« AnteriorContinuar »
gles Carth describe angle Eed, that thiher that the
square of the second, and, consequently, equal also to the square of the inverse ratio of the distances : therefore, if the square of the radius vector be multiplied by the angle which it describes in a given time raso 24 hours for instance), the product will always be the same quantity. Now, as the most accurate observations verify this property for all positions of the Earth in its orbit, it ought to be admitted as one of the laws of its annual movement. Therefore, if from S there be two radii vectores SE and SE' drawn to the extremities E and E' of the arc described by the Earth in given small time, the product of the radius SE and ab, which measures the angle s, is the same throughout the whole extent of the orbit; but care should be taken to have the radius of the arc ab the same for all the angles described. The arc EE of the ecliptic, which the Earth describes in the same time, is seen from the Sun under the angle ESE'.
But it must be remarked, that this supposes the points E and E' are so near each other that the arc EE of the orbit may be equal in length to the circular arc Ee, described about the centre S; so that the radii SE and SE' may be considered as equal to each other. Now it is evident that the times may easily be taken so short that this condition may be sensibly fulfilled, and, particularly, as the curye differs so little from the arc of a circle whose centre is S; for the greatest axis' exceeds the least only by about th, and this happens only in two points, the perigee and apogee. The unit of time may therefore be taken as small as we please, as, an hour, a minute, &c.; and then the above product becomes constant, and the circular sector SEe will be equal to that of SEE' of the orbit. From this property, the two following consequences may be derived :
Ist. Since the area of the circular sector SEe is always proportional to the product of the square of
the radius SE and the arc ab, it follows that the radius vector describes equal areas in equal times : for, in the preceding figure, we have
SE . ab Sa : SE :: ab : Ee = and hence the area of the sector SEE', which is equal USE X Ee = " ; and Sa being the same quantity for the whole of the orbit, the area of the sector SEE' is proportional to ab . SE”, which is a constant quantity. In proportion as the radius SE increases, the angle S diminishes, and the area of SEE remains the same. Therefore, the area described by the radius vector in a double time is double, and triple in a triple time, &c. Hence, in general, the areas described by the radius vector are proportional to the times employed in their descrip
See these twory small equipo ritional to the of the rac
2d. As the products of the squares of two radii vectores, by, the angle each describes in the same time, are equal, by changing this equation into a proportion, we conclude that the squares of the radii vectores are inversely proportional to the arcs they describe in very small equal times : for, let r and ģ be these two radii, and a, a', the arcs thus described ; then
gamza', and, by converting this equation into a proportion, we have
p2 : gol? :: a': a. Now, in apogee, the angle described in 24 hours is 57'.192 ; we may, therefore, from this proportion, find the length of the mean radius vector, between those corresponding to the apogee and perigee, when the angle it describes in a small given time is known; for the arc when the time is given. For the square of the mean distance is to the square of that in apogee, as 57'.192 is to the angle described by the mean radius ; or,
235242 : 239732 :: 57'.192 : 59'; which is the angle required, or that answering to the
which distances distanc
Hence, the distance of the Earth from the Sun may be found without recurring to either bis parallax or his apparent diameter, by making use of the angles he describes, and these observation gives daily with great accuracy.
From what precedes we may also derive the following proportion, viz. Any radius vector is to the mean distance as the square root of 57'.192 (or 7'.6895) is to the square root of the angle described by the first radius.
But, in order to simplify the calculation, it is convenient to take the mean distance equal to unity; and then the different distances will be expressed in terms of this mean distance; and, consequently, to find the terrestrial radii contained in any of these distances, it must be multiplied by 23524, the number of ràdii in the mean distance. The proportion will then become, .
Any radius vector is to 1, as 7'.6895 is to the square root of the angle described by the first radius. Hence, when all is known but the first term, that is readily obtained for any particular part of the annual orbit.
[To be concluded next month.]
The Naturalist's Diary.
Copious dispenser of delight, bright June,
Shed from thy lavish band. The innumerable beautiful herbs and flowers which, at this season of the year, meet our eye in every direction, appear designed only to ornament our earth, or to gratify our sense of smelling; but, upon a more intimate acquaintance with their peculiar properties and operations, we find, that, while they contribute to embellish our gardens, they also promote the purification and renovation of the atmosphere, which becomes contaminated from various causes.
Herbs and flowers may be regarded by some persons as objects of inferior consideration in philosophy; but every thing must be great which hath God for its author. To him all the parts of nature are equally related. The flowers of the earth can raise our thoughts up to the Creator of the world as effectually as the stars of heaven; and till we make this use of both, we cannot be said to think properly of either. The contemplation of nature should always be seasoned with a mixture of devotion; the highest faculty of the human mind; by which alone contemplation is improved, and dignified, and directed to its proper object.
The first thing that engages the curiosity of man, and tempts him to bestow so much of his labour and attention upon this part of the creation, is the beautiful form and splendid attire of plants. They who practise this labour know how delightful it is. It seems to restore man in his fallen state to a participation of that felicity, which he enjoyed while innocent in Paradise.
When we cast our eyes upon this part of nature, it is first observable that herbs and trees compose a scene so agreeable to the sight, because they are invested with that green colour, which, being exactly in the middle of the spectrum of the coloured rays of light, is tempered to a mildness which the eye can bear.. The other brighter and more simple colours are sparingly bestowed on the flowers of plants; and which, if diffused over all their parts, would have been too glaring, and consequently offensive. The smaller and more elegant parts are adorned with
that brightness which attracts the admiration without endangering the sense.
But while the eye is delighted with the colouring of a flower, the reason may be still more engaged with the natural use and design of a flower in the economy of vegetation. The rudiment of the fruit, when young and tender, requires some covering to protect it; and, accordingly, the flower-leaves surround the seat of fructification : when the sun is warm, they are expanded by its rays, to give the infant fruit the benefit of the heat: to forward its growth when the sun sets, and the cold of the evening prevails, the flower-leaves naturally close, that the air of the night may not injure the seed-vessel. As the fructification advances, and the changes of the air are no longer hurtful, the flower-leaves have answered their end, and so they wither and fall away. How elegant, therefore, as well as apposite, is that allusion in the Gospel ; I say unto you, that Solomon in all his glory was not arrayed like one of these': for the flower, which is the glory of the lily and other plants, is literally and physically a raiment for the clothing of the seed-vessel ! And a raiment it is, whose texture surpasses all the laboured productions of art for the clothing of an eastern monarch. The finest works of the loom and the needle, if examined with a microscope, appear so rude and coarse, that a savage might be ashamed to wear them : but when the work of God in a flower is brought to the same test, we see how fibres, too minute for the naked eye, are composed of others still more minute ; and they of others ; till the primordial threads or first principles of the texture are utterly undiscernible; while the whole substance presents a celestial radiance in its colouring, with a richness superior to silver and gold—as if it were intended for the clothing of an angel. The whole
* Matt. vi, 29.