From hence may be shewed the error of that geographical paradox, _viz._ If a place A bears from another B due West, B shall not bear from A due East. I find this paradox vindicated by an author, who at the same time gives a true definition of a rhumb line: But his arguments are ungeometrical; for if it be admitted that the East and West lines make the same angles with all the meridians through which they pass, it will follow that these lines are the parallels of latitude: For any parallel of latitude is the continuation of the surface of a _Cone_, whose sides are the radii of the sphere, and circumference of its base the said parallel; and it is evident, that all the meridians cut the said surface at right (and therefore at equal) angles; whence it follows, that the rhumbs of East and West are the parallels of latitude, though the case may seem different, when we draw inclining lines (like meridians) upon paper, without carrying our ideas any farther. PROB. IX. _To find the_ Antœci, Periœci, _and_ Antipodes _to any given place._ Bring the given place to the meridian; and having found its latitude, count the same number of degrees on the meridian from the equator towards the contrary Pole, and that will give the place of the _Antœci_. The globe being still in the same position, set the hour index to XII at noon, then turn the globe about ’till the index points to the lower XII; the place which then lies under the meridian, having the same latitude with the given place, is the _Periœci_ required. As the globe now stands, the _Antipodes_ of the given place are under the same point of the meridian, that its _Antœci_ stood before: Or, if you reckon 180 degrees upon the meridian from the given place, that point will be the _Antipodes_. Let the given place be _London_, in the latitude of 51½ degrees North, that place which lies under the same meridian and the latitude 51½ degrees South, is the _Antœci_; that which lies in the same parallel with _London_, and 180 degrees of longitude from it, is the _Periœci_, and the _Antipodes_ is the place whose longitude from _London_ is 180 degrees, and latitude 51½ degrees South. PROB. X. _The Hour of the Day at one place being given; to find the correspondent Hour (or what o’Clock it is at that time) in any other place._ The difference of time betwixt two places is the same with their difference of longitude; wherefore having found their difference of longitude, reduced into time (by allowing one hour for every 15 degrees, _&c._) and if the place where the hour is required lies (Easterly/Westerly) from the place where the hour is given, (add/subtract) the difference of longitude reduced into time (to/from) the hour given; and the sum or remainder will accordingly be the hour required. Or,