guifhed rays. At fuch diftances its figure could not be difcerned by fenfe, unless it was affifted by a telefcope or fome equivalent inftrument. 10. The ocean, which covers a great part of the furface of the earth, is more accurately globular than the folid parts; and it is manifeft that this arifes from the gravitation of its parts towards the earth, acting in right lines perpendicular to its furface. For if its direction formed an acute angle with the furface, the fluid water would neceffarily move towards that fide, and could not be in equilibrio till the direction of gravity became perpendicular to the furface every where, fo as to give no inclination to the fluid to move towards either fide. The perpendiculars to a fpherical furface meet all in the centre of the fphere. Therefore, fince the earth is nearly a fphere, the direction of the gravity is nearly towards it centre; not as if there was really any virtue or charm in the point called the centre, by which it attracted bodies, But because this is the refult of the gravitation of bodies towards all the parts of which the earth confifts; as will appear more fully afterwards. The direction of gravity is not any one fixed or determined one, as the vulgar are apt to imagine; nor is there any occafion for pillars or instruments of any kind to fupport the earth; that direction being always downwards which is towards the centre, or (to fpeak more accurately) which is perpendicular to the fluid furface or level, on the concave fide; and that direction being upwards which lies in a perpendicular to the furface on the convex fide. Was the earth all fluid, all the furface would be on one level, and no one part would have a pre-eminence above the reft in this refpect; and bodies would be fuftained by the earth equally round all its furface with equal firmness and fecurity.. Thus there is no difficulty in conceiving that there are Antipodes; and it appears equally abfurd that bodies fhould fall off from any other part of the earth, as that they should rise here into the air. 11. This principle of gravity extends to all bodies. around the earth. For the gravity of the air being established beyond all difpute, by the celebrated experiments of Galileo and Torricelli, and many others of the fame kind, it easily appears that all terrestrial bodies whatsoever are heavy, or gravitate towards the earth; and that the apparent levity of fome of them proceeds only from the greater gravity of the ambient air, which makes them rife upwards, for the fame reason that cork rifes in water, and lead in quick-filver; or from their being carried off by fome medium entangled in its parts. The gravity of terreftrial bodies must the rather be allowed to be univerfal, because, by the most accurate experiments, it is always found to obferve the fame proportion as their quantities of matter; and not to depend on the figure or bulk of bodies, or the contexture of their parts, but always to measure their quantity of matter, and to be measured by it only, abftracting from the influence of the medium in which they fwim. For gravity always generates the fame velocity, in bodies of all forts, in the fame time; and therefore muft act equally on equal portions of matter, and on a greater portion with a force proportionally greater. The direction of this power is nearly towards the centre of the earth; for, at prefent, we abstract from the variation of its figure from that of a perfect sphere, arifing from its motion on its axis. The force of this power is fuch, that it carries all bodies downwards about 15 feet, of Paris meafure, in a second of time. This is the refult of accurate experiments; every body would fall just fo R 3 much Book III. much if it defcended freely in the plump line, or perpendicular to the horizon, and met with no refiftance from the air or ambient medium. When a body is projected in a right line that is not perpendicular to the horizon, it moves in a curve, but fo as to fall always below the point in the line of projection which is directly over it, as much as it would have fallen by defcending freely in the perpendicular in the fame time; provided we fuppofe gravity to act in parallel lines, as was ufual before Sir Ifaac Newton found it neceffary to confider this fubject more accurately, and which may be admitted, without any fenfible error, in fuch motions as our engines are able to produce. 12. The globular figure of the earth, with the direction and force of gravity, being difcovered by this analyfis, a great variety of phænomena may be thence deduced by the Synthetic method. The whole doctrine of the fphere may be explained from the figure of the earth, either in the Pythagorean or Ptolemaic fyftem. As the fun appears to go round the whole circle of 360 degrees in 24 hours, fo in one hour he appears to defcribe 15 degrees, and one degree in 4 minutes of time, on the equator or its parallels. Hence the diftance of meridians at two places, measured upon the equator, or their difference of longitude, being known, it is easy to compute how much the hours at one place precede the fame hours at the other, by allowing 4 minutes of time for each degree of that distance; and converfely, the difference of time being given, the difference of longitude is computed by allowing one degree for each 4 minutes of time, and proportionally in greater or leffer differences. And it is obvious that the hours of the day, which are fucceffive in any one place, are co-exiftent when you take in the whole globe; globe; fo that no hour of the day can be affigned, but a meridian can be likewife affigned where it is that hour at this prefent time. The fenfible horizon of any place is a plane perpendicular to the plumbline at that place, and tangent to the earth's surface there. The rational horizon is a plane thro' the earth's centre parallel to this, whofe poles are the zenith and nadir, in the fame manner as the north and fouth poles of the world are the poles of the equator. The particular phænomena of places depend upon the pofition of their horizon with refpect to the circles of the apparent diurnal motion of the fun and stars. The horizon of a place at the equator paffes thro' the poles, and divides equally the equator and its parallels. Hence the days and nights are always equal in fuch places, and each of the stars performs one half of its revolution above their horizon, and the other half under it. The circles of diurnal motion are all perpendicular to their horizon, and therefore they are faid to be in a right fphere. When the fun moves in the equator, he rifes directly from their horizon to their zenith, and then defcends directly to their horizon again; in other cafes, after rifing perpendicularly, he flopes away in his parallel towards the north or fouth fide of their zenith, according to the feafon of the year; which must be a confiderable relief to them, as the heat mult thereby be abated. At the poles, their horizon coincides with the equator; fo that the northern celeftial hemifphere must be always in view of the northern pole, being above their horizon, while no part of the fouthern hemifphere is vifible to them, being always beneath it. The circles of the diurnal motion being parallel to the æquator, and confequently to their horizon, the fun and ftars appear to them to move in parallels to their horizon; the fixed ftars never rife nor fet, and the fun rifes at the vernal equinox and fets at the autumnal; fo that they have day for one half year and night for the other. They are faid to be under a parallel sphere. In intermediate places, the circles of the diurnal motion are oblique to their horizon; one pole is always elevated above it by an arc equal to the latitude of the place, and the other pole is depreffed under it by an equal arc. All the ftars whofe diftance from the elevated pole exceeds not the latitude of the place are constantly above their horizon; and thofe within the fame distance of the other pole are depreffed under it, and are never vifible to them. The equator and horizon being great circles divide each other equally, whence the days and nights are equal every where when the fun defcribes the celeftial equator. But when the fun is on the fame fide with the elevated pole, a greater portion of his parallel is above the horizon than under it, and therefore the days are longer than the nights: and when the fun is on the other fide of the equator, a greater portion of his diurnal parallel is below the horizon than above it; and confequently the nights are longer than the days. Thefe are faid to be under an oblique fphere. In all thofe different places, the time in which they have day (that is, when the centre of the fun is above the horizon) is equal to the time in which they have night, or when the centre of the fun is beneath their horizon, taking the whole year together; abftracting from the effects of refraction and the elliptic figure of the earth's orbit, which are not confidered in the doctrine of the fphere. But thefe equal times are diftributed with a good deal of variety. At the equator they have 12 hours day and 12 hours night, perpetually fucceeding each other. At the poles they have their day all at once and their night at once, each of half a year. In intermediate places, the |