Chapter VI: Part 6

We notice that U^2 in (26) can be positive, and the gyrostatic chain
stable, even when T is negative, and the chain is supporting a thrust,
provided [kappa]n is large enough, and the thrust does not exceed

(28) ([kappa]n - an^2)(1 + l/a);

while U'^2 in (27) will not be positive and the straight chain will be
unstable unless the tension exceeds

(29) ([kappa]n + [alpha]n^2)(1 + l/a).

15. _Gyrostat suspended by a Thread._--In the discussion of the small
vibration of a single gyrostat fly-wheel about the vertical position
when suspended by a single thread of length 2l = b, the suffix k can
be omitted in the preceding equations of S 14, and we can write

(1) A :[~omega] - K .[~omega]i + Ta[~omega] - Ta[sigma] = 0,

(2) M :w + T[sigma] = 0, with T = gM,

(3) w - a[~omega] - b[sigma] = 0.

Assuming a periodic solution of these equations

(4) w, [~omega], [sigma], = (L, P, Q) exp nti,

and eliminating L, P, Q, we obtain

(5) (-An^2 + Kn + gMa)(g - n^2b) - gMn^2a^2 = 0,

and the frequency of a vibration in double beats per second is
n/2[pi], where n is a root of this quartic equation.

For upright spinning on a smooth horizontal plane, take b = [oo] and
change the sign of a, then

(6) An^2 - Kn + gMa = 0,

so that the stability requires

(7) K^2 > 4gAMa.

Here A denotes the moment of inertia about a diametral axis through
the centre of gravity; when the point of the fly-wheel is held in a
small smooth cup, b = 0, and the condition becomes

(8) (A + Ma^2)n^2 - Kn + gMa = 0,

requiring for stability, as before in S 3,

(9) K^2 > 4g(A + M^2)Ma.

For upright spinning inside a spherical surface of radius b, the sign
of a must be changed to obtain the condition at the lowest point, as
in the gyroscopic horizon of Fleuriais.

For a gyrostat spinning upright on the summit of a sphere of radius b,
the signs of a and b must be changed in (5), or else the sign of g,
which amounts to the same thing.

Denoting the components of horizontal displacement of the point of the
fly-wheel by [xi], [eta], then

(10) br = [xi], bs = [eta], b[sigma] = [xi] + [eta]i = [lambda]
(suppose),

(11) [omega] = [alpha][~omega] + [lambda].

If the point is forced to take the motion ([xi], [eta], [zeta]) by
components of force X, Y, Z, the equations of motion become

(12) -A :q + K .p = Ya - Zaq,

(13) A :p + K .q = -Xa + Zap,

(14) M :w = X + Yi, M( :[zeta] - g) = Z;

so that

(15) A :[~omega] - K .[~omega]i + gMa[~omega] + Ma :w
= Ma[~omega] :[zeta],

or

(16) (A + Ma^2) :[~omega] - K .[~omega]i + gMa[~omega] + Ma[lambda] =
Ma[~omega] :[zeta].

Thus if the point of the gyrostat is made to take the periodic motion
given by [lambda] = R exp nti, [zeta] = 0, the forced vibration of the
axis is given by [~omega] = P exp nti, where

(17) P{-(A + Ma^2)n^2 + Kn + gMa} - RMn^2a = 0;

and so the effect may be investigated on the Fleuriais gyroscopic
horizon of the motion of the ship.

Suppose the motion [lambda] is due to the suspension of the gyrostat
from a point on the axis of a second gyrostat suspended from a fixed
point.

Distinguishing the second gyrostat by a suffix, then [lambda] =
b[~omega]1, if b denotes the distance between the points of suspension
of the two gyrostats; and the motion of the second gyrostat influenced
by the reaction of the first, is given by

(18) (A1 + M1h1^2) :[~omega]1 - K1 .[~omega]1 i
= -g(M1h1 + Mb)[~omega]1 - b(X + Yi)
= -g(M1h1 + Mb)[~omega]1 - Mb(a :[~omega] + :[lambda]);

so that, in the small vibration,

R / \
(19) -- ( -(A1 + M1h1^2)n^2 + K1n + g(M1h1 + Mb) ) = Mn^2b(aP + R),
b \ /

(20) R { -(A1 + M1h1^2 + Mb^2)n^2 + K1n + g(M1h1 + Mb)} - PMn^2ab^2 = 0.

Eliminating the ratio of P to R, we obtain

(21) { -(A + Ma^2)n^2 + Kn + gMa}
X {-(A1 + M1h1^2 + Mb^2)n^2 + K1n + g (M1h1 + Mb)} - M^2n^4a^2b^2 = 0,

a quartic for n, giving the frequency n/2[pi] of a fundamental
vibration.

Change the sign of g for the case of the gyrostats spinning upright,
one on the top of the other, and so realize the gyrostat on the top of
a gyrostat described by Maxwell.

In the gyrostatic chain of S 14, the tension T may change to a limited
pressure, and U^2 may still be positive, and the motion stable; and so
a motion is realized of a number of spinning tops, superposed in a
column.

16. _The Flexure Joint._--In Lord Kelvin's experiment the gyrostats
are joined up by equal light rods and short lengths of elastic wire
with rigid attachment to the rod and case of a gyrostat, so as to keep
the system still, and free from entanglement and twisting due to pivot
friction of the fly-wheels.

When this gyrostatic chain is made to revolve with angular velocity n
in relative equilibrium as a plane polygon passing through Oz the axis
of rotation, each gyrostatic case moves as if its axis produced was
attached to Oz by a flexure joint. The instantaneous axis of resultant
angular velocity bisects the angle [pi] - [theta], if the axis of the
case makes an angle [theta] with Oz, and, the components of angular
velocity being n about Oz, and -n about the axis, the resultant
angular velocity is 2n cos 1/2([pi] - [theta]) = 2n sin 1/2[theta];
and the components of this angular velocity are

(1) -2n sin 1/2[theta] sin 1/2[theta] = -n(1-cos[theta]), along the
axis, and

(2) -2n sin 1/2[theta] cos 1/2[theta] = -n sin [theta], perpendicular
to the axis of the case. The flexure joint behaves like a pair of
equal bevel wheels engaging.

The component angular momentum in the direction Ox is therefore

(3) L = -An sin [theta] cos [theta] - Cn (1 - cos [theta]) sin [theta]
+ K sin [theta],

and Ln is therefore the couple acting on the gyrostat.

If [alpha] denotes the angle which a connecting link makes with Oz,
and T denotes the constant component of the tension of a link parallel
to Oz, the couple acting is

(4) Ta cos [theta]_k(tan [alpha]_(k+1) + tan [alpha]_k)
- 2T[alpha]sin[theta]_k,

which is to be equated to Ln, so that

(5) -An^2 sin [theta]_k cos [theta]_k
- Cn(1 - cos [theta]_k) sin [theta]_k
+ Kn sin [theta]_k
- T[alpha] cos [theta]_k(tan [alpha]_(k+1) + tan [alpha]_k)
+ 2T[alpha] sin [theta]_k = 0.

In addition

(6) Mn^2[chi]_k + T(tan [alpha]_(k+1) - tan [alpha]_k) = 0,

with the geometrical relation

(7) [chi]_(k+1) - [chi]_k - [alpha](sin [theta]_(k+1) + sin [theta]_k)
- 2l sin{k + 1} = 0.

When the polygon is nearly coincident with Oz, these equations can be
replaced by

(8) (-An^2 + Kn + 2Ta)[theta]_k - Ta([alpha]_(k+1) + [alpha]_k) = 0,

(9) Mn^2x_k + T([alpha]_(k+1) - [alpha]_k) = 0,

(10) x_(k+1) - x_k - a([theta]_(k+1) + [theta]_k) - 2la_k = 0,

and the rest of the solution proceeds as before in S 14, putting

(11) x_k, [theta]_k, [alpha]_k = (L, P, Q) exp cki.

A half wave length of the curve of gyrostats is covered when ck =
[pi], so that [pi]/c is the number of gyrostats in a half wave, which
is therefore of wave length 2[pi](a + l)/c.

A plane polarized wave is given when exp cki is replaced by exp (nt +
ck)i, and a wave circularly polarized when w, [~omega], [sigma] of S
14 replace this x, [theta], [alpha].

_Gyroscopic Pendulum._--The elastic flexure joint is useful for
supporting a rod, carrying a fly-wheel, like a gyroscopic pendulum.

Expressed by Euler's angles, [theta], [phi], [psi], the kinetic energy
is

(12) T = 1/2A( .[theta]^2 + sin^2 [theta] .[psi]^2)
+ 1/2C'(1 - cos [theta])^2 .[psi]^2
+ 1/2C( .[phi] + .[psi] cos [theta])^2,

where A refers to rod and gyroscope about the transverse axis at the
point of support, C' refers to rod about its axis of length, and C
refers to the revolving fly-wheel.

The elimination of .[psi] between the equation of conservation of
angular momentum about the vertical, viz.

(13) A sin^2 [theta] .[psi] - C'(1 - cos [theta]) cos [theta] .[psi] +
C( .[phi] + .[psi] cos [theta]) cos [theta] = G, a constant, and the
equation of energy, viz.

(14) T - gMh cos [theta] = H, a constant, with [theta] measured from
the downward vertical, and

(15) .[phi] + .[psi] cos [theta] = R, a constant, will lead to an
equation for d[theta]/dt, or dz/dt, in terms of cos [theta] or z, the
integral of which is of hyperelliptic character, except when A = C'.

In the suspension of fig. 8, the motion given by .[phi] is suppressed
in the stalk, and for the fly-wheel .[phi] gives the rubbing angular
velocity of the wheel on the stalk; the equations are now

(16) T = 1/2A( .[theta]^2 + sin^2 [theta] .[psi]^2)
+ 1/2C' cos^2 [theta] .[psi]^2 + 1/2CR^2 = H + gMh cos [theta],

(17) A sin^2 [theta][.[psi]] + C' cos^2 [theta] .[psi] + CR cos [theta]
= G,

and the motion is again of hyperelliptic character, except when A =
C', or C' = 0. To realize a motion given completely by the elliptic
function, the suspension of the stalk must be made by a smooth ball
and socket, or else a Hooke universal joint.

Finally, there is the case of the general motion of a top with a
spherical rounded point on a smooth plane, in which the centre of
gravity may be supposed to rise and fall in a vertical line. Here

(18) T = 1/2(A + Mh^2 sin^2 [theta]) .[theta]^2 + 1/2A sin^2 [theta] .[psi]^2
+ 1/2CR^2 = H - gMh cos [theta],

with [theta] measured from the upward vertical, and

(19) A sin^2 [theta] .[psi] + CR cos [theta] = G,

where A now refers to a transverse axis through the centre of gravity.
The elimination of [.[psi]] leads to an equation for z, = cos [theta],
of the form

/dz\^2 g Z g (z1 - z)(z2 - z)(z3 - z)
(20) ( -- ) = 2 -- ---------------- = 2 -- ------------------------,
\dt/ h 1 - z^2 + A/Mh^2 h (z4 - z)(z - z5)

with the arrangement

(21) z1, z4 > / > z2 > z > z3 > - / > z5;

so that the motion is hyperelliptic.

AUTHORITIES.--In addition to the references in the text the following
will be found useful:--_Ast. Notices_, vol. i.; _Comptes rendus_,
Sept. 1852; Paper by Professor Magnus translated in Taylor's _Foreign
Scientific Memoirs_, n.s., pt. 3, p. 210; _Ast. Notices_, xiii.
221-248; _Theory of Foucault's Gyroscope Experiments_, by the Rev.
Baden Powell, F.R.S.; _Ast. Notices_, vol. xv.; articles by Major J.
G. Barnard in _Silliman's Journal_, 2nd ser., vols. xxiv. and xxv.; E.
Hunt on "Rotatory Motion," _Proc. Phil. Soc. Glasgow_, vol. iv.; J.
Clerk Maxwell, "On a Dynamical Top," _Trans. R.S.E._ vol. xxi.; _Phil.
Mag._ 4th ser. vols. 7, 13, 14; _Proc. Royal Irish Academy_, vol.
viii.; Sir William Thomson on "Gyrostat," _Nature_, xv. 297; G. T.
Walker, "The Motion of a Celt," _Quar. Jour. Math._, 1896; G. T.
Walker, _Math. Ency._ iv. 1, xi. 1; Gallop, _Proc. Camb. Phil. Soc._
xii. 82, pt. 2, 1903, "Rise of a Top"; Price's _Infinitesimal
Calculus_, vol. iv.; Worms, _The Earth and its Mechanism_; Routh,
_Rigid Dynamics_; A. G. Webster, _Dynamics_ (1904); H. Crabtree,
_Spinning Tops and Gyroscopic Motion_ (1909). For a complete list of
the mathematical works on the subject of the Gyroscope and Gyrostat
from the outset, Professor Cayley's Report to the British Association
(1862) on the _Progress of Dynamics_ should be consulted. Modern
authors will be found cited in Klein and Sommerfeld, _Theorie des
Kreisels_ (1897), and in the _Encyclopadie der mathematischen
Wissenschaften_. (G. G.)

GYTHIUM, the harbour and arsenal of Sparta, from which it was some 30 m. distant. The town lay at the N.W. extremity of the Laconian Gulf, in a small but fertile plain at the mouth of the Gythius. Its reputed founders were Heracles and Apollo, who frequently appear on its coins: the former of these names may point to the influence of Phoenician traders, who, we know, visited the Laconian shores at a very early period. In classical times it was a community of _perioeci_, politically dependent on Sparta, though doubtless with a municipal life of its own. In 455 B.C., during the first Peloponnesian War, it was burned by the Athenian admiral Tolmides. In 370 B.C. Epaminondas besieged it unsuccessfully for three days. Its fortifications were strengthened by the tyrant Nabis, but in 195 B.C. it was invested and taken by Titus and Lucius Quintius Flamininus, and, though recovered by Nabis two or three years later, was recaptured immediately after his murder (192 B.C.) by Philopoemen and Aulus Atilius and remained in the Achaean League until its dissolution in 146 B.C. Subsequently it formed the most important of the Eleutherolaconian towns, a group of twenty-four, later eighteen, communities leagued together to maintain their autonomy against Sparta and declared free by Augustus. The highest officer of the confederacy was the general ([Greek: strategos]), who was assisted by a treasurer ([Greek: tamias]), while the chief magistrates of the several communities bore the title of ephors ([Greek: ephoroi]).

Pausanias (iii. 21 f.) has left us a description of the town as it existed in the reign of Marcus Aurelius, the agora, the Acropolis, the island of Cranae (Marathonisi) where Paris celebrated his nuptials with Helen, the Migonium or precinct of Aphrodite Migonitis (occupied by the modern town of Marathonisi or Gythium), and the hill Larysium (Koumaro) rising above it. The numerous remains extant, of which the theatre and the buildings partially submerged by the sea are the most noteworthy, all belong to the Roman period.

The modern town is a busy and flourishing port with a good harbour protected by Cranae, now connected by a mole with the mainland: it is the capital of the prefecture ([Greek: nomos]) of [Greek: Lakonike] with a population in 1907 of 61,522.

See G. Weber, _De Gytheo et Lacedaemoniorum rebus navalibus_
(Heidelberg, 1833); W. M. Leake, _Travels in the Morea_, i. 244 foll.;
E. Curtius, _Peloponnesos_, ii. 267 foll. Inscriptions: Le
Bas-Foucart, _Voyage archeologique_, ii. Nos. 238-248 f.;
Collitz-Bechtel, _Sammlung d. griech. Dialekt-Inschriften_, iii. Nos.
4562-4573; _British School Annual_, x. 179 foll. Excavations: [Greek:
A. Skias, Praktika tes Arch. Hetaireias], 1891, 69 foll. (M. N. T.)

GYULA-FEHERVAR (Ger. _Karlsburg_), a town of Hungary, in Transylvania, in the county of Also-Felier, 73 m. S. of Kolozsvar by rail. Pop. (1900) 11,507. It is situated on the right bank of the Maros, on the outskirts of the Transylvanian Erzgebirge or Ore Mountains, and consists of the upper town, or citadel, and the lower town. Gyula-Fehervar is the seat of a Roman Catholic bishop, and has a fine Roman Catholic cathedral, built in the 11th century in Romanesque style, and rebuilt in 1443 by John Hunyady in Gothic style. It contains among other tombs that of John Hunyady. Near the cathedral is the episcopal palace, and in the same part of the town is the Batthyaneum, founded by Bishop Count Batthyany in 1794. It contains a valuable library with many incunabula and old manuscripts, amongst which is one of the _Nibelungenlied_, an astronomical observatory, a collection of antiquities, and a mineral collection. Gyula-Fehervar carries on an active trade in cereals, wine and cattle.

Gyula-Fehervar occupies the site of the Roman colony _Apulum_. Many Roman relics found here, and in the vicinity, are preserved in the museum of the town. The bishopric was founded in the 11th century by King Ladislaus I. (1078-1095). In the 16th century, when Transylvania separated from Hungary, the town became the residence of the Transylvanian princes. From this period dates the castle, and also the buildings of the university, founded by Gabriel Bethlen, and now used as barracks. After the reversion of Transylvania in 1713 to the Habsburg monarchy the actual strong fortress was built in 1716-1735 by the emperor Charles VI., whence the German name of the town.

H The eighth symbol in the Phoenician alphabet, as in its descendants, has altered less in the course of ages than most alphabetic symbols. From the beginning of Phoenician records it has consisted of two uprights connected by transverse bars, at first either two or three in number. The uprights are rarely perpendicular and the cross bars are not so precisely arranged as they are in early Greek and Latin inscriptions. In these the symbol takes the form of two rectangles [symbol] out of which the ordinary H develops by the omission of the cross bars at top and bottom. It is very exceptional for this letter to have more than three cross bars, though as many as five are occasionally found in N.W. Greece. Within the same inscription the appearance of the letter often varies considerably as regards the space between and the length of the uprights. When only one bar is found it regularly crosses the uprights about the middle. In a few cases the rectangle is closed at top and bottom but has no middle cross bar [symbol]. The Phoenician name for the letter was Heth (Het). According to Semitic scholars it had two values, (1) a glottal spirant, a very strong _h_, (2) an unvoiced velar spirant like the German _ch_ in _ach_. The Greeks borrowed it with the value of the ordinary aspirate and with the name [Greek: eta]. Very early in their history, however, most of the Greeks of Asia Minor lost the aspirate altogether, and having then no further use for the symbol with this value they adopted it to represent the long _e_-sound, which was not originally distinguished by a different symbol from the short sound (see E). With this value its name has always been [Greek: eta] in Greek. The alphabet of the Asiatic Greeks was gradually adopted elsewhere. In official documents at Athens H represented the rough breathing or aspirate ' till 403 B.C.; henceforth it was used for [eta]. The Western Greeks, however, from whom the Romans obtained their alphabet, retained their aspirate longer than those of Asia Minor, and hence the symbol came to the Romans with the value not of a long vowel but of the aspirate, which it still preserves. The Greek aspirate was itself the first or left-hand half of this letter |-, while the smooth breathing ' was the right-hand portion -|. At Tarentum |- is found for H in inscriptions. The Roman aspirate was, however, a very slight sound which in some words where it was etymologically correct disappeared at an early date. Thus the cognate words of kindred languages show that the Lat. _anser_ "goose" ought to begin with _h_, but nowhere is it so found. In none of the Romance languages is there any trace of initial or medial _h_, which shows that vulgar Latin had ceased to have the aspirate by 240 B.C. The Roman grammarians were guided to its presence by the Sabine forms where _f_ occurred; as the Sabines said _fasena_ (sand), it was recognised that the Roman form ought to be _harena_, and so for _haedus_ (goat), _hordeum_ (barley), &c. Between vowels _h_ was lost very early, for _ne-hemo_ (no man) is throughout the literature _nemo_, _bi-himus_ (two winters old) _bimus_. In the Ciceronian age greater attention was paid to reproducing the Greek aspirates in borrowed words, and this led to absurd mistakes in Latin words, mistakes which were satirized by Catullus in his epigram (84) upon Arrius, who said _chommoda_ for _commoda_ and _hinsidias_ for _insidias_. In Umbrian _h_ was often lost, and also used without etymological value to mark length, as in _comohota_ (= Lat. _commota_), a practice to which there are some doubtful parallels in Latin.

In English the history of _h_ is very similar to that in Latin. While the parts above the glottis are in position to produce a vowel, an aspirate is produced without vibration of the vocal chords, sometimes, like the pronunciation of Arrius, with considerable effort as a reaction against the tendency to "drop the h's." Though _h_ survives in Scotland, Ireland and America as well as in the speech of cultivated persons, the sound in most of the vulgar dialects is entirely lost. Where it is not ordinarily lost, it disappears in unaccented syllables, as "_Give it 'im_" and the like. Where it is lost, conscious attempts to restore it on the part of uneducated speakers lead to absurd misplacements of _h_ and to its restoration in Romance words when it never was pronounced, as _humble_ (now recognized as standard English), _humour_ and even _honour_. (P. Gi.)

HAAG, CARL (1820- ), a naturalized British painter, court painter to the duke of Saxe-Coburg and Gotha, was born in Bavaria, and was trained in the academies at Nuremburg and Munich. He practised first as an illustrator and as a painter, in oil, of portraits and architectural subjects; but after he settled in England, in 1847, he devoted himself to water colours, and was elected associate of the Royal Society of Painters in Water Colours in 1850 and member in 1853. He travelled much, especially in the East, and made a considerable reputation by his firmly drawn and carefully elaborated paintings of Eastern subjects. Towards the end of his professional career Carl Haag quitted England and returned to Germany.

See _A History of the "Old Water-Colour" Society, now the Royal
Society of Painters in Water Colours_, by John Lewis Roget (2 vols.,
London, 1891).

HAAKON (Old Norse _Hakon_), the name of several kings of Norway, of whom the most important are the following:--

HAAKON I., surnamed "the Good" (d. 961), was the youngest son of Harald Haarfager. He was fostered by King Aethelstan of England, who brought him up in the Christian religion, and on the news of his father's death in 933 provided him with ships and men for an expedition against his half-brother Erik, who had been proclaimed king. On his arrival in Norway Haakon gained the support of the landowners by promising to give up the rights of taxation claimed by his father over inherited real property. Erik fled, and was killed a few years later in England. His sons allied themselves with the Danes, but were invariably defeated by Haakon, who was successful in everything he undertook except in his attempt to introduce Christianity, which aroused an opposition he did not feel strong enough to face. He was killed at the battle of Fitje in 961, after a final victory over Erik's sons. So entirely did even his immediate circle ignore his religion that a court skald composed a poem on his death representing his welcome by the heathen gods into Valhalla.

HAAKON IV., surnamed "the Old" (1204-1263), was declared to be the son of Haakon III., who died shortly before the former's birth in 1204. A year later the child was placed under the protection of King Inge, after whose death in 1217 he was chosen king; though until 1223 the church refused to recognize him, on the ground of illegitimacy, and the Pope's dispensation for his coronation was not gained until much later. In the earlier part of his reign much of the royal power was in the hands of Earl Skule, who intrigued against the king until 1239, when he proceeded to open hostility and was put to death. From this time onward Haakon's reign was marked by more peace and prosperity than Norway had known for many years, until in 1263 a dispute with the Scottish king concerning the Hebrides, a Norwegian possession, induced Haakon to undertake an expedition to the west of Scotland. A division of his army seems to have repulsed a large Scottish force at Largs (though the later Scottish accounts claim this battle as a victory), and, having won back the Norwegian possessions in Scotland, Haakon was wintering in the Orkneys, when he was taken ill and died on the 15th of December 1263. A great part of his fleet had been scattered and destroyed by storms. The most important event in his reign was the voluntary submission of the Icelandic commonwealth. Worn out by internal strife fostered by Haakon's emissaries, the Icelandic chiefs acknowledged the Norwegian king as overlord in 1262. Their example was followed by the colony of Greenland.

HAAKON VII. (1872- ), the second son of Frederick VIII., king of Denmark, was born on the 3rd of August 1872, and was usually known as Prince Charles of Denmark. When in 1905 Norway decided to separate herself from Sweden the Norwegians offered their crown to Charles, who accepted it and took the name of Haakon VII., being crowned at Trondhjem in June 1906. The king married Maud, youngest daughter of Edward VII., king of Great Britain, their son, Prince Olav, being born in 1903.

HAARLEM, a town of Holland in the province of North Holland, on the Spaarne, having a junction station 11 m. by rail W. of Amsterdam. It is connected by electric and steam tramways with Zandvoort, Leiden, Amsterdam and Alkmaar. Pop. (1900) 65,189. Haarlem is the seat of the governor of the province of North Holland, and of a Roman Catholic and a Jansenist bishopric. In appearance it is a typical Dutch town, with numerous narrow canals and quaintly gabled houses. Of the ancient city gates the Spaarnewouder or Amsterdam gate alone remains. Gardens and promenades have taken the place of the old ramparts, and on the south the city is bounded by the Frederiks and the Flora parks, between which runs the fine avenue called the Dreef, leading to the Haarlemmer Hout or wood. In the Frederiks Park is a pump-room supplied with a powerful chalybeate water from a spring, the Wilhelminabron, in the Haarlemmer Polder not far distant, and in connexion with this there is an orthopaedic institution adjoining. In the great market place in the centre of the city are gathered together the larger number of the most interesting buildings, including the quaint old Fleshers' Hall, built by Lieven de Key in 1603, and now containing the archives; the town hall; the old Stadsdoelen, where the burgesses met in arms; the Groote Kerk, or Great Church; and the statue erected in 1856 to Laurenz Janszoon Koster, the printer. The Great Church, dedicated to St Bavo, with a lofty tower (255 ft.), is one of the most famous in Holland, and dates from the end of the 15th and the beginning of the 16th centuries. Its great length (460 ft.) and the height and steepness of its vaulted cedar-wood roof (1538) are very impressive. The choir-stalls and screen (1510) are finely carved, and of further interest are the ancient pulpit sounding-board (1432), some old stained glass, and the small models of ships, copies dating from 1638 of yet earlier models originally presented by the Dutch-Swedish Trading Company. The church organ was long considered the largest and finest in existence. It was constructed by Christian Muller in 1738, and has 4 keyboards, 64 registers and 5000 pipes, the largest of which is 15 in. in diameter and 32 ft. long. Among the monuments in the church are those of the poet Willem Bilderdyk (d. 1831) and the engineer Frederik Willem Conrad (d. 1808), who designed the sea-sluices at Katwyk. In the belfry are the _damiaatjes_, small bells presented to the town, according to tradition, by William I., count of Holland (d. 1222), the crusader. The town hall was originally a palace of the counts of Holland, begun in the 12th century, and some old 13th-century beams still remain; but the building was remodelled in the beginning of the 17th century. It contains a collection of antiquities (including some beautiful goblets) and a picture gallery which, though small, is celebrated for its fine collection of paintings by Frans Hals. The town library contains several _incunabula_ and an interesting collection of early Dutch literature. At the head of the scientific institutions of Haarlem may be placed the Dutch Society of Sciences (_Hollandsche Maatschappij van Wetenschappen_), founded in 1752, which possesses valuable collections in botany, natural history and geology. Teyler's Stichting (i.e. foundation), enlarged in modern times, was instituted by the will of Pieter Teyler van der Hulst (d. 1778), a wealthy merchant, for the study of theology, natural science and art, and has lecture-theatres, a large library, and a museum containing a physical and a geological cabinet, as well as a collection of paintings, including many modern pictures, and a valuable collection of drawings and engravings by old masters. The Dutch Society for the Promotion of Industry (_Nederlaandsche Maatschappij ter Bevordering van Nijverheid_), founded in 1777, has its seat in the Pavilion Welgelegen, a villa on the south side of the Frederiks Park, built by the Amsterdam banker John Hope in 1778, and afterwards acquired by Louis Bonaparte, king of Holland. The colonial museum and the museum of industrial art were established in this villa by the society in 1871 and 1877 respectively. Besides these there are a museum of ecclesiastical antiquities, chiefly relating to the bishopric of Haarlem; the old weigh-house (1598) and the orphanage for girls (1608), originally an almshouse for old men, both built by the architect Lieven de Key of Ghent.

The staple industries of Haarlem have been greatly modified in the course of time. Cloth weaving and brewing, which once flourished exceedingly, declined in the beginning of the 16th century. A century later, silk, lace and damask weaving were introduced by French refugees, and became very important industries. But about the close of the 18th century this remarkable prosperity had also come to an end, and it was not till after the Belgian revolution of 1830-1831 that Haarlem began to develop the manufactures in which it is now chiefly engaged. Cotton manufacture, dyeing, printing, bleaching, brewing, type-founding, and the manufacture of tram and railway carriages are among the more important of its industries. One of the printing establishments has the reputation of being the oldest in the Netherlands, and publishes the oldest Dutch paper, _De Opragte Haarlemmer Courant_. Market-gardening, especially horticulture, is extensively practised in the vicinity, so that Haarlem is the seat of a large trade in Dutch bulbs, especially hyacinths, tulips, fritillaries, spiraeas and japonicas.

Haarlem, which was a prosperous place in the middle of the 12th century, received its first town charter from William II., count of Holland and king of the Romans, in 1245. It played a considerable part in the wars of Holland with the Frisians. In 1492 it was captured by the insurgent peasants of North Holland, was re-taken by the duke of Saxony, the imperial stadholder, and deprived of its privileges. In 1572 Haarlem joined the revolt of the Netherlands against Spain, but on the 13th of July 1573, after a seven months' siege, was forced to surrender to Alva's son Frederick, who exacted terrible vengeance. In 1577 it was again captured by William of Orange and permanently incorporated in the United Netherlands.

See Karl Hegel, _Stadte und Gilden_ (Leipzig, 1891); Allan,
_Geschiedenis en beschrijving van Haarlem_ (Haarlem, 1871-1888).

HAARLEM LAKE (Dutch _Harlemmer Meer_), a commune of the province of North Holland, constituted by the law of the 16th of July 1855. It has an area of about 46,000 acres, and its population increased from 7237 in 1860 to 16,621 in 1900. As its name indicates, the commune was formerly a lake, which is said to have been a relic of a northern arm of the Rhine which passed through the district in the time of the Romans. In 1531 the Haarlemmer Meer had an area of 6430 acres, and in its vicinity were three smaller sheets of water--the Leidsche Meer or Leiden Lake, the Spiering Meer, and the Oude Meer or Old Lake, with a united area of about 7600 acres. The four lakes were formed into one by successive inundations, whole villages disappearing in the process, and by 1647 the new Haarlem Lake had an area of about 37,000 acres, which a century later had increased to over 42,000 acres. As early as 1643 Jan Adriaanszoon Leeghwater proposed to endike and drain the lake; and similar schemes, among which those of Nikolaas Samuel Cruquius in 1742 and of Baron van Lijnden van Hemmen in 1820 are worthy of special mention, were brought forward from time to time. But it was not till a furious hurricane in November 1836 drove the waters as far as the gates of Amsterdam, and another on Christmas Day sent them in the opposite direction to submerge the streets of Leiden, that the mind of the nation was seriously turned to the matter. In August 1837 the king appointed a royal commission of inquiry; the scheme proposed by the commission received the sanction of the Second Chamber in March 1839, and in the following May the work was begun. A canal was first dug round the lake for the reception of the water and the accommodation of the great traffic which had previously been carried on. This canal was 38 m. in length, 123-146 ft. wide, and 8 ft. deep, and the earth which was taken out of it was used to build a dike from 30 to 54 yds. broad containing the lake. The area enclosed by the canal was rather more than 70 sq. m., and the average depth of the lake 13 ft. 1-1/2 in., and as the water had no natural outfall it was calculated that probably 1000 million tons would have to be raised by mechanical means. This amount was 200 million tons in excess of that actually discharged. Pumping by steam-engines began in 1848, and the lake was dry by the 1st of July 1852. At the first sale of the highest lands along the banks on the 16th of August 1853, about L28 per acre was paid; but the average price afterwards was less. The whole area of 42,096 acres recovered from the waters brought in 9,400,000 florins, or about L780,000, exactly covering the cost of the enterprise; so that the actual cost to the nation was only the amount of the interest on the capital, or about L368,000. The soil is of various kinds, loam, clay, sand and peat; most of it is sufficiently fertile, though in the lower portions there are barren patches where the scanty vegetation is covered with an ochreous deposit. Mineral springs occur containing a very high percentage (3.245 grams per litre) of common salt; and in 1893 a company was formed for working them. Corn, seeds, cattle, butter and cheese are the principal produce. The roads which traverse the commune are bordered by pleasant-looking farm-houses built after the various styles of Holland, Friesland or Brabant. Hoofddorp, Venneperdorp or Nieuw Vennep, Abbenes and the vicinities of the pumping-stations are the spots where the population has clustered most thickly. The first church was built in 1855; in 1877 there were seven. In 1854 the city of Leiden laid claim to the possession of the new territory, but the courts decided in favour of the nation.

HAASE, FRIEDRICH (1827- ), German actor, was born on the 1st of November 1827, in Berlin, the son of a valet to King Frederick William IV., who became his godfather. He was educated for the stage under Ludwig Tieck and made his first appearance in 1846 in Weimar, afterwards acting at Prague (1849-1851) and Karlsruhe (1852-1855). From 1860 to 1866 he played in St Petersburg, then was manager of the court theatre in Coburg, and in 1869 (and again in 1882-1883) visited the United States. He was manager of the Stadt Theater in Leipzig from 1870 to 1876, when he removed to Berlin, where he devoted his energies to the foundation and management of the Deutsches Theater. He finally retired from the stage in 1898. Haase's aristocratic appearance and elegant manner fitted him specially to play high comedy parts. His chief roles were those of Rocheferrier in the _Partie Piquet_; Richelieu; Savigny in _Der feiner Diplomat_, and der Furst in _Der geheime Agent_. He is the author of _Ungeschminkte Briefe and Was ich erlebte 1846-1898_ (Berlin, 1898).

See Simon, _Friedrich Haase_ (Berlin, 1898).

HAASE, FRIEDRICH GOTTLOB (1808-1867), German classical scholar, was born at Magdeburg on the 4th of January 1808. Having studied at Halle, Greifswald and Berlin, he obtained in 1834 an appointment at Schulpforta, from which he was suspended and sentenced to six years' imprisonment for identifying himself with the _Burschenschaften_ (students' associations). Having been released after serving one year of his sentence, he visited Paris, and on his return in 1840 he was appointed professor at Breslau, where he remained till his death on the 16th of August 1867. He was undoubtedly one of the most successful teachers of his day in Germany, and exercised great influence upon all his pupils.

He edited several classic authors: Xenophon ([Greek: Lakedaimonion
politeia], 1833); Thucydides (1840); Velleius Paterculus (1858);
Seneca the philosopher (2nd ed., 1872, not yet superseded); and
Tacitus (1855), the introduction to which is a masterpiece of
Latinity. His _Vorlesungen uber lateinische Sprachwissenschaft_ was
published after his death by F. A. Eckstein and H. Peter (1874-1880).
See C Bursian, _Geschichte der klassischen Philologie in Deutschland_
(1883); G. Fickert, _Friderici Haasii memoria_ (1868), with a list of
works; T. Oelsner in _Rubezahl (Schlesische Provinzialblatter)_, vii.
Heft 3 (Breslau, 1868).

HAAST, SIR JOHANN FRANZ JULIUS VON (1824-1887), German and British geologist, was born at Bonn on the 1st of May 1824. He received his early education partly in that town and partly in Cologne, and then entered the university at Bonn, where he made a special study of geology and mineralogy. In 1858 he started for New Zealand to report on the suitability of the colony for German emigrants. He then became acquainted with Dr von Hochstetter, and rendered assistance to him in the preliminary geological survey which von Hochstetter had undertaken. Afterwards Dr Haast accepted offers from the governments of Nelson and Canterbury to investigate the geology of those districts, and the results of his detailed labours greatly enriched our knowledge with regard to the rocky structure, the glacial phenomena and the economic products. He discovered gold and coal in Nelson, and he carried on important researches with reference to the occurrence of _Dinornis_ and other extinct wingless birds (Moas). His _Geology of the Provinces of Canterbury and Westland, N.Z._, was published in 1879. He was the founder of the Canterbury museum at Christchurch, of which he became director, and which he endeavoured to render the finest collection in the southern hemisphere. He was surveyor-general of Canterbury from 1861 to 1871, and professor of geology at Canterbury College. He was elected F.R.S. in 1867; and he was knighted for his services at the time of the colonial exhibition in London in 1887. He died at Wellington, N.Z., on the 15th of August 1887.

HABABS (AZ-HIBBEHS), a nomadic pastoral people of Hamitic stock, living in the coast region north-west of Massawa. Physically they are Beja, by language and traditions Abyssinians. They were Christians until the 19th century, but are now Mahommedans. Their sole wealth consists in cattle.

HABAKKUK, the name borne by the eighth book of the Old Testament "Minor Prophets." It occurs twice in the book itself (i. 1, iii. 1) in titles, but nowhere else in the Old Testament. The meaning of the name is uncertain. If Hebrew, it might be derived from the root [Hebrew: habak] (to embrace) as an intensive term of affection. It has also been connected more plausibly with an Assyrian plant name, _[h)]ambakuku_ (Delitzsch, _Assyrisches Handworterbuch_, p. 281). The Septuagint has [Greek: Ambakoum]. Of the person designated, no more is known than may be inferred from the writing which bears his name. Various legends are connected with him, of which the best known is given in the Apocryphal story of "Bel and the Dragon" (v. 33-39); but none of these has any historic value.[1]

The book itself falls into three obvious parts, viz. (1) a dialogue between the prophet and God (i. 2-ii. 4); (2) a series of five woes pronounced on wickedness (ii. 5-ii. 20); (3) a poem describing the triumphant manifestation of God (iii.). There is considerable difficulty in regard to the interpretation of (1), on which that of (2) will turn; while (3) forms an independent section, to be considered separately.

In the dialogue, the prophet cries to God against continued violence and injustice, though it is not clear whether this is done _within_ or _to_ Israel (i. 2-4). The divine answer declares that God raises up the Chaldaeans, whose formidable resources are invincible (i. 5-11). The prophet thereupon calls God's attention to the tyranny which He apparently allows to triumph, and declares his purpose to wait till an answer is given to his complaint (i. 12-ii. 2). God answers by demanding patience, and by declaring that the righteous shall live by his faithfulness (ii. 3-4).

The interpretation of this dialogue which first suggests itself is that the prophet is referring to wickedness _within_ the nation, which is to be punished by the Chaldaeans as a divine instrument; in the process, the tyranny of the instrument itself calls for punishment, which the prophet is bidden to await in patient fidelity. On this view of the dialogue, the subsequent woes will be pronounced against the Chaldaeans, and the date assigned to the prophecy will be about 600 B.C., i.e. soon after the battle of Carchemish (605 B.C.), when the Chaldaean victory over Egypt inaugurated a period of Chaldaean supremacy which lasted till the Chaldaeans themselves were overthrown by Cyrus in 538 B.C. Grave objections, however, confront this interpretation, as is admitted even by such recent defenders of it as Davidson and Driver. Is it likely that a prophet would begin a complaint against Chaldaean tyranny (admittedly central in the prophecy) by complaining of that wickedness of his fellow-countrymen which seems partly to justify it? Are not the terms of reference in i. 2 f. and 1. 12 f. too similar for the supposition that two distinct, even contradictory, complaints are being made (cf. "wicked" and "righteous" in i. 4 and i. 13, interchanged in regard to Israel, on above theory)? And if i. 5-11 is a genuine _prophecy_ of the raising up of the Chaldaeans, whence comes that long experience of their rule required to explain the _detailed_ denunciation of their tyranny? To meet the last objection, Davidson supposes i. 5-11 to be really a reference to the past, prophetic in form only, and brings down the whole section to a later period of Chaldaean rule, "hardly, one would think, before the deportation of the people under Jehoiachin in 597" (p. 49). Driver prefers to bisect the dialogue by supposing i. 2-11 to be written at an earlier period than i. 12 f. (p. 57). The other objections, however, remain, and have provoked a variety of theories from Old Testament scholars, of which three call for special notice. (1) The first of these, represented by Giesebrecht,[2] Nowack and Wellhausen, refers i. 2-4 to Chaldaean oppression of Israel, the same subject being continued in i. 12 f. Obviously, the reference to the Chaldaeans as a divine instrument could not then stand in its present place, and it is accordingly regarded as a misplaced earlier prophecy. This is the minimum of critical procedure required to do justice to the facts. (2) Budde, followed by Cornill, also regards i. 2-4 as referring to the oppression of Israel by a foreign tyrant, whom, however, he holds to be Assyria. He also removes i. 5-11 from its present place, but makes it part of the divine answer, following ii. 4. On this view, the Chaldaeans are the divine instrument for punishing the tyranny of the Assyrians, to whom the following woes will therefore refer. The date would fall between Josiah's reformation (621) and his death (609). This is a plausible and even attractive theory; its weakness seems to lie in the absence of any positive evidence in the prophecy itself, as is illustrated by the fact that even G. A. Smith, who follows it, suggests "Egypt from 608-605" as an alternative to Assyria (p. 124). (3) Marti (1904) abandons the attempt to explain the prophecy as a unity, and analyses it into three elements, viz. (a) The original prophecy by Habakkuk, consisting of i. 5-10, 14 f., belonging to the year 605, and representing the emergent power of the Chaldaeans as a divine scourge of the faithless people; (b) Woes against the Chaldaeans, presupposing not only tyrannous rule over many peoples, but the beginning of their decline and fall, and therefore of date about 540 B.C. (ii. 5-19); (c) A psalm of post-exilic origin, whose fragments, i. 2-4, 12 a, 13, ii. 1-4, have been incorporated into the present text from the margins on which they were written, its subject being the suffering of the righteous. Each of these three theories[3] encounters difficulties of detail; none can be said to have secured a dominant position. The great variety of views amongst competent critics is significant of the difficulty of the problem, which can hardly be regarded as yet solved; this divergence of opinion perhaps points to the impossibility of maintaining the unity of chs. i. and ii., and throws the balance of probability towards some such analysis as that of Marti, which is therefore accepted in the present article.

In regard to the poem which forms the third and closing chapter of the present book of Habakkuk, there is much more general agreement. Its most striking characteristic lies in the superscription ("A prayer of Habakkuk the prophet, set to Shigionoth"), the subscription ("For the chief musician, on my stringed instruments"), and the insertion of the musical term "Selah" in three places (v. 3, 9, 13). These liturgical notes make extremely probable the supposition that the poem has been taken from some collection like that of our present book of Psalms, probably on the ground of the authorship asserted by the superscription there attached to it. It cannot, however, be said that the poem itself supports this assertion, which carries no more intrinsic weight than the Davidic titles of the Psalms. The poem begins with a prayer that God will renew the historic manifestation of the exodus, which inaugurated the national history and faith; a thunderstorm moving up from the south is then described, in which God is revealed (3-7); it is asked whether this manifestation, whose course is further described, is against nature only (8-11); the answer is given that it is for the salvation of Israel against its wicked foes (12-15); the poet describes the effect in terror upon himself (16) and declares his confidence in God, even in utter agricultural adversity (17-19). As Wellhausen says (p. 171): "The poet appears to believe that in the very act of describing enthusiastically the ancient deed of deliverance, he brings home to us the new; we are left sometimes in doubt whether he speaks of the past to suggest the new by analogy, or whether he is concerned directly with the future, and simply paints it with the colours of the past." In any case, there is nothing in this fine poem to connect it with the conception of the Chaldaeans as a divine instrument. It is the nation that speaks through the poet (cf. v. 14), but at what period of its post-exilic history we have no means of inferring.

Our estimate of the theological teaching of this book will naturally be influenced by the particular critical theory which is adopted. The reduction of the book to four originally independent sections requires that the point of each be stated separately. When this is done, it will, however, be found that there is a broad unity of subject, and of natural development in its treatment, such as to some extent justifies the instinct or the judgment of those who were instrumental in effecting the combination of the separate parts. (1) The poem (iii.), though possibly latest in date,[4] claims first consideration, because it avowedly moves in the circle of primitive ideas, and supplicates a divine intervention, a direct and immediate manifestation of the transcendent God. He is conceived as controlling or overcoming the forces of nature; and though an earlier mythology has supplied some of the ideas, yet, as with the opening chapters of Genesis, they are transfigured by the moral purpose which animates them, the purpose to subdue all things that could frustrate the destiny of God's anointed (v. 13). The closing verses strike that deep note of absolute dependence on God, which is the glory of the religion of the Old Testament and its chief contribution to the spirit of the Gospels. (2) The prophecy of the Chaldaeans as the instruments of the divine purpose involves a different, yet related, conception of the divine providence. The philosophy of history, by which Hebrew prophets could read a deep moral significance into national disaster and turn the flank of resistless attack, became one of the most important elements in the nation's faith. If the world-powers were hard as flint in their dealings with Israel, the people of God were steeled to such moral endurance that each clash of their successive onsets kindled some new flame of devotion. Through the Chaldaeans God worked a work which required centuries of life and literature to disclose its fulness (i. 5). (3) When we turn from this view of the Chaldaeans to the denunciation of their tyranny in "taunt songs" (ii. 5-20), we have simply a practical application of the doctrine of divine government. God being what He is, at once moral and all-powerful, the immoral life is doomed to overthrow, whether the immorality consist in grasping rapacity, proud self-aggrandizement, cruel exaction, exulting triumph or senseless idolatry. (4) Yet, because the doom so often tarries, there arises the problem of the suffering of the innocent and the upright. How can God look down with tolerance that seems favour on so much that conflicts with His declared will and character? This is the great problem of Israel, finding its supreme expression for all time in the book of Job (q.v.). In that book the solution of the problem of innocent suffering lies hidden from the sufferer, even to the end, for he is not admitted with the reader to the secret of the prologue; it is the practical solution of faithfulness resting on faith which is offered to us. So here, with the principle of ii. 4, "the righteous shall live by his faithfulness." The different application of these words in the New Testament to "faith" is well known (Rom. i. 17; Gal. iii. 11; Heb. x. 38) though the difference is apt to be exaggerated by those who forget how much of the element of [Hebrew: emuna]: lies in Paul's conception of [Greek: pistis]. In G. A. Smith's words, "as Paul's adaptation, 'the just shall live by faith,' has become the motto of evangelical Christianity, so we may say that Habakkuk's original of it has been the motto and the fame of Judaism: 'the righteous shall live by his faithfulness.'"

The Hebrew text of this impressive and varied book is unfortunately
corrupt in many places; even so cautious a critic as Driver accepts or
favourably notices eighteen textual emendations in the three chapters,
and suspects the text in at least seven other cases. For the
interpretation of the book in detail, the English reader will find
Driver's commentary (1906) the most useful.

References to earlier literature will be found in the following
noteworthy studies of recent date: Davidson, "Nahum, Habakkuk and
Zephaniah," in _Cambridge Bible_ (1896); Nowack, _Die kleinen
Propheten_ (Hdkr.) (1897); Wellhausen, _Die kleinen Propheten_^3
(1898); G. A. Smith, "The Book of the Twelve Prophets," in _The
Expositor's Bible_, vol. ii. (1898); Driver, article "Habakkuk" in
Hastings' _Dictionary of the Bible_, vol. ii. pp. 269-272 (1900);
Budde, article "Habakkuk" in _Ency. Biblica_, vol. ii., c. 1921-1928
(1901); Stevenson, "The Interpretation of Habakkuk," in _The
Expositor_ (1902), pp. 388-401; Peake, _The Problem of Suffering in
the Old Testament_ (1904), pp. 4-11 and app. A, "Recent Criticism of
Habakkuk"; Marti, _Dodekapropheton_ (K. H. C.) (1904); Driver, "Minor
Prophets," vol. ii., in _Century Bible_ (1906); Duhm, _Das Buch
Habakkuk_ (Text, Ubersetzung und Efklarung), 1906 (regards the book as
a unity belonging to the time of Alexander the Great). Max L. Margolis
discusses the anonymous Greek version of Habakkuk iii. in a volume of
_Old Test. and Semitic Studies: in Memory of William Rainey Harper_
(Chicago, 1908). (H. W. R.*)

FOOTNOTES:

[1] These legends are collected in Hastings, D. B. vol. ii. p. 272.
He is the watchman of Is. xxi. 6 (cf. Hab. ii. 1); the son of the
Shunammite (2 Kings iv. 16); and is miraculously lifted by his hair
to carry his own dinner to Daniel in the lions' den (_supra_).

[2] Followed by Peake in _The Problem of Suffering_, pp. 4 f., 151
f., to whose appendix (A) reference may be made for further details
of recent criticism.

[3] For the less probable theories of Rothstein, Lauterburg, Happel
and Peiser (amongst others), cf. Marti's _Commentary_, pp. 328 f. and
332. Stevenson (_The Expositor_, 1902) states clearly the
difficulties for those who regard ch. i. as a unity. He sees two
independent sections, 2-4 + 12-13, and 5-11 + 14-17.

[4] Earlier, however, than Ps. lxxvii. 17-20, which is drawn from it.