Axis sentence example
The purpose of his paper was to show that there is no problem if the axis is moved to the left.
The axis of the temple ran from S.W.
The minor axis, on the other hand, is not constant, but, as we have already seen, depends on the latitude, being the product of the major axis into the sine of the latitude.
The anthelion (a) may be explained as caused by two internal reflections of the solar rays by a hexagonal lamellar crystal, having its axis horizontal and one of the diagonals of its base vertical.
The long axis of the wings, when at rest, lies parallel to the body axis.Advertisement
The diurnal rotation of the earth furnishes two fixed points or poles, the axis joining which is fixed or nearly so in its direction in space.
Sometimes the pad is reduced to a ventral semi-ring or meniscus; it retains its largest almost original shape and size in the second vertebra, the axis or epistropheus, where it forms a separately ossifying piece which connects, and coossifies with, the odontoid process (the centrum of the atlas) and the centrum of the second vertebra.
The heart lies in the middle line of the body, its long axis being parallel with that of the trunk.
In the intervening space (the object-box) are contained a number of fragments of brilliantly coloured glass, and as the tube is turned round its axis these fragments alter their positions and give rise to the various patterns.
In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and in 1754 he solved the problem of the precession of the equinoxes, determined its quantity and explained the phenomenon of the nutation of the earth's axis.Advertisement
The form he recommends for the needle is that of "a true circle, having his Axis going out beyond the circle, at each end narrow and narrower, unto a reasonable sharpe point, and being pure steele as the circle it selfe is, having in the middest a convenient receptacle to place the capitell in."
He did not succeed in making the wire or the magnet revolve on its own axis.
The general structure of the trans-Himalayan chains appears to indicate that the main axis of upheaval of the whole vast mass of the Tibetan highlands is to be found on two approximately parallel lines, represented the one by the Kuen-lun and the other by a line which is more or less coincident with the watershed between India and the central lake region, extending from Lake Pangong to Tengri Nor, the plateau enclosed between the two being wrinkled by minor folds, of which the relative elevation is comparatively low, averaging from woo to 1500 ft.
In representing on a diagram the phenomena of equilibrium in a two-component system we require a third axis along which p to plot the composition of a variable phase.
The islands, which are long and narrow (the long axis lying parallel with the coast of the mainland), rise rather abruptly to elevations of a few hundred feet, while on the mainland, notably in the magnificent inlet of the Bocche di Cattaro, lofty mountains often fall directly to the sea.Advertisement
There are traces of an altar near the Heraeum which was probably older than the great altar of Zeus; this was probably the original centre of worship. The great altar of Zeus was of elliptic form, the length of the lozenge being directed from south-south-west to north-north-east, in such a manner that the axis would pass through the Cronion.
It differs considerably from the other members of the Sundanese group both in the direction of its main axis and in the prevalence of old rocks and slighter volcanic character.
But it is obvious that certain distributions will predominate, for the crystals will tend to fall so as to offer the least resistance to their motion; a needle-shaped crystal tending to keep its axis vertical, a plate-shaped crystal to keep its axis horizontal.
Here the outermost circle represents a section of that portion of the axis bearing the lowest leaf, the innermost represents the highest.
In many Pteridophytes the solid haplostele is maintained throughout the axis.Advertisement
To this type of steIn having a ground-tissue pith, whether with or without internal phloem, is given the name siphonostele to distinguish it from the solid haplostele characteristic of the root, the first-formed portion of the stem, and in the more primitive Pteridophytes, of the whole of the axis.
This localization takes place first at the two free ends of the primary axis, the descending part of which is the primary root, and the ascending the primary shoot.
Later, the axis branches by the formation of new growing-points, and in this way the complex system of axes forming the body of the ordinary vascular plant is built up. In the flowering plants the embryo, after developing up to a certain point, stopf growing and rests, enclosed within the seed.
In most Pteridophytes there is a single large apical cell at the end of each stem and root axis.
The connections of its stele witl that of the parent axis are made across the pericycle of the latter Its cortex is never in connection with the cortex of the parent, but with its pericycle.Advertisement
But some stems grow parallel to the surface of the soil, while the branches both of stems and roots tend to grow at a definite angle to the main axis from which they come.
In a differentiated body the stem (caulome) is an axis capable of bearing leaves and (directly or indirectly) the proper reproductive organs.
The circular outline had given way in geographical opinion to the elliptical with the long axis lying east and west, and Aristotle was inclined to view it as a very long and relatively narrow band almost encircling the globe in the temperate zone.
The angle which the earth's axis makes with the plane in which the planet revolves round the sun determines the varying seasonal distribution of solar radiation over the surface and the mathematical zones of climate.
In Wellhausen's words, each petty state " revolved on its own axis " of social-religious life till the armies of Tiglath-Pileser III.
This gigantic nebulous mass, of which the sun was only the central and somewhat more condensed portion, is supposed to have a movement of rotation on its axis.
In place of the six stamens we commonly find but one (two in Cypripedium), and that one is raised together with the stigmatic surfaces on an elongation of the floral axis known as the "column."
There are considerable spaces where the strike, or axis, of the main ranges is transverse to the water-parting, which is then represented by intermediate highlands forming lacustrine regions with an indefinite watershed.
The necessary and immediate results of such periodical changes of pressure are winds, which, speaking generally, blow from the area of greatest to that of least pressure - subject, however, to certain modifications of direction, arising from the absolute motion of the whole body of the air due to the revolution of the earth on its axis from west to east.
But the main axis of the transverse upheavals would appear to be continued in a north-eastern direction in the Andi and other parallel ranges of Daghestan, as stated under Caucasus.
Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.
The anomaly is then the angle BFP which the radius vector makes with the major axis.
The principal structural feature is the broad anticline, its axis running north and south, which has brought up the Carboniferous Limestone; this uplifted region is the southern extremity of the Pennine Range.
It corresponds to the right of the two primitive ctenidia in the untwisted archaic condition of the molluscan body, and does not project freely into the branchial cavity, but its axis is attached (by concrescence) to the mantle-skirt (roof of the branchial chamber).
Occupying the axis, and exposed by the section, is seen the "columella " or spiral pillar.
Let the curve represent an elliptic orbit, AB being the major axis, DE the minor axis, and F the focus in which the centre of attraction is situated, which centre we shall call the sun.
The semi-major axis, CA or CB, is called the mean distance, and is represented by the symbol a.
Benzoic acid is pseudo-tetragonal, the principal axis being remarkably long; there is no cleavage at right angles to this axis.
Direct nitration gives (principally) m-nitrobenzoic acid, also pseudotetragonal with a much shorter principal axis.
It is of Tertiary formation (Miocene), and has a chain of volcanic elevations along the axis, reaching a height of 2600 ft.
The shell thus formed is then cut along the line of the intended equator into two hemispheres, they are then again glued together and made to revolve round an axis the ends of which passed through the poles and entered a metal meridian circle.
The globe itself rotates within a metallic meridian to which its axis is attached.
The central and umbonal muscles effect the direct opening and closing of the shell, the laterals enable the valves to move forward and backward on each other, and the transmedians allow the similar extremities (the rostral) of the valves to turn from each other to the right or the left on an axis subcentrically situated, that is, the medio-transverse region of the dorsal valve.
Thus what have been called seminvariants are not all of them invariants for the general substitution, but are invariants for the particular substitution xl = X11 + J-s12, X 2 = 112 Again, in plane geometry, the most general equations of substitution which change from old axes inclined at w to new axes inclined at w' =13 - a, and inclined at angles a, l3 to the old axis of x, without change of origin, are x-sin(wa)X+sin(w -/3)Y sin w sin ' _sin ax y sin w a transformation of modulus sin w' sin w' The theory of invariants originated in the discussion, by George Boole, of this system so important in geometry.
This is called the direct orthogonal substitution, because the sense of rotation from the axis of X i to the axis of X, is the same as that from that of x i to that of x 2.
The regions of greatest attraction have received the name of poles, and the line joining them is called the axis of the magnet; the space around a magnet in which magnetic effects are exhibited is called the field of magnetic force, or the magnetic field.
Upon one of these is based the principle of the mariner's compass, which is said to have been known to the Chinese as early as I ioo B.C., though it was not introduced into Europe until more than 2000 years later; a magnet supported so that its axis is free to turn in a horizontal plane will come to rest with its poles pointing approximately north and south.
In the internal field of a long coil of wire carrying an electric current, the lines of force are, except near the ends, parallel to the axis of the coil, and it is chiefly for this reason that the field due to a coil is particularly well adapted for inductively magnetizing iron and steel.
If a magnetized needle were supported so that it could move freely'about its centre of gravity it would not generally settle with its axis in a horizontal position, but would come to rest with its north-seeking pole either higher or lower than its centre.
For the practical observation of this phenomenon it is usual to employ a needle which can turn freely in the plane of the magnetic meridian upon a horizontal axis passing through the centre of gravity of the needle.
The angle which the magnetic axis makes with the plane of the horizon is called the inclination or Along an irregular line encircling the earth in the neighbourhood of the geographical equator the needle takes up a horizontal position, and the dip is zero.
A wire or rod in this condition is said to be circularly magnetized; it may be regarded as consisting of an indefinite number of elementary ring-magnets, having their axes coincident with the axis of the wire and their planes at right angles to it.
The field at the centre of a circular conductor of radius r through which current is passing is H = 27ri/r, (3) the direction of the force being along the axis and related to the direction of the current as the thrust of a corkscrew to its rotation.
The direction of the force is parallel to the axis of the coil, and related to the direction of the current as the thrust of a corkscrew to its rotation.
The moment, M, M or V, of a uniformly and longitudinally magnetized bar-magnet is the product of its length into the strength of one of its poles; it is the moment of the couple acting on the magnet when placed in a field of unit intensity with its axis perpendicular to the direction of the field.
The direction of the magnetization is that of the magnetic axis of the element;'in isotropic substances it coincides with the direction of the magnetic force at the point.
The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.
If r and r' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.
The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is V=M cos 0/r 2, (io) where 0 is the angle between r and the axis of the magnet.
If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.
If the magnetization is parallel to the major axis, and the lengths of the major and minor axes are 2a and 2C, the poles are situated at a distance equal to 3a from the centre, and the magnet will behave externally like a simple solenoid of length 3a.
Suppose the whole space in which induction exists to be divided up into unit tubes, such that the surface integral of the induction over any cross-section of a tube is equal to unity, and along the axis of each tube let a line of induction be drawn.
An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.
At a point whose distance from the axis of the wire is r the tangential magnetic force is H = 21r /a 2 (39) it therefore varies directly as the distance from the axis, where it is zero.'
If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.
The body (or each element of it) will tend to set itself with its axis of greatest susceptibility parallel to the lines of force, while, if the field is not uniform, each volume-element will also tend to move towards places of greater or smaller force (according as the substance is paramagnetic or diamagnetic), the tendency being a maximum when the axis of greatest susceptibility is parallel to the field, and a minimum when it is perpendicular to it.
Thus if the magnet is suspended horizontally by a fine wire, which, when the magnetic axis points north and south, is free from torsion, and if 0 is the angle through which the upper end of the wire must be twisted to make the magnet point east and west, then MH = CB, or M = C6/H, where C is the torsional couple for r 0.
A compass having a very short needle is placed on the line which bisects the axis of the magnet at right angles, and is moved until a neutral point is found where the force due to the earth's field H is balanced by that due to the magnet.
The sample, arranged as a bundle of rectangular strips, is caused to rotate about a central horizontal axis between the poles of an upright C-shaped magnet, which is supported near 'its middle upon knife-edges in such a manner that it can oscillate about an axis in a line with that about which the specimen rotates; the lower side of the magnet is weighted, to give it some stability.
The curve thus constructed should be a straight line inclined to the horizontal axis at an angle 0, the tangent of which is 1.6.
Rowland, believing that the curve would continue to fall in a straight line meeting the horizontal axis, inferred that the induction corresponding to the point B-about 17,500-was the highest I Phil.
It has, however, been shown that, if the magnetizing force is carried far enough, the curve always becomes convex to the axis instead of meeting it.
The celluloid sheet is laid upon the squared paper, and in plotting a curve horizontal distances are reckoned from the proper demagnetization line instead of from the vertical axis.
One pole has a V-shaped notch for the rod to rest in; the surface of the other is slightly rounded, forming a portion of a cylinder, the axis of which is perpendicular to the direction of the length of the rod.
It is shown in the paper that the greatest possible force which the isthmus method can apply at a point in the axis of the bobbin is F = 11, 137 I, log i n b/a, I, being the saturation value of the magnet pores, a the radius of the neck on which the cones converge, and b the radius of the bases of the cones.
When the curve after its steep descent has almost reached the axis, it bends aside sharply and becomes a nearly horizontal straight line; the authors suggest that the critical temperature should be defined as that corresponding to the point of maximum curvature.
Most of the permeability-temperature curves were more or less convex towards the axis of temperature, and in all the experiments except those with annealed iron and steel wire, the permeability was greatest at the lowest temperature.
Weber therefore supposed each molecule to be acted on by a force tending to preserve it in its original direction, the position actually assumed by the axis being in the direction of the resultant of this hypothetical force and the applied magnetizing force.
Maxwell (Electricity and Magnetism, § 444), recognizing that the theory in this form gave no account of residual magnetization, made the further assumption that if the deflection of the axis of the molecule exceeded a certain angle, the axis would not return to its original position when the deflecting force was removed, but would retain a permanent set.
It can be shown that if a current i circulates in a small plane circuit of area S, the magnetic action of the circuit for distant points is equivalent to that of a short magnet whose axis is perpendicular to the plane of the circuit and whose moment is iS, the direction of the magnetization being related to that of the circulating current as the thrust of a right-handed screw to its rotation.
If the structure of the molecule is so perfectly symmetrical that, in the absence of any external field, the resultant magnetic moment of the circulating electrons is zero, then the application of a field, by accelerating the right-handed (negative) revolutions, and retarding those which are left-handed, will induce in the substance a resultant magnetization opposite in direction to the field itself; a body composed of such symmetrical molecules is therefore diamagnetic. If however the structure of the molecule is such that the electrons revolving around its atoms do not exactly cancel one another's effects, the molecule constitutes a little magnet, which under the influence of an external field will tend to set itself with its axis parallel to the field.
Each consists of an axis, bearing numerous blunt tooth-like processes arranged in a series.
The elongated axis which opens at the stigma in Scorpio and which can be cleared of soft, surrounding tissues and co agulated blood so as to present the appearance of a limb axis carrying the book-like leaves of the lung is not really, as it would seem to be at first sight, the limb axis.
The apparent axis or basal support of the scorpion's lung-books shown in the figures, is a false or secondary axis and merely a part of the infolded surface which forms the air-chamber.
The maceration of the soft parts of a scorpion preserved in weak spirit and the cleaning of the chitinized in-grown 1nus cuticle give rise to the false appearance of a limb axis carrying the lamellae.
These bands are often concealed by more recent deposits, but it is clear that in this region the Devonian beds form a basin or synclinal with the Amazon for its axis.
The latter completely encloses a large area of ground in a semicircle of which Besancon itself is the centre, and the whole of the newer works taken together form an irregular ellipse of which the major axis, lying north-east by south-west, is formed by the Doubs.
Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
When light passes through a small circular or annular aperture, the illumination at any point along the axis depends upon the precise relation between the aperture and the distance from it at which the point is taken.
The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.
It is thus sufficient to determine the intensity along the axis of p. Putting q = o, we get C = ffcos pxdxdy=2f+Rcos 'px 1/ (R2 - x2)dx, R being the radius of the aperture.
In different gratings the lengths of the spectra and their distances from the axis were inversely proportional to the grating interval, while with a given grating the distances of the various spectra from the axis were as i, 2, 3, &c. To Fraunhofer we owe the first accurate measurements of wave-lengths, and the method of separating the overlapping spectra by a prism dispersing in the perpendicular direction.
If we suppose that the force impressed upon the element of mass D dx dy dz is DZ dx dy dz, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).
For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (r).
The oldest rocks in the country are the granites, gneisses, &c., of the southern massif and the crystalline schists which form the axis of the Cordillera and the Caribbean chain.
It is roughly elliptical, its major axis, 180 m.
Even here, however, the main central water-divide, or axis of the chain, is apparently not the line of highest peaks, which must be looked for to the south, where the great square-headed giant called Tirach Mir dominates Chitral from a southern spur.
The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
The blower then heats the end of the cylinder again and rapidly spins the pipe about its axis; the centrifugal effect is sufficient to spread the soft glass at the end to a radius equal to that of the rest of the cylinder.
He supposed that the filaments of water which graze along the sides of the pipe lose a portion of their velocity; that the contiguous filaments, having on this account a greater velocity, rub upon the former, and suffer a diminution of their celerity; and that the other filaments are affected with similar retardations proportional to their distance from the axis of the pipe.
He then supposed this cylindrical column of water to be divided into two parts, - the first, which he called the " cataract," being an hyperboloid generated by the revolution of an hyperbola of the fifth degree around the axis of the cylinder which should pass through the orifice, and the second the remainder of the water in the cylindrical vessel.
Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.
To give a simple instance, hanging to the stereographic projection by putting tan 20=x, ill give a possible state of motion of the axis of the body; and the otion of the centre may then be inferred from (22).
The effective angular inertia of the body in the medium is now required; denote it by C 1 about the axis of the figure, and by C2 about a diameter of the mean section.
A rotation about the axis of a figure of revolution does not set the medium in motion, so that C 1 is.
This spot increases in size; in the stalks it assumes an oval shape, with its long axis parallel to the stalk, whilst in the leaves and grapes it is more or less circular in outline.
The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix.
From every point of the curve of intersection, perpendiculars are drawn to the axis.
The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected.
It consists of a number of tubes mounted vertically on a horizontal circular disk which rotates about a vertical axis in a cylindrical vessel.
The vapour pressure-composition curve will now be concave to the axis of composition, the minima corresponding to the pure components.
Hence, if a prism is placed in front of the eye with its base towards the nose, a ray of light falling upon it will be bent inwards, and seem to come from a point farther out from the axis of vision.
Conversely, if the base of the prism is turned towards the temple, the ray of light will seem to come from a point nearer the axis, and will induce the eye to turn inwards, to converge towards its fellow.
Two eggs are produced at a time, each measuring about three-fourths of an inch in its long and half an inch in its short axis, and enclosed in a strong, flexible, white shell.
In North Hondo the great Bandai arc forms the axis of the island and stretches into Yezo (HokkaidO).
A hummocky irregular country spreads southward, where the Silurian axis is encountered, in continuation of the southern uplands of Scotland.
This flying machine consisted of a light frame covered with strong canvas and provided with two large oars or wings moving on a horizontal axis, and so arranged that the upstroke met with no resistance while the downstroke provided the lifting power.
Although firmly anchylosed to the bone, the tooth, which when at rest is laid backwards, is erectile, - the bone itself being mobile and rotated round its transverse axis.
One species of Limnophilus uses small but entire leaves; another, the shells of the pondsnail Planorbis; another, pieces of stick arranged transversely with reference to the long axis of the tube.
Each cone cuts out an area on the surface equally inclined to the cone axis.
Since the potential of a small charge of electricity dQ at a distance r is equal to dQ/r, and since the potential of all parts of a conductor is the same in those cases in which the distribution of surface density of electrification is uniform or symmetrical with respect to some point or axis in the conductor, we can calculate the potential by simply summing up terms like rdS/r, where dS is an element of surface, o- the surface density of electricity on it, and r the distance from the symmetrical centre.
Accordingly the distribution of electricity is such that equal parallel slices of the ellipsoid of revolution taken normal to the axis of revolution carry equal charges on their curved surface.
Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.
R - A, Accordingly var where R is the distance of the point in the interspace from the axis, and A is a constant.
The function G is represented by the negative area D"DM under the isothermal, bounded by the isopiestic DM and the axis of pressure.
The lift is effected by cams acting on the under surface of tappets, and formed by cylindrical boxes keyed on to the stems of the lifter about onefourth of their length from the top. As, however, the cams, unlike those of European stamp mills, are placed to one side of the stamp, the latter is not only lifted but turned partly round on its own axis, whereby the shoes are worn down uniformly.
The Bingemma range, rising 726 ft., is nearly at right angles to the axis of the main island.
They differ from all the forms already noticed in being shrubby and epiphytal in habit, and in having the branches compressed and dilated so as to resemble thick fleshy leaves, with a strong median axis and rounded woody base.
It is a very heterogeneous group, being fleshy-stemmed with a woody axis, the branches being angular, winged, flattened or cylindrical, and the flowers small, short-tubed, succeeded by small, round, peashaped berries.
The counterpoise w balances the head about its axis of rotation.
There is also a position circle, attached at m to the eye-end, provided with a slide to move the eye-piece radially from the axis of the telescope, and with a micrometer to measure the distance of an object from that axis.
Complete rotation of the head is obviously impossible because of the interference of the declination axis with the rods, and therefore, in some angles, objects cannot be measured in two positions of the circle.
For this purpose the position angle of the eye-piece micrometer is set to that of the head, and the eye-piece is displaced from the axis of the tube (in the direction of the movable segment) by an amount equal to half the angle under measurement.
The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured.
Of these methods Bessel generally employed the first because of its simplicity, notwithstanding that it involved a resetting of the right ascension and declination of the axis of the tube with each reversal of the segments.
The chief objections to the method are that, as one star is in the axis of the telescope and the other displaced from it, the images are not both in focus of the eye-piece,3 and the rays from the two stars do not make the same angle with the optical axis of each segment.
The brass tube, strengthened at the bearing points by strong truly turned collars, rotates in the cast iron cradle q attached to the declination axis.
It must be mentioned 4 _ 28 that the pressure of the cushion C on the type-wheels 6 - 30 has no influence whatever upon the micrometer-screw, 7 -32 because the type-wheels are mounted on a hollow cylindrical axis, concentric with the axis of the screw, but entirely disconnected from the screw itself.
Having selected the most suitable one he directs the axis of the finder to the estimated middle point between the comet and the star, turns the finder-micrometer in position angle until the images of comet and star lie symmetrically between the parallel position wires, and then turns the micrometer screw (which moves the distance-wires symmetrically from the centre in opposite directions) till one wire bisects the comet and the other the star.
When the inclination of the movable half with respect to the axis of the telescope is changed by rotation about an axis at right angles to the plane of division, two images are produced.
Helmholtz in his " Ophthalmometer " has employed Clausen's principle, but arranges the plates so that both move symmetrically in opposite directions with respect to the telescope axis.
If Struve had employed a properly proportioned double circular diaphragm, fixed symmetrically with the axis of the telescope in front of the divided lens and turning with the micrometer, it is probable that his report on the instrument would have been still more favourable.
In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion.
The surface arrangements of a modern deep colliery are of considerable extent and complexity, the central feature being the head gear or pit frame carrying the guide pulleys Surface which lead the winding roes from the axis of the it arrange= g P P to the drum.
The tub when brought to the surface, after passing over a weigh-bridge where it is weighed and tallied by a weigher specially appointed for the purpose by the men and the owner jointly, is run into a " tippler," a cage turning about a horizontal axis which discharges the load in the first half of the rotation and brings the tub back to the original position in the second.
When the force acts on a body free to turn about a fixed axis only, it is convenient to express the work done by the transformed product TO, where T is the average turning moment or torque acting to produce the displacement 0 radians.
If the brake is not balanced, its moment about the axis must be included.
The external forces holding the brake from turning are W, distant R from the axis, and the reaction, W 1 say, of the lever against the fixed pin P, distant R1 from the axis.
Both these forces usually act at the same radius R, the distance from the axis to the centre line of the rope, in which case the torque T is (W-p)R, and consequently the brake horse-power is (W - p)RX21rN, When µ 33,000 changes the weight W rises or falls against the action of the spring balance until a stable condition of running is obtained.
The moments of the components of these actions and reactions in a plane to which the axis of rotation is at right angles are the two aspects of the torque acting, and therefore the torque acting on B through the shaft is measured by the torque required to hold A still.
The value n = 2 is appropriate to bodies of which the shape is that of a solid of revolution, so that there is no rotation about the axis of symmetry.
The Louisiade and the d'Entrecasteaux Islands consist of the same slates and schists as form the main axis of the eastern peninsula, and they are auriferous.
It appears to consist in the main of a continuation of an axis of old schists and slates, with granite intrusions, and flanked by coastal plains with Cretaceous or Jurassic, and Miocene beds, with Pleistocene sands and reefs and volcanic rocks.
Until the 9th century the only means for sighting cannon was by the " line of metal " - a line scored_ along the top of the gun, which, owing to the greater thickness of metal at the breech than at the muzzle, was not parallel to the axis.
Owing to the conical shape of the early muzzle-loading guns, if one trunnion were higher than the other, the " line of metal " would no longer be in the same vertical plane as the axis; in consequence of this, if a gun with, say, one wheel higher than the other were layed by this line, the axis would point off the target to the side of the lower wheel.
Now the height to which the tangent sight has been raised in order to direct the axis on G' is evidently proportional to the tangent of the angle OMS =AXS.
To overcome drift the axis must be pointed to the left of the target, and the amount will increase with the range.
Now if the notch of the tan gent sight be carried to H' in order to lay on T, the fore-sight, and with it the axis, H will be moved to F', the line of fire will be HF'D', and the shot will strike T since D'T = DT.
These V's are so arranged that the axis of the sight frame is always parallel to that of the gun.
By means of a cross-level the frame can be so adjusted that the cross axis on which the telescope is mounted is always truly horizontal.
This complication is eliminated in Scott's sight by simply levelling the cross axis of the telescope.
The pattern is that of a true sight, that is to say, the base plate is capable of movement about two axes, one parallel to and the other at right angles to the axis of the gun, and has cross spirit-levels and a graduated elevating drum and independent deflection scale, so that compensation for level of wheels can be given and quadrant elevation.
There must be two sets of elevating gears, one which brings the axis of the gun and the sights together on to the target, thus finding the angle of sight and also pointing the axis of the gun at the target, and a second by which, independent of the sight which remains fixed, the elevation due to the range can be given to the gun and read by means of a pointer and dial marked in yards for range.
Similarly a surface of revolution can be divided by planes at right angles to the axis into elements, each of which is approximately a section of the surface of a right circular cone.
Draw the tangents at A and B, meeting at T; draw TV parallel to the axis of the parabola, meeting the arc in C and the chord in V; and M draw the tangent at C, meeting AT and BT in a and b.
The line TCV is parallel to the axis of the parabola.
Hence the area of an ellipse whose axes are 2a and 2b is Trab; and the volume of an ellipsoid whose axes are 2a, 2b and 2c is t rabc. The area of a strip of an ellipse between two lines parallel to an axis, or the volume of the portion (frustum) of an ellipsoid between two planes parallel to a principal section, may be found in the same way.
The top is then a parabola whose axis is at right angles to the base; and the area can therefore (§ 34) be expressed in terms of the two bounding ordinates and the midordinate.
Thus we find from (i) that Simpson's second formula, for the case where the top is a parabola (with axis, as before, at right angles to the base) and there are three strips of breadth h, may be replaced by area = 8h(3u i + 2U 1 + 3us).
In cases other than those described in § 82, the pth moment with regard to the axis of u is given by Pp = XPrA where A is the total area of the original trapezette, and S 2 _ 1 is the area of a trapezette whose ordinates at successive distances h, beginning and ending with the bounding ordinates, are o, x1P -1A, x2 P-1 (AI+AI),.
This approaches most nearly to the wild stock, from which it is distinguished by the non-jointed axis and somewhat shorter awns.
At the points ABCD there is no displacement, and the line AD through these points is called the axis.
Forward displacement is represented by height above the axis, backward displacement by depth below it.
At A the air occupies its original position, while at H it is displaced towards the right or away from A since HP is above the axis.
At J the displacement is forward, but since the curve at Q is parallel to the axis the displacement is approximately the same for all the points close to J, and the air is neither extended nor compressed, but merely displaced bodily a distance represented by JQ.
The distribution of velocity then is represented by the dotted curve and is forward when the curve is above the axis and Dackward when it is below.
Seebeck (1805-1849) is the simplest form of apparatus thus designated, and consists of a large circular disk mounted on a central axis, about which it may be made to revolve with moderate rapidity.
This second plate is capable of rotation about an axis perpendicular to its plane and passing through its centre.
For this purpose the axis is furnished at its upper part with a screw working into a toothed wheel, and driving it round, during each revolution of the plate, through a space equal to the interval between two teeth.
The cylinder is mounted on an axis and turned round, while the style attached to the vibrating body is in light contact with it, and traces therefore a wavy circle, which, on taking off the paper and flattening it, becomes a wavy straight line.
Koenig's arrangement (Quelques experiences d'acoustique, p. I) the axis of the cylinder is fashioned as a screw, which works in fixed nuts at the ends, causing a sliding as well as a rotatory motion of the cylinder.
It is set so that it can be turned at any desired and determined speed about a horizontal axis, and when going fast enough it appears grey.
For this purpose four vertical mirrors are arranged round the vertical sides of a cube which is rapidly revolved about a vertical axis.
Let ABCD be drawn at such level that the areas above and below it are equal; then ABCD is the axis of the curve.
Since the curve represents a longitudinal disturbance in air it is always continuous, at a finite distance from the axis, and with only one ordinate for each abscissa.
The tangent to the displacement curve is always parallel to the axis, that is, for a small distance the successive particles are always equally displaced, and therefore always occupy the same volume.
A glass or metal rod, the " sounder," is clamped at its middle point, and fixed along the prolongation of the axis of the dust-tube as in fig.
The component of T perpendicular to the axis is Tdy/ds=Tdy/dx.
In fact, the forces are then no longer parallel to the axis.
The flame appears to lengthen, but if the reflection is viewed in a vertical mirror revolving about a vertical axis or in Koenig's cube of mirrors, it is seen that the flame is really intermittent, jumping up and down once with each vibration, sometimes apparently going within the jet tube at its lowest point.
An "anchor ring" or "tore" results when a circle revolves about an axis in its plane.
Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.
The axis is of forged steel 21 in.
The axis has eight bearings, consisting of rings of live rollers 4 i 7 zin.
If it revolves about a vertical axis d its centre of gravity must always lie in that axis; if it rolls the centre of gravity must always lie over the e abutment.
Thus if the members are pinned together, the, joint consisting of a single circular pin, the centre of which lies in the axis of the piece, it is clear that the direction of the only stress which can be transmitted from pin to pin will coincide with this axis.
The axis becomes, therefore, a line of resistance, and in reasoning of the stresses on frames we may treat the frame as consisting of simple straight lines from joint to joint.
Then the deviation y= DE of the neutral axis of the bent beam at any point D from the axis OX is given by the relation d 2 y Ml dx 2 = EI' where M is the bending moment and I the amount of inertia of the beam at D, and E is the coefficient of elasticity.
A remarkable feature of the belt is the longitudinal chain of broad valleys - the Great Appalachian Valley - which, in the southerly sections divides the mountain system into two subequal portions, but in the northernmost lies west of all the ranges possessing typical Appalachian features, and separates them from the Adirondack group. The mountain system has no axis of dominating altitudes, but in every portion the summits rise to rather uniform heights, and, especially in the central section, the various ridges and intermontane valleys have the same trend as the system itself.
In spite of the existence of the Great Appalachian Valley, the master streams are transverse to the axis of the system.
It consists of a disk of aluminium, the axis of which is geared to a counting mechanism and which runs between the poles of permanent magnets that create eddy currents in it and therefore exert a retarding force.
These screes are however very flat and their lower edges generally reach all the way down to the central part of the basin, which is occupied by an expanse of yellow clay, perfectly flat and fairly hard, as well as dry and barren, often cracked into polygonal cakes and drawn out in the direction of the long axis of the valley....
To become a medusa, the actinula grows scarcely at all in the direction of the principal axis, but greatly along a plane at right angles to it.
From the ring-canal are given off tentacle-canals which run down the axis of each tentacle; in many cases, however, the cavity of the tentacle is obliterated and instead of a canal the tentacle contains a solid core of endoderm.
To produce a medusa the actinula grows greatly along a plane at right angles to the vertical axis of the body, whereby the aboral surface of the actinula becomes the exumbrella, and the peristome becomes the subumbrella.
This typically consists of two concentric zones, the trochus and cingulum, often separated by a groove or gutter which may be finely ciliated; but in several genera of no close affinity, where it is very oblique to the longitudinal axis of the body, it is represented by a general ciliation of the surface (Taphrocampa, Rattulus, Copeus, Adineta).
In the space between them is suspended a "needle" which consists of a light aluminium axis, to which are affixed a number of paddle-shaped aluminium blades.
In other types of electrostatic instruments the movable system rotates round a horizontal axis or rests upon knife edges like a scale beam; in others again the movable system is suspended by a wire.
This motion is resisted by the torsion of a spiral spring resembling the hair-spring of a watch having one end fixed to the coil axis, and there is therefore a definite position of the needle on the scale corresponding to each potential difference between the terminals, provided it is within the range of the control.
He first brought the revolutions of our satellite within the domain of Kepler's laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus.
The direction of the great volcanic cones, which rise in an irregular line above it, is not identical with the main axis of the Sierra itself, except near the Mexican frontier, but has a more southerly trend, especially towards Salvador; here the base of many of the igneous peaks rests among the southern foothills of the range.
Farther north in Montana, beyond the gorge of the Missouri river, the structure of the Front Range is altogether different; it is here the carved residual of a great mass of moderately bent Palaeozoic strata, overthrust eastward upon the Mesozoic strata of the plains; instead of exposing the oldest rocks along the axis and the youngest rocks low down on the flanks, the younger rocks of the northern range follow its axis, and the oldest rocks outcrop along its eastern flanks, where they override the much younger strata of the plains; the harder strata, instead of lapping on the mountain flanks in great slab-like masses, as in the Bighorns, form out-facing scarps, which retreat into the mountain interior where they are cut down by outfiowing streams.
Many streams descend from the ravines only to wither away on the desert basin floors before uniting in a trunk river along the axis of a depression; others succeed in uniting in the winter season, when evaporation is much reduced, and then their trunk flows for a few score miles, only to disappear by sinking (evaporating) farther on.
In January the northern water areas of the continent are frozen and snow-covered; Hudson Bay becomes unduly cold, and the greatest southward bending of the isotherms is somewhat east of the continental axis, with an extension of its effects out upon the Atlantic; but the southward bending isotherms are somewhat looped back about the unfrozen waters of the lower Great Lakes.
The earliest form of shutter weir, known as a bear-trap, introduced in the United States in 1818, and subsequently erected across the Marne in France, consists of two wooden gates, each turning on a horizontal axis laid across the apron, inclined towards one another and abutting together at an angle in the centre when the weir is closed; the up-stream one serves as the weir, and the down-stream one forms its support, and both fall flat upon the apron for opening the weir.'
The drum weirs erected across shallow, regulating passes on the river Marne in1857-1867comprise a series of upper and under wrought-iron paddles, which can make a quarter of a revolution round a central axis laid along the sill of the weir.
Obviously these equations show that the curves intersect in four points, two of which lie on the intersection of the line, 2 (g - g')x +2 (f - f')y+c - c'=o, the radical axis, with the circles, and the other two where the lines x2+y2= (x+iy) (x - iy) =o (where i = - - I) intersect the circles.
The line la+ma+ny is the radical axis, and since as+43 c-y =o is the line infinity, it is obvious that equation (I) represents a conic passing through the circular points, i.e.
The line AB is termed the " radical axis."
A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis - considered as a circle of infinite radius.
In the case of two non-intersecting circles it may be shown that the radical axis has the same metrical relations to the line of centres.
There are several methods of constructing the radical axis in this case.
To construct circles coaxal with the two given circles, draw the tangent, say XR, from X, the point where the radical axis intersects the line of centres, to one of the given circles, and with centre X and radius XR describe a circle.
The radical axis is x = o, and it may be shown that the length of the tangent from a point (o, h) is h 2 k 2, i.e.
The main axis of disturbance and the highest remaining land runs through the south-eastern part of Quebec,forming the Notre Dame Mountains, and terminates in the Gaspe peninsula as the Shickshock Mountains.
The Molluscan ctenidium is typically a plume like structure, consisting of a vascular axis, on each side of which is set a row of numerous lamelliform or filamentous processes.
These processes are hollow, and receive the venous blood from, and return it again aerated into, the hollow axis, in which an afferent and an efferent blood-vessel may be differentiated.
The filaments of the gill (ctenidium) of Mytilus and Arca thus form two closely set rows which depend from the axis of the gill like two parallel plates.
As the axis of the ctenidium lies by the side of the body, and is very frequently connate with the body, as so often happens in Gastropods also, we find it convenient to speak of the two plate-like structures formed on each ctenidial axis as the outer and the inner gill-plate; each of these is composed of two lamellae, an outer (the reflected) and an adaxial in the case of the outer gill plate, and an adaxial and an inner (the reflected) in the case of the inner gill-plate.
Section across the axis of a ctenidium with a pair of plates - flattened and shortened filaments - attached.
The axis of each ctenidium, right and left, starts from a point well forward FIG.
This is difficult to see in Anodonta, but if the mantle-skirt be entirely cleared away, and if the dependent lamellae which spring from the ctenidial axis be carefully cropped so as to leave the axis itself intact, we obtain the form shown in fig.
If we were to make a vertical section across the long axis of a Lamellibranch which had the axis of its ctenidium free from its origin onwards, we should find such relations as are shown in the diagram fig.
The gill axis d is seen lying in the sub-pallial chamber between the foot b and the mantle c. From it depend the gillfilaments or lamellae - formed by united filaments - drawn as black lines f.
The axis of the ctenidium is seen to be adherent to, or fused by concrescence with, the body-wall, and moreover on each side the outer lamella of the outer gill-plate is fused to the mantle, whilst the inner lamella of the inner gill-plate is fused to the foot.
Portion of the axis of the left ctenidium which is fused with the base of the foot, the two dotted lines indicating the origins of the two rows of gill-filaments.
In addition to this, its long axis forms a marked angle with that of the vagina, so that the whole uterus is bent forward or anteverted.
It lies in the side wall of the pelvis with its long axis nearly vertical and having its blunt end (tubal pole) upward.
It is made of brass, and is provided with a spheroidal bulb the axis of which is 2 in.
In common with all other Coelomata, the Mollusca are at one period of life possessed of a prostomium or region in front of the mouth, which is the essential portion of the " head," and is connected with the property of forward locomotion in a definite direction and the steady carriage of the body (as opposed to rotation of the body on its long axis).
Each is an outgrowth of the body-wall at the side of the body, and consists of an axis containing two main vessels, an afferent and efferent, and bearing on either side a series of transverse plates whose blood-sinuses communicate with the vessels of the axis.
The "line of apsides" is that which joins them, forming the major axis of the orbit.
The oscillation of the earth's axis may arise in two distinct ways; distinguished as " nutation of the axis " and " variation of latitude.
This star was seen to possess an apparent motion similar to that which would be a consequence of the nutation of the earth's axis; but since its declination varied only one half as much as in the case of y Draconis, it was obvious that nutation did not supply the requisite solution.
It has an oval shape, the longer axis running from N.W.
The geometrical axis of the magnet is sometimes defined by means of a mirror rigidly attached to the magnet and having the normal to the mirror as nearly as may be parallel to the magnetic axis.
In this case the geometrical axis is the line joining the central division of the scale to the optical centre of the lens.
The magnet having been attached, the instrument is rotated about its vertical axis till the centre division of the scale appears to coincide with the vertical cross-wire of the telescope.
This mirror can rotate about a horizontal axis which is at right angles to the line of collimation of the telescope, and is parallel to the surface of the mirror.
If, however, a theodolite, fitted with a telescope which can rotate about a horizontal axis and having an altitude circle, is employed, so that when observing a transit the altitude of the sun or star can be read off, then the time need only be known to within a minute or so.
The auxiliary magnet has a plane mirror attached, the plane of which is at right angles to the axis of the magnet.
The axis of the magnet is horizontal and at the same level as the mirror magnet, while when the central division of the scale B appears to coincide with the vertical cross-wire of the telescope the axes of the two magnets are at right angles.
What is known as the method of sines is used, for since the axes of the two magnets are always at right angles when the mirror magnet is in its zero position, the ratio M/H is proportional to the sine of the angle between the magnetic axis of the mirror magnet and the magnetic - = meridian.
The difference between the two sets of readings gives twice the angle which the magnetic axis of the mirror magnet makes with the magnetic meridian.
Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.
The leaves are of their arrangement on the numbered in their order, from below axis of the cone.
The chief difficulty in this method lay in determining the effective distances of the bulbs of the thermometers from the axis of the cylinder, and in ensuring uniformity of flow of heat along different radii.
It is a diamond-shaped peninsula jutting out from the mainland in a north-easterly direction, the longer axis, from Muir of Ord station to the South Sutor at the entrance to Cromarty Firth, measuring 20 m., and the shorter, from Ferryton Point to Craigton Point, due north and south, 12 m., and it has a coastline of 52 m.
One end only, for example, may appear to move, as if rotating round the other; or the two ends may move in opposite directions, as if the arc were rotating about a vertical axis through its summit.
The limbs of the U are further twisted together in a looser or tighter coil, the axis of which may be traversed by a "spindle" muscle arising from the posterior end of the body.
Since the movements of the ground are frequently accompanied by a slight tilting, which would cause b or b' to swing or wander away from its normal position, a sufficient stability is given to the weights by inclining the axis of the instrument slightly forwards.
The adjustment of the instrument is effected by means of screws in the bed-plate, by turning which the axis o'o" may be brought into a position nearly vertical.
On the different days of the year each hour was determined by a fixed star culminating or nearly culminating in it, and the position of these stars at the time is given in the tables as in the centre, on the left eye, on the right shoulder, &c. According to the texts, in founding or rebuilding temples the north axis was determined by the same apparatus, and we may condude that it was the usual one for astronomical observations.
A little later the breaking down of the whole axon, both axis cylinder and myelin sheath alike, seems to occur simultaneously throughout its entire length distal to the place of severance.
This death of the sheath as well as of the axis cylinder shows that it, like the axis cylinder, is a part of the nerve cell itself.
Immediately on the axle (6Ecov, axis), without springs of any kind, rested the basket or body (S14pos) of the chariot, which consisted of a floor to stand on, and a semicircular guard round the front about half the height of the driver.
It appears that the four peninsulas are traversed in the direction of their longitudinal axis by mountain chains 3000 to 4000 ft.
In rare cases the main axis is unbranched and ends in a flower, as, for instance, in the tulip, where scale-leaves, forming the underground bulb, green foliage-leaves and coloured floral leaves are borne on one and the same axis.
Series 2, Disciflorae, takes its name from a development of the floral axis which forms a ring or cushion at the base of the ovary or is broken up into glands; the ovary is superior.
Each leaf has a slender stem-like axis, which twines round a support and bears leaflets at intervals; it goes on growing indefinitely.
Caulerpa sp., showing portion 'of axis with leaf-like and root C. Pandorina sp., a 16-celled colony.
In all Conjugatae and most have the same unlimited growth as the main axis.
The movement of the zoospore is effected by the lashing of the cilia and is in the direction of the beak, while the zoospore slowly rotates on its long axis at the same time.
In these cases, however, the portions of the hairs behind the growing region become agglutinated together into a solid cylindrical pseudo-parenchymatous axis.
The segment so cut off does not usually divide again by means of a transverse wall, nor indeed by a longitudinal wall which passes through the organic axis of the cell.
In Champia and allied genera, the cylindrical axis is due not to the derivatives of one axial filament, but of several, the growth of which is co-ordinated to form a septated tube.
When such a lateral branch overtops the main axis whose growth has become limited, as in Plocamium and Dasya, a sympodium is formed.
In Iridaea the thallus is an entire lamina; in Callophyllis a lobed lamina; in Delesseria it is provided with midrib and veins, simulating the appearance of a leaf of the higher plants; in Constantinea the axis remains cylindrical, and the lateral branches assume the form of leaves.
In all these cases, however, the end-cells of the filaments each give rise to a carpospore, and the aggregate of such sporiferous filaments is a cystocarp. Again, in the family of the Gelidiaceae, the single filament arising from the carpogonium grows back into the tissue and preys upon the cells of the axis and larger branches, after which the end-cells give rise to carpospores and a diffused cystocarp is formed.
As a general rule, the molars, and more especially the first, are partially brachyodont (short-crowned); although they are taller in the chital (Cervus axis).
The most noteworthy point of distinction is in the skull, in which the facial portion is sharply bent down on the posterior basal axis in the fashion characteristic of the hollow-horned ruminants (oxen, antelopes, &c.), and the American prongbuck, instead of running more or less nearly parallel to the same, as in deer.
In the Theorie nouvelle de la rotation des corps (1834) he treats the motion of a 'rigid body geometrically, and shows that the most general motion of such a body can be represented at any instant by a rotation about an axis combined with a translation parallel to this axis, and that any motion of a body of which one point is fixed may be produced by the rolling of a cone fixed in the body on a cone fixed in space.
The line FL perpendicular to the axis, G D and passing through the focus, is the semilatus rectum, the latus rectum being the focal chord parallel to the directrix.
Any line parallel to the axis is a diameter, and the parameter of any diameter is measured by the focal chord drawn FIG.
The simplest equation to the parabola is that which is referred to its axis and the tangent at the vertex as the axes of co-ordinates, when it assumes the form y 2 = 4ax where as = semilatus rectum; this may be deduced directly from the definition.
The optical apparatus generally consists of a mirror mounted on an axis parallel to the axis of the earth, and rotated with the same angular velocity as the sun.
One of the simplest consists of a plane mirror rigidly connected with a revolving axis so that the angle be tween the normal to the mirror and the axis of the instrument equals half the sun's polar distance, the mirror being adjusted so that the normal has the same right ascension as the sun.
It is easily seen that if the mirror be rotated at the same angular velocity as the sun the right ascensions will remain equal throughout the day, and therefore this device reflects the rays in the direction of the earth's axis; a second fixed mirror reflects them in any other fixed direction.
The axis of rotation AB bears a rigidly attached rod DBC inclined to it at an angle equal to the sun's polar distance.
By adjusting the right ascension of the plane ABC and rotating the axis with the angular velocity of the sun, it follows that BC will be the direction of the solar rays throughout the day.
The framework is attached to two independent circular arcs Cs and rr having their centres at 0 and provided with clamps D and A on the axis F of the instrument.
The fruit, or haw, as in the apple, consists of the swollen floral axis, which is usually scarlet, and forms a fleshy envelope surrounding the hard stone.
These furnaces possess a large cylindrical shell (e), lined with fire-bricks, and made to revolve round its horizontal axis by means of a toothed wheel fixed on its exterior; (if) are tire-seats holding tires (gg), which work in friction rollers (h).
At the northeastern angle of that frontier, the Dihang river, the connecting link between the Tsanpo of Tibet and the Brahmaputra of Assam, bursts through the main axis of the range.
The chital or spotted deer (C. axis) is generally admitted to be the most beautiful inhabitant of the Indian jungles.
He demonstrated the rotation of the satellites of Jupiter round the planet, and gave rough predictions of their configurations, proved the rotation of the sun on its axis, established the general truth of the Copernican system as compared with that of Ptolemy, and fairly routed the fanciful dogmas of the philosophers.
When the axis of the eye-lens coincides with that of the object-glass, and the focal point of the eye-lens is coincident with the principal focus of the object-lens, parallel rays.
The mere size of the apparent field of view depends upon obtaining the oblique pencils of light emerging from it to cross the axis at the great possible angle, and to this end the presence of a field-lens is indispensable, which is separated from the eye-lens by a considerable interval.
A A and B B are concave mirrors having a common axis and their concavities facing each other.
A A is a concave mirror whose axis is a a.
Where accurate differential observations or photographs involving other than instantaneous exposures have to be made, the additional condition is required that the optical axis of the telescope shall accurately and automatically follow the object under observation in spite of the apparent diurnal motion of the heavens, or in some cases even of the apparent motion of the object relative to neighbouring fixed stars.
In its simplest form the mounting of an equatorial telescope consists of an axis parallel to the earth's axis, called" the polar axis "; a second axis at right angles to the polar axis called" the declination axis "; and the telescope tube fixed at right angles to the declination axis.
The telescope is counterpoised by a weight attached to the opposite end of the declination axis.
A vertical plane passing through A A is therefore in the meridian, and the polar axis is inclined to the horizon at an angle equal to that of the latitude of the place of observation.
Thus, when the declination axis is horizontal the telescope moves in the plane of the meridian by rotation on the declination axis only.
Thus one important attribute of an equatorially mounted telescope that, if it is directed to any fixed star, it will follow the diurnal motion of that star from rising to setting by rotation of the polar axis only.
If we now attach to the polar axis a graduated circle D D, called the" hour circle,"of which the microscope or vernier R reads o h when the declination axis is horizontal, we can obviously read off the hour angle from the meridian of any star to which the telescope may be directed at the instant of observation.
Further, by causing the hour circle, and with it the polar axis, to rotate by clockwork or some equivalent mechanical contrivance, at the same angular velocity as the earth on its axis, but in the opposite direction, the telescope will, apart from the effects of refraction, automatically follow a star from rising to setting.
The declination axis rests on bearings attached to opposite sides of the polar axis.
The telescope is attached to one end of the declination axis, and counterpoised by a weight at the other end, as in fig.
Mountings of types A and B - that is, with a long polar axis supported at both ends - are often called the" English mounting,"and type C, in which the declination axis is placed on the extension of the upper pivot of the polar axis, is called the" German mounting,"from the first employment of type C by Fraunhofer.
The polar axis was similar in shape to that of fig.
In Smyth's celebrated Bedford telescope the polar axis was of mahogany.
Probably the best example of this type of mounting applied to a refractor is that made by the elder Cooke of York for Fletcher of Tarnbank; the polar axis is of cast iron and the mounting very satisfactory and convenient, but unfortunately no detailed description has been published.
The double polar axis is composed of hollow metal beams of triangular section.
The hour circle has two toothed circles cut upon it, one acted upon by a worm screw mounted on the pier and driven by clockwork, the other by a second worm screw attached to the polar axis, which can be turned by a handle in the observer's hand and thus a slow movement can be given to the telescope in right ascension inde FIG.
Slow motion in declination can be cornmunicated by a screw acting on a long arm, which latter can be clamped at pleasure to the polar axis.
The peculiar form of the tube is eminently suited for rigid preservation of the relative parallelism of the axes of the two telescopes, so that,;i the image of a certain selected star is retained on the intersection of two wires of the micrometer, by means of the driving clock, aided by small corrections given by the observer in right ascension and declination (required on account of irregularity in the clock movement, error in astronomical adjustment of the polar axis, or changes in the star's apparent place produced by refraction), the image of a star will continue on the same spot of the photographic film during the whole time of exposure.
The driving circle is also much too small, so that a very slight mechanical freedom of the screw in the teeth involves a large angular freedom of the telescope in right ascension, while its position at the lower end of a too weak polar axis tends to create instability from torsion of that axis.
The driving circle was greatly increased in diameter and placed at the upper end of the polar axis, and both the polar and declination axes were made much stronger in proportion to the mass of the instrument they were designed to carry.
It is not a little curious that the obvious improvement of trans ferring the declination axis as well as the declination-clamp to the telescope end of the declination axis was so long delayed; we can explain the delay only by the desire to retain the declination circle as a part of the counterpoise.
The observer's eye is applied to the small telescope E, which (by means of prisms numbered I, 2, 3, 4) views the vernier attached to the cross-head simultaneously with the hour circle attached to the upper end of the polar axis.
Prism i is in the axis of the declination circle and always reflects rays along?
Through the eyepiece of the bent 1 telescope E' another hour circle attached to the lower end of the polar axis can be seen; thus an assistant is able to direct the telescope by a handle at H to any desired hour angle.