LET. 1 %. OF THE LATITUDE AND LONGITUDE. 153

which have been used to discover the distancesof places from the equator.

In this enquiry, the first method that suggestsitself, is that of finding the height of the pole.

For as this point is immoveable in the heavens,and is found to be elevated or depressed accord-ing as we are farther from, or nearer to, theequator, it becomes, by this means, a criterionby which we can judge of our distance fromthat circle. Supposing ourselves, therefore, tobe in the northern hemisphere, we will take thispoint for our guide, and endeavour to find thelatitude of the place. The star, usually calledthe north pole star, is not exactly in the northpoint of the heavens : but, for the fake of il-lustrating the subject, we will suppose it was,and fee what will follow from its having thissituation.

Let N S, therefore, be the axis of the earth, ivEQ^the equator, and Z the zenith, or place of 9 'observation: then, since Z O, the distance ofthe zenith from the horizon, is ninety degrees ;and N E, the distance of the pole from theequator, is also ninety degrees; the arc O Ztvill consequently be equal to the arc N E; andif the arc N Z, which is common to them both,be taken away, the remainder O N will be equalto the remainder Z E: but O N is the height ofthe pole above the horizon, and ZE is the lati-tude of the place, or its distance from the

equator;