154 OF THE LATITUDE and longitude.

plate IV.fig. 9 .

equator; and therefore, if the height of thepole above the horizon be taken by means of aquadrant, or any other instrument proper forthe purpose, it will evidently give the latitudeof the place where the observation was made.Thus, the height of the north pole at Londonis found to be about fifty-one degrees, thirty-two minutes ; and therefore this is the latitudeof the place, or its distance north from theequator.

But as the pole star is not exactly in the northpoint of the heavens, let some other star be takenwhich is about eight or nine degrees from thatpoint; and find, with a quadrant, its greatest andleast altitude, in the same manner as before.Then, as the star moves in a small circle roundthe pole, which it describes in about 24 hours,it is evident that, if the least of the two alti-tudes be added to half their difference, it willgive the height of the pole, or the latitude ofthe place required. For, let b and a be the twopositions of the star at its greatest and least alti-tudes, and N the true north point of the world;then, since b and a are diametrically oppositeto each other, and N is exactly in the middlebetween them, it is plain that if O s, the leastaltitude, be added to a N, half the difference ofthe altitudes, it will give O N, the height ofthe pole above the horizon; which, as was

before