and the Distance of the Places in which we have one Side, the Complement of the Latitude of the one, and two Angles; the one is the Difference of Longitude; and the other the Point made by the Meridian and the Distance, to find the Distance. The Solution by the Globe and the Planifphere is eafy, and by Logarithmical Calculation accurate enough; and even by common Calculation: we fhall only use the way by the Globe for the Reafon before mentioned; though by the Planisphere 'tis easier; but that by the Globe gives the Triangle itself.

SUPPOSE the firft Meridian to be that of the place whofe Latitude is not given; count the Difference of Longitude on the Equator, and mark the ending with Chalk, and bring it to the Meridian which will be the Meridian of the other place; count on it the given Latitude; and elevate the Pole for that Latitude; the Globe being fixed, bring the Quadrant to the Zenith, and turn it 'till it come to the Point on the Horizon; the Place where the Quadrant cuts the first Meridian will be the one place, and the Arc between the Zenith; and that Point is the Distance fought. And at the fame time you will fee the Latitude of the other place.

PROPOSITION XII.

Having the Distance of two Places in the fame Meridian, and the Points in which a third lies from the other two, to find the Distance of the third from the other two.

WE have here again a spherical Triangle, in which the three Sides are the three Distances of the Places, and one Side is given; the Distance of the two in the fame Meridian, and the two

R 3

adjacent

adjacent Angles, and the other two Sides are wanted.

OMITTING the Methods by Calculation, and by the Planisphere (tho' more accurate) we fhall give that by the Globe; which exhibits the thing to the Eye.

TAKE the Distance of the two places in the brafs Meridian; then elevate the Pole for the Latitude of the one, and fix the Quadrant at the Zenith, and bring it to the Point the third place lies in, and draw a Line along it with Chalk; then fix the Quadrant at the other place brought to the Zenith, and turn it 'till it come to the Point the third place lies in from the fecond place; and where it cuts the Arch by the Chalk, you have the third place, whofe Distance from the other two is easily measured,

CHA P. XXXIV.

Of the Senfible or Vifible Horizon.

TH

HE Senfible Horizon is a Periphery on the Superficies of the Earth, which terminates the Sight all round, or which terminates that Part of the Superficies vifible to the Eye, whilft the Spectator turns himself round; or from which Rays can come to the Eye. It's Semidiameter is an Arc of a great Circle on the Earth, between the Foot of the Spectator and the Periphery, which is therefore perpendicular to that Periphery.

PROPOSITION I.

The Extenfion of the Senfible Horizon is various, according to the Height of the Eye; or as the Semidiameter of the Earth is fuppofed to be.

Let MPNF (Fig. 49.) be a great Circle on the Earth, T the Center, TP the Semidiameter, PO the Altitude of the Eye, and O the Eye; draw from O the Tangents ON, OM; and let us conceive the Ray NO to be carried round, and to describe a Periphery on the Earth; which will be the Senfible Horizon, whofe Semidiameter is P N, PM, for NO, MO, are the last Rays that can come to the Eye from the Earth; which we here suppose perfectly round.

AND 'tis plain if we take a greater or less Altitude PO, then PN will be a greater or leffer

Arc; and if TP be more or fewer Miles, then PN will be so alfo.

THESE two feem to be the Causes why the Antients differ fo much in their Opinions of the bignefs of this Horizon. Macrobius makes the Semidiameter of it one hundred and eighty Furlongs, or twenty two Miles and a half; and Eratosthenes three hundred and fifty Furlongs, or forty four Miles; Albertus Magnus a thousand Furlongs, or one hundred and twenty five Miles; Proclus two thoufand Furlongs, or two hundred and fifty Miles; a great many make it five hundred Furlongs, or fixty two Miles and a half: which Diverfity proceeds alfo from the different Lengths of Furlongs, as appears from the following Propofition.

PROPOSITION II.

Having the Height of the Eye above the Ground, and the Semidiameter of the Earth; to find the Semidiameter of the Senfible Horizon.

Let PO (Fig. 49.) be the Man's Stature, O the Eye, TP the Semidiameter, ON the Ray touching the Earth, which terminates that Horizon; therefore PN is it's Semidiameter, whofe Length is wanted: PO being fuppofed five Foot, is added to the Semidiameter TP, which makes TO 19598300 Feet; and in the Triangle NTO we have TO and TN, and the Angle TNO ninety Degrees; the Angle NTO is found thus, As TO is to TN, So is the whole Sine to the Sine of the Angle NOT; whofe Complement is the Angle NTO, or Arc NP, which may be turned to Miles,

COROL

COROLLARY

FROM hence we may fee, that if TP or PO be taken of different Lengths, there will come out different Degrees in the Arc NP.

PROPOSITION III.

Having the Height of the Eye on a Tower, or Mountain, to find how far the Sight extends on the Sea.

Let PO (Fig. 49.) be the Altitude of the Tower, and work as before; for here the Height of a Man is not confiderable.

PROPOSITION IV.

The greatest Length that the Sight extends being given; or the Semidiamer of the Senfible Horizon; to find at what Height the Eye is placed.

OR, which is the fame thing, having the greatest Distance that the Top of a Mountain can be seen at, to find the Altitude of the Mountain.

IN the Triangle NTO (Fig. 49.) there is given the Angle at N of ninety Degrees; and the Arc NP, which is the Meafure NTO, and the Semidiameter NT, to find TO, from which take TP, and you have PO.

t

WE may therefore, by fuppofing a certain Measure of the Semidiameter of the Earth, find, from the Quantity affigned, by different Authors, to the vifible Horizon, what Height of the Eye each Author affumed.

PRO