# Perpendicular sentence example

perpendicular

- The old woodwork is fine, part being Perpendicular, but the greater portion dates from 1621.
- A massive collection of sinister looking implements was growing—tools of their trade, all apparently necessary in order to remain aloft when maneuvering up or down perpendicular columns of frozen water.
- The church of St Nicholas is a cruciform Perpendicular structure with a beautiful central tower, and some portions of earlier date.
- The church of St Andrew retains some ornate Norman work, but is mainly a Perpendicular reconstruction.
- The church of St Luke is Perpendicular, enlarged in modern times.Advertisement
- The smaller church of St Nicholas is Perpendicular in appearance, though parts of the fabric are older.
- At a further stage of their growth the particles disperse in the perpendicular direction a light which is no longer fully polarized.
- The church of St Peter is Perpendicular, with a lofty tower and spire.
- In the early stages of the precipitation the polarization is complete in a perpendicular direction, and incomplete in oblique directions.
- The average perpendicular distance between the two lines, which are roughly parallel, is 2.8 m.Advertisement
- It is beautifully placed near the river, and is a fine cruciform structure, partly Early English and partly Perpendicular, with a central tower and lofty octagonal spire.
- The main assimilating tissue, on the other hand, is under the upper epidermis, where it is well illuminated, and consists of oblong cells densely packed with chloroplasts and with their long axes perpendicular to the surface (palisade tissue).
- St Michael's, the parish church, has a striking Perpendicular tower, an arch of carved oak dividing its nave and chancel, a magnificent rood-loft, and a 13th-century monument doubtfully described as the tomb of Bracton, the famous lawyer, whose birthplace, according to local tradition, was Bratton Court in the vicinity.
- This is the moment to examine whether there is a more complete polarization in a direction somewhat oblique; and it is found that with 0 positive there is, in fact, a direction of more complete polarization, while with 0 negative the polarization is more imperfect than in the perpendicular direction itself.
- In the old town of Bridlington the church of St Mary and St Nicholas consists of the fine Decorated and Perpendicular nave, with Early English portions, of the priory church of an Augustinian foundation of the time of Henry I.Advertisement
- Over the surface of the plate and between it and the indicator there was passed, at a regularly uniform speed, in a direction perpendicular to the line of motion of the indicator, a material capable of being acted on physically by the sparks, through either their chemical action, their heat, or their perforating force.
- The north-west tower has a Perpendicular upper portion, but the south-west tower is destroyed.
- The cruciform church of St Mary, with a central tower and short spire, is in great part Early English, with Perpendicular additions; but considerable traces of a Norman building were revealed during a modern restoration.
- "Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.
- The church of St John the Baptist, though largely altered by modern restoration, retains Early English to Perpendicular portions, and some early monuments and brasses.Advertisement
- The slope dropped at a precarious angle, impossible to maneuver unsecured, only a few degrees from the perpendicular.
- So long as the precipitated particles are very fine, the light dispersed in a perpendicular direction is sky-blue and fully polarized.
- A picturesque avenue leads to the church of St Mary, principally Early English and Perpendicular, with remains of Norman work, having a lofty tower surmounted by a spire, and containing several fine monuments, tombs and brasses.
- N.N.E., on the opposite side of the Pulwar, rises a perpendicular wall of rock, in which four similar tombs are cut, at a considerable height from the bottom of the valley.
- The body of the church, which has five aisles, is principally Perpendicular.Advertisement
- The almshouse known as the hospital of St John the Baptist and St John the Evangelist was founded in 1437 on the site of an earlier establishment, and retains a Perpendicular chapel, hall and other portions.
- The church of St George has Norman portions, but the building is in the main Perpendicular.
- In addition to these remarkable inland mountains, Formosa's eastern shores show magnificent cliff scenery, the bases of the hills on the seaside taking the form of almost perpendicular walls as high as from 150o to 2 500 ft.
- The church of St Leonard, founded before 1451, was frequently altered before it was rebuilt in1866-1868in the Perpendicular style.
- The church of St Peter and St Paul is Perpendicular (largely restored) with a lofty tower.Advertisement
- The church of St Gwendoline, restored in 1873, is in Perpendicular style, with an embattled tower restored in 1898.
- In 1361 Archbishop Thoresby (1352-73) began the lady chapel and presbytery, both in the Early Perpendicular style.
- It lies on a gentle eminence in the flat fen country, and the fine Perpendicular tower and spire of the church of St Mary are a landmark from far.
- Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d?
- Let the bob be a sphere, and from the centre of that sphere draw BH=y perpendicular to OA.Advertisement
- Then its motion may be analysed into (I) a translation of its centre of gravity; and (2) a rotation about an axis through its centre of gravity perpendicular to its plane of motion.
- After an interval the polarization begins to be incomplete in the perpendicular direction, the light which reaches the eye when the nicol is set to minimum transmission being of a beautiful blue, much richer than anything that can be seen in the earlier stages.
- There remains also the Perpendicular gateway, serving as the town-hall.
- The church of the Holy Trinity, mainly Perpendicular, was also partly demolished during the Civil War, but was restored by the countess of Pembroke.
- The church of St Margaret is Decorated and Perpendicular.Advertisement
- The large parish church of St Teilo has a low embattled Perpendicular tower.
- The church of St John the Baptist, founded in 1050, contains some portions of Norman architecture, the remainder being Decorated and Perpendicular.
- The church of St Nicholas (Perpendicular with Early English portions, but much restored) has a tomb of the Walsingham family, who had a lease of the manor from Elizabeth; Sir Francis Walsingham, the statesman, being born here in 1536.
- The church of St Mary is Perpendicular and has been enlarged in modern times.
- York also possesses a large number of churches of special architectural interest, including All Saints, North Street, Early English, Decorated and Perpendicular, with a spire 120 ft.Advertisement
- The guild-hall, with a fine old room in Perpendicular style erected in 1446, contains a number of stained-glass windows.
- The church of St Michael is a fine Perpendicular and Decorated building of black flint, surmounted by a tower 96 ft.
- Considerable additions of later date, in the Decorated and Perpendicular styles, are due to the Despensers and to Beauchamp, earl of Warwick, while the present residential part is of various dates ranging from the 15th century down to the last half of the r 9th, when a thorough restoration, including the addition of a superbly ornamented clock-tower, was carried out.
- The only other building of historic interest is the church of St John the Baptist, which is in the Perpendicular style, its fine tower having been built about 1443 by Hart, who also built the towers of Wrexham and St Stephen's, Bristol.
- St Mary's church is principally Perpendicular, but has Norman and Decorated portions; the church of St Andrew is also Decorated and Perpendicular.Advertisement
- The church of All Saints has Early English and Perpendicular remains.
- The plane of the optic axes may be either perpendicular or parallel to the plane of symmetry of the crystal, and according to its position two classes of mica are distinguished.
- To the first class, with the optic axial plane perpendicular to the plane of symmetry, belong muscovite, lepidolite, paragonite, and a rare variety of biotite called anomite; the second class includes zinnwaldite, phlogopite, lepidomelane and most biotites.
- Close by are the remains of St Mary's Priory, which comprise a large Perpendicular gatehouse, refectory, precinct wall, abbot's gate and still-house.
- The Perpendicular church of St Mary contains a number of interesting tombs and effigies dating from the 15th century onwards, and much excellent carved work.
- Every other concomitant is a rational integral function of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.
- It has a fine Perpendicular church dedicated to St Mary, with a lofty, well-proportioned tower and many interesting monuments.
- Among many places of worship may be mentioned the restored parish church of Holy Trinity, which dates from the 12th century and contains some interesting monuments and brasses; and the Perpendicular Hermitage or Tory chapel, with a 15th or 16th century chantry-house.
- 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.
- (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.
- 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.
- (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.
- 8, where AB is the vertical rod and M indicates the position of the magnetometer needle, which is supposed to be perpendicular to the plane of the paper.
- 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.
- A small coil of fine wire, connected in series with a ballistic galvanometer, is placed in the field, with its windings perpendicular to the lines of force, and then suddenly reversed or withdrawn from the field, the integral electromotive force being twice as great in the first case as in the second.
- 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.
- For those orbits whose projection upon a plane perpendicular to the field is righthanded, the period of revolution will be accelerated by the field (since the electron current is negative), and the magnetic moment consequently increased; for those which are left-handed, the period will be retarded and the moment diminished.
- The church of St Helen is a fine Perpendicular building, restored and enlarged (1880); it contains monuments of the Huntingdon family, and an old finger-pillory for the punishment of misbehaviour in church.
- Tong church, of fine early Perpendicular work, contains a remarkable series of ornate tombs, mainly of the 15th and 16th centuries, to members of the Vernon and Stanley families, former owners of the castle.
- The Golden Chapel on the south side is rich late Perpendicular, with a roof of fan-tracery, showing signs of the original decoration in colours.
- Adjoining the town hall is the Anglican cathedral of St Andrew, in the Perpendicular style; it has two towers at the west end and a low central tower above the intersection of the nave and transepts, with a very handsome chapter house.
- It continues to the foot of the Drakensberg range, the mountains rising towards the S.W., with almost perpendicular sides, 6000 to 7000 ft.
- There is but one cactus indigenous to Natal; it is found hanging from perpendicular rocks in the midlands.
- An admissible error of phase of 4X will correspond to an error of IX in a reflecting and 2X in a (glass) refracting surface, the incidence in both cases being perpendicular.
- We have seen that in perpendicular reflection a surface error not exceeding IX may be admissible.
- 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.
- In order that a large part of the field of view may be in focus at once, it is desirable that the locus of the focused spectrum should be nearly perpendicular to the line of vision.
- In theoretical investigations these problems are usually treated as of two dimensions only, everything being referred to the plane passing through the luminous point and perpendicular to the diffracting edges, supposed to be straight and parallel.
- When, in order to apply Huygens's principle, the wave is supposed to be broken up, the phase is the same at every element of the surface of resolution which lies upon a line perpendicular to the plane of reference, and thus the effect of the whole line, or rather infinitesimal strip, is related in a constant manner to that of the element which lies O in the plane of reference, and may be considered to be represented thereby.
- Then the displacement at 0 will take place in a direction perpendicular to 0 1 0, and lying in the plane Z0 1 0; and, if 1' be the displacement at 0, reckoned positive in the direction nearest to that in which the incident vibrations are reckoned positive, = 4?y (1 +cos 0) sin 4 f' (bt - r).
- 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).
- This displacement, which we may denote by; is in the plane containing z and r, and perpendicular to the latter.
- Thu: church of St Peter and St Paul has a double nave, with aisles, the north arcade being Norman; but the rest of the building is mainly Decorated and Perpendicular.
- There are remains of a Norman west tower; the Perpendicular tower stands on the north side.
- The parish church of St Mary is Perpendicular, with a fine carved roof of the 17th century.
- The west boundary of Achradina is marked farther south by a perpendicular cutting in the rock, on the top of which a wall must have run (see above).
- These oscillations of opinion arP frequent, if not universal, and it is only after more than one or two swings that the pendulum remains at the perpendicular.
- The church of St Peter and St Paul is a spacious building in various styles of architecture, but principally Perpendicular.
- Rahere's tomb remains in the church; the canopy is Perpendicular work, but the effigy is believed to be original.
- Among other ancient churches within the City, that of All Hallows Barking, near the Tower of London, is principally Perpendicular and contains some fine brasses.
- St Giles, Cripplegate, was founded c. 1090, but the existing church is late Perpendicular.
- There are occasional outcrops of rock and low perpendicular cliffs.
- The modern Roman Catholic cathedral is Perpendicular in style and cruciform in plan.
- Take any two arbitrary directions in the plane of the paper, and draw a small isosceles triangle abc, whose sides are perpendicular to the two directions, and consider the equilibrium of a small triangular prism of fluid, of which the triangle is the cross section.
- This is proved by taking any two points A and B at the same level, and considering the equilibrium of a thin prism of liquid AB, bounded by planes at A and B perpendicular to AB.
- The resultant horizontal thrust in any direction is obtained by drawing parallel horizontal lines round the boundary, and intersecting a plane perpendicular to their direction in a plane curve; and then investigating the thrust on this plane area, which will be the same as on the curved surface.
- 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.
- Taking 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.
- A 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.
- As before in § 31, the rotation may be resolved into a shear-pair, in planes perpendicular to Ox and Oy.
- (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.
- In operation the coulter makes a perpendicular cut separating the furrow-slice which is divided from the "sole" of the furrow Crested Furrow.
- The church of St John the Baptist, principally Perpendicular, - has in its tower three bells presented by Charles Both this town and the adjacent urban district of Radstock (pop. 3355) have a considerable trade in coal, which is mined in the vicinity.
- The tower leans or deviates from the perpendicular, to a striking extent, which has gradually increased: it was 152 ft.
- The church of St Mary the Virgin stands high, and is surmounted by a lofty spire; it shows good Decorated and Perpendicular work.
- The church of St Mary is of good Perpendicular work, with Early English tower and Decorated spire.
- The rest of the church is Decorated and Perpendicular.
- The church of St Mary is fine Early English with Perpendicular clerestory.
- Thus if a lacquer box in the form of a parallelogram is the object, Japanese artists will not divide it in two equal parts by a perpendicular line, but by a diagonal, as offering a more pleasing line and division.
- The church of St Nicholas is a fine Perpendicular structure exhibiting the flint-work common to the district, and possessing a beautiful south porch and the ruin of a massive western tower which partly collapsed early in the 18th century.
- It was restored to use in 1882 by a French Benedictine community, the fine Perpendicular abbot's tower remaining, while other parts have been rebuilt on the original lines.
- This mass is equal to 47rabcp,u; therefore Q = A47rabcp s and b =pp, where p is the length of the perpendicular let fall from the centre of the ellipsoid on the tangent plane.
- We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or orthogonal to the lines of electric force.
- Consider the two faces perpendicular to the x-axis.
- But the force perpendicular to the curved surface of this cylinder is everywhere zero.
- Then since the generating lines of the tube are lines of force, the component of the electric force perpendicular to the curved surface of the tube is everywhere zero.
- St Peter's church, a Perpendicular building, is said to have been the scene of the ordination of Cardinal Wolsey in 1498.
- The church of St Edmund is mainly Perpendicular, but there are Transitional Norman and Early English portions.
- The church of All Saints is good Perpendicular, though considerably restored.
- There 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.
- Exceptions occur in the case of the satellites of Uranus, which are nearly perpendicular to the plane of the orbit.
- 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.
- All deep-sea measurements are subject to uncertainty because the sounding machine merely measures the length of wire which runs out before the lead touches bottom, and this agrees with the depth only when the wire is perpendicular throughout its run.
- Freezing takes place by the formation of pure ice in flat crystalline plates of the hexagonal system, which form in perpendicular planes and unite in bundles to form grains so that a thick covering of ice exhibits a fibrous structure.
- Ekman shows further that in a pure drift current the mean direction of the whole mass of the current is perpendicular to the direction of the wind which sets it in motion.
- Sometimes, but rarely, it happens that it is necessary to cut vertical grooves in the face to determine the limit of the fall, such limits being usually dependent upon the cleet or divisional planes in the coal, especially when the work is carried perpendicular to them or on the end.
- The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...
- The church of St Mary and All Saints, originally collegiate, is Perpendicular, and only the nave with aisles, and the tower surmounted by an octagon, remain; but the building is in the best style of its period.
- The church of St Mary is Decorated and Perpendicular.
- It is mainly Early English, and a fine example of the style; but some of the windows including the nave clerestory, and the beautiful carved wooden roof, are Perpendicular.
- If the scale is only slightly out of the perpendicular, a few taps of the hammer will modify any trifling error."
- The church of St John the Baptist, with a lofty spire, is a good example of Decorated work, with Perpendicular additions.
- The church of St Nicholas is a modern reconstruction with the exception of the Perpendicular tower.
- If a connected point belongs to a turning piece, the direction of its motion at a given instant is perpendicular to the plane containing the axis and crank-arm of the piece.
- If a connected point belongs to a shifting piece, the direction of its motion at any instant is given, and a plane can be drawn perpendicular to that direction.
- The line of intersection of the planes perpendicular to the paths of the two connected points at a given instant is the instantaneous axis of the link at that instant; and the velocities of the connected points are directly as their distances from that axis.
- Draw BE perpendicular to CB, cutting CD produced in E, then E is the instantaneous axis of the bar ADB; and the direction of motion of A is at every instant perpendicular to EAthat is, along the straight line ACa.
- If a force be applied to a turning piece in a line pot passing through its axis, the axis will press against its bearings with an equal and parallel force, and the equal and opposite reaction of the bearings will constitute, together with the first-mentioned force, a couple whose arm is the perpendicular distance from the axis to the line of action of the first force.
- Its magnitude is the product of the normal pressure or force which presses the rubbing surfaces together in~ a direction perpendicular to themselves into a specific constant already mentioned in 14, as the coefficient of friction, which depends on the nature and condition of the surfaces of the unguent, if any, with which they are covered.
- The total pressure exerted between the rubbing surfaces is the resultant of the normal pressure and of the friction, and its obliquity, or inclination to the common perpendicular of the surfaces, is the angle of repose formerly mentioned in 14, whose tangent is the coefficient of friction.
- The plane through 0 to which the shaft is perpendicular is called the reference plane, because all the transferred forces act in that plane at the point 0.
- According to the principles of statics, the resultant of the force P, applied at G perpendicular to the plane OG, and the couple M is a force equal and parallel to P, but applied at a distance GC from G, in the prolongation of the perpendicular OG, whose value is GC = M/P = R2/OG.
- As the chief authority of their tenets, the Nimavats recognize the Bhagavata-purana; though several works, ascribed to Nimbarka - partly of a devotional character and partly expository of Vedanta topics - are still extant, Adherents of this sect are fairly numerous in northern India, their frontal mark consisting of the usual two perpendicular white lines, with, however, a circular black spot between them.
- The sectarial mark of the adherents consists of two red perpendicular lines, meeting in a semicircle at the root of the nose, and having a round red spot painted between them.
- St Peter's church, originally consecrated as a chapel by Leofric, bishop of Exeter, in 1073, is a beautiful Perpendicular building.
- On the summit is the tower of the old castle, leaning about 17° from the perpendicular.
- Further great alterations took place in the 15th century, and the general effect of the building as it stands is Perpendicular.
- The church of All Saints, late Perpendicular, consisting of chancel with aisles and two chapels, was restored in 1630 and in modern times.
- The church of St Andrew here has interesting details from Early English to Perpendicular date, and in the neighbouring woods is a ruined chapel of St Mary.
- This platen had a perpendicular motion, being guided in grooves and worked by a connecting rod fixed to a cross beam and crank, which acquired its motion from the main shaft.
- This type was fixed, both in vertical and in perpendicular positions, upon a cylinder, round which rotated other cylinders, which held and compressed the sheets against the larger one, which also revolved and carried the printing surface.
- The church of St Michael, standing high above the valley, is a fine embattled Perpendicular building with western tower and spire.
- The church of St Nicholas and St Faith has an early Norman tower, and part of the fabric is considered to date from before the Conquest; but there was much alteration in the Decorated and Perpendicular periods.
- If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their " perpendicular height of incidence," i.e.
- If the object point 0 be infinitely distant, u, and u 2 are to be replaced by h l and h 2, the perpendicular heights of incidence; the " sine condition " then becomes sin u',/h 1 = sin u' 2 /h 2 .
- The heart and pericardial chamber in the oyster lie along the anterior face of the adductor muscle, almost perpendicular to the direction of the gills, with which in Anodon they are parallel.
- The church of SS Peter and Paul, mainly Perpendicular, has a lofty and ornate tower and spire.
- The chief buildings, apart from the abbey, are the church of St John Baptist, Perpendicular in style, with a fine tower and some 15th-century monuments; St Benedict's, dating from 1493-1524; St John's hospital, founded 1246; and the George Inn, built in the time of Henry VII.
- The church of St Dionysius is Decorated and Perpendicular, with a fine tower and spire.
- The town has a Perpendicular church (St Andrew), a corn exchange and some agricultural trade.
- The church of St Andrew ranges in date from Early English to Perpendicular.
- In the members of the typical genus Potorous (formerly known as Hypsiprymnus) the head is long and slender, with the auditory bullae somewhat swollen; while the ridges on the first two premolars are few and perpendicular, and there are large vacuities on the palate.
- The church of St Mildred is Early English and later, and its tall, massive Perpendicular tower is well known for the legend connecting it with Goodwin Sands.
- The ascription to Wykeham of the invention of the Perpendicular style of medieval architecture is now an abandoned theory.
- 6 to represent a vertical section perpendicular to the plates, we may calculate the rise of the liquid.
- Also, since the axis is a tangent to the rolling curve, the ordinate PR is the perpendicular from the tracing point P on the tangent.
- Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the ordinate PR of the traced curve.
- Electricity, as has long been known, has an extraordinary influence upon the appearance of a fine jet of water ascending in a nearly perpendicular direction.
- Division planes always perpendicular to the long axis.
- Divisions perpendicular to the long axis: - Vibrio (Muller-Ldffler), commashaped, motile, monotrichous; Spirillum (Ehrenb.), more strongly curved in open spirals, motile, lopho trichous; Spirochaete (Ehrenb.), spirally coiled in numerous close turns, motile, but apparently owing to flexile movements, as no cilia are found.
- There is a fine Perpendicular tomb in the choir.
- On the 19th of September 1 9 01 trilithon 56 was successfully raised to a perpendicular position.
- Of the ancient Benedictine abbey, the only remains are a part of a gateway, a lodge (a beautiful Perpendicular relic) and some buttresses, while some broken stone arches and walls remain of the conventual buildings.
- The body of the church of St Mary was rebuilt in brick after its collapse in 1713, but the Perpendicular tower remains.
- The Perpendicular church of St Martin, with a tower of earlier date, having a Norman arch, is one of the largest ecclesiastical buildings in the county.
- The church of St Edmund's is a Perpendicular flint structure.
- The church of St Mary is a fine building, mainly Decorated and Perpendicular, wherein are preserved relics of John Wycliffe, who was rector here from 1374 until his death in 1384.
- The church of St Nicholas is Perpendicular, greatly restored.
- It consists of a perpendicular chalk cliff 532 ft.
- He, in fact, endeavours to prove that a bird wedges itself forward upon the air by the perpendicular vibration of its wings, the wings during their action forming a wedge, the base of which (c b e) is directed towards the head of the bird, the apex (a f) being directed towards the tail (d).
- In the 1 96th proposition of his work (De motu animalium, Leiden, 1685) he states that " If the expanded wings of a bird suspended in the air shall strike the undisturbed air beneath it with a motion perpendicular to the horizon, the bird will fly with a transverse motion in a plane parallel with the horizon."
- The same argument is re stated in different words as under: - " If the air under the wings be struck by the flexible portions of the wings (flabella, literally fly flaps or small fans) with a motion perpendicular to the horizon, the sails (vela) and flexible portions of the wings (flabella) will yield in an upward direction and form a wedge, the point of which is directed towards the tail.
- Draw any line DE perpendicular to AB and meeting the circle in E, and take a point P on DE such that the line DP =arc BE; then the locus of P is the companion to the cycloid.
- It is mainly decorated, with perpendicular additions, but retains some Early English details.
- The church of St Mary, entirely Perpendicular, with parvise, chancel, nave, aisles, porch, and tower 80 ft.
- The church of St Wendreda, in Early English and later styles, is remarkable for a magnificent Perpendicular timber roof, beautifully carved.
- One result of the action of the water has been the formation of numerous isolated flat-topped hills or small plateaus, known as ambas, with nearly perpendicular sides.
- The church of St Michael and All Angels is a fine specimen of a late Perpendicular building (principally of the time of Henry VIII.).
- The Royal Exchange (1872) in Boar Lane is an excellent Perpendicular building.
- The church of St Bartholomew, however, is a fine Perpendicular building, standing high.
- The parish church of St James is a fine Perpendicular building, with a lofty spire, and a beautiful open-work roof over the nave.
- It was founded in or soon after the time of the Confessor, but the present building is Perpendicular, of greater beauty within than without.
- The architect was Sir Charles Barry, and the style is late Perpendicular.
- Its church of All Saints has a beautiful Perpendicular tower with rich vaulting within.
- Crystals of this class possess neither planes nor centre of symmetry, but only axes of symmetry: perpendicular to the principal triad axis there are three uniterminal dyad axes of symmetry.
- In mineral veins and lodes crystallized quartz is usually the most abundant gangue mineral; the crystals are often arranged perpendicular to the walls of the lode, giving rise to a "comby" structure.
- The neighbouring church of St Breock is Decorated and Perpendicular, with a fine font of the earlier period.
- The parish church of St Mary is Early English and Perpendicular, with a small octagonal tower, but has been largely restored in modern times.
- The church of St Mary is Perpendicular, but extensively restored.
- But as the result of a controversy with Montalembert, Carnot abandoned the official, or Vauban, theories of the art of fortification, and went over to the "perpendicular" school of Montalembert.
- The church of All Saints is Perpendicular, with an Early English tower, and contains some interesting monuments.
- The church of St Mary Magdalen and St Denis is a large Perpendicular building.
- The church of St Mary is cruciform and mainly Perpendicular.
- The rectangle, for instance, has so far been regarded as a plane figure bounded by one pair of parallel straight lines and another pair at right angles to them, so that the conception of " rectangularity " has had reference to boundary rather than to content; analytically, the rectangle must be regarded as the figure generated by an ordinate of constant length moving parallel to itself with one extremity on a straight line perpendicular to it.
- Volume =height X area of end =length of edge X area of cross-section; the " height " being the perpendicular distance between the two ends.
- If R and S are the ends of a prismoid, A and B their areas, h the perpendicular distance between them, and C the area of a section by a plane parallel to R and S and midway between them, the volume of the prismoid is *h(A+4C+B).
- In the case of a plane area or a plane continuous line the moment with regard to a straight line in the plane is the same as the moment with regard to a perpendicular plane through this line; it is the sum of the products of each element of area or length by its distance from the straight line.
- (In 1901 a violent storm further damaged the temples and forced the gateway out of the perpendicular.) The other ruins include a triumphal arch of Constantine, a still serviceable bridge and a square keep or tower of late date.
- The church of St Peter is a fine building with Early English, Decorated and Perpendicular porticos, with a western tower and lofty spire.
- The church of All Saints has a fine Perpendicular tower, left uninjured when the nave and chancel were burned down in 1842.
- The church of All Saints is mainly Perpendicular, and contains some fine woodwork, mostly of the 17th century, and some good memorial tombs.
- If we take one of these spheres a distance from the source very great as compared with a single wave-length, and draw a radius to a point on the sphere, then for some little way round that point the sphere may be regarded as a plane perpendicular to the radius or the line of propagation.
- Every particle in the plane will have the same displacement and the same velocity, and these will be perpendicular to the plane and parallel to the line of propagation.
- Let ON(= OP cos 0) be the perpendicular on PQ.
- Thus, for instance, sound is refracted towards the perpendicular when passing into air from water, 0 or into carbonic acid gas from air; the converse is the case when the passage takes place the opposite way.
- This second plate is capable of rotation about an axis perpendicular to its plane and passing through its centre.
- Since the conditions in the region PQ remain always the same, the momentum perpendicular to AB entering the region at Q is equal to the momentum perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no momentum there perpendicular to AB.
- The component of T perpendicular to the axis is Tdy/ds=Tdy/dx.
- The church of St Peter and St Paul shows fine Perpendicular work, especially in the ornate interior of the nave.
- The extremities of the diameter perpendicular to a small circle are called the "poles" of that circle, and the distance from the pole to the circle, measured by the arc of the great circle through the pole, is the "polar distance" of the small circle.
- Let s be the perpendicular from 0, the join of C and T on the direction of S; t the perpendicular from A, the join of C and S on the direction of T; and c the perpendicular from B, the join of S and T on the direction of C. Taking moments about 0, Rx - W 1 (x+a) - W 2 (x+2a) =Ss; taking moments about A, R3a-W 1 2a-W 2 a =Tt; and taking moments about B, Rea-W I a = Cc.
- Perpendicular churches, though numerous, are less remarkable, but the fine glass of this period in Nettlestead church may be noticed.
- Its foundations were the first to be laid of the present church (which is on the site of an earlier one), but the construction was arrested until the Perpendicular period, of the work of which it is a magnificent example.
- Besides the parish church of St Mary Magdalene, a fine and massive Perpendicular building with an ancient pulpit of carved stone, there are a guildhall and market house.
- The church of St Andrew is cruciform and had formerly a central tower; the existing western tower is of fine and ornate Perpendicular work.
- The inland slope is gradual, but on the northern shore the range terminates in abrupt and almost perpendicular declivities, and here, consequently, some of the finest coast scenery in the island is found, widely differing, with its unbroken lines of cliffs, from the indented coast-line of the west.
- The most remarkable cliffs are those formed of perpendicular basaltic columns, extending for many miles, and most strikingly displayed in Fair Head and the celebrated Giant's Causeway.
- The parish church of St Mary, Hornsey, retains its Perpendicular tower (c. 1500) and a number of interesting monuments.
- The church of St Lawrence is a good Early English, Decorated and Perpendicular building, with a fine western Perpendicular tower.
- Those faces which were perpendicular to the pressure would grow slowly, as the great pressure would promote solution, and inhibit deposition; the edges or sides, on the other hand, being less exposed to the pressure would receive fresh deposits.
- The crumpled bands mark the bedding, and the fine perpendicular striae in front are the cleavage planes; the fine lines on the darkened side merely represent shadow, and must not be taken for planes of division in the rock.
- In passing from a slate to a grit the direction of the cleavage changes so that it tends to be more nearly perpendicular to the bedding planes.
- Such veins often attain a thickness of several feet, and sometimes possess a columnar structure perpendicular to the enclosing walls; they are met with in the crystalline limestones and other Laurentian rocks of New York and Canada, in the gneisses of the Austrian Alps and the granulites of Ceylon.
- The parish church of All Saints, occupying the site of a building dating from Anglo-Saxon times, was erected in the reign of Edward IV., and is among the best specimens of Perpendicular in the north of England.
- Perpendicular insertions are insignificant.
- The Public Walks forms a pleasant promenade parallel to the wall, and in the centre of it stands a picturesque octagonal Chapel of the Red Mount, exhibiting ornate Perpendicular work, and once frequented by pilgrims. The church of St Margaret, formerly the priory church, is a fine building with two towers at the west end, one of which was formerly surmounted by a spire, blown down in 1741.
- Norman or transitional work appears in the base of both towers, of which the southern also shows Early English and Decorated work, while the northern is chiefly Perpendicular.
- There is a fine Perpendicular east window of circular form.
- St Nicholas chapel, at the north end of the town, is also of rich Perpendicular workmanship, with a tower of earlier date.
- Of a Franciscan friary there remains the Perpendicular Grey Friars' Steeple, and the doorway remains of a priests' college founded in 1502.
- The nave is of ornate Norman work, with a massive triforium, surmounted by a Perpendicular clerestory and a beautiful wooden roof.
- It comprises the university buildings proper, the medical school, the natural history museum, the Wilson Hall, a magnificent building in the Perpendicular style, and the three affiliated colleges, Trinity College (Anglican), Ormond College (Presbyterian) and Queen's College (Wesleyan).
- The church, chiefly late Perpendicular, contains a large number of monuments of the Sidney family and an effigy of Sir Stephen de Penchester, Warden of the Cinque Ports in the time of Edward I.
- The parish church of St Peter is Perpendicular, dating from 1485, and occupies the site of a Norman church.
- The church of St John the Baptist is a perpendicular cruciform structure, consisting of chancel, nave of seven bays, aisles, transepts and lofty western tower.
- The church of St John, built in 1744, and enlarged in 1879, was supplemented, in 1880, by St Crass Church, in Perpendicular style.
- The equation x 2 +y 2 =o denotes a pair of perpendicular imaginary lines; it follows, therefore, that circles always intersect in two imaginary points at infinity along these lines, and since the terms x 2 +y 2 occur in the equation of every circle, it is seen that all circles pass through two fixed points at infinity.
- Take AB equal to one-fourth of the given line; on AB describe a square ABCD; join AC; in AC produced find, by a known process, a point C 1 such that, when C 1 B 1 is drawn perpendicular to AB produced and C 1 D 1 perpendicular to BC produced, the rectangle BC,.
- In the shell of Lamellibranchs three distinct layers can be distinguished: an external chitinous, non-calcified layer, the periostracum; a middle layer composed of calcareous prisms perpendicular to the surface, the prismatic layer; and an internal layer composed of laminae parallel to the surface, the nacreous layer.
- Hinge pliodont, that is to say, it has numerous teeth on either side of the umbones and the teeth are perpendicular to the edge.
- The church of St Peter and St Paul is cruciform, and as a whole Perpendicular in appearance, but retains a nave arcade and ornate tower-arches of the Early English period.
- Consisting of a chancel, clerestoried nave, and aisles, it is Early English and Perpendicular in style, and contains a beautiful 13th-century oak roof of 350 panels, each with a different design; a 15th-century pulpit of carved stone; and some interesting old monuments of the Strode, Mallet and Gournay families.
- The church of St John is mainly Perpendicular, 'What the Fihrist (p. 13 seq.) has about various forms of Persian writing certainly refers in part at least to the species of Pahlavi.
- The church of St Peter and St Paul, mainly Perpendicular, retains a Norman font and other remains of an earlier building.
- These spurs are covered with luxuriant vegetation, excepting their perpendicular faces and the slopes occupied by the suburbs.
- The nave is Perpendicular, a fine example of the style.
- The church of All Saints is a large cruciform structure, Norman, Early English and Perpendicular, with a central tower 80 ft.
- Alexis Claude Clairaut gave this figure: Imagine rain to be falling vertically, and a person carrying a thin perpendicular tube to be standing on the ground.
- Every star, therefore, describes an apparent orbit, which, if the line joining the sun and the star be perpendicular to the plane Abcd, will be exactly similar to that of the earth, i.e.
- The face is perpendicular and where the rock is naturally less precipitous it has been scarped.
- The church of St Petrock, with a massive roodstone in the churchyard, is mainly Perpendicular, with an Early English.
- The church of St Mary is Perpendicular.
- The nave, portions of the central tower, and two bays of the choir are Perpendicular,'having been rebuilt towards the close of the 15th century.
- The church of St Andrew is mainly Perpendicular, but has Early English portions; it contains several ancient monuments and brasses, and flanks the market-place, with its modern cross.
- The church of St Michael and All Angels is mainly Perpendicular, but the tower (formerly central) and the portion west of it are Norman.
- The principle of the method consists in deflecting the compass needle by means of a horizontal magnet supported vertically over the compass card, the axis of the deflecting magnet being always perpendicular to the axis of the magnet attached to the card.
- This is a beautiful specimen of Perpendicular work, embattled, flanked by spired turrets, and covered with panel work.
- The church of St Mary is a handsome cruciform Perpendicular building.
- It surrendered at once, whereas Myrina, with its very strong citadel built on a perpendicular rock, sustained a siege.
- While in early times a mere perpendicular shaft led to these excavations, at a later date stairs were constructed down to the chambers.
- The church of St Mary, founded in 1111, retains the south door of the original building in the Transition style, but the greater portion of the structure is Perpendicular, of the time of Henry VIII.
- A horizontal incision is made in the bark quite down to the wood, and from this a perpendicular slit is drawn upwards to the extent of perhaps an inch, so that the slit has a resemblance to the letter T, as at a.
- The bark on each side of the perpendicular slit being then cautiously opened, as at b, with the handle of the knife, the bud and shield are inserted as shown at c. The upper tip of the shield is cut off horizontally, and brought to fit the bark of the stock at the transverse incision.
- In the vicinity, Monk Bretton Priory, a Cluniac foundation of 1157, retains a Perpendicular gatehouse, some Decorated domestic remains, and fragments of the church.
- The church of St Lawrence is of Perpendicular and earlier date, largely restored; it contains fine woodwork and some interesting monuments.
- The church of the Holy Trinity, Early English and Late Perpendicular, enlarged in 1879, contains a fine Norman font and the tomb of Bishop Vesey.
- The church of St George was built in 1866 on the site of an ancient Perpendicular church.
- The minster, dedicated to St Mary the Virgin, illustrates every style of architecture from Norman to Perpendicular.
- The main street leads up a slope from the river to the fine Perpendicular church of All Saints.
- Close to this an archway crosses the road, bearing a Perpendicular building known as the hanging chapel.
- Not far distant is the church of Huish Episcopi, with one of the finest of the Perpendicular towers for which Somersetshire is noted.
- The church of St John the Baptist is Perpendicular.
- The upper plate is bored through the centre and carries a conical pillar, which rotates freely in it and supports a horizontal plate, to the extreme ends of which are attached, by means of capstan screws or otherwise, two vertical supports, on which the telescope, which is constructed to be perpendicular to the vertical axis of the instrument, rests and rotates with it.
- The church or minster of St Cuthberga is a fine cruciform structure of various styles from Early Norman to Perpendicular, and consists of a central lantern tower, nave and choir with aisles, transepts without aisles, western or bell tower, north and south porches, crypt and vestry or sacristy, with the library over it.
- It retains Perpendicular portions, a south porch of brick of the 16th century and numerous ancient monuments and brasses.
- The parish church of All Saints, well placed above the river, is a fine Early English and Decorated building, with Perpendicular additions.
- No sooner is the object of alarm scented or seen than each one seeks safety in the most inaccessible situations, which are often reached by a series of astounding leaps over crevasses, up the faces of seemingly perpendicular rocks, or down the sides of equally precipitous chasms. The chamois will not hesitate, it is said, thus to leap down 20 or even 30 ft., and this it effects with apparent ease by throwing itself forward diagonally and striking its feet several times in its descent against the face of the rock.
- The church of St Just is Perpendicular, with portions of the fabric of earlier date.
- Remnants of a mansion of the 14th century, Damory Court, are seen in a farmhouse, and an adjoining Perpendicular chapel is used as a barn.
- The church of St John is a fine building, Perpendicular and earlier in date, picturesquely placed on an elevation above the town, with a lofty tower and spire.
- The " rate of transmission of heat " is here understood to mean the quantity of heat transferred in unit time through unit area of cross-section of the substance, the unit area being taken perpendicular to the lines of flow.
- (I) This relation applies accurately to the case of the steady flow of heat in parallel straight lines through a homogeneous and isotropic solid, the isothermal surfaces, or surfaces of equal temperature, being planes perpendicular to the lines of flow.
- The ancient church of St Peter (restored in 1878) is principally Perpendicular, but contains some Norman and Decorated portions.
- The church of St Augustine, Broxbourne, is a fine example of Perpendicular work, and contains interesting monuments, including an altar tomb with enamelled brasses of 1473.
- The church of St Botolph is of Norman foundation, but the nave is principally Decorated and the chancel Perpendicular, and the tower, having fallen down, was rebuilt in 1628.
- The church preserves some remnants of Norman work and a Perpendicular south chapel of rare beauty.
- These rays are more or less perpendicular to the arc or band; sometimes they are very approximately parallel to one another, on other occasions they converge towards a paint.
- The church of St Andrew is mainly Perpendicular.
- The short streak of light thus obtained moves with Mirror, .l 4,Stindd Boom Balance Weight, j/?/?j?jj/ Masonry Column Lamp Br.mide Paper_ On- Need,Le o 0 the movement of the boom over a second slit perpendicular to the first and made in the lid of a box containing clockwork driving a band of bromide paper.
- The glaciers front, with a perpendicular ice-wall, a shore of debris on which a few low plants are found to grow - poppies, mosses and the like.
- The central tower is Norman, and there are good Decorated and Perpendicular details in the body of the church.
- The abbey, cruciform, is in the Decorated and Perpendicular styles, with pronounced French influence, due probably to the master mason John Morow, or Morreau, who, according to an inscription on the south transept wall, was born in Paris.
- It has a beautiful Perpendicular church (St Mary's) and an agricultural trade, with flour mills.
- Parts of this castle date from the 11th century, but there are many additions such as the late Norman circular chapel, the Decorated state rooms, and details in Perpendicular and Tudor styles.
- The parish church of St Lawrence is a cruciform Perpendicular building, with a lofty central tower, and a noteworthy east window, its 15th-century glass showing the martyrdom of St Lawrence.
- Among these are a Roman slab, carved with figures of a horseman trampling upon an enemy, several fine tombs and stones of the 13th and 14th centuries, the frith or fridstool of stone, believed to be the original bishop's throne, and the fine Perpendicular roodscreen of oak, retaining its loft.
- Westward again is Leigh-on-Sea (an urban district, pop. 3667); its lofty Perpendicular church tower is visible from afar.
- Vast vertical walls of rock shoot up to a height of 600 ft., cut by their perpendicular joints into quadrangular piers and projections, some of which stand out alone as cathedral-like islets in front of the main cliff.
- That which is inscribed with the name of "Midas the King" is the most remarkable example of one class, in which a large perpendicular surface of rock is covered with a geometrical pattern of squares, crosses and maeanders, surmounted by a pediment supported in the centre by a pilaster in low relief.
- The church of St Mary the Virgin, a beautiful specimen of the Perpendicular style, dating from the reign of Henry VII., but frequently repaired and restored, contains the tomb of Lord Audley, chancellor to Henry VIII.
- The monasteries stand on the summit of these pinnacles; they are accessible only by aid of rope and net worked by a windlass from the top, or by a series of almost perpendicular ladders climbing the cliff.
- 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.
- The mirror mm is attached to the framework pafe, the members of which are parallel to the incident and reflected rays SO, OR, and the diagonal pf is perpendicular to the mirror.
- Among beautiful specimens of carved stalls may be mentioned the Early Decorated stalls in Winchester Cathedral, the Early Perpendicular ones in Lincoln Minster, and the early 15th-century canopies in Norwich Cathedral.
- The only side from which the rock can be ascended is the east; the other sides being for the most part perpendicular, and generally presenting lofty columnar forms, though not so regular as those of Staffa.
- St James's church is also a fine Perpendicular building, with a modern chancel, and without a tower.
- The parish church of St Stephen is Early English, and later, with a Perpendicular tower.
- The church of Holy Cross, formerly collegiate, is a noble Perpendicular building with Early English and other early portions, and a fine central tower.
- Except when the line of sight is perpendicular to the plane of the orbit, the revolution of the two bodies will result in a periodic variation of the motion in the line of sight.
- Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
- The church of St Mary, Carisbrooke, has a beautiful Perpendicular tower, and contains transitional Norman portions.
- His constructions are based on the idea that the imaginaries d - 1 represent a unit line, and its reverse, perpendicular to the line on which the real units 1 are measured.
- - r is constructed by measuring a length a along the fundamental line (for real quantities), and from its extremity a line of length b in some direction perpendicular to the fundamental line.
- Also, if 0 be the angle between them, and x", y", z" the direction-cosines of a line perpendicular to each of them, we have xx' +yy'+zz' =cos 0, yz' - zy" = x" sin 0, &c., so that the product of two unit lines is now expressed as - cos0+ (ix" +jy" +kz") sin 0.
- If it be perpendicular to the factor lines, (a) shows that it must have simultaneously every such direction.
- But there is nothing to prevent its being represented by a directed line if, as further applications of (a) and (b) show we must do, we take it perpendicular to each of the factor lines.
- Vq/Sq, and that of the foot of perpendicular from centre on plane is Srg i.
- The site of the primitive city, which later became the citadel, is occupied by the modern town; it is situated at the end of a long plateau between two valleys, and protected by perpendicular tufa cliffs some 60 ft.
- In the Eschenhagen pattern instrument, in which a single quartz fibre is used for the suspension, two magnets are placed in the vicinity of the suspended magnet and are so arranged that their field partly neutralizes the earth's field; thus the torsion required to hold the magnet with its axis perpendicular to the earth's field is reduced, and the arrangement permits of the sensitiveness being altered by changing the position of the deflecting magnets.
- The church of St Nicholas is Early English and Perpendicular.
- The town, with its Perpendicular church and its picturesque market-cross, lies below the south-western face of the Mendip Hills, which rise sharply from 600 to Soo ft.
- Close to the church, but detached from it, stands a beautiful Perpendicular building, the school-house, founded by Archbishop Chichele in 1422.
- The plain forming the plateau is well watered with numerous small lakes and streams. These several small streams, one of which, the San Francisco, passes through the city, unite near the south-western extremity of the plateau and form the Rio Funza, or Bogota, which finally plunges over the edge at Tequendama in a beautiful, perpendicular fall of about 475 ft.
- It is Early English, Decorated and Perpendicular, the tower being of the last period.
- (3) For equilibrium we must have R=o, which requires Xo, Y=o; in words, the sum of, the components of the system must be zero for each of two perpendicular directions in the plane.
- The moment of a force about a point 0 is the product of the force into the perpendicular drawn to its line of action from o 0, this perpendicular being reckoned J~ positive or negative according as 0 lies on one side or other of the line of action.
- Again it is necessary and sufficient for equilibrium that the sum of the projections of the forces on each of two perpendicular directions should vanish, and (moreover) that the sum of the moments about some one point should be zero.
- Thus three forces acting perpendicular FIG.
- If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel.
- 36, if OA, OB, OC be three mutually perpendicular lines in the solid, we may denote by O the angle which OC makes with a fixed direction OZ, by ~ the azimuth of the plane ZOC measured from some fixed plane through OZ, and by f~ the inclination of the plane COA to the plane ZOC In fig.
- Those planes in the body which are perpendicular to this axis obviously remain parallel to their original positions.
- Hence, if ~, tr denote the initial and final positions of any figure in one of these planes, the displacement could evidently have been effected by, (I) a translation perpendicular to the planes in question, bringing ointo some position o- in the plane of a., and (2) a rotation about a normal to the planes, bringing a.
- Successive halfturns about intersecting axes a, b are equivalent to a rotation about the common perpendicular to a, b at their intersection, Of amount equal to twice the acute angle between them, in the direction from a to b.
- Successive half-turns about two skew axes a, b are equivalent to a twist about a screw whose axis is the common perpendicular to a, b, the translation being double the shortest distance, and the angle of rotation being twice the acute angle between a, b, in the direction from a to b.
- The displacement of the point C of the body is made up of 10 tangential to the meridian ZC and sin 0 ~,1 perpendicular to the plane of this meridian.
- This is displaced relatively to A through a space 1~ perpendicular to the plane of the meridian, whilst A itself is displaced y through a space cos 0 hl in the same direction.
- In the first place, a cyhindroid can be constructed so as to have its axis coincident with the common perpendicular to the axes of the two given screws and to satisfy thi-ee other conditions, for the position of the centre, the parameter, and the orientation about the axis are still at our disposal.
- But it may be reduced to simpler elements in a variety of ways., For example, it may be reduced to two forces in perpendicular skew lines, For consider any plane, and let each force, at its intersection with the plane, be resolved into two components, one (P) normal to the plane, the other ~ in the plane.
- If the plane in question be chosen perpendicular to the direction of the vector-sum of the given forces, the vector-sum of the components Q is zero, and these components are therefore equivalent to a couple (~ 4).
- Hence any three-dimensional system can be reduced to a single force R acting in a certain line, together with a couple G in a plane perpendicular to the line.
- From the analogy of couples to translations which was pointed out in 7, we may infer that a couple is sufficiently represented by a free (or non-localized) vector perpendicular to its plane.
- Thus, let the plane of the paper be perpendicular to the planes of two couples, and therefore perpendicular to the line of intersection of these planes.
- The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.
- By properly choosing 0 we can make the plane of the couple perpendicular to the resultant force.
- Since the given wrench can be replaced by a force acting through any assigned point P, and a couple, the locus of the null-lines through P is a plane, viz, a plane perpendicular to the vector which represents the couple.
- Projecting orthogonally on a plane perpendicular to the central axis we obtain two reciprocal figures.
- The work of a couple in any infinitely small rotation of a rigid body about an axis perpendicular to the plane of the couple is equal to the product of the moment of the couple into the angle of rotation, proper conventions as to sign being observed.
- Draw JBA perpendicular to the lines of action, and let e be the angle of rotation.
- /n be the perpendicular distances from any given axis, the sum ~(mp2) is the quadratic moment with respect to the axis; it is also called the moment of inertia about the axis.
- If we write A=Ma, B=M/32, C=M~y, the formula (37), when referred to the principal axes at 0, becomes if p denotes the perpendicular drawn from 0 in the direction (X, u, e) to a tangent plane of the ellipsoid ~+~+~=I (43)
- The motion is therefore the resultant of two simple vibrations in perpendicular directions, of periods 22r ./ (pug), 2ir ~I (pf/g).
- In symbols, if v be the velocity and p the perpendicular from 0 to the tangent to the path, pv=h, (1)
- If it, v be the component velocities at P along and perpendicular to OP (in the direction of 0 increasipg), FIG.
- Again, the velocities parallel and perpendicular to OP change in the time & from it, v to uvb0, v+ubG, ultimately.
- Thus in the case of a plane orbit, if v be the velocity of P, ~l the inclination of the direction of motion to some fixed direction, the polar co-ordinates of V may be taken to be v, hence the velocities of V along and perpendicular to OV will be dv/dt and vdi,t/dt.
- Now the moment of this localized vector with respect to any axis through G is zero, to the first order of &, since the perpendicular distance of G from the tangent line at G is of the order (ot)2.
- A plane through G perpendicular to this vector has a fixed direction in space, and is called the invariable plane; it may sometimes be conveniently used as a plane of reference.
- We note further that if a body be free to turn about a fixed point 0, there are three mutually perpendicular lines through this point about which it can rotate steadily, without further constraint.
- We have seen (~ 18) that this vector coincides in direction with the perpendicular OH to the tangent plane of the momental ellipsoid at J; also that ~ (2)
- The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.
- 83, which c c are 0 and sin 0~ along and perpendicular to the meridian ZC, we see that the com ponent angular velocities about the lines B
- The displacements of P due to small variations of these co-ordinates are or along OP, rOO perpendicular to OP in the plane ZOP, and r sinO O~ perpendicular to this plane.
- R is the radial component of force, is the moment about a lilie through 0 perpendicular to the plane ZOP, and 4 is the moment about OZ.
- Condition of Stability of FrictionIf the resistance to be N exerted at a joint is always perpendicular ~ to the surfaces which abut at and form that joint, there is no tendency of the P pieces to be displaced by sliding.
- Let a represent the area of the section of a piston made by a plane perpendicular to its direction of motion, and v its velocity, which is to be considered as positive when outward, and negative when inward.
- The line T on the surface bbb has for the instant no velocity it a direction perpendicular to AB; becau2e for the instant it touches, without sliding, the line T on the fixed surface aaa.
- To find, then, the direction and velocity at the given instant of any point P, either in or rigidly attached to the rolling cylinder T, draw the plane PT; the direction of motion of P will be perpendicular to that plane, and towards the right or left hand according to the direction of the rotation of bbb; and the velocity of P will be v~=y.PT, (3)
- Demonstralion.From C draw CF perpendicular to OA, and CG
- From E draw EH perpendicular to OB, and EK to OA.
- The path of a point P in or attached to the rolling cone is a spherical epitrochoid traced on the surface of a sphere of the radius OP. From P draw PQ perpendicular to the instantaneous axis.
- Then the motion of P is perpendicular to the plane OPQ, and its velocity is v,.= y.
- 32~ Screw-like or Helical Motson.Since any displacement in a plane can berepresented in general by a rotation, it follows that the only combination of translation and rotation, in which a complex movement which is not a mere rotation is produced, occurs when there is a translation perpendicular to the plane and parallel to the axis of rotation.
- Let r denote the perpendicular distance of a point in a body moving helically from the axis.
- Through any point T in that line draw TV1, TV2, respectively paral- p, id to the simultaneous direction of Inotion of the pieces; through any other point A in the line of con- T nexion draw a plane perpendicular to that line, cutting TV~, TV2 in A V1 V2 then, velocity of piece I:
- Application to a Shifting Piece and a Turning Piece.Let a shifting piece be connected with a turning piece, and at a given instant let ai be the angular velocity of the turning piece, r~ the common perpendicular of its axis of rotation and the line of connection, Oi the angle made by the line of connection with the plane of rotation, Oi the angle made by the line of connection with the direction of motion 01 the shifting piece, v2 the linear velocity -of that piece.
- The direction of motion of a point in a turning piece being perpendicular to a plane passing through its axis, the condition that each pair of points in contact with each other must move in the same direction leads to the following consequences:
- That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.
- That the linear velocity of a shifting piece in rolling contact with a turning piece is equal to the product of the angular velocity of the turning piece by the perpendicular distance from its axis to a pair of points of contact.
- Cylindrical Wheels and Smooth Racks.In designing cylindrical wheels and smooth racks, and determining their comparati* motion, it is sufficient to consider a section of the pair of pieces made by a plane perpendicular to the axis or axes.
- To work with a wheel of any other figure, its section must be a rolling curve, subject to the condition that the perpendicular distance from the pole or centre of the wheel to a straight line parallel to the direction of the motion of the rack shall be constant.
- 100, let B,C~, B2Ci be the two axes; B~Bi their common perpendicular.
- Through any point 0 in this common perpendicular draw 0A1 parallel to B~C~ and OAi parallel to B2C,; make those lines pro B1 C2 portional to the angular velocities D ~ about the axes to which they are P respectively paiallel; complete the ~ B2 parallelogram OA1 EA2, and draw the diagonal OE; divide BiBf in D into C, two parts, inversely proportional to the angular velocities about the axes which they respectively adjoin; A2 through D parallel to OE draw DT.
- Sliding Contact: Forms of the Teeth of Spur-wheels am Racks.A line of connection of two pieces in sliding contact is line perpendicular to their surfaces at a point where they touch Bearing this in mind, the principle of the comparative motion of pair of teeth belonging to a pair of spur-wheels, or to a spur-whee and a rack, is found by applying the principles stated generally ii 36 and 37 to the case of parallel axes for a pair of spur-wheels, am to the case of an axis perpendicular to the direction of shifting for wheel and a rack.
- It also determines the forms of the teeth of straight racks, if one of the centres be removed, and a straight line EIE, parallel to the direction of motion of the rack, and perpendicular to CilCi, be substituted for a pitch-circle.
- Draw CiP1, C2P2 perpendicular to P~IP2, and with those lines as radii describe about the centres of the wheels the,circles DiD1, D2D2, called base-circles.
- Perpendicular to 01 draw A1IA2, cutting the axe8 in Ai, A2 make the outer rims of the patterns and of the wheels portions of the cones A1B1I, A,B2I, of which the narrow zones occupied by the teeth will be sufficiently near to a spherical surface described about 0 for practical purposes.
- The effect of the link is to maintain the distance between the axes of those pins invariable; hence the common perpendicular of the axes of the pins is the line of connection, and its extremities may be called the connected points.
- In a turning piece, the perpendicular let fall from its connected point upon its axis of rotation is the arm or crank-arm.
- The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common perpendiculars let fall from the me of connection upon the respective axes of rotation.
- If at any instant the direction of one of the crank-arms coincides with the line of connection, the common perpendicular of the line sf connection and the axis of that crank-arm vanishes, and the 3irectional relation of the motions becomes indeterminate.
- The church of St Nicholas, founded about 1375, is Perpendicular with a low tower rising from the centre.
- In the parish churches, many of which are of great interest, the predominant styles are Decorated and Perpendicular.
- Among the Perpendicular additions to the church last named may be noted a very beautiful oaken roodscreen.
- To illustrate Decorated and Perpendicular the churches of Clifton and of Marston Moretaine, with its massive detached campanile, may be mentioned; and Cople church is a good specimen of fine Perpendicular work.
- Finally there is the envelope of still vaster extent and of unknown constitution which gives the zodiacal light; its greatest extent is along the ecliptic, but it can also be certainly traced for 35° in a perpendicular direction.
- The canyon of the Patia through the Western Cordillera is known as the "Minima gorge," and has been cut to a depth of 1676 ft., above which the perpendicular mountain sides rise like a wall some thousands of feet more.
- The parish church of St Dunstan, Stepney, is a perpendicular building, much restored, containing many monuments and curious inscriptions.
- The church of St Mary the Virgin has fine Perpendicular work and traces of Norman work.
- Then, in order to connect with these the effect of the rightand left-hand slopes, there should be at least one gauge on each side about the middle height, and approximatel y in a line perpendicular to the axis of the valley passing through the central gauge.
- It is clear that errors will arise if the pieces of steel are not truly perpendicular to the plane of the beam, and the adjust - ment of great accuracy would be very tedious.
- The church of St Mary is Perpendicular, with a fine porch, a painting of the Adoration of the Magi, attributed to Rubens, a small crypt said to have been used by Cromwell as a prison for the Royalists, and many interesting monuments.
- There are now three churches - St Peter's, St Cuthbert's and St Mary's - principally of Perpendicular flint work; of these St Mary's, on the Suffolk side, is the largest.
- F B is the evolute of this circle, and for any radius DE at an angle a and corresponding tangent EG terminated by the evolute, the perpendicular distance of G from the line AD is c(cos a+a sin a).
- A circular arc, centre D and radius c/2, meets D E in K, and the perpendicular KL gives 2c sin a.
- This margin is normally furnished with a perpendicular spine (virgella) and occasionally with two shorter lateral spines or lobes.
- The remains of the old church, originally erected in 1244, contain good Perpendicular work, and the family vault of the Londonderrys; there are also the parish church and Presbyterian church, with lofty spires, and a Roman Catholic chapel.
- It was elliptical, and its long Diameter was perpendicular to the Horizon, verging below farthest from the moon."
- The church of St Peter is Perpendicular; those of Holy Trinity and St James are in the main modern reconstructions.