The aberration of the stars furnishes us with a com plete demonstration of the motion of the earth round the sun, and confirms at the same time the discovery of the successive propagation of light, which, as we shall presently see, Roemer deduced from the eclipses of Ju piter's satellites. It appears, from the aberration of the fixed stars, that light passes from the sun to the earth in 8' 7". For farther information upon this subject, sec the references under the article ABERRATION.
The principle of universal gravitation, by which all bodies attract one another like magnets, with a force proportional to the quantity of matter, and inversely as the squares of their distances, has already been partly es tablished under the article ATTRACTION, and is consi dered at full length in the fifth Chapter of Physical As Titollomy. In virtue of this universal principle, the moon attracts the waters of the earth, and raises them on the side next the moon, and also on the opposite side, as ithewn in Plate XLIV.•Fig. 2. where ABCD is the earth, supposed to be wholly covered with water. The attrac tion of the moon at S raises the waters to the height Cc on the side next the moon, and also to the height Oo on the opposite side of the moon. The parts of the earth at A and B, therefore, arc deprived of their water, and therefore it is low water at those places when it is high water at o and c. While the earth performs its diurnal revolution in 24 hours, the elevated water at o being al ways directed to the moon, will, in the course of 24 hours, move over the earth, and therefore every place beneath it will have high water every 24 hours from the eleva tion at o. In like manner the cleated water at c will move over the earth every 24 hours, and will arrive at any place 12 hours behind the other elevated portion, so that every place will have high water twice a-day. For the same reason every place will have low water every 12 hours. The various phenomena of the tides, however, depend chiefly upon the position of the earth's axis with regard to the line oc. When the moon AI has no de clination, or is in the equator, as in Plate XXXIX. Fig. 5. the rotation of the earth round its axis NS will make the two tides exactly equal on every part of the earth : thus a place which is carried through the parallel will have the height of one tide T2, and the height of the other T 3 The tides are in this case greatest at the equator, and diminish gradually to the poles, where it will be low water during the whole day. When the
moon is north of the equator, as in Fig. 6. at her great est northern declination, a place describing the parallel Tgrs will have 2:63 for the height of the tide, when the moon is in the meridian, and T2 for the height of the tide when the moon is below the horizon on the opposite meridian ; so that in this case all places north of the equa tor will have the highest tide when the moon is above the horizon, and the lowest when she is below it ; the difference of the tides diminishing towards the equator, where they are equal. In like manner, places south of the equator have the highest tides when the moon is below the horizon, and the lowest when she is above it. In the present case, the highest tides will take place in those places that are situated under the tropics. When the moon has her greatest southern declination, the phe nomena are exactly the reverse of what takes place when she is in her greatest northern declination. When she has any intermediate degrees of declination, the phe nomena will be different; but they may be easily dedu ced from the explanation which has been already given.
From the remarks which have been made it will ap pear, that the tides ought to be highest under the moon, or when the moon is ornithe meridian of the place, or on the opposite meridian. This, however, is not exactly the case ; for it is found from observation, that the high est tide happens about two hours after the southing of the moon. This arises from the impulse which has been communicated to the waters when the moon reaches the meridian. The impulse continues after the cause which produced it has begun to diminish, in the same manner as the hottest time of the day is not at 12 o'clock, but about 2, and the hottest season of the year not on the 21st of June, but in the middle of July. The inertia of the waters, therefore, and perhaps the friction on the bottom of th, sea, arc the causes of the retardation of the highest tide.