curved-lines concave to the sun, and Kepler had proved that they moved round the sun in such a manner, that a line, drawn from the planet to the sun, passes over areas proportional to the times; from which Newton brought forward his first great inference given in the 2d prop. of the Principia, viz. "Every body that moves in any curve-line described in a plane, and by a radius drawn to a point, either immoveable or moving forward with an uniform rectilinear motion, describes about that point areas proportional to the times, is urged by a centripetal force tending to that point;" a general proposition, applying both to the planets revolving round the sun, and to the satellites revolving round their primaries. But it must be observed, Newton as yet had attained nothing but the direction: he says nothing of the manner of acting,-it may be a stream of fluid, a gaseous medium moving toward the centre, or in fact any thing that can cause this effect; but whatever this may be, this is the direction. He calls it a centripetal force.

Having now determined that the sun was the great seat and regulator of the planetary motions, he proceeds to investigate its nature and intensity. Hence, Kepler having proved that the planets move in ellipses having the sun in one of their foci; Newton proves further, that the deflective force in any of the conic sections varies as the reciprocal of the square of the distance. This forms the 13th, 14th, and 15th, props. of the Principia. Here then we have an epitome of the properties of the curvilinear motion in the celestial bodies.

But an objection is raised here. "As the right-lined force," it is said, "must always be equal to itself, it will be in danger of being diminished by the resistance of the air." It will not be necessary to take much time in answering this point, for as far as I have gone it is shewn that Newton proved that the sun is the seat of deflection, and if by facts he can prove that the attractive power of the sun is the cause of this deflection, then it follows of course that the air can afford no sensible resistance, as the velocity is not decreased. But still, by the way, we may remark, that from some very accurate observations it has been shewn (the thermometer and barometer being at stated heights) that were the atmosphere homogeneous, its height would be short of 5 miles, (See Vince's Hyd.) and that at the altitude of 7 miles the air is four times rarer than at the earth's surface; at 14 miles, sixteen times rarer; at 21 miles, sixty-four times rarer; at 70 miles, a million times rarer: so that we may see from

this alone, that we have every reason to conclude that the celestial space is filled with air too rare to offer any sensible resistance.

3. We come now to the facts proving the mutual attraction of the heavenly bodies. Newton remarked, that in all changes of motion observable in our sublunary world, the changes in the acting bodies are equal and opposite. In all impulsions, one body is observed to lose as much as another gains, all magnetical and electrical attractions and repulsions are the same. Every action seems to be accompanied by an equal re-action in the opposite direction. He therefore affirmed this law obtained also in the celestial motions, and that not only the planets were continually impelled toward the sun, but also the sun was impelled toward the planets: also, in a similar manner, the satellite was impelled to the primary, and the primary to the satellite; and lastly, that the planets were impelled or drawn to one another. In support of this, we bring forward the following facts.

1. With regard to the earth and the moon. The waters of the ocean are observed every day to heap up on that side of our globe which is under the moon. In this situation the weight of the water is diminished by the attraction of the moon, and it requires a greater elevation, or a greater quantity of the water, to compensate for the diminished weight. On the other hand, we see the waters abstracted from all those parts which have the moon in the horizon. Here is a very strong proof of the attraction of the moon. But again: when the astronomers had obtained instruments of nice construction, and had improved the art of observing, there was found an irregularity in the calculation of the sun's place, which had an evident relation to the moon.

At new moon, the observations corresponded exactly with the sun's calculated place; but seven or eight days after, the sun is observed to be about 8" or 10" to the eastward of his calculated place, when the moon is in quadrature; and he is observed as much to the westward, when she is in her last quadrature. In intermediate situations the error is observed to increase in the proportion of the sine of the moon's distance from conjunction or opposition, Things must be so, if we suppose that the deflection of the moon toward the earth is accompanied with an equal deflection of the earth to the moon. For the moon will not revolve round the earth, but both the earth and moon will revolve round their common centre of position, as might easily be

shewn. When the moon is in her first quadrature, her position will be represented by M,

m

It

sensible, and susceptible of measure. sometimes amounts to 38", and must never be omitted in calculations subservient for finding the longitude at sea. Here is a proof positive of the mutual action of the planets.

while the earth is at E, and the common centre is at A. A spectator in a will see the sun s in his calculated place в; but in the earth E, he sees the sun at c, to the left or eastward of B. At new moon, A, E, and s, are in a straight line, so that B and C coincide. At the last quadrature the moon is at m, the earth at e, and the common centre at a. Now the sun is seen at c, 8" or 10" to the westward of his calculated place. This correction was first pointed out by Newton as the consequence of mutual attraction, but it was not observed at first; though it was soon recognized, and now makes an article among the various equations used in calculating the sun's place. Here then is a very strong proof of the action and re-action of the earth and the moon.

3. It was probably the re-action of the earth and the moon, that first suggested the idea of the mutual action of all the planets; but be that as it may, the consequences are very important, and have explained several phenomena which had caused much perplexity to the practical astronomers. The following is one out of different examples that might be adduced of this mutual action.

Suppose Jupiter and Mars to be in conjunction, lying in the same line from the sun. As Mars revolves much quicker than Jupiter, he gets before him, but, being attracted by Jupiter, his motion is retarded; and Jupiter being attracted by Mars, is accelerated. On the contrary, before Mars arrives at conjunction with Jupiter, Mars is accelerated and Jupiter retarded.

Farther, the attraction of Mars by Jupiter must diminish the tendency of Mars to the sun, or must act in opposition to the action of the sun; therefore, the curvature of Mars' orbit in that place must be diminished. On the contrary, the tendency of Jupiter to Mars acting in the same direction as his tendency to the sun, must increase the curvature of that part of Jupiter's orbit. If Jupiter be at this time advancing to his aphelion, this increase of curvature will the sooner bend the line of his motion from an obtuse angle in a right angle with the radius vector. Therefore, his aphelion will the sooner be attained, and it will appear to have shifted to the westward.

2. With regard to the action and reaction of the sun and the planets, we notice the following fact. As the art of observation continued to improve, astronomers were able to remark abundant proofs of the tendency of the sun to the planets. When the great planets Jupiter and Saturn are in quadrature with the earth, to the right hand of the line drawn from the earth to the sun's calculated place, the sun is observed to shift to the left of that line, keeping always on the opposite side of the common centre of position. These deviations are indeed very minute, because the sun is vastly more massive than all the planets collected into one lump. But in favourable situations of these planets they are perfectly sensible, and have been calculated, and they must be taken into account in every calculation of the sun's place, in order to have it with the accuracy that is now attainable. The quantity corresponding to one planet, is too small of itself to be distinctly observed, but by occasionally combining with others of the same kind, the sum becomes very

There are other situations of the planets, where the contrary effects will happen. In each revolution, each planet will be alternately accelerated twice, and twice retarded, and the apsides of the exterior planet will continually recede, and that of the interior will advance. It is obvious, this disturbance of the motion of the planet by its deflection to another, though probably very minute, yet being continued for a tract of time, its accumulated result will become sensible. These changes are all susceptible of accurate calculation. This fact was not discovered until pointed out by Newton, but now it is confirmed by the fullest testimony of all practical astronomers. now gone through what I intended in as few words as possible. I have not quoted any authorities, but have taken what suited my purpose, sometimes in abridgment, and at other times verbatim. Manchester.

I have

J. S.

ASTRONOMICAL OCCURRENCES FOR

NOVEMBER.

THE Sun enters Sagittarius on the 23d, at two minutes past one in the morning. The Moon is full on the 3d, enters her last quarter on the 11th, her change takes place on the 19th, and she enters her first quarter on the 25th. She is in apogee on the 8th, and in perigree on the 20th; she passes Saturn on the 9th, Mars on the 15th, Jupiter on the 17th, Venus on the 19th, Mercury on the 20th, and the Georgian planet on the 23d.

The Georgian planet sets on the 1st at twenty-six minutes past nine in the evening, and on the 21st at eight minutes past eight; he may be observed near the same spot as in October, his situation having scarcely altered. Mercury sets on the 1st at twentytwo minutes past five in the evening, and on the 25th at forty-two minutes past four; he arrives at his greatest elongation on the 10th, when his elevation above the horizon being very small, his position is unfavourable for observation. He is stationary on the 20th, in conjunction with Venus on the 24th, and passes the Sun at his inferior conjunction on the 30th. Venus sets on the 1st at seven minutes past five in the evening, and on the 25th at forty-seven minutes past four; her proximity to the Sun renders her invisible this month. Saturn still continues the most conspicuous planet in the heavens; he rises on the 1st at fifty-seven minutes past eight in the evening, and on the 25th at seventeen minutes past seven; he is consequently above the horizon nearly the whole of the night, and will afford the astronomer ample opportunities for pursuing his observations on him, and the wonderful ring with which he is surrounded; he is stationary on the 2d, and his motion is afterwards retrograde. He is first observed near the spot which he occupied at the end of October, approaching with a very slow motion the line drawn from Castor to Procyon, which he reaches on the 30th.

During the evenings of this month the constellation of the Waggoner is in a very favourable position for observation ; Capella, the first of this constellation, being on the meridian on the 1st, at twenty-five minutes past two in the morning. A line drawn from the eleventh of Orion, through the second of the Bull, will direct the observer to Capella; this star is the summit of an isosceles triangle, Castor and Aldebaran forming the base.

A line drawn from Procyon, through the sixth of the Twins, will point out the second, which is to the east of Capella. The fourth is northward of the first and second, form

ing a scalene triangle with them. The third is nearly in a line with the first and fourth, below the former star. The sixth and seventh are a little below the third, and form a scalene triangle with the first and second. The eighth is noticed midway between Capella and the fifth of the Twins; it also forms an isosceles triangle with the first and second. The ninth is the apex of an isosceles triangle, Capella and the eighth forming the base; it is also in a line with the second, and one hundred and twentyfifth of the Bull, and midway between Capella and Aldebaran. The tenth is observed between the eighth of the Waggoner and the third of the Twins, nearest the former star. The twelfth forms a scalene triangle with the eighth and ninth; it is also observed between the seventh of the Waggoner and the second of the Bull, nearest the former star.

The boundary of this constellation, commencing to the west of a line drawn from Capella to Aldebaran, passes under the ninth, and between the twenty-second of the Waggoner and the second of the Bull, nearest the latter star; it then continues under the tenth, between the fifth of the Twins and some small stars in the Waggoner, and passes above the eighth of the Twins and Castor. There are a considerable number of small stars in this constellation, the total number, according to Flamsteed, being sixty-six. The Milky Way passes through the western part of this constellation; the western edge passing very near the ninth; and the eastern between the eighth aud twenty-second, and very near the seventh and third. The constellation of the Great Dog will be described in the next number.

Mars is a morning star, rising on the 1st at thirty-four minutes past three, and on the 25th at nineteen minutes past three; he is at first observed between the second and seventh of the Virgin, approaching the latter star, which he passes on the 4th: as he recedes from this star, he directs his course under the third of the Virgin. On the 12th he passes it; and on the 17th may be observed in a line with the second of the Lion, and the third of the Virgin; he is also in a line with the fourth and fifth of the Virgin his course is then directed to the eighth of this constellation, which he passes on the 25th: he finishes his course nearly under the sixth. During the month he forms a scalene triangle with the second of the Lion and Arcturus, and on the 27th an isosceles triangle with these stars. Jupiter rises on the 1st at seven minutes past six in the morning, and on the 25th at forty