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axis

The plot of land extends on an axis from north-west to south-east over some 36,000 acres.

250177The purpose of his paper was to show that there is no problem if the axis is moved to the left.

179144Elements of the graph are shown from an axis through 0 and at right angles to OX.

3332The movable coil of the wattmeter is normally suspended so that its axis is at right angles to that of the fixed coil, and is constrained by the torsion of a spiral spring.

2526The swivel-head type of lamp will normally have an adjustable front shade portion that usually swivels along the horizontal and the vertical axis and allows you to control the direction of the light source.

1815According to the story, the Pentagon held meetings with the world's leading scientists and concluded that once the magnetic pole aligned with the true North, it would continue moving to the equator, causing the earth to shift upon its axis.

1311Axis Long Sleeve Repeat Stripe Polynosic Sport Shirt: This one's fairly versatile as well, and it's available in a color selection that will make anyone happy: ink, nutmeg, and olive brown.

99Axis Curator Knit Zip Polo: This is an item almost any guy will appreciate, since it's great for adding another layer without additional bulk on those days or nights when the air's just starting to get crisp.

910You'll see shirts like the Axis Big and Tall Camas Silk Swirls Shirt, the Axis Big & Tall Tulaire Embroidery Camp Shirt, the Axis Big & Tall Solid Pleated Front Camp Shirt in Tan and Black, and more.

911A front loader is gentler on your clothes because instead of an agitator, which beats the clothes through the water and thus stresses and twists the fabric, the machines boast a horizontal axis, which tumbles them in and out of the water.

87This produces an opening and closing of the edges symmetrically with respect to the telescope axis.

00By De la Rue's advice, Pritchard began his career there with a determination of the physical libration of the moon, or the nutation of its axis.

00An important property is: the difference of the focal distances of any point on the curve equals the transverse axis.

00The axis of this band, almost a meridian line, is 156 statute miles long.

00- Vacuolated Endoderm Cells of cartilaginous consistence from the axis of the tentacle of a Medusa (Cunina).

00the youngest polyp of the system is the one nearest to the topmost polyp; and the axis of the system is a true axis.

00- Stomotoca axis of the umbrella; the other of non- divisa, one of the Tiaridae striated fibres running longitudinally, (Anthomedusae).

00that is to say, in a radial direction from, or (in the manubrium) parallel to, the same ideal axis.

00Ea c h cordylus is a tentacle-like structure with an endodermal axis containing an axial cavity which may be continuous with the ring-canal, or may be partially occluded.

00c, Cordylus, composed of flattened ectoderm ec covering a large-celled endodermal axis en.

00In addition to tentacles, there may be marginal cirri (Laodice) with a solid endodermal axis, spirally coiled, very contractile, and bearing a terminal battery of nematocysts.

00A typical graptolite consists of an axis bearing a series of tooth-like projections, like a saw.

00The supposed hydrothecae may be present on one side of the axis only (monoprionid) or on both sides (diprionid); the first case may be conjectured to be the result of uniserial (helicoid) budding, the second to be produced by biserial (scorpioid) budding.

00In one 'division (Retiolitidae) the axis is reticulate.

00The tentacles are always solid, containing an axis of endoderm-cells resembling notochordal tissue or plantparenchyma, and are but moderately flexible.

00Hence the principal axis of the future medusa corresponds, not to the longitudinal axis of the planula, but to a transverse axis.

00Both these medusae have sense-organs of a peculiar type, which are said to contain an endodermal axis like the sense-organs of Trachylinae, but the fact has recently been called in question for FIG.

00The coenosarc may consist of a single elongated tube or stolon, forming the stem or axis of the cormus on which, usually, the appendages are arranged in groups termed cormidia; or it may take the form of a compact mass of ramifying, anastomosing tubes, in which case the cormus as a whole has a compact form and cormidia are not distinguishable.

00The difference between the theories of Haeckel and Chun is connected with a further divergence in the interpretation of the stem or axis of the cormus.

00an opening to the exterior S From a comparison of the two embryological types there can be no doubt on two points; first, that the pneumatophore and the protocodon are strictly homologous, and, therefore if the nectocalyx is comparable to the umbrella of a medusa, as seems obvious, the pneumatophore must be so too; secondly, that the coenosarcal axis arises from the ex-umbrella of the medusa and cannot be compared to a manubrium, but is strictly comparable to the " bud-spike " of a Narcomedusan.

00this interpretation there is still a, Axis of the colony.

00Thus the umbrella of the Siphonula became the protocodon, and its manubrium, the axis or stolon, which, by a process of dislocation of Organs, escaped, as it were, from the sub-umbrella through a cleft and became secondarily attached to the ex-umbrella.

00The embryo consists of an axis bearing two or more cotyledons and ending below in a radicle; it lies in a generally copious food-storing tissue (endosperm) which is the remains of the female prothallus.

00The embryo consists of an axis bearing one (Monocotyledons) or two (Dicotyledons) cotyledons, which protect the stem bud (plumule) of the future plant, and ending below in a radicle.

00ax., Green axis creeping on the surface of damp soil; rh., colorless rhizoids penetrating the soil; asc. ax., ascending axes of green cells.

00The second type of differentiation is that between supporting axis and assimilating appendages.

00The cells of the axis are commonly stouter and have much less chlorophyll than those of the appendages (Draparnaldia).

00In the Mosses the plant-body (gametophyte) is always separable into a radially organized, supporting and conducting axis (stem)

00In the stalk of the sporogonium there is a similar strand, which is of course not in direct connection with, but continues the conduction of water from, the strand of the gametophytic axis.

00In the more highly developed series, the mosses, this last division of labor takes the form of the differentiation of special assimilative organs, the leaves, commonly with a midrib containing elongated cells for the ready removal of the products of assimilation; and in the typical forms with a localized absorptive region, a well-developed hydrom in the axis of the plant, as well as similar hydrom strands in the leaf-midribs, are constantly met with.

00The primary root is a downward prolongation of the primary axis of the plant.

00The whole tissue system is known as the stelar system (from the way in which in primitive forms it runs through the whole axis of the plant in the form of a column).

00In the downward growing part of the axis (primary root), Aflangehowever, the peripheral mantle of phloem is interrupted, ~7ii ~.

00Such a vascular cylinder is called a haplostele, and the axis containing it is said to be haplostelic. In the stele of the root the strands of tracheids along the lines where the xylem touches the pericycle are spiral or annular, and are the xylem elements first formed when the cylinder is developing.

00In many Pteridophytes the solid haplostele is maintained throughout the axis.

00To 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.

00This 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.

00Later, 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.

00In cases where the development of the embryo is advanced at the resting period, traces run from the cotyledons and determine the symmetry of the stele of the primitive axis, the upperpart of which often shows stem-structure, in some respects at least, and is called the hypocoty- ledonary stem or hypocotyl, while the lower part is the primary root .~-,

00In most Pteridophytes there is a single large apical cell at the end of each stem and root axis.

00This usually has the form of a tetrahedron, with its points base occupying the surface of the body of the axis and its apex pointing towards the interior.

00Thi vascular system is connected in various ways with that of th(parent axis by the differentiation of bundle-connections across thi cortex of the latter.

00The 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.

00But 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.

00In a differentiated body the stem (caulome) is an axis capable of bearing leaves and (directly or indirectly) the proper reproductive organs.

00The root is an axis which never bears either leaves or the proper reproductive organs (whether sexual or asexual) of the plant.

00The 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.

00The 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.

00The 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.

00Sometimes 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.

00The heart lies in the middle line of the body, its long axis being parallel with that of the trunk.

00In the ostrich, Struthio, the craze of overloading the stomach with pebbles which, when triturated into sand, are not voided, has brought about a dislocation, so that the enormously widened and stretched space between proventriculus and gizzard forms a bag, directed downwards, whilst the gizzard itself with part of the duodenum is rotated round its axis to more than loo°.

00In 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.

00In 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.

00In Wellhausen's words, each petty state " revolved on its own axis " of social-religious life till the armies of Tiglath-Pileser III.

00This 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.

00From the central peaks, of which the axis runs from W.N.W.

00described, but with the ovules on the walls of the cavity (not in its axis or centre), a six-parted perianth, a stamen or stamens and stigmas.

00In 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."

00There 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.

00The 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.

00But 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.

00Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.

00The anomaly is then the angle BFP which the radius vector makes with the major axis.

00Drop the perpendicular RPQ through P, the position of the planet, upon the major axis.

00The 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.

00(Lankester.) x, y, The median antero-posterior axis.

00It 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).

00not having its axis fused Fam.

00Occupying the axis, and exposed by the section, is seen the "columella " or spiral pillar.

00The long axis of the wings, when at rest, lies parallel to the body axis.

00When the wing is spread, its long axis is more or less at a right angle to the body axis.

00Thus arose, beside minor streets, the imposing central avenue which, starting from a triumphal arch near the great temple of the Sun, formed the main axis of the city from south-east to north-west for a length of 1240 yards, and at one time consisted of not less than 750 columns of rosy-white limestone, each 55 ft.

00Its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20.

00The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.

00In Nemertines the everted proboscis is retracted in the same way as the tip of a glove finger would be if it were pulled backwards by a thread situated in the axis and attached to the tip. The comparison may be carried still further.

004), which is surrounded by another coil having its axis at right angles to that of the fixed coil.

00In this he showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolution.

00The axis of the temple ran from S.W.

00adopted the line of this avenue in adding an extensive court to the work of Amenophis, producing a curious change of axis.

00Let 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.

00The semi-major axis, CA or CB, is called the mean distance, and is represented by the symbol a.

00The equivalent volumes and topic parameters are tabulated: From these figures it is obvious that the first three compounds form a morphotropic series; the equivalent volumes exhibit a regular progression; the values of x and t,t, corresponding to the a axes, are regularly increased, while the value of w, corresponding to the c axis, remains practically unchanged.

00Benzoic acid is pseudo-tetragonal, the principal axis being remarkably long; there is no cleavage at right angles to this axis.

00Direct nitration gives (principally) m-nitrobenzoic acid, also pseudotetragonal with a much shorter principal axis.

00If the crystal structure be regarded as composed of 0 three interpenetrating point systems, one consisting of sulphur atoms, the second of four times as many oxygen atoms, and the third of twice as many potassium atoms, the systems being so arranged that the sulphur system is always centrally situated with respect to the other two, and the potassium system so that it would affect the vertical axis, then it is obvious that the replacement of potassium by an element of greater atomic weight would specially increase the length of w (corresponding to the vertical axis), and cause a smaller increase in the horizontal parameters (x and 1/ '); moreover, the increments would advance with the atomic weight of the replacing metal.

00along the axis of the disturbance, and the mission station of Wairoa (8 m.

00It is of Tertiary formation (Miocene), and has a chain of volcanic elevations along the axis, reaching a height of 2600 ft.

00The 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.

00The globe itself rotates within a metallic meridian to which its axis is attached.

00io08), Zarkala (Azarchel), who determined the meridian distance between his observatory in Toledo and Bagdad to amount to 51° 30', an error of 3° only, as compared with Ptolemy's error of 18°, and Abul Hassan (1230) who reduced the great axis of the Mediterranean to 44°.

00The 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.

00Thus 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.

00This 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.

00The 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.

00Upon 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.

00In 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.

00If 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.

00For 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.

00The 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.

00A 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.

00A magnet attached to a cork and [[[Terminology And Principles]] floated upon water will set itself with its axis in the magnetic meridian, but it will be drawn neither northward nor southward; the forces acting upon the two poles have therefore no horizontal resultant.

00The line joining the two poles is called the axis of the magnet.

00The 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.

00The 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.

00(5) The uniformity of the field is not in this case disturbed by the influence of ends, but its strength at any point varies inversely as the distance from the axis of the ring.

00The 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.

00The 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.

00The 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.

00If 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.

00(9) At the point where a line of force intersects the perpendicular bisector of the axis r=r'=r o, say, and cos 0 - cos 0 obviously =l/r o, l being FIG.

00The 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.

00If 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.

00The potential due to a uniformly magnetized sphere of radius a for an external point at a distance r from the centre is V =:I ra 3 I cos 0/r 22, (23) 0 being the inclination of r to the magnetic axis.

00If 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.

00Suppose 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.

00An 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.

00- An electric current i flowing uniformly through a cylindrical wire whose radius is a produces inside the wire a magnetic field of which the lines of force are concentric circles around the axis of the wire.

00At 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.'

00If 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.

00The 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.

00Thus 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.

00A 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.

00(I) The rod is set in a horizontal position level with the suspended needle, its axis being in a line which is perpendicular to the magnetic meridian, and which passes through the centre of suspension of the needle.

00AB is the rod and C the middle point of its axis; NS is the magnetometer needle; AM bisects the undeflected needle NS at right angles.

00175), the true value of H for any point on the curve being that measured from the sloping line instead of from the vertical axis.

00The 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.

00The curve thus constructed should be a straight line inclined to the horizontal axis at an angle 0, the tangent of which is 1.6.

00Rowland, 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.

00It 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.

00The 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.

00One 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.

00It 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.

0024 was converted into an almost perfectly straight line passing through the origin, and lying below the horizontal axis; while the permeability of the metal was greatly diminished by the operation.

00For soft iron, tungsten-steel and nickel little difference appeared to result from lowering the temperature down to - 186° C. (the temperature of liquid air); at sufficiently high temperatures, 600 to 1000° or more, it was remarked that the changes of length in iron, steel and cobalt tended in every case to become proportional to the magnetic force, the curves being nearly straight lines entirely above the axis.

00When 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.

00Most 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.

00Weber 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.

00Maxwell (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.

00It 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.

00The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).

00If 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.

00Each consists of an axis, bearing numerous blunt tooth-like processes arranged in a series.

0015); but we are yet in need of evidence as to the exact equivalence of margins, axis, &c., obtaining between the lung-book of Scorpio and the gill-book of Limulus.

00The 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.

00The 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.

00The 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.

0015) and appear to be free, are really those which are attached to the blood-holding axis.

00- The plane of the articulation of the appendages of the 1st pair to the prosoma (the retrovert) vertical, the basal segment pro jecting straight forwards at its proximal end, the t raegcn - distal segment or fang closing backwards in a direction subparallel to the long axis of the body.

00or fang closing inwards nearly or quite at right (Original.) angles to the long axis of the body.

00Colchicum illustrates the corm-development which is rare in Liliaceae though common in the allied order Iridaceae; a corm is formed by swelling at the base of the axis (figs.

00These 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.

00The 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.

00Legendre, 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.

00When 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.

00The 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.

00It 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.

004, AB represents the axis of an optical instrument (telescope or microscope), A being a point of the object and B a point of the image.

00In 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.

00If x and y be co-ordinates in the plane of the wave-surface, the axis of y being parallel to the lines of the grating, and the origin corresponding to the centre of the beam, we may take as an approximate equation to the wave-surface -- -} z =+Bxy 2, +ax 3 13x2 2pp p y+-yxy2-?-Sy3+..

00Denoting them by x, y, so that AB is axis of y and a perpendicular through A the axis of x, and rationalizing (26), we have 2 ax 2 - V 2 Xy 2 - V 2 aAy = o, which represents a hyperbola with vertices at 0 and A.

00The intrinsic equation, expressing the relation between the arc 0- (measured from 0) and the inclination 4) of the tangent at any points to the axis of x, assumes a very simple form.

00If 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).

00dr r In like manner we find TZ x d e ikr 2 - 471b 2 r dr From (to), (13), (24) we see that, as might have been expected, the rotation at any point is about an axis perpendicular both to the direction of the force and to the line joining the point to the source of disturbance.

00For 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).

00It is apparent, therefore, that all drops transmitting intense light after one internal reflection to the eye will lie on the surfaces of cones having the eye for their common vertex, the line joining the eye to the sun for their axis, and their semi-vertical angles equal to about 41° for the violet rays and 43° for the red rays.

00The 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.

00(x 300 diam.) colour, situated specially at the poles of the fibre nucleus and extending short distance in the long axis of the fibre.

00It is roughly elliptical, its major axis, 180 m.

00Even 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.

00The 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 '.

00The 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.

00He 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.

00He 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.

00Suppose 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.

00An inclining couple due to moving a weight about in a ship will heel the ship about an axis perpendicular to the plane of the couple, only when this axis is a principal axis at F of the momental ellipse of the water-line area A.

00of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.

00Taking the fixed direction parallel to the axis of x, the time-rate of increase of momentum, due to the fluid which crosses the surface, is - f'fpuq cos OdS = - f f (lpu 2 -+mpuv+npuw)dS, (1) which by Green's transformation is (d(uiu 2) dy dz dxdydz.

00Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

00A single vortex will remain at rest, and cause a velocity at any point inversely as the distance from the axis and perpendicular to its direction; analogous to the magnetic field of a straight electric current.

0035 A circular vortex, such as a smoke ring, will set up motion symmetrical about an axis, and provide an illustration; a half vortex ring can be generated in water by drawing a semicircular blade a short distance forward, the tip of a spoon for instance.

00Again, since d4)/dv =d /ds, d4)/ds= - d4y/dv, (13) T = 1 p f(1 9 d = - 2 p f4' d (14) With the Stokes' function, y for motion symmetrical about an axis.

00The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.

00This is so when the axis of revolution is a principal axis, say Oz; when S21=0, t 2 =0, =o, o=0.

00(17) ellipsoid of liquid of three unequal axes, rotating bodily about the least axis;.

00Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.

00There is no Stokes' function when the axis of the doublet at S does not pass through 0; the image system will consist of an inclined doublet at H, making an equal angle with OS as the doublet S, and of a parallel negative line doublet, extending from H to 0, of moment varying as the distance from O.

00The motion of these cylinders across the line of centres is the equivalent of a line doublet along each axis.

00(22) Y (F2 x2) Suppose x 3 -F is a repeated factor of X3, then y 3 = G, and X 3 = (x 3 -F)2 [P' _ P(X3+F)2+2' _ G(X +F) -G 2 ], (23) nd putting x3-F=y, (y) 2= 7'3'2- [41' r 1' F 2 -{-4 g r qFG - G2 +2 (2P'r 19F+9 r q G) y+ r y (24) o that the stability of this axial movement is secured if A = 4 P' r ?'F 2 + 4 Y q FG - G 2 (25) s negative, and then the axis makes r J l (-A)/7r nutations per second.

00therwise, if A is positive rt= J y-s1 (A+2By+Cy') dy sh1 A'/ (A+2By+Cy 2) I ch1 A+By (26) -V A ch1 31, (B2--AC) - A sh - 1 (B2-AC)' nd the axis falls away ultimately from its original direction.

00To 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).

00In the steady motion under no force of such a body in medium, the centre of gravity describes a helix, while the axis escribes a cone round the direction of motion of the centre of ravity, and the couple causing precession is due to the dislacement of the medium.

00Consider a submarine boat or airship moving freely with the direction of the resultant momentum horizontal, and the axis at a slight inclination 0.

00proceeds in a straight line, and the axis of rotation through the C.G.

00preserves its original direction, if a principal axis of the body; otherwise the axis describes a cone, right circular if the body has uniaxial symmetry, and a Poinsot cone in the general case.

00Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .

00The 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.

00A rotation about the axis of a figure of revolution does not set the medium in motion, so that C 1 is.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00As the ring is moved from 0 to 0' in time t, with velocity Q, and angular velocity R, the components of liquid momentum change from aM'U +E and SM'V along Ox and Oy to aM'U'+ and /3M'V' along O'x' and O'y', (I) the axis of the ring changing from Ox to O'x'; and U = Q cos 0, V = Q sin 0, U' =Q cos (o - Rt), V' =Q sin (0 - Rt), (2) so that the increase of the components of momentum, X 1, Y 1, and N1, linear and angular, are X 1 = (aM'U'+ 0 cos Rt - aM'U - - 1 3M'V' sin Rt =(a - (3)M'Q sin_(0 - Rt) sin Rt - ver Rt (3) Y 1 = (aM'U'+) sin Rt-[-13M'V' cos Rt - (3M'V = (a - (3) M'Q cos (0 - Rt) sin Rt +t sin RT, N1=[ - (aM'U'+E) sin (0 - Rt)+ 1 3M'V' cos (o - Rt)]OO' = [- (a - 1 3) M'Q cos (o - Rt) sin (o - Rt) - sin (o - Rt) ]Qt.

00This 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.

00(I) Let a spiral line be drawn on a right circular cylinder; a screw surface is then obtained by drawing lines from every point of this spiral perpendicular to its axis.

00The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix.

00(2) A right cylinder having for its base an Archimedean spiral is intersected by a right circular cone which has the generating line of the cylinder passing through the initial point of the spiral for its axis.

00From every point of the curve of intersection, perpendiculars are drawn to the axis.

00The 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.

00It consists of a number of tubes mounted vertically on a horizontal circular disk which rotates about a vertical axis in a cylindrical vessel.

00The vapour pressure composition curve will be convex to the axis of compositions, the maximum vapour pressures corresponding to pure A and pure B, and the minimum to some mixture of A and B.

00The vapour pressure-composition curve will now be concave to the axis of composition, the minima corresponding to the pure components.

004 let AB be the axis of composition, AP be the vapour pressure of pure A, BQ the vapour pressure of pure B.

00In its more complete form a still has in addition the following fittings: - The dome is provided with openings to admit (I) the axis of the stirring gear (in some stills the stirring gear rotates on a horizontal axis which traverses the side and not the head of the still), (2) the inlet and outlet tubes of a closed steam coil, (3) a tube reaching to nearly the bottom of the still to carry live steam, (4) a tube to carry a thermometer, (5) one or more manholes for charging purposes, (6) sight-holes through which the operation can be watched, and (7) a safety valve.

00Hence, 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.

00Conversely, 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.

00Two 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.

00In North Hondo the great Bandai arc forms the axis of the island and stretches into Yezo (HokkaidO).

00A hummocky irregular country spreads southward, where the Silurian axis is encountered, in continuation of the southern uplands of Scotland.

00This 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.

00"In the beginning of my mathematical studies, when I was perusing the works of the celebrated Dr Wallis, and considering the series by the interpolation of which he exhibits the area of the circle and hyperbola (for instance, in this series of curves whose common base 0 or axis is x, and the ordinates respectively (I -xx)l, (i (I &c), I perceived that if the areas of the alternate curves, which are x, x 3x 3, x &c., could be interpolated, we should obtain the areas of the intermediate ones, the first of which (I -xx) 1 is the area of the circle.

00Although 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.

00One 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.

00Each cone cuts out an area on the surface equally inclined to the cone axis.

00Since 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.

0021rry/dx units, and the potential V at a point on the axis at a distance x from the annulus due to this elementary charge is ll2 2?rrc V=2 j o (r2+x2) dx=47rrvj log e (2l+1,/ r2 +412 ') - loge'} If, then, r is small compared with 1, we have V =47rry log e llr.

00Accordingly 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.

00Hence 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.

00R - A, Accordingly var where R is the distance of the point in the interspace from the axis, and A is a constant.

00The function G is represented by the negative area D"DM under the isothermal, bounded by the isopiestic DM and the axis of pressure.

00The 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.

00The Bingemma range, rising 726 ft., is nearly at right angles to the axis of the main island.

00There is a perfect cleavage perpendicular to the trigonal axis of the crystals: the fact that only two (opposite) corners of the cube-like crystals can be truncated by cleavage at once distinguishes them from true cubes.

00The Cacti may be described in general terms as plants having a woody axis, overlaid with thick masses of cellular tissue forming the fleshy stems. These are extremely various in character and form, being globose, cylindrical, columnar or flattened into leafy expansions or thick joint-like divisions, the surface being either ribbed like a melon, or developed into nipple-like protuberances, or variously angular, but in the greater number of the species furnished copiously with tufts of horny spines, some of which are exceedingly keen and powerful.

00They 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.

00It 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.

00the Canadian Corps, were to be engaged, the main axis of the attack being the line of the Arras-Cambrai road; the two remaining corps were to stand fast, while making all endeavours to deceive the enemy and prevent him dispatching reinforcements to other threatened points.

00p. 551) in which he shows that a micrometer can be much more easily constructed by dividing a single object-glass through its axis than by the employment of two object-glasses.

00The counterpoise w balances the head about its axis of rotation.

00There 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.

00Complete 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.

00- One of the segments is fixed in the axis of the telescope, and the eye-piece is also placed in the axis.

00For 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.

00

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