are parallel, or 0=0, the product, which is now the square of any (unit) line is 1. And when the two factor lines are at right angles to one another, or = /2, the product is simply ix +jy+kz", the unit line perpendicular to both. Hence, and in this lies the main element of the symmetry and simplicity of the quaternion calculus, all systems of three mutually rectangular unit lines in space have the same properties as the fundamental system i, j, k. In other words, if the system (considered as rigid) be made to turn about till the first factor coincides with i and the second with j, the product will coincide with k. This fundamental system, therefore, becomes unnecessary; and the quaternion method, in every case, takes its reference lines solely from the problem to which it is applied. It has therefore, as it were, a unique internal character Hamilton, having gone thus far, proceeded to evolve these results .rom a characteristic train of a priori or metaphysical reasoning. its own. Let it be supposed that the product of two directed lines is something which has quantity; ie. it may be halved, or doubled, for instance. Also let us assume (a) space to have the same properties in all directions, and make the convention (b) that to change the sign of any one factor changes the sign of a product. Then the product of two lines which have the same direction cannot be, even in part, a directed quantity. For, if the directed part have the same direction as the factors, (b) shows that it will be reversed by reversing either, and therefore will recover its original direction when both are reversed. But this would obviously be inconsistent with (a). If it be perpendicular to the factor lines, (a) shows that it must have simultaneously every such direction. Hence it must be a mere number. Again, the product of two lines at right angles to one another cannot, even in part, be a number. For the reversal of either factor must, by (b), change its sign. But, if we look at the two factors in their new position by the light of (a), we see that the sign must not change. But there is nothing to prevent its being represented by a directed line if, as further applications of (a) and (b) show we must do, we take it perpendicular to each of the factor lines. Hamilton seems never to have been quite satisfied with the apparent heterogeneity of a quaternion, depending as it does on a numerical and a directed part. He indulged in great deal of speculation as to the existence of an extra-spatial unit, which was to furnish the raison d'être of the numerical part, and render the quaternion homogeneous as well as linear. But for this we must refer to his own works. Hamilton was not the only worker at the theory of sets. The year after the first publication of the quaternion method, there appeared a work of great originality, by Grassmann, in which results closely analogous to some of those of Hamilton were given. In particular, two species of multiplication ("inner and " outer") of directed lines in one plane were given. The results of these two kinds of multiplication correspond respectively to the numerical and the directed parts of Hamilton's quaternion product. But Grassmann distinctly states in his preface that he had not had leisure to extend his method to angles in space. Hamilton and Grassmann, while their earlier work had much in common, had very different objects in view. Hamilton had geometrical application as his main object; when he realized the quaternion system, he felt that his object was gained, and thenceforth confined himself to the development of his method. Grassmann's object seems to have been, all along, of a much more ambitious character, viz. to discover, if possible, a system or systems in which every conceivable mode of dealing with sets should be included. That he made very great advances towards the attainment of this object all will allow; that his method, even as completed in 1862, fully attains it is not so certain. But his claims, however great they may be, can in no way conflict with those of Hamilton, whose mode of multiplying couples (in which the "inner" and "outer" multiplication are essentially involved) was produced in 1833, and whose quaternion system was completed and published before Grassmann had elaborated for press even the rudimentary portions of his own system, in which the veritable difficulty of the whole subject, the application to angles in space, had not even been attacked. Grassmann made in 1854 a somewhat savage onslaught on Cauchy and De St Venant, the former of whom had invented, while the latter had exemplified in application, the system of " clefs algébriques," which is almost precisely Die Ausdehnungslehre, Leipsic, 1844: 2nd ed., vollständig und in strenger Form bearbeitet, Berlin, 1862. See also the collected works of Möbius, and those of Clifford, for a general explanation of Grassmann's method. XXII 12 that of Grassmann. But it is to be observed that Grassmann, though he virtually accused Cauchy of plagiarism, does not appear to have preferred any such charge against Hamilton. He does not allude to Hamilton in the second edition of his work. But in 1877, in the Mathematische Annalen, xii., he gave a paper "On the Place of Quaternions in the Ausdehnungslehre," in which he condemns, as far as he can, the nomenclature and methods of Hamilton. have been given for application to geometry of directed lines, but There are many other systems, based on various principles, which those which deal with products of lines are all of such complexity as to be practically useless in application. Others, such as the Barycentrische Calcul of Möbius, and the Méthode des equipollences of Bellavitis, give elegant modes of treating space problems, so long as we confine ourselves to projective geometry and matters of that order; but they are limited in their field, and therefore need not be discussed here. More general systems, having close analogies to quaternions, have been given since Hamilton's discovery was published. As instances we may take Goodwin's and O'Brien's papers in the Cambridge Philosophical Transactions for 1849. (See also ALGEBRA: special kinds.) Relations to other Branches of Science.-The above narrative shows how close is the connexion between quaternions and the ordinary Cartesian space-geometry. Were this all, the gain by their introduction would consist mainly in a clearer insight into the mechanism of co-ordinate systems, rectangular or not-a very important addition to theory, but little advance so far as practical application is concerned. But, as yet, we have not When that is done, the full value of Hamilton's grand step taken advantage of the perfect symmetry of the method. becomes evident, and the gain is quite as extensive from the practical as from the theoretical point of view. Hamilton, in fact, remarks, "I regard it as an inelegance and imperfection in this calculus, or rather in the state to which it has hitherto been unfolded, whenever it becomes, or seems to become, necessary to have recourse . . . to the resources of ordinary algebra, for the solution of equations in quaternions." This refers to the use of the x, y, z co-ordinates,-associated, of course, with i, j, k. But when, instead of the highly artificial expression ix+jy+kz, to denote a finite directed line, we employ a single letter, a (Hamilton uses the Greek alphabet for this purpose), and find that we are permitted to deal with it exactly as we should have dealt with the more complex expression, the immense gain is at least in part obvious. Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, By, or the quotient, de-, of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c. Perhaps to the student there is no part of elementary mathematics so repulsive as is spherical trigonometry. Also, everything relating to change of systems of axes, as for instance in the kinematics of a rigid system, where we have constantly to consider one set of rotations with regard to axes fixed in space, and another set with regard to axes fixed in the system, is a matter of troublesome complexity by the usual methods. But every quaternion formula is a proposition in spherical (sometimes degrading to plane) trigonometry, and has the full advantage of the symmetry of the method. And one of Hamilton's earliest advances in the study of his system (an advance independently made, only a few months later, by Arthur Cayley) was the interpretation of the singular operator q()q1, where q is a quaternion. Applied to any directed line, this operator at once turns it, conically, through a definite angle, about a definite axis. Thus rotation is now expressed in symbols at least as Had simply as it can be exhibited by means of a model. quaternions effected nothing more than this, they would still have inaugurated one of the most necessary, and apparently impracticable, of reforms. 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 Lectures on Quaternions, § 513. same is true of physical quantities such as potential, temperature, | method quaternions have from the beginning received much &c., throughout small regions in which their variations are attention from mathematicians. An attempt has recently been continuous; and also, without restriction of dimensions, of made under the name of multenions to systematize this algebra. moments of inertia, &c. Hence, in addition to its geometrical We select for description stage (3) above, as the most charapplications to surfaces of the second order, the theory of quadric acteristic development of quaternions in recent years. For functions of position is of fundamental importance in physics. (3) (a) we are constrained to refer the reader to Joly's own Here the symmetry points at once to the selection of the three Manual of Quaternions (1905). principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind. But it is not so. Even in Hamilton's earlier work it was shown that all such questions were reducible to the solution of linear equations in quaternions; and he proved that this, in turn, depended on the determination of a certain operator, which could be represented for purposes of calculation by a single symbol. The method is essentially the same as that developed, under the name of "matrices," by Cayley in 1858; but it has the peculiar advantage of the simplicity which is the natural consequence of entire freedom from conventional reference lines. out. + dy2 The impulse of W. K. Clifford in his paper of 1873 (" Preliminary Sketch of Bi-Quaternions," Mathematical Papers, p. 181) seems to have come from Sir R. S. Ball's paper on the Theory of Screws, published in 1872. Clifford makes use of a quasi-scalar w, commutative with quaternions, and such that if p, q, &c., are quaternions, when p+wq=p'+wq', then necessarily p=p', q=d. He considers two cases, viz. w2=1 suitable for non-Euclidean space, and w2=o suitable for Euclidean space; we confine ourselves to the second, and will call the indicated bi-quaternion p+wg an octonion. In octonions the analogue of Hamilton's vector is localized to the extent of being confined to an indefinitely long axis parallel to itself, and is called a rotor; if p is a rotor then wp is parallel and equal to p, and, like Hamilton's vector, wp is not localized; wp is therefore called a vector, though it differs from Hamilton's vector in that the product of any two such vectors wp and wo is zero because w2=o.ptwo where p, σ are rotors (i.e. p is a rotor and wo a vector), is called a motor, and has the geometrical significance of Ball's wrench upon, or twist about, a screw. Clifford considers an octonion p+wq as the quotient of two motors p+wo, p'two'. This is the basis of a method parallel throughout to the quaternion method; in the specification of rotors and motors it is independent of the origin which for these purposes the quaternion method, pure and simple, requires. Sufficient has already been said to show the close connexion between quaternions and the theory of numbers. But one most important connexion with modern physics must be pointed In the theory of surfaces, in hydrokinetics, heat-conduction, potentials, &c., we constantly meet with what is called ď d2 "Laplace's operator," viz. + We know that this dx2 d22. is an invariant; i.e. it is independent of the particular directions chosen for the rectangular co-ordinate axes. Here, then, is a case specially adapted to the isotropy of the quaternion system; d d d and Hamilton easily saw that the expression idx + k dz could be, like ix+jy+kz, effectively expressed by a single letter. He chose for this purpose V. And we now see that the square of V is the negative of Laplace's operator; while V itself, when applied to any numerical quantity conceived as having a definite value at each point of space, gives the direction and the rate of most rapid change of that quantity. Thus, applied to a potential, it gives the direction and magnitude of the force; to a distribution of temperature in a conducting solid, it gives (when multiplied by the conductivity) the flux of heat, &c. Combebiac is not content with getting rid of the origin in these limited circumstances. The fundamental geometrical conceptions are the point, line and plane. Lines and combut points and planes cannot be so treated. He glances at plexes thereof are sufficiently treated as rotors and motors, Grassmann's methods, but is repelled because he is seeking a unifying principle, and he finds that Grassmann offers him not one but many principles. He arrives at the tri-quaternion as the suitable fundamental concept. We believe that this tri-quaternion solution of the very interesting problem proposed by Combebiac is the best one. No better testimony to the value of the quaternion method could be desired than the constant use made of its notation by mathematicians like Clifford (in his Kinematic) and by physicists like ClerkMaxwell (in his Electricity and Magnetism). Neither of these men professed to employ the calculus itself, but they recognized fully the extraordinary clearness of insight which is gained even by merely translating the unwieldy Cartesian expressions met with in hydrokinetics and in electrodynamics into the pregnant language of quaternions. (P. G. T.) Supplementary Considerations.-There are three fairly wellmarked stages of development in quaternions as a geometrical method. (1) Generation of the concept through imaginaries and development into a method applicable to Euclidean geometry. This was the work of Hamilton himself, and the above account (contributed to the 9th ed. of the Ency. Brit. by Professor P. G. Tait, who was Hamilton's pupil and after him the leading exponent of the subject) is a brief résumé of this first, and by far the most important and most difficult, of the three stages. (2) Physical applications. Tait himself may be regarded as the chief contributor to this stage. (3) Geometrical applications, different in kind from, though more or less allied to, those in connexion with which the method was originated. These last include (a) C. J. Joly's projective geometrical applications starting from the interpretation of the quaternion as a point-symbol; these applications may be said to require no addition to the quaternion algebra; (b) W. K. Clifford's biquaternions and G. Combebiac's tri-quaternions, which require the addition of quasi-scalars, independent of one another and of true scalars, and analogous to true scalars. As an algebraic It appears from Joly's and Macfarlane's references that J. B. Shaw, in America, independently of Joly, has interpreted the quaternion as a point-symbol. consist of three quatrains of alternate rhyme, not repeated in the successive quatrains, and the whole closes with a couplet. A more perfect example of the form could hardly be found than the following, published by Michael Drayton in 1602:Dear, why should you commend me to my rest, When now the night doth summon all to sleep? Methinks this time becometh lovers best; Litersects the transversal; the axis is on a fixed ruled surface | Sidney, Spenser and Daniel, are really quatorzains. They to which the plane of the ellipse is a tangent plane, the ellipse being the section of the ruled surface by the plane; the ruled surface is a cylindroid deformed by a simple shear parallel to the transversal. In the third-order complex the centre locus becomes a finite closed quartic surface, with three (one always real) intersecting nodal axes, every plane section of which is a trinodal quartic. The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic scalar finds no place among them, and in consequence Q1 is meaningless. Putting 1-n- we get Combebiac's tri-quaternion under the form Q-p+ng+wr. This has a reciprocal Q1=&p1=ng ̃1 -wp-rg-, and a conjugate KQ (such that_K[QQ']= KQKQ, K[KQ]=Q) given by KQ=Kq+nKp+wKr; the product QQ of Q and Q' is {pp'+ngq'+w(pr'+rg'); the quasi-vector (1-K)Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) (1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane. Combebiac does not use K; and in place of έ, n he uses μn-, so that μ2=1,wμ==μw =w, w2=o. Combebiac's tri-quaternion may be regarded from many simplifying points of view. Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar. Again a unit point u may be regarded as by multiplication changing (a) from octonion to point-plane-scalar, (b) from point-plane-scalar to octonion, (c) from plane-scalar to linear element, (d) from linear element to plane-scalar. If Q=&p+ng+wr and we put Q=(1+}wt)(§p+nq)× | (1+w) we find that the quaternion / must be 2f(r){f(q—p), where f(r)=rq-Kpr. The point p=Vt may be called the centre of Q and the length St may be called the radius. If Q and Q are commutative, that is, if QQʻ=Q'Q, then Q and Q' have the same centre and the same radius. Thus Q1, Q, Q, Q',... have a common centre and common radius. Q and KQ have a common centre and equal and opposite radii; that is, the t of KQ is the negative conjugate of that of Q When Su=0, (1+1wu) ( ) (1+wu) is an operator which shifts (without further change) the tri-quaternion operand an amount given by u in direction and distance. BIBLIOGRAPHY.-In 1904 Alexander Macfarlane published a Bibliography of Quaternions and allied systems of Mathematics for the International Association for promoting the study of Quaternions and allied systems of Mathematics (Dublin University Press); the pamphlet contains 86 pages. In 1899 and 1901 Sir W. R. Hamilton's classical Elements of Quaternions of 1866 was republished under C. J. Joly's editorship, in two volumes (London). Joly adds valuable notes and thirteen important appendices. In 1890 the 3rd edition of P. G. Tait's Elementary Treatise on Quaternions appeared (Cambridge). In 1905 C. J. Joly published his Manual of Quaternions (London); the valuable contents of this are doubled by copious so-called examples; every earnest student should take these as part of the main treatise. The above three treatises may be regarded as the great storehouses; the handling of the subject is very different in the three. The following should also be mentioned: A. McAulay, Octonions, a development of Clifford's Bi-quaternions (Cambridge, 1898); G. Combebiac, Calcul des triquaternions (Paris, 1902); Don Francisco Pérez de Muñoz, Introduccion al estudio del cálculo de Cuaterniones y otras Algebras especiales (Madrid, 1905); A. McAulay, Algebra after Hamilton, or Multenions (Edinburgh, 1908). (A. MCA.) " QUATORZAIN (from Fr. quatorze, fourteen), the term used in English literature, as opposed to sonnet," for a poem in fourteen rhymed iambic lines closing (as a sonnet strictly never does) with a couplet. The distinction was long neglected, because the English poets of the 16th century had failed to apprehend the true form of the sonnet, and called Petrarch's and other Italian poets' sonnets quatorzains, and their own incorrect quatorzains sonnets. Almost all the so-called sonnets of the Elizabethan cycles, including those of Shakespeare, Night was ordained together friends to keep. Which though the day conjoin by several flight, And cach returns unto his love at night, Why should'st thou, Night, abuse me only thus, If, when night comes, you bid me go away. Donne, and afterwards Milton, fought against the facility and incorrectness of this form of metre and adopted the Italian form of sonnet. During the 19th century, most poets of model of the sonnet, and particularly in avoiding the final distinction prided themselves on following the strict Petrarchan couplet. In his most mature period, however, Keats returned to the quatorzain, perhaps in emulation with Shakespeare; and some of his examples, such as "When I have fears," "Standing aloof in giant ignorance," and "Bright Star," are The "Fancy in the most beautiful in modern literature. Nubibus," written by S. T. Coleridge in 1819, also deserves notice as a quatorzain of peculiar beauty. This form has QUATRAIN, sometimes spelt Quartain (from Fr. quatre, four), a piece of verse complete in four rhymed lines. The length or measure of the verse is immaterial, but they must be bound together by a rhyme-arrangement. always been popular for use in the composition of epigrams, on account of its brevity and neatness, and may be considered as a modification of the Greek or Latin epigram at its concisest. QUATREFAGES DE BRÉAU, JEAN LOUIS ARMAND DE (1810-1892), French naturalist, was born at Berthezène, near Vallerangue (Gard), on the 10th of February 1810, the son of a Protestant farmer. He studied medicine at Strassburg, where he took the double degree of M.D. and D.Sc., one of his theses being a Théorie d'un coup de canon (November 1829); next year he published a book, Sur les aérolithes, and in 1832 a treatise on L'Extraversion de la vessie. Removing to Toulouse, he practised medicine for a short time, and contributed various memoirs to the local Journal de médecine and to the Annales des sciences naturelles (1834-36). But being unable to continue his researches in the provinces, he resigned the chair of zoology to which he had been appointed, and in 1839 settled in Paris, where he found in H. Milne-Edwards a patron and a friend. Elected professor of natural history at the Lycée Napoléon in 1850, he became a member of the Academy of Sciences in 1852, and in 1855 was called to the chair of anthropology and ethnography at the Musée d'histoire naturelle. Other distinctions followed rapidly, and continued to the end of his otherwise uneventful career, the more important being honorary member of the Royal Society of London (June 1879), member of the Institute and of the Académie de médecine, and commander of the Legion of Honour (1881). He died in Paris on the 12th of January 1892. He was an accurate observer and unwearied collector of zoological materials, gifted with remarkable descriptive power, and possessed of a clear, vigorous style, but somewhat deficient in deep philosophic insight. Hence his serious studies on the anatomical characters of the lower and higher organisms, man included, will retain their value, while many of his theories and generalizations, especially in the department of ethnology, are already forgotten. " le système nerveux, l'embryogénie, les organs des sens, et la circulation des annélides" (Ibid., 1844-50); "Sur les affinités et les analogies des lombrics et des sangsues (Ibid.); "Sur l'histoire naturelle des tarets (Ibid., 1848-49). Then there is the vast series issued under the general title of Études sur les types inférieurs de l'embranchement des annelés," and the results of several scientific expeditions to the Atlantic and Mediterranean coastlands, Italy and Sicily, forming a series of articles in the Revue des deux mondes, or embodied in the Souvenirs d'un naturaliste (2 vols., 1854). These were followed in quick succession by the Physiologie comparée, metamorphoses de l'homme et des animaux (1862); Les Polynésiens et leurs migrations (1866); Histoire naturelle des annelés marins et de l'eau douce (2 vols., 1866); La Rochelle et ses environs (1866); Rapport sur les progrès de l'anthropologie (1867); Ch. Darwin et ses précurseurs français (1870), a study of evolution in which the writer takes somewhat the same attitude as A. R. Wallace, combating the Darwinian doctrine in its application to man; La Race prussienne (1871); Crania Ethnica, jointly with Dr Hamy (2 vols., with 100 plates, 1875-82), a classical work based on French and foreign anthropological data, analogous to the Crania Britannica of Thurnam and Davis, and to S. G. Morton's Crania Americana and Crania Aegyptiaca; L'Espèce humaine (1877); Nouvelles Etudes sur la distribution géographique des négritos (1882); Hommes fossiles et hommes sauvages (1884); and Histoire générale des races humaines (2 vols., 1886-89), the first volume being introductory, while the second attempts a complete classification of mankind. QUATREFOIL, in Gothic architecture, the piercing of tracery in a window or balustrade with small semicircular openings known as foils "; the intersection of these foils is termed the cusp. QUATREMÈRE, ÉTIENNE MARC (1782-1857), French Orientalist, the son of a Parisian merchant, was born in Paris on the 12th of July 1782. Employed in 1807 in the manuscript department of the imperial library, he passed to the chair of Greck in Rouen in 1809, entered the Academy of Inscriptions in 1815, taught Hebrew and Aramaic in the Collège de France from 1819, and finally in 1827 became professor of Persian in the School of Living Oriental Languages. vast takes the form of Fr. quai, older cay or caye, cf. Spanish caya, a bar, barrier or reef. The earlier form in English is "kay," and it was so pronounced. Key" was also earlier pronounced "kay," and the change in pronunciation in the one was followed also in the other. In spelling also the word was assimilated to "key," in the sense of a reef, or, especially, of the low range of reefs or islets on the coasts of Spanish America, e.g. on the coast of Florida, the chain of islets known as Florida Keys. QUEBEC, a province of the Dominion of Canada, bounded S. by New Brunswick and the United States, W. by Ontario, N. by the district of Ungava, and E. by the gulf of St Lawrence and the strip of castern Labrador which belongs to Newfoundland. If Ungava be considered as added to the province of Quebec, Hudson Strait is the northern boundary. The province includes the island of Anticosti, the Bird Islands and the Magdalen Islands, in the gulf of St Lawrence. The western boundary, separating Quebec from Ontario, extends through Point au Baudet on the river St Lawrence to Point Fortune on the Ottawa river, from which place the boundary follows the Ottawa to Lake Temiscaming. From the north end of this latter lake it runs due north to Hudson Bay. The province of Quebec thus extends from Blanc Sablon, a fishing harbour at the western end of the Strait of Belle Isle (which separates Canada from Newfoundland) in 59° 7′ W. to Lake Temiscaming in 79° 40′ W., a distance of about 1350 miles. The area of the province is 351,873 sq. m. The general direction of the province is north-east and south-west, following the course of its chief physical feature, the river St Lawrence. Speaking generally, it may be said that the province of Quebec comprises the hydrographical basin of the river St Lawrence as far west as the intersection of the parallel of 45° N. with the latter. The St Lawrence flows near the southern edge of its basin, only some 50,000 sq. m. of the area of the province lying south of the river. Quatremère's first work was Recherches ... sur la langue et la The province of Quebec falls into three main physiographical litterature de l'Egypte (1808), showing that the language of ancient divisions, viz.: (1) the Laurentian Highlands, (2) the Valley Egypt must be sought in Coptic. His translation of Makrizi's Arabic history of the Mameluke sultans (2 vols., 1837-41) shows his of the St Lawrence, and (3) the Notre Dame Mountains and erudition at the best. He published among other works Mémoires the rolling country lying to the south-east of this range. sur les Nabatéens (1835); a translation of Rashid al-Din's Hist. (1) The Laurentian Highlands are sometimes referred to as the des Mongols de la Perse (1836); Mém. géog, et hist. sur l'Égypte "Laurentian Mountains," as they appear to constitute a mountain (1810); the text of Ibn Khaldūn's Prolegomena; and a range when viewed from the gulf or the river St Lawrence. This number of useful memoirs in the Journal asiatique. His numerous portion of the province, however, is really a plateau having an reviews in the Journal des savants should also be mentioned. clevation of 1000 to 2000 ft. above sea level, but this plateau Quatremère made great lexicographic collections in Oriental north of latitude 55° falls away to lower levels toward Hudson Bay languages, fragments of which appear in the notes to his various and Hudson Strait. Along the extreme eastern border of these works. His MS. material for Syriac has been utilized in Payne Laurentian Highlands on the coast of Labrador, however, the Smith's Thesaurus; of the slips he collected for a projected Arabic, country rises to much greater altitudes, forming an extremely Persian and Turkish lexicon some account is given in the preface rugged district which attains in places an elevation of 6000 ft. to Dozy, Supp. aux dicit. arabes. They are now in the Munich above sea-level. This plateau forms what is known as the Laurentian library. peneplain and is hummocky in character, the surface, however, A biographical notice by M. Barthélemy Sainte-Hilaire is prefixed being but slightly accentuated and the sky line seen from the to Quatremère's Mélanges d'histoire et de philologie orientale (1861). higher points in the area being nearly level. It is densely wooded and everywhere abounds in lakes, great and small, lying either in QUAY, MATTHEW STANLEY (1833-1904), American poli- basins etched in the rock surface by glacial action or else bounded tical "boss," was born in Dillsburg, York county, Pennsyl- by the irregularly distributed drift which more or less completely vania, on the 30th of September 1833. He graduated at covers the surface of the underlying rocks. From these lakes Jefferson College (now Washington and Jefferson College) in issue very numerous streams tributary to the larger rivers. These lakes and rivers form so continuous a series of waterways that 1850 and was admitted to the bar in 1854. He served in a traveller who knows their courses, and the portages connecting various capacities in the Civil War, and in 1865-1867 was a them, can traverse this immense tract of country in any direction member of the state House of Representatives, becoming by canoe. These streams also, cascading down from the elevated surface of the plateau to sea-level, afford immense water power, secretary of the commonwealth in 1873-1878 and again in which is used to an increasing extent as the methods of long-distance 1879-1882, recorder of Philadelphia in 1878-1879, and state electrical transmission of power become more and more perfect. treasurer in 1886-1887. He was chairman of the Republican These waters are, moreover, clear and pure, and the country is one national executive campaign committee in 1888, and was a in which malaria and similar diseases are unknown. Some of the member of the United States Senate in 1887-1899 and again walled valleys or fjords cut in the solid rock; a number of which, rivers draining the Laurentian country run in very deep, highin 1901-1904. For nearly twenty years he dominated the comparable in character although perhaps not in depth to those government of Pennsylvania, and also played a very prominent of Norway and Greenland, pass outward from the central portion part in national affairs. In 1899 he was brought to trial on a of the peneplain north, east and south. As an example of such charge of misappropriating state funds, and, although he was fjords in the province of Quebec, those occupied by the waters of the Hamilton, Mingan and Saguenay rivers may be cited as well acquitted, the feeling among the reform element in his own as that, now partially silted up, which is occupied by Lake Temisparty was so bitter against him that the legislature was dead-caming and the Mattawa river. The walls of solid gneiss between locked and his re-election was postponed for two years. which the Saguenay flows are in places from 1500 to 1800 ft. in died on the 28th of May 1904. height, while the waters of the river in places reach a depth of 1400 ft. He QUAY, a wharf or landing-place for the loading and unloading of water-borne cargo. The word, now pronounced like "key," This Laurentian country in the province of Quebec and its continuation into the adjacent province contain the chief timber |