Parallel Sentence Examples

It runs parallel to the river.

They walked parallel to an abandoned highway for a couple of hours until they reached the second fed site.

The farm of today already has tractors that use GPS to make perfectly parallel rows with great precision.

The road ran parallel to the highway, with the Uncompahgre River separating the unpaved road from the main thoroughfare to the east.

The parallel, yellow lines in the center of this stretch of road seemed to go on forever.

She trotted until she was parallel to the lights then plunged into the deep snow, forcing her way into the forest.

Whatever may be the shape or size of the particles, there is no scattered light in a direction parallel to the primary electric displacements.

The double webs composing the sides of the fixed square shall be strictly parallel, and shall form a true square of exactly ten revolutions of the screw on the side.

Their progress and success are without parallel.

Indeed, its progress there, during these twenty years, is probably without parallel in the history of any other country.

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

The northern boundary, after an arbitrary beginning, finds a natural extension along the Great Lakes, and thence continues along the 49th parallel of north latitude to the Pacific (see Bulletin 171, U.S. Geological Survey).

To connect the idea of parallel lines to geography, the teacher us taught about latitude and longitude.

Hibil's contest with darkness has its prototype in Marduk's battle with chaos, the dragon Tiamat, which (another striking parallel) partially swallows Marduk, just as is related of Hibil and the Manichaean primal man.

The foliation is often parallel to the bedding, but may cross it obliquely or at right angles; or the bedding may be folded and contorted while the foliation maintains a nearly uniform orientation.

Brisson's work was in French, with a parallel translation (edited, it is said, by Pallas) in Latin, which last was reprinted separately at Leiden three years afterwards.

Abich (Sur la structure et la geologic du Daghestan, 1862), the successive folds of Jurassic limestones and slates, all nearly parallel to the Caucasus, which form lofty, narrow plateaus.

The mineral has a very perfect cleavage parallel to the faces c and m, and the cleavage surfaces are perfectly smooth and bright.

Twinning is represented only by twinlamellae, which are parallel to the planes m and f and are of secondary origin, having been produced by pressure.

This current catches the silt brought down by the rivers and projects it in long banks, or lidi, parallel with the shore.

Parallel with the senate, but extraneous to the main lines of the constitution, came the Council of Ten.

Two large rivers, which numerous tributaries, drain the government - the Dniester, which forms its boundary with Bessarabia and is navigable throughout its length, and the Bug, which flows almost parallel to the former in a higher, sometimes swampy, valley, and is interrupted at several places by rapids.

Podolia is traversed by a railway which runs parallel to the Dniester, from Lemberg to Odessa, and has two branch lines, to Kiev (from Zhmerinka) and to Poltava (from Balta).

In the Macarthy roller gin, the lint, drawn by a roller covered with leather (preferably walrus hide), is drawn between a metal plate called the " doctor " (fixed tangentially to the roller and very close to it) and a blade called the " beater " or knife, which rapidly moves up and down immediately behind, and parallel to, the fixed plate.

A system of parallel ranges of mountains, culminating in the Chinese Chang pai Shan, " the long white mountains," on the Korean frontier, runs in a north-easterly direction from the shores of the Gulf of Liao-tung.

The samson-post is placed flush with one side of the main sill, the band-wheel jack-post being flush with the other side, so that the walking-beam, which imparts motion to the string of tools, works parallel with the main sill.

The folds are approximately parallel to those of the Taurus, and geologically these mountains may be said to belong to that range.'

In the popular literature of Spain he holds a place such as has no parallel in other countries.

In constructing a hot-wire instrument for the measurement of high frequency currents it is necessary to make the working wire of a number of fine wires placed in parallel and slightly separated from one another, and to rpass the whole of the current to be measured through this strand.

The coil is so situated that, in its zero position when no current is passing through it, the plane of the coil is parallel to the direction of the lines of force of the field.

If there be two parallel wires through which currents are passing, then these wires are drawn together if the currents are in the same direction and pressed apart if they are in opposite directions.

The trousers are short and of a peculiar cut and material, being coloured many hues in parallel horizontal lines.

The numerous harbours are chiefly artificial, usually located at the mouths of streams, the improvements consisting of two parallel piers extending into the lake and protecting a dredged channel.

Parallel to the Carpathians are the Marsgebirge (1915 ft.) and its continuation, the Steinitzer Wald (1450 ft.).

The design of connecting Athens with the Peiraeus by long parallel walls is ascribed by Plutarch to Themistocles.

The middle wall, beginning south of the Pnyx near the Melitan Gate, gradually approached the northern wall and, following a parallel course at an interval of 550 ft., diverged to the east near the modern New Phalerum and joined the Peiraeus walls on the height of Munychia where they turn inland from the sea.

The existence of any third wall was denied by Leake, according to whose theory the southern parallel wall would be identical with the Phaleric. The language of Thucydides, however, seems decisive with regard to the existence of three walls.

We parallel it with the Arthurian story, and hold that, just as there was probably a real Arthur, however different from the hero of the trouveres, so there was a real Hood, however now enlarged and disguised by the accretions of legend.

Two parallel triangular faces are removed from a cardboard model of a regular octahedron, and on the remaining six faces tetrahedra are then placed; the hydrogen atoms are at the free angles.

This progress has perhaps no parallel in any art, and certainly none in music, for even Beethoven's progress was purely an increase in range and power.

The step from Rienzi to Der fliegende Hollander is without parallel in the history of music, and would be inexplicable if Rienzi contained nothing good and if Der fliegende Hollander did not contain many reminiscences of the decline of Italian opera; but it is noticeable that in this case the lapses into vulgar music have a distinct dramatic value.

And as the twofold musical and dramatic achievement of one mind, it already places Wagner beyond parallel in the history of art.

It matters little that Parsifal requires two nameless attendant characters in a long opening scene, for the sole purpose of telling the antecedents of the story, when a situation is thereby revealed which for subtlety and power has hardly a parallel since Greek tragedy.

It is no exaggeration to say that a parallel condition in literature would be produced by a strong public opinion to the effect that any Enelish style was hopelessly out of date unless it consisted exclusively of the most difficult types of phrase to be found in the works of Browning and Meredith.

Dicaearcus of Messana in Sicily, a pupil of Aristotle (326-296 B.C.), is the author of a topographical account of Hellas, with maps, of which only fragments are preserved; he is credited with having estimated the size of the earth, and, as far as known he was the first to draw a parallel across a map. 4 This parallel, or dividing line, called diaphragm (partition) by a commentator, extended due east from the Pillars of Hercules, through the Mediterranean, and along the Taurus and Imaus (Himalaya) to the eastern ocean.

In his text Eratosthenes ignored the popular division of the world into Europe, Asia and Libya, and substituted for it a northern and southern division, divided by the parallel of Rhodes, each of which he subdivided into sphragides or plinthia - seals or plinths.

Parallels and meridians were represented by straight lines intersecting each other at right angles, the relative proportions between degrees of longitude and latitude being retained only along the parallel of Rhodes.

The correct relations in the length of degrees of latitude and longitude are maintained in the first case along the latitude of Thule and the equator, in the second along the parallel of Agisymba, the equator and the parallels of Meroe, Syene and Thule.

Blocks of dressed stone overgrown by grass lie in regular formation; a series of parallel revetment walls on hills commanding passes exist, as do relics of ancient water-tanks.

South of Berbera are two ranges nearly parallel with the coast.

To the above we have a good parallel in the Book of Daniel; for the variations of its two chief Greek Versions - that of the Septuagint and of Theodotion - go back to variations in the Semitic.

Parallel with this great production of learned and imaginative works, Dahn published some twenty small volumes of poetry.

And a parallel change is found in the practical policy of the state.

The great motor of the parallel effort in England was the Christian spirit; in France it was the enthusiasm of humanity which was associated with the revolutionary movement.

Cain's subsequent founding of a city finds a parallel in the legend of the origin of Rome through the swarms of outlaws and broken men of all kinds whom Romulus attracted thither.

The list of Cain's descendants reflects the old view of the beginnings of civilization; it is thrown into the form of a genealogy and is parallel to Gen.

In 1907 active preliminary work was begun on the Louisiana section of a great interstate inland waterway projected by the national government between the Mississippi and Rio Grande rivers, almost parallel to the Gulf Coast and running through the rice and truck-farm districts from the Teche to the Mermenton river (92 m.).

It is then possible to define by a parallel elaboration what is meant by classes of classes, classes of relations, relations between classes, and so on.

There are numerous high valleys shut in among the mountains of this range; the most noteworthy being the plain of Livno, which lies parallel to the Dalmatian border, at a height of 500 ft.

They descend in parallel ridges of grey Karst limestone, south-westwards to the sea; their last summits reappear in the multitude of rocky islands along the Dalmatian littoral.

In 1893 the bones of a cave-bear (Ursus spelaeus) were taken from a cavern of the Bjelasnica range, in Herzegovina, a discovery without parallel in the Balkan Peninsula.

On the 7th of October the Grande Armee lay in three parallel columns along the roads leading over the mountains to Hof, Schleiz and Kronach; on the right lay the IV.

Meanwhile the Russians and Prussians had concentrated all available men and were moving on an almost parallel line, but somewhat to the south of the direction taken by the French.

Blucher followed by parallel and inferior roads on their northern flank, but Schwarzenberg knowing that the Bavarians also had forsaken the emperor and were marching under Wrede, 50,000 strong, to intercept his retreat, followed in a most leisurely fashion.

The Anti-Atlas or Jebel Saghru, also known as the Lesser Atlas, running parallel to and south of the central range, is one of the least elevated chains in the system, having a mean altitude of not more than 5000 ft., although some peaks and even passes exceed 6000 ft.

On the 64th parallel the mean annual temperature at an elevation of 6560 ft.

The goal, which is well preserved at the upper end, is similar to that at Olympia; it consists of a sill of stone sunk level with the ground, with parallel grooves for the feet of the runners at starting, and sockets to hold the posts that separated the spaces assigned to the various competitors, and served as guides to them in running.

They consist of a long rectangular building, with a proscenium or column front which almost forms a tangent to the circle of the orchestra; at the middle and at either end of this proscenium are doors leading into the orchestra, those at the end set in projecting wings; the top of the proscenium is approached by a ramp, of which the lower part is still preserved, running parallel to the parodi, but sloping up as they slope down.

Some interesting manoeuvres now took place, Wellington moving parallel and close to Marmont, but more to the north, making for the fords of Aldea Lengua and Santa Marta on the Tormes nearer to Salamanca, and being under the belief that the Spaniards held the castle and ford at Alba on that river.

It runs almost parallel to the western shore of the Caspian, and west of Astara is only io or 12 m.

The Elburz then splits into three principal ranges running parallel to one another and connected at many places by secondary ranges and spurs.

Roughly speaking, the river may be said so far to run parallel to the main chain of the Himalaya at a distance of Too m.

In such cases the molten rock cannot have been homogeneous, and as it flowed along the ground the different portions of it were drawn out into long parallel streaks.

When crystals are present they generally have their long axes parallel to the fluxion.

In polarized light they show a weak grey colour with a black cross, the arms of which are parallel to the cobwebs in the eyepiece of the microscope and remain stationary when the section is rotated.

In an age when, with the evolution of the feudal organization cf society, even everyday costume was becoming a uniform, symbolizing in material and colour the exact status of the wearer, it was natural that in the parallel organization of the Church the official vestments should undergo a similar process of differentiation and definition.

These two islands lie parallel to each other, Tamara to the west; they form a sort of basin, in the centre of which is the islet of Crawford.

On the other hand, there are on the western outskirts of the plateau a few mountain chains which take a direction at right angles to the above (that is, from north-west to south-east), and parallel to the great line of upheavals in south-west Asia.

If the constituent solenoids are parallel and of equal strength, the magnet is also uniformly magnetized.

If the magnetization is parallel to the major axis, and the lengths of the major and minor axes are 2a and 2C, the poles are situated at a distance equal to 3a from the centre, and the magnet will behave externally like a simple solenoid of length 3a.

An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.

It can be shown 3 that in a uniform field an elongated piece of any non-crystalline material is in stable equilibrium only when its length is parallel to the lines of force; for diamagnetic substances, however, the directing couple is exceedingly small, and it would hardly be possible to obtain a uniform field of sufficient strength to show the effect experimentally.

If each of these axes successively is placed parallel to the lines of force in a uniform field H, we shall have = 12 = 13=K3H, the three susceptibilities being in general unequal, though in some cases two of them may have the same value.

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.

An iron bar shaped like an inverted L projects upwards from each of the yokes, the horizontal portions of the bars being parallel to the rods, and nearly meeting at a height of about 8 in.

This conception, which finds its parallel in Dan.

Here the main line from Milan divides, one portion going on parallel to the line of the ancient Via Aemilia (which it has followed from Piacenza downwards) to Rimini, Ancona and Brindisi, and the other through the Apennines to Florence and thence to Rome.

From Chieng Khan the river again turns eastwards along the 18th parallel, forcing its way through its most serious rapid-barrier, and receiving some important tributaries from the highlands of Tung Chieng Kum and Chieng Kwang, the finest country in Indo-China.

The whole of this line, however, was subject to future adjustments, Peru claiming all that part of the Amazon valley extending eastward to the Madeira and lying between the Beni and the east and west boundary line agreed upon by Spain and Portugal in 1750 and 1777, which is near the 7th parallel.

The first consists of an almost continuous range crossing the northern end of Rio Grande do Sul and following the coast northward to the vicinity of Cape Frio, and thence northward in broken ranges to the vicinity of Cape St Roque, and a second parallel range running from eastern Sao Paulo northeast and north to the eastern margin of the Sao Francisco basin in northern Bahia, where that river turns eastward to the Atlantic. The first of these is generally known as the Serra do Mar, or Coast Range, though it is locally known under many names.

Both of these lakes lie nearly parallel with the coast line, are separated from the ocean by broad sand beaches filled with small lakes, and communicate with the ocean through the same channel.

Second in importance to George Street is Pitt Street, which runs parallel to it from the Circular Quay to the railway station; Macquarie Street runs alongside the Domain and contains a number of public buildings, including the treasury, the office of public works, the houses of parliament and the mint.

The Umzimkulu river rises in Bamboo Castle, in the Drakensberg, and, with bolder curves than the Umkomaas, runs in a course generally parallel with that stream S.E.

It is the only complete and independent system between the decline of ancient thought and the system of Aquinas in the 13th century, if indeed we ought not to go further, to modern times, to find a parallel.

It even became customary to draw a parallel between him as the praecursor Christi in naturalibus and John the Baptist, the praecursor Christi in gratuitis.

The graph will then be made up of a succession of parallel lines.

Like the Kunduz, it probably drains the northern slopes of the Hindu Kush by deep lateral valleys, more or less parallel to the crest, reaching westwards towards the Khawak pass.

Water from the river is carried to factories by a canal on each side of the river and parallel to it; the first canal was built on the north side in1845-1847and is 1 m.

His two newspapers, the Illyrian National Gazette and the Danica Ilirska (Illyrian Daystar) provided a literary focus for the rising generation; while his reform of Croat orthography, planned on parallel lines with Vuk Karadzic's epochmaking philological work in Serbia, assured to modern SerboCroat literature a definitely unitary development.

The treason trial which opened at Zagreb in March 1909 pursued the parallel aims of intimidating the Serbs of Croatia, of splitting the new-found unity of Serb and Croat and of proving to the outside world the existence of a dangerous Pan-Serb movement organized from Belgrade inside the monarchy and amply justifying the countermove of annexation.

By this time it was sufficiently obvious that the Yugosla y s were tacitly if not explicitly agreed upon a triple parallel policy, framed for all contingencies.

Against Bulgaria the Yugoslav delegation claimed considerable frontier rectifications - (a) the Strumnica salient, which threatened the Vardar railway from the east, (b) the district of Kochana (Tocana) and the Bregalnitsa (Bregalnica), (c) a strip of territory running parallel with the old Serbo-Bulgarian frontier the whole way from Zajecar to Kyustendil, and (d) the town of Vidin on the Danube and the salient between it and the Timok.

An interesting exception to the general rule that full brightness requires the existence of the first zone occurs when the obstacle assumes the form of a small circular disk parallel to the plane of the incident waves.

We will now apply the integrals (2) to the case of a rectangular aperture of width a parallel to x and of width b parallel to y.

When parallel rays fall directly upon a spherical mirror the longitudinal aberration is only about one-eighth as great as for the most favourably shaped single lens of equal focal length and aperture.

In these instruments the lines are ruled upon a spherical surface of speculum metal, and mark the intersections of the surface by a system of parallel and equidistant planes, o; of which the middle member passes through the centre of the sphere.

If the subject of examination be a luminous line parallel to n, we shall obtain what we require by integrating (4) with respect to 77 from - oo to + oo.

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.

If we suppose that the force impressed upon the element of mass D dx dy dz is DZ dx dy dz, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).

The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.

According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).

None agrees in every point, but almost every detail finds a close parallel in some tomb or other.

It may be readily deduced that the directions of minimum deviation for a pencil of parallel rays lie on the surface of cones, the semi-vertical angles of which are equal to the values given in the above table.

This was first suggested by Thomas Young, who showed that the rays producing the bows consisted of two systems, which, although emerging in parallel directions, traversed different paths in the drop. Destructive interference between these superposed rays will therefore occur, and, instead of a continuous maximum illumination in the direction of minimum deviation, we should expect to find alternations of brightness and darkness.

They are formed by parallel rays of light emanating from two sources, as, for example, the sun and its image in a sheet of water, which is situated between the observer and the sun.

The Semites who visited Egypt wore a larger and coloured cloth, ornamented with parallel stripes of patterns similar to those found upon some early specimens of Palestinian pottery.

The distinctive feature is the spiral arrangement of the garment,the body being wrapped to a greater or less extent with a bandage of varying length in more or less parallel stripes.

Nevertheless veils were not usually worn out of doors, the countrywoman of to-day is not veiled, and it is uncertain whether there is any early parallel for the yashmak, the narrow strip which covers the face below the eyes and hangs down to the feet.

In archaic figures the hair is most frequently arranged over the brow and temples in parallel rows of small curls which must have been kept in their places by artificial means.

The nearest parallel to his literary position may be found in the aim which Virgil puts before himself in his Bucolics.

This branch consists of parallel chains enclosing elevated valleys, in one of which lies the town of Merida at the height of 5410 ft., overlooked by the highest summit of the chain (Picacho de la Sierra, 15,420 ft.).

Beyond the Cojedes begin two parallel ranges known as the Maritime Andes of Venezuela, which stretch east and west along the coast.

The Sierra Madre crosses the southern part of the state parallel with the coast, separating the low, humid, forested districts on the frontier of Tabasco from the hot, drier, coastal plain on the Pacific. The mountain region includes a plateau of great fertility and temperate climate, which is one of the best parts of Mexico and contains the larger part of the population of the state.

These cells of various shapes are seen in large numbers, mainly lying in a direction parallel to the new vessels and capillaries, which all run at right angles to the wound surface.

The surface of the state is much broken by the Sierra Madre Occidental, which extends through it from north to south and covers its entire width with parallel ranges, enclosing fertile valleys.

If a point be in motion in any orbit and with any velocity, and if, at each instant, a line be drawn from a fixed point parallel and equal to the velocity of the moving point at that instant, the extremities of these lines will lie on a curve called the hodograph.

Near the ferry are a row of long parallel cuttings in the rock, which must be remains of the ancient docks, each being intended to take a ship.

In the Flyting of Dunbar and Kennedie, an outstanding specimen of a favourite northern form, analogous to the continental estrif, or tenzone, he and his rival reach a height of scurrility which is certainly without parallel in English literature.

As in the parallel case of the Roman conquest of Greece, the superior culture of the conquered race asserted its supremacy over their Arab conquerors.

The great Morgagni, the founder of morbid anatomy, himself set the example of carrying on this study parallel with clinical observation; and always insisted that the clinical story of the case should be brought side by side with the revelations of the necropsy.

From Basel to Mainz the Rhine flows through a wide and shallow valley, bordered on the east and west by the parallel ranges of the Black Forest and the Vosges.

The tendency to divide into parallel branches has been curbed in the interests of navigation, and many windings have been cut off by leading the water into straight and regular channels.

The Rhine now pursues a westerly course almost parallel with that of the Waal.

Before joining the Rhine the Ill runs almost parallel with it and at no great distance for upwards of 50 m.

In the flatter parts of the valley occur large beds of loam and rubble, sometimes in terraces parallel with, but several hundred feet above, the river, proving by their disposition and appearance that the valley has been formed by the action of water.

But this superficiality was accompanied by such wonderful acuteness within a certain range, by such an absolutely unsurpassed literary aptitude and sense of style in all the lighter and some of the graver modes of literature, by such untiring energy and versatility in enterprise, that he has no parallel among ready writers anywhere.

A street named after it runs south from the Mansion House parallel with its course.

It rose on the heights of Hampstead, traversed Paddington, may be traced in the course of the Serpentine lake in Hyde Park, ran parallel to and east of Sloane Street, and joined the Thames close to Chelsea Bridge.

It has two naves parallel, originally for the use of the nuns and the parishioners respectively.

Following the river down from the Tower these docks, with dates of original opening and existing extent, are - St Katherine's (1828; 102 acres), London (1805; 571 acres), West India, covering the northern part of the peninsula called the Isle of Dogs (1802; 1212 acres), East India, Blackwall (1806; 38 acres), Royal Victoria and Albert Docks (1876 and 1880 respectively), parallel with the river along Bugsby's and Woolwich Reaches, nearly 3 m.

It runs parallel to the ocean, from which it is separated by sandhills.

Its point of confluence with the Maputa (which empties into Delagoa Bay) marks the parallel along which the frontier between Zululand and Portuguese East Africa is drawn.

As the mine is opened the deposit is subdivided into blocks of convenient size by parallel passages, which form later the main haulage roads, and by transverse openings for ventilation.

In order to lessen the cost of handling the rock-filling, the excavation sometimes takes the form of inclined working-places, parallel to the slope naturally taken by the rock when dumped from above into the working 7 -,, , --,, ?

A man-engine consists of two heavy wooden rods (like the rods of a Cornish pumping plant), placed parallel and close to each other in a special shaft compartment, and suspended at the surface from a pair of massive walking beams (or " bobs ").

Many sections, however, contained in the corresponding part of Mark have no parallel in Luke, while the parallel to one of them is placed later and differs considerably in form.

In the second of these passages the disciples are exhorted to choose a life of voluntary poverty; the nearest parallel is the ideal set before the rich young man at Mark x.

Successive flexures or ridges are ranged in more or less parallel lines, and from between the bands of hard, unyielding rock of older formation the soft beds of recent shale have been washed out, to he carried through the enclosing ridges by rifts which break across their axes.

The Arakan Yomas starting from Cape Negrais extend northwards more or less parallel with the coast till they join the Chin and Naga hills.

It is probable that Burma is the Chryse Regio of Ptolemy, a name parallel in meaning to Sonaparanta, the classic Pali title assigned to the country round the capital in Burmese documents.

In their coarsest forms such striae are readily visible to the unaided eye, but finer ones escape detection unless special means are taken for rendering them visible; such special means conveniently take the form of an apparatus for examining the glass in a beam of parallel light, when the striae scatter the light and appear as either dark or bright lines according to the position of the eye.

Plate glass of the usual quality, which appears to be perfectly homogeneous when looked at in the ordinary way, is seen to be a mass of fine striae, when a considerable thickness is examined in parallel light.

By the application of a pointed iron hook, while the glass is still ductile, the parallel coils can be distorted into bends, loops or zigzags.

This leaves a cylinder with roughly parallel ends; these ends are cut by the use of a diamond applied internally and then the cylinder is split longitudinally by the same means.

If the table has a pattern engraved upon it the glass will show the same pattern in relief, the most frequent pattern of the kind being either small parallel ridges or larger ribs crossing to form a lozenge pattern.

Between the Jur and the Nile, and following a course generally parallel with these rivers, several streams run north from the Congo-Nile watershed and join the Bahr-el-Ghazal.

This term of course includes as special cases the qualities of "malleability" (capability of being flattened out under the hammer) and "ductility" (capability of being drawn into wire); but these two special qualities do not always go parallel to each other, for this reason amongst others - that ductility in a higher degree than malleability is determined by the tenacity of a metal.

Parallel experiments with layers of dough or sand plus some connecting material proved that the particles in all cases moved along the same tracks as would be followed by a flowing cylinder of liquid.

A high wall runs behind these buildings parallel with the Nile.

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.

The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of gyration about FF' of the water-line area.

Thus if d,/ is the increase of 4, due to a displacement from P to P', and k is the component of velocity normal to PP', the flow across PP' is d4 = k.PP'; and taking PP' parallel to Ox, d,, = vdx; and similarly d/ ' = -udy with PP' parallel to Oy; and generally d4,/ds is the velocity across ds, in a direction turned through a right angle forward, against the clock.

For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.

Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

An angular velocity R, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -R parallel to Ox, and R parallel to Oy; and then ik is resolved into 4'1+1'2, such that 4/ 1 -R-Rx 2 and 1//2+IRy2 is constant over the boundary.

Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans.

This is a closed Sumner line for n =I, when the boundary consists of two parallel walls; and n= z gives an Elastica.

The Pallacopas, called Pallukkatu in the NeoBabylonian texts, started from Pallukkatu or Faluja, and running parallel to the western bank of the Euphrates as far as Iddaratu or Teredon (?) watered an immense tract of land and supplied a large lake near Borsippa.

Until, therefore, through parallel passages or through explanatory lists prepared by the Babylonian and Assyrian scribes in large numbers as an aid for the study of the language, 5 the exact phonetic reading of these divine names was determined, scholars remained in doubt or had recourse to conjectural or provisional readings.

This spot increases in size; in the stalks it assumes an oval shape, with its long axis parallel to the stalk, whilst in the leaves and grapes it is more or less circular in outline.

About the time of Ergamenes, or (according to some authorities) before, a vernacular came to be employed in inscriptions, written in a special alphabet of 23 signs in parallel hieroglyphic and cursive forms. The cursive is to be read from right to left, the hieroglyphic, contrary to the Egyptian method, in the direction in which the figures face.

Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.

It follows a generally easterly course, roughly parallel with that of the Dee, and a few miles to the south of it, falling into the North Sea close to Old Aberdeen, after a run of 82 m.

At the two extremities of New Caledonia, parallel longitudinal ranges of mountains enclose valleys; for the rest the island consists essentially of confused masses and ranges of mountains, rising to an extreme elevation of 5387 ft., the plains being chiefly the deltas of rivers.

There is no exact parallel in England to the conflict between these two classes in Scotland in the 16th century, or to the great continental revolution of the 13th and 14th centuries, by which the crafts threw off the yoke of patrician government and secured more independence in the management of their own affairs and more participation in the civic administration.

There are perfect cleavages parallel to the dome (oiI).

There are perfect cleavages parallel to the rhombohedral faces, and the crystals exhibit a strong negative double refraction, like calcite.

Some fortysix or more retorts, arranged in parallel horizontal rows, are heated in one furnace.

In the Silesian process the distillation is conducted in specially constructed muffles of a prismatic shape arched above, which are arranged in two parallel rows within a low-vaulted furnace, similar to the pots in a glass furnace.

To the precarium German institutions offered no close parallel.

Sirhan is continuous with the depression known as the Jauf, situated on the northern edge of the Nefud or Nafud, and the halfway station between Damascus and Hail; and it is possible that this depression continues eastward towards the Euphrates along a line a little north of the thirtieth parallel, where wells and pasturages are known to exist.

South-western Arabia, from the twenty-first parallel down to the Gulf of Aden, including the Taif district of Hejaz, Asir and Yemen, South forms one province geographically.

The Gulf of Akaba is a strip of country which has been let down between two parallel faults, and several similar faulted troughs occur in the Sinai peninsula.

The Anophelinae have narrow bodies, and generally spotted wings, and when at rest keep body and proboscis in a straight line, often at a considerable angle with the supporting surface; in this way they can be distinguished from Culicinae, which have a humped-up thorax with which the proboscis forms an angle, and in the resting position keep the body parallel to the support.

The two chains, which run parallel and near each other on the western side, are of identical origin, and have been separated by the action of water during many centuries.

The main commercial street runs inland parallel with the Praya.

The apparent scattering or diversity of the flights is merely an effect of perspective upon objects really traversing parallel lines.

Many of the chief characteristics of the ancient Greek heroes are reproduced in those of the Teutonic North, the parallel being in some cases very striking; Siegfried, for instance, like Achilles, is vulnerable only in one spot, and Wayland Smith, like Hephaestus, is lame.

Hence in its condition of repose such an eye cannot distinctly see parallel rays from a distance and, still less, divergent rays from a near object.

The upper surface of the lateral edges of the mandible has also a number of parallel fine transverse ridge, like those on the bill of a duck.

Old schists, free from fossils and rich in quartz, overlie it in parallel chains through the whole length of the peninsula, especially in the central and highest ridges, and bear the ores of Chu-goku (the central provinces), principally copper pyrites and magnetic pyrites.

South and west of the Fossa Magna the beds are thrown into folds which run approximately parallel to the general direction of the coast, and two zones may be recognizedan outer, consisting of Palaeozoic and Mesozoic beds, and an inner, consisting of Archaean and Palaeozoic rocks, with granitic intrusions.

Towards the Fossa Magna the folds bend sharply round until they are nearly parallel to the Fossa itself.

It is worked plankwise to a surface parallel with the grain, and not across it.

Many families of sword artists sprang up at a later period, furnishing treasures for the collector even down to the present day, and their labors reached a level of technical mastery and refined artistic judgment almost without parallel in the art industries of Europe.

Namako disposed in straight parallel lines originally ranked at the head of this kind of work.

Thus, for a diamond-petal diaper the chisel is carried across the face of the metal horizontally, tracing a number of parallel bands divided at fixed intervals by ribs which are obtained by merely straightening the chisel and striking it a heavy blow.

A broad central avenue led straight to the palace, and on either side of it ran four parallel streets, crossed at right angles by smaller thoroughfares.

A line runs the whole length of the land, for the most part parallel with the Rhine, while branches cross obliquely from east to west.

Constructed by the Great Central Railway Co., the dock in 1921 comprised a square basin and two long arms (including a graving dock) running parallel to each other on the western side, of a total area of 45 ac., with 5,400 ft.

Long jetties spring out on either side of the entrance, curving round about midway in order to run parallel to the river, thus forming a huge funnelshaped entrance; the eastern jetty forms a landing-stage for passenger traffic and the western is designed for the shipment of bunker and cargo coal.

They were built on a rectangular plan, with a large central square and straight thoroughfares running at right angles or parallel to one another, this uniformity of construction being well exemplified in the existing bastide of Monpazier (Dordogne) founded by the English in 1284.

Kellner has also patented a "bleaching-block," as he terms it, consisting of a frame carrying parallel plates similar in principle to those last described.

The relations of Lord Holland to his sons would be difficult to parallel.

In that year Chile decided to explore the desert coast, and in 1843 that part of the desert extending north to the 26th parallel was organized into the province of Atacama.

For the Iranian parallel, see § 8, and on the Hebrew Priestly Writer, Gunkel, Genesis 2, pp. 2 33 ff.

If now we cut the freezing-point surface by planes parallel to the base ABC we get curves giving us all the alloys whose freezing-point is the same; these isothermals can be projected on to the plane of the triangle and are seen as dotted lines in fig.

Most of the mountain spurs run from east to west, but in northern Lebanon the prevailing direction of the valleys is north-westerly, and in the south some ridges run parallel with the principal chain.

The 'Auwali and the Nahr el-Zaherani, the only other considerable streams before we reach the Litany, flow northeast to south-west, in consequence of the interposition of a ridge subordinate and parallel to the central chain.

On the eastern side the parallel valley of `Asal el-Ward deserves special mention; the descent towards the plain eastwards, as seen for example at Ma'lula, is singular - first a spacious amphitheatre and then two deep very narrow gorges.

The northern Doris, for example, spoke Aeolic, while Elis, Phocis, and many non-Dorian districts of north-west Greece spoke dialects akin to Doric. Many Dorian states had additional " nonDorian tribes "; Sparta, which claimed to be of pure and typical Dorian origin, maintained institutions and a mode of life which were without parallel in Peloponnese, in the Parnassian and in the Asiatic Doris, and were partially reflected in Crete only.

The leaves, which show great variety in size and form, are generally broad and net-veined, but in sweet-flag (Acorus Calamus) are long and narrow with parallel veins.

Accordingly the distribution of electricity is such that equal parallel slices of the ellipsoid of revolution taken normal to the axis of revolution carry equal charges on their curved surface.

The capacity of two parallel planes can be calculated at once if we neglect the distribution of the lines of force near the edges of the plates, and assume that the only field is the uniform field between the plates.

If all the plates on one side are connected together and also those on the other, the condensers are j oined i n parallel.

If one condenser is charged, and then joined in parallel with another uncharged condenser, the charge is divided between them in the ratio of their capacities.

Hence, multiplying these normal forces by the areas of the corresponding faces, we have the total flux parallel to the x-axis given by - (d 2 V/dx 2)dxdydz, and similar expressions for the other sides.

Then the potential at any point P in this ideal plane PO is equal to q/AP-q/BP=0, whilst the resultant force at P due to the two point charges is 2gAO/AP 3, and is parallel to AB or normal to PO.

There are several series of parallel beds, interstratified with quartzite and schist, the most important being the "main reef" series.

It is not, however, a revision of the Fragmentary Targum - for it is clearly independent of that version - but is rather a parallel, if somewhat later, production, in which the text of Onkelos is already combined with a number of variants and additions.

They are a monotonous sandstone range, covered with extensive forests, which up to the sources of the rivers Ung and San are also called the eastern Beskids, and are formed of small parallel ranges.

The artillery was posted on the Dunbar side of the burn, directly opposite and north of Doon, the infantry and cavalry crossed where they could, and formed up gradually in a line south of and roughly parallel to the Berwick road, the extreme left of horse and foot, acting as a reserve, crossed at Brocksmouth House on the outer flank.

The station is built on a flat peninsula connected by a narrow strip of land with a ridge which runs parallel with the river.

The plain fact is that the same facts were taught in Palestine, Asia Minor and Gaul, whether gathered up in a parallel creed form or not.

Parallel to it is the Faith of St Jerome discovered in 1903 by Dom.

It is possible that Leo's letter to Flavian gave the impulse to put it forward because it contained a parallel to words which Leo quoted from the Old Roman Creed, " born of the Holy Ghost and the Virgin Mary," " crucified and buried," which do not occur in the first Nicene Creed.

There are phrases in the writings of Vincentius of Lerins and of Faustus, bishop of Riez, which are parallel to the teaching of the creed, though they cannot with any confidence be called quotations.

So also he has drawn a close parallel between the moral and the aesthetic criteria.

In 1803 Wilkinson was one of the commissioners to receive Louisiana from France, and in 1805 became governor of that portion of the Purchase above the 33rd parallel, with headquarters at St Louis.

There is a system of lesser faults, parallel to the Great Fault, dividing the area into a number of blocks, some of which have fallen more than others.

There are also indications of another series of faults roughly parallel to the south-east coast, which point to the islands being fragments of a former extensive plateau.

The Tegean territory occupied the southern part of this space; the northern half, sundered by projecting spurs from the parallel ranges, belonged to Mantineia.

On the south of the plateau we find a similar succession of narrow valleys dividing parallel flexures, or anticlinals, formed under similar geological conditions to those which appear to be universally applicable to the Himalaya, the Hindu Kush, and the Indus frontier mountain systems. From one of these long lateral valleys the Hari Rud receives its principal tributary, which joins the main river below Obeh, 180 m.

This Persian title became in later times the special designation of the Kushan kings and is curiously parallel to the use of Arabic and Persian titles (padishah, sultan, &c.) by the Ottoman Turks.

The Yue-Chi and Turks, however, may both represent parallel developments of similar or even originally identical tribes.

All that is wanting in his writings, especially in his Isagoge in artem analyticam (1591), in order to make them look like a modern school algebra, is merely the sign of equality - a want which is the more striking because Robert Recorde had made use of our present symbol for this purpose since 1 557, and Xylander had employed vertical parallel lines since 1575.

The diameter of a quadric surface is a line at the extremities of which the tangent planes are parallel.

The peroration contains a noble appeal to the Italian liberator of his dreams, and a parallel from Macedonian history, which, read by the light of this century, sounds like a prophecy of Piedmont.

The ignorance of the compiler regarding the sequence of the kings finds a parallel in that of the author of the book of Daniel; see C. C. Torrey, Amer.

This micrometer is provided with two pairs of parallel webs.

Having selected the most suitable one he directs the axis of the finder to the estimated middle point between the comet and the star, turns the finder-micrometer in position angle until the images of comet and star lie symmetrically between the parallel position wires, and then turns the micrometer screw (which moves the distance-wires symmetrically from the centre in opposite directions) till one wire bisects the comet and the other the star.

Again, in an ocular heliometer by Steinheil double image is similarly produced by a divided prism of total reflection placed in parallel rays.

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.

Thus the three groups form parallel accounts and contain the same or closely related material.

Spitta takes verse 6 to be an addition of the redactor, which describes proleptically what follows, while Gunkel sees in 6 and 7-16 parallel accounts.

Captain Sherard Osborn in 1870 was the first to recognize that the North Atlantic Basin was divided by a central rise running generally from north to south into two parallel depressions.

The zones of surface temperature are arranged roughly parallel to the equator, especially in the southern hemisphere.

The first process in laying out the workings consists in driving a gallery on the level along the course of the coal seam, which is known as a " dip head level," and a lower parallel one, in which the water collects, known as a " lodgment level."

In the former, which is also known as " post and stall" or "bord and pillar " in the north of England, " pillar and stall " in South Wales, and " stoop and room " in Scotland, the field is divided into strips by numerous openings driven parallel to the main rise headings, called " bords " or " bord gates," which are again divided by cutting through them at intervals, so as to leave a series of pillars arranged chequer-wise over the entire area.

The area is laid out by two pairs of level drifts, parallel to each other, about 150 yds.

In driving levels it is necessary to cut grooves vertically parallel to the walls, a process known as shearing; but the most important operation is that known as holing or kirving, which consists in cutting a notch or groove in the floor of the seam to a depth of about 3 ft., measured back from the face, so as to leave the overhanging part unsupported, which then either falls of its own accord within a few hours, or is brought down either by driving wedges along the top, or by blasting.

For flat ropes the drum or bobbin consists of a solid disk, of the width of the rope fixed upon the shaft, with numerous parallel pairs of arms or horns, arranged radially on both sides, the space between being just sufficient to allow the rope to enter and coil regularly upon the preceding lap. This method has the advantage of equalizing the work of the engine throughout the journey, for when the load is greatest, with the full cage at the bottom and the whole length of rope out, the duty required in the first revolution of the engine is measured by the length of the smallest circumference; while the assistance derived from gravitating action of the descending cage in the same period is equal to the weight of the falling mass through a height corresponding to the length of the largest lap, and so on, the speed being increased as the weight diminishes, and vice versa.

These consist essentially of links formed of a pair of parallel plates joined by a central bolt forming a scissors joint which is connected by chain links to the cage below and the winding-rope above.

To these things used to y listen at the time, through the mercy of God vouchsafed to me, noting them down, not on paper but in my heart, and constantly by the grace of God brood over my accurate recollections."These are priceless words, for they establish a chain of tradition (John-Polycarp-Irenaeus) which is without a parallel in early church history.

H is a pulley to guide the approaching and receding parts of the belt to and from the beam in parallel directions.

Parallel to this river, but more to the eastward, is the course of the Betwa.

Mimus polyglottus, the northern mocking-bird, inhabits the southern part of the United States, being in the north only a summer visitant; it breeds rarely in New England, is seldom found north of the 38th parallel, and migrates to the south in winter, passing that season in the Gulf States and Mexico.

They were to be, in general terms, the Sabine river, the 94th meridian (approximately), the Red river, the tooth meridian, the Arkansas river, and the 42nd parallel.

The western boundary claimed by the republic was the Rio Grande to its source and the meridian of longitude from that point to the forty-second parallel, although as a political division of Mexico its limits never extended farther west than the Nueces and the Medina.

Each of the molecules enumerated in expression (9) will move parallel to the edge of this cylinder, and each will describe a length equal to its edge in time dt.

The ground between the hills and the marshy valley of the Danube forms a defile through which the main road from DonauwOrth led to Ulm; parallel streams divide the narrow plain into strips.

The Orontes rises in the great springs of Labweh on the east side of the Buka`a, or inter-Lebanon district, very near the fountains of the southward-flowing Litani, and it runs due north, parallel with the coast, falling 2000 ft.

Other ranges, mostly of lower altitude, run parallel mainly to the east and west coasts.

Since the mountains as a rule traverse the island parallel to its coasts, the eastern shores have far less rain than the western.

Parallel to this shrinkage was the decrease in ranging sheep (82.0% from 1850-1900; 34.2% from 1890-1900), and cattle, once numerous in the hill counties of the west, and in the Connecticut Valley; Boston, then ranking after London as the second wool market of the world, and being at one time the chief packing centre of the country.

But it is important to notice that a parallel story (xx.) is without this distinctively Philistine background, and this variation is significant.

The male god Dagon has his partner Astarte (qq.v.), and Baal-zebub, a famous oracle of Ekron (2 Kings i.) finds a parallel in the local " baals " of Palestine.'

Head coverings also were gradually tabooed south of the 49th parallel.

Until the 9th century the only means for sighting cannon was by the " line of metal " - a line scored_ along the top of the gun, which, owing to the greater thickness of metal at the breech than at the muzzle, was not parallel to the axis.

These V's are so arranged that the axis of the sight frame is always parallel to that of the gun.

The pattern is that of a true sight, that is to say, the base plate is capable of movement about two axes, one parallel to and the other at right angles to the axis of the gun, and has cross spirit-levels and a graduated elevating drum and independent deflection scale, so that compensation for level of wheels can be given and quadrant elevation.

The fore-sight of the Krag-Jorgensen rifle, used in the United States army until 1906, consisted of a blade with parallel sides.

The highest mountain of the province is in its eastern part, Mount Savelan, with an elevation of 15,792 ft., and the Talish Mountains, which run from north to south, parallel to and at no great distance from the Caspian, have an altitude of 9000 ft.

As he surveyed the field from the windmill north of Fleurus it struck him as significant that Blucher's troops were disposed parallel to the Namur road, as if to cover a forward concentration, and not at right angles to it, as they would be had they been covering a retreat.

If the Prussians now retired northwards, parallel to the direction which Wellington would follow perforce on the morrow, the chance of co-operating in a decisive battle would still remain to the allies; and Gneisenau's order issued by moonlight, directing the retreat on Tilly and Wavre, went far to ensuring the possibility of such combined action.

There are also traces of the division of the lands in the immediate vicinity of the town into squares by parallel paths (decumani and cardines) at regular intervals of 1111 - Roman feet, postulating as the basis of the division a square with a side of 10,000 Roman feet, divided into 81 smaller squares - an arrangement which could not have existed at Puteoli, and must have arisen elsewhere.

The use of the square bricks familiarizes the scholar with the ideas of parallel lines, of equality of lengths, and of right angles.

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.

This implies the treatment of a plane or solid figure as being wholly comprised between two parallel lines or planes, regarded by convention as being vertical; the figure being generated by an ordinate or section moving at right angles to itself through a distance which is called the breadth of the figure.

The figures considered in § 22 are particular cases of the trapezium, which is a quadrilateral with two parallel sides.

The most important form of trapezium is that in which one of the two remaining sides of the figure is at right angles to the two parallel sides.

Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.

More briefly, the figure may be defined as a polyhedron with two parallel faces containing all the vertices.

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).

These formulae also hold for converting moments of a solid figure with regard to a plane into moments with regard to a parallel plane through the centroid; x being the distance between the two planes.

The first moment of a plane figure with regard to a line in its plane may be regarded as obtained by dividing the area into elementary strips by a series of parallel lines indefinitely close together, and concentrating the area of each strip at its centre.

Similarly the first moment of a solid figure may be regarded as obtained by dividing the figure into elementary prisms by two sets of parallel planes, and concentrating the volume of each prism at its centre.

This also holds for higher moments, provided that the edges of the elementary strips or prisms are parallel to the line or plane with regard to which the moments are taken.

Draw the tangents at A and B, meeting at T; draw TV parallel to the axis of the parabola, meeting the arc in C and the chord in V; and M draw the tangent at C, meeting AT and BT in a and b.

The line TCV is parallel to the axis of the parabola.

Hence the area of an ellipse whose axes are 2a and 2b is Trab; and the volume of an ellipsoid whose axes are 2a, 2b and 2c is t rabc. The area of a strip of an ellipse between two lines parallel to an axis, or the volume of the portion (frustum) of an ellipsoid between two planes parallel to a principal section, may be found in the same way.

In the case of the briquette the position of the foot of the ordinate u is expressed by co-ordinates x, y, referred to a pair of axes parallel to a pair of sides of the base of the briquette.

The briquette may usually be regarded as divided into a series of minor briquettes by two sets of parallel planes, the planes of each set being at successively equal distances.

A plane parallel to either pair of sides of the briquette is a " principal plane."

Suppose that we take a pair of parallel planes, such that the solid extends from one to the other of these planes.

The section by any intermediate parallel plane will be called a " cross-section."

The solid may then be regarded as generated by the cross-section moving parallel to itself and changing its shape, or its position with regard.

If the area of the cross-section, in every position, is known in terms of its distance from one of the bounding planes, or from a fixed plane A parallel to them, the volume of the solid can be expressed in terms of the area of a trapezette.

Then it may be shown that DE is parallel to AB, and that the area of the figure between chord DE and arc DE is half the sum of the areas DHA and EJB.

It follows from §§ 48 and 51 that, if V is a solid figure extending from a plane K to a parallel plane L, and if the area of every cross-section parallel to these planes is a quadratic function of the distance of the section from a fixed plane parallel to them, Simpson's formula may be applied to find the volume of the solid.

In the case of a pyramid, of height h, the area of the section by a plane parallel to the base and at distance x from the vertex is clearly x 2 /h 2 X area of base.

In the case of a wedge with parallel ends the ratio x2/h2 is replaced by x/h.

For a tetrahedron, two of whose opposite edges are AB and CD, we require the area of the section by a plane parallel to AB and CD.

Let the distance between the parallel planes through AB and CD be h, and let a plane at distance x from the plane through AB cut the edges AC, up -f- .

By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and r, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.

To extend these methods to a briquette, where the ordinate u is an algebraical function of x and y, the axes of x and of y being parallel to the sides of the base, we consider that the area of a section at distance x from the plane x = o is expressed in terms of the ordinates in which it intersects the series of planes, parallel to y=o, through the given ordinates of the briquette (§ 44); and that the area of the section is then represented by the ordinate of a trapezette.

Suppose, for instance, that u is of degree not exceeding 3 in x, and of degree not exceeding 3 in y, that it contains terms in x3y3, x 3 y 2, x2y3, &c.; and suppose that the edges parallel to which x and y are measured are of lengths 2h and 3k, the briquette being divided into six elements by the plane x=xo+h and the planes y = yo+k, y = yo+2k, and that the 12 ordinates forming the edges of these six elements are given.

To find the quantity of timber in a trunk with parallel ends, the areas of a few sections must be calculated as accurately as possible, and a formula applied.

At the Royal Mint the blanks are passed between the parallel faces of a revolving steel plate and fixed block.

A parallel is afforded by the history of Congregationalism in Scotland, which arose early in the 19th century through the evangelistic fervour of the Haldanes in an era of " moderatism "; also by the rise of the kindred Evangelical Union, shortly before the Disruption in 1843.

The horse-drawn hoe is steered by means of handles in the rear, but its successful working depends on accurate drilling of the seed, because unless the rows are parallel the roots of the plants are liable to be cut and the foliage injured.

The New York Central & Hudson River railway, nearly parallel with the water route from New York City to Buffalo, was formed by the union, in 1869, of the New York Central with the Hudson River railway.

The ripe ears of the last hang so as to become almost parallel with the stem; they are narrower and longer than in (b), owing to the grains being placed farther apart on the rachis; it includes the Chevalier variety, one of the best for malting purposes.

The latter have been connected by Ewald and others with the later doctrine of seven chief angels 25, parallel to and influenced by the Ameshaspentas (Amesha Spenta), or seven great spirits of the Persian mythology, but the connexion is doubtful.

There seems, however, no parallel to such a use of " angel," and it is doubtful whether the monarchical government of churches was fully developed when the Apocalypse was written.

The Northern Pacific sends a branch line south from Tacoma parallel with the coast to Portland on the Columbia river, where it meets the Southern Pacific and the Oregon Railroad & Navigation Company's line (a subsidiary of the Union Pacific), thus affording communication southwards, and up the valley of the Columbia to the east.

Following the increase of population north of the Columbia, the territory was divided, and Washington Territory was established on the 2nd of March 1853, with the river as the southern boundary to the point where it is intersected by the forty-sixth parallel, and thence along that parallel to the summit of the Rocky Mountains, thereby including portions of the present states of Idaho and Montana.

At J the displacement is forward, but since the curve at Q is parallel to the axis the displacement is approximately the same for all the points close to J, and the air is neither extended nor compressed, but merely displaced bodily a distance represented by JQ.

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.