Directions Sentence Examples

Her directions hadn't been far off.

She hated to ask for directions to another store.

Frustrated, Katie looked both directions down the pristine, eerily quiet hallway before following the kid toward the far end, where a bright red exit sign hung over the door.

I'm not good at directions.

While Dean wasn't familiar with the city, the rental-car agent marked directions to the hospital morgue and he had no trouble locating it.

In other directions the polarization becomes less and less complete as we approach the vertical.

In the distance, over the walls, he saw the flaming arrows streaking in both directions.

He changed directions and pulled on loose judo pants that settled low on his hips before replacing the red gem at his throat.

Garibaldi and a few followers, including his devoted wife Anita, after vainly attempting to reach Venice, where the tricolor still floated, took refuge in the pine forests of Ravenna; the Austrians were seeking him in all directions, and most of his legionaries were captured and shot.

The lush Scottish Highlands around him were covered in a blanket of snow that stretched for miles, the white world interrupted only by a few narrow roads snaking in different directions.

Carmen flipped through the book to the part on kidding problems and scanned down the directions.

Lana listened, chilled at the coldness and precision of his directions.

Winston assumed Dean would know his way back, and Dean was too embarrassed to ask for directions.

Without looking up or pausing in her typing she issued directions.

He took his time strolling down row after row of tents, paus­ing briefly to answer a young man's question about directions.

As I expected, Memon has doubled his presence to the north and is hedging in from all other directions.

In the early stages of the precipitation the polarization is complete in a perpendicular direction, and incomplete in oblique directions.

In place of its ancient fortifications Angouleme is encircled by boulevards known as the Remparts, from which fine views may be obtained in all directions.

After this victory the three princes Toghrul Beg, Chakir Beg and Ibrahim Niyal separated in different directions and conquered the Mahommedan provinces east of the Tigris; the last named, after conquering Hamadan and the province of Jebel (Irak i Ajami), penetrated as early as 1048, with fresh Ghuzz troops, into Armenia and reached Manzikert, Erzerutn and Trebizond.

If V be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth's centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have r2 (d/dr) (r 2 dV/dr) - - 4.rp = o.

But in other directions also she did good service.

The centres of the cotton trade are Hubli and Gadag, junctions on the Southern Mahratta railway, which traverses the district in several directions.

The manufacture of the cable, begun early in the following year, was finished in June, and before the end of July it was stowed partly in the American ship " Niagara " and partly in decided to begin paying out in mid-ocean, the two vessels, after splicing together the ends of the cable they had on board, sailing away from each other in opposite directions.

There is set up at once a certain hydrostatic pressure, due to the turgidity which ensues upon such absorption, and the extensible cell wall stretches, at first in all directions.

The growing apex of such a stem will alternately incline, first to one side and then to the other, exhibiting a kind of nodding movement in the two directions.

The reaction of the cells may be in two directions, moreover.

In these, under favorable conditions, streaming movements of the cytoplasm in various directions can be observed.

At each pole of this spindle figure there often occur fibres radiating in all directions into the cytoplasm, and sometimes a minute granular body, the centrosome, is also found there.

Surveys were then undertaken in several directions.

But in the 19th century and after exploring work was so generally and steadily maintained in all directions, and was in so many cases narrowed down from long journeys to detailed surveys within relatively small areas, that i t becomes desirable to cover the whole period at one view for certain great divisions of the world.

The rotation of the earth thus fixes the directions of north and south and defines those of east and west.

Further, the combinations B X Y and A X Y cannot be derived from each other, but both directly from A B X Y in two different directions.

The walls of these tertiary tubes send out, in all directions, canaliculi aeriferi which, ending in slight swellings, recall the mammalian aveoli.

But, close as the likeness is, it is merely a superficial likeness, because it is the result of opposite causes working in opposite directions.

In the course of this ceremony, after the sacrifice, men rush in all directions carrying torches; the women also carry fire-brands, or knock on the houses with rice-crushers and other heavy implements, and thus the evil spirits are considered to be driven away.

In the article on Solon (ad fin.) it is shown that the Solonian reforms, though they made a great advance in some directions, failed on the whole.

They at once began to conquer the surrounding country in all directions, and before two centuries had passed they had established themselves firmly at Kiev on the Dnieper, invaded.

Progress was to be made in certain directions and in a certain way.

This difficulty is not peculiar to railways; but it was in the history of railway economy and railway control that certain characteristics which are now manifesting themselves in all directions where large investments of fixed capital are involved were first brought prominently to public notice.

These rights, whether of monopoly or of subsidy, form a means of abuse in many directions.

It is not possible to do anything better with two-cylinder locomotives unless bobweights be added, but with four-cylinder four-crank engines complete balance is possible both in the vertical and in the horizontal directions.

The long hauls in the United States make it specially important that the cars should carry a load in both directions, and so bcx cars which have carried grain or merchandise one way are filled with wool, coal, coke, ore, timber and other coarse articles for the return journey.

A straight length of not less than 60 metres for the largest gauge and 40 metres for the smallest must be made between two curves having opposite directions.

In the old Egyptian church order, known as the Canons of Hippolytus, there are numerous directions for the service of the agape, held on Sundays, saints' days or at commemorations of the dead.

Lavas dip in all directions from the central crystalline core, pointing to the conclusion that the main portion of the mountain represents a single volcanic mass.

To what extent specific Babylonian influence showed itself in other directions is not completely known.

But the dispersion of the Jews was proceeding in directions which carried masses from the Asiatic inland to the Mediterranean coasts and to Europe.

In other directions progress was more rapid.

In other orchids movements take place in different ways and in other directions.

Meanwhile, the acquisition of Burma and the demarcation of boundaries had opened the way to the extension of geographical surveys in directions hitherto untraversed.

The Triassic deposits of the Verkhoyansk Range show that this land did not extend to the Bering Sea; while the marine Mesozoic deposits of Japan on the east, the western Tian-shan on the west and Tibet on the south give us some idea of its limits in other directions.

Among the islands of the Malay Archipelago the force of the monsoons is much interrupted, and the position of this region on the equator otherwise modifies the directions of the prevailing winds.

The China Sea is fully exposed to both monsoons, the normal directions of which nearly coincide with the centre of the channel between the continent of Asia and the eastern islands.

Climate.-Owing in part to the great differences in altitude in different regions of Caucasia and in part to the directions in which the mountain ranges run, and consequently the quarters towards which their slopes face, the climate varies very greatly according to locality.

In accordance with his directions, his body was dissected in the presence of his friends, and the skeleton is still preserved in University College, London.

The author then points out the great advantages of enclosure; recommends " quycksettynge, dychynge and hedgeyng "; and gives particular directions about settes, and the method of training a hedge, as well as concerning the planting and management of trees.

Meantime, while recurring again and again, as was his custom, to this cardinal difficulty, Mill worked indefatigably in other directions where he saw his way clear.

In the earliest times for which we have abundant material the economic life of England had already reached in certain directions a high degree of complexity.

There has never been in the history of English industry such licence as we find in certain directions in the earlier part of the 19th century.

It consists essentially of two rollers either both of wood, or one of wood and one of iron, geared to revolve in contact in opposite directions; the seed cotton is fed to the rollers, the lint is drawn through, and the seed being unable to pass between the rollers is rejected.

A powerful stimulus was thus given to the growth of cotton in all directions; a degree of activity and enterprise never witnessed before was seen in India, Egypt, Turkey, Greece, Italy, Africa, the West Indies, Queensland, New South Wales, Peru, Brazil, and in short wherever cotton could be produced; and there seemed no room to doubt that in a short time there would be abundant supplies independently of America.

Between these systems run the main rivers; and these naturally rise near the medial ridge, in the lacustrine district of el-Buka`a, or Coelesyria, and flow in opposite directions.

This aggressive character has a different aspect in several genera which are destitute of a central stylet, but in which the surface that is turned outwards upon eversion of the proboscis is largely pro- P. vided with nematocysts, sending the urticating rods of different sizes in all directions.

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.

Apart from the important part which he took in helping to co-ordinate and draft the Civil Code, Cambaceres did the state good service in many directions, notably by seeking to curb the impetuosity of the emperor, and to prevent enterprises so fatal as the intervention in Spanish affairs (1808) and the invasion of Russia (1812) proved to be.

Sailing directions for Lake Michigan, Green Bay, and the Strait of Mackinac, U.S. Navy Hydrographic office publication No.

Such a wall would be required to protect the clusters of dwellings around the Acropolis as well as the springs issuing from the rock, while the gates opening in various directions would give access to the surrounding pastures and gardens.

Coplanar substitution in four hydrogen atoms would involve the pushing apart of the iodine atoms in four horizontal directions.

These Dutch maps and charts are generally accompanied by descriptive notes or sailing directions printed on the back of them.

Combination can be made in five directions, viz.

But the progress in all directions has been too rapid to admit of any one adequate characterization.

Beyond the wall line on that side vestiges of ancient buildings are visible in various directions, and the plain is strewn with fragments of bricks, tiles and rubbish.

An extensive water-parting in the north central part of the state, an elevation whose inclination is almost imperceptible, determines the course of three great continental river systems. From this central elevation the land slopes off in all directions, rising again in the extreme north-east corner, where the rugged granite uplift in Cook county, known as the Misquah Hills, reaches an altitude of 2230 ft., the highest point in the state; and in the south-west corner, where an altitude of 1800 ft.

Kohlrausch formulated a theory of electrolytic conduction based on the idea that, under the action of the electric forces, the oppositely charged ions moved in opposite directions through the liquid, carrying their charges with them.

The verification of Kohlrausch's theory of ionic velocity verifies also the view of electrolysis which regards the electric current as due to streams of ions moving in opposite directions through the liquid and carrying their opposite electric charges with them.

In the additional explanatory notes at the end of the book, after directions as to the wearing of surplice and hood in quire, in cathedral and collegiate churches (they are not made obligatory elsewhere), bishops are directed to wear, besides the rochet, a surplice or alb, and a cope or vestment, with a pastoral staff borne either by themselves or their chaplains.'

His instructions were to demand an armistice, to intercept all supplies coming to the Turkish forces in the Morea from Africa or Turkey in general, and to look for directions to Stratford Canning (Lord Stratford de Redcliffe), the British ambassador at Constantinople.

Sheets of mica which have been subjected to earth-movements are frequently cracked and ridged parallel to these directions, and are then valueless for economic purposes.

The streets are of all widths, and of all degrees of crookedness, and run in all directions.

A network of military routes, constructed and kept in repair by the soldiers, led from Lambaesa in all directions, and stretched along the frontier as far as Leptis Magna, passing Theveste (Tebessa), Thenae and Tacape (Gabes).

Mention should also be made of a third method which has hardly yet been tried, namely, that of endeavouring to isolate one of the three "directions" by the method of suggestion or even hypnotic trance observations.

The planets in question appeared in the telescope as star-like objects which could be compared with the stars with much greater accuracy than a planetary disk like that of Mars, the apparent form of which was changed by its varying phase, due to the different directions of the sun's illumination.

His intellect was active in many directions; universal learning indeed was perhaps one of his foibles.

According to this theory the molecules of any magnetizable substance are little permanent magnets the axes of which are, under ordinary conditions, disposed in all possible directions indifferently.

For small bodies other than spheres the coefficient will be different, but its sign will always be negative for diamagnetic substances and positive for others; hence the forces acting on any small body will be in the same directions as in the case of a sphere' Directing Couple acting on an Elongated Body.

Ewing (Magnetic Induction, § 194) has devised an arrangement in which two similar test bars are placed side by side; each bar is surrounded by a magnetizing coil, the two coils being connected to give opposite directions of magnetization, and each pair of ends is connected by a short massive block of soft iron having holes bored through it to fit the bars, which are clamped in position by set-screws.

If, however, the permeability of the test rod differs from that of the standard, the number of lines of induction flowing in opposite directions through the two rods will differ, and the excess will flow from one yoke to the other, partly through the air, and partly along the path provided by the bent bars, deflecting the compass needle.

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

From these we can pass by gradual transitions in two directions, viz.

The interior of Cutch is studded with hills of considerable elevation, and a range of mountains runs through it from east to west, many of them of the most fantastic shapes, with large isolated masses of rock scattered in all directions.

In several directions many places once to be described among the environs have practically become suburbs of Edinburgh.

As a result of this compromise the budget of 1899 was passedlin little more than a month, and the commercial and tariff treaty with Austria were renewed till 1903.2 But the government had to pay for this complacency with a so-called " pactum," which bound its hands in several directions, much to the profit of the opposition during the " pure " elections of 1901.

But in five other directions also the frontiers were unregulated.

If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.

In directions other than these it is a more delicate question how the partial effects should be compounded.

The directions of the lateral spectra are such that the passage from one element of the grating to the corresponding point of the next implies a retardation of an integral number of wave-lengths.

If now we suppose the aperture AB to be covered by a great number of opaque strips or bars of width d, separated by transparent intervals of width a, the condition of things in the directions just spoken of is not materially changed.

These directions, in which the retardation between A and B is exactly mnX, may be called the principal directions.

In considering the relative brightnesses of the different spectra, it is therefore sufficient to attend merely to the principal directions, provided that the whole deviation be not so great that its cosine differs considerably from unity.

This is the ordinary formula for a reflecting plane grating, and it shows that the spectra are formed in the usual directions.

Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.

For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (r).

The affinities of this tribe have been sought in various directions, and the evidence suggests that it was itself of mixed blood.

Pretoria, Rustenberg, Lydenburg, and other smaller towns had been placed in a position of defence under the directions of Colonel Bellairs, who remained in command at Pretoria, the garrison consisting of a small number of troops and the loyal inhabitants.

In spite of this fact, however, the commission reported in favour of reform in various directions.

In the re- establishment of the field comets and in other directions a return was made to the republican forms of administration, and on the education question an agreement satisfactory to both the British and Dutch-speaking communities was reached.

The drop will consequently be more intensely illuminated when viewed along these directions of minimum deviation, and since it is these rays with which we are primarily concerned, we shall proceed to the determination of these directions.

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.

These vascular buds grow out in various directions as little solid projections of cells; they then become channelled and form the new but temporary meshwork.

But it was not in these directions that improvement was first looked for.

Broussais had done much to destroy the notion of fever as an entity, but by extravagances in other directions he had discredited the value of his main propositions.

Discovery in these various directions then led physicians to regard fever and inflammation not as separable entities, but as fluctuating symptomgroups, due to swervings of function from the normal balance under contingent forces.

In our conceptions of the later stages of assimilation and of excretion, with the generation of poisons (auto-intoxication) in the intestinal tract, there is still much obscurity and much guess-work; yet in some directions positive knowledge has been gained, partly by the physiologist, partly by the physician himself.

The postal area excludes part of Woolwich within the county; but includes considerable areas outside the county in other directions, as West Ham, Leyton, &c., on the east; Woodford, Chingford, &c., on the north-east; Wood Green, Southgate and Finchley on the north; Hendon and Willesden on the north-west; Acton and Ealing, Barnes and Wimbledon on the west; and Penge and Beckenham on the south, wholly or in part.

If, for a twocompartment shaft, a pair of drums (or a single wide drum) be keyed to the engine shaft, with the ropes wound in opposite directions, the hoisting is " in balance," that is, the cages and cars counterbalance each other, so that the engine has to raise only the useful load of mineral, plus the rope.

Thus they move simultaneously in opposite directions through a fixed length of stroke, say from 10 to 12 ft.

These books, except the Definitiones, mostly consist of directions for obtaining, from given parts, the areas or volumes, and other parts, of plane or solid figures.

Access to Chitral from the north is therefore but a matter of practicable tracks, or passes, in two or three directions, and the measure of practicability under any given conditions can best be reckoned from Chitral itself.

Regular crystals expand equally in all directions; rhombic and quadratic expand differently in different directions.

The coefficient of expansion is constant for such metals only as crystallize in the regular system; the others expand differently in the directions of the different axes.

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.

In the absence of a medium the inertia of the body to transtion is the same in all directions, and is measured by the (3) But the change of the resultant momentum F of the medium as.

The empire of Assyria was again ex- Assurnazir- tended in all directions, and the palaces, temples and pal III.

Gamaliel himself had given directions that his body was to be wrapped in the simplest possible shroud.

Not only does water move upwards, but it is transferred by capillarity in all directions through the soil.

He then proceeded to build a fortress there and gradually compelled the surrounding tribes to pay him tribute, extending his conquests in all directions (883-903) at the expense of the Khazars, who hitherto had held all southern Russia to tribute.

These pairs of observations have shown a parallax from which the elevation of the objects above the earth, the lengths and directions of their courses, &c. could be computed.

When the members of a shower are observed with special regard to their directions it is seen that they diverge from a common focus.

The process is gradual, and takes place in two directions, as heat or cold predominates.

Along with high intellectual powers in certain directions, he had a simplicity of nature charming in itself, but often calculated to render him the easy prey of sharpers.

Since the beginning of the 10th century strenuous efforts have been made to improve the sanitary condition by a new system of drainage, a better water service, the filling up of marshes wherein the malarial mosquito breeds, and in other directions.

Indeed, it may be doubted whether, in several directions, he ever surpassed the glorious things to be found in this most exquisite and most precious book.

In other directions also the expansion has been rapid; the village of Bornheim was incorporated in Frankfort in 1877, the former Hessian town of Bockenheim in 1895, and the suburbs of Niederrad, Oberrad and Seckbach in 1900.

To the specialists in sciences which were advancing rapidly and in divergent directions to results which often reacted on and transformed their initial assumptions, Spencer has often appeared too much of a philosopher and defective in specialist knowledge.

Plot he disregards, and he is fond of throwing his dialogues into regular dramatic form, with by-play prescribed and stage directions interspersed.

Pilate's place in the Christian tragedy, and perhaps also in the Creed, stimulated legend about him in two directions, equally unhistorical.

Laennec, to whom we are indebted for the practice of auscultation, freely admits that the idea was suggested to him by study of Hippocrates, who, treating of the presence of morbid fluids in the thorax, gives very particular directions, by 1 " Hippocrates Cous, primus quidem ex omnibus memoria dignus, ab studio sapientiae disciplinam hanc separavit, vir et arte et facundia insignis " (Celsus, De medicina).

During the greater part of the year it is either dry or occupied in part by a string of saline lakes (limans or ilmens); but in spring when the streams swell which empty into it, the water flows in two opposite directions from the highest point (near Shara-Khulusun).

Let a source of fluid be a point from which an incompressible fluid is emitted in all directions.

Internal communications include a railway about eight miles long from Valletta to Notabile; there are electric tramways and motor omnibus services in-several directions.

During his march a messenger from Omar arrived with a letter containing directions to return if he should have received it in Syria, but if in Egypt to advance, in which case all needful assistance would be instantly sent to him.

From this central point great lines of communication radiate in all directions to Russian, British, Persian and Afghan.

As far as the order to which he carried the approximations - which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.

Reynolds, in his investigation, introducing no new form of law of distribution of velocities, uses a linear quantity, proportional to the mean free path of the gaseous molecules, which he takes to represent (somewhat roughly) the average distance from which molecules directly affect, by their convection, the state of the medium; the gas not being uniform on account of the gradient of temperature, the change going on at each point is calculated from the elements contributed by the parts at this particular distance in all directions.

Taxation was in many directions reduced, and the financial exactions of the imperial officers controlled by the erection of a special court.

In other directions, though we find many salutary civil measures, yet there were no far-reaching schemes of reform.

Until modern times the city was built largely on floating pontoons or on piles at the edges of the innumerable canals and water-courses which formed the thoroughfares, but to meet the requirements of modern life, well-planned roads and streets have been constructed in all directions, crossing the old canals at many points and lined with well-built houses, for the most part of brick, in which the greater part of the erstwhile riparian population now resides.

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.

Helmholtz in his " Ophthalmometer " has employed Clausen's principle, but arranges the plates so that both move symmetrically in opposite directions with respect to the telescope axis.

In large mines where the air-ways are numerous and complicated, it often happens that currents travelling in opposite directions are brought together at one point.

The hills in the south of the duchy are a continuation of the Lorraine plateau, and the northern districts are crossed in all directions by outrunners from the Ardennes.

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

In the region of Galveston, along the northern section of the coast, where southerly or south-easterly winds from the Gulf prevail throughout the year, the climate is warm, moist and equable, but the moisture decreases westward and south-westward, and the equability, partly because of northerly winds during the winter months, decreases in all directions inland.

Yet besides the particular contribution that Aristotle made to idealistic philosophy in his logical and ethical interpretations, he advanced the case in two directions.

Railways run to Cuneo and Airasca (the latter on the TurinPinerolo line) and steam tramways in various directions.

They were restricted from granting peerages, and from dissolving parliament without directions from the successor.

As a matter of fact, no grass-plot is truly circular; and it might be found that if the breadth in various directions were measured more accurately the want of circularity would reveal itself.

We have therefore B in the first place to see whether the difference can be expressed in terms of the directions of the tangents.

The island is throughout mountainous, presenting from the sea in some directions the appearance of a series of jagged peaks.

When the armature is rotated, these two coils endeavour to place themselves in certain directions in the field so as to be perforated by the greatest magnetic flux.

The drainage of New York finds its way to the sea in various directions.

On both sides of the entrance to Delaware Bay Samuel Godyn, Samuel Blomaert and five other directors who were admitted to partner ship in the second year (1630) established the manor and colony of Swaanendael; on a tract opposite the lower end of Manhattan Island and including Staten Island, Michael Pauw established the manor and colony of Pavonia; on both sides of the Hudson and extending in all directions from Fort Orange (Albany) Kilian van Rensselaer established the manor and colony of Rensselaerwyck.

For the good of the Turkish race and the ultimate Ottoman State the Committee intended reformation in these directions as well.

In other directions, too, the teachings of Maholnet were to be judiciously revised, on the principle that the Prophet himself would never have allowed observance of any of his precepts to put his followers at a permanent disadvantage in competition with infidels.

Beyond the ground rises in steep slopes to a general level of over 1000 ft., the plateau being traversed in several directions by hills rising 2000 ft.

Let T, and T2 be the observed times of passage in the two directions.

If the rod is circular in section and perfectly uniform the end will describe a circle, ellipse or straight line; but, as the elasticity is usually not exactly the same in all directions, the figure usually changes and revolves.

Then, as we shall prove later, the vibrations of the string may be represented by the travelling of two trains in opposite directions each with velocity /tension=mass per unit length each half the height of the train represented in fig.

These are not really waves in the ordinary sense, but the disturbance arising from the passage through the medium in opposite directions of two equal trains.

The ordinate of the curve changes sign as we pass through a node, so that successive sections are moving always in opposite directions and have opposite displacements.

In order to justify the use of stationary waves we must show that two such trains can move in opposite directions over the same ground without modifying each other so long as the displacement in either is small.

To form stationary waves two equal trains must be able to travel in opposite directions with equal velocities, and to be superposed.

Let two trains of equal waves moving in opposite directions along such a string of indefinite length form the stationary system of fig.

The period during which the province had been a self-governing colony had been one of steady progress in most directions, but was greatly embittered by the educational policy pursued by General Hertzog.

To the south-east of this basin are the greatest mountain masses of the state; lofty and rugged ranges radiate in all directions, and in many instances rise to heights of 10,000-11,000 ft., the highest peak in the state being Granite Peak (12,834 ft.) in Carbon county.

From the standpoint of the post-exilic age, the older delineation of the history of Israel, especially in the books of Samuel and Kings, could not but appear to be deficient in some directions, while in other respects its narrative seemed superfluous or open toi misunderstanding, as for example by recording, and that without.

Steel has only a small difference of quality in different directions.

Generally a structure should be anchored at one point and free to move if possible in other directions.

Or generally, if M 1 M2 M3 are the moments of the external forces to the left of 0, A, and B respectively, and s, t and c the perpendiculars from 0, A and B on the directions of the forces cut by the section, then Ss=M11 Tt=M2andCc=M3.

The lines in the diagram represent the directions of a series of forces which must all be in equilibrium; these lines may, for an object to be explained in the next paragraph, be conveniently named by the letters in the spaces which they separate instead of by the method usually employed in geometry.

In other directions, too, Bienerth's period of government was filled with hostile nationalist proceedings.

Since Ultramontanism cannot hope to realise its political ambitions unless it succeeds in controlling the intellectual and religious life of Catholic Christendom, it attempts to extend its sphere of influence in all directions over culture, science, education, literature and the forms taken by devotion.

The current to be measured is passed through the coils of the electromagnet, then enters the mercury disk at the centre, flows through it radially in all directions, and emerges at the periphery.

The latter is slit radially, and the magnetic field is so arranged that it perforates each half of the disk in opposite directions.

Freeman advanced the study of history in England in two special directions, by insistence on the unity of history, and by teaching the importance and right use of original authorities.

The floor of the valley consequently slopes away in both directions, like the Chimen valley between the Akato-tagh and the Chimen-tagh; and in so far as it slopes westwards towards the Kum kol lakes it differs from nearly all the other great latitudinal valleys that run parallel with it, because they slope generally towards the east.

Some of its main streets (as their names indicate) follow the lines of canals, which still (though now covered) traverse the city in various directions.

Neither in the East nor in the West was a separation desired; but it was inevitable, since the lives of East and West were moving in different directions.

These treaties provided for reductions of duties in all directions, the most important concessions being on certain agricultural products.

But it is no more than an accident that this year constitutes the dividing line in both cases, the change in the United States being due to the Civil War, which so profoundly influenced the fiscal, economic and political history of the country in all directions.

The old gentleman in his aristocratic imperiousness frequently reminds us of the amusing directions given by Sir John Wynne to his chaplain, quoted in Pennant's Tour in Wales.

On the terraces the streets generally intersect at right angles, but on the hills their directions are irregular.

Sodamide was introduced by Claisen (Ber., 1905, 3 8, p. 6 93) as a condensing agent in organic chemistry, and has since been applied in many directions.

The prophets not only consoled and exhorted by the recital of what God had done and by predictions of the future, but they uttered extempore thanksgivings in the congregational assemblies, and delivered special directions, which might extend to the most minute details, as, for example, the disposal of the church funds.

After the beginning of the 3rd century there were still no doubt men under the control of the hierarchy who experienced the prophetic ecstasy, or clerics like Cyprian who professed to have received special directions from God; but prophets by vocation no longer existed and these sporadic utterances were in no sense placed on a level with the contents of the sacred Scriptures.

In ethical precepts, in directions for right living (that is, asceticism), the two systems approximate more and more closely.

The works of the pseudoDionysius contain a gnosis in which, by means of the teaching of Iamblichus and Proclus, the church's theology is turned into a scholastic mysticism with directions on matters of practice and ritual.

It was retarded and took false directions until the revival of learning in Italy.

He proposed the term " mutations " for the minute progressive changes of single characters in definite directions as observed in successive stratigraphic levels.

This definitely directed evolution, or development in a few determinable directions, has since been termed " orthogenetic evolution," and is recognized by all workers in invertebrate palaeontology and phylogeny as fundamental because the facts of invertebrate palaeontology admit of no other interpretation.

Starting with the stem forms the descendants of which have passed through either persistent or changed habitats, we reach the underlying idea of the branching law of Lamarck or the law of divergence of Darwin, and find it perhaps most clearly expressed in the words "adaptive radiation" (Osborn), which convey the idea of radii in many directions.

Among extinct Tertiary mammals we can actually trace the giving off of these radii in all directions, for taking advantage of every possibility to secure food, to escape enemies and to reproduce kind; further, among such well-known quadrupeds as the horses, rhinoceroses and titanotheres, the modifications involved in these radiations can be clearly traced.

The only inkling of possible underlying principles in this orderly process is that there appears to be in respect to certain characters a potentiality or a predisposition through hereditary kinship to evolve in certain definite directions.

Medusae capture their prey, consisting of small organisms of various kinds, especially Crustacea, by means of the tentacles which hang out like fishing-lines in all directions.

Scarcely was the Society launched when its members dispersed in various directions to their new tasks.

The country about the Laguna de Terminos is low and flat, and is traversed in all directions by deep, sluggish streams. Many of the rivers crossing the lowlands bordering the Gulf have short navigable channels, the most important of which is the Panuco and its tributaries.

When this large body of scholars were set down to their task, an elaborate set of rules was drawn up for their guidance, which contained a scheme of revision as well as general directions for the execution of their work.

Thus, animism is in some directions little developed, so far as we can see, among the Australian aborigines; but from those who know them best we learn that they believe in innumerable spirits and bush bogies, which wander, especially at night, and can be held at bay by means of fire; with this belief may be compared the ascription in European folk belief of prophylactic properties to iron.

The old town centres in the Plaza del Mercado, from which narrow and tortuous lanes radiate in various directions; the new one dates, from about the middle of the 18th century, and its streets are wide and straight.

The remaining fragments were, under the directions of the Royal Society, reduced by Dr Wallis to a compact form, with the heading Astronomia Kepleriana defensa et promota, and published with numerous extracts from the letters of Horrocks to Crabtree, and a sketch of the author's life, in a volume entitled Jeremiae Horroccii opera posthuma (London, 1672).

But many of the directions are much too serious and fundamental to have been given in this form; one can hardly imagine that Paul considered Timothy (or Titus) still in need of elementary advice and warning upon such matters, and especially on personal purity.

In addition to these non-marine formations of the west, there is the widespread Lafayette formation, which covers niuch of the Atlantic and Gulf coastal plain, reaching far to the north from the western Gulf regio,1, and having uncertain limits, so far as now worked out, in various directions.

After the war of 1812 new outlets were found in all directions, and the I

In the course of time the status of the ceorl was probably reduced; but although his political power was never large, and in some directions his freedom was restricted, it hardly seems possible previous to the Norman Conquest to class him among the unfree.

In 1788 when the Danes unexpectedly invaded Sweden and threatened Gothenburg, it was Armfelt who under the king's directions organized the Dalecarlian levies and led them to victory.

He extended the rights of the natives, and in certain directions curtailed the privileges of Europeans.

The divide between the rivers flowing west and those flowing east and north is very sharp in the southern Rocky Mountains, but there are two lakes, the Committee's Punch Bowl and Fortress Lake, right astride of it, sending their waters both east and west; and there is a mountain somewhat south of Fortress Lake whose melting snows drain in three directions into tributaries of the Columbia, the Saskatchewan and the Athabasca, so that they are distributed between the Pacific, the Atlantic (Hudson Bay) and the Arctic Oceans.

After The Dates Of Commencement Of The Successive Hebrew Years Are Finally Adjusted, Conformably With The Foregoing Directions, An Estimation Of The Consecutive Intervals, By Taking The Differences, Will Show The Duration And Character Of The Years That Respectively Intervene.

Mazarin was not a Frenchman, but a citizen of the world, and always paid most attention to foreign affairs; in his letters all that could teach a diplomatist is to be found, broad general views of policy, minute details carefully elaborated, keen insight into men's characters, cunning directions when to dissimulate or when to be frank.

Main lines run also from Turin toVercelli and thence to Novara and Milan (the direct route), to Casale Monferrato, to Alessandria (and thence to Piacenza or Genoa), to Genoa via Asti and Acqui, to Bra and Savona, and branch lines to Lanzo, Torre Pellice, Aosta, Rivoli, Rivarolo, &c., and steam tramways in various directions.

It is connected with the Zuider Zee by a fine canal protected by a large sea-lock (1828), and has regular steam-boat communication in various directions.

As a fact, the commanders-in-chief on the East Indies and Cape of Good Hope stations were instructed that in consequence of the great practical difficulty of proving - at ports so remote from the scene of war operations as Aden and Perim - the real destination of contraband of war carried by vessels visiting those parts, directions were to be given to the officers concerned to cease to search such vessels, and to merely report to the commander-in-chief at the Cape the names of ships suspected of carrying contraband, and the date of clearance.

The main effects we have to discuss are (I) a symmetrical widening, (2) a shift of wave-length, which when it accompanies expansion in both directions may appear as an unsymmetrical widening, (3) a change in the relative intensities of the lines.

The cadmium line having a wave-length of 2288 A broadens by pressure equally in both directions, but if mercury be added the broadening is more marked on the less refrangible side.

The establishment of Dominion government agencies, the formation of a local government, the machinery required for the government of the province, the influx of a small army of surveyors who mapped out and surveyed wide districts of the country, and the taking up of free lands in all directions by Canadian settlers, all tended to build up the hamlet of Winnipeg into a considerable town.

Somewhere about this period of More's life two things happened which gave in opposite directions the determining impulse to his.

On the other hand, under the influence of the mechanics of his day, which had hardly distinguished between inertia, or the inability of a body to change itself, and resistance or the ability of bodies to oppose one another, he concluded that, as inertia is passive, so is resistance, and refused to recognize that in collision the mutual resistance of moving bodies is a force, or active power, of changing their movements in opposite directions.

Asturias consists of a portion of the northern slope of the Cantabrian Mountains,and is covered in all directions with offshoots from the main chain, by which it is almost completely shut in on the south.

Following the first chart of lines of equal variation compiled by Edmund Halley in 1700, charts of similar type have been published from time to time embodying recent observations and corrected for the secular change, thus providing seamen with values of the variation accurate to about 30' of arc. Possessing these data, it is easy to ascertain by observation the effects of the iron in a ship in disturbing the compass, and it will be found for the most part in every vessel that the needle is deflected from the magnetic meridian by a horizontal angle called the deviation of the compass; in some directions of the ship's head adding to the known variation of the place, in other directions subtracting from it.

The additions of velocity which the two bodies receive respectively, relative to such a base, are in opposite directions, and if the bodies are alike their magnitudes are equal.

When, as in the case of contact, a mutual relation is perceived between the motions of two particles, the changes of velocity are in opposite directions, and the ratio of their magnitudes determines the ratio of the masses of the particles; the motion being reckoned relative to any base which is unaffected by the change.

The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.

Thus each mutual action is associated with a pair of equal forces in opposite directions.

No correction for any defect in it has been found necessary; moreover, no rotation of the base relative to the directions of the stars without proper motion has been detected.

The movement in opposite directions of these charged ions constitutes the electric current in the solution.

But recent experiments have shown that the simple theory of coagulation here outlined needs amplification in certain directions.

Besides various sermons, Gleig was the author of Directions for the Study of Theology, in a series of letters from a bishop to his son on his admission to holy orders (1827); an edition of Stackhouse's History of the Bible (1817); and a life of Robertson the historian, prefixed to an edition of his works.

In 1710, after the lords proprietors had issued directions for "the building of a town to be called Beaufort Town," in honour of Henry Somerset, duke of Beaufort (1629-1700), the first permanent settlement was established on the island.

Gears are provided for elevating, levelling, aligning the upper and lower optical systems, adjusting the inclination of the reflector and rotating the mast around a vertical axis so that observations may be made and azimuth angles taken in all directions.

This ceased at Rome at the same time as the apparel disappeared; but two relics of it survive - (I) in the directions of the Missal for putting on the amice, (2) in the ordination of subdeacons, when the bishop lays the vestment on the ordinand's head with the words, "Take the amice, which symbolizes discipline over the tongue, &c."

In the case of the two leading Church of England societies, the bishops (being members) are ex officio on all executive committees; but their labours in other directions prevent their ordinarily attending.

In shape Milan is a fairly regular polygon, and its focus is the splendid Piazza del Duomo, from which a number of broad modern streets radiate in all directions.

This, between the Dauphine and the borders of Hungary, forms a broad band convex towards the north, while most of the valleys lie between the directions west to east and south-west to north-east.

Pruning, or the removal of superfluous growths, is practised in order to equalize the development of the different parts of trees, or to promote it in particular directions so as to secure a certain form, and, by checking undue luxuriance, to promote enhanced fertility.

Care should be taken, however, not to hem in the garden by crowded plantations, shelter from the prevailing strong winds being all that is required, while the more open it is in other directions the better.

As therefore the disks revolve, these carriers travel in opposite directions, coming at intervals in opposition to each other.

Besides the Reit Diep, there are the Ems Canal and the Damster Diep, connecting it with Delfzyl and the Dollart, the Kolonel's Diep with Leeuwarden, the Nord Willem's Canal with Assen and the south and the Stads-Canal south-east with the Ems. Hence steamers ply in all directions, and there is a regular service to Emden and the island of Borkum via Delfzyl, and via the Lauwers Zee to the island of Schiermonnikoog.

The remarkable stability of the mountain appears to be due to the innumerable dikes which penetrate the lava flows and tuff beds in all directions and thus bind the whole mass together.

The notes of this journey are written in a light and amusing style, showing Hume's usual keenness of sight in some directions and his almost equal blindness in others.

The new house to which he alludes was built under his own directions at the corner of what is now called St David Street after him; it became the centre of the most cultivated society of Edinburgh.

These plateaus, with an average elevation of Boo to 1000 ft., are mostly covered with forests of oak, beech and lime, and are deeply cut by river valleys, some being narrow and craggy, and others broad, with gentle slopes and marshy bottoms. Narrow ravines intersect them in all directions, and they often assume, especially in the east, the character of wild, impassable, woody and marshy tracts.

We find traces of such additions within the New Testament itself in such directions as are contained in Col.

An important character of blende is the perfect dodecahedral cleavage, there being six directions of cleavage parallel to the faces of the rhombic dodecahedron, and angles between which are 600.

The management of the Prussian railway system is committed to the charge of twenty directions, into which the whole network of lines is divided, being those of Altona, Berlin, Breslau, Bromberg, Danzig, Elberfeld, Erfurt, Essen ad.

It is probable, therefore, that in other directions also the Germans had considerably advanced their frontier southwards at a comparatively recent period.

It is in these directions that the reign of Henry the Fowler marks a stage in the history of, ,Germany.

Yet, notwithstanding his policy, in these directions the German nobles appear to have been enthusiastically devoted to Frederick.

In other directions, however, he was more fortunate.

About 1323 Louis had secured the mark of Brandenburg for his son Louis, and he was eager to aggrandize his family in other directions.

In 1576, when Milan was visited by the plague, he went about giving directions for accommodating the sick and burying the dead, avoiding no danger and sparing no expense.

Even smaller mean values have been found for the angle between the auroral and magnetic " zeniths " - as the two directions have been called - e.g.

Birkeland (19), who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.

At Tasiusak (10) in 1898-1899 the magnetic directions of the principal types were noted separately.

One end only, for example, may appear to move, as if rotating round the other; or the two ends may move in opposite directions, as if the arc were rotating about a vertical axis through its summit.

Under such directions the Murabtis were brought to excellent order.

Motion of the ground in the direction os actuates only the lever so'p', motion in the direction o's actuates only sop, whilst motion in inter mediate directions actuates both.

So much for abrogated readings; the case is somewhat different when we come to the abrogation of laws and directions to the Moslems, which often occurs in the Koran.

Thus, for example, the Koran contains very different directions, suited to varying circumstances, as to the treatment which idolaters are to receive at the hands of believers.

Believers receive general moral instruction, as well as directions for special circumstances.

A part of the Medina pieces consists of formal laws belonging to the ceremonial, civil and criminal codes; or directions about certain temporary complications.

The death of Heinrich Brugsch in 1895 was a very severe blow to demotie studies; but it must be admitted that his brilliant gifts lay in other directions than exact grammatical analysis.

This method was carried on up to the point of getting contact with the facingplate at every inch of the surface; the cuts cross in various directions.

This continuum was held to render possible conduction in all directions throughout the grey matter of the whole nervous system.

The fact that conduction occurred preponderantly in certain directions was explained by appeal to a hypothetical resistance to conduction which, for reasons unascertained, lay less in some directions than in others.

Among the properties of the neuron is conductivity in all directions.

It is a plausible conjecture that the original narratives of J and E also contained directions for the construction of an ark,' as a substitute for the personal presence of Yahweh, and also for the erection of a "tent of meeting" outside the camp, and that these commands were omitted by R P in favour of the more elaborate instructions given in ch.

Extensions of pragmatism in a variety of directions readily suggest themselves, and indeed only the doctrine of truth in the above sketch can be treated as strictly indispensable.

There is no exclusive apical growth, and the cells divide in all directions.

On some of the platforms there are upwards of a dozen images, now thrown from their pedestals and lying in all directions.

Where a rock yields to weather with considerable uniformity in all directions it is likely to assume conical forms in the progress of denudation.

In 1833 Scottish burghs were for the first time entitled to be governed by directly-elected bodies, and at various times since that date fuller powers of legal self-government were granted in different directions.

But there are several directions in which the field of variation appears to be not only limited but defined in a certain direction.

The book contains rules for the conduct of the anchoresses, and gives liturgical directions for divine service; but the greater part of it is taken up with the purely spiritual side of religion.

Information as to the field sports of the ancients is in many directions extremely fragmentary.

While in some counties the sport has suffered, towns men who formerly would have been too far from a meet can now secure transport for themselves and their horses in all directions; and as a consequence, meets of certain packs are not advertised because of the number of strangers who would be induced to attend.

Round about London a man who is bent on the pursuit of fox or stag may gratify his desire in many directions.

The Franco-German War engaged Flach's activities in other directions, and he spent two years (described in his Strasbourg apres le bonabardement, 1873) at work on the rebuilding of the library and the museum, which had been destroyed by Prussian shells.

Many of these risings were due to the intrigues of the Church party, and in view of these circumstances President Alfaro curtailed the influence of the clergy in several directions.

It consists of two parabolic branches tending in opposite directions.

Incidentally this involved an extension of plebeian privilege in two directions.

When there are fissures radiating in several directions it is called "star shake."

This last sentence has led some modern writers to suppose that he made two different voyages; but this is improbable; the expressions of Polybius imply that his explorations in both directions, first towards the north and afterwards towards the east, formed part of the same voyage.

While they are journeying two and two in various directions St Mark takes occasion to tell us the current conjectures as to who Jesus really was.

Since CE equals BE these directions are equally inclined to, and coplanar with, the normal to the mirror.

But in those forms where curving must take place in different directions the layers or fibres of metal are made to glide over one another, extension taking place in some layers but not in others, and this goes on without producing much reduction in the thickness.

The cliffs are honeycombed in all directions with military works.

The shaken masses then gave way one after the other, and the Scots fled in all directions.

Later on, by the discovery of a new continent, commerce was diverted into new directions.

But the name of Clive exercised a decisive effect in both directions.

In the sailing directions, issued in 1561, for the use of this expedition the phrase " las Islas Filipinas " was used as applying to the entire archipelago.

If both the bodies are luminous, especially if they do not differ much in brilliancy, the motion of revolution is shown by a periodic doubling of the lines of the spectrum; when one body is moving towards us and the other away their spectral lines are displaced (according to Doppler's principle) in opposite directions, so that all the lines strong enough to appear in both spectra appear double; when the two bodies are in conjunction, and therefore moving transversely, their spectra are merged into one and show nothing unusual.

The Streams. motion of the stars in the mean towards Canis Major is thus a resultant motion, which, when examined more minutely, is found to be due to the intermingling of two great streams of stars moving in very different directions.

This hypothesis of two star-drifts does not imply that all the stars move in one or other of two directions.

The older one - which may be called the " one-drift " hypothesis, since according to it the stars appear to form a single drift moving away from the solar apex - requires that the apparent directions of motion should be so distributed that fewest stars are moving directly towards the solar apex, and most stars along the great circle away from the solar apex, the number decreasing symmetrically, for directions inclined on either side of this great circle, according to a law which can be calculated.

The deviation is unmistakable; in general the direction from the solar apex is not the one in which most stars are moving; and, what is even more striking, the directions, in which most and fewest stars respectively move, are not by any means opposite to one another.

Our first inquiry is whether the universe extends indefinitely in all directions, or whether there are limits beyond which the stars Limits of are not distributed.

Various considerations tend to show that this apparent crowding does not imply a really greater density or clustering of the stars in space, but is due to the fact that in these directions we look through a greater depth of stars before coming to the boundary of the stellar system.

Imagine this stratum to be uniformly filled with stars (of course in the actual universe instead of sharply defined boundaries AB and CD, we shall have a gradual thinning out of the stars) it follows that in the two directions SP and SP' the fewest stars will be seen; these then are the directions of the galactic poles.

As we consider a direction such as SQ farther and farther from the pole the boundary of the universe in that direction becomes more and more remote so that more stars are seen, and finally in the directions SR and SR' in the galactic plane, the boundary is perhaps beyond the limits of our telescopes.

That the universe must have a boundary in the directions SR and SR', we can hardly doubt, but nothing is known of its shape or distance except that in all directions it must be far greater than SP or SP'; in particular it is not known whether the sun is near the centre or otherwise.

A glance at the Milky Way, with its sharply defined irregular boundaries, its clefts and diverging spur, is almost sufficient to assure us that it is a real cluster of stars, and does not merely indicate the directions in which the universe extends farthest.

The god here states that he is about to send a deluge, which will cause destruction to all mankind, and he gives directions for the building of a great ship in which "the beasts of the field and the birds of heaven" may be saved, along with Ut-napishtim and his family; he fixes the size of the ship and directs that it should be covered with a strong roof or deck.

His services to industry included his improvements in the processes for the manufacture of sulphuric acid (1818) and oxalic acid (1829); methods of estimating the amount of real alkali in potash and soda by the volume of standard acid required for neutralization, and for estimating the available chlorine in bleaching powder by a solution of arsenious acid; directions for the use of the centesimal alcoholometer published in 1824 and specially commended by the Institute; and the elaboration of a method of assaying silver by a standard solution of common salt, a volume on which was published in 1833.

As was to be expected, they were worsted; eleven small flying columns of the Moslems, sent out in various directions, sufficed to quell the revolt.

After the restoration of peace his capacity for organization was displayed in all directions.

The fact that a great number of these serfs had been enjoying protection as free ceorls in former ages made itself felt, however, in three directions.

Quaternions (as a mathematical method) is an extension, or improvement, of Cartesian geometry, in which the artifices of co-ordinate axes, &c., are got rid of, all directions in space being treated on precisely the same terms. It is therefore, except in some of its degraded forms, possessed of the perfect isotropy of Euclidian space.

Also let us assume (a) space to have the same properties in all directions, and make the convention (b) that to change the sign of any one factor changes the sign of a product.