A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

.578 PTOLEMAEUS. PTOLEMAEUS.
places, of the shadow cast by a gnomon of the same meridians of longitude and parallels of latitude, on
altitude at noon of the samne day. This system of a sphere, and on a plane surface. This subject is disclimates was, in fact, an imperfect development of cussed by Ptolemy in the last seven chapters of his
the more complete system of parallels of latitude. first book (18-24), in which he points out the imIt was, however, retained for convenience of refer- perfections of the system of delineation adopted by
ence. For a further explanation of it, and for an Marinus, and expounds his own. Of the two kinds
account of the climates of Ptolemy, see the Dic- of delineation, he observes, that on a sphere is the
tionary of Antiquities, art. Clima, 2nd ed. easier to make, as it involves no method of projecNext, as to the size of the earth. Various at- tion, but is a direct representation; but, on the
tempts had been made, long before the time of Pto- other hand, it is inconvenient to use, as only a
lemy, to calculate the circumference of a great circle small portion of the surface can be seen at once:
of the earth by measuring the length of an are of a while the converse is true of a map on a plane surmeridian, containing a known number of degrees. face. The earliest geographers had no guide for
Thus Eratosthenes, who was the first to attempt their maps but reported distances and general
any complete computation of this sort from his own notions of the figures of the masses of land and
observations, assuming Syene and Alexandria to water. Eratosthenes was the first who called in the
lie under the same meridian*, and to be 5000 aid of astronomy, but he did not attempt any comstadia apart, and the are between them to be 1- plete projection of the sphere (see ERATOSTHENES,
50th of the circumference of a great circle, ob- and Ukert, vol. i. pt. 2, pp. 192, 193, and plate ii.,
tained 250,000 stadia for the whole circumference, in which Ukert attempts a restoration of the map
and 694- stadia for the length of a degree; but, of Eratosthenes). Hipparchus, in his work against
in order to make this a convenient whole number, Eratosthenes, insisted much more fully on the nehe called it 700 stadia, and so got 252,000 stadia cessary connection between geography and astrofor the circumference of a great circle of the earth nomy, and was the first who attempted to lay
(Cleomed. Cyc. Theor. i. 8; Ukert, Geogr. d. Griech. down the exact positions of places according to
u. Ro;ner, vol. i. pt. 2, pp. 42-45). The most their latitudes and longitudes. In the science of
important of the other computations of this sort projection, however, he went no further than the
were those of Poseidonius, (for he made two,) which method of representing the meridians and parallels
were founded on different estimates of the distance by parallel straight lines, the one set intersecting
between Rhodes and Alexandria: the one gave, the other at right angles. Other systems of prolike the computation of Eratosthenes, 252,000 jection were attempted, so that at the time of Mastadia for the circumference of a great circle, and rinus there were several methods in use, all of
700 stadia for the length of a degree; and the which he rejected, and devised a new system,
other gave 180,000 stadia for the circumference of which is described in the following manner by
a great circle, and 500 stadia for the length of a Ptolemy (i. 20, 24, 25). On account of the imdegree (Cleomed. i. 10; Strab. ii. pp. 86,93,95,125; portance of the countries round the Mediterranean,
Ukert, 1. c. p. 48). The truth lies just between he kept as his datum line the old standard line of
the two; for, taking the Roman mile of 8 stadia as Eratosthenes and his successors, namely the pa1-75th of a degree, we have (75 x 8=) 600 stadia rallel through Rhodes, or the 36th degree of latifor the length of a degree.+ tude. He then calculated, from the length of a
Ptolemy followed the second computation of Po- degree on the equator, the length of a degree on this
seidonius, namely, that which made the earth parallel; taking the former at 500 stadia, he reckoned
180,000 stadia in circumference, and the degree the latter at 400. Having divided this parallel into
500 stadia in length; but it should be observed degrees, he drew perpendiculars through the points
that he, as well as all the ancient geographers, of division for the meridians; and his parallels of
speaks of his computation as confessedly only an latitude were straight lines parallel to that through
approximation to the truth. He describes, in bk. Rhodes. The result, of course, was, as Ptolemy
i. c. 3, the method of finding, from the direct dis- observes, that the parts of the earth north of the
tance in stadia of two places, even though they be parallel of Rhodes were represented much too long,
not under the same meridian, the circumference of and those south of that line much too short; and
the whole earth, and conversely. There having further that, when Marinus came to lay down the
been found, bymeans of an astronomical instrument, positions of places according to their reported distwo fixed stars distant one degree from each other, tances, those north of the line were too near, and
the places on the earth were sought to which those those south of it too far apart, as compared with
stars were in the zenith, and the distance between the surface of his map. Moreover, Ptolemy obthose places being ascertained, this distance was, of serves, the projection is an incorrect representation,
course (excluding errors), the length of a degree inasmuch as the parallels of latitude ought to be
of the great circle passing through those places, circular arcs, and not straight lines.
whether that circle were a meridian or not. Ptolemy then proceeds to describe his bwn meThe next point to be determined was the mode thod, which does not admit of an abridged stateof representing the surface of the earth with its ment, and cannot be understood without a figure.
The reader is therefore referred for it to Ptolemy's
* As we are not dealing here with the facts of own work (i. 24), and to the accounts given by
geography, but only with the opinions of the ancient Ukert (I. c. pp. 195, &c.), Mannert (vol. i. pp. 127,
geographers, we do not stay to correct the errors &c.), and other geographers. All that can be said
in the data of these computations. of it here is that Ptolemy represents the parallels
t It will be observed that we recognise no other of latitude as arcs of concentric circles (their centre
stadium than the Olympic, of 600 Greek feet, or representing the North Pole), the chief of which
1-8th of a Roman mile. The reasons for this are are those passing through Thule, Rhodes, and
stated in the Dictionary of Antiquities, art. Sta- Meroi, the Equator, and the one through Prasum.
diule. The meridians of longitude are represented by