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mountain, &c. in feet or miles; the second, the height of the quicksilver; and the third, the descent of the quicksilver in the barometer; and this at a mcan density of the air.
Feet. Iligh Barom. Descent. Feet. High Barom.] Descent
The Table continued, in Miles. Miles. High Barom. Descent. Miles. High Barom. Descent.
1.25 1.50 1 75 2.
23.62 22.60 21.62 20.68
15.63 16.23 16.80 17.35
2.25 2.50 2.75 3.
19.78 18.93 18.11 17.32
9.72 10.57 11 39 12.18
17 88 18 38 18.86 19.32
This table is made from a table of the air's density, made as in Scho. lium; and, then multiplying all the numbers thereof by 29.5, the mean density of the air. For the density of the air, at any height above the earth, is as the weight of the atmosphere kļuvo it, and that is as the height of the mercury in the barometer. Fig. 15.
There is another sort of barometer, which shows the ascent and descent of the mercury at the bottom.
ABC (fig. 16,) is a recurve tube, close at the top, where the bucket C is, and open at the end A. The length of CB is 32 or 33 inches, and of AB 6 or 7. The bucket C should contain about as much as the end AB; and the bucket and end EB must be quite filled with mercury, as far as B, a little beyond the turn. The wider the bucket Cis, the better. The scale set to the end AB must be graduated downwards; for the mercury falls in this, when it rises in the other sort. This being placed against a wall, will show the height of the mercury, as in the common ones: and this way is more commodious, as it saves the labour of clambering up upon chairs to see it, as one must do, in the common sort, to see exactly.
A barometer may also be made of water, as in fig. 17, wbich is a water. barometer. AB is a glass tube open at both ends, and cemented close in the month of the bottle EF, and reaching very near the bottom; then, warming the bottle at the fire, part of the air will fly out; then the end A is put into a vessel of water mixed with cochineal, which will go through the pipe into the bottle as it grows cold. Then it is set upright; and the water may be made to stand at any point C, by sucking or blowing at A. And, if this barometer be kept to the same degree of heat, by putting it in a vessel of sand, it will be very correct for taking small altitudes; for a little alteration in the weight of the atmosphere will make the water at Crise or fall in the tube very sensibly: but, if it be suffered to grow warmer, the water will rise too high in the tube, and spoil the use of it; so that it must be kept to the same temper. If a barometer was to be made of water put into an exhausted tube, after the manner of quicksilver, it would require a tube 36 feet long or more; which could hardly find room within doors: but then it would go 14 times more exact than quicksilver; because, for every inch the quicksilver rises, the water would rise 14, from whence every minute change in the atmosphere would be discernible.
And the water-barometer above described will show the variation of the air's gravity as minutely as the other, if the bottle be large, to bold a great quantity of air. And, in any case, by reducing the botile (so far as the air is contained,) to a cylinder; and put D = diameter of the bottle, d= diameter of the pipe, p = height of air, x = rising in the pipe, all
408dd in inches. Then the height of a hill in feet will be nearly 1 +
408dd x 713. And if y = height of the hill or any ascent, Q=
very near, at a mean density of the air.
Fig. 18, is a Thermometer, or au instrument to measure the degrees of heat and cold. AB is a bollow tube near two feet long, with a ball at the bottom: it is filled with spirits-of-wine, mixed with cochineal, halfway np the neck; which done, it is beated very much, till the liquor fill the tube; and then it is sealed hermetically at the end A: then the spirit contracts within the tube as it cools. It is enclosed in a frame, wbich is graduated into degrees, for heat and cold: for hot weather dilates the spirit, and makes it run further up the tube; and cold weather, on the contrary, contracts it, and make it sink lower in the tube. And the particular divisions show the several degrees of heat and cold; against the principal of which the words heat, cold, temperate, &c. are written.
Those who are desirous of pursuing the delightful and useful study of MECHANICS, may consult Dr. Gregory's Treatise, where the inquisitive Rearler will find this branch of Mathematics, with all its recent improrements, treated, not only in the most scientific manner, but so as to erplain the priuciples, and illustrate the best practical modes for putting thein in execution, by descriptive examples of machinery.
I. On the Nature of Light, and the Laws of Reflection and
Refraction. By Optics, we understand that branch of natural philosoply which treats of the nature, properties, and accidents, of light, and the theory of vision.
Modern philosopliers have invented two hypotheses to explain the manner in which vision is produced by luminous objects. Des Cartes, Huygens, and Euler, suppose that there is a subtile elastic medium, which penetrates all bodies and fills all space; and that vibrations, excited in this fluid by the luminous body, are propa. gated thence to the eye, and produce the sensation of vision, in the same manner that the vibrations of the air, striking against the ear, produce the sensation of sound.
The other hypothesis, adopted by Sir I. Newton and his followers, states, that light consists of very small particles of matter, which are constantly thrown off from luminous bodies, and which produce the sensation of vision by actual impact upon the proper organ.
Chemistry, and the actual phenomena of Combustion, qualify the first hypothesis, and impeach the second; but, though we may, in many respects, be ignorant of the actual operation of light, we inay, in reasoning upon it, adopt the notion that it consists of distinct and independent parts.
Definitions.-1. The least portion of light, which may be stopped alone, or propagated alone, or does or suffers any thing which The rest of the light does not or suffers not, is called a ray of light.
Rays of light may be represented by lines, drawn in the directions in which the particles move, or are affected.
2. Whatever affords a passage to the flow of light is called a medium, as glass, water, air, &c.; and, in this sense, a vacuum is called a medium.
3. The density of light is measured by the number of parts, or atoms, or particles, uniformly diffused over a given surface.
Cor.-If the surface be not given, the density varies as the number of pa ticles directly, and inversely as the area over wbich they are diffused.
There is something extremely subtile in the nature of light; and its properties can with difficulty be explained, either on the supposition of its materiality, or on that of its being only an accident of an elastic medium. The facility and regularity with which it is transmitted through bodies of considerable density, cannot be accounted for on either bypothesis. If it consist of particles of matter, which is the Newtonian supposition, their minuteness greatly exceeds the limits of our facullies, even the power of human imagination. Noiwithstanding the astonisining velocity of these par. ticles, their momentum is not so great as to discompose the delicate texture of the eye; and, when they are collected in the focus of a powerful burning-glass, it seems doubtful whether they are capable of communicating motion to the thinnest lamina of metal that can be exposed to their impact.
Prop. 1.-A ray of light, whilst it continues in the same uni. form medium, proceeds in a straight line
For, objects cannot be seen througı bent tubes ; and the shadows of bodies are terminated by straight lines. Also, the conclusions, drawn from calculations made on this supposition, are found by experience to be true.
PROP. 2.-The density of light varies inversely as the square of the distance from a luminous point; supposing no particles to be stopped in their progress.
For, if the point from which the light proceeds be considered as the common centre of two spherical surfaces, the saine particles, which are uniformly diffused over the first, will afterwards be diffused, in the same mamer, over the latter; and, since the density of light varies, in general, as the number of particles directly, and inversely as the space over which they are uniformly diffused, in this case it varies inversely as the space over which they are diffused, because the number of particles is the same; therefore, the deissity at the first surface : the density at the latter :: the area of the latter sursace : the area of the former; that is, :: the square of the distance in the latter case : the square of the distance in the former.
Definitions.-1. When a ray of light, incident upon any surface, is turned back into the medium in which it was moving, it is said to be reflected.
2. When a ray of light passes out of one medium into another, and has its direction changed at the common surface of the two mediums, it is said to be refracted.
3. The angle contained between the incident ray and the perpendicular to the reflecting, or refracting, surface at the point of incidence, is called the angle of incidence.
4. The angle contained between the reflected ray and the per. pendicular to the reflecting surface at the point of incidence, is called the angle of reflection.
5. The angle contained between the refracted ray and the per. pendicular to the refracting surface, at the point of incidence, is called the angle of refraction.
6. The angle contained between the incident ray produced, and the reflected or refracted ray, is called the angle of deviation.
If RS (fig. 1,) be the reflecting surface, AC a ray incident upon it, CB the reflected ray, and PCQ be drawn, through C, perpendicular to RS, and AC be produced to E; then ACP is the angle of incidence, PCB the angle of reflection, and BCE the angle of deviation.
If RS be a refracting surface, and CD the refracted ray, then QCD is the angle of refraction, and ECD the angle of deviation.