Editing Pytheas (section)

=== Latitude by the elevation of the north pole ===
A second method of determining the latitude of the observer measures the angle of elevation of a [[celestial pole]], north in the northern hemisphere. Seen from zero latitude the north pole's elevation is zero; that is, it is a point on the horizon. The [[declination]] of the observer's [[zenith]] also is zero and therefore so is their latitude.

As the observer's latitude increases (traveling north) so does the declination. The pole rises over the horizon by an angle of the same amount. The elevation at the terrestrial [[North Pole]] is 90° (straight up) and the celestial pole has a declination of the same value. The latitude also is 90.<ref>{{cite book|title=The American Practical Navigator: an Epitome of Navigation|first=Nathaniel|last=Bowditch|author-link=Nathaniel Bowditch|publisher=National Geospatial-Intelligence Agency |date=2002 | edition=Bicentennial  |url=http://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-15.pdf |page=243 |quote=That is, the altitude of the elevated pole is equal to the declination of the zenith, which is equal to the latitude|access-date=7 June 2012}}</ref>

Moderns have [[Polaris]] to mark the approximate location of the North celestial pole, which it does nearly exactly. This was not the case in Pytheas' time, due to the [[precession of the equinoxes]]. Pytheas reported that the pole was an empty space at the corner of a quadrangle, the other three sides of which were marked by stars.<ref>The report survives in the ''Commentary on the Phainomena of Aratos and Eudoxos'', 1.4.1, fragments of which are preserved in [[Hipparchos]].</ref> Their identity has not survived but based on calculations these are believed to have been α and κ in [[Draco (constellation)|Draco]] and β in [[Ursa Minor]].<ref>{{cite web | first=T.E. | last=Rihll | title=Greek and Roman Science and Technology, V3; Specific subjects; Astronomy | url=http://www.swan.ac.uk/grst/Home%20Page%20G&RS&T.htm | publisher=Swansea University | access-date=7 June 2012 | location=Note 14 | archive-date=6 July 2012 | archive-url=https://web.archive.org/web/20120706153833/http://www.swan.ac.uk/grst/Home%20Page%20G%26RS%26T.htm | url-status=dead }}</ref>

Pytheas sailed northward with the intent of locating the Arctic Circle and exploring the "frigid zone" to the north of it at the extreme of the Earth. He did not know the latitude of the circle in degrees. All he had to go by was the definition of the frigid zone as the latitudes north of the line where the celestial arctic circle was equal to the celestial Tropic of Cancer, the ''tropikos kuklos'' (refer to the next subsection). Strabo's angular report of this line as being at 24° may well be based on a tangent known to Pytheas, but he did not say that. In whatever mathematical form Pytheas knew the location, he could only have determined when he was there by taking periodic readings of the elevation of the pole (''eksarma tou polou'' in Strabo and others).{{citation needed|date=December 2017}}

Today the elevation can be obtained easily on ship with a [[Quadrant (instrument)|quadrant]]. Electronic navigational systems have made even this simple measure unnecessary. Longitude was beyond Pytheas and his peers, but it was not of as great a consequence, because ships seldom strayed out of sight of land. East–west distance was a matter of contention to the geographers; they are one of Strabo's most frequent topics. Because of the [[Gnomon|gnōmōn]] north–south distances were accurate often to within a degree.{{citation needed|date=December 2017}}

It is unlikely that any gnōmōn could be read accurately on the pitching deck of a small vessel at night. Pytheas must have made frequent overnight stops to use his gnōmōn and talk to the natives, which would have required interpreters, probably acquired along the way. The few fragments that have survived indicate that this material was a significant part of the ''periplus'', possibly kept as the ship's log. There is little hint of native hostility; the Celts and the Germans appear to have helped him, which suggests that the expedition was put forward as purely scientific. In any case all voyages required stops for food, water and repairs; the treatment of voyagers fell under the special "guest" ethic for visitors.{{citation needed|date=December 2017}}