the nected system the new mode of thinking, and to the incomparable power and eloquence with which he expounded and enforced it.
The function of the sand is simply that of a diluent to prevent undue shrinkage and cracking in drying.
The function of the veins which consist of vessels and fibres is to form a rigid framework for the leaf and to conduct liquids.
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.
The function of these peculiar structures is unknown.
The function of this pair of muscles is the closing of the valves.
The function Zap 1 a 2 P2 ...an n being as above denoted by a partition of the weight, viz.
The general monomial symmetric function is a P1 a P2 a P3.
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)...
The growth of this department, parallel with the general progress of finance, is significant of its function.
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 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.
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.
The labial commissure gives off a subradular commissure which also bears two ganglia, these being in close relation to a special sense-organ called the subradular organ, an epithelial projection with nerve-endings, lying in front of the radula and probably gustatory in function.
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.
The latter is therefore called the generating function of the former.
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.
The load on an element bx of the beam may be represented by wbx, where - w is in general a function of x.
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.
The logarithmic function is most naturally introduced into analysis by the equation log x= x ?
The making of railways was from the outset regarded by some German states as exclusively a function of the government.
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 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 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.
The measures by which the government of India chiefly endeavours to reduce the liability of the country to famine are the promotion of railways; the extension of canal and well irrigation; the reclamation of waste lands, with the establishment of fuel and fodder reserves; the introduction of agricultural improvements; the multiplication of industries; emigration; and finally the improvement where necessary of the revenue and rent systems. In times of famine the function of the railways in distributing the grain is just as important as the function of the irrigation-canals in increasing the amount grown.
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.
The most characteristic dental feature is, however, the assumption of the form and function of a canine by the first lower premolar; the lower canine being incisor-like.
The 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.
The most important function they have to perform, that of seizing and holding firmly animals of considerable size and strength, violently struggling for life, is provided for by the great, sharp-pointed and sharp-edged canines, placed wide apart at the angles of the mouth, the incisors between them being greatly reduced in size and kept back nearly to the same level, so as not to interfere with their action.
The most important public function whose transformation into a private possession was assisted by the growth of the immunity was the judicial.
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.
The next case is that in which u is a quadratic function of x, i.e.
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 number of exites is less constant, but, in A pus, two are present, the proximal branchial in function and the distal forming a stiffer plate which probably aids in swimming.
The officials were called by two names, "elders" and "bishops," the former denoting the office, the latter the function (exercising the oversight).
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.
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 other chief function of diplomacy is to be the courteous medium of conveying messages from one government to another.
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.
The past is now filled with a glory which could not be so fully perceived at the time, but which, as St John tells, it was the function of the Holy Spirit to reveal to Christ's disciples.
The physical properties of a heterogeneous body (provided they vary continuously from point to point) are known to depend, in the neighbourhood of any one point of the body, on a quadric function of the co-ordinates with reference to that point.
The polyps are all non-sexual individuals whose function is purely nutritive.
The power of a spectroscope to perform its main function, which is to separate vibrations of different but closely adjacent frequencies, is called its " resolving power."
The prevalent political economy, in which that theory was embodied, made a principle of neglecting the very evils which it should be the great function of government to remedy.
The primary function of the flower is to bear the spores.
The principal function of these courts is the hearing of appeals both civil and criminal from the courts of first instance; only in.
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 qualification that the circular function must apply to all time is important, and unless it is recognized as a necessary condition of homogeneity, confusion in the more intricate problems or radiation becomes inevitable.
The reason of this is readily understood when it is borne in mind how disadvantageous to the function of sight is the unpigmented condition of an albino's eyeball; a disadvantage which would be probably much accentuated, in the cases now under consideration, by the bright glare from the surface of the snow, which forms the natural environment of these animals at the particular period of the year when the winter change occurs.
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 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.
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 Revival of Learning must be regarded as a function of that vital energy, an organ of that mental evolution, which brought into existence the modern world, with its new conceptions of philosophy and religion, its reawakened arts and sciences, its firmer grasp on the realities of human nature and the world, its manifold inventions and discoveries, its altered political systems, its expansive and progressive forces.
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.
The scathing vehemence of his denunciations led to his being summoned before the vice-chancellor, who suspended him "from the exercise of his ecclesiastical function and from all degrees taken or to be taken."
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 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.
The simplest case is that in which u is constant or is a linear function of x, i.e.
The skeleton is meaningless apart from reference to its function in the life of an organism, yet there are laws of skeleton structure which can be studied with most advantage if other characters of the organism are relegated to the background.
The sole function of the university was to examine, and its examinations for matriculation and for degrees in arts and science were carried on by means of written papers not only in London but in many centres in the United Kingdom and the colonies.
The special function of the so-called "Socratic dialectic" was to show the inadequacy of popular beliefs.
The specific heats may be any function of the temperature consistently with the characteristic equation provided that their difference is constant.
The spiritual function and character of the Anglican bishops, allowing for the doctrinal changes effected at the Reformation, are similar to those of the Roman.
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 sub-aquatic habits of the present species probably render such a function impossible, hence the absence of the glands.
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.
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!
The terminal part of the male ducts may be protrusible and act as an intromittent organ, or this function may be discharged by some of the appendages, as, for instance, in the Brachyura.
The theory of utility above referred to, namely, that the degree of utility of a commodity is some continuous mathematical function of the quantity of the coin modity available, together with the implied doctrine that economics is essentially a mathematical science, took more definite form in a paper on "A General Mathematical Theory of Political Economy," written for the British Association in 1862.
The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?
The vapour tension may approximate to a linear function of the composition, and the curve will then be practically a straight line.
The variable first maxillae are seldom pediform, their function being concerned chiefly with nutrition, sensation and respiration.
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.
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 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.
The weight of the function is the sum of the numbers in the bracket, and the degree the highest of those numbers.
The whole apparatus is so exactly analogous in structure to the poison-gland and tooth of a venomous snake as to suggest a similar function, and there is now evidence that it employs this organ as an offensive weapon.
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.
The working chamber indeed is the furnace proper, in which the whole of the open-hearth process is carried out, and the function of all the rest of the apparatus, apart from the tilting mechanism, is simply to pre-heat the air and gas, and to lead them to the furnace proper and thence to the chimney.
Their chief function is to ordain, and to act as "intercessors."
Their function being at an end they give way to these cells which carry on the process of absorption.
Their function is not quite clear.
Their function is the twofold one of protecting the embryo and of aiding in dissemination; they may also directly promote germination.
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.
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.
Their present function in scorpions is not ascertained.
Their principal function is to bring about the removal of foreign, dead or degenerating material.
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.
Theorem.- The function symbolized by (n), viz.
There are no special respiratory organs, their function is carried on by the internal surface of the mantle.
There is a tendency, moreover, to accord to the conferences the function of determining the tests of ministerial standing in the Congregational denomination.
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.
There remains, indeed, one other sacred function of great importance in the ancient world in which the Greek priests had a share.
There was also a third kind of priest called the zammaru, whose function it was to sing hymns.
There was scope for diversity of view and there was diversity of view, according as the vital issue of the formula was held to lie in the relation of intellectual function to organic function or in the not quite equivalent relation of thinking to being.
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.
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.
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.
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.
This acted at once and without any consciousness of difference of function, as judiciary, as legislature, in so far as there was any in the feudal period, and as council, and it exercised final supervision and control over revenue and administration.
This capacity is then a function of the geometrical dimensions of the conductor, and can be mathematically determined in certain cases.
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.
This function is named the "power" of the two spheres, and it is important in the investigation of systems of spheres.
This gives an average value of the conductivity over the range, but it is better to observe the temperatures at three distances, and to assume k to be a linear function of the temperature, in which case the solution of the equation is still very simple, namely, 0+Ze6 2 =a log r+b, (3) where e is the temperature-coefficient of the conductivity.
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.
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.
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.
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.
This latter function, however, is one unknown to the English common law.
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.
This mechanism as a whole is unique, although, as Sars observes, the epipod of the first maxillipeds has a respiratory function also in the Lophogastridae and Mysidae and in the cheliferous isopods.
This ordinate will be an algebraical function of x, and we can again apply a suitable formula.
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.
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.
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.
This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in mathematics a function depends on a variable; and that even Newton's third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.
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.
Thus for the function = 1 I -x.
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 =..
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.
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.
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 .
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".
To find the work done when m is brought to the point P in the neighbourhood of a solid body, the density of which is a function of the depth v below the surface, we have only to write instead of a pdz, and to integrate ?
To his function as a preacher we owe some of his most characteristic and stimulating works, especially the discourses by which it may be said he won his way to wide and influential recognition - Endeavours after the Christian Life, 1st series, 1843; 2nd series, 1847; Hours of Thought, 1st series, 1876; 2nd series, 1879; the various hymn-books he issued at Dublin in 1831, at Liverpool in 1840, in London in 1873; and the Home Prayers in 1891.
To this end he examined such immediate vital products as blood, bile and urine; he analysed the juices of flesh, establishing the composition of creatin and investigating its decomposition products, creatinin and sarcosin; he classified the various articles of food in accordance with the special function performed by each in the animal economy, and expounded the philosophy of cooking; and in opposition to many of the medical opinions of his time taught that the heat of the body is the result of the processes of combustion and oxidation performed within the organism.
To this high conception of a preacher's function the prophet was faithful throughout his career.
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.
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."
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.
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.
Unable to function from shock, he sat down on a rock overlooking the lake.
Under these conditions both S and s may be regarded as approximately constant, so that L is a linear function of the temperature.
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.
Very often the basal segment of the protopodite bears, on the outer side, a lamellar appendage (more rarely, two), the epipodite, which may function as a gill.
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.
We may observe that the equation (51) is accurately true for an ideal vapour, for which pv = (S-s)0, provided that the total heat is defined as equal to the change of the function (E+pv) between the given limits.
We thus at last attain a definite conclusion with regard to forms, and it appears clear that in Bacon's belief the true function of science was the search for a few fundamental physical qualities, highly abstract and general, the combinations of which give rise to the simple natures and complex phenomena around us.
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.
What has made this cult attach itself more especially to the Saiva creed is doubtless the character of Siva as the type of reproductive power, in addition to his function as destroyer which, as we shall see, is likewise reflected in some of the forms of his Sakti.
When Ethel did the inviting, the function was nearly always out of town.
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.
When it persists as a massive element of the seed its nutritive function is usually apparent, for there is accumulated within its cells reserve-food, and according to the dominant substance it is starchy, oily, or rich in cellulose, mucilage or proteid.
When the function of protection and local supervision could be resumed by the general government the feudal age ended.
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'.
While in opposition he devoted special attention to naval affairs, and in speeches that attracted much notice declared that the function of the French navy was to secure and develop colonial enterprise, deprecated all attempts to rival the British fleet, and advocated the construction of commerce destroyers as France's best reply to England.
While little importance is to be given to such characters as the unsegmented body, the small number of limbs and the absence of a shell-fold and of paired eyes, it has, on the other hand, preserved archaic features in the form of the limbs and the masticatory function of the antenna.
With all the other prophets the primary function is spiritual teaching; miracles, even though numerous and many of them symbolical like Elisha's, are only accessory.
With Elisha, on the other hand, miracles seem the principal function, and the teaching is altogether subsidiary.
With one more denunciation of the house of Ahab, Elijah's function as a messenger of wrath was fully discharged (2 Kings i.).
Yet Mill's view of the function of " universal " propositions had been historically suggested by a theory - Dugald Stewart's - of the use of axioms!'