tor of Glarus 1506. He studied the Greek New Testament very carefully, and copied it with his own hand; preached against the mercenary service of his countrymen; in 1516 accepted a call to St. Mary's at Einsiedeln, and began to attack superstitious practices, but with the consent of his superiors; he even received for a while, as one of the most popular preachers, a pension from the papal nuncio in Switzerland to aid him in his studies and to secure his political influence. In Dec., 1518, he was called to the cathedral at Zurich, where he labored till his death. He preached "Christ from the fountains" and "inserted the pure Christ into the hearts:" broke loose gradually from Romanism; introduced the Reformation in Zurich 1524, after some public disputations with the champions of the old system; led the Reform movement in the other German cantons of Switzerland; attended the conference at Berne 1528, which resulted in the abolition of the mass. He was invited to a personal conference with Luther and Melanchthon at Marburg Sept., 1529, to adjust the only serious doctrinal difference between them on the Eucharistic Presence. He counselled energetic measures for the promotion of the Reform in his native land, but was defeated by the policy of hesitation which prevailed in Berne. He also entered into bold political coinbinations with Philip of Hesse for the triumph of the Protestant cause in Germany, and addressed the emperor of Germany and the king of France with a confession of his faith. But he was cut down in the midst of his career. At the outbreak of the war between the Roman Catholic and Protestant cantons he accompanied the Zurich regiment as chaplain, according to Swiss custom, and was pierced by a lance in the disastrous battle at Cappel, Oct. 11, 1531, while stooping to comfort a dying soldier. His last audible words were, "What of that? They can indeed kill the body, but they cannot kill the soul." His remains were burned, and the ashes scattered to the four winds. A plain monument in granite erected in 1838 marks the spot where he died.

Zwingli was a bold Reformer, an able scholar, an eloquent preacher, a patriotic republican, and far-sighted statesman. He lacked the genius and depth of Luther and Calvin, the learning of Melanchthon and Ecolampadius, but he was their equal in honesty of purpose, integrity of character, heroic courage, and devotion to the cause of Reformation, and surpassed them in liberality. His prominent intellectual trait was clear, strong common sense. He had no organ for the mystic element in religion. He loved music and poetry, but in public worship he favored puritanic simplicity, and removed all pictures from the churches to prevent the temptation to idolatry. In his theological views he was more radical than Luther, and departed farther from the medieval traditions. He differed chiefly from his view of the real presence of Christ's body and blood in the sacrament, and held this ordinance to be merely a commemoration of the atoning death of Christ: but notwithstanding this difference he offered him with tears the hand of brotherhood, which Luther refused. In some articles he was ahead of his age, and held opinions which were then deemed dangerous and heretical. He had a milder view on original sin and guilt than the other Reformers, and believed that all infants dying before the age of responsibility, whether baptized or not, and all the nobler heathen who lived up to their standard of virtue and longed after the true religion, are saved by the grace of Christ, which may operate upon the heart without the ordinary means and visible signs. His principal works are a Commentary on the True and False Religion (1525), a sermon On Providence (preached at Marburg, 1529), his Confession of Faith, addressed to Charles V. at the Diet of Augsburg (1530), a similar Exposition of Faith, addressed to Francis I. of France (July, 1531, three months before his death). This last document is clear, bold, spirited, and full of hope for the triumph of the truth, warns the king against the slanderous misrepresentations of Protestant doctrines, and entreats him to give free course to the gospel, and to forgive the boldness with which he dared to approach His Majesty. A few years afterward (1536) Calvin dedicated in a most eloquent preface his famous Christian Institutes to the same monarch, but with equal want of direct sucIt is questionable whether he ever read either document. Zwingli represents only the first stage in the history of the Reformed Church. His work was completed after his death by his successor, Bullinger, at Zurich, and still more by Calvin at Geneva. The fourth centennial of his birth was extensively celebrated Jan. 1, 1884, in Reformed churches in Switzerland, Holland, and the U. S.

cess.

Literature.-H. Zwinglii Opera, ed. Schuler and Schulthess (Zurich, 1828-42, 8 vols.); a popular edition of his works by Christoffel (Zurich, 1843 seq., 15 vols.); Bingraphies of Zwingli by Myconius (1536), Nüscheler (1776),

Hess (1811; trans. by Aiken, London, 1812), Schuler (1819), Hottinger (1843; trans. by Th. C. Porter, Harrisburg, 1856), Robins (in Bibliotheca Sacra for 1851), Röder (1855), Christoffel (1857: trans. by John Cochran, Edinburg, 1858), Güder (in Herzog's Encykl., 1864), and especially Mörikofer (Ulrich Zwingli nach den Quellen, Leipsic, 1867-69, 2 vols.). On the theological system of Zwingli see Zeller, Das theolog. System Zwingli's (1855); Siegwart, Ulrich Zwingli der Charakter seiner Theologie (1855); Spörri, Zwingli-Studien (1866). Compare also Merle d'Aubigné's History of the Reformation, 4th vol.; and Fisher, The Reformation (1873, pp. 137 seq.). A large number of pamphlets and articles were called forth by the fourth centennial celebration, in 1884. PHILIP SCHAFF.

Zwir'ner (ERNST FRIEDRICH), b. at Jakobswald, Silesia, Feb. 28, 1802; studied at the building-school of Breslau, afterward at the architectural academy of Berlin; worked several years under Schinkel, and was appointed in 1833 architect to the cathedral of Cologne. He finished the restoration of the old building and erected the transept and the northern and southern portals. He also built a number of villas, palaces, and churches in the regions along the Rhine. D. at Cologne Sept. 22, 1861.

Zwolle, town of the Netherlands, capital of the prorince of Overyssel, on the Zwarte-Water, is one of the finest and handsomest cities of the country, with broad and straight streets and many public squares. It is the seat of many educational and benevolent institutions, and has extensive manufactures of oil, beer, spirits. linens, and iron Vechte, and has a trade in corn, butter, cheese, cattle, fish, goods. By canals it communicates with the Yssel and and oysters. P. 22,759.

Zygade'nus, or, less correctly, Zygabenus (EUTHYMIUS), a Byzantine theologian of the twelfth century, and "the last of the Greek commentators." He was monk of a convent dedicated to the Virgin Mary near Constantinople, and flourished under Alexius Comnenus (1081-1118 a. D.), at whose request he wrote his Panoply against all Heresies. His commentaries on the Psalms and Gospels are still referred to by scholars. Other commentaries (on the Pauline and Catholic Epistles), and other works (including letters), are in manuscript in the Vatican. R. D. HITCHCOCK.

the ancient name-a name of the typical genus], a family Zygæn'idæ [Lat. Zygæna-Zúyaiva, from ¿vyór, “ yoke,” of selachians of the order Squali, and containing the hamand like that of the typical sharks; the scales are rhom mer-headed sharks. The body is moderately elongated, boid or leaf-like: the head is depressed, transverse, and extended outward or sidewise to a greater or less extent: the eyes are lateral and near the angles of the lateral extension of the head, and provided each with a nictitating membrane; the nostrils are developed in the front of the head; the mouth is inferior and convex forward; the teeth are moderate and in several rows (in all the known species nearly alike in both jaws, oblique and with a notch); the branchial apertures are five, of moderate size, and the last are above the pectoral fins; the spiracles are nullified in the adult; the dorsal fins are two, the first between the pectorals and ventrals, the second above the anal; the anal is normally developed; the caudal elongated, and with a well-developed liver-lobe: the pectoral fins are moderate; the ventrals small. The family is anomalous by reason of the peculiar extension of the sides of the head; this extension is carried to its maximum in the Eusphyra Blockii (Zygana laticeps of some authors), and is least developed in the Reniceps tiburo; in the former it is T-shaped, and in the latter kidney-shaped. The common hammer-headed shark (Sphyrna zygæna = Zygæna malleus) exhibits an intermediate condition. Five species are known, which by are differentiated into three genera-Eusphyra, Sphyrna, and Reniceps. The Sphyrna zygana is not uncommon on the U. S. coasts, and the Reniceps tiburo is an occasional visitor. (See, also, HAMMER-HEAD.) THEO. GILL. Zylonite. See APPENDIX.

some

Zymot'ic Diseases. (See definition and list of, in article on NosOLOGY; see also GERM THEORY OF DISEASE.) The so-called zymotic diseases are characterized by their division into successive periods and more or less regular sequence of symptoms and uniform duration. The period between exposure to the source of disease and its final development is termed the stage of "incubation" or "formative stage," and it is especially during this period that the morbific matter has multiplied by zymosis or ferment. The "germ theory," which has many supporters, assumes that each zymotic disease has peculiar cellular or organized vi talized elements, and that each, by its individual peculiarities of development, determines the stages and symptoms of the sickness which its access to the blood has created. E. DARWIN HUDSON, JR. REVISED BY WILLARD PARKER. Zytomierz', a town of Russia. See JITOMIR.

M

1

1

D3g 1-38

If & be 90°, y The maximum elevation of the water is therefore double its maximum depression. In case of the earth, & is about , and the factor in which it enters amounts to but 13. But were the earth a homogeneous fluid throughout, this coefficient would become; and we find in that case the direct effect due to the foreign attraction exaggerated in that ratio by the mutual attractions (or want of them) in raised and depressed portions. The factor in question will be omitted hereafter, its effect being understood.

We have now to refer the tidal configuration we have

found to the co-ordinates by which we usually express position on the surface of the earth. Since it revolves daily about its axis P P', while the configuration remains fixed in relation to the moon, any point of the nucleus, as h, will be borne along a parallel of latitude, and will at h1 have, above it, high water-at h2 (when the great circle g g is intersected), its lowest water-at 3, high water again, but yet of inferior height to that belonging to position h1; unless, indeed, the moon be on the equator, when the two opposite high waters will be equal. In the difference between the high tides h1 and h3 we have what is called the diurnal inequality; and the phenomena just delineated indicate the analysis into diurnal and semi-diurnal tide.

Lete represent the polar distance (complement of the latitude) of a fluid particle; &, its longitude measured from a meridian fixed on the earth's surface; nt, the angle that this diurnally-rotating meridian makes at any moment with a fixed celestial meridian (in which t represents the time and n the angular velocity of the earth's rotation on its axis);, the moon's right ascension (measured from the same celestial meridian), and v its declination N. or S. as may be.

The cos of the foregoing equation (a) becomes transformed, so that the equation reads thus:

The value of y is thus made up of three terms of marked characteristics, indicated by the diagrams I., II., III. of Fig. 2, on which protuberant portions are shaded. (I.) is independent of the earth's diurnal rotation nt, and also of the longitude, w, of the locality. It is the same, therefore, at all hours, and the same throughout each parallel of latitude. It is zero for latitude which makes 1+ 3 cos 200, or for lat. 35° 16' (N. or S.); it is negative (a depression) for higher latitudes; it is positive (a protuberance) for the equatorial belt between these parallels. It is least when the moon has its greatest declination, but is the same whether that be positive or negative (N. or S.). It is a secular disturbance, depending on the moon's variable angular distance from the equator, and is what would be produced were an imaginary moon and anti-moon each of half the mass of the actual moon distributed in two parallel circles of radius equal to the moon's distance from the earth's axis. "As these circles of matter gradually move each fortnight from the equator to maximum declination and back, the tide produced will be exactly the 'fortnightly tide.'" (Thomson and Tait, Nat. Philos.) A "half-yearly" one will also be due to the sun.

The term II. (Fig. 2) goes through all its phases as the

are nt +

increases from zero to 360°, whether (for the same place) it depends on the time-term, nt, which thus increases in 24 hours, or (for the same instant) the longitude, . It gives high tide in the northern hemisphere (vice versâ for the southern) when, the moon's declination being northern, the meridian of the locality is under the moon, low tide when opposed to it. Its highest or lowest water occurs for the parallel of latitude for which the product sine cose is maximum (i. e. when = 45°). Its neutral lines are the equator and the meridian PeP' at right angles to that passing through the moon. As depending on the declination, it is maximum when that has its highest attainable value, and vanishes when that is zero.

The oblateness of the earth, as having no sensible influence on the amount and distribution of tidal elevation, has not been hitherto referred to. But, as pertinent to this diurnal tide, I remark that if we attribute to Diagram II. the small ellipticity e of the earth, the distortion expressed is a slight turning of the figure about an equatorial axis perpendicular to the plane of the diagram through the M angle

sin v cos v; but if the spheroid were wholly D3ge fluid, the distortion would be magnified two and a half times (by coefficient of formula (c)), and if it have a rotation, n, about PP', then gen2, and the above angle beM comes 3 sin v cos v. If the planes of diurnal rotaD3,12

P' Semi-diurnal.

tion (or parallels of latitude) be tilted through the small fraction of this angle denoted by 2e (through about% second of arc)-that is, if they all be that much deviated from true perpendicularity to the axis of rotation-the distortion of Fig. II. will result; hence, this is the internal motion by which this tidal development would be accomplished in a homogeneous fluid ellipsoid of revolution; a fact important in its relations to the phenomenon of the precession of the equinoxes.

The term III. (Fig. 2) goes through all its phases twice while nt +- increases from zero to 2, whether by increments of time for the same place, or without change of time, by following a parallel of latitude. It is a semidiurnal tide. As effected by latitude, it is proportional to the sin of the polar distance of the locality. If we reckon longitude from the meridian under the moon, the neutral (or zero-elevation) lines will be the two meridians PeP'; the line of low water will be the meridian at right angles to that which passes through the attracting body.

Thus, we find the total distortion represented by our Fig. 1 to be susceptible of analysis into the three distinct distortions represented by Diagrams (Fig. 2) I., II., IIL (spherical harmonics), which, superimposed one upon the other, would reproduce it.

In what precedes, the earth has been treated as if it were a truly spherical solid enveloped by water. No account has been taken of the diurnal rotation (except as it

relates to the manifestation), none of the motion required in the waters themselves to assume the attributed forms.

3M

693

rium theory" of the tides, first indicated by Newton, and developed into its ultimate form by Daniel Bernouilli in his work Du Flux et Reflux de la Mer.

u = C cos (nt +ŵ − ↓); v = C sin (ut+);

cos O sin @

cos V, we shall have from the expressions (A)— 3M sin v cos v sine cos e cos (nt + ŵ − ¥), D3g

p ༡

ration represented by there must to produce this acdt2

celeration be an increment of the pressure (or head) northdp

ward, (negative sign due to decreasing northward).

do

To these two conditions of tidal motion must be added

another derived from the principle of fluid continuity. It is not necessary here to introduce the analytical expression.

It is clear that the pressure, the differential coefficients of which are expressed by equations (A), will (divided by the gravity or weight of the water) be so much height taken from or added to the tidal rise expressed by I., II., III., so that, for the diurnal tide, for instance, we should have y II.+, in which the diurnal currents only are

5 5-38'

The secular disturbance expressed by I. is so slowly developed that (Thomson and Tait, Nat. Philos., 2 844) it may in all cases be expressed with sufficient accuracy by I., multiplied by the coefficient which, for the case of nature (8, nearly) differs little from unity. The equilibrium configuration indicated by Diagram II. for the diurnal tide has its axis of figure at e normal to the plane of the paper; a situation quite incompatible with the relative motion around the earth's axis of this figure as an ordinary wave. It may be regarded, however, as a sta tionary wave developing itself meridionally between the northern and southern hemispheres, the equator being the locus of its "nodes," and its phases varying progressively from meridian to meridian. It can, however, be shown (see Proceedings A. A. A. S., 1876) that (if the ocean be continuous and the depth uniform) the relative motions of the water due to a shifting of the axis of diurnal rotation of the fluid (as if it were a solid shell), through the angle

This stationary wave, rising and falling synchronously with the waxing and waning of the forces which generate it, would tend, however, to an indefinitely increased development, as Laplace's analyses show, were it not for the counteracting resistances of friction, etc.

The motion (progressive) of the folds of a shaken carpet, or of the waves seen rolling up our sea-beaches, is, as regards formmotion, illustrative of the ordinary wave; that of a vibrating ! string with "nodal points " (see art. VIBRATION, Fig. 6) illustrates the stationary wave.

which exactly neutralizes II. (the lunar attraction), and reduces y to zero. The expressions just given for the displacements u and v indicate an elliptical orbit, very much elongated meridionally as we approach the equator (where it is purely a meridional oscillation) to each particle. It appears by the foregoing that the motion in such an orbit more or less completely neutralizes the diurnal (II.) tideproducing force.

In what precedes is found the rationale of Laplace's discovery, that for uniform ocean-depths there is no diurnal tide. It relates to a continuous ocean, and depends upon the exclusion of the right ascension and declination motion of the attracting body. A continuous change in the angle of separation is made necessary by the latter-a change which cannot be effected without disturbing this equalization of pressures by which the diurnal tide is neutralized. The right-ascensional motion is even more incompatible with the theorems. This celebrated dictum expresses, therefore, a mere mechanical theorem alien to essential conditions under which the "tides" of nature are generated.

With regard to the semi-diurnal tide, III., supposing a uniform depth to a continuous ocean, or an ocean limited by parallels of latitude equidistant from the equator, or, finally, a depth increasing from nothing at the poles, with the sin of the polar distance, we find that elevations (or depressions) and motions corresponding to a wave of semidiurnal period having the same neutral lines as Fig. III., fulfil the condition y = III.+2. But, curiously, for small or even moderate depths these elevations and depressions under certain circumstances change places. "By a remarkable singularity, the low water takes place when the two bodies" (sun and moon)" are in the meridian, and the high water when they are in the horizon; so that the tide subsides, at the equator, under the body that attracts it." (Méc. Céleste, Bowditch.)

g

The kind of motion required for this tide may be inferred by reference to Diagram III., considered as representing a wholly fluid spheroid revolving around its axis PP'. In this case it is that of a minute approximation of normally equidistant meridional planes toward the meridian under or opposite the moon (where there is high tide), and an eloignment of those at right angles (low tide). As a consequence, the former are moving slower, the latter faster, than the earth's rotation; both, however, by differences quite inappreciable. If there be, however, a solid nucleus with uniform ocean depth, and we conceive the water down to the bottom divided by equidistant meridians, their relative motions to produce the same elevations will become quite sensible, and, through the equations (A), give rise to meridional motions which importantly augment the development of these elevations. The waters on the meridians of low tide will be running east-those on meridians where there is high water running west, or retrograde; at the place of mean elevation the current will be slack. And were it the question of a cylindrical instead of a spherical surface, this would be throughout a true wave-motion, as it will be so quite nearly on the earth's surface between the tropics, where the elliptical orbits of the fluid particles lie nearly in vertical planes, of which the range from low to high water is the dimension of the conjugate diameter. The single case which furnishes a finite integral (i. e. when the depth increases from pole to equator as sine) illustrates this. The meridional motion disappears at the equator, and the oscillation becomes that of a true wave. motion, increasing the centrifugal force at place of low water and increasing it at high water, has the same tendency as the superficial elliptical motion of the diurnal

This