cumstances in their motions. The mean sidereal motion of the first, added to twice that of the third, will be always equal to three times that of the second. This may be easily verified by referring to the following table of their sidereal revolutions, and their mean distances, as given in the Systême du Monde. The same relation also takes place with respect to the mean synodic motions, which are as their sidereal motions diminished by that of Jupiter. If the synodic motions be, therefore, substituted in the equation above indicated, the conditions will be fulfilled. For if we put m', m", and m", for the mean sidereal motions of the first, second, and third satellite in a Julian year; and denote the sidereal motion of Jupiter in the same time by s; the synodic motions of the three satellites are, m'—s, m"—s, and m" And as, by the hypothesis, we have m' +2m"-3m"=0, we have, therefore, (m'—s)+2(m"—s)—3 (m”—s)=0; in which equation the s in the plus terms evidently destroys that in the minus one. The above law, relative to the mean motions, only influences the mean longitudes, reckoned from a given instant; but the absolute mean longitudes themselves are subject to a law equally remarkable: this is, that the mean longitude of the first satellite minus three times that of the second, plus twice that of the third, is always equal to a semicircumference, or 180°. The relation applies equally to the mean longitudes, either synodic or sidereal. Theory shows that the relations always subsist, and consequently the three satellites can never be all eclipsed at the same time; for then their longitudes would be equal, and the above sum would be nothing. The honour of discovering these laws is due to the celebrated author of the Mécanique Céleste. The satellites of Saturn are much less, and can be seen only with large telescopes, and therefore have engaged much less of the attention of astronomers. Huyghens was the first who discovered one of Saturn's satellites. This was the largest, and was long regarded as the fourth. Dominique Cassini discovered the fifth, and then the third, and a little time afterwards the first and second. But these numbers have since been changed by the discoveries of Herschel, who perceived two other satellites belonging to this planet, at a time when the ring could only be seen with his forty-feet telescope. Cassini observed that the five satellites then known were subject to the laws of Kepler; and all the seven, with the exception of the last, revolve sensibly in the plane of the ring. The orbit of the seventh makes an angle of about 3° with that plane. The following table exhibits the sidereal revolutions and proportional distances of these satellites, the radius of Saturn being taken for unity : The satellites of Uranus are still more difficult to be seen than those of Saturn: Dr. Herschel is the only person who has yet followed them with any constancy. Their proportional distances and sidereal revolutions are as follow, the radius of the planet being taken for unity : Triumphant o'er the thirsty lawn, now heat BIDLAKE. JULY is generally accounted the hottest month in the year. In consequence of the excessive heat, an evaporation takes place from the surface of the earth and waters, and large clouds are formed, which pour down their watery stores, and deluge the country with floods, frequently laying the full-grown corn. Haymaking usually commences about this time, or rather earlier, in fine seasons. The flowers which blossomed in the last month soon mature their seeds, and hasten to decay. A new race succeeds, which demands all the fervid rays of a solstitial sun to bring it to perfection. The different tribes of insects which, for the most part, are hatched in the spring, are now in full vigour. We wonder at a thousand insect forms, These hatched and those resuscitated worms, COWPER. 兽 Summer may be said to commence with this month the meadows begin to whiten, and the flowers that adorn them are mowed down. The corn gradually assumes a yellow hue, and the colours that decorate the rural scene are no longer so numerous. The principal parts of a summer's day, but more particularly morning, evening, and night, have been the favourite theme of poets, from the most remote antiquity. Each has something picturesque and beautiful that affects every sense with unspeakable pleasure, particularly the sight, which is the most perfect and beautiful of all our senses; which fills the mind with the greatest variety of ideas, converses with its objects at the remotest distance, and continues the longest in action without being tired or satiated with its proper enjoyments. Beside the glowing colours of the flowers, and the still enlivening verdure of the woods, the eye beholds an innumerable quantity of fruits, which, by virtue of the secret laws of Nature, grow in our fields and gardens, and which, after thus delighting the sense of vision, may be gathered and preserved to contribute to our subsistence. The flowers present to our senses the most agreeable diversity we not only admire the richness of their attire, but the fecundity of Nature in the numberless species of them. What variety too, what beauty in every plant, from the lowly moss to the towering oak! If we wander from flower to flower, the eye is still unsated with the view. If we ascend the highest mountains, pierce into the midnight depth of groves, or descend into the spacious vale, we discover new beauties spread around in wonderful profusion. Agreeably to the method we have adopted, of enriching our pages with poetical description, we shall here present our readers with the most striking parts of a summer's day, which, not to multiply quotations, we shall select only from the poet of the Seasons. MORNING, Short is the doubtful empire of the Night, White break the clouds away. With quickened step, The dripping rock, the mountain's misty top, The native voice of undissembled joy ; And thick around the woodland hymns arise. But yonder comes the powerful King of Day, And sheds the shining day, that burnished plays FORENOON. Now, flaming up the heavens, the potent Sun NOON. 'Tis raging noon; and, vertical, the Sun |