ASTRONOMY.

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and the force at H in the same direction tends to separate H and O,and since the force which tends to separate them is the greater, theparticles about II will recede from O ; thus also the Moon ’s forceat O which tends to separate O and I), is greater than the force atD, which tends to unite them : therefore the particles about Dwill recede from O, and consequently the particles about B andF will fall toward the centre till there be an equilibrium ; and sincethis would happen to every fluid ring passing the place to whichthe Moon is'vertical, if the surface of the Earth were entirely sea toa great depth, it would assume a spheroidical form, having itslongest axis directed toward the Moon .

(15S.) From the preceding reasoning, it appears, that thp partsof the Earth directly under the Moon , as at II, and also the op-posite parts at D, will have the flood or high-water at the sametime, while the parts at B and F, at 90° distance, or where theM oon appears in the horizon, will then have the ebbs, or lowestwaters, lienee, as the Earth, turns round her axis from the Moon tothe Moon again in 24h. 48m. this oval of water must, shift with it,and thus there will be two tides of flood, and two of ebb, in thattime. It farther appears, that by the motion of the Earth on heraxis, the most elevated part of the water is carried beyond theMoon , in the direction of the rotation ; so that the water continuesto rise after it has passed directly under the Moon , though the im-mediate action of the Moon there begins to decrease ; and comesnot to its greatest elevation, till it has got about half a quadrantfarther. It continues to descend after it has passed at 90° fromthe point below the Moon , to a like distance of half a quadrant.The greatest elevation, therefore, is not in the line drawn throughthe centres of the Earth and Moon , nor the lowest points, wherethe Moon appears in the horizon, but all these are removed abouthalf a quadrant eastward from these points in the direction of themotion of rotation. Thus, in open seas, where the water flowsfreely, the Moon , M, is generally past the north and south me-ridian, as at /), when the high-water is at Z, and at n; the reason ofwhich is plain, because the Moon acts with the same force aftershe has passed the meridian, and thus adds to the libratory orwaving motion which the water acquired, when she was in themeridian.

(150.) Besides, the tides answer not always to (he distance ofthe Moon from the meridian, at the same places, for the action ofthe Sun brings them on sooner when the Moon is in her 1st and3d quarters, and keeps them back later when she is in her 2d and4th; because, in the former case, the tide, raised by the Sun alone, would be earlier, than that raised by the Moon , and in thelatter case, later. We have hitherto adverted only to the actionof the Moon , in producing the tides: but it is evident, that for thesame reasons, the inequality of the Suu’s action, on different partsof the Earth , would produce a like effect, and a like deviationfrom an exact spherical figure ; so that, in reality, there are twotides, every natural day, from the action of the "Sun , as there arein a lunar day, from the action of the Moon , subject to the samelaws ; and tV . lunar tide, as lias been observed, is somewhatchanged by if- action of the Sun , the change varying every day,on account of the inequality between the natural"ami lunar dav.Although the gravitation of the Earth towards the Sun , is muchgreater than its gravitation towards the Moon , yet, by reason of theSun's immense distance, to which the Earth ’s diameter bears asmall proportion, his action upon the side of the Earth next to himdiffers but little from that which is exerted on the side farthestfrom him, and it is only the inequalities in that action that producethe tide. However, the effect of the Sun is still very sensible, butthat of the Moon is much more so: for by its proximity to theEarth , there is a considerable inequality, both in the direction ofits action, and in the intensity of that action upon different parts ofthe Earth .

(160.) Hence it is easy to see, that the tides must be greatest atNew and at Full Moon , because the actions of the Sun and Moonare then exerted in the same directions. These are called springtides; whereas, when the Sun and Moon are 90° distant, theaction of the one luminary raises the tides, just where that of theother depresses them, and thus are produced what are called neaptides. Newton lias calculated the effects of the Sun and Moonrespectively upon the tides from their attractive powers ; the for-mer he finJs to he, to the force of gravity, as 1 to 12868200. Tofind the force of the latter upon the water", he compares the spring-tides at the mouth of the river Avon, below Bristol, with the neap-

tides, and finds the proportion as 9 to 5 : whence after several ne-cetsary corrections, he concludes, that tlic force of the Moon , mmoving the waters, is to that of the Sun , as 4,4815 to 1. Dr.Horsley, however, in his edition of Newton’s l’rincipia, estimatesthe force of the Moon to that of the Sun , as 5,0469 to 1, and otherauthors have given different proportions; but Newton computes,from his proportion, that the Moon may raise the waters 9 feet,1^ inch, and the Sun and Moon together may produce an eleva-tion of about 1 1 feet, 2 inche.-,, and about 12t feel, when the Moon is at her nearest distance. Now this is found by observation, tobe nearly the height to which the water rises, on the coasts of theopen and deep ocean. It must be observed, that the spring-tidesdo not happen precisely at New and Full Moon , nor the neap-tidesprecisely at the quarters, but a day or two after, because, as inother cases, so in this, the effect is not greatest or least, when theimmediate influence of the cause is greatest or least, for if the ac-tions of the Bun and Moon were to cease, yet the tides would con-tinue for some time ; as the waves of the sea continue their motionafter a storm. The different distances of the Moon from the Earth produce a sensible variation in the tides ; and Newton has shewn,that they increase as the cubes of the distances decrease ; so thatthe Moon at half her distance, would produce a tide S timesgreater. The Moon describes an ellipsis round the Earth ; and ather nearest distance, produces a tide, sensibly greater than at herfarthest distance. Hence two great spring-tides never succeedeach other, at the distance of 14 days ; for, if the Moon be at herleast distance at the change, and therefore produce a great spring-tide, she will be at her greatest distance at the full, and therefore,the spring-tide will be less. The spring-tides are highest, and theneap-tides lowest, about the lime of the equinoxes ; because, w erethe Sun or Moon in the pole of the world, there would be no tide;for their action would raise the water at the equator, or any pa-rallel, equally round the Earth : therefore, the nearer they are tothe equator, the greater must be their effect. When the Sun andMoon traverse the equator, the tides, which are under them, willtraverse the greatest circle, and the waters will be put into thegreatest agitation. They will also be the greater at these limes,because the Earth is nearer to the Sim, about the beginning ofMarch, and end of September, than in the summer months. Asthe greatest of the two tides, happening in every diurnal revolu-tion of the Moon, is that in wdiich the Moon is nearest the zenithor nadir, therefore, while the Sun is in the northern signs, thegreater of the two diurnal tides, in our climate, will be that arisingfrom the Moon when above the horizon ; and when the Sun is inthe southern signs, the greatest is that arising from the Moon be-low the horizon. Tims, the evening-tides in summer exceed th.-morning-tides, and the ■ morning-tides in winter exceed the even- 'mg-tides. This difference is found at Bristol to be 15 inches, ar.dat Plymouth 12 indies.

(161.) Such would the tides regularly be; if the Earth were co-vered all over with the sea, to a great depth, so that the watersmight freely follow the influence of the Sun and Moon ; but, asthe tides pass over shoals, and run through straights into bays of thesea, their motion becomes more various, and their height "dependsupon a great many circumstances. That the tides may have theirfull motion, the ocean, in which they are produced, ought to beat least 90° extended from east to west, because that is the distancebetween the greatest elevation, and the greatest depression,produced in the waders bv the Moon . Hence it appears,that it is only in the great oceans that such tides as w •have described can be produced, and why jn the larger Facileocean they exceed those in the Atlantic ocean , ncnce it is ob-vious why the tides are not so great in the torrid zone, betweenAfrica and America , w here the ocean is narrower, as in the tem-perate zones on either side ; and hence also, we see why the tidesare so small in islands, at great distances from the shores. Itlike-wdse appears, tjiat the waters cannot rise on one shore of the At-lantic ocean , but by descending on the other, so that at the inter-mediate islands, it must remain at a mean height, between its e'evations on those two shores. The tides that enter the mouths ofrivers from the ocean are greatly retarded in their progress bvthe currents of the rivers. M. Condamine, while in SouthAmerica , observed, that in the river Amazon, there were firehiabwaters, and. four intermediate low-waters at once; and a similarcircumstance takes place in the Thames. For the tide, propaga-ted bv the Moon in the German ocean, when she is three hours"4 piM