and also to a tangent to its circumference. Into these holes are screwed steel screws with capstan heads and flat ends. The tangent screw consists only of a single turn of a large square thread which works in the teeth or notches of the plate. This thread is pierced by 90 equally distant holes, all parallel to the axis of the screw, and at the same distance from it. Into each of these holes is inserted a steel screw exactly similar to those in the teeth, but with its end rounded. It is the rounded and flat ends of these sets of screws coming together that stop the engine plate at the desired position, and the exact point can be nicely adjusted by suitably turning the screws. In the Memoirs of the Astronomical Society, of date June 1843, a description is given of a dividing engine made by William Simms. From experience he became convinced that to copy upon smaller circles the divisions which had been put upon a large plate with very great accuracy was not only more expeditious but better than original graduation, and hence he determined to construct a machine which would do this work as perfectly as possible. That machine involved essentially the same principle as Troughton s, and, with some slight modifications, is at present to be seen at work in the workshop of the eminent firm of Troughton &. Simms at Charlton near London. The accompanying figure is taken by permission from a photograph of that instrument.
[ Dividing Engine. ]
The plate A is 4t> inches in diameter, and is composed of gun-metal cast in one solid piece. It has two sets of 5 divisions one very faint on an inlaid ring of silver, and the other stronger on the gun metal. These were put on by original graduation, mainly on the plan of Edward Troughton. One very great improvement in this engine is that the axis B is tubular, as seen at C. The object of this hollow is to receive the axis of the circle to be divided, so that it can be fixed flat to the plate by the clamps E, without having first to be de tached from the axis and other parts to which it lias already been carefully fitted. This obviates the necessity for resetting, which can hardly be done without some error. D is the tangent screw, and F the frame carrying it, which turns on carefully polished steel pivots. The screw is pressed against the edge of the plate by a spiral spring acting under the end of the lever G, and by screwing the lever down the screw can be altogether removed from contact with the plate. The edge of the plate is ratched by 4320 teeth which were cut opposite the original division by a circular cutter attached to the screw frame. II is the spiral barrel round which the catgut band is wound, one end of which is attracted to the crank L on the end of the axis J and the other to a counterpoise weight not seen. On the other end of J is another crank inclined to L and carrying a band and counterpoise weight seen at K. The object of this weight is to balance the former and give steadiness to the motion. On the axis J is seen a pair of bevelled wheels which move the rod I, which, by another pair of bevelled wheels attached to the box N, gives motion to the axis M, on the end of which is an eccentric for moving the bent lever O, which actuates the bar carrying the cutter. Between the eccentric and the point of the screw P is an undulating plate by which long divisions, at required intervals, can be cut. It will be seen that the cutting apparatus is supported upon the two parallel rails which can be elevated or depressed at pleasure by the nuts Q. Also the cutting apparatus can be moved fons ardor backward upon these rails to suit circles of different diameters. The box N is mov able upon the bar K, and the rod I is also adjustable as to length by having a kind of telescope joint. The engine is quite self-acting, and can be driven either by hand or by a steam-engine or other motive power. When driven by the latter it can be thrown in or out of gear at once by a handle seen at S. II r Simms has also provided an ingenious arrangement whereby that is done automatically directly any piece of work was finished. Spaca permits of but the mere mention of Donkiu s linear dividing engine, in which the principle employed is a compensating arrangement whereby great accuracy is obtained notwithstanding the inequalities of the screw used to advance the cutting tool. Dividing engines have also been made by Reichenbach and others in Germany, and Gambey in Paris.
In addition to those already mentioned, the following references may be given : Bird, Method of dividing Astronomical Instru ments, London, 1767 ; Due de Chaulnes, Nouvclle Methodc pour diviser Ics Instruments de Matheinatiquc ct d Astronomic, 1768 ; Kamsden, Description of an Engine for dividing Mathematical Instruments, London, 1777; Troughton s memoir, 1 ldl. Trans., 1809 ; Memoirs of the Royal Astronomical Society, vol. v. p. 325, vol. viii. p. 141, vol. ix. pp. 17 and 35 ; Holtzapll el, Turning and Mechanical Manipulation, pp. 651-955.
GRÆCIA, Magna ([Greek]), was the name
given to tha Greek cities along the coast of South Italy,
while the people were called Italiotes ( IroAiomu). Like
must Greek colonies, they were established first as trading
stations, which grew into independent cities. At a very
early time a trade in copper was carried on between Greece
and the Terimean Gulf (Homer, Od., i. 181). The trade
for long lay chiefly in the hands of the Euboeans ; and
Cyme in Campania was founded far back in the pre-historic
time, when the Eubccan Cyme was still a great city. To
strengthen the connexion with the far off Cyme, the Clial-
cidians, who became early the leaders of Euboean enterprise,
established Rhegium (about 730 B.C.). After this the
energy of Chalcis went onward to Sicily, and the states of
the Corinthian Gulf carried out the colonization of Italy.
Sybaris (720) and Crotona (710) were Achaean settlements ;
Locri Epizephyrii (about 710) was settled by Ozolian
Locrians, and when (about 708) the Spartans wished to
get rid of a band of unruly citizens, the connexion formed
by the trade in purple that was common to the shores of
Laconia and Tarenturn directed their colony thither.
Ionian Greeks fleeing from fureign invasion founded Siris
and, much later, Elea (540).
The Italian colonies were planted among friendly, almost
kindred, races (comp. the legend in Herod., vii. 183), and
grew much more rapidly than the Sicilian Greek states,
which had to contend against the power of Carthage. After
the Achaean cities had combined to destroy the Ionic Siris,
and had founded Metapontum as a counterpoise to the
Dorian Tarentum, there seems to have been little strife
among the Italiotes. An amphictyonic league, meeting in
common rites at the temple of Hera on the Lacinian pro
montory, fostered a feeling of unity among them. In the
7th and 6th centuries B.c , they reached such a pitch of
wealth and power as to justify the name Great Greece in
contrast to the poor and weak mother country. The
Pythagorean and Eleatic systems of philosophy had their
chief seat in Magna Gr?ecia. Other departments of litera
ture do not seem to have been so much cultivated among
them. The poet Ibycus, though a native of Rhegium, led
a very wandering life. They maintained some social inter
course with Greece proper (Herod., iii. 131) and sent com
petitors to the Olympic games (among them the famous
Milo) ; but politically they appear to have generally kept
themselves separate. One ship of Crotona, however, fought
at Salamis, though it is not recorded that Greece asked the
Italiotes for help when it sent ambassadors to Gelon of
