The flattening of the spherical earth was not suspected until in 1672 a clock regulated to beat seconds at Paris, when taken to Cayenne near the equator was found to lose two and one-half minutes a day. Newton proved that this was due to the fact that the earth is an oblate spheroid. In 1735 accurate measurements were undertaken to determine the size and shape of the earth. The equatorial diameter has been found to be 7926.6 miles and the polar diameter 7899.6 miles, the difference, or 27 statute miles, being the amount of the flattening at the poles.

The first sailing directions. The early Greek and Roman writers do not allude to charts or maps intended especially for the use of seafarers. There are, however, extant several peripli or descriptions of the coast. Some of these appear certainly to have been intended for use as nautical guides, corresponding to the modern sailing directions. It is probable that they were explanatory of or accompanied by coast charts, now lost. They are of interest therefore as being probably the first compilations for the guidance of seamen. One of the earliest, written apparently in the fifth and fourth centuries B.C., is entitled "Scylax of Caryanda, his circumnavigation of the sea of the inhabited part of Europe and Asia and Libya." It contains a systematic description of the coasts of the Mediterranean, Black Sea, and part of the west coast of Africa. The following are some extracts which indicate the character of the work. It is to be noted that no bearings are given, and that distances are usually stated by day's sail: Africa is referred to as Libya.

"Europe. I shall begin from the Pillars of Hercules in Europe and continue to the Pillars of Hercules in Libya, and as far as the land of the great Ethiopians. The Pillars of Hercules are opposite each other, and are distant from each other by one day's sail.... From Thonis the voyage to Pharos, a desert island (good harborage but no drinking water), is 150 stadia. In Pharos are many harbors. But ships water at the Marian mere, for it is drinkable.... From Chersonesus is one day's sail; but from Naustathmus to the harbor of Cyrene, 100 stadia. But from the harbor to Cyrene, 80 stadia; for Cyrene is inland. These harbors are always fit for putting into. And there are other refuges at little islands, and anchorages and many beaches, in the district between.... After the isthmus is Carthage, a city of the Phœnicians, and a harbor. Sailing along from Hermæa it is half a day to Carthage. There are islands off the Hermæan cape, Pontia island and Cosyrus. From Hermæa to Cosyrus is a day's sail. Beyond the Hermæan cape, towards the rising sun, are three islands belonging to this shore, inhabited by Carthaginians; the city and harbor of Melite, the city of Gaulus, and Lampas; this has two or three towers.... The sailing along Libya from the Canopic mouth in Egypt to the Pillars of Hercules ... takes 74 days if one coast round the bays.... From the cape of Hermæa extend great reefs, that is, from Libya towards Europe, not rising above the sea; it washes over them at times.... From Thymiateria one sails to cape Soloes, which juts far into the sea. But all this district of Libya is very famous and very sacred.... This whole coasting from the Pillars of Hercules to Cerne Island takes twelve days. The parts beyond the isle of Cerne are no longer navigable because of shoals, mud, and sea-weed. This sea-weed has the width of a palm, and is sharp towards the points, so as to prick."

That there were many other similar writings in the following centuries is shown by the following quotation from Marcianus, in a preface to sailing directions written in the fifth century A.D.: "This I write after having gone through many sailing directions, and spent much time on their examination. For it behooves all who are men of education, to scrutinise such attempts at learning in this subject, so as neither rashly to believe the things that are said, nor incredulously to set their private opinions against the careful decisions of others."

The oldest extant sailing directions of the middle ages bear date 1306 to 1320.

Development of chart making. The application of the compass to nautical use in the twelfth century A.D. had a marked effect in encouraging voyages of exploration, and therefore indirectly on chart making. The following, written toward the close of the twelfth century, is the first known mention of the use of the compass in Europe: "The sailors, moreover, as they sail over the sea, when in cloudy weather they cannot longer profit by the light of the sun, or when the world is wrapped in the darkness of the shades of night, and they are ignorant to what part of the horizon the prow is directed, place the needle over the magnet, which is whirled round in a circle, until, when the motion ceases, the point of it (the needle) looks to the north." The nautical compass of that time appears to have consisted of a magnetized needle, floated in a vessel of water by a cork or reed, and having no index nor compass card. Peregrinus in 1269 made notable improvements in the compass, including a pivot suspension for the needle, a graduation, a lubber line, and an azimuth bar for sighting on the sun or other object.

Nautical charts are known to have been in use since the thirteenth century A.D., but the earliest extant of which the date can be fixed is Vesconte's loxodromic chart of 1311.

The loxodromic charts first appeared in Italy, and were so called from the fact that they were crossed by loxodromes (or rhumb lines) radiating from a number of crossing points distributed regularly over the map. Compass roses carefully drawn were later added at these crossing points, the first appearing on a chart of 1375. The earliest known mention of the variation of the compass from true north was on the first voyage of Columbus, who discovered this important fact in 1492, and as a consequence his "seamen were terrified and dismayed." Before that time it was assumed in Europe that the compass pointed "true to the north pole." The apparent failure to detect the variation earlier was doubtless to some extent due to its small amount at that time along the Mediterranean. The earlier charts showed both lines and compass roses apparently oriented with the true meridian, though there is some evidence to indicate that they were actually oriented with the magnetic meridian, the designer not recognizing any difference. The variation of the compass was first marked on a map in 1532 and on a printed chart in 1595, but the placing of magnetic compasses on charts did not become customary until about fifty years ago. These early charts were drawn on parchment, using bright colors. They were copied by hand, one from another, with gradual variations. They had no projections, and the draftsmen evidently had no idea of the sphericity of the earth. Islands and points were usually exaggerated; shallows were indicated, but no soundings; no information was given as to the interior of the countries; a scale of distances was nearly always provided.