above. The obvious antidote is atropine, which may often succeed; and the
other measures are those usually employed to stimulate the circulation and
respiration. Unfortunately the antagonism between physostigmine and
atropine is not perfect, and Sir Thomas Fraser has shown that in such cases
there comes a time when, if the action of the two drugs be summated, death
results sooner than from either alone. Thus atropine will save life after
three and a half times the fatal dose of physostigmine has been taken, but
will hasten the end if four or more times the fatal dose has been ingested.
Thus it would be advisable to use the physiological antidote only when the
dose of the poison--assuming estimation to be possible--was known to be
comparatively small.
CALABASH (from the Span. _calabaza_, a gourd or pumpkin, possibly derived
from the Pers. _kharlunza_, a melon), the shell of a gourd or pumpkin made
into a vessel for holding liquids; also a vessel of similar shape made of
other materials. It is the name of a tree (_Crescentia Cujete_) of tropical
America, whose gourd-like fruit is so hard that vessels made of it can be
used over a fire many times before being burned.
CALABASH TREE, a native of the West Indies and South America, known
botanically as _Crescentia Cujete_ (natural order, Bignoniaceae). The fruit
resembles a gourd, and has a woody rind, which after removal of the pulp
forms a calabash.
CALABOZO, or CALABOSO, an inland town of Venezuela, once capital of the
province of Caracas in the colonial period, and now capital of the state of
Guárico. Pop. (1891) 5618. Calabozo is situated in the midst of an
extensive _llano_ on the left bank of the Guárico river, 325 ft. above
sea-level and 123 m. S.S.W. of Caracas. The plain lies slightly above the
level of intersecting rivers and is frequently flooded in the rainy season;
in summer the heat is most oppressive, the average temperature being 88°F.
The town is regularly laid out with streets crossing at right angles, and
possesses several fine old churches, a college and public school. It is
also a bishop's see, and a place of considerable commercial importance
because of its situation in the midst of a rich cattle-raising country. It
is said to have been an Indian town originally, and was made one of the
trading stations of the Compañia Guipuzcoana in 1730. However, like most
Venezuelan towns, Calabozo made little growth during the 19th century. In
1820 the Spanish forces under Morales were defeated here by the
revolutionists under Bolívar and Paez.
CALABRESELLA (sometimes spelt Calabrasella), an Italian card-game ("the
little Calabrian game") for three players. All the tens, nines and eights
are removed from an ordinary pack; the order of the cards is three, two,
ace, king, queen, &c. In scoring the ace counts 3; the three 2; king, queen
and knave 1 each. The last trick counts 3. Each separate hand is a whole
game. One player plays against the other two, paying to each or receiving
from each the difference between the number of points that he and they
hold. Each player receives twelve cards, dealt two at a time. The remainder
form the stock, which is left face downwards. There are no trumps. The
player on the dealer's left declares first: he can either play or pass. The
dealer has the last option. If one person announces that he plays, the
others combine against him. If all decline to play, the deal passes, the
hands being abandoned. The single player may demand any "three" he chooses,
giving a card in exchange. If the three demanded is in the stock, no other
card may be asked for. If a player hold all the threes, he may demand a
two. The single player must take one card from the stock, in exchange for
one of his own (which is never exposed) and may take more. He puts out the
cards he wishes to exchange face downwards, and selects what he wishes from
the stock, which is now exposed; the rejected cards and cards left in the
stock form the "discard." The player on the dealer's left then leads. The
highest card wins the trick, there being no trumps. Players must follow
suit, if they can. The single player and the allies collect all the tricks
they win respectively. The winner of the last trick, besides scoring three,
adds the discard to his heap. The heaps are then searched for the scoring
cards, the scores are compared and the stakes paid. It is important to
remember that the value and the order of the cards are not the same, thus
the ace, whose value is 3, is only third as a trick-winner; also that it is
highly important to win the last trick. Thirty-five is the full score.
CALABRIA, a territorial district of both ancient and modern Italy.
(1) The ancient district consisted of the peninsula at its southeast
extremity, between the Adriatic Sea and the Gulf of Tarentum, ending in the
lapygian promontory (Lat. _Promunturium Sallentinum_; the village upon it
was called Leuca--Gr. [Greek: Leuka], white, from its colour--and is still
named S. Maria di Leuca) and corresponding in the main with the modern
province of Lecce, Brundisium and Tarentum being its most north-westerly
cities, though the boundary of the latter extends somewhat farther [v.04
p.0964] west. It is a low terrace of limestone, the highest parts of which
seldom reach 1500 ft.; the cliffs, though not high, are steep, and it has
no rivers of any importance, but despite lack of water it was (and is)
remarkably fertile. Strabo mentions its pastures and trees, and its olives,
vines and fruit trees (which are still the principal source of prosperity)
are frequently spoken of by the ancients. The wool of Tarentum and
Brundisium was also famous, and at the former place were considerable
dye-works. These two towns acquired importance in very early times owing to
the excellence of their harbours. Traces of a prehistoric population of the
stone and early bronze age are to be found all over Calabria. Especially
noticeable are the menhirs (_pietre fitte_) and the round tower-like
_specchie_ or _truddhi_, which are found near Lecce, Gallipolli and Muro
Leccese (and only here in Italy); they correspond to similar monuments, the
_perdas fittas_ and the _nuraghi_, of Sardinia, and the inter-relation
between the two populations which produced them requires careful study. In
272-266 B.C. we find six triumphs recorded in the Roman _fasti_ over the
Tarentini, Sallentini and Messapii, while the name Calabria does not occur;
but after the foundation of a colony at Brundisium in 246-245 B.C., and the
final subjection of Tarentum in 209 B.C., Calabria became the general name
for the peninsula. The population declined to some extent; Strabo (vi. 281)
tells us that in earlier days Calabria had been extremely populous and had
had thirteen cities, but that in his time all except Tarentum and
Brundisium, which retained their commercial importance, had dwindled down
to villages. The Via Appia, prolonged to Brundisium perhaps as early as 190
B.C., passed through Tarentum; the shorter route by Canusium, Barium and
Gnathia was only made into a main artery of communication by Trajan (see
APPIA, VIA). The only other roads were the two coast roads, the one from
Brundisium by Lupiae, the other from Tarentum by Manduria, Neretum, Aletium
(with a branch to Callipolis) and Veretum (hence a branch to Leuca), which
met at Hydruntum. Augustus joined Calabria to Apulia and the territory of
the Hirpini to form the second region of Italy. From the end of the second
century we find Calabria for juridical purposes associated either with
Apulia or with Lucania and the district of the Bruttii, while Diocletian
placed it under one _corrector_ with Apulia. The loss of the name Calabria
came with the Lombard conquest of this district, when it was transferred to
the land of the Bruttii, which the Byzantine empire still held.
(2) The modern Calabria consists of the south extremity of Italy (the "toe
of the boot" in the popular simile, while the ancient Calabria, with which
the present province of Lecce more or less coincides, is the "heel"),
bounded on the N. by the province of Potenza (Basilicata) and on the other
three sides by the sea. Area 5819 sq. m. The north boundary is rather
farther north than that of the ancient district of the Bruttii (_q.v._).
Calabria acquired its present name in the time of the Byzantine supremacy,
after the ancient Calabria had fallen into the hands of the Lombards and
been lost to the Eastern empire about A.D. 668. The name is first found in
the modern sense in Paulus Diaconus's _Historia Langobardorum_ (end of the
8th century). It is mainly mountainous; at the northern extremity of the
district the mountains still belong to the Apennines proper (the highest
point, the Monte Pollino, 7325 ft., is on the boundary between Basilicata
and Calabria), but after the plain of Sibari, traversed by the Crati (anc.
Crathis, a river 58 m. long, the only considerable one in Calabria), the
granite mountains of Calabria proper (though still called Apennines in
ordinary usage) begin. They consist of two groups. The first extends as far
as the isthmus, about 22 m. wide, formed by the gulfs of S. Eufemia and
Squillace; its highest point is the Botte Donato (6330 ft.). It is in
modern times generally called the Sila, in contradistinction to the second
(southern) group, the Aspromonte (6420 ft.); the ancients on the other hand
applied the name Sila to the southern group. The rivers in both parts of
the chain are short and unimportant. The mountain districts are in parts
covered with forest (though less so than in ancient times), still largely
government property, while in much of the rest there is good pasture. The
scenery is fine, though the country is hardly at all visited by travellers.
The coast strip is very fertile, and though some parts are almost deserted
owing to malaria, others produce wine, olive-oil and fruit (oranges and
lemons, figs, &c.) in abundance, the neighbourhood of Reggio being
especially fertile. The neighbourhood of Cosenza is also highly cultivated;
and at the latter place a school of agriculture has been founded, though
the methods used in many parts of Calabria are still primitive. Wheat,
rice, cotton, liquorice, saffron and tobacco are also cultivated. The coast
fisheries are important, especially in and near the straits of Messina.
Commercial organization is, however, wanting. The climate is very hot in
summer, while snow lies on the mountain-tops for at least half the year.
Earthquakes are frequent and have done great damage: that of the autumn of
1905 was very disastrous (O. Malagodi, _Calabria Desolata_, Rome, 1905),
but it was surpassed in its effects by the terrible earthquake of 1908, by
which Messina (_q.v._) was destroyed, and in Calabria itself Reggio and
numerous smaller places ruined. The railway communications are sufficient
for the coast districts; there are lines along both the east and west
coasts (the latter forms part of the through route by land from Italy to
Sicily, ferry-boats traversing the Strait of Messina with the through
trains on board) which meet at Reggio di Calabria. They are connected by a
branch from Marina di Catanzaro passing through Catanzaro to S. Eufemia;
and there is also a line from Sibari up the valley of the Crati to Cosenza
and Pietrafitta. The interior is otherwise untouched by railways; indeed
many of the villages in the interior can only be approached by paths; and
this is one of the causes of the economic difficulties of Calabria. Another
is the unequal distribution of wealth, there being practically no middle
class; a third is the injudicious disforestation which has been carried on
without regard to the future. The natural check upon torrents is thus
removed, and they sometimes do great damage. The Calabrian costumes are
still much worn in the remoter districts: they vary considerably in the
different villages. There is, and has been, considerable emigration to
America, but many of the emigrants return, forming a slightly higher class,
and producing a rise in the rate of payment to cultivators, which has
increased the difficulties of the small proprietors. The smallness and
large number of the communes, and the consequently large number of the
professional classes and officials, are other difficulties, which,
noticeable throughout Italy, are especially felt in Calabria. The
population of Calabria was 1,439,329 in 1901. The chief towns of the
province of Catanzaro were in 1901:--Catanzaro (32,005), Nicastro (18,150),
Monteleone (13,481), Cotrone (9545), total of province (1871) 412,226;
(1901) 498,791; number of communes, 152; of the province of Cosenza,
Cosenza (20,857), Corigliano Calabro (15,379), Rossano (13,354), S.
Giovanni in Fiore (13,288), Castrovillari (9945), total of province (1871)
440,468; (1901) 503,329, number of communes, 151; of the province of
Reggio, Reggio di Calabria (44,569), Palmi (13,346), Cittanova (11,782),
Gioiosa Ionica(11,200), Bagnara Calabra (11,136), Siderno Marina (10,775),
Gerace (10,572), Polistena (10,112); number of communes 106; total of
province (1871) 353,608; (1901) 437,209. A feature of modern Calabria is
the existence of several Albanian colonies, founded in the 15th century by
Albanians expelled by the Turks, who still speak their own language, wear
their national costume, and worship according to the Greek rite. Similar
colonies exist in Sicily, notably at Piana dei Greci near Palermo.
(T. AS.)
CALAFAT, a town of Rumania in the department of Doljiu; on the river
Danube, opposite the Bulgarian fortress of Vidin. Pop. (1900) 7113. Calafat
is an important centre of the grain trade, and is connected by a branch
line with the principal Walachian railways, and by a steam ferry with
Vidin. It was founded in the 14th century by Genoese colonists, who
employed large numbers of workmen (_Calfats_) in repairing ships--which
industry gave its name to the place. In 1854 a Russian force was defeated
at Calafat by the Turks under Ahmed Pasha, who surprised the enemy's camp.
CALAH (so in the Bible; _Kalah_ in the Assyrian inscriptions), an ancient
city situated in the angle formed by the Tigris and [v.04 p.0965] the upper
Zab, 19 m. S. of Nineveh, and one of the capitals of Assyria. According to
the inscriptions, it was built by Shalmaneser I. about 1300 B.C., as a
residence city in place of the older Assur. After that it seems to have
fallen into decay or been destroyed, but was restored by Assur-nasir-pal,
about 880 B.C., and from that time to the overthrow of the Assyrian power
it remained a residence city of the Assyrian kings. It shared the fate of
Nineveh, was captured and destroyed by the Medes and Babylonians toward the
close of the 7th century, and from that time has remained a ruin. The site
was discovered by Sir A.H. Layard, in 1845, in the _tel_ of Nimrud. Hebrew
tradition (in the J narrative, Genesis x. 11, 12) mentions Calah as built
by Nimrod. Modern Arabic tradition likewise ascribes the ruins, like those
of Birs Nimrud, near Babylon, to Nimrod, because they are the most
prominent ruins of that region. Similarly the ancient dike in the river
Tigris at this point is ascribed to Nimrod. The ruin mounds of Nimrud
consist of an oblong enclosure, formed by the walls of the ancient city, of
which fifty-eight towers have been traced on the N. and about fifty on the
E. In the S.W. corner of this oblong is an elevated platform in the form of
a rectangular parallelogram, some 600 yds. from N. to S. and 400 yds. from
E. to W., raised on an average about 40 ft. above the plain, with a lofty
cone 140 ft. high in the N.W. corner. This is the remains of the raised
platform of unbaked brick, faced with baked bricks and stone, on which
stood the principal palaces and temples of the city, the cone at the N.W.
representing the _ziggurat_, or stage-tower, of the principal temple.
Originally on the banks of the Tigris, this platform now stands some
distance E. of the river. Here Layard conducted excavations from 1845 to
1847, and again from 1849 to 1851. The means at his disposal were
inadequate, his excavations were incomplete and also unscientific in that
his prime object was the discovery of inscriptions and museum objects; but
he was wonderfully successful in achieving the results at which he aimed,
and the numerous statues, monuments, inscribed stones, bronze objects and
the like found by him in the ruins of Calah are among the most precious
possessions of the British Museum. Excavations were also conducted by
Hormuzd Rassan in 1852-1854, and again in 1878, and by George Smith in
1873. But while supplementing in some important respects Layard's
excavations, this later work added relatively little to his discoveries
whether of objects or of facts. The principal buildings discovered at Calah
are:--(_a_) the North-West palace, south of the _ziggurat_, one of the most
complete and perfect Assyrian buildings known, about 350 ft. square,
consisting of a central court, 129 ft. by 90 ft., surrounded by a number of
halls and chambers. This palace was originally constructed by
Assur-nasir-pal I. (885-860 B.C.), and restored and reoccupied by Sargon
(722-705 B.C.). In it were found the winged lions, now in the British
Museum, the fine series of sculptured bas-reliefs glorifying the deeds of
Assur-nasir-pal in war and peace, and the large collection of bronze
vessels and implements, numbering over 200 pieces; (_b_) the Central
palace, in the interior of the mound, toward its southern end, erected by
Shalmaneser II. (860-825 B.C.) and rebuilt by Tiglath-pileser III. (745-727
B.C.). Here were found the famous black obelisk of Shalmaneser, now in the
British Museum, in the inscription on which the tribute of Jehu, son of
Omri, is mentioned, the great winged bulls, and also a fine series of slabs
representing the battles and sieges of Tiglath-pileser; (_c_) the
South-West palace, in the S.W. corner of the platform, an uncompleted
building of Esarhaddon (681-668 B.C.), who robbed the North-West and
Central palaces, effacing the inscriptions of Tiglath-pileser, to obtain
material for his construction; (_d_) the smaller West palace, between the
South-West and the North-West palaces, a construction of Hadad-nirari or
Adadnirari III. (812-783 B.C.); (_e_) the South-East palace, built by
Assur-etil-ilani, after 626 B.C., for his harem, in the S.E. corner of the
platform, above the remains of an older similar palace of Shalmaneser;
(_f_) two small temples of Assur-nasir-pal, in connexion with the
_ziggurat_ in the N.W. corner; and (_g_) a temple called E-Zida, and
dedicated to Nebo, near the South-East palace. From the number of colossal
figures of Nebo discovered here it would appear that the cult of Nebo was a
favourite one, at least during the later period. The other buildings on the
E. side of the platform had been ruined by the post-Assyrian use of the
mound for a cemetery, and for tunnels for the storage and concealment of
grain. While the ruins of Calah were remarkably rich in monumental
material, enamelled bricks, bronze and ivory objects and the like, they
yielded few of the inscribed clay tablets found in such great numbers at
Nineveh and various Babylonian sites. Not a few of the astrological and
omen tablets in the Kuyunjik collection of the British Museum, however,
although found at Nineveh, were executed, according to their own testimony,
at Calah for the _rab-dup-[vs]arr[=e]_ or principal librarian during the
reigns of Sargon and Sennacherib (716-684 B.C.). From this it would appear
that there was at that time at Calah a library or a collection of archives
which was later removed to Nineveh. In the prestige of antiquity and
religious renown, Calah was inferior to the older capital, Assur, while in
population and general importance it was much inferior to the neighbouring
Nineveh. There is no proper ground for regarding it, as some Biblical
scholars of a former generation did, through a false interpretation of the
book of Jonah, as a part or suburb of Nineveh.
See A.H. Layard, _Nineveh and its Remains_ (London, 1849); George Smith,
_Assyrian Discoveries_ (London, 1883); Hormuzd Rassam, _Ashur and the Land
of Nimrod_ (London and New York, 1897).
(J. P. PE.)
CALAHORRA (anc. _Calagurris_), a city of northern Spain, in the province of
Logroño; on the left bank of the river Cidacos, which enters the Ebro 3 m.
E., and on the Bilbao-Saragossa railway. Pop. (1900) 9475. Calahorra is
built on the slope of a hill overlooking the wide Ebro valley, which
supplies its markets with an abundance of grain, wine, oil and flax. Its
cathedral, which probably dates from the foundation of the see of Calahorra
in the 5th century, was restored in 1485, and subsequently so much altered
that little of the original Gothic structure survives. The Casa Santa,
annually visited by many thousands of pilgrims on the 31st of August, is
said to contain the bodies of the martyrs Emeterius and Celedonius, who
were beheaded in the 3rd or 4th century, on the site now occupied by the
cathedral. Their heads, according to local legend, were cast into the Ebro,
and, after floating out to sea and rounding the Iberian peninsula, are now
preserved at Santander.
The chief remains of the Roman Calagurris are the vestiges of an aqueduct
and an amphitheatre. Calagurris became famous in 76 B.C., when it was
successfully defended against Pompey by the adherents of Sertorius. Four
years later it was captured by Pompey's legate, Afranius, after starvation
had reduced the garrison to cannibalism. Under Augustus (31 B.C.-A.D. 14)
Calagurris received the privileges of Roman citizenship, and at a later
date it was given the additional name of _Nassica_ to distinguish it from
the neighbouring town of _Calagurris Fibularensis_, the exact site of which
is uncertain. The rhetorician Quintilian was born at Calagurris Nassica
about A.D. 35.
CALAIS, a seaport and manufacturing town of northern France, in the
department of Pas-de-Calais, 18 m. E.S.E. of Dover, and 185 m. N. of Paris
by the Northern railway. Pop. (1906) 59,623. Calais, formerly a celebrated
fortress, is defended by four forts, not of modern construction, by a
citadel built in 1560, which overlooks it on the west, and by batteries.
The old town stands on an island hemmed in by the canal and the harbour
basins, which divide it from the much more extensive manufacturing quarter
of St Pierre, enveloping it on the east and south. The demolition of the
ramparts of Old Calais was followed by the construction of a new circle of
defences, embracing both the old and new quarters, and strengthened by a
deep moat. In the centre of the old town is the Place d'Armes, in which
stands the former hôtel-de-ville (rebuilt in 1740, restored in 1867), with
busts of Eustache de St Pierre, Francis, duke of Guise, and Cardinal
Richelieu. The belfry belongs to the 16th and early 17th century. Close by
is the Tour du Guet, or watch-tower, used as a lighthouse until 1848. The
church of Notre-Dame, built during the English occupancy of Calais, has a
[v.04 p.0966] fine high altar of the 17th century; its lofty tower serves
as a landmark for sailors. A gateway flanked by turrets (14th century) is a
relic of the Hôtel de Guise, built as a gild hall for the English
woolstaplers, and given to the duke of Guise as a reward for the recapture
of Calais. The modern town-hall and a church of the 19th century are the
chief buildings of the quarter of St Pierre. Calais has a board of
trade-arbitrators, a tribunal and a chamber of commerce, a commercial and
industrial school, and a communal college.
The harbour is entered from the roads by way of a channel leading to the
outer harbour which communicates with a floating basin 22 acres in extent,
on the east, and with the older and less commodious portion of the harbour
to the north and west of the old town. The harbour is connected by canals
with the river Aa and the navigable waterways of the department.
Calais is the principal port for the continental passenger traffic with
England carried on by the South-Eastern & Chatham and the Northern of
France railways. The average number of passengers between Dover and Calais
for the years 1902-1906 inclusive was 315,012. Trade is chiefly with the
United Kingdom. The principal exports are wines, especially champagne,
spirits, hay, straw, wool, potatoes, woven goods, fruit, glass-ware, lace
and metal-ware. Imports include cotton and silk goods, coal, iron and
steel, petroleum, timber, raw wool, cotton yarn and cork. During the five
years 1901-1905 the average annual value of exports was £8,388,000
(£6,363,000 in the years 1896-1900), of imports £4,145,000 (£3,759,000 in
1896-1900). In 1905, exclusive of passenger and mail boats, there entered
the port 848 vessels of 312,477 tons and cleared 857 of 305,284 tons, these
being engaged in the general carrying trade of the port. The main industry
of Calais is the manufacture of tulle and lace, for which it is the chief
centre in France. Brewing, saw-milling, boat-building, and the manufacture
of biscuits, soap and submarine cables are also carried on. Deep-sea and
coast fishing for cod, herring and mackerel employ over 1000 of the
inhabitants.
Calais was a petty fishing-village, with a natural harbour at the mouth of
a stream, till the end of the 10th century. It was first improved by
Baldwin IV., count of Flanders, in 997, and afterwards, in 1224, was
regularly fortified by Philip Hurepel, count of Boulogne. It was besieged
in 1346, after the battle of Crécy, by Edward III. and held out resolutely
by the bravery of Jean de Vienne, its governor, till after nearly a year's
siege famine forced it to surrender. Its inhabitants were saved from
massacre by the devotion of Eustache de St Pierre and six of the chief
citizens, who were themselves spared at the prayer of Queen Philippa. The
city remained in the hands of the English till 1558, when it was taken by
Francis, duke of Guise, at the head of 30,000 men from the ill-provided
English garrison, only 800 strong, after a siege of seven days. From this
time the _Calaisis_ or territory of Calais was known as the _Pays
Reconquis_. It was held by the Spaniards from 1595 to 1598, but was
restored to France by the treaty of Vervins.
CALAIS, a city and sub-port of entry of Washington county, Maine, U.S.A.,
on the Saint Croix river, 12 m. from its mouth, opposite Saint Stephens,
New Brunswick, with which it is connected by bridges. Pop. (1890)
7290;(1900) 7655 (1908 being foreign-born); (1910) 6116. It is served by
the Washington County railway (102.5 m. to Washington Junction, where it
connects with the Maine Central railway), and by steamboat lines to Boston,
Portland and Saint Johns. In the city limits are the post-offices of
Calais, Milltown and Red Beach. The city has a small public library. The
valley here is wide and deep, the banks of the river bold and picturesque,
and the tide rises and falls about 25 ft. The city has important interests
in lumber, besides foundries, machine shops, granite works--there are
several granite (notably red granite) quarries in the vicinity--a tannery,
and manufactories of shoes and calcined plaster. Big Island, now in the
city of Calais, was visited in the winter of 1604-1605 by Pierre du Guast,
sieur de Monts. Calais was first settled in 1779, was incorporated as a
town in 1809, and was chartered as a city in 1851.
CALAÏS and ZETES (the Boreadae), in Greek mythology, the winged twin sons
of Boreas and Oreithyia. On their arrival with the Argonauts at Salmydessus
in Thrace, they liberated their sister Cleopatra, who had been thrown into
prison with her two sons by her husband Phineus, the king of the country
(Sophocles, _Antigone_, 966; Diod. Sic. iv. 44). According to another
story, they delivered Phineus from the Harpies (_q.v._), in pursuit of whom
they perished (Apollodorus i. 9; iii. 15). Others say that they were slain
by Heracles near the island of Tenos, in consequence of a quarrel with
Tiphys, the pilot of the Argonauts, or because they refused to wait during
the search for Hylas, the favourite of Heracles (Hyginus, _Fab._, 14. 273;
schol. on Apollonius Rhodius i. 1304). They were changed by the gods into
winds, and the pillars over their tombs in Tenos were said to wave whenever
the wind blew from the north. Like the Harpies, Calaïs and Zetes are
obvious personifications of winds. Legend attributed the foundation of
Cales in Campania to Calaïs (Silius Italicus viii. 512).
CALAMINE, a mineral species consisting of zinc carbonate, ZnCO_3, and
forming an important ore of zinc. It is rhombohedral in crystallization and
isomorphous with calcite and chalybite. Distinct crystals are somewhat
rare; they have the form of the primitive rhombohedron (rr' = 72° 20'), the
faces of which are generally curved and rough. Botryoidal and stalactitic
masses are more common, or again the mineral may be compact and granular or
loose and earthy. As in the other rhombohedral carbonates, the crystals
possess perfect cleavages parallel to the faces of the rhombohedron. The
hardness is 5; specific gravity, 4.4. The colour of the pure mineral is
white; more often it is brownish, sometimes green or blue: a bright-yellow
variety containing cadmium has been found in Arkansas, and is known locally
as "turkey-fat ore." The pure material contains 52% of zinc, but this is
often partly replaced isomorphously by small amounts of iron and manganese,
traces of calcium and magnesium, and sometimes by copper or cadmium.
Calamine is found in beds and veins in limestone rocks, and is often
associated with galena and blende. It is a product of alteration of blende,
having been formed from this by the action of carbonated waters; or in many
cases the zinc sulphide may have been first oxidized to sulphate, which in
solution acted on the surrounding limestone, producing zinc carbonate. The
latter mode of origin is suggested by the frequent occurrence of calamine
pseudomorphous after calcite, that is, having the form of calcite crystals.
Deposits of calamine have been extensively mined in the limestones of the
Mendip Hills, in Derbyshire, and at Alston Moor in Cumberland. It also
occurs in large amount in the province of Santander in Spain, in Missouri,
and at several other places where zinc ores are mined. The best crystals of
the mineral were found many years ago at Chessy near Lyons; these are
rhombohedra of a fine apple-green colour. A translucent botryoidal calamine
banded with blue and green is found at Laurion in Greece, and has sometimes
been cut and polished for small ornaments such as brooches.
The name calamine (German, _Galmei_), from _lapis calaminaris_, a Latin
corruption of cadmia ([Greek: kadmia]), the old name for zinc ores in
general (G. Agricola in 1546 derived it from the Latin _calamus_, a reed),
was early used indiscriminately for the carbonate and the hydrous silicate
of zinc, and even now both species are included by miners under the same
term. The two minerals often closely resemble each other in appearance, and
can usually only be distinguished by chemical analysis; they were first so
distinguished by James Smithson in 1803. F.S. Beudant in 1832 restricted
the name calamine to the hydrous silicate and proposed the name
"smithsonite" for the carbonate, and these meanings of the terms are now
adopted by Dana and many other mineralogists. Unfortunately, however, in
England (following Brooke and Miller, 1852) these designations have been
reversed, calamine being used for the carbonate and smithsonite for the
silicate. This unfortunate confusion is somewhat lessened by the use of the
terms zinc-spar and hemimorphite (_q.v._) for the carbonate and silicate
respectively.
(L. J. S.)
[v.04 p.0967] CALAMIS, an Athenian sculptor of the first half of the 5th
century B.C. He made statues of Apollo the averter of ill, Hermes the
ram-bearer, Aphrodite and other deities, as well as part of a chariot group
for Hiero, king of Syracuse. His works are praised by ancient critics for
delicacy and grace, as opposed to breadth and force. Archaeologists are
disposed to regard the bronze charioteer recently found at Delphi as a work
of Calamis; but the evidence is not conclusive (see GREEK ART).
CALAMY, EDMUND, known as "the elder" (1600-1666), English Presbyterian
divine, was born of Huguenot descent in Walbrook, London, in February 1600,
and educated at Pembroke Hall, Cambridge, where his opposition to the
Arminian party, then powerful in that society, excluded him from a
fellowship. Nicholas Felton, bishop of Ely, however, made him his chaplain,
and gave him the living of St Mary, Swaffham Prior, which he held till
1626. He then removed to Bury St Edmunds, where he acted as lecturer for
ten years, retiring when his bishop (Wren) insisted on the observance of
certain ceremonial articles. In 1636 he was appointed rector (or perhaps
only lecturer) of Rochford in Essex, which was so unhealthy that he had
soon to leave it, and in 1639 he was elected to the perpetual curacy of St
Mary Aldermanbury in London, where he had a large following. Upon the
opening of the Long Parliament he distinguished himself in defence of the
Presbyterian cause, and had a principal share in writing the conciliatory
work known as _Smectymnuus_, against Bishop Joseph Hall's presentation of
episcopacy. The initials of the names of the several contributors formed
the name under which it was published, viz., S. Marshal, E. Calamy, T.
Young, M. Newcomen and W. Spurstow. Calamy was an active member in the
Westminster assembly of divines, and, refusing to advance to
Congregationalism, found in Presbyterianism the middle course which best
suited his views of theology and church government. He opposed the
execution of Charles I., lived quietly under the Commonwealth, and was
assiduous in promoting the king's return; for this he was afterwards
offered the bishopric of Coventry and Lichfield, but declined it, it is
said, on his wife's persuasion. He was made one of Charles's chaplains, and
vainly tried to secure the legal ratification of Charles's declaration of
the 25th of October 1660. He was ejected for Nonconformity in 1662, and was
so affected by the sight of the devastation caused by the great fire of
London that he died shortly afterwards, on the 29th of October 1666. He was
buried in the ruins of his church, near the place where the pulpit had
stood. His publications are almost entirely sermons. His eldest son
(Edmund), known as "the younger," was educated at Cambridge, and was
ejected from the rectory of Moreton, Essex, in 1662. He was of a retiring
disposition and moderate views, and died in 1685.
CALAMY, EDMUND (1671-1732), English Nonconformist divine, the only son of
Edmund Calamy "the younger," was born in London, in the parish of St Mary
Aldermanbury, on the 5th of April 1671. He was sent to various schools,
including Merchant Taylors', and in 1688 proceeded to the university of
Utrecht. While there, he declined an offer of a professor's chair in the
university of Edinburgh made to him by the principal, William Carstares,
who had gone over on purpose to find suitable men for such posts. After his
return to England in 1691 he began to study divinity, and on Baxter's
advice went to Oxford, where he was much influenced by Chillingworth. He
declined invitations from Andover and Bristol, and accepted one as
assistant to Matthew Sylvester at Blackfriars (1692). In June 1694 he was
publicly ordained at Annesley's meeting-house in Little St Helen's, and
soon afterwards was invited to become assistant to Daniel Williams in Hand
Alley, Bishopsgate. In 1702 he was chosen one of the lecturers in Salters'
Hall, and in 1703 he succeeded Vincent Alsop as pastor of a large
congregation in Westminster. In 1709 Calamy made a tour through Scotland,
and had the degree of doctor of divinity conferred on him by the
universities of Edinburgh, Aberdeen and Glasgow. Calamy's forty-one
publications are mainly sermons, but his fame rests on his nonconformist
biographies. His first essay was a table of contents to Baxter's
_Narrative_ of his life and times, which was sent to the press in 1696; he
made some remarks on the work itself and added to it an index, and,
reflecting on the usefulness of the book, he saw the expediency of
continuing it, as Baxter's history came no further than the year 1684.
Accordingly, he composed an abridgment of it, with an account of many other
ministers who were ejected after the restoration of Charles II.; their
apology, containing the grounds of their nonconformity and practice as to
stated and occasional communion with the Church of England; and a
continuation of their history until the year 1691. This work was published
in 1702. The most important chapter (ix.) is that which gives a detailed
account of the ministers ejected in 1662; it was afterwards published as a
distinct volume. He afterwards published a moderate defence of
Nonconformity, in three tracts, in answer to some tracts of Benjamin,
afterwards Bishop, Hoadly. In 1713 he published a second edition (2 vols.)
of his _Abridgment of Baxter's History_, in which, among various additions,
there is a continuation of the history through the reigns of William and
Anne, down to the passing of the Occasional Bill. At the end is subjoined
the reformed liturgy, which was drawn up and presented to the bishops in
1661. In 1718 he wrote a vindication of his grandfather and several other
persons against certain reflections cast upon them by Laurence Echard in
his _History of England_. In 1719 he published _The Church and the
Dissenters Compar'd as to Persecution_, and in 1728 appeared his
_Continuation of the Account_ of the ejected ministers and teachers, a
volume which is really a series of emendations of the previously published
account. He died on the 3rd of June 1732, having been married twice and
leaving six of his thirteen children to survive him. Calamy was a kindly
man, frankly self-conscious, but very free from jealousy. He was an able
diplomatist and generally secured his ends. His great hero was Baxter, of
whom he wrote three distinct memoirs. His eldest son Edmund (the fourth)
was a Presbyterian minister in London and died 1755; another son (Edmund,
the fifth) was a barrister who died in 1816; and this one's son (Edmund,
the sixth) died in 1850, his younger brother Michael, the last of the
direct Calamy line, surviving till 1876.
CALARASHI (_C[)a]l[)a]rasi_), the capital of the Jalomitza department,
Rumania, situated on the left bank of the Borcea branch of the Danube, amid
wide fens, north of which extends the desolate Baragan Steppe. Pop. (1900)
11,024. Calarashi has a considerable transit trade in wheat, linseed, hemp,
timber and fish from a broad mere on the west or from the Danube. Small
vessels carry cargo to Braila and Galatz, and a branch railway from
Calarashi traverses the Steppe from south to north, and meets the main line
between Bucharest and Constantza.
CALAS, JEAN (1698-1762), a Protestant merchant at Toulouse, whose legal
murder is a celebrated case in French history. His wife was an Englishwoman
of French extraction. They had three sons and three daughters. His son
Louis had embraced the Roman Catholic faith through the persuasions of a
female domestic who had lived thirty years in the family. In October 1761
another son, Antoine, hanged himself in his father's warehouse. The crowd,
which collected on so shocking a discovery, took up the idea that he had
been strangled by the family to prevent him from changing his religion, and
that this was a common practice among Protestants. The officers of justice
adopted the popular tale, and were supplied by the mob with what they
accepted as conclusive evidence of the fact. The fraternity of White
Penitents buried the body with great ceremony, and performed a solemn
service for the deceased as a martyr; the Franciscans followed their
example; and these formalities led to the popular belief in the guilt of
the unhappy family. Being all condemned to the rack in order to extort
confession, they appealed to the parlement; but this body, being as weak as
the subordinate magistrates, sentenced the father to the torture, ordinary
and extraordinary, to be broken alive upon the wheel, and then to be burnt
to ashes; which decree was carried into execution on the 9th of March 1762.
Pierre Calas, the surviving son, was banished for life; the rest were
acquitted. The distracted widow, however, found some friends, and among
them Voltaire, who laid her case before the council of state at [v.04
p.0968] Versailles. For three years he worked indefatigably to procure
justice, and made the Calas case famous throughout Europe (see VOLTAIRE).
Finally the king and council unanimously agreed to annul the proceeding of
the parlement of Toulouse; Calas was declared to have been innocent, and
every imputation of guilt was removed from the family.
See _Causes célèbres_, tome iv.; Raoul Allier, _Voltaire et Calas, une
erreur judiciaire au XVIII^e siècle_ (Paris, 1898); and biographies of
Voltaire.
CALASH (from Fr. _calèche_, derived from Polish _kolaska_, a wheeled
carriage), a light carriage with a folding hood; the Canadian calash is
two-wheeled and has a seat for the driver on the splash-board. The word is
also used for a kind of hood made of silk stretched over hoops, formerly
worn by women.
CALASIAO, a town of the province of Pangasinán, Luzon, Philippine Islands,
on a branch of the Agno river, about 4 m. S. by E. of Dagupan, the N.
terminal of the Manila & Dagupan railway. Pop. (1903) 16,539. In 1903,
after the census had been taken, the neighbouring town of Santa Barbara
(pop. 10,367) was annexed to Calasiao. It is in the midst of a fertile
district and has manufactures of hats and various woven fabrics.
CALASIO, MARIO DI (1550-1620), Italian Minorite friar, was born at a small
town in the Abruzzi whence he took his name. Joining the Franciscans at an
early age, he devoted himself to Oriental languages and became an authority
on Hebrew. Coming to Rome he was appointed by Paul V., whose confessor he
was, to the chair of Scripture at Ara Coeli, where he died on the 1st of
February 1620. Calasio is known by his _Concordantiae sacrorum Bibliorum
hebraicorum_, published in 4 vols. (Rome, 1622), two years after his death,
a work which is based on Nathan's _Hebrew Concordance_ (Venice, 1523). For
forty years Calasio laboured on this work, and he secured the assistance of
the greatest scholars of his age. The _Concordance_ evinces great care and
accuracy. All root-words are treated in alphabetical order and the whole
Bible has been collated for every passage containing the word, so as to
explain the original idea, which is illustrated from the cognate usages of
the Chaldee, Syrian, Rabbinical Hebrew and Arabic. Calasio gives under each
Hebrew word the literal Latin translation, and notes any existing
differences from the Vulgate and Septuagint readings. An incomplete English
translation of the work was published in London by Romaine in 1747. Calasio
also wrote a Hebrew grammar, _Canones generates linguae sanctatae_ (Rome,
1616), and the _Dictionarium hebraicum_ (Rome, 1617).
CALATAFIMI, a town of the province of Trapani, Sicily, 30 m. W.S.W. of
Palermo direct (51½ m. by rail). Pop. (1901) 11,426. The name of the town
is derived from the Saracenic castle of _Kalat-al-Fimi_ (castle of
Euphemius), which stands above it. The principal church contains a fine
Renaissance reredos in marble. Samuel Butler, the author of _Erewhon_, did
much of his work here. The battlefield where Garibaldi won his first
victory over the Neapolitans on the 15th of May 1860, lies 2 m. S.W.
CALATAYÚD, a town of central Spain, in the province of Saragossa, at the
confluence of the rivers Jalón and Jiloca, and on the Madrid-Saragossa and
Calatayúd-Sagunto railways. Pop. (1900) 11,526. Calatayúd consists of a
lower town, built on the left bank of the Jalón, and an upper or Moorish
town, which contains many dwellings hollowed out of the rock above and
inhabited by the poorer classes. Among a number of ecclesiastical
buildings, two collegiate churches are especially noteworthy. Santa Maria,
originally a mosque, has a lofty octagonal tower and a fine Renaissance
doorway, added in 1528; while Santo Sepulcro, built in 1141, and restored
in 1613, was long the principal church of the Spanish Knights Templar. In
commercial importance Calatayúd ranks second only to Saragossa among the
Aragonese towns, for it is the central market of the exceptionally fertile
expanse watered by the Jalón and Jiloca. About 2 m. E. are the ruins of the
ancient _Bilbilis_, where the poet Martial was born c. A.D. 40. It was
celebrated for its breed of horses, its armourers, its gold and its iron;
but Martial also mentions its unhealthy climate, due to the icy winds which
sweep down from the heights of Moncayo (7705 ft.) on the north. In the
middle ages the ruins were almost destroyed to provide stone for the
building of Calatayúd, which was founded by a Moorish amir named Ayub and
named _Kalat Ayub_, "Castle of Ayub." Calatayúd was captured by Alphonso I.
of Aragon in 1119.
CALATIA, an ancient town of Campania, Italy, 6 m. S.E. of Capua, on the Via
Appia, near the point where the Via Popillia branches off from it. It is
represented by the church of St. Giacomo alle Galazze. The Via Appia here,
as at Capua, abandons its former S.E. direction for a length of 2000 Oscan
ft. (1804½ English ft.), for which it runs due E. and then resumes its
course S.E. There are no ruins, but a considerable quantity of débris; and
the pre-Roman necropolis was partially excavated in 1882. Ten shafts lined
with slabs of tufa which were there found may have been the approaches to
tombs or may have served as wells. The history of Calatia is practically
that of its more powerful neighbour Capua, but as it lay near the point
where the Via Appia turns east and enters the mountains, it had some
strategic importance. In 313 B.C. it was taken by the Samnites and
recaptured by the dictator Q. Fabius; the Samnites captured it again in
311, but it must have been retaken at an unknown date. In the 3rd century
we find it issuing coins with an Oscan legend, but in 211 B.C. it shared
the fate of Capua. In 174 we hear of its walls being repaired by the
censors. In 59 B.C. a colony was established here by Caesar.
See Ch. Hülsen in Pauly-Wissowa, _Realencyclopädie_, iii. 1334 (Stuttgart,
1899).
CALAVERAS SKULL, a famous fossil cranium, reported by Professor J.D.
Whitney as found (1886) in the undisturbed auriferous gravels of Calaveras
county, California. The discovery at once raised the still discussed
question of "tertiary man" in the New World. Doubt has been thrown on the
genuineness of the find, as the age of the gravels is disputed and the
skull is of a type corresponding exactly with that of the present Indian
inhabitants of the district. Whitney assigns the fossil to late Tertiary
(Pliocene) times, and concludes that "man existed in California previous to
the cessation of volcanic activity in the Sierra Nevada, to the epoch of
the greatest extension of the glaciers in that region and to the erosion of
the present river cañons and valleys, at a time when the animal and
vegetable creation differed entirely from what they now are...." The
specimen is preserved in the Peabody museum, Cambridge, Mass.
CALBÁYOG, a town of the province of Sámar, Philippine Islands, on the W.
coast at the mouth of the Calbáyog river, about 30 m. N.W. of Catbalogan,
the capital, in lat. 12° 3' N. Pop. (1903) 15,895. Calbáyog has an
important export trade in hemp, which is shipped to Manila. Copra is also
produced in considerable quantity, and there is fine timber in the
vicinity. There are hot springs near the town. The neighbouring valleys of
the Gándara and Hippatan rivers are exceedingly fertile, but in 1908 were
uncultivated. The climate is very warm, but healthy. The language is
Visayan.
CALBE, or KALBE, a town of Germany, on the Saale, in Prussian Saxony. It is
known as Calbe-an-der-Saale, to distinguish it from the smaller town of
Calbe on the Milde in the same province. Pop. (1905) 12,281. It is a
railway junction, and among its industries are wool-weaving and the
manufacture of cloth, paper, stoves, sugar and bricks. Cucumbers and onions
are cultivated, and soft coal is mined in the neighbourhood.
CALCAR (or KALCKER), JOHN DE (1499-1546), Italian painter, was born at
Calcar, in the duchy of Cleves. He was a disciple of Titian at Venice, and
perfected himself by studying Raphael. He imitated those masters so closely
as to deceive the most skilful critics. Among his various pieces is a
Nativity, representing the angels around the infant Christ, which he
arranged so that the light emanated wholly from the child. He died at
Naples.
CALCEOLARIA, in botany, a genus belonging to the natural order
Scrophulariaceae, containing about 150 species of herbaceous or shrubby
plants, chiefly natives of the South American Andes of Peru and Chile. The
calceolaria of the present day has [v.04 p.0969] been developed into a
highly decorative plant, in which the herbaceous habit has preponderated.
The plants are now very generally raised annually from seed, which is sown
about the end of June in a mixture of loam, leaf-mould and sand, and, being
very small, must be only slightly covered. When the plants are large enough
to handle they are pricked out an inch or two apart into 3-inch or 5-inch
pots; when a little more advanced they are potted singly. They should be
wintered in a greenhouse with a night temperature of about 40°, occupying a
shelf near the light. By the end of February they should be moved into
8-inch or 10-inch pots, using a compost of three parts good turfy loam, one
part leaf-mould, and one part thoroughly rotten manure, with a fair
addition of sand. They need plenty of light and air, but must not be
subjected to draughts. When the pots get well filled with roots, they must
be liberally supplied with manure water. In all stages of growth the plants
are subject to the attacks of the green-fly, for which they must be
fumigated.
The so-called shrubby calceolarias used for bedding are increased from
cuttings, planted in autumn in cold frames, where they can be wintered,
protected from frost by the use of mats and a good layer of litter placed
over the glass and round the sides.
CALCHAQUI, a tribe of South American Indians, now extinct, who formerly
occupied northern Argentina. Stone and other remains prove them to have
reached a high degree of civilization. They offered a vigorous resistance
to the first Spanish colonists coming from Chile.
CALCHAS, of Mycenae or Megara, son of Thestor, the most famous soothsayer
among the Greeks at the time of the Trojan war. He foretold the duration of
the siege of Troy, and, when the fleet was detained by adverse winds at
Aulis, he explained the cause and demanded the sacrifice of Iphigeneia.
When the Greeks were visited with pestilence on account of Chryseis, he
disclosed the reasons of Apollo's anger. It was he who suggested that
Neoptolemus and Philoctetes should be fetched from Scyros and Lemnos to
Troy, and he was one of those who advised the construction of the wooden
horse. When the Greeks, on their journey home after the fall of Troy, were
overtaken by a storm, Calchas is said to have been thrown ashore at
Colophon. According to another story, he foresaw the storm and did not
attempt to return by sea. It had been predicted that he should die when he
met his superior in divination; and the prophecy was fulfilled in the
person of Mopsus, whom Calchas met in the grove of the Clarian Apollo near
Colophon. Having been beaten in a trial of soothsaying, Calchas died of
chagrin or committed suicide. He had a temple and oracle in Apulia.
Ovid, _Metam._ xii. 18 ff.; Homer, _Iliad_ i. 68, ii. 322; Strabo vi. p.
284, xiv. p. 642.
CALCITE, a mineral consisting of naturally occurring calcium carbonate,
CaCO_3, crystallizing in the rhombohedral system. With the exception of
quartz, it is the most widely distributed of minerals, whilst in the
beautiful development and extraordinary variety of form of its crystals it
is surpassed by none. In the massive condition it occurs as large
rock-masses (marble, limestone, chalk) which are often of organic origin,
being formed of the remains of molluscs, corals, crinoids, &c., the hard
parts of which consist largely of calcite.
The name calcite (Lat. _calx_, _calcis_, meaning burnt lime) is of
comparatively recent origin, and was first applied, in 1836, to the
"barleycorn" pseudomorphs of calcium carbonate after celestite from
Sangerhausen in Thuringia; it was not until about 1843 that the name was
used in its present sense. The mineral had, however, long been known under
the names calcareous spar and calc-spar, and the beautifully transparent
variety called Iceland-spar had been much studied. The strong double
refraction and perfect cleavages of Iceland-spar were described in detail
by Erasmus Bartholinus in 1669 in his book _Experimenta Crystalli Islandici
disdiaclastici_; the study of the same mineral led Christiaan Huygens to
discover in 1690 the laws of double refraction, and E.L. Malus in 1808 the
polarization of light.
An important property of calcite is the great ease with which it may be
cleaved in three directions; the three perfect cleavages are parallel to
the faces of the primitive rhombohedron, and the angle between them was
determined by W.H. Wollaston in 1812, with the aid of his newly invented
reflective goniometer, to be 74° 55'. The cleavage is of great help in
distinguishing calcite from other minerals of similar appearance. The
hardness of 3 (it is readily scratched with a knife), the specific gravity
of 2.72, and the fact that it effervesces briskly in contact with cold
dilute acids are also characters of determinative value.
[Illustration: FIGS. 1-6.--Crystals of Calcite.]
Crystals of calcite are extremely varied in form, but, as a rule, they may
be referred to four distinct habits, namely: rhombohedral, prismatic,
scalenohedral and tabular. The primitive rhombohedron, r {100} (fig. 1), is
comparatively rare except in combination with other forms. A flatter
rhombohedron, e {110}, is shown in fig. 2, and a more acute one, f {11-1},
in fig. 3. These three rhombohedra are related in such a manner that, when
in combination, the faces of r truncate the polar edges of f, and the faces
of e truncate the edges of r. The crystal of prismatic habit shown in fig.
4 is a combination of the prism m {2-1-1} and the rhombohedron e {110};
fig. 5 is a combination of the scalenohedron v {20-1} and the rhombohedron
r {100}; and the crystal of tabular habit represented in fig. 6 is a
combination of the basal pinacoid c {111}, prism m {2-1-1}, and
rhombohedron e {110}. In these figures only six distinct forms (r, e, f, m,
v, c) are represented, but more than 400 have been recorded for calcite,
whilst the combinations of them are almost endless.
Depending on the habits of the crystals, certain trivial names have been
used, such, for example, as dog-tooth-spar for the crystals of
scalenohedral habit, so common in the Derbyshire lead mines and limestone
caverns; nail-head-spar for crystals terminated by the obtuse rhombohedron
e, which are common in the lead mines of Alston Moor in Cumberland;
slate-spar (German _Schieferspath_) for crystals of tabular habit, and
sometimes as thin as paper: cannon-spar for crystals of prismatic habit
terminated by the basal pinacoid c.
Calcite is also remarkable for the variety and perfection of its twinned
crystals. Twinned crystals, though not of infrequent occurrence, are,
however, far less common than simple (untwinned) crystals. No less than
four well-defined twin-laws are to be distinguished:--
[Illustration: FIG. 7-10.--Twinned Crystals of Calcite.]
i. Twin-plane c (111).--Here there is rotation of one portion with respect
to the other through 180° about the principal (trigonal) axis, which is
perpendicular to the plane c (111); or the same result may be obtained by
reflection across this plane. Fig. 7 shows a prismatic crystal (like fig.
4) twinned in this manner, and fig. 8 represents a twinned scalenohedron v
{20-1}.
ii. Twin-plane e (110).--The principal axes of the two portions are
inclined at an angle of 52° 30½'. Repeated twinning on this plane is very
common, and the twin-lamellae (fig. 9) to which it gives rise are often to
be observed in the grains of calcite of crystalline limestones which have
been subjected to pressure. This lamellar twinning is of secondary origin;
it may be readily produced artificially by pressure, for example, by
pressing a knife into the edge of a cleavage rhombohedron.
[v.04 p.0970] iii. Twin-plane r (100).--Here the principal axes of the two
portions are nearly at right angles (89° 14'), and one of the directions of
cleavage in both portions is parallel to the twin-plane. Fine crystals of
prismatic habit twinned according to this law were formerly found in
considerable numbers at Wheal Wrey in Cornwall, and of scalenohedral habit
at Eyam in Derbyshire and Cleator Moor in Cumberland; those from the last
two localities are known as "butterfly twins" or "heart-shaped twins" (fig.
10), according to their shape.
iv. Twin-plane f (11-1).--The principal axes are here inclined at 53° 46'.
This is the rarest twin-law of calcite.
Calcite when pure, as in the well-known Iceland-spar, is perfectly
transparent and colourless. The lustre is vitreous. Owing to the presence
of various impurities, the transparency and colour may vary considerably.
Crystals are often nearly white or colourless, usually with a slight
yellowish tinge. The yellowish colour is in most cases due to the presence
of iron, but in some cases it has been proved to be due to organic matter
(such as apocrenic acid) derived from the humus overlying the rocks in
which the crystals were formed. An opaque calcite of a grass-green colour,
occurring as large cleavage masses in central India and known as hislopite,
owes its colour to enclosed "green-earth" (glauconite and celadonite). A
stalagmitic calcite of a beautiful purple colour, from Reichelsdorf in
Hesse, is coloured by cobalt.
Optically, calcite is uniaxial with negative bi-refringence, the index of
refraction for the ordinary ray being greater than for the extraordinary
ray; for sodium-light the former is 1.6585 and the latter 1.4862. The
difference, 0.1723, between these two indices gives a measure of the
bi-refringence or double refraction.
Although the double refraction of some other minerals is greater than that
of calcite (_e.g._ for cinnabar it is 0.347, and for calomel 0.683), yet
this phenomenon can be best demonstrated in calcite, since it is a mineral
obtainable in large pieces of perfect transparency. Owing to the strong
double refraction and the consequent wide separation of the two polarized
rays of light traversing the crystal, an object viewed through a cleavage
rhombohedron of Iceland-spar is seen double, hence the name
doubly-refracting spar. Iceland-spar is extensively used in the
construction of Nicol's prisms for polariscopes, polarizing microscopes and
saccharimeters, and of dichroscopes for testing the pleochroism of
gem-stones.
Chemically, calcite has the same composition as the orthorhombic aragonite
(_q.v._), these minerals being dimorphous forms of calcium carbonate.
Well-crystallized material, such as Iceland-spar, usually consists of
perfectly pure calcium carbonate, but at other times the calcium may be
isomorphously replaced by small amounts of magnesium, barium, strontium,
manganese, zinc or lead. When the elements named are present in large
amount we have the varieties dolomitic calcite, baricalcite,
strontianocalcite, ferrocalcite, manganocalcite, zincocalcite and
plumbocalcite, respectively.
Mechanically enclosed impurities are also frequently present, and it is to
these that the colour is often due. A remarkable case of enclosed
impurities is presented by the so-called Fontainbleau limestone, which
consists of crystals of calcite of an acute rhombohedral form (fig. 3)
enclosing 50 to 60% of quartz-sand. Similar crystals, but with the form of
an acute hexagonal pyramid, and enclosing 64% of sand, have recently been
found in large quantity over a wide area in South Dakota, Nebraska and
Wyoming. The case of hislopite, which encloses up to 20% of "green earth,"
has been noted above.
In addition to the varieties of calcite noted above, some others, depending
on the state of aggregation of the material, are distinguished. A finely
fibrous form is known as satin-spar (_q.v._), a name also applied to
fibrous gypsum: the most typical example of this is the snow-white
material, often with a rosy tinge and a pronounced silky lustre, which
occurs in veins in the Carboniferous shales of Alston Moor in Cumberland.
Finely scaly varieties with a pearly lustre are known as argentine and
aphrite (German _Schaumspath_); soft, earthy and dull white varieties as
agaric mineral, rock-milk, rock-meal, &c.--these form a transition to
marls, chalk, &c. Of the granular and compact forms numerous varieties are
distinguished (see LIMESTONE and MARBLE). In the form of stalactites
calcite is of extremely common occurrence. Each stalactite usually consists
of an aggregate of radially arranged crystalline individuals, though
sometimes it may consist of a single individual with crystal faces
developed at the free end. Onyx-marbles or Oriental alabaster (see
ALABASTER) and other stalagmitic deposits also consist of calcite, and so
do the allied deposits of travertine, calc-sinter or calc-tufa.
The modes of occurrence of calcite are very varied. It is a common gangue
mineral in metalliferous deposits, and in the form of crystals is often
associated with ores of lead, iron, copper and silver. It is a common
product of alteration in igneous rocks, and frequently occurs as
well-developed crystals in association with zeolites lining the
amygdaloidal cavities of basaltic and other rocks. Veins and cavities in
limestones are usually lined with crystals of calcite. The wide
distribution, under various conditions, of crystallized calcite is readily
explained by the solubility of calcium carbonate in water containing carbon
dioxide, and the ease with which the material is again deposited in the
crystallized state when the carbon dioxide is liberated by evaporation. On
this also depends the formation of stalactites and calc-sinter.
Localities at which beautifully crystallized specimens of calcite are found
are extremely numerous. For beauty of crystals and variety of forms the
haematite mines of the Cleator Moor district in west Cumberland and the
Furness district in north Lancashire are unsurpassed. The lead mines of
Alston in Cumberland and of Derbyshire, and the silver mines of Andreasberg
in the Harz and Guanajuato in Mexico have yielded many fine specimens. From
the zinc mines of Joplin in Missouri enormous crystals of golden-yellow and
amethystine colours have been recently obtained. At all the localities here
mentioned the crystals occur with metalliferous ores. In Iceland the mode
of occurrence is quite distinct, the mineral being here found in a cavity
in basalt.
The quarry, which since the 19th century has supplied the famous
Iceland-spar, is in a cavity in basalt, the cavity itself measuring 12 by 5
yds. in area and about 10 ft. in height. It is situated quite close to the
farm Helgustadir, about an hour's ride from the trading station of
Eskifjordur on Reydar Fjordur, on the east coast of Iceland. This cavity
when first found was filled with pure crystallized masses and enormous
crystals. The crystals measure up to a yard across, and are rhombohedral or
scalenohedral in habit; their faces are usually dull and corroded or coated
with stilbite. In recent years much of the material taken out has not been
of sufficient transparency for optical purposes, and this, together with
the very limited supply, has caused a considerable rise in price. Only very
occasionally has calcite from any locality other than Iceland been used for
the construction of a Nicol's prism.
(L. J. S.)
CALCIUM [symbol Ca, atomic weight 40.0 (O=16)], a metallic chemical
element, so named by Sir Humphry Davy from its [v.04 p.0971] occurrence in
chalk (Latin _calx_). It does not occur in nature in the free state, but in
combination it is widely and abundantly diffused. Thus the sulphate
constitutes the minerals anhydrite, alabaster, gypsum, and selenite; the
carbonate occurs dissolved in most natural waters and as the minerals
chalk, marble, calcite, aragonite; also in the double carbonates such as
dolomite, bromlite, barytocalcite; the fluoride as fluorspar; the
fluophosphate constitutes the mineral apatite; while all the more important
mineral silicates contain a proportion of this element.
_Extraction._--Calcium oxide or lime has been known from a very remote
period, and was for a long time considered to be an elementary or
undecomposable earth. This view was questioned in the 18th century, and in
1808 Sir Humphry Davy (_Phil. Trans._, 1808, p. 303) was able to show that
lime was a combination of a metal and oxygen. His attempts at isolating
this metal were not completely successful; in fact, metallic calcium
remained a laboratory curiosity until the beginning of the 20th century.
Davy, inspired by his successful isolation of the metals sodium and
potassium by the electrolysis of their hydrates, attempted to decompose a
mixture of lime and mercuric oxide by the electric current; an amalgam of
calcium was obtained, but the separation of the mercury was so difficult
that even Davy himself was not sure as to whether he had obtained pure
metallic calcium. Electrolysis of lime or calcium chloride in contact with
mercury gave similar results. Bunsen (_Ann._, 1854, 92, p. 248) was more
successful when he electrolysed calcium chloride moistened with
hydrochloric acid; and A. Matthiessen (_Jour. Chem. Soc._, 1856, p. 28)
obtained the metal by electrolysing a mixture of fused calcium and sodium
chlorides. Henri Moissan obtained the metal of 99% purity by electrolysing
calcium iodide at a low red heat, using a nickel cathode and a graphite
anode; he also showed that a more convenient process consisted in heating
the iodide with an excess of sodium, forming an amalgam of the product, and
removing the sodium by means of absolute alcohol (which has but little
action on calcium), and the mercury by distillation.
The electrolytic isolation of calcium has been carefully investigated, and
this is the method followed for the commercial production of the metal. In
1902 W. Borchers and L. Stockem (_Zeit. für Electrochemie_, 1902, p. 8757)
obtained the metal of 90% purity by electrolysing calcium chloride at a
temperature of about 780°, using an iron cathode, the anode being the
graphite vessel in which the electrolysis was carried out. In the same
year, O. Ruff and W. Plato (_Ber._ 1902, 35, p. 3612) employed a mixture of
calcium chloride (100 parts) and fluorspar (16.5 parts), which was fused in
a porcelain crucible and electrolysed with a carbon anode and an iron
cathode. Neither of these processes admitted of commercial application, but
by a modification of Ruff and Plato's process, W. Ruthenau and C. Suter
have made the metal commercially available. These chemists electrolyse
either pure calcium chloride, or a mixture of this salt with fluorspar, in
a graphite vessel which serves as the anode. The cathode consists of an
iron rod which can be gradually raised. On electrolysis a layer of metallic
calcium is formed at the lower end of this rod on the surface of the
electrolyte; the rod is gradually raised, the thickness of the layer
increases, and ultimately a rod of metallic calcium, forming, as it were, a
continuation of the iron cathode, is obtained. This is the form in which
calcium is put on the market.
An idea as to the advance made by this method is recorded in the variation
in the price of calcium. At the beginning of 1904 it was quoted at 5s. per
gram, £250 per kilogram or £110 per pound; about a year later the price was
reduced to 21s. per kilogram, or 12s. per kilogram in quantities of 100
kilograms. These quotations apply to Germany; in the United Kingdom the
price (1905) varied from 27s. to 30s. per kilogram (12s. to 13s. per lb.).
_Properties._--A freshly prepared surface of the metal closely resembles
zinc in appearance, but on exposure to the air it rapidly tarnishes,
becoming yellowish and ultimately grey or white in colour owing to the
information of a surface layer of calcium hydrate. A faint smell of
acetylene may be perceived during the oxidation in moist air; this is
probably due to traces of calcium carbide. It is rapidly acted on by water,
especially if means are taken to remove the layer of calcium hydrate formed
on the metal; alcohol acts very slowly. In its chemical properties it
closely resembles barium and strontium, and to some degree magnesium; these
four elements comprise the so-called metals of the "alkaline earths." It
combines directly with most elements, including nitrogen; this can be taken
advantage of in forming almost a perfect vacuum, the oxygen combining to
form the oxide, CaO, and the nitrogen to form the nitride, Ca_3N_2. Several
of its physical properties have been determined by K. Arndt (_Ber._, 1904,
37, p. 4733). The metal as prepared by electrolysis generally contains
traces of aluminium and silica. Its specific gravity is 1.54, and after
remelting 1.56; after distillation it is 1.52. It melts at about 800°, but
sublimes at a lower temperature.
_Compounds._--Calcium hydride, obtained by heating electrolytic calcium in
a current of hydrogen, appears in commerce under the name hydrolite. Water
decomposes it to give hydrogen free from ammonia and acetylene, 1 gram
yielding about 100 ccs. of gas (Prats Aymerich, _Abst. J.C.S._, 1907, ii p.
460). Calcium forms two oxides--the monoxide, CaO, and the dioxide, CaO_2.
The monoxide and its hydrate are more familiarly known as lime (_q.v._) and
slaked-lime. The dioxide was obtained as the hydrate, CaO_2·8H_2O, by P.
Thénard (_Ann. Chim. Phys._, 1818, 8, p. 213), who precipitated lime-water
with hydrogen peroxide. It is permanent when dry; on heating to 130° C. it
loses water and gives the anhydrous dioxide as an unstable, pale
buff-coloured powder, very sparingly soluble in water. It is used as an
antiseptic and oxidizing agent.
Whereas calcium chloride, bromide, and iodide are deliquescent solids, the
fluoride is practically insoluble in water; this is a parallelism to the
soluble silver fluoride, and the insoluble chloride, bromide and iodide.
_Calcium fluoride_, CaF_2, constitutes the mineral fluor-spar (_q.v._), and
is prepared artificially as an insoluble white powder by precipitating a
solution of calcium chloride with a soluble fluoride. One part dissolves in
26,000 parts of water. _Calcium chloride_, CaCl_2, occurs in many natural
waters, and as a by-product in the manufacture of carbonic acid (carbon
dioxide), and potassium chlorate. Aqueous solutions deposit crystals
containing 2, 4 or 6 molecules of water. Anhydrous calcium chloride,
prepared by heating the hydrate to 200° (preferably in a current of
hydrochloric acid gas, which prevents the formation of any oxychloride), is
very hygroscopic, and is used as a desiccating agent. It fuses at 723°. It
combines with gaseous ammonia and forms crystalline compounds with certain
alcohols. The crystallized salt dissolves very readily in water with a
considerable absorption of heat; hence its use in forming "freezing
mixtures." A temperature of -55°C. is obtained by mixing 10 parts of the
hexahydrate with 7 parts of snow. A saturated solution of calcium chloride
contains 325 parts of CaCl_2 to 100 of water at the boiling point (179.5°).
Calcium iodide and bromide are white deliquescent solids and closely
resemble the chloride.
_Chloride of lime_ or "bleaching powder" is a calcium chlor-hypochlorite or
an equimolecular mixture of the chloride and hypochlorite (see ALKALI
MANUFACTURE and BLEACHING).
_Calcium carbide_, CaC_2, a compound of great industrial importance as a
source of acetylene, was first prepared by F. Wohler. It is now
manufactured by heating lime and carbon in the electric furnace (see
ACETYLENE). Heated in chlorine or with bromine, it yields carbon and
calcium chloride or bromide; at a dull red heat it burns in oxygen, forming
calcium carbonate, and it becomes incandescent in sulphur vapour at 500°,
forming calcium sulphide and carbon disulphide. Heated in the electric
furnace in a current of air, it yields calcium cyanamide (see CYANAMIDE).
_Calcium carbonate_, CaCO_3, is of exceptionally wide distribution in both
the mineral and animal kingdoms. It constitutes the bulk of the chalk
deposits and limestone rocks; it forms over one-half of the mineral
dolomite and the rock magnesium limestone; it occurs also as the dimorphous
minerals aragonite (_q.v._) and calcite (_q.v._). Tuff (_q.v._) and
travertine are calcareous deposits found in volcanic districts. Most
natural waters contain it dissolved in carbonic acid; this confers
"temporary hardness" on the water. The dissipation of the dissolved carbon
dioxide results in the formation of "fur" in kettles or boilers, and if the
solution is falling, as from the roof of a cave, in the formation of
stalactites and stalagmites. In the animal kingdom it occurs as both
calcite and aragonite in the tests of the foraminifera, echinoderms,
brachiopoda, and mollusca; also in the skeletons of sponges and corals.
Calcium carbonate is obtained as a white precipitate, almost insoluble in
water (1 part requiring 10,000 of water for solution), by mixing solutions
of a carbonate and a calcium salt. Hot or dilute cold solutions deposit
minute orthorhombic crystals of aragonite, cold saturated or moderately
strong solutions, hexagonal (rhombohedral) crystals of calcite. Aragonite
is the least stable form; crystals have been found altered to calcite.
_Calcium nitride_, Ca_3N_2, is a greyish-yellow powder formed by heating
calcium in air or nitrogen; water decomposes it with evolution of ammonia
(see H. Moissan, _Compt. Rend._, 127, p. 497).
_Calcium nitrate_, Ca(NO_3)_2·4H_2O, is a highly deliquescent salt, [v.04
p.0972] crystallizing in monoclinic prisms, and occurring in various
natural waters, as an efflorescence in limestone caverns, and in the
neighbourhood of decaying nitrogenous organic matter. Hence its synonyms,
"wall-saltpetre" and "lime-saltpetre"; from its disintegrating action on
mortar, it is sometimes referred to as "saltpetre rot." The anhydrous
nitrate, obtained by heating the crystallized salt, is very phosphorescent,
and constitutes "Baldwin's phosphorus." A basic nitrate,
Ca(NO_3)_2·Ca(OH)_2·3H_2O, is obtained by dissolving calcium hydroxide in a
solution of the normal nitrate.
_Calcium phosphide_, Ca_3P_2, is obtained as a reddish substance by passing
phosphorus vapour over strongly heated lime. Water decomposes it with the
evolution of spontaneously inflammable hydrogen phosphide; hence its use as
a marine signal fire ("Holmes lights"), (see L. Gattermann and W.
Haussknecht, _Ber._, 1890, 23, p. 1176, and H. Moissan, _Compt. Rend._,
128, p. 787).
Of the calcium orthophosphates, the normal salt, Ca_3(PO_4)_2, is the most
important. It is the principal inorganic constituent of bones, and hence of
the "bone-ash" of commerce (see PHOSPHORUS); it occurs with fluorides in
the mineral apatite (_q.v._); and the concretions known as coprolites
(_q.v._) largely consist of this salt. It also constitutes the minerals
ornithite, Ca_3(PO_4)_2·2H_2O, osteolite and sombrerite. The mineral
brushite, CaHPO_4·2H_2O, which is isomorphous with the acid arsenate
pharmacolite, CaHAsO_4·2H_2O, is an acid phosphate, and assumes monoclinic
forms. The normal salt may be obtained artificially, as a white gelatinous
precipitate which shrinks greatly on drying, by mixing solutions of sodium
hydrogen phosphate, ammonia, and calcium chloride. Crystals may be obtained
by heating di-calcium pyrophosphate, Ca_2P_2O_7, with water under pressure.
It is insoluble in water; slightly soluble in solutions of carbonic acid
and common salt, and readily soluble in concentrated hydrochloric and
nitric acid. Of the acid orthophosphates, the mono-calcium salt,
CaH_4(PO_4)_2, may be obtained as crystalline scales, containing one
molecule of water, by evaporating a solution of the normal salt in
hydrochloric or nitric acid. It dissolves readily in water, the solution
having an acid reaction. The artificial manure known as "superphosphate of
lime" consists of this salt and calcium sulphate, and is obtained by
treating ground bones, coprolites, &c., with sulphuric acid. The di-calcium
salt, Ca_2H_2(PO_4)_2, occurs in a concretionary form in the ureters and
cloaca of the sturgeon, and also in guano. It is obtained as rhombic plates
by mixing dilute solutions of calcium chloride and sodium phosphate, and
passing carbon dioxide into the liquid. Other phosphates are also known.
_Calcium monosulphide_, CaS, a white amorphous powder, sparingly soluble in
water, is formed by heating the sulphate with charcoal, or by heating lime
in a current of sulphuretted hydrogen. It is particularly noteworthy from
the phosphorescence which it exhibits when heated, or after exposure to the
sun's rays; hence its synonym "Canton's phosphorus," after John Canton
(1718-1772), an English natural philosopher. The sulphydrate or
hydrosulphide, Ca(SH)_2, is obtained as colourless, prismatic crystals of
the composition Ca(SH)_2·6H_2O, by passing sulphuretted hydrogen into milk
of lime. The strong aqueous solution deposits colourless, four-sided prisms
of the hydroxy-hydrosulphide, Ca(OH)(SH). The disulphide, CaS_2 and
pentasulphide, CaS_5, are formed when milk of lime is boiled with flowers
of sulphur. These sulphides form the basis of Balmain's luminous paint. An
oxysulphide, 2CaS·CaO, is sometimes present in "soda-waste," and
orange-coloured, acicular crystals of 4CaS·CaSO_4·18H_2O occasionally
settle out on the long standing of oxidized "soda- or alkali-waste" (see
ALKALI MANUFACTURE).
_Calcium sulphite_, CaSO_3, a white substance, soluble in water, is
prepared by passing sulphur dioxide into milk of lime. This solution with
excess of sulphur dioxide yields the "bisulphite of lime" of commerce,
which is used in the "chemical" manufacture of wood-pulp for paper making.
_Calcium sulphate_, CaSO_4, constitutes the minerals anhydrite (_q.v._),
and, in the hydrated form, selenite, gypsum (_q.v._), alabaster (_q.v._),
and also the adhesive plaster of Paris (see CEMENT). It occurs dissolved in
most natural waters, which it renders "permanently hard." It is obtained as
a white crystalline precipitate, sparingly soluble in water (100 parts of
water dissolve 24 of the salt at 15°C.), by mixing solutions of a sulphate
and a calcium salt; it is more soluble in solutions of common salt and
hydrochloric acid, and especially of sodium thiosulphate.
_Calcium silicates_ are exceptionally abundant in the mineral kingdom.
Calcium metasilicate, CaSiO_3, occurs in nature as monoclinic crystals
known as tabular spar or wollastonite; it may be prepared artificially from
solutions of calcium chloride and sodium silicate. H. Le Chatelier
(_Annales des mines_, 1887, p. 345) has obtained artificially the
compounds: CaSiO_3, Ca_2SiO_4, Ca_3Si_2O_7, and Ca_3SiO_5. (See also G.
Oddo, _Chemisches Centralblatt_, 1896, 228.) Acid calcium silicates are
represented in the mineral kingdom by gyrolite, H_2Ca_2(SiO_3)_3·H_2O, a
lime zeolite, sometimes regarded as an altered form of apophyllite
(_q.v._), which is itself an acid calcium silicate containing an alkaline
fluoride, by okenite, H_2Ca(SiO_3)_2·H_2O, and by xonalite 4CaSiO_3·H_2O.
Calcium silicate is also present in the minerals: olivine, pyroxenes,
amphiboles, epidote, felspars, zeolites, scapolites (_qq.v._).
_Detection and Estimation._--Most calcium compounds, especially when
moistened with hydrochloric acid, impart an orange-red colour to a Bunsen
flame, which when viewed through green glass appears to be finch-green;
this distinguishes it in the presence of strontium, whose crimson
coloration is apt to mask the orange-red calcium flame (when viewed through
green glass the strontium flame appears to be a very faint yellow). In the
spectroscope calcium exhibits two intense lines--an orange line ([alpha]),
([lambda] 6163), a green line ([beta]), ([lambda] 4229), and a fainter
indigo line. Calcium is not precipitated by sulphuretted hydrogen, but
falls as the carbonate when an alkaline carbonate is added to a solution.
Sulphuric acid gives a white precipitate of calcium sulphate with strong
solutions; ammonium oxalate gives calcium oxalate, practically insoluble in
water and dilute acetic acid, but readily soluble in nitric or hydrochloric
acid. Calcium is generally estimated by precipitation as oxalate which,
after drying, is heated and weighed as carbonate or oxide, according to the
degree and duration of the heating.
CALCULATING MACHINES. Instruments for the mechanical performance of
numerical calculations, have in modern times come into ever-increasing use,
not merely for dealing with large masses of figures in banks, insurance
offices, &c., but also, as cash registers, for use on the counters of
retail shops. They may be classified as follows:--(i.) Addition machines;
the first invented by Blaise Pascal (1642). (ii.) Addition machines
modified to facilitate multiplication; the first by G.W. Leibnitz (1671).
(iii.) True multiplication machines; Léon Bollés (1888), Steiger (1894).
(iv.) Difference machines; Johann Helfrich von Müller (1786), Charles
Babbage (1822). (v.) Analytical machines; Babbage (1834). The number of
distinct machines of the first three kinds is remarkable and is being
constantly added to, old machines being improved and new ones invented;
Professor R. Mehmke has counted over eighty distinct machines of this type.
The fullest published account of the subject is given by Mehmke in the
_Encyclopädie der mathematischen Wissenschaften_, article "Numerisches
Rechnen," vol. i., Heft 6 (1901). It contains historical notes and full
references. Walther von Dyck's _Catalogue_ also contains descriptions of
various machines. We shall confine ourselves to explaining the principles
of some leading types, without giving an exact description of any
particular one.
[Illustration: FIG. 1.]
Practically all calculating machines contain a "counting work," a series of
"figure disks" consisting in the original form of horizontal circular disks
(fig. 1), on which the figures 0, 1, 2, to 9 are marked. Each disk can turn
about its vertical axis, and is covered by a fixed plate with a hole or
"window" in it through which one figure can be seen. On turning the disk
through one-tenth of a revolution this figure will be changed into the next
higher or lower. Such turning may be called a "step," _positive_ [Sidenote:
Addition machines.] if the next higher and _negative_ if the next lower
figure appears. Each positive step therefore adds one unit to the figure
under the window, while two steps add two, and so on. If a series, say six,
of such figure disks be placed side by side, their windows lying in a row,
then any number of six places can be made to appear, for instance 000373.
In order to add 6425 to this number, the disks, counting from right to
left, have to be turned 5, 2, 4 and 6 steps respectively. If this is done
the sum 006798 will appear. In case the sum of the two figures at any disk
is greater than 9, if for instance the last figure to be added is 8 instead
of 5, the sum for this disk is 11 and the 1 only will appear. Hence an
arrangement for "carrying" has to be introduced. This may be done as
follows. The axis of a figure disk contains a wheel with ten teeth. Each
figure disk has, besides, one long tooth which when its 0 passes the window
turns the next wheel to the left, one tooth forward, and hence the figure
disk one step. The actual mechanism is not quite so simple, because the
long teeth as described would gear also into the wheel to the right, and
besides would interfere with each other. They must therefore be replaced by
a somewhat more complicated arrangement, which has been done in various
ways not necessary to describe more fully. On the way in which this is
done, however, depends to a great extent the durability and trustworthiness
of any arithmometer; in fact, it is often its weakest point. If to the
series of figure disks arrangements are added for turning each disk through
a required number of steps, [v.04 p.0973] we have an addition machine,
essentially of Pascal's type. In it each disk had to be turned by hand.
This operation has been simplified in various ways by mechanical means. For
pure addition machines key-boards have been added, say for each disk nine
keys marked 1 to 9. On pressing the key marked 6 the disk turns six steps
and so on. These have been introduced by Stettner (1882), Max Mayer (1887),
and in the comptometer by Dorr Z. Felt of Chicago. In the comptograph by
Felt and also in "Burrough's Registering Accountant" the result is printed.
These machines can be used for multiplication, as repeated addition, but
the process is laborious, depending for rapid execution [Sidenote: MODIFIED
ADDITION MACHINES.] essentially on the skill of the operator.[1] To adapt
an addition machine, as described, to rapid multiplication the turnings of
the separate figure disks are replaced by one motion, commonly the turning
of a handle. As, however, the different disks have to be turned through
different steps, a contrivance has to be inserted which can be "set" in
such a way that by one turn of the handle each disk is moved through a
number of steps equal to the number of units which is to be added on that
disk. This may be done by making each of the figure disks receive on its
axis a ten-toothed wheel, called hereafter the A-wheel, which is acted on
either directly or indirectly by another wheel (called the B-wheel) in
which the number of teeth can be varied from 0 to 9. This variation of the
teeth has been effected in different ways. Theoretically the simplest seems
to be to have on the B-wheel nine teeth which can be drawn back into the
body of the wheel, so that at will any number from 0 to 9 can be made to
project. This idea, previously mentioned by Leibnitz, has been realized by
Bohdner in the "Brunsviga." Another way, also due to Leibnitz, consists in
inserting between the axis of the handle bar and the A-wheel a "stepped"
cylinder. This may be considered as being made up of ten wheels large
enough to contain about twenty teeth each; but most of these teeth are cut
away so that these wheels retain in succession 9, 8, ... 1, 0 teeth. If
these are made as one piece they form a cylinder with teeth of lengths from
9, 8 ... times the length of a tooth on a single wheel.
[Illustration: FIG. 2.]
In the diagrammatic vertical section of such a machine (fig. 2) FF is a
figure disk with a conical wheel A on its axis. In the covering plate HK is
the window W. A stepped cylinder is shown at B. The axis Z, which runs
along the whole machine, is turned by a handle, and itself turns the
cylinder B by aid of conical wheels. Above this cylinder lies an axis EE
with square section along which a wheel D can be moved. The same axis
carries at E' a pair of conical wheels C and C', which can also slide on
the axis so that either can be made to drive the A-wheel. The covering
plate MK has a slot above the axis EE allowing a rod LL' to be moved by aid
of a button L, carrying the wheel D with it. Along the slot is a scale of
numbers 0 1 2 ... 9 corresponding with the number of teeth on the cylinder
B, with which the wheel D will gear in any given position. A series of such
slots is shown in the top middle part of Steiger's machine (fig. 3). Let
now the handle driving the axis Z be turned once round, the button being
set to 4. Then four teeth of the B-wheel will turn D and with it the
A-wheel, and consequently the figure disk will be moved four steps. These
steps will be positive or forward if the wheel C gears in A, and
consequently four will be added to the figure showing at the window W. But
if the wheels CC' are moved to the right, C' will gear with A moving
backwards, with the result that four is subtracted at the window. This
motion of all the wheels C is done simultaneously by the push of a lever
which appears at the top plate of the machine, its two positions being
marked "addition" and "subtraction." The B-wheels are in fixed positions
below the plate MK. Level with this, but separate, is the plate KH with the
window. On it the figure disks are mounted.
This plate is hinged at the back at H and can be lifted up, thereby
throwing the A-wheels out of gear. When thus raised the figure disks can be
set to any figures; at the same time it can slide to and fro so that an
A-wheel can be put in gear with any C-wheel forming with it one "element."
The number of these varies with the size of the machine. Suppose there are
six B-wheels and twelve figure disks. Let these be all set to zero with the
exception of the last four to the right, these showing 1 4 3 2, and let
these be placed opposite the last B-wheels to the right. If now the buttons
belonging to the latter be set to 3 2 5 6, then on turning the B-wheels all
once round the latter figures will be added to the former, thus showing 4 6
8 8 at the windows. By aid of the axis Z, this turning of the B-wheels is
performed simultaneously by the movement of one handle. We have thus an
addition machine. If it be required to multiply a number, say 725, by any
number up to six figures, say 357, the buttons are set to the figures 725,
the windows all showing zero. The handle is then turned, 725 appears at the
windows, and successive turns add this number to the first. Hence seven
turns show the product seven times 725. Now the plate with the A-wheels is
lifted and moved one step to the right, then lowered and the handle turned
five times, thus adding fifty times 725 to the product obtained. Finally,
by moving the piate again, and turning the handle three times, the required
product is obtained. If the machine has six B-wheels and twelve disks the
product of two six-figure numbers can be obtained. Division is performed by
repeated subtraction. The lever regulating the C-wheel is set to
subtraction, producing negative steps at the disks. The dividend is set up
at the windows and the divisor at the buttons. Each turn of the handle
subtracts the divisor once. To count the number of turns of the handle a
second set of windows is arranged with number disks below. These have no
carrying arrangement, but one is turned one step for each turn of the
handle. The machine described is essentially that of Thomas of Colmar,
which was the first that came into practical use. Of earlier machines those
of Leibnitz, Müller (1782), and Hahn (1809) deserve to be mentioned (see
Dyck, _Catalogue_). Thomas's machine has had many imitations, both in
England and on the Continent, with more or less important alterations.
Joseph Edmondson of Halifax has given it a circular form, which has many
advantages.
The accuracy and durability of any machine depend to a great extent on the
manner in which the carrying mechanism is constructed. Besides, no wheel
must be capable of moving in any other way than that required; hence every
part must be locked and be released only when required to move. Further,
any disk must carry to the next only after the carrying to itself has been
completed. If all were to carry at the same time a considerable force would
be required to turn the handle, and serious strains would be introduced. It
is for this reason that the B-wheels or cylinders have the greater part of
the circumference free from teeth. Again, the carrying acts generally as in
the machine described, in one sense only, and this involves that the handle
be turned always in the same direction. Subtraction therefore cannot be
done by turning it in the opposite way, hence the two wheels C and C' are
introduced. These are moved all at once by one lever acting on a bar shown
at R in section (fig. 2).
In the Brunsviga, the figure disks are all mounted on a common horizontal
axis, the figures being placed on the rim. On the side of each disk and
rigidly connected with it lies its A-wheel with which it can turn
independent of the others. The B-wheels, all fixed on another horizontal
axis, gear directly on the A-wheels. By an ingenious contrivance the teeth
are made to appear from out of the rim to any desired number. The carrying
mechanism, too, is different, and so arranged that the handle can be turned
either way, no special setting being required for subtraction or division.
It is extremely handy, taking up much less room than the others. Professor
Eduard Selling of Würzburg has invented an altogether different machine,
which has been made by Max Ott, of Munich. The B-wheels are replaced by
lazy-tongs. To the joints of these the ends of racks are pinned; and as
they are stretched out the racks are moved forward 0 to 9 steps, according
to the joints they are pinned to. The racks gear directly in the A-wheels,
and the figures are placed on cylinders as in the Brunsviga. The carrying
is done continuously by a train of epicycloidal wheels. The working is thus
rendered very smooth, without the jerks which the ordinary carrying tooth
produces; but the arrangement has the disadvantage that the resulting
figures do not appear in a straight line, a figure followed by a 5, for
instance, being already carried half a step forward. This is not a serious
matter in the hands of a mathematician or an operator using the machine
constantly, but it is serious for casual work. Anyhow, it has prevented the
machine from being a commercial success, and it is not any longer made. For
ease and rapidity of working it surpasses all others. Since the lazy-tongs
allow of an extension equivalent to five turnings of the handle, if the
multiplier is 5 or under, one push forward will do the [v.04 p.0974] same
as five (or less) turns of the handle, and more than two pushes are never
required.
[Illustration: FIG. 3.]
The _Steiger-Egli_ machine is a multiplication machine, of which fig. 3
gives a picture as it appears to the manipulator. The lower [Sidenote:
Multiplication machines.] part of the figure contains, under the covering
plate, a carriage with two rows of windows for the figures marked ff and
gg. On pressing down the button W the carriage can be moved to right or
left. Under each window is a figure disk, as in the Thomas machine. The
upper part has three sections. The one to the right contains the handle K
for working the machine, and a button U for setting the machine for
addition, multiplication, division, or subtraction. In the middle section a
number of parallel slots are seen, with indices which can each be set to
one of the numbers 0 to 9. Below each slot, and parallel to it, lies a
shaft of square section on which a toothed wheel, the A-wheel, slides to
and fro with the index in the slot. Below these wheels again lie 9 toothed
racks at right angles to the slots. By setting the index in any slot the
wheel below it comes into gear with one of these racks. On moving the rack,
the wheels turn their shafts and the figure disks gg opposite to them. The
dimensions are such that a motion of a rack through 1 cm. turns the figure
disk through one "step" or adds 1 to the figure under the window. The racks
are moved by an arrangement contained in the section to the left of the
slots. There is a vertical plate called the multiplication table block, or
more shortly, the _block_. From it project rows of horizontal rods of
lengths varying from 0 to 9 centimetres. If one of these rows is brought
opposite the row of racks and then pushed forward to the right through 9
cm., each rack will move and add to its figure disk a number of units equal
to the number of centimetres of the rod which operates on it. The block has
a square face divided into a hundred squares. Looking at its face from the
right--_i.e._ from the side where the racks lie--suppose the horizontal
rows of these squares numbered from 0 to 9, beginning at the top, and the
columns numbered similarly, the 0 being to the right; then the
multiplication table for numbers 0 to 9 can be placed on these squares. The
row 7 will therefore contain the numbers 63, 56, ... 7, 0. Instead of these
numbers, each square receives two "rods" perpendicular to the plate, which
may be called the units-rod and the tens-rod. Instead of the number 63 we
have thus a tens-rod 6 cm. and a units-rod 3 cm. long. By aid of a lever H
the block can be raised or lowered so that any row of the block comes to
the level of the racks, the units-rods being opposite the ends of the
racks.
The action of the machine will be understood by considering an example. Let
it be required to form the product 7 times 385. The indices of three
consecutive slots are set to the numbers 3, 8, 5 respectively. Let the
windows gg opposite these slots be called a, b, c. Then to the figures
shown at these windows we have to add 21, 56, 35 respectively. This is the
same thing as adding first the number 165, formed by the units of each
place, and next 2530 corresponding to the tens; or again, as adding first
165, and then moving the carriage one step to the right, and adding 253.
The first is done by moving the block with the units-rods opposite the
racks forward. The racks are then put out of gear, and together with the
block brought back to their normal position; the block is moved sideways to
bring the tens-rods opposite the racks, and again moved forward, adding the
tens, the carriage having also been moved forward as required. This
complicated movement, together with the necessary carrying, is actually
performed by one turn of the handle. During the first quarter-turn the
block moves forward, the units-rods coming into operation. During the
second quarter-turn the carriage is put out of gear, and moved one step to
the right while the necessary carrying is performed; at the same time the
block and the racks are moved back, and the block is shifted so as to bring
the tens-rods opposite the racks. During the next two quarter-turns the
process is repeated, the block ultimately returning to its original
position. Multiplication by a number with more places is performed as in
the Thomas. The advantage of this machine over the Thomas in saving time is
obvious. Multiplying by 817 requires in the Thomas 16 turns of the handle,
but in the Steiger-Egli only 3 turns, with 3 settings of the lever H. If
the lever H is set to 1 we have a simple addition machine like the Thomas
or the Brunsviga. The inventors state that the product of two 8-figure
numbers can be got in 6-7 seconds, the quotient of a 6-figure number by one
of 3 figures in the same time, while the square root to 5 places of a
9-figure number requires 18 seconds.
Machines of far greater powers than the arithmometers mentioned have been
invented by Babbage and by Scheutz. A description is impossible without
elaborate drawings. The following account will afford some idea of the
working of Babbage's difference machine. Imagine a number of striking
clocks placed in a row, each with only an hour hand, and with only the
striking apparatus retained. Let the hand of the first clock be turned. As
it comes opposite a number on the dial the clock strikes that number of
times. Let this clock be connected with the second in such a manner that by
each stroke of the first the hand of the second is moved from one number to
the next, but can only strike when the first comes to rest. If the second
hand stands at 5 and the first strikes 3, then when this is done the second
will strike 8; the second will act similarly on the third, and so on. Let
there be four such clocks with hands set to the numbers 6, 6, 1, 0
respectively. Now set the third clock striking 1, this sets the hand of the
fourth clock to 1; strike the second (6), this puts the third to 7 and the
fourth to 8. Next strike the first (6); this moves the other hands to 12,
19, 27 respectively, and now repeat the striking of the first. The hand of
the fourth clock will then give in succession the numbers 1, 8, 27, 64,
&c., being the cubes of the natural numbers. The numbers thus obtained on
the last dial will have the differences given by those shown in succession
on the dial before it, their differences by the next, and so on till we
come to the constant difference on the first dial. A function
y = a + bx + cx^2 + dx^3 + ex^4
gives, on increasing x always by unity, a set of values for which the
fourth difference is constant. We can, by an arrangement like the above,
with five clocks calculate y for x = 1, 2, 3, ... to any extent. This is
the principle of Babbage's difference machine. The clock dials have to be
replaced by a series of dials as in the arithmometers described, and an
arrangement has to be made to drive the whole by turning one handle by hand
or some other power. Imagine further that with the last clock is connected
a kind of typewriter which prints the number, or, better, impresses the
number in a soft substance from which a stereotype casting can be taken,
and we have a machine which, when once set for a given formula like the
above, will automatically print, or prepare stereotype plates for the
printing of, tables of the function without any copying or typesetting,
thus excluding all possibility of errors. Of this "Difference engine," as
Babbage called it, a part was finished in 1834, the government having
contributed £17,000 towards the cost. This great expense was chiefly due to
the want of proper machine tools.
Meanwhile Babbage had conceived the idea of a much more powerful machine,
the "analytical engine," intended to perform any series of possible
arithmetical operations. Each of these was to be communicated to the
machine by aid of cards with holes punched in them into which levers could
drop. It was long taken for granted that Babbage left complete plans; the
committee of the British Association appointed to consider this question
came, however, to the conclusion (_Brit. Assoc. Report_, 1878, pp. 92-102)
that no detailed working drawings existed at all; that the drawings left
were only diagrammatic and not nearly sufficient to put into the hands of a
draughtsman for making working plans; and "that in the present state of the
design it is not more than a theoretical possibility." A full account of
the work done by Babbage in connexion with calculating machines, and much
else published by others in connexion therewith, is contained in a work
published by his son, General Babbage.
[Illustration: FIG. 4.]
Slide rules are instruments for performing logarithmic calculations
mechanically, and are extensively used, especially where [Sidenote: Slide
rules.] only rough approximations are required. They are almost as old as
logarithms themselves. Edmund Gunter drew a "logarithmic line" on his
"Scales" as follows (fig. 4):--On a line AB lengths are set off to scale to
represent the common logarithms of the numbers 1 2 3 ... 10, and the points
thus obtained are marked with these numbers. [v.04 p.0975] As log 1 = 0,
the beginning A has the number 1 and B the number 10, hence the unit of
length is AB, as log 10 = 1. The same division is repeated from B to C. The
distance 1,2 thus represents log 2, 1,3 gives log 3, the distance between 4
and 5 gives log 5 - log 4 = log 5/4, and so for others. In order to
multiply two numbers, say 2 and 3, we have log 2 × 3 = log 2 + log 3.
Hence, setting off the distance 1,2 from 3 forward by the aid of a pair of
compasses will give the distance log 2 + log 3, and will bring us to 6 as
the required product. Again, if it is required to find 4/5 of 7, set off
the distance between 4 and 5 from 7 backwards, and the required number will
be obtained. In the actual scales the spaces between the numbers are
subdivided into 10 or even more parts, so that from two to three figures
may be read. The numbers 2, 3 ... in the interval BC give the logarithms of
10 times the same numbers in the interval AB; hence, if the 2 in the latter
means 2 or .2, then the 2 in the former means 20 or 2.
Soon after Gunter's publication (1620) of these "logarithmic lines," Edmund
Wingate (1672) constructed the slide rule by repeating the logarithmic
scale on a tongue or "slide," which could be moved along the first scale,
thus avoiding the use of a pair of compasses. A clear idea of this device
can be formed if the scale in fig. 4 be copied on the edge of a strip of
paper placed against the line A C. If this is now moved to the right till
its 1 comes opposite the 2 on the first scale, then the 3 of the second
will be opposite 6 on the top scale, this being the product of 2 and 3; and
in this position every number on the top scale will be twice that on the
lower. For every position of the lower scale the ratio of the numbers on
the two scales which coincide will be the same. Therefore multiplications,
divisions, and simple proportions can be solved at once.
Dr John Perry added log log scales to the ordinary slide rule in order to
facilitate the calculation of a^x or e^x according to the formula log
loga^x = log loga + logx. These rules are manufactured by A.G. Thornton of
Manchester.
Many different forms of slide rules are now on the market. The handiest for
general use is the Gravet rule made by Tavernier-Gravet in Paris, according
to instructions of the mathematician V.M.A. Mannheim of the École
Polytechnique in Paris. It contains at the back of the slide scales for the
logarithms of sines and tangents so arranged that they can be worked with
the scale on the front. An improved form is now made by Davis and Son of
Derby, who engrave the scales on white celluloid instead of on box-wood,
thus greatly facilitating the readings. These scales have the distance from
one to ten about twice that in fig. 4. Tavernier-Gravet makes them of that
size and longer, even ½ metre long. But they then become somewhat unwieldy,
though they allow of reading to more figures. To get a handy long scale
Professor G. Fuller has constructed a spiral slide rule drawn on a
cylinder, which admits of reading to three and four figures. The handiest
of all is perhaps the "Calculating Circle" by Boucher, made in the form of
a watch. For various purposes special adaptations of the slide rules are
met with--for instance, in various exposure meters for photographic
purposes. General Strachey introduced slide rules into the Meteorological
Office for performing special calculations. At some blast furnaces a slide
rule has been used for determining the amount of coke and flux required for
any weight of ore. Near the balance a large logarithmic scale is fixed with
a slide which has three indices only. A load of ore is put on the scales,
and the first index of the slide is put to the number giving the weight,
when the second and third point to the weights of coke and flux required.
By placing a number of slides side by side, drawn if need be to different
scales of length, more complicated calculations may be performed. It is
then convenient to make the scales circular. A number of rings or disks are
mounted side by side on a cylinder, each having on its rim a log-scale.
The "Callendar Cable Calculator," invented by Harold Hastings and
manufactured by Robert W. Paul, is of this kind. In it a number of disks
are mounted on a common shaft, on which each turns freely unless a button
is pressed down whereby the disk is clamped to the shaft. Another disk is
fixed to the shaft. In front of the disks lies a fixed zero line. Let all
disks be set to zero and the shaft be turned, with the first disk clamped,
till a desired number appears on the zero line; let then the first disk be
released and the second clamped and so on; then the fixed disk will add up
all the turnings and thus give the product of the numbers shown on the
several disks. If the division on the disks is drawn to different scales,
more or less complicated calculations may be rapidly performed. Thus if for
some purpose the value of say ab³ [root]c is required for many different
values of a, b, c, three movable disks would be needed with divisions drawn
to scales of lengths in the proportion 1: 3: ½. The instrument now on sale
contains six movable disks.
_Continuous Calculating Machines or Integrators._--In order to measure the
length of a curve, such as the road on a map, a [Sidenote: Curvometers.]
wheel is rolled along it. For one revolution of the wheel the path
described by its point of contact is equal to the circumference of the
wheel. Thus, if a cyclist counts the number of revolutions of his front
wheel he can calculate the distance ridden by multiplying that number by
the circumference of the wheel. An ordinary cyclometer is nothing but an
arrangement for counting these revolutions, but it is graduated in such a
manner that it gives at once the distance in miles. On the same principle
depend a number of instruments which, under various fancy names, serve to
measure the length of any curve; they are in the shape of a small meter
chiefly for the use of cyclists. They all have a small wheel which is
rolled along the curve to be measured, and this sets a hand in motion which
gives the reading on a dial. Their accuracy is not very great, because it
is difficult to place the wheel so on the paper that the point of contact
lies exactly over a given point; the beginning and end of the readings are
therefore badly defined. Besides, it is not easy to guide the wheel along
the curve to which it should always lie tangentially. To obviate this
defect more complicated curvometers or kartometers have been devised. The
handiest seems to be that of G. Coradi. He uses two wheels; the
tracing-point, halfway between them, is guided along the curve, the line
joining the wheels being kept normal to the curve. This is pretty easily
done by eye; a constant deviation of 8° from this direction produces an
error of only 1%. The sum of the two readings gives the length. E.
Fleischhauer uses three, five or more wheels arranged symmetrically round a
tracer whose point is guided along the curve; the planes of the wheels all
pass through the tracer, and the wheels can only turn in one direction. The
sum of the readings of all the wheels gives approximately the length of the
curve, the approximation increasing with the number of the wheels used. It
is stated that with three wheels practically useful results can be
obtained, although in this case the error, if the instrument is
consistently handled so as always to produce the greatest inaccuracy, may
be as much as 5%.
[Illustration: FIG. 5.]
Planimeters are instruments for the determination by mechanical means of
the area of any figure. A pointer, generally called the [Sidenote:
Planimeters.] "tracer," is guided round the boundary of the figure, and
then the area is read off on the recording apparatus of the instrument. The
simplest and most useful is Amsler's (fig. 5). It consists of two bars of
metal OQ and QT, [v.04 p.0976] which are hinged together at Q. At O is a
needle-point which is driven into the drawing-board, and at T is the
tracer. As this is guided round the boundary of the figure a wheel W
mounted on QT rolls on the paper, and the turning of this wheel measures,
to some known scale, the area. We shall give the theory of this instrument
fully in an elementary manner by aid of geometry. The theory of other
planimeters can then be easily understood.
[Illustration: FIG. 6.]
Consider the rod QT with the wheel W, without the arm OQ. Let it be placed
with the wheel on the paper, and now moved perpendicular to itself from AC
to BD (fig. 6). The rod sweeps over, or generates, the area of the
rectangle ACDB = lp, where l denotes the length of the rod and p the
distance AB through which it has been moved. This distance, as measured by
the rolling of the wheel, which acts as a curvometer, will be called the
"roll" of the wheel and be denoted by w. In this case p = w, and the area P
is given by P = wl. Let the circumference of the wheel be divided into say
a hundred equal parts u; then w registers the number of u's rolled over,
and w therefore gives the number of areas lu contained in the rectangle. By
suitably selecting the radius of the wheel and the length l, this area lu
may be any convenient unit, say a square inch or square centimetre. By
changing l the unit will be changed.
[Illustration: FIG. 7.]
Again, suppose the rod to turn (fig. 7) about the end Q, then it will
describe an arc of a circle, and the rod will generate an area ½l²[theta],
where [theta] is the angle AQB through which the rod has turned. The wheel
will roll over an arc c[theta], where c is the distance of the wheel from
Q. The "roll" is now w = c[theta]; hence the area generated is
P = ½ l²/c w,
and is again determined by w.
[Illustration: FIG. 8.]
Next let the rod be moved parallel to itself, but in a direction not
perpendicular to itself (fig. 8). The wheel will now not simply roll.
Consider a _small_ motion of the rod from QT to Q'T'. This may be resolved
into the motion to RR' perpendicular to the rod, whereby the rectangle
QTR'R is generated, and the sliding of the rod along itself from RR' to
Q'T'. During this second step no area will be generated. During the first
step the roll of the wheel will be QR, whilst during the second step there
will be no roll at all. The roll of the wheel will therefore measure the
area of the rectangle which equals the parallelogram QTT'Q'. If the whole
motion of the rod be considered as made up of a very great number of small
steps, each resolved as stated, it will be seen that the roll again
measures the area generated. But it has to be noticed that now the wheel
does not only roll, but also slips, over the paper. This, as will be
pointed out later, may introduce an error in the reading.
[Illustration: FIG. 9.]
We can now investigate the most general motion of the rod. We again resolve
the motion into a number of small steps. Let (fig. 9) AB be one position,
CD the next after a step so small that the arcs AC and BD over which the
ends have passed may be considered as straight lines. The area generated is
ABDC. This motion we resolve into a step from AB to CB', parallel to AB and
a turning about C from CB' to CD, steps such as have been investigated.
During the first, the "roll" will be p the altitude of the parallelogram;
during the second will be c[theta]. Therefore
w = p + c[theta].
[Illustration: FIG. 10.]
The area generated is lp + ½ l^2[theta], or, expressing p in terms of w, lw
+ (½l^2 - lc)[theta]. For a finite motion we get the area equal to the sum
of the areas generated during the different steps. But the wheel will
continue rolling, and give the whole roll as the sum of the rolls for the
successive steps. Let then w denote the whole roll (in fig. 10), and let
[alpha] denote the sum of all the small turnings [theta]; then the area is