Difference of Latitude.
2. Difference of latitude is the nearest distance betwixt any two parallels of latitude, shewing how far the one is to the Northward or Southward of the other, which can never exceed 180 degrees. And when the two places are in the same hemisphere (or on the same side of the equator) the lesser latitude subtracted from the greater, and when they are on different sides of the equator, the two latitudes added, gives the difference of latitude.
Longitude.
3. The Longitude of any place (upon the Earth) is an arch of the equator, contained betwixt the meridian of the given place, and some fixed or known meridian; or, it is equal to the angle formed by the two meridians, which properly can never exceed 180 degrees, tho’ sometimes the Longitude is counted Easterly quite round the globe.
Since the meridians are all moveable, and not one that can be fixed in the heavens, (as the equinoctial circle is fixed, from whence the latitudes of all places are determined to be so much either North or South) the longitudes of places cannot so well be fixed from any other meridian, but every Geographer is at his liberty to make which he pleases his first meridian, from whence to calculate the longitudes of other places. Hence it is that geographers of different nations reckon their longitudes from different meridians, commonly choosing the meridian passing through the metropolis of their own country for their first: Thus, the English geographers generally make the meridian of London to be their first, the French that of Paris, and the Dutch that of Amsterdam, &c. and mariners generally reckon the longitude from the last known land they saw. This arbitrary way of reckoning the longitude from different places, makes it necessary, whenever we express the longitude of any place, that the place from whence it is counted be also expressed.
From the preceding definitions arise the following corollaries:
1. If a body should steer directly North, or directly South, quite round the globe, he’ll continually change his latitude; and pass through the two Poles of the world, without deviating the least from the meridian of the place he departed from; and consequently on his return will not differ in his account of time from the people residing in the said place.
2. If a body should steer round the globe either due East, or due West, he’ll continually change his longitude, but will go quite round without altering his latitude; and if his course should be due East, he’ll gain a day compleatly in his reckoning, or reckon one day more than the inhabitants of the place from whence he departed; or if his course had been West, he would have lost one day, or reckon one less.
The reason of which is evident; for admitting our traveller steers due East; so many miles in one day as to make his difference of longitude equivalent to a quarter of an hour of time, it is evident that the next day the Sun will rise to him a quarter of an hour sooner than to the inhabitants of the place from whence he departed; and so daily, in proportion to the rate he travels, which in going quite round, will make up one natural day. In like manner, if he steers due West after the same rate, he’ll lengthen each day a quarter of an hour, and consequently the Sun will rise to him so much later every day; by which means, in going quite round, he’ll lose one day compleat in his reckoning. From whence it follows,
3. If two bodies should set out from the same place, one steering East, and the other West, and so continue their courses quite round, until they arrive at the place from whence they set out, they’ll differ two days in their reckoning at the time of their return.