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of the latitudes of the two stations resulting from the observations, would be greater than it really is. If, then, the true difference of their latitudes be determined by measuring the distance between the two stations on the ground, the excess of the difference, found by the observations of the star above that found by this measurement, must have been produced by the attraction of the mountain; and the half of it will be the effect of such attraction on the plumb-line at each observation, provided that the mountain attracts equally on both sides.

The first idea for determining the quantity of this attraction was suggested by Newton, in his treatise of the System of the World; but no farther notice was taken of it till M. Bougner and M. de la Condamine, in the year 1738, while they were employed in measuring three degrees of the meridian, near Quito in Peru, thought they

time. For that space is a third proportional to the diameter of the moon's orbit, and the arc described in the same time. And 235389600 (the diameter of the moon's orbit in Paris feet) is to 188489 (the arc described in a minute,) as 188489 is to 15. Thus the motion agrees in quantity as well as in direction, with the legitimate inferences from the motions of projectiles near the earth. And these pheno. mena are so perfectly coincident and similar, that they must be zeferred to the same principles, namely, a projectile force and a gravitating force varying inversely as the squares of the distances. ATTRACTION of Mountains.-According to the Newtonian theory of attraction, this principle pervades the minutest particles of matter, and the combined action of all the parts of the earth forms the attractions of the whole. For the same reason, therefore, that a heavy body tends downwards in a perpendicular to the earth's sur-perceived a deflection of their face, it must be attracted towards plumb-line from the effect of the the centre of a neighbouring moun- attraction of Chimboraco, a mountain by a force greater or less, ac- taiu in that neighbourhood, which cording to the quantity of matter by a rough computation they sup contained in it; and the effect of posed to be equal to about the this attraction, or the accelerative 2000th part of the attraction of the force produced by it, must depend whole earth. on the distance of the mountain Nothing was afterwards done, till from the gravitating body, because Dr. Maskelyn made a proposal to this force increases as the squares the Royal Society for this purpose, of the distances decrease. Upon in the year 1772; and, in 1774, he these principles, it is obvious that was deputed to make the trial, ac. the plumb of a quadrant, or of companied with proper assistants, any other astronomical instrument, and furnished with the most accu must be deflected from its proper rate instruments. For the scene of situation, by a small quantity, to his observations, he made choice wards the mountain; and the ap. of the mountain Schehallien, in parent altitudes and zenith dis- Scotland, the direction of which is tances of the stars, taken with the nearly from east to west: its mean instrument, be altered according-height above the surrounding vally; viz. if the zenith distance of a ley about 2000 feet, and its highest star were observed at two stations, part above the level of the sea under the same meridian, one on 3550 feet. Two stations for obser the south side of a mountain, the vations were selected, one on the other on the north; and the plumb- north and the other on the south line of the instrument were at side of the mountain. Every cir tracted out of its vertical position cumstance that could contribute to by the mountain, the star must apthe accuracy of the experiment pear too much to the north, by the was regarded; and from the obser observation at the southern sta-vation of ten stars near the zenith, tion, and too much to the south, it was found that the apparent dif by that at the northern station; ference of the altitudes of the two and, consequently, the difference stations was 54 6"; and from a

measurement by triangles, formed from two bases on different sides of the mountain.

ing all the larger and coarser sorts
of goods; and all metals, except
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16 oz.
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28 lb.
4 qrs.... 1 hun. weght cwt.
20 cwt.

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The avoirdupoise is less than the troy ounce, in the proportion of 700 to 768; but the avoirdupoise pound is greater than the troy pound, in the proportiou of 700 to 576; viz.

These data seemed to offer the means of determining the mean density of the earth; but the calculation necessarily required great accuracy, as well as immense labour. The task, however, was undertaken by Dr. Hutton, who gave an account of it, and the result of his investigation, in the Phil. Trans. as also in his Tracts lately published, from which it appears, that the mean density of the earth is to that of common 7000z. troy 7680z. avoirdupoise. water in about the ratio of 5 to 1.700lbs. troy=576lbs. avoirdupoise. Sir Richard Phillips (Essays, p. 8. et seq.) treats the doctrine of attraction as a mere assumption; and he sums up the objections which may be urged against it in these words:

1. "That matter is not itself an agent, or source of power.

2. "That it has no consciousness of any distant matter to be moved or attracted.

3. "That it has no means of knowing the relative quantity, and of moving accordingly.

AURORA, the morning twilight, or that faint light which appears in the morning when the sun is within eighteen degrees of the horizon. It is produced by the refractive power of the atmosphere.

AURORA Borealis, or NORTHERN Light, sometimes also called streamers, is an extraordinary meteor, or luminous appearance, showing itself in the night-time in the northern parts of the heavens, and most commonly in frosty wea ther.

It is usually of a reddish colour ano-inclining to yellow, and sends out frequent corruscations of pale light, which seem to arise from the horizon in pyramidal undulating forms, and shoots with great velocity up to the zenith.

4. "That the direction of motion in bodies said to attract one ther, is from their further, remote, or opposite sides; consequently, each is assumed to receive a mu tual impulse from parts in which neither are situated.

5. "That, through a vacuum, no obligation of equal mechanical momenta, in a system of bodies exists, such as we discover to be the fact in nature.

6. "That the sun, planets, and satellites, do not fall together, as the system requires.

7. "That, for the first four reasons, bodies do not attract or repel one another in any other branch of philosophy, more than in physics." Centre of ATTRACTION. CENTRE.

AUSTRAL, the same as southern. AUTOMATON, a seemingly selfmoving machine; or one so constructed, by means of weights, levers, pulleys, springs, &c. as to move for a considerable time as if it were endued with animal life. And according to this description, clocks, watches, and all machines of that kind, are automata.

AUTUMN, the third season of the year: this begins at the descend. Seeing equinox, which, in the northern hemisphere, is when the sun enters the sign Libra, about the twentysecond of August, and ends about the same day in December.

ATTRITION, the striking or rubbing of bodies against each other. ATWOOD's Machine, a very ingenious apparatus invented by the late Mr. Atwood, of Trinity College, Cambridge, to illustrate the doctrine of accelerated motion.

AVOIRDUPOISE Weight, a weight used in England for weigh

AUTUMNAL, something relating to autumn.

AUTUMNAL Equinox, the time when the sun enters the descending point of the ecliptic where it crosses the equinoctial.

AUTUMNAL Point, the point of the ecliptic answering to the autumnal equinox.

AUTUMNAL Signs, are the signs Libra, Scorpio, Sagittary, through which the sun passes during the

autumn.

AXIOM, a self-evident truth, or a proposition, the truth of which is perceived at first sight. It is also an established principle in some science. Thus, it is an axiom in geometry that things which are equal to the same thing, are equal to each other; that if to equal things, equal things be added, the wholes will be equal, &c.

AXIS, in Astronomy, an imaginary right line, supposed to pass through the earth, sun, planets, satellites, &c. and about which they perform their respective diurnal rotations.

The earth and planets, in their progress through the annual orbit, inove in such a manner that the axis of each always keeps parallel to itself, or points to the same parts of the heavens.

two principal vertices of the figure. In the hyperbola it is the shortest diameter, but in the ellipse it is the longest.

Conjugate Axis, or Second Axis, in the ellipse and hyperbola, is the diameter passing through the centre, and perpendicular to the transverse axis. It is the shortest of all the conjugate diameters.

AXIS of a Curve Line, is still more generally used for that diameter which has its ordinates at right angles to it, when that posi tion is possible.

AXIS, in Mechanics, a certain line about which a body may turn. Axis are of various kinds; as

Axis of a Balance, the line upon which it moves or turns.

Axis of Rotation, the line about which a body really revolves, when it is put into motion. The impulse given to a homogeneous sphere, in a direction which does not pass through its centre, will cause it to revolve constantly round the diameter, which is perpendicular to a plane passing through its centre, The axis of the earth is inclined and the line of direction of the imto the ecliptic, in an angle of nearly pressed force. New forces acting 66°, a position which is well adapt-on all its parts, and of which the ed for promoting the fertility of the earth and rendering it habitable.

Axis of the Horizon, Equator, &c. is a right line drawn through the centre of the respective circle, perpendicular to its plane.

Axis, in Geometry, the straight line in a plane figure, about which it revolves, to produce or generate a solid.

AXIS is yet more generally used for a right line conceived to be drawn from the vertex of a figure to the middle of the base. So the AXIS of a Circle or Sphere, is any line drawn through the centre, and terminated at the circumference, on both sides.

result passes through its centre, will not change the parallelism of its axis of rotation. Thus it is that the axis of the earth remains always nearly parallel to itself in its revolution round the sun, without its being necessary to suppose, with Copernicus, an annual motion of the poles of the earth round those of the ecliptic.

If the body possess a certain figure, its axis of rotation may change every instant. The determination of these changes, whatever may be the forces acting on the bodies, is one of the most interesting problems of mechanics respecting hard bodies, on account of its connection with the precesAxis of a Cone, is the line from sion of the equinoxes, and the the vertex to the centre of the base.libration of the moon. The solu Axis of a Cylinder, is the line from the centre of the one end to that of the other.

Axis of a Conic Section. See CONIC Section.

Transverse AXIS, in the ellipse and hyperbola, is the diameter passing through the two foci, and the

tion of this problem has led to a curious and very useful result; namely, that in all bodies there exist three axes perpendicular to each other, round which the body may turn uniformly when not solicited by external forces. On this account these axes are pro

perly called principal axes of rota tion.

Axis of Oscillation, is a line parallel to the horizon, passing through the centre, about which a pendulum vibrates, and perpendicular to the plane in which it oscillates.

Axis in Peritrochio, one of the five mechanical powers, consisting of a peritrochium or wheel, and moveable_together with it about its axis. The power is applied at the circumference of the wheel, and the weight is raised by a rope that is gathered up on the axis while the machine turns round. The power may be conceived as applied at the extremity of the arm of a lever, equal to the radius of the wheel; and the weight as ap plied at the extremity of a lever, equal to the radius of the axis; only those arms do not meet at one centre of motion, as in the lever; but in place of this centre we have an axis of motion, viz. the axis of the whole machine.

Axis, in Optics. The optic axis, or visual axis, is a ray passing through the centre of the eye, or falling perpendicularly on the eye.

Axis of a Lens, or Glass, is the axis of the solid of which the lens is a segment. Or the axis of a glass, is the line joining the two vertices or middle points of the two opposite surfaces of the glass. Axis of a Magnet, is a line passing through the middle of a magnet lengthwise, in such a manner as that, however the magnet is divided, provided the division is made according to a plane in which such line is found, the magnet will be cut or separated into two loadstones and the extremes of such lines are called the poles of the magnet.

AZIMUTH, in Astronomy, an arc of the horizon intercepted between the meridian of the place, and the verticle circle passing through the centre of an object, and is equal to an angle at the zenith, formed by the said meridian and verticle circle, which is measured by the forementioned

arc.

The azimuth is reckoned eastward in the morning, and westward in the afternoon, and is usually estimated to the north or south, as it is nearer to one or other of those points:

To find the Azimuth, at the Time of the Equinox. Say,

As radius,

Is to the tangent of the latitude; So is the tangent of the altitude of the sun or star,

To the cosine of the azimuth from the south.

Magnetical AZIMUTH, an arc of the horizon contained between the azimuth circle of the celestial object and the magnetical meridian; or it is the apparent distance of the object from the north or south point of the compass. This is found by observing the object with an azimuth compass, when it is about 10° or 15° high, either in the forenoon or afternoon.

AZIMUTH Compass, is a compass used at sea, for finding the sun's magnetical azimuth. See Compass.

AZIMUTH Circles, called also vertical circles, are great circles of the sphere, intersecting each other in the zenith and nadir, and cutting the horizon at right angles.

AZIMUTH Dial, is a dial whose style, or gnomon, is at right angles to the plane of the horizon.

B.

distribution of the weight of each arm and scale of the balance, as well as from the equal length of the former; for on this depends the accuracy of its action.

BACK-Staff, an Instrument formerly used for taking the sun's altitude at sea; being so called be cause the back of the observer is turned towards the sun when he makes the observation. This instrument is also called Davis'slowing remarks on the accuracy Quadrant.

It consists of two co-centric arches of box-wood, and three vanes, the arch of the longer radius being of 30°, and that of the shorter of 60, forming together 90°, or a quadrant.

BALANCE, in Mechanics, a peculiar application of the lever, in order to determine the difference or equality of weights in heavy bodies; and, consequently, their masses or quantity of matter. There are various kinds of balances; the principal of which, however, are the common balance, the bent lever balance, the Roman balance, and the Swedish or Danish balance. Balances also receive other denominations, according to the circumstances under which they are employed, or the principles on which they act, as assay balance hydrostatic balance, &c.

Assay BALANCE, a very delicate balance used for determining the exact weight of minute bodies, in the different processes of assaying, and of frequent use and application in chemical analysis: for a description of which, see Gregory's Mechanics, vol. ii. p. 94; Nicholson's Journal, 4to. vol. v. p. 303; see also the Annales de Chemie, xxxvi. 50.

Bent Lever BALANCE. This instrument operates by a fixed weight at the end of a bent lever, supported on its axis in a pillar, and having a scale suspended from the other extremity.

Common BALANCE, or Scale-beam. This instrument is too well known to need any particular description; it consists of a lever with equal arms, at the extremity of each of which is attached a scal and before loading it with any weights the whole ought to preserve a perfect equilibrium; and this equilibrium must arise from an exact

Professor Playfair has the fol

of the balance.

"1. It should rest in a horizontal position when loaded with equal weights. 2. It should have great sensibility. 3. It should have great stability; that is, when disturbed, it should quickly return to a state of rest. That the first requisite may be obtained, the beam must have equal arms, and the centre of suspension must be higher than the centre of gravity. Were these centres to coincide, the beam, when the weights were equal, would rest in any position, and the addition of the smallest weight would overset the balance, and place the beam in a vertical situation, from which it would have no tendency to return. The sensibility, in this case, would be the greatest possible; but the other two requisites of level and stability would be entirely lost. The case would be worse, if the centre of gravity were lower than the centre of suspension, as the balance, when deranged, would make a revolution of no less than a semi-circle. When the centre of suspension is higher than the centre of gravity, if the weights be equal, the beam will be horizontal; and if they be unequal, it will take an oblique position, and will raise the centre of gravity of the whole, making the momentum on the side of the lighter weight equal to that on the side of the heavier, so that an equilibrium will again take place.

"The second requisite is the sensibility of the balance, or the smallness of the weight, by which a given angle of inclination is produced. If a be the length of the arm of the balance, and b the distance between the centre of suspension and the centre of gravity, P the load in either scale, and W the weight of the beam, the sensi

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