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with the axis of orbital momentum. When x is very small, the equation becomes Y=-1/x. Hence the axis of Y is asymptotic on both sides to the curve of energy. If the line of momentum intersects the curve of rigidity, the curve of energy has a maximum vertically underneath the point of intersection nearer the origin❘ and a minimum underneath the point more remote. But if there are no intersections, it has no maximum or minimum. Fig. 8 shows these curves when drawn to scale for the case of the earth and moon, that is to say, with h=4. The points a and b, which are the maximum and minimum of the curve of energy, are supposed to be on the same ordinates as A and B, the intersections of the curve of rigidity with the line of momentum. The intersection of the line of momentum with the axis of orbital momentum is

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denoted by D, but in a figure of this size it necessarily remains indistinguishable from B. As the zero of energy is quite arbitrary the origin for the energy curve is displaced downwards, and this prevents the two curves from crossing one another in a confusing manner. On account of the limitation imposed we neglect the case where the quartic has no real roots. Every point of the line of momentum gives by its abscissa and ordinate the square root of the satellite's distance and the rotation of the planet, and the ordinate of the energy curve gives the energy corresponding to each distance of the satellite. Part of the figure has no physical meaning, for it is impossible for the satellite to move round the planet at a distance less than the sum of the radii of the planet and satellite. For example, the moon's diameter being about 2200 m. and the earth's about 8000, the moon's distance cannot be less than 5100 miles. Accordingly a strip is marked off and shaded on each side of the vertical axis within which the figure has no physical meaning. The point P indicates the present configuration of the earth and moon. The curve of rigidity x'y-1 is the same for all values of h, and by moving the line of momentum parallel to itself nearer to or further from the origin, we may represent Least Moall possible moments of momentum of the whole system. mentum The smallest amount of moment of momentum with for which which it is possible to set the system moving as a rigid no Relative Motion body, with centrifugal force enough to balance the mutual attraction, is when the line of momentum touches Possible. the curve of rigidity. The condition for this is clearly that the equation x-hx+1=0 should have equal roots. If it has equal roots, each root must be th, and therefore

({h)3—h(}h)3+1=0,

whence h=4/33, or h= 4/33 = 1·75. The actual value of k for the moon and earth is about 4; hence, if the moon-earth system were started with less than of its actual moment of momenMaximum Number of tum, it would not be possible for the two bodies to move so that the earth should always show the same Days in face to the moon. Month. Again, if we travel along the line of momentum, there must be some point for which yx is a maximum, and since yx=n/w there must be some point for which the number of planetary rotations is greatest during one revolution of the satellite; or, shortly, there must be some configuration for which there is a maximum number of days in the month. Now yx is equal to x (h-x), and this is a maximum when x= and the maximum number of days in the month is (h)(hth) or 3h/4; if h is equal to 4, as is nearly the case for the earth and moon, this becomes 27. Hence it follows that we now have very nearly the maximum number of days in the month. A more accurate investigation in a paper on the "Precession of a Viscous Spheroid in Phil. Trans. (1879), pt. i., showed that, taking account of solar tidal friction and of the obliquity to the ecliptic, the maximum number of days is about 29, and that we have already passed through the phase of maximum.

We will now consider the physical meaning of the figure. It is assumed that the resultant moment of momentum of the whole Discussion system corresponds to a positive rotation. Now imagine two points with the same abscissa, one on the of Figure. momentum line and the other on the energy curve, and suppose the one on the energy curve to guide that on the momentum line. Since we are supposing frictional tides to be raised on the planet, the energy must degrade, and however the two points

Satellite

are set initially the point on the energy curve must always slide down a slope, carrying with it the other point. Looking at the figure, we see that there are four slopes in the energy curve, two running down to the planet and two down to the minimum. There are therefore four ways in which the system may degrade, according to the way it was started; but we shall only consider one, that corresponding to the portion ABba of the figure. For the part of the line of momentum AB the month is History of longer than the day, and this is the case with all known satellites except the nearer one of Mars. Now, if a satellite as Energy be placed in the conditionA-that is to say, moving rapidly Degrades. round a planet which always shows the same face to the satellitethe condition is clearly dynamically unstable, for the least distur bance will determine whether the system shall degrade down the slopes ac or ab-that is to say, whether it falls into or recedes from the planet. If the equilibrium breaks down by the satellite receding. the recession will go on until the system has reached the state corresponding to B. It is clear that, if the intersection of the edge of the shaded strip with the line of momentum be identica with the point A, which indicates that the satellite is just touching the planet, then the two bodies are in effect parts of a single body in an unstable configuration. If, therefore, the moon was originally part of the earth, we should expect to find this identity. Now in fig. 9, drawn to scale to represent the earth and moon, there is so close an approach between the edge of the shaded band and the intersection of the line of momentum and curve of rigidity that it would be scarcely possible to distinguish them. Hence, there seems a probability that the two bodies once formed parts of a single one, which broke up in consequence of some kind of instability. This view is confirmed by the more detailed consideration of the case in the paper on the "Precession of a Viscous Spheroid," already. referred to, and subsequent papers, in the Phil. Trans.

$36. Effects of Tidal Friction on the Elements of the Moon's Orbit and on the Earth's Rotation.-It would be impossible within the limits of the present article to discuss completely the effects of tidal friction; we therefore confine ourselves to certain general considerations which throw light on the nature of those effects. We have in the preceding section supposed that the planet's axis is perpendicular to the orbit of the satellite, and that the latter is circular; we shall now suppose the orbit to be oblique to the equator and eccentric. For the sake of brevity the planet will be called the earth, and the satellite the moon. The complete investigation was carried out on the hypothesis that the planet was a viscous spheroid, because this was the only theory of frictionally resisted tides which had been worked out. Although the results would be practically the same for any system of frictionally resisted tides, we shall speak below of the planet or earth as a viscous body.

the Ecliptic Increases.

FIG. 9.

We shall show that if the tidal retardation be small the obliquity of the ecliptic increases, the earth's rotation is retarded, and the moon's distance and peri- Obliquity of odic time are increased. Fig. 9 represents the earth as seen from above the south pole, so that S is the pole and the outer circle the equator. The earth's rotation is in the direction of the curved arrow at S. The half of the inner circle which is drawn with a full line is a semi-small-circle of south latitude, and the dotted semicircle is a semi-small-circle in the same north latitude. Generally dotted lines indicate parts of the figure which are below the plane of the paper. If the moon were cut in two and one half retained at the place of the moon and the other half transported to a point diametrically opposite to the first half with reference to the earth, there would be no material change in reference to § 11. These two halves may be described as moon and the tide-generating forces. It is easy to verify this statement by Let M and M' be the projections of the moon and anti-moon on to anti-moon, and such a substitution will facilitate the explanation. perfectly frictionless, or if the earth were a perfect fluid or perfectly the terrestrial sphere. If the fluid in which the tides are raised were elastic, the apices of the tidal spheroid would be at M and M'. I. tides will lag, and we may suppose the tidal apices to be at T and T'; however, there is internal friction, due to any sort of viscosity, the Now suppose the tidal protuberances to be replaced by two equal heavy particles at T and T', which are instantaneously rigidly connected with the earth. Then the attraction of the moon on Tis greater

1 For further consideration of this subject see a series of papers by G. H. Darwin in Proceed, and Trans. of the Royal Society from 1878 to 1881, and app. G. (b) t. pt. ii. vol. i. of Thomson and Tait's Nat. Phil. (1883); or Scientific Papers, vol. ii.

These explanations, together with other remarks, are to be found in the abstracts of G. H. Darwin's memoirs in Proc. Roy. Soc., 1878 to 1881.

We here suppose the tides not to be inverted. If they are inverted the conclusion is precisely the same.

of Plane of Orbit Generally Decreases.

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than on T', and that of the anti-moon on T' is greater than on T. great a compression of its figure that it cannot continue to exist The resultant of these forces is clearly a pair of forces acting on the in an ellipsoidal form with stability; or else it is so nearly unstable earth in the direction TM, T'M'. These forces cause a couple about that complete instability is induced by the solar tides. the axis in the equator, which lies in the same meridian as the moon The planet then separates into two masses, the larger Genesis of Conjectural and anti-moon. The direction of the couple is shown by the being the earth and the smaller the moon. It is Moon from curved arrows at L,L'. If the effects of this couple be compounded not attempted to define the mode of separation, or Earth. with the existing rotation of the earth according to the principle to say whether the moon was initially a chain of of the gyroscope, the south pole S will tend to approach M and the meteorites. At any rate it must be assumed that the smaller mass north pole to approach M'. Hence, supposing the moon to move in became more or less conglomerated and finally fused into a spheroid, the ecliptic, the inclination of the earth's axis to the ecliptic dimin- perhaps in consequence of impacts between its constituent meteorishes, or the obliquity increases. Next the forces TM, T'M' clearly ites, which were once part of the primeval planet. Up to this produce, as in the simpler case considered in § 9, a couple about the point the history is largely speculative, for the investigation of the earth's polar axis, which tends to retard the diurnal rotation. conditions of instability in such a case surpasses the powers of the This general explanation remains a fair representation of the mathematician. We have now the earth and moon nearly in constate of the case so long as the different harmonic constituents of tact with one another, and rotating nearly as though Earth and the aggregate tide-wave do not suffer very different amounts of they were parts of one rigid body. This is the system retardation; and this is the case so long as the viscosity is not great. which was the subject of dynamical investigation. As Moon SubThe rigorous result for a viscous planet shows that in general the the two masses are not rigid, the attraction of each Ject of In obliquity will increase, and it appears that, with small viscosity of distorts the other; and, if they do not move rigorously vestigation. the planet, if the period of the satellite be longer than two periods with the same periodic time, each raises a tide in the other. Also of rotation of the planet, the obliquity increases, and vice versa. the sun raises tides in both. In consequence of the frictional resistHence, zero obliquity is only dynamically stable when the period ance to these tidal motions, such a system is dynamically unstable. of the satellite is less than two periods of the planet's rotation. If the moon had moved orbitally a little faster than the earth It is possible, by similar considerations, to obtain some insight rotated, she must have fallen back into the earth; thus the exist into the effect which tidal friction must have on the plane of the ence of the moon compels us to believe that the equilibrium broke lunar orbit, but as the subject is somewhat complex down by the moon revolving orbitally a little slower than the earth Inclination we shall not proceed to a detailed examination of the rotates. In consequence of the tidal friction the periodic times question. It must suffice to say that in general the inclin- both of the moon (or the month) and of the earth's rotation (or ation of the lunar orbit must diminish. Now let us con- the day) increase; but the month increases in length at a much sider a satellite revolving about a planet in an elliptic greater rate than the day. At some early stage in the history of orbit, with a periodic time which is long compared with the system the moon was conglomerated into a spheroidal form, the period of rotation of the planet; and suppose that frictional tides and acquired a rotation about an axis nearly parallel to that of the are raised in the planet. The major axis of the tidal spheroid earth. always points in advance of the satellite, and exercises The axial rotation of the moon is retarded by the attraction of Eccentricity on it a force which tends to accelerate its linear velocity. the earth on the tides raised in the moon, and this retardation takes of Orbk When the satellite is in perigee the tides are higher, and place at a far greater rate than the similar retardation Generally As soon as the moon rotates this disturbing force is greater than when the satellite is of the earth's rotation. The Moon. Increases. in apogee. The disturbing force may therefore be repre- round her axis with twice the angular velocity with which she sented as a constant force, always tending to accelerate the motion revolves in her orbit, the position of her axis of rotation_(parallel of the satellite, to which is added a periodic force accelerating in with the earth's axis) becomes dynamically unstable. The obliperigee and retarding in apogee. The constant force causes a quity of the lunar equator to the plane of the orbit increases, attains secular increase of the satellite's mean distance and a retardation a maximum, and then diminishes. Meanwhile the lunar axial of its mean motion. The accelerating force in perigee causes the rotation is being reduced towards identity with the orbital satellite to swing out farther than it would otherwise have done, motion. Finally, her equator is nearly coincident with the plane so that when it comes round to apogee it is more remote from the of the orbit, and the attraction of the earth on a tide, which degeneplanet. The retarding force in apogee acts exactly inversely, and rates into a permanent ellipticity of the lunar equator, causes her diminishes the perigean distance. Thus, the apogean distance in- always to show the same face to the earth. creases and the perigean distance diminishes, or in other words, the All this must have taken place early in the history of the earth, eccentricity of the orbit increases. Now consider another case, and to which we now return. At first the month is identical with the suppose the satellite's periodic time to be identical with that of the day, and as both these increase in length the lunar orbit planet's rotation. Then, when the satellite is in perigee, its angular will retain its circular form until the month is equal to The Earth motion is faster than that of the planet's rotation, and when in 1 days. From that time the orbit begins to be eccen- and Lunar apogee it is slower; hence at apogee the tides lag, and at perigee tric, and the eccentricity increases thereafter up to its they are accelerated. Now the lagging apogean tides give rise to an present magnitude. The plane of the lunar orbit is at first practically accelerating force on the satellite, and increase the peri- identical with the earth's equator, but as the moon recedes from gean distance, whilst the accelerated perigean tides give the earth the sun's attraction begins to make itself felt. We Decrease. rise to a retarding force, and decrease the apogean dis- shall not attempt to trace the complex changes by which the plane tance. Hence in this case the eccentricity of the orbit will diminish. of the lunar orbit is affected. It must suffice to say that the It follows from these two results that there must be some inter-present small inclination of the lunar orbit to the ecliptic accords mediate periodic time of the satellite for which the eccentricity does with the theory. not tend to vary.

But It May

But the preceding general explanation is in reality somewhat less satisfactory than it seems, because it does not make clear the existence of certain antagonistic influences, to which, however, we shall not refer. The full investigation for a viscous planet shows that in general the eccentricity of the orbit will increase. When the viscosity is small the law of variation of eccentricity is very simple: if eleven periods of the satellite occupy a longer time than eighteen rotations of the planet, the eccentricity increases, and vice versa. Hence in the case of small viscosity a circular orbit is only dynamically stable if the eleven periods are shorter than the eighteen rotations.

VIII. COSMOGONIC SPECULATIONS FOUNDED ON TIDAL FRICTION

37. History of the Earth and Moon.-We shall not attempt to discuss the mathematical methods by which the complete history of a planet, attended by one or more satellites, is to be traced. The laws indicated in the preceding sections show that there is such a problem, and that it may be solved, and we refer to G. H. Darwin's papers for details (Phil. Trans., 1879-1881). It may be interesting, however, to give the various results of the investigation in the form of a sketch of the possible evolution of the earth and moon, followed by remarks on the other planetary systems and on the solar system as a whole. We begin with a planet not very much more than 8000 m. in diameter, and probably partly solid, partly fluid, and partly gaseous. It is rotating about an axis inclined at about 11 or 12 to the normal to the ecliptic, with a period of from two to four hours, and is revolving about the sun with a period not much shorter than our present year. The rapidity of the planet's rotation causes so

Orbil.

Distortion

As soon as the earth rotates with twice the angular velocity with which the moon revolves in her orbit, a new instability sets in. The month is then about twelve of our present hours, and the day about six such hours in length. The inclination of the equator to the ecliptic now begins to increase and continues to do so until finally it reached its present value of 231°. All these changes continue and no new phase now supervenes, and at length we have the system in its present configuration. The minimum time in which the changes from first to last can have taken place is 54,000,000 years. There are other collateral results which must arise from a supposed primitive viscosity or plasticity of the earth's mass. For during this course of evolution the earth's mass must have suffered a screwing motion, so that the polar regions have travelled a little from west to east relatively to the of Plastic north and south trend of our great continents. The whole of this equator. This affords a possible explanation of the argument reposes on the imperfect rigidity of solids and on the internal friction of semi-solids and fluids; these are verae causae. Thus changes of the kind here discussed must be going on, and must have gone on in the past. And for this The Theory history of the earth and moon to be true throughout, Postulates and that there is not enough matter diffused through rapse of it is only necessary to postulate a sufficient lapse of time, space materially to resist the motions of the moon and earth in perhaps 200,000,000 years. It seems hardly too much to say that, granting these two postulates, and the existence of a

Planet.

Sufficient

Time.

1 See criticism, by Nolan, Genesis of Moon (Melbourne, 1885); also Nature (Feb. 18, 1886).

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two satellites will be likely to differ in mass; we cannot, of course, tell which of the two planets would generate the larger satellite. Thus, if the genesis of the moon was deferred until a late epoch in the history of the terrestrial mass, the mass of the moon relatively to the earth would be likely to differ from the mass of other satellites relatively to their planets. If the contraction of the planetary mass be almost completed before the genesis of the satellite, tidal friction will thereafter be the great cause of change in the system; and thus the hypothesis that it is the sole cause of change will give an ap proximately accurate explanation of the motion of the planet and satellite at any subsequent time. We have already seen that the theory that tidal friction has been the ruling power in the evolution of the earth and moon co-ordinates the present motions of the two bodies and carries us back to an initial state when the moon first had a separate existence as a satellite; and the initial configuration of the two bodies is such that we are led to believe that the moon is a portion of the primitive earth detached by rapid rotation or by

other causes.

Let us now turn to the other planetary sub-systems. The satellites of the larger planets revolve with short periodic times; for the smallness of their masses would have prevented tidal friction from being a very efficient cause of change in the dimensions of their orbits, and the largeness of the planet's masses would have caused them to proceed slowly in their evolution. The satellites of Mars present one of the most remarkable features in the solar system, for, 18m. and Phobos of only 7h. 39m. The minuteness of these satellites precludes us from supposing that they have had much influence on the rotation of the planet, or that the dimensions of their own orbits have been much changed.

of Mars.

The theory of tidal friction would explain the shortness of the periodic time of Phobos by the solar retardation of the planet's rotation, which would operate without directly affecting Satellites the satellites' orbital motion. We may see that, given sufficient time, this must be the ultimate fate of all satellites. Numerical comparison shows that the efficiency of solar tidal friction in retarding the terrestrial and martian rotations is of about the same degree of importance, notwithstanding the much greater distance of the planet Mars. In the above discussion it will have been apparent that the earth and moon do actually differ from the other planets to such an extent as to permit tidal friction to have been the most important factor in their history.

primeval planet such as that above described, a system would necessarily be developed which would bear a strong resemblance to our own. A theory, reposing on verae causae which brings into quantitative correlation the lengths of the present day and month, the obliquity of the ecliptic, and the inclination and eccentricity of the lunar orbit should have claims to acceptance. $ 38. The Influence of Tidal Fration on the Evolution of the Solar System and of the Planetary Sub-systems-According to the nebular hypothesis of Kant and Laplace the planets and satellites are portions detached from contracting nebulous masses, and other theories have been advanced subsequently in explanation of the present configuration of the solar system. We shall here only examine what changes are called for by the present theory of tidal friction. It may be shown that the reaction of the tides raised in the sun by the planets must have had a very small influence in changing the dimensions of the planetary orbits round the sun, and it appears improbable that the planetary orbits have been sensibly enlarged by tidal friction since the origin of the several planets. Similarly it appears unlikely that the satellites of Mars, Jupiter and Saturn originated very much nearer the present surfaces of the planets that we now observe them. But, the data being Planetary insufficient, we cannot feel sure that the alteration Sub-systems. in the dimensions of the orbits of these satellites has not been considerable. It remains, however, nearly certain that they cannot have first originated almost in contact with the present surfaces of the planets, in the same way as in the pre-whereas Mars rotates in 24h. 37m., Deimos has a period of 30h. ceding sketch has been shown to be probable with regard to the moon and earth. Numerical data concerning the distribution of moment of momentum in the several planetary sub-systems exhibit so striking a difference between the terrestrial system and those of the other planets that we should from this alone have grounds for believing that the modes of evolution have been considerably different. The difference appears to lie in the genesis of the moon close to the present surface of the planet, and we shall see below that solar tidal friction may be assigned as a reason to explain how it has happened that the terrestrial planct had contracted to nearly its present dimensions before the genesis of a satellite, but that this was not the case with the exterior planets. The efficiency of solar tidal friction is very much greater in its action on the nearer planets than on the farther ones. The time, however, during which solar tidal friction has been operating on the external planets is probably much longer than the period of its efficiency for the interior ones, and a series of numbers proportional to the total amount of rotation destroyed in the several planets would present a far less rapid decrease as we recede from the sun than numbers simply expressive of the efficiency of tidal friction at the several planets. Nevertheless it must be admitted that the effect produced by solar tidal friction on Jupiter and Saturn has not been nearly so great as on the interior planets. And, as already stated, it is very improbable that so large an amount of momentum should have been destroyed as materially to affect the orbits of the planets round the sun. We will now examine how the difference of distances from the sun may have affected the histories of the several planets. According to the nebula hypothesis, as a planetary nebula contracts, the increasing rapidity of the rotation causes it to of Satellites become unstable, and an equatorial portion of matter Amongst detaches itself. The separation of that part of the mass which before the change had the greatest angular momentum permits the central portion to resume a planetary shape. The contraction and the increase of rotation proceed continually until another portion is detached, and so on. There thus recur at intervals epochs of instability, and something of the same kind must have occurred according to other rival theories. Now tidal friction raust diminish the rate of increase of rotation due to contraction, and therefore if tidal friction and contraction are at work together the epochs of instability must recur more rarely than if contraction alone acted. If the tidal retardation is sufficiently great, the increase of rotation due to contraction will be so far counteracted as never to permit an epoch of instability to occur. Since the rate of retardation due to solar tidal friction decreases rapidly as we recede from the sun, these considerations accord with what we observe in the solar system. For Mercury and Venus have no satellites, and there is progressive increase in the number of satellites as we recede from the sun. Whether this be the true cause of the observed distribution of satellites amongst the planets or not, it is remarkable that the same cause also affords an explanation, as we shall now show, of that difference between the earth with the moon and the other planets with their satellites which has caused tidal friction to be the principal agent of change with the former, but not with the In the case of the contracting terrestrial mass we may suppose that there was for a long time nearly a balance between the retardation due to solar tidal friction and the acceleration due to contraction, and that it was not Moon Differ until the planetary mass had contracted to nearly its present dimensions that an epoch of instability could others. occur. It may also be noted that if there be two equal planetary masses which generate satellites, but under very different conditions as to the degree of condensation of the masses, the A review of this and of cognate subjects is contained in G. H. Darwin's presidential address to the Brit. Assoc. in 1995.

Distribution

the Planets.

latter.

Case of
Earth and

ent from

By an examination of the probable effects of solar tidal friction on a contracting planetary mass, we have been led to assign a cause for the observed distribution of satellites in the solar system, and this again has itself afforded an explanation Summary. of how it happened that the moon so originated that the tidal friction of the lunar tides in the earth should have been able to exercise so large an influence. We have endeavoured not only to set forth the influence which tidal friction may have, and probably has had in the history of the system, if sufficient time be granted, but also to point out what effects it cannot have produced. These investigations afford no grounds for the rejection of theories more or less akin to the nebular hypothesis; but they introduce modifica tions of considerable importance. Tidal friction is a cause of change of which Laplace's theory took no account; and, although the activity of that cause may be regarded as mainly belonging to a later period than the events described in the nebular hypothesis, yet it seems that its influence has been of great, and in one instance of even paramount, importance in determining the present condition of the planets and their satellites. Throughout the whole of this discussion it has been supposed that sufficient time is at our disposal. Yet arguments have been adduced which seemed to show that this supposition is not justifiable, Limitation for Helmholtz, Lord Kelvin and others have attempted of Time. to prove that the history of the solar system must be comprised within a period considerably less than a hundred million years. But the discovery of radio-activity and the consequent remarkable advances in physics throw grave doubt on all such arguments, and we believe that it is still beyond our powers to assign definite numerical limits to the age of the solar system.

Dr T. J. J. See (Researches on the Evolution of Stellar Systems; vol. ii. (1910) Capture Theory) rejects the applicability of tidal friction to the cosmogony of the solar system, and argues that the satellites were primitively wandering bodies and were captured by the gravitational attraction of the planets. Such captures are considered by Dr See to be a necessary result of the presence in space of a resisting medium; but the present writer does not feel convinced by the arguments adduced. (G. H.D.)

TIDORE or TIDOR, an island of the Malay Archipelago, off the W. coast of Halmahera, S. of Ternate. It is nearly circular and has an area of about 30 sq. m. Several quiescent volcanic peaks, reaching 5700 ft., occupy most of the island, and are covered with forests. The capital, Tidore, on the east coast, is a walled town and the seat of a sultan tributary to the Dutch *Thomson and Tait's Nat. Phil, app. E; Nature (Jan. 27, 1887); Wolf, Théories cosmogoniques (1886).

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(1789-1878); Shakespeares Vorschule (2 vols., 1823-1829); the
works of H. von Kleist(1826) and of J. M. R. Lenz (1828). In
1841 Friedrich Wilhelm IV. of Prussia invited him to Berlin
where he enjoyed a pension for his remaining years.
died on the 28th of April 1853.

He

Tieck's importance lay rather in the readiness with which he adapted himself to the new ideas which arose at the close of the 18th century, than in any conspicuous originality or genius. His importance as an immediate force in German poetry is restricted to his early period. In later years it was as the helpful friend and adviser of others, or as the well-read critic of wide sympathies, that Tieck distinguished himself. Tieck's Schriften appeared in 20 vols. (1828-1846), and his Gesammelte Novellen in 12 (1852-1854). Nachgelassene Schriften were published in 2 vols. in 1855. There are several modern editions of Ausgewählte Werke by H. Welti (8 vols., 1886-1888); by J. Minor (in Kürschner's Deutsche Nationalliteratur, 144, 2 vols., 1885); by G. Klee (with an excellent biography, 3 vols., 1892), and G. Witkowski (4 vols., 1903). The Elves and The Goblet were translated by Carlyle in German Romance (1827), The Pictures and The Betrothal by Bishop Thirlwall (1825). A translation of Vittoria Accorombona was published in 1845. Ticck's Letters have not yet been collected, but Briefe an Tieck were published in 4 vols. by K. von Holtei in 1864. See for Tieck's carlier life R. Köpke, Ludwig Tieck (2 vols., 1855); for the Dresden period, H. von Friesen, Ludwig Tieck: Erinnerungen (2 vols., 1871); also A. Stern, Ludwig Tieck in Dresden (Zur Literatur der Gegenwart, 1879); J. Minor, Tieck als Novellendichter (1884); B. Steiner, L. Tieck und die Volksbücher (1893); H. Bischof, Tieck als Dramaturg (1897); W. Miessner, Tiecks Lyrik (1902).

TIEDEMANN, FRIEDRICH (1781-1861), German anatomist and physiologist, eldest son of Dietrich Tiedemann (17481803), a philosopher and psychologist of considerable repute, was born at Cassel on the 23rd of August 1781. He graduated in medicine at Marburg in 1804, but soon abandoned practice. He devoted himself to the study of natural science, and, betaking

and of a Dutch controleur (commissioner or agent). By an agreement of 1879 the sultan exercises authority over some parts of Halmahera, the Papuan Islands, the western half of New Guinea and the islands in Geelvink Gulf. The sultanate is included in the residency of Ternate (q.v.). The population, of Malay race and Mahommedans in religion, is about 8000. They live by agriculture (cotton, tobacco, nutmegs, &c.) and fishing. TIECK, JOHANN LUDWIG (1773-1853), German poet, novelist and critic, was born in Berlin on the 31st of May 1773, his father being a rope-maker. He was educated at the Friedrich-Werdersche Gymnasium, and at the universities of Halle, Göttingen and Erlangen. At Göttingen Shakespeare and the Elizabethan drama were the chief subjects of his study. In 1794 he returned to Berlin, resolved to make a living by his pen. He contributed a number of short stories. (1795-1798) to the series of Straussfedern, published by the bookseller C. F. Nicolai and originally edited by J. K. A. Musäus, and wrote Abdallah (1796) and a novel in letters, William Lovell (3 vols. 1795-1796). These works are, however, immature and sensational in tone. Tieck's transition to romanticism is to be seen in the series of plays and stories published under the title Volksmärchen von Peter Lebrecht (3 vols., 1797), a collection which contains the admirable fairy-tale Der blonde Eckbert, and the witty dramatic satire on Berlin literary taste, Der gestiefelte Kater. With his school and college friend W. H. Wackenroder (17731798), he planned the novel Franz Sternbalds Wanderungen (vols. i-ii. 1798), which, with Wackenroder's Herzensergiessungen (1798), was the first expression of the romantic enthusiasm for old German art. In 1798 Tieck married and in the following year settled in Jena, where he, the two brothers Schlegel and Novalis were the leaders of the new Romantic school. His writings between 1798 and 1804 include the satirical drama, Prinz Zerbino (1799), and Romantische Dich-himself to Paris, became an ardent follower of Baron Cuvier. tungen (2 vols., 1799-1800). The latter contains Tieck's most ambitious dramatic poems, Leben und Tod der heiligen Genoveva, Leben und Tod des kleinen Rotkäppchens, which were followed in 1804 by the remarkable "comedy" in two parts, Kaiser Oktavianus. These dramas, in which Tieck's poetic powers are to be seen at their best, are typical plays of the first Romantic school; although formless, and destitute of dramatic qualities, they show the influence of both Calderon and Shakespeare. Kaiser Oktavianus is a poetic glorification of the middle ages. In 1801 Tieck went to Dresden, then lived for a time near Frankfort-on-the-Oder, and spent many months in Italy. In 1803 he published a translation of Minnelieder aus der schwäbischen Vorzeit, between 1799 and 1804 an excellent version of Don Quixote, and in 1811 two volumes of Elizabethan dramas, Allenglisches Theater. In 1812-1817 he collected in three volumes a number of his earlier stories and dramas, under the title Phantasus. In this collection appeared the stories Der Runenberg, Die Elfen, Der Pokal, and the dramatic fairy tale, Fortunat. In 1817 Tieck visited England in order to collect materials for a work on Shakespeare (unfortunately never finished) and in 1819 he settled permanently in Dresden; from 1825 on he was literary adviser to the Court Theatre, and his semi-public readings from the dramatic poets gave him a reputation which extended far beyond the Saxon capital. The new series of short stories Five miles W.N.W. of Tiel is the small town of Buren, which he began to publish in 1822 also won him a wide popu- which contains some interesting old houses and is an important larity. Notable among these are Die Gemälde, Die Reisenden, market for horses. Buren was the seat of an independent Die Verlobung, Des Lebens Überfluss. More ambitious and on a lordship which is mentioned as early as 1152. In later times wider canvas are the historical or semi-historical novels, Dichter- it was held in fief, first from the dukes of Brabant, then from the leben (1826), Der Aufruhr in den Cevennen (1826, unfinished), dukes of Gelderland. In 1492 the emperor Charles V. raised Der Tod des Dichters (1834); Der junge Tischlermeister (1836; it to a countship, and in 1551 it passed by marriage to Prince but begun in 1811) is an excellent story written under the in-William of Orange Nassau. The title is now sometimes used fluence of Goethe's Wilhelm Meister; Vittoria Accorombona by the royal family of the Netherlands when travelling incog(1840), in the style of the French Romanticists, shows a fallingoff. In later years Tieck carried on a varied literary activity as critic (Dramaturgische Blätter, 2 vols., 1825-1826; Kritische Schriften, 2 vols., 1848); he also edited the translation of Shakespeare by A. W. Schlegel, who was assisted by Tieck's daughter Dorothea (1799-1841) and by Graf Wolf Heinrich Baudissin

On his return to Germany he maintained the claims of patient and sober anatomical research against the prevalent speculations of the school of Lorenz Oken, whose foremost antagonist he was long reckoned. His remarkable studies of the development of the human brain, as correlated with his father's studies on the development of intelligence, deserve mention. He spent most of his life as professor of anatomy and physiology at Heidelberg, a position to which he was appointed in 1816, after having filled the chair of anatomy and zoology for ten years at Landshut, and died at Munich on the 22nd of January 1861.

TIEL, a town in the province of Gelderland, Holland, on the right bank of the Waal (here crossed by a pontoon bridge), 25 m. by rail west of Nijmwegen. Pop. (1900), 10,788. It possesses fine streets and open places, but of its fortifications the Kleiberg Gate (1647) alone remains. The principal buildings are St Martin's church (15th century), the town hall, court-house and the historical castle of the family of van Arkel. In 1892 a harbour was built, but the shipping of Tiel is now chiefly confined to craft for inland navigation. It carries on a flourishing trade, especially in fruit, and is an important market for horses and cattle. It also manufactures agricultural implements, furniture, paper, tobacco, &c.

nito. The castle was destroyed in the beginning of the 19th century, and the site of it is now marked by the park on the west side of the town. It contained not less than 170 apartments and was memorable for the imprisonment within its walls of Arnoud duke of Gelderland (d. 1473), and as the birthplace of Philip William of Orange in 1554.

province during a great portion of the year. The town is built on a vast alluvial plain, which extends from the mountains beyond Peking to the sea, and through which the Peiho runs a circuitous course, making the distance by water from Tientsin to the coast about 70 m. as against 30 m. by railway.

tons.

The

1907 averaged 3s. 3d.); viz. foreign imports 61,200,000, native
In 1907 the imports amounted to 79.500,000 taels (a tael in
imports 18,317,000 tacls; the exports in the same year amounted to
17,253,000. Valuable cargoes of tea are landed here for carriage
overland, via Kalgan and Kiakhta, to Siberia. During the winter
the river is frozen. The principal articles of import are shirtings,
drills, jeans and twills, opium, woollens, steel, lead, needles,
Japanese sea-weed and sugar; and of export, wool, skins, beans
and pease, straw braid, coal, dates, tobacco and rhubarb.
coal exported is brought from the Kaiping colliery to the east of
Tientsin; its output in 1885 was 181,039 tons and in 1904 28,956
The importance of Tientsin has been enhanced by the railways
connecting it with Peking on the one hand and with Shanhai-kwan
and Manchuria on the other. The British concession, in which
below the native city, and occupies some 200 acres.
the trade centres, is situated on the right bank of the river Peiho
It is held
on a lease in perpetuity granted by the Chinese government to the
British Crown, which sublets plots to private owners in the same
way as is done at Hankow. The local management is entrusted
obtain at Shanghai. Besides the British concession the French,
to a municipal council organized on lines similar to those which
Germans, Russians, Japanese, Austrians, Italians and Belgians
have separate settlements, five miles in all, the river front being
governed by foreign powers.

TIELE, CORNELIS PETRUS (1830-1902), Dutch theologian | foreign treaties, become the residence of the viceroy of the and scholar, was born at Leiden on the 16th of December 1830. He was educated at Amsterdam, first studying at the Athenaeum Illustre, as the communal high school of the capital was then named, and afterwards at the seminary of the Remonstrant Brotherhood. He was destined for the pastorate in his own brotherhood. After steadily declining for a considerable period, The appearance of the city has greatly changed since the this had increased its influence in the second half of the 19th Boxer rising in 1900. After that event the city walls, which century by widening the inelastic tenets of the Dutch Methodists, measured about three quarters of a mile each way, were razed, which had caused many of the liberal clergy among the Luth-wide streets were made, the course of the river straightened, erans and Calvinists to go over to the Remonstrants. Tiele electric lighting and tramways introduced and a good water certainly had liberal religious views himself, which he early service supplied. Among the public buildings are a university enunciated from the pulpit, as Remonstrant pastor of Moor- (in which instruction is given in western learning) and an drecht (1853) and at Rotterdam (1856). Upon the removal of arsenal. There are several cotton mills and important rice and the seminary of the brotherhood from Amsterdam to Leiden salt markets. The city has always been a great commercial in 1873, Tiele was appointed one of its leading professors. In depot; a wharf nearly two miles long affords ample facilities 1877 followed his appointment at the university of Leiden as for vessels able to cross the bar of the Peiho, over which there is a professor of the history of religions, a chair specially created depth of water varying from 9 to 12 ft. for him. Of his many learned works, the Vergelijkende geschiedenis van de egyptische en mesopotamische Godsdiensten (1872), and the Geschiedenis van den Godsdienst (1876; new ed. 1891), have been translated into English, the former by James Ballingall (1878-1882), the latter by J. Estlin Carpenter (1877) under the title "Outlines of the History of Religion" (French translation, 1885; German translation, 1895). A French translation of the Comparative History was published in 1882. Other works by Ticle are: De Godsdienst van Zarathustra, van het Ontstaan in Baktrië, tot den Val van het Oud-Perzische Rijk (1864) a work now embodied, but much enlarged and improved by the latest researches of the author, in the History of Religions (vol. ii. part ii., Amsterdam, 1901), a part which appeared only a short time before the author's death; De Vrucht der Assyriologie voor de vergelijkende geschiedenis der Godsdiensten (1877; German ed., 1878); Babylonisch-assyrische Geschichte (two parts, Leipzig, 1886-1888); Western Asia, according to the most Recent Discoveries (London, 1894). He was also the writer of the article “Religions" in the 9th edition of the Ency. Brit. A volume of Tiele's sermons appeared in 1865, and a collection of his poems in 1863. He also edited (1868) the poems of Petrus Augustus de Génestet. Tiele was best known to English students by his Outlines and the Gifford Lectures "On the Elements of the Science of Religion," delivered in 1896-1898 at Edinburgh University. They appeared simultaneously in Dutch at Amsterdam, in English in London and Edinburgh (1897-1899, 2 vols.). Edinburgh University in 1900 conferred upon Tiele the degree of D.D. honoris causâ, an honour bestowed upon him previously by the universities of Dublin and Bologna. He was also a fellow of at least fifteen learned societies in Holland, Belgium, France, Germany, Italy, Great Britain and the United States. He died on the 11th of January 1902. In 1901 he had resigned his professorship at Leiden University. Tiele's zeal and power for work were as extraordinary as his vast knowledge of ancient languages, peoples and religions, upon which his researches, according to F. Max Müller, have shed a new and vivid light. With Abraham Kuenen and J. H. Scholten, amongst others, he founded the Leiden School" of modern theology. From 1867 he assisted A. Kuenen, A. D. Loman and L. W. Rauwenhoff editing the Theologisch Tijdschrift.

which had been detached from the main force at Nanking for the
In 1853 Tientsin was besieged by an army of T'aip'ing rebels,
capture of Peking. The defences of Tientsin, however, saved the
capital, and the rebels were forced to retreat. Five years later
Lord Elgin, accompanied by the representative of France, steamed
up the Peiho, after having forced the barriers at Taku, and took
Here the treaty of 1858 was
peaceable possession of the town.
signed. But in 1860, in consequence of the treacherous attack
made on the British plenipotentiary the preceding year at Taku,
the city and suburbs were occupied by an allied British and French
force, and were held for two years. The city was constituted an
open port. On the establishment of Roman Catholic orphanages
some years later the pretensions of the priests so irritated the people
that on the occurrence of an epidemic in the schools in the year
1870 they attacked the French and Russian establishments and
murdered twenty-one of the foreign inmates, besides numbers of
their native followers. The Chinese government suppressed the
riot, paid £80,000 in compensation and sent a representative to
Europe to apologize for the outbreak.

During the period 1874-1894, when Li Hung-Chang was viceroy of Chih-li and ex officio superintendent of trade, he made Tientsin and naval education. As a consequence the city became the chief his headquarters and the centre of his experiments in military focus of enterprise and foreign progress. Having arrogated to himself the practical control of the foreign policy of the nation, Li's yamen became the scene of many important negotiations, and attracted distinguished visitors from all parts of the globe. The loss of prestige consequent on the Japanese War brought about the retirement of Li, and with it the political importance of Tientsin ceased. Both the foreign concessions and the native city suffered severely during the hostilities resulting from the Boxer movement in June-July, 1900. (See CHINA: History § D.)

His brother PIETER ANTON TIELE (1834-1888) acted for many years as the librarian of Utrecht University, and distinguished himself by his bibliographical studies, more especially by his several works on the history of colonization in Asia. Among these the most noteworthy are: De Opkomst van het nederlandsch Gezag in Oost-Indie (1886); De Vestiging der Portugcezen, in Indie (1873), and other books on the early TIEPOLO, GIOVANNI BATTISTA (1692–1769), Italian painter, Portuguese colonization in the Malay Archipelago. was born at Venice, and acquired the rudiments of his art from TIENTSIN, the largest commercial city in Chih-li, the metro-Gregorio Lazzarini, and probably from Piazzetta, though the politan province of China. Pop. (1907), about 750,000. It decisive influence on the formation of his style was the study is situated at the junction of the Peiho and the Hun-ho, which of Paolo Veronese's sumptuous paintings. When hardly out is connected by the grand Canal with the Yangtsze-kiang. It of his teens he developed an extraordinary facility of brushwork, is a prefectural city, and has, since the conclusion of the and proved himself, as a fresco-painter, a colourist of the first

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