lin, the oldest and most famous of them all, pointing to the sun emblazoned behind the chair in which Washington had presided through the whole struggle, said to those about him, "In the vicissitudes of hope and fear, I was not able to tell whether it was rising or setting. Now, I know that it is the rising sun." After more than a century's trial of their work, the sun which Franklin saw is not yet near the zenith much has been done, but vastly more remains to be accomplished, and it is still morning with our young Republic.

Consult Carson, H. L., History of the Supreme Court of the United States, with Biographies of all Justices' (2 vols., Philadelphia 1902); Curtis, B. R., Jurisdiction, Practice and Peculiar Jurisprudence of the Courts of the United States' (2d ed., Boston 1896); Moore, B. F., The Supreme Court and Unconstitutional Legislation' (New York 1913).

JOSEPH H. CHOATE.

SURABAYA, soo-rä-bi'ä (Dutch, SOERABAJA), Java, (1) the seaport and capital of the province of the same name on the north coast of the island of Java. The city is situated on the Strait of Surabaya, which separates Madura Island from Java. It is, next to Batavia, the most important port and commercial station in the Dutch East Indies, and has machine-shops, an arsenal, a mint, sugar and furniture factories, shipbuilding yards and foundries. It exports sugar, coffee and the various products of the region. Pop. about 150,000 including about 10,000 Europeans. (2) The province of Surabaya has an area of 2,327 square miles and a population of over 2,115,000.

SURAJAH DOWLAH, soo-rä'jä dow’la, the last independent nabob of Bengal, under whom was perpetrated the massacre of the Black Hole (q.v.). He succeeded his grandfather, Ali Verdy Khan, in 1756, and within two months of his accession found a pretext for marching on Calcutta. On the arrival of Clive and Admiral Watson he retreated to Moorshedabad, but was routed at the battle of Plassey (23 June 1757). He then fled up the Ganges, but was betrayed by a fakir, and was put to death by order of the son of Meer Jaffier, the new nabob. Surajah Dowlah's reign lasted 15 months, his age at the time of his death being barely 20.

SURAKARTA, soo-rä-kär'tä, a town in central Java, connected by rail with Samarang on the north and Surabaya on the east. It is the residence of the native sultan of Surakarta, who is a vassal of the Dutch government and is advised by a resident. The town (pop. 125,000) is the capital of his kingdom, a mountainous but in part very fertile region, with an area of 2,191 square miles and a population of about 1,100,000.

SURAT, soo-rät', India, a city in the Gujarat division of Bombay, extends for some distance in crescent form along the south bank of river Tapti, (spanned by an iron bridge) in a fertile valley. It is 160 miles by rail north of Bombay. The Nawab's palace lies within the confines of the fort. The remarkable buildings are four handsome Mohammedan mosques, two Parsi fire-temples, several Hindu temples, and a clock-tower (80 feet

high). There is also an extensive bazaar, and a Hindu hospital for sick animals. The city in 1512 was burned by the Portuguese, again in 1530 and 1531. The English established themselves there in 1612, and the city came under British rule in 1800. Industry is limited to the manufacture of cotton and silk goods, shawls, etc., articles of ornamentation, jewelry and ivory objects, indigo and pottery. The exports are cotton and grain. The commercial importance of Surat was established in the 16th century, and it was the starting point for pilgrimages to Mecca. Its decline dates from the removal of the East Indian Company to Bombay. Fire and flood contributed subsequently to its decadence. It fourished during the American Civil War through its cotton export. Pop. about 115,000.

SURCOUF, sür-koof, Robert, French naval officer: b. 1773; d. 1827. Much of his life at sea was devoted to privateering and he was known as "the king of the Corsairs." From 1798 to 1801 and from 1809 to 1811, he scoured the sea for English merchantment as Paul Jones did some years previously. His life was divided between building French ships on shore and scouring the high seas for English merchant vessels. It was his advice to Napoleon: "Attack rich England in her riches in her merchant vessels; leave your ships of the line at home and send out light privateers!"

SURETY. See SURETYSHIP.

SURETYSHIP, a word derived from the French sûreté, from the Latin securitas, which means freedom from care. It signifies the obligation of a person to answer for the debt, default or non-performance of another, and to make good any loss occasioned thereby to the extent provided in the contract. The difference between suretyship and guarantee is an essential one, a contract of suretyship being a direct liability to the creditor for the act to be performed by the debtor, whereas a guarantee is liability only for the debtor's ability to perform this act. A contract of suretyship is an immediate and direct undertaking that the act shall be done, and if the act is not done, the surety becomes responsible at once.

The Constitution of the United States makes it impossible for any State to enforce a law which might be construed as impairing the rights of a creditor under a contract of suretyship, but like other contracts it may be vitiated and annulled through fraud or duress in the execution. The surety is entitled to such information both from creditor and debtor as will enable him to know the nature of the obligation which he is assuming, and if there is fraudulent misrepresentation or suppression of the facts with the purpose of obtaining his agreement to the undertaking the surety can obtain relief in a court of equity. On the other hand this relief would not be granted against innocent parties who had, without notice from the surety, incurred expenditure or assumed obligations on account of the existence of the suretyship contract. Of course in such a case the surety would have a right to redress from the creditor or debtor, or both, who had caused him loss by deceiving him.

It should be understood that there is no obligation on the part of the creditor or of the

debtor to disclose all facts relating to the risk, but only those the withholding of which, if known to them, or either of them, would constitute intent to mislead. The surety, on the other hand, is expected to use reasonable judgment and precaution in making the contract. The presumption of law is that the suretyship, the surety's signature being admitted, is valid, and upon him rests the onus of attacking its validity, if he so desires.

The surety's responsibility cannot be changed or the contract modified in any manner without his consent, and should any change be made in the contract without such consent, the surety is discharged from his obligation. It does not matter whether the change would be advantageous to the surety or otherwise; he has a right to stand upon the original terms, and cannot be held responsible for any different terms. This applies also to any extension of the term of credit specified in the contract without the surety's approval in legal form.

Upon discharge of his obligation by the debtor, the surety is of course released. The surety is likewise released by tender of payment by the debtor and refusal to receive it by the creditor. In some States the surety is released if the creditor does not sue the principal upon request of the surety. Should the debtor default and the surety have to pay, the surety becomes entitled to all the rights and securities previously held by the creditor against the debtor. If there are several sureties, and the creditor's claim is enforced against one only, the latter can compel his cosureties to pay their several shares, and he also has a claim against the principal for the amount which he has expended in meeting the obligation. See GUARANTEE.

SURF-BIRD, a shore-bird (Aphriza virgata), having a distinct place of its own between the sandpipers and plovers. It is about 10 inches long, with the wing seven; dark brown above, lighter on the wing coverts, with white spots and stripes on the head and neck; upper tail coverts and basal half of tail white, the latter terminated with brownish black; under parts white, tinged with ashy in front, each feather having a brownish black crescent. The bill is about as long as the head, with vaulted obtuse tip and compressed sides; wings long and pointed. It is found on the Pacific Coast of North and South America, and in the Sandwich Islands, migrating from northern to temperate regions in winter and back again in summer. It is usually seen on the edge of steep rocks, among the retreating waves, searching for small mollusks and marine animals, allowing the surf sometimes to dash over it, whence the common name; its flight is short, with a quick and jerking motion.

SURF-CLAM. See CLAM.

SURF DUCK, or SURF SCOTER. See SCOTER.

SURF-FISH, one of the many small ovoid fishes of the family Embiotocida, related to the percoids, which abound upon the Pacific Coast of North America, where they are found numerously in the surf on sandy beaches, and in the mouths of rivers. They are often gayly colored, sometimes in extraordinary patterns of spots or bars; and are easily caught but not

valued much as food. The most familiar one is Amphisticus argenteus; several others are locally known as the blue, black, red and white perches, the alfione, etc. All are vivipa

rous.

SURF-SMELT, a small, eminently toothsome smelt (Hypomesus pretiosus), numerous along the coast of California and northward, where it spawns in the surf, and is caught in great quantities in nets. See SMELTS; WHITEFISHES.

SURFACE, Joseph, a character in Sheridan's comedy, The School for Scandal.' He is a mean hypocrite who affects great seriousness and sentimentality.

SURFACE. (1) A physical surface may be defined as formed by the boundaries or limiting portions of a given body. (2) A mathematical surface is the boundary between two given portions of space. It may be of various orders, a plane surface being of the first order, a quadric surface of the second order, etc. A surface through all points of which a straight line may be so drawn as to rest entirely within the said surface, is termed a ruled surface. The cone, conoid and cylinder are examples of this class. A surface is said to be of the nth order when it is intersected at n points, either imaginary or real, by a given arbitrary line. For a treatment of the subject, consult Eisenhart, L. P., (Treatise on Differential Geometry on Curves and Surfaces (Boston 1909); Michaelis, M. L., 'Dynamics of Surfaces' (New York 1914); Smith, Charles, 'Solid Geometry) (3d ed., New York 1891).

SURFACE TENSION, that property of liquids in virtue of which they tend to take such a form as to have the smallest surface possible. The name "surface tension" has reference to the fact that liquids, when freed from the action of gravity and other comparatively powerful forces, behave as though their surfaces were elastic membranes, which are everywhere in a state of uniform tension. Beginners in the study of physics often form the idea, from their textbooks, that this hypothetical tension is real and that the surface of a liquid really is membranous in nature, and subject to an actual, physical tension. This is not at all the case; for the behavior of the liquid is due to an entirely different cause, as will be understood by reference to Fig. 1. AB here represents a liquid surface, and m m m m m represents a molecule of the liquid, which is originally in the interior of the liquid, but which is removed from it in the manner illustrated by the successive figures 1, 2, 3, 4 and 5. Consider, first, the state of the molecule m in the position 1. It is here surrounded by the liquid on all sides, and the attractive influence that the other molecules of the liquid exert upon it is sensibly the same in all directions. The circle that is drawn about m represents a sphere whose radius is the "radius of sensible. molecular attraction"; that is, it is equal to the (unknown) distance at which we may suppose that the attraction of one molecule of the liquid for another one ceases to be sensible. The attractive influence of those parts of the liquid which are external to this sphere being by hypothesis insensible, we may regard m as influenced solely by such molecules as are within

a sphere of the radius shown. It is easily seen, therefore, that the attraction of the liquid for m will be the same in all directions (and therefore without any resultant effect), so long as the sphere remains totally submerged. But when the molecule m approaches the surface so nearly that a part of its sphere projects into the air as shown at 2, it is equally evident that the attractive force upon m is no longer the same in all directions. In order to make it so, we should have to cut off, from the bottom of the sphere at 2, a segment equal to the segment that projects into the air, as indicated by the little shaded area. The mass of fluid that lies between this shaded segment and the surface of the liquid is without any resultant effect upon

m, on account of its symmetry with respect to m; and hence in the position 2 we may regard m as subject only to the unbalanced downward attraction that the shaded segment exerts upon it. In position 3 the molecule has reached the surface of the liquid, and it is subject to a downward attractive force due to the mass of liquid contained in the entire lower half of the sphere. In bringing the molecule from position 1 to position 3, we therefore have to move it upward against a force which tends to pull it back into the liquid again; this force becoming active from the moment that the sphere of sensible molecular attraction first becomes tangent to the surface of the liquid, and increasing in magnitude until it attains its maximum value when the molecule actually reaches that surface. Hence we have to perform work, in order to transport a molecule from the interior of a liquid to the surface; and this amounts to saying that we have to perform work in order to increase the surface of a liquid. But this is just what we should have to do if the surface of the liquid were an elastic membrane; and hence it is permissible to imagine that the surface is such a membrane; and it is found that such a conception makes it easier to understand and describe the phenomena that result from molecular attractions in liquids. It will be noted, however, that in extending the surface of a liquid we do not actually stretch the existing surface. We merely bring more molecules from the interior, where the forces acting upon them are balanced, to the surface, where these forces are not balanced.

The phenomena of surface tension are most obvious in soap films and in foams, where the mass of the liquid concerned is so small (relatively to the surface) that the molecular forces which give rise to the so-called "surface tension" can easily preponderate over gravity, which is relatively powerful in liquid bodies of large mass and small surface. The French physicist Plateau devoted a vast amount of attention to

the phenomena that are manifested by liquid films, and by masses of liquid that are freed from the influence of gravity by being suspended in other liquids with which they will not mix, but which have the same density as the liquid to be studied. Olive oil can readily be freed from the action of gravity, by submerging it in a mixture of alcohol and water, whose composition is regulated by trial until the mixture has precisely the same specific gravity as the oil. A mass of oil which is submerged in this manner, and is not constrained in any way, at once assumes a spherical form; for the sphere has a smaller surface than any other solid of the same volume.

The existence of surface tension can be shown readily and strikingly, even in a large mass of water, by several very simple experiments. Of these, the camphor-movement experiment is one of the best known. To perform it, a perfectly clean vessel is filled with clean water, some of the water being allowed to flow over the sides of the vessel, so that any superficial impurities may be washed away. Very fine scrapings of camphor are then allowed to fall upon the surface of the water; and if the water surface is sufficiently clean, these scrapings at once begin to execute the most violent movements. The motion of the camphor is due to the fact that the surface tension of a solution of camphor in water is less than that of pure water. The camphor particles do not dissolve evenly on all sides; and the horizontal pull exerted upon them by the water is greatest in those directions in which the concentration of the solution in immediate contact with the particles is least. Hence the motions. The great importance of absolute cleanliness in this experiment is well illustrated by touching with a slightly greasy finger a water surface upon which camphor particles are in rapid motion. The entire surface becomes contaminated almost instantly, so that the camphor movements become deadened, or cease altogether.

The effects of surface tension are observable in large masses of liquid, where those masses come in contact with the walls of their containing vessels. The slight elevation of the water in a drinking glass, where the water touches the glass, is due to this cause. This particular phenomenon is more marked in the case of a glass tube of small diameter, dipping in a vertical position into a vessel of water (or any other liquid which actually wets the glass). Let the glass tube be inserted into the water, so that it is wetted up to a certain level, and let the tube be then raised slightly. The glass, in the region which has been submerged below the general level of the water and is now raised above it again, adheres to the water, and as the tube is raised, the column of water within it sinks at the centre, so that its surface becomes concave, as is illustrated in Fig. 2. The weight of that part of the water within the tube which stands above the general level of the water in the external vessel (that is, the weight of that portion which lies between the actual water surface in the tube, and the dotted horizontal line), is sustained by the tension of the curved surface (or "meniscus") that bounds the column at the top; this tension acting everywhere in the direction of the surface of the water, and therefore having an obliquely-upward di

stands at a lower level than corresponds to the general level of the liquid surface in the containing vessel. In a barometer, the meniscus of the column is convex upward, and the depression of the column due to the surface tension of the mercury is usually quite sensible; so that in order to be in a position to know the exact height at which the mercury in the column would stand if the tube were large enough in diameter for the effects of surface tension to be negligible, it is necessary to investigate, very carefully, the way in which the depression varies with the diameter of the tube, and with the height of the meniscus itself. Numerous observers have made extensive investigations of this sort, and have given their results in tables. A very good table of this kind, due to Mendeléeff, is given in Guillaume's Thermométrie de Précision,' and other tables will be found in nearly all of the works upon meteorology. The property of liquids in virtue of which they stand, in a vertical tube, at an elevation different from that in the vessel into which the tube dips, is commonly called "capillarity," in reference to the small diameter of the tubes in which the effect is most noticeable (Latin, capillus, "hair").

TABLE OF SURFACE TENSIONS AT 20° C. (68° F.).

and quoted by Maxwell. Mercury, for example, is capable of exerting a pull of 21.58 grains upon a straight line one inch long, lying in its surface. The value of the surface tension of water given in this table is certainly too great. Brunner found it to be 75.2 dynes per centimeter, and Wolf found 76.5 and 77.3. Rayleigh's determination, based upon a study of the wave-length of ripples, gave 73.9 dynes at 18° C.; and T. Proctor Hall found that at T° C. the surface tension of water, in the same units, is given by the expression.

75.48 0.140T.

Bibliography.- Boys, 'Soap Bubbles and How to Make Them'; Plateau, Statique expérimentale et théorique des liquides soumis aux seules forces moleculaires'; Risteen, Molecules and the Molecular Theory of Matter.' Also, any extended treatise on physics.

ALLAN D. RISTEEN.

This

SURFACES, Theory of. Surface, in the mathematical sense, is the common boundary of two contiguous regions of space. The developments in this vast field of mathematical investigation are essentially of modern origin. The geometers of the Greek school were acquainted with some of the elementary properties of a few surfaces, notably those of sphere, cylinder and cone, but the systematic and fruitful study of surfaces began with their representation by means of equations in Cartesian co-ordinates (see GEOMETRY, CARTESIAN). was not done until the method of co-ordinates had been employed with success in the study of plane curves, whereupon its application to surfaces presented itself as a natural extension. According to Cantor, Geschichte der Mathematik, Parent (1666-1716) was the first to represent surfaces analytically by means of a single equation F(x, y, z)=0. To each set of values of x, y, z satisfying this equation corresponds a point of the surface. With the introduction of co-ordinates two distinct phases in the study of surfaces present themselves. the one hand the surface is defined in some purely geometric way, and the problem is to find an equation analytically representative o the surface. On the other hand an equation i assumed, and the problem is to arrive at th properties of the surface from its analytica definition. In the first case no less than i the second, the deduction of geometric proper ties proceeds, in the main, along analytica lines. It is at once evident that the secon phase of the general problem greatly broader the scope of investigation, and it is from th point of view that the mathematicians hav studied the surfaces defined by algebraic equa tions of second, third, fourth and higher d grees. The algebra brings in imaginaries, ar this leads to the introduction of surfaces th are altogether imaginary, and to the sideration of imaginary points and elements connection with real surfaces.

Or

CO

two-dimensiona continuum of planes, i.e., as the envelope of its tangent planes, or as a threedimensional continuum of lines, i.e., the envelope of its tangent lines. The theory of a surface as the envelope of its 3 of tangent lines constitutes a special chapter in the general theory of complexes of straight lines (see GEOMETRY, LINE, AND ALLIED THEORIES). Along with the analytical method, the synthetic or projective method has been employed, and with special elegance and completeness in the case of surfaces of the second order. With this brief introduction we now pass to a more detailed account of the developments in this branch of mathematics.

1. Algebraic Surfaces in General.-Any surface which can be analytically expressed by an algebraic equation between the Cartesian co-ordinates x, y, z of a point of space is called an algebraic surface. The order of the surface is the number of points of intersection (real or imaginary) of the surface by an arbitrary straight line. The order of the surface is obviously the same as the degree n of its equation. The class is the number of tangent planes of the surface that pass through an arbitrary line. When there is no singularity (see 7) on the surface the class is n(n-1)3. The rank of the surface is the order of a circumscribing cone whose vertex is an arbitrary point of space. The rank is n(n-1). The intersection of the surface by a plane is a curve of nth order, and, by the foregoing, the class of this curve is the same as the rank of the surface.

2. The Plane.- This is the simplest of all surfaces, and its equation in the variables x, y, z is of the first degree: Ax + By + Ciz + D=0, in which A, B, C, D are constants. It is the only surface of first order.

3. Surfaces of the Second Order, or Quadric Surfaces. The earliest investigations were connected with the surfaces of the second order, namely, those defined by the general equation of the second degree: Ar+ By + C☞+2Fyz +2Gzx + 2Hxy +2Lx+2My + 2Nz + P=0. This equation contains 10 coefficients which enter homogeneously. However, only the nine ratios of the coefficients are essential, as the equation may be divided through by any coefficient that is not zero. From this fact comes an important theorem. The substitution of the co-ordinates of a given point in the general equation imposes one equation of condition upon the coefficients; nine such equations determine the ratios of the coefficients, and herewith the equation, and with it the surface. The theorem follows: A surface of second order is in general determined by nine points through which it is to pass.

4. Classification of Quadric Surfaces.There are in all 16 surfaces of the second order, when the purely imaginary and degenerate cases are included in the numeration. The grouping of the individual surfaces varies with the principle employed. The principle of division may be based on analytical criteria or on geometrical characteristics. Four different varieties of geometrical classification are known. In one the surfaces are divided into (a) the surfaces with centre or central surfaces, (b) the non-central surfaces. A second VOL. 26-5

classification gives, (a) ruled surfaces with real generating lines (see 16), (b) non-ruled surfaces (analytically these latter surfaces are ruled surfaces with imaginary generating lines). A third classification rests upon the presence or absence of vertices on the surface. For example, a cone has a vertex and two intersecting planes are a degenerate form of a surface of second order with the line of intersection as a line of vertices. An ellipsoid is without a vertex. The fourth classification is based upon the nature of the conic that is cut from the surface by the plane at infinity.

We now present a classification based upon analytical criteria. This is effected by means of the values of two polynomials 4 and D, functions of the coefficients, and of the roots k=λ, μ, v, of a cubic equation in k called the discriminating cubic. The polynomials may be conveniently put in the determinant form, as also the cubic equation:

are all negative.

4' Δ' Δ

(ii) Hyperboloid of one sheet if two of the quantities are negative.

(iii) Hyperboloid of two sheets if one of the quantities is negative.

(iv) Ellipsoid, imaginary, if all the quantities are positive.

These are surfaces with centre. By a suitable transformation of the co-ordinate axes to the centre the general equation can be thrown into the form λx2 + μy2 + vg2 + d = 0, in which 4 and λ, μ, v are the roots of the discrimiD nating cubic.

d

=

(B) D=0, (i) Elliptic paraboloid if λ and μ have the same sign.

(ii) Hyperbolic paraboloid if 2 and u have different signs.

When D=0, one of the roots 2, μ, vis zero, and it is here assumed that v 0. By a suitable transformation of the origin of coordinates to a point of the surface, the equation may be made to take the form x2 +μÿ2 + 2Qz = 0.

The surfaces (a) and (B) are surfaces without vertices.