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