above the

Elevation of the Pole, or its Distance from the Ho- Lecture rizon, is the Arch PO, the Latitude of the Place XVIII or its Distance from the Equator is Z E. And because the Arch P E between the Pole and the Equator is a Quadrant, or fourth Part of a Circle, The Height and the Arch ZO, from the Zenith to the Hori. of the Pule zon is likewise a Quadrant, these two Arches ZÆHrzon is and PO must be equal. Take away the Arch Z P, always ewhich is common to both, and there will remain qua to the the Arch ZÆ equal to the Arch PO; that is, the the Place. Latitude of Latitude of the Place, is equal to the Altitude or Height of the Pole above the Horizon.

HENCE we have a Method of measuring the Circumference of the whole Earth, and of knowing how many Miles it is round the Earth: For if we go directly Northward till the Pole be elevated one Degree higher, and then if we measure the length of the Way we have gone Northward, and have the Number of Miles it contains, we shall have the Number of Miles in a Degree of a great Circle of the Earth's Globe; and this Number multiplied by 360, the Degrees in the whole Periphery, it will give the Length of the Circumference of the Earth in Miles. By the most accurate Obfervations, the Length of a Degree is found to be 69 English Miles, which was commonly reputed to be only 60 Miles.

LECTURE

Lecture
XIX.

LECTURE XIX.

Of the Doctrine of the Sphere.

The Right Pofition of the Sphere.

T

the

HE Angle contained between Æquator and the Horizon, is measured by the Arch of the Meridian EH, which is the Complement of the Latitude to a Quadrant. And therefore if that Angle be right, the Latitude of the Place will be nothing, or the Place will be in the Equator; or the Equinoctial Circle will pass thro the Vertex of the Place, and all the Parallels of the Æquator will be perpendicular to the Horizon; and therefore this Pofition of the Sphere is call'd a Right Pofition, in which all these Parallels are cut by the Horizon into equal Portions; whence the Stars are as long above the Horizon, as they lie hid under it Here likewife the Poles lie in the Horizon without any Elevation, as is manifest by the Figure, where the Point of the Æquinoctial Æ is in the Vertex, and the Poles Pp, in the HoriPlate XVI. Zon. If we go from the Equator towards either of the Poles, the Equator will then appear to depart from the Vertex or Zenith, and to come nearer to the Horizon, making with it an oblique An oblique Angle; whence fuch a Situation is called an oblique Sphere; or Pofition of the Sphere, and the Pole towards which an oblique Pofition of we move, doth rife more and more above the the Sphere. Horizon, the nearer we approach it; its Eleva

Fig. 5.

Fig. 6.

tion being always equal to the Latitude of the Place, while the other continues as much depreffed below it. The Figure does clearly fhew this fort of Pofition, which we and all that live in the temperate Zones obtain, where the Equator A Q is bifected by the Horizon, as it is in a right

Sphere.

Sphere: Wherefore when the Sun, by his apparent Lecture
Diurnal Motion, describes this Circle, it makes XIX.
the Day equal to the Night; but the Parallels of
the Æquator, in this Oblique Pofition, are not cut
into two equal Parts by the Horizon; but those
which are towards the elevated Pole, each of them
have a greater Portion above than under the Ho-
rizon: And as each Parallel is nearer the Pole, fo
much the larger Potion of it ftands above the
Horizon. But when the Distance of the Parallel
from the Pole becomes less than the Elevation of
the Pole, or the Latitude of the Place, then that
Parallel, and all thofe included within it, are
wholly above the Horizon, no Part of them ever
fetting under it. The contrary happens in the
Parallels which lie towards the deprefs'd Pole, a
smaller Portion of them being above the Horizon,
and the greater Part lying under it. And thofe
Parallels, which are nearer to the depreffed Pole
than the Latitude of the Place, remain perpetually,
together with the Stars included within them, un-
der the Horizon, and are never visible to us.
Hence it is neceffary, fince the Sun each Day de-
fcribes by his apparent Diurnal Motion fome Par-
allel, that from the Vernal Equinox to the Sum-
mer Solstice, the Days growing longer and longer,
will be continually longer than the Nights; after
the Solstice, tho' the Days continue till the Au-
tumnal Equinox to be longer than the Nights, yet
they become shorter and fhorter, and at the Equi-
nox, they but juft equal the Nights: From thence
to the Winter Solstice, the Days continually become
fhorter than the Nights, and are the shortest when
the Sun is in that Solftice; but as the Sun leaves
it, they increase again, and in the Vernal Equinox
the Day is as long as the Night,

IN an Oblique Sphere the Stars all obliquely rife and fet. And as the Right Afcenfion of a Star is the Arch of the Equator contained between the firft of Aries, and that Point which comes to the Meridian with the Star, or that Point which in a Right Sphere rifes with the Star: So the Oblique

Afcen

Lecture Afcenfion is the Arch of the Equator between the XIX. firft of Aries, and that Point of the Equator which

Plate XVI.
Fig. 7.

rifes together with the Star in an Oblique Sphere, and numbred from West to Eaft, which according to the Obliquity of the Sphere is various. The Difference between the Right and the Oblique Afcenfion is called the Afcenfional Difference.

IN an Oblique Sphere there is one Parallel as much diftant from the elevated Pole, as the Place is from the Equator, which is called the Circle of Perpetual Apparition, or the biggest of all those which conftantly appear; which is fuch, that all Stars inclosed within it never either rife or fet; though they fometimes rife higher, fometimes defcend lower towards the Horizon. Towards the other Pole, there is another Circle oppofite to this, which is the Circle of Perpetual Occultation, within which all the Stars that are contained never rise, but conftantly lie hid under the Horizon, and fo are not to be seen.

IF the Equator makes no Angle with the Horizon, but thofe two Circles coincide; in fuch a Situation the Pole and Vertex coincide, and all the Parallels of the Equator become Parallels to A Parallel the Horizon; and fuch a Situation is call'd a Sphere, Parallel Sphere, in which no fixed Stars do ever either rife or fet, but turn round in Circles parallel to the Horizon. And when the Sun enters the Equinoctial, it then glides the whole Day along the Horizon. When he rises towards the elevated Pole, he never fets, but makes a very long Day of fix Months: But when he goes from the Equinoctial towards the depreffed Pole, he never rifes, and then there is conftant Night of fix Months Length. This Pofition of the Sphere belongs only to them who live at the Pole, if any are fo miferable as to have fuch a Place for their Habitation.

THE ancient Geographers divided the Earth by Climates and Parallels; for they who live under the Equinoctial, being in a Right Sphere, have their Days and Nights equal: If we remove from

thence

thence towards either Pole, the Days in Summer Lecture become longer than the Nights, and the nearer we XIX. approach the Pole, the greater is the Difference between Day and Night, when the Day is at the longeft; till we come under the Polar Circles, where there is no Night at all. Hence the Geographers did fo divide the Earth by such Parallels, as made the longest Day increase by Quarters of an Hour; that is, each Parallel was fo far distant from the next, that the longest Day in the more romote from the Equator, was a Quarter of an Hour longer than that Day at the Parallel nearer to the Æquator: And therefore reckoning the Aquator as the firft Parallel, the fecond Parallel paffed through those Parts of the Earth, where the longest Day was twelve Hours and a Quarter long. Under the third Parallel, the longest Day was twelve Hours and two Quarters. In the fourth, the longeft Day was twelve Hours and three Quarters, c. Now two fuch Parallels made up a Climate, which were therefore diftinguifhed by the longest Day, increafing half an Hour from the one to the other. Now the Excefs of the Solftitial Day above twelve Hours may grow ftill bigger, till we come to the Polar Circle, where the Sun not fetting, makes the Day twenty-four Hours long, which is greater than the Equinoctial Day of twelve Hours by twenty-four half Hours, or forty eight Quarters of an Hour. From hence we gather, that the Number of Climates between the Equator and Polar Circles must be twenty-four, and the Number of the Parallels forty-eight.

BECAUSE the Civil Year of the Ancients did The rifing not keep Pace or agree with the apparent annual and fetting Motion of the Sun; having the Day of the Month, of the Stars Cofmical, and the Year when any memorable Action fell Achronical, out, it could not be from thence immediately and Heliaknown in what Seafon of the Year it was done, cal. And therefore, when the Husbandmen fettled the Times for the feveral diftinct Parts of their Bufinefs, they could not point out that Time by a certain Day of their Kalendar; for the fame

Day