fame again between the twenty first of September, and the twenty firft of March.

ONE Summer is between the first of Aries, and the second of Taurus, or Tenth of March, and Eleventh of April.

AUTUMN between the fecond of Taurus, and the firft of Cancer; or Eleventh of April, and Tenth of June.

WINTER between the first of Cancer, and the twenty eighth of Leo or the Tenth of June, and Tenth of Auguft.

SPRING between the twenty eighth of Leo, and first of Libra ; or Tenth of Auguft, and Twelfth of September.

AND the fame Seafons return when the Sun is in the oppofite Places of the Ecliptic; which is eafily demonftrated on the Globe, according to the forefaid Definitions, or the Sun's Distance from the Zenith. But as to the terreftrial Seafons, they are different in feveral Places under the Equator.

2. THE Places in the North Torrid Zone have the end of Autumn, and beginning of Winter at the fame time on the twenty firft of December; but the beginning and end of the other Seafons of Summer and Spring, and alfo the beginning of Autumn, are not at the fame time, but are on different Days in different Places; for the end of Autumn, and beginning of Winter, is there when the Sun is furtheft from the Zenith, when in the Meridian, which happens in the first Degree of Capricorn. The other Part is alfo plain, for if the Places have different Latitudes, the Sun will be in their Zenith on different Days; that is, their Summer begins at different Times, and will have a mean Distance from the Zenith at different Times, and fo their Summer will end, and Autumn begin at different Times. And in the fame way, their Winter will end, and Spring begin at

different

SECT. VI. different times; because the mean Distance from their Zenith will be different; tho' it will, in all Places, begin between the Tenth of December, and the Tenth of March.

3. THE Places in the South Torrid Zone havé the end of Autumn, and beginning of Winter at the fame Time i. e. the Tenth of June; but the beginning of Summer and Spring, and the beginning of Autumin, are not at the fame Time, but different in different Places; yet fo as the Summer there falls always between the Tenth of September, and the Tenth of December; and the end of Autumn, and beginning of Summer, between the Tenth of March, and the Tenth of June; and the beginning of Spring, and end of Winter, between the Tenth of June, and the Tenth of September. This may be proved as the former was; for the Sun, being in the first of Cancer, is then at it's greatest Distance from them; and then it's Winter in them all and the Sun being vertical to them in different times, their Summer, and confequently Autumn and Spring, are at different times.

4. THOSE Places between the Equator and the eighth Degree of North, or South, Latitude have fomething peculiar; viz. the Sun, by approaching to, and withdrawing from their Zenith, makes two Summers, two Springs, and but one Autumn, and one Winter in a perverted order, thus; Spring, Summer, Spring, Summer, Autumn, Winter.

THE Caufe of this Paradox is this: fuppofe a Place in the eighth Degree of North Latitude, the Sun is vertical to it in the tenth Degree of Aries, and then Summer and Winter will be to them when the Sun is in the first of Capricorn, which is twenty feven Degrees thirty Minutes from the Parallel of the eighth Degree of North

Latitude

Latitude; and the Sun will have a mean Distance when 'tis thirteen Degrees forty five Minutes from them; which happens four times in a Year; 1. when in the third of Gemini, then the Spring begins, because the Sun begins then nearly to approach to the Zenith of the Place, where it will be Summer again in the twentieth of Virgo; and when it comes to the twenty fifth of Libra, 'tis at a mean Distance again, and then begins Autumn; the Sun withdrawing from them; and at the first of Capricorn it is Winter; and at five Degrees of Pifces 'tis at a mean Distance again, and then begins Spring, for the Sun is approaching to them and the fame happens in Places under the eighth Degree of South Latitude.

BUT if the Place be above eight Degrees Latitude, then it doth not hold good; for the Sun in Gancer, or Capricorn, is here a lefs Distance than a Mean for if in the ninth Degree of North Latitude the greatest Distance will be at the first of Capricorn, which is thirty two Degrees of Declination North and South; and the Mean fixteen, which is more than the firft of Cancer's Distance, which is but fourteen Degrees thirty Minutes; therefore Summer will then laft 'till the Sun be fixteen Degrees from their Zenith, which is not 'till the Sun comes to the twenty fourth Degree of Libra, about the Sixth of October.

THERE feem to be here fome new Difficulties; 1. That it cannot be Summer with them when the Sun is in Cancer, Leo, Virgo, for the Sun is in them both going from and to the Zenith; but that 'tis Summer only in the going from the Zenith. I anfwer, that Summer confifts in it's going back from the Zenith to a mean Distance, which it never does 'till it come to the twenty fourth of Libra, when the Summer must end.

2. IN Places under the eighth Degree of Latitude, or in the fourth, as was fuppofed, the Spring could not begin when the Sun is in the third of Gemini, for then 'tis going further from the Zenith; but it goes only one Degree further, and therefore we faid it was nearly Spring, and we cannot make a fifth Seafon for that fmall Matter.

OTHERS may think we should not put Spring between two Summers, but count it all Summer, while the Sun is at lefs than a mean Distance from the Zenith. And tho' it go a Degree further, yet that will not cool the Air fenfibly, but rather, by it's Continuance, increase it; tho' we fhall not difpute that matter, only think the Method laid down is beft. But enough, or too much, of this (a).

(a) Mr. Ditton has given a geometrical and cafier DemonAtration of this Paradox. By the Definitions explained un der Prop. 2. Each of thofe Places fhould be fo fituated, that two Points may be taken in its Meridian, one lying to the North, the other at an equal Distance to the South; the Diftance whereof fuppofe from the Vertex equal to the mean Diftance of the Sun from the fame. Let now AB be the Equator, (Fig. 32.) CD and EF the Tropics, and CAE, FBD, the Meridian of the Place, and a Place therein b, as remote as poffible from the Equator to the North. The North Point therefore is C, whofe Distance bC is equal to the mean Diftance of the Sun,

or half bE (for because there is no leaft Distance of the Sun, therefore the mean Distance is half the greater) that is, to a third of CE. or 47=3 15. Therefore as CA is 231, Ab will be nearly eight Degrees; and therefore all thefe Places are nearly within eight Degrees of the Equator. "But the Sun proceeding in its annua! Motion from E to C, and then again returning to E, produces the abovementioned Seafons in this Order. When in the Point E, where the Distance is greatest from the Place b, it begins Winter, in d the Spring (viz. bd=bC) in b the Summer, in C the fecond Spring, in b the second Summer, and in d the Au tump.

PRO

PROPOSITION IV.

A Place being given in the Torrid Zone, to find the Days when the Summer, Autumn, Spring, and Winter begin and end there.

1. IF the Place be in the Equator, we fhewed in the preceding Propofition when the Seasons of the Year begin; each returning twice in one Year.

2. IF the Place be beyond the eighth Degree of Latitude, bring it to the brafs Meridian, and mark with Chalk the Place it is under; then turning the Globe obferve what Part of the Ecliptic comes under the Mark, and when the Sun comes there, Summer begins; then obferve the middle Degree between the Mark, and the Tropic of Capricorn, if the Place have a North Latitude, but the Tropic of Cancer if South; and turn the Globe 'till two Points of the Ecliptic come under that middle Degree: the one is the Place the Sun is in when Spring, the other when Autumn begins; and Winter will be when the Sun is in the first of Capricorn, if the Place be to the North, but Cancer, if to the South of the Equator. The fame may be done by the Maps, but more accurately by the Tables of Declination.

IN which find the Declination equal to the Latitude, and againft it you will have four Days of the Year; and take that Day for the beginning of Summer which is between the Tenth of March and June, if the Place be North; and between the Tenth of September, and Tenth of December, if South Latitude.

THEN take the half of the Latitude from eleven Degrees ninety five Minutes, and find the Remainder in the Table, you will fee again four Days against it, in two of which the Sun is at a VOL. II.

E

mean