Distances Sentence Examples

This pumping action results in an extremely rapid circulation of the heating agent, enabling long distances to be traversed without much loss of heat.

Birds are even more effective than wind in transporting seeds to long distances.

He looked away and turned his back to her, stance guarded as he paced short distances back and forth, like a caged panther.

The problem, however, of constructing a deep-sea cable satisfactorily, with suitable inductance coils inserted at short distances apart, is a difficult one, and one which it cannot be said has been solved.

Eusebius in his Onomasticon uses it as a central point from which the distances of other towns are measured.

These include the mutual distances of some of the stars in the Pleiades, a few observations of the apparent diameter of the sun, others of the distance of the moon from neighbouring stars, and a great number of measurements of the diameter of the moon.

That to fit the actions and distances covered by Alexander into such a scheme, assuming that he went by Seistan and Kandahar, would involve physical impossibilities has been pointed out by Count Yorck v.

The tangent at any point bisects the angle between the focal distances of the point, and the normal is equally inclined to the focal distances.

Owing to the great distances which must be covered, and also to the defective means of communication in sparsely settled districts, the costs of the postal service in Argentina are unavoidably high in relation to the receipts.

This only answers, however, for telephoning musical sounds to short distances.

In the first, the Periplus of the Outer Sea, in two books, in which he proposed to give a complete description of the coasts of the eastern and western oceans, his chief authority is Ptolemy; the distances from one point to another are given in stades, with the object of rendering the work easier for the ordinary student.

Others are navigable only for short distances by steamers of light draught.

The fundamental difference between the two methods is that while the mechanical energy developed by a steam engine is in the first case applied directly to the driving-axle of the locomotive, in the second case it is transformed into electrical energy, transmitted over relatively long distances, and retransformed into mechanical energy on the driving-axles of the train.

The horsemen were splendidly audacious in riding for long distances into the heart of a hostile country, without support, striking some terrific blows, and then returning rapidly beyond reach of pursuit.

It is obliged also to form entrepots for the storage of the crops at reasonable distances from each other, and, on certain conditions, to grant advances to cultivators to aid them in raising the leaf.

Mine cars are sometimes run long distances, singly or in trains, over roads which are given sufficient grade to impart considerable speed by gravity, say from I to 21%.

Locomotive haulage is applicable to large mines, where trains of cars are hauled long distances on flat or undulating roads of moderate gradients.

Brushwood and rough pasturage of some sort is found almost everywhere, except in the neighbourhood of the larger settlements, where forage and firewood have to be brought in from long distances.

It is the point from which all distances in Japan are measured.

Migrants proceeding long distances generally go by preference to one of the great cities of commerce or industry.

However, the development of electric power, and the possibility of transmitting it for long distances, have worked a noteworthy change in this respect, and a large number of industries have been added in recent years.

Hence also sick persons are frequently conveyed long distances to a sacred river to heal them of their maladies; and for a dying man to breathe his last at the side of the Ganges is devoutly believed to be the surest way of securing for him salvation and eternal bliss.

It can be moved (by its own locomotive power, if desired) long distances without requiring any complicated means of conveying power to it; and it is rapid in work, fairly economical, and can be adapted to the most varying circumstances.

In this manner Trowbridge showed that signalling might be carried on over considerable distances by electric conduction through the earth or water between places not metallically connected.

The magnetic and electric forces are directed alternately in one direction and the other, and at distances which are called multiples of a wave length the force is in the same direction at the same time, but in the case of damped waves h.as not quite the same intensity.

In his method three vertical antennae are employed, placed at equidistant distances, and oscillations are created in the three with a certain relative difference of phase.

Pupin showed that by placing inductance coils in circuit, at distances apart of less than half the length of the shortest component wave to be transmitted, a non-uniform conductor could be made approximately equal to a uniform conductor.

The capacity of camels for travelling long distances without water - owing to special structural modifications in the stomach - is familiar to all.

There are, however, considerable reductions for distances over 93 m., on a scale increasing in proportion to the distance.

The Rhone and the Saone are navigable for considerable distances in the department; the chief railway is that of the Paris-LyonMediterranee Company, whose line from Macon to Culoz traverses the department.

A mean degree of the meridian being assumed to be 69-09 statute miles of 5280 ft., the nautical mile (A l b - degree) is taken as 6080 ft., which is a sufficiently close approximation for practical purposes, and the distances between the knots are made to bear the same relation to 6080 ft.

They can apply to the police commissaries (stanovoti) or to the justices of the peace; but the great distances to be traversed in a country so sparsely populated makes this course highly inconvenient.

So much of the expense of the handling, both of freight and of passengers, was independent of the length of the journey that a mileage rate sufficiently large for short distances was unnecessarily burdensome for long ones, and was bound to destroy long-distance traffic, if the theory were consistently applied.

For suburban traffic with a service at a few minutes' interval and short distances between the stations electric traction has proved itself to be superior in many respects to the steam locomotive, but for main line traffic and long distance runs it has not yet been demonstrated that it is commercially feasible, though it is known to be practically possible.

In America and other countries where distances are great and passengers have to spend several days continuously in a train sleeping and restaurant cars are almost a necessity, and accordingly are to be found on most important through trains.

In the United Kingdom, where the distances are comparatively small, sleeping and dining cars must be regarded rather as luxuries; still even so, they are to be met with very frequently.

Over shorter distances still more rapid running is occasionally arranged, and in Great Britain, France and the United States there are instances of trains scheduled to maintain an average speed of 60 m.

On the other hand, where, as in America, the great volume of freight is raw material and crude food-stuffs, and the distances are great, a low charge per unit of transportation is more important than any consideration such as quickness of delivery; therefore full car-loads of freight are massed into enormous trains, which run unbroken for distances of perhaps 1000 m.

The other, or central, pair of tracks is for trains making stops at longer distances.

At a printing-press established in Walther's house by Regiomontanus, Purbach's Theoricae planetarum novae was published in 1472 or 1473; a series of popular calendars issued from it, and in 1474 a volume of Ephemerides calculated by Regiomontanus for thirty-two years (1474-1506), in which the method of "lunar distances," for determining the longitude at sea, was recommended and explained.

The forests of Peak and Duffield had their separate courts and officers, the justice seat of the former being in an extra-parochial part at equal distances from Castleton, Tideswell and Bowden, while the pleas of Duffield Forest were held at Tutbury.

In 1879, at Kilburn, the competition was of railway waggons to convey perishable goods long distances at low temperatures.

The lemniscate of Bernoulli may be defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and is equal to the square of half the distance between these points.

Among these lavas is the "pipe" amygdaloid of which many blocks have been transported great distances down the Vaal river.

Many ingenious devices for forming bars have been produced; but generally a strong frame is used, across which steel wires are stretched at distances equal to the size of the bars to be made, the blocks being first cut into slabs and then into bars.

In the case of more considerable distances, however, a globe of suitable size should be consulted, or - and this seems preferable - they should be calculated by the rules of spherical trigonometry.

These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle.

These direct distances may of course differ widely with the distance which it is necessary to travel between two places along a road, down a winding river or a sinuous coast-line.

Distances such as these can be measured only on a topographical map of a fairly large scale, for on general maps many of the details needed for that purpose can no longer be represented.

On the other hand a map drawn on the surface of a sphere representing a terrestrial globe will prove true to nature, for it possesses, in combination, the qualities which the ingenuity of no mathematician has hitherto succeeded in imparting to a projection intended for a map of some extent, namely, equivalence of areas of distances and angles.

Other accessories are an hour-circle, around the north pole, a compass placed beneath the globe, and a flexible quadrant used for finding the distances between places.

In compiling his map he was able to avail himself of the information obtained by the bematists (surveyors who determined distances by pacing) who accompanied Alexander the Great on his campaigns; of the results of the voyage of Nearchus from the Indus to the Euphrates, and of the " Periplus " of Scylax of Caryanda, which described the coast from between India and the head of the Arabian Gulf.

The errors due to an exaggeration of distances were still further increased on account of his assuming a degree to be equal to Soo stadia, as determined by Posidonius, instead of accepting the 700 stadia of Eratosthenes.

These charts are based upon estimated bearings and distances between the principal ports or capes, the intervening coast-line being filled in from more detailed surveys.

On the i r th of October, when they began their march, the road along the Danube was swept into the river, carrying with it several guns and teams, and hours were consumed in passing the shortest distances.

Both the eastern and the western part of the city were formerly enclosed by brick walls, with large round towers at the principal angles and smaller towers intervening at shorter distances, the whole surrounded by a deep fosse.

Owing to the distances over which they are carried and the bad organization of trade, all manufactured articles are exceedingly dear, especially in the east.

By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the parallax derived from each.

The distances of these bodies at the times of opposition were somewhat less than unity, though more than twice as great as that of Mars in 1877.

At shorter distances the magnetism induced in the weaker magnet will be stronger than its permanent magnetism, and there will be attraction; two magnets with their like poles in actual contact will always cling together unless the like poles are of exactly equal strength.

The yoke has two projecting pieces C, C' at unequal distances from the knife-edges, and separated from the blocks B, B' by narrow air-gaps.

The celluloid sheet is laid upon the squared paper, and in plotting a curve horizontal distances are reckoned from the proper demagnetization line instead of from the vertical axis.

Mangrove swamps, lagoons and marshes, with inland canals following the coast line for long distances, are characteristic features of a large extent of the Brazilian coast.

The former reach the coastal plain over long and gradual descents, and are navigable for considerable distances.

The latter descend from the plateau much nearer the coast, and are in most cases navigable for short distances only.

Brazil is lamentably deficient in steamship communication considering its importance in a country where the centres of population are separated by such distances of coasts and river.

Laplace was, moreover, the first to offer a complete analysis of capillary action based upon a definite hypothesis - that of forces "sensible only at insensible distances"; and he made strenuous but unsuccessful efforts to explain the phenomena of light on an identical principle.

The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

In different gratings the lengths of the spectra and their distances from the axis were inversely proportional to the grating interval, while with a given grating the distances of the various spectra from the axis were as i, 2, 3, &c. To Fraunhofer we owe the first accurate measurements of wave-lengths, and the method of separating the overlapping spectra by a prism dispersing in the perpendicular direction.

In order to find the difference of optical distances between the courses QAQ', QPQ', we have to express QP-QA, PQ'-AQ'.

Land went up in value, and farms, many of them at comparatively remote distances from the goldfields, were sold at enormously enhanced prices.

The spurious bows he showed to consist of a series of dark and bright bands, whose distances from the principal bows vary with the diameters of the raindrops.

The prince, seeing the opportunity for a battle, immediately issued orders for an enveloping attack on Miinchengratz by his whole army, but, owing to distances and the number of units now requiring direction, it was late in the following day before all were in readiness for action.

The mass of water falling down the shaft is converted into spray, which is carried by the force of the fall long distances into the workings.

That it is possible to work with safety beneath rivers, lakes and even the ocean has been proved in numerous instances; mines in different parts of the world having been extended long distances under the sea.

Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.

The shoots are cut back to buds close to the stem, which should be encouraged to form alternately at equal distances right and left, by removing those buds from the original shoot which are not conveniently placed.

They feed chiefly on roots and grasses, in search of which they often travel considerable distances; and when eating they sit on their haunches, holding their food in their fore-paws.

This work is little more than a sailor's handbook of places and distances all round the coast of the Mediterranean and its branches, and then along the outer Libyan coast as far as the Carthaginians traded.

The landscape is rich and beautiful, varied with grand rock scenery, the coast-line being broken by numerous small bays, into which flow streams rarely navigable even for short distances, but often skilfully utilized by the natives for irrigation; and sometimes flowing in subterranean channels.

It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.

But this proves nothing because, in the case of distances so great, centuries or even thousands of years of accurate observation will be required to show any action.

To the eastward numerous spurs extend for varying distances into the great plain of the Amazons.

Where, on the other hand, there is no tendency to squinting, care must be taken in selecting spectacles that the distances between the centres of the glasses and the centres of the pupils are quite equal, otherwise squinting, or at any rate great fatigue, of the eyes may be induced.

Japanese rivers and lakes are the habitation of severalseven or eightspecies of freshwater crab (kani), which live in holes on the shore and emerge in the day-time, often moving to considerable distances from their homes.

Shadows and reflections were ignored, and perspective, approximately correct for landscape distances, was isometrical for near objects, while the introduction of a symbolic sun or moon lent the sole distinction between a day and a night scene.

For constant charges and distances the mechanical force is inversely as the dielectric constant.

The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.

So far, however, from being ahead of the Germans on the road to Verdun, the French were actually, late in the afternoon of the 15th of August, bivouacked on the plateau of Rezonville, and there their outposts were placed, not where they could see the surrounding country, but at the regulation distances of 600 to loon paces from the bivouacs.

The bodies of this class consist of eight major planets moving round the sun at various distances, and of an unknown number of minor planets, much smaller than the major planets, forming a separate group. Thirdly, satellites, or secondary planets revolving around the major planets, and therefore accompanying them in their revolutions around the sun.

Newton defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.

By successive trials two beads, of known density, say di, d 2, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube.

Of course, for many purposes, mean conditions may be adopted and mean scale-values be found which are applicable with considerable pre cision to small angles or to comparatively crude observations of large distances; but the highest refinement is lost unless means are provided for determining the scale-value for each observer at each epoch of observation.

The substitution of machinery for hand labour in cutting coal has long been a favourite problem with inventors, the earliest plan being that of Michael Meinzies, in 1761, who proposed to work a heavy pick underground by power transmitted from an engine at the surface, through the agencies of spear-rods and chains passing over pulleys; but none of the methods suggested proved to be practically successful until the general introduction of compressed air into mines furnished a convenient motive power, susceptible of being carried to considerable distances without any great loss of pressure.

The law of this force, for all distances greater than say the thousandth of an inch, is an attraction varying as the inverse square of the distance.

For smaller distances the force is an attraction for one distance and a repulsion for another, according to some law not yet discovered.

In a gas the state of things is very different; an odour is known to spread rapidly through great distances, even in the stillest air, and a gaseous poison or corrosive will attack not only those objects which are in contact with its source but also all those which can be reached by the motion of its molecules.

It follows that the average distance apart of the molecules in the gaseous state is roughly ten times as great as in the solid or liquid state, and hence that in the gaseous state the molecules are at distances apart which are large compared with their linear dimensions.

A simple approximate calculation of the pressure exerted by a gas on its containing vessel can be made by supposing that the molecules are so small in comparison with their distances apart that they may be treated as of infinitesimal size.

The number of men arrayed under one banner, the time during which they might cohere, the distances from home they could march, their ability to hold permanently what they had gained, together form an excellent metric scale of the culture grade in the several American provinces, and nowhere, even in the most favoured, is this mark high.

His only extant work is a short treatise (with a commentary by Pappus) On the Magnitudes and Distances of the Sun and Moon.

His method of estimating the relative lunar and solar distances is geometrically correct, though the instrumental means at his command rendered his data erroneous.

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.

In cases other than those described in § 82, the pth moment with regard to the axis of u is given by Pp = XPrA where A is the total area of the original trapezette, and S 2 _ 1 is the area of a trapezette whose ordinates at successive distances h, beginning and ending with the bounding ordinates, are o, x1P -1A, x2 P-1 (AI+AI),.

In the latter case the two sections are taken at distances t 2H/ A l 3 = = 2887H from the middle section, where H is the total internal length; and their arithmetic mean is taken to be the mean section of the cask.

All the flowers of each triplet are fertile as in (ii.), but the rows are not arranged regularly at equal distances round the rachis.

The Anatolian troops, ever the bulk of Ottoman armed strength, had to be conveyed great distances by inadequate means of transportation.

The most uncommon natural feature of the district, the Pink and White Terraces, was blown up in the eruption of Mount Tarawera in 1886, when for great distances the country was buried beneath mud and dust, and a chasm 9 m.

Regnault used two different distances, viz.

The reason of this is, that the segments of the plate AOD, BOC always vibrate in the same direction, but oppo sitely to the segments AOB, DOC. Hence, when the pasteboard is in its place, there are two waves of same phase starting from the two former segments, and reaching the ear after equal distances of transmission through the air, are again in the same phase, and produce on the ear a conjunct impression.

Similar researches have also established the fact that in prehistoric times nearly all the lakes of Switzerland, and many in the adjoining countries - in Savoy and the north of Italy, in Austria and Hungary and in Mecklenburg and Pomerania - were peopled, so to speak, by lake-dwelling communities, living in villages constructed on platforms supported by piles at varying distances from the shores.

Transverse girders are hung from the chains at distances of 18 ft.

The most ordinary type of staging consists of timber piles at nearly equal distances of 20 ft.

When the headway is great or the river deep, timberbraced piers or clusters of piles at distances of 50 ft.

Let W 1, W2, W3 traverse the girder from the left at fixed distances a, b.

The three heavily dotted curves are curves of maximum moment under each of the loads, for the three loads passing over the bridge, at the given distances, from left to right.

Set off these distances along AB and let Y1, y2,.

The water is muddy; and the course for shipping considerably exceeds in length the distances given above, by reason of the numerous shoals it is necessary to avoid.

The spawn of the herring is adhesive, and is deposited on rough gravelly ground at varying distances from the coast and always in comparatively shallow water.

It is well placed on the brow of the hill at the southern extremity of the rue de la Regence (the prolongation of the rue Royale), and can be seen from great distances.

They are often carried on floating ice to great distances, and to more southern latitudes than their own, no fewer than twelve Polar bears having been known to reach Iceland in this way during one winter.

For while the self-contained basins of Tibet generally possess a salt lake in the middle, into which brooks and streams of greater or less magnitude gather, often from very considerable distances, these self-contained basins of the Astintagh are very small in area, and it is extremely seldom that their central parts receive any water at all, only in fact after copious rain.

During the voyage he experimented upon the determination of longitude by lunar distances, and ultimately effected the introduction of the method into navigation (q.v.).

In 1763 he published the British Mariner's Guide, which includes the suggestion that in order to facilitate the finding of longitude at sea lunar distances should be calculated beforehand for each year and published in a form accessible to navigators.

The duration of the war was due to the nature of the country and the enormous distances to be traversed, not to any want of energy, for the armies were in deadly earnest and their battles and combats (of which two thousand four hundred can be named) sterner than those of almost any war in modern history.

Long forward strides of the Napoleonic type were rarely attempted; "changes of base" were indeed made across country, and over considerable distances, as by Sherman in 1864, but ordinarily either the base and the objective were connected by rail or water, or else every forward step was, after the manner of Marlborough's time, organized as a separate campaign.

The lameness of the Greeks in angular measurement would alone show that they could not derive itinerary measures from long and accurately determined distances on the earth.

The rivers of the Pacific coast have no navigable channels worth mentioning, but many on the Gulf coast are navigable for considerable distances.

The winters are usually long and severe, and the summers cool and salubrious, but the diversity of surface together with unequal distances from the sea cause marked variations for the different regions.

The basic lavas are usually darker and denser than lavas of acid type, and when fused they tend to flow to great distances, and may thus form far-spreading sheets, whilst the acid lavas, being more viscous, rapidly consolidate after extrusion.

He early attained to the settled conviction that for the actual disposition of the solar system some abstract intelligible reason must exist, and this, after much meditation, he believed himself to have found in an imaginary relation between the "five regular solids" and the number and distances of the planets.

This extraordinary production is memorable as having announced the discovery of the "third law" - that of the sesquiplicate ratio between the planetary periods and distances.

But the fantastic relations imagined by him of planetary movements and distances to musical intervals and geometrical constructions seemed to himself discoveries no less admirable than the achievements which have secured his lasting fame.

As regards the British farmer, it does not appear as if he had improved his position; for he has to send his wheat to greater distances, owing to the collapse of many country millers or their removal to the seaboard, while railway rates have fallen only to a very small extent; again the farmer's wheat is worth only half of what it was formerly; it may be said that the British farmer has to give up one bushel in nine to the railway company for the purpose of transportation, whereas in the 'seventies he gave up one in eighteen only.

Appended to the London edition of the solar and lunar tables are two short tracts - the one on determining longitude by lunar distances, together with a description of the repeating circle (invented by Mayer in 1752), the other on a formula for atmospheric refraction, which applies a remarkably accurate correction for temperature.

He mastered them thoroughly, gained a minute acquaintance with every detail of the soldier's life, learned the precise amount of food required for every mouth, the exact weight that could be carried, the distances that could be traversed without exhaustion, the whole body of conditions in short which govern the military activity of man and beast.

From the measured distances of the diffraction bands the width of the slit may be easily deduced.

A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.

Preston that all the lines of the same series show identical effects when measured on the frequency scale, arfrl the fact recently announced by Runge 3 that even in the more complicated cases mentioned some simple relation between the distances of the components exists.

If a is the distance shown by the normal triplets the type of separation observed in the line D2 shows distances from the central line equal to a /3, 3a/3, 5a/3, while the type of D 1 gives 2a/3, 4a/3.

In all observed cases the distances are multiples of some number which itself is a sub-mutiple of a.

The value of the constants P and Q can be obtained by making deflexion experiments at three distances.

Thus it is usual, if the magnets are of similar shape, to make the deflected magnet 0.467 of the length of the deflecting magnet, in which case Q is negligible, and thus by means of deflexion experiments at two distances the value of P can be obtained.

In autumn the withered weeds are torn up by the wind and driven immense distances.

At short distances from the town are the intermittent artesian spring Solensprudel, the Schonbornsprudel and the Theresienquelle; and in the same valley as Kissingen are the minor spas of Bocklet and Briickenau.

These angular;distances are attained only when the sun is on the horizon, and they increase as it rises.

Immediately above this plane surface and almost touching it is a system of wires which enables angular distances from the centre of the field to be read at the eyepiece below.

Within the Alps, when normally developed, we may trace the individual folds for long distances and observe how they arise, increase and die out, to be replaced by others of similar direction.

Owing to their growth in length at, or rather in the immediate vicinity of, their tips, roots are enabled to traverse long distances by surmounting some obstacles, penetrating others, and insinuating themselves into narrow crevices.

During winter, grafts may be conveyed long distances, if carefully packed.

The tree would thus consist of ten shoots, to be laid out at regular distances, and then if closely cut the frame-work of the tree would be as in fig.

The pins E, F rise out of the back of the fixed plates A and C, at unequal distances from the axis.

Many fungi (Phallus, Agaricus, Fumago, &c.) when strongly growing put out ribbon-like or cylindrical cords, or sheet-like mycelial plates of numerous parallel hyphae, all growing together equally, and fusing by anastomoses, and in this way extend long distances in the soil, or over the surfaces of leaves, branches, &c. These mycelial strands may be white and tender, or the outer hyphae may be hard and black, and very often the resemblance of the subterranean forms to a root is so marked that they are termed rhizomorphs.

Thus the apparatus is analogous to the common transformers used for inducing from currents of great electromotive force and small quantity, which carry energy through long distances, currents of great quantity and small electromotive force for incandescent lights and for welding.

The wheel carries a series of cups placed at equal distances around the circumference.

At distances greater than this it is impossible to see anything clearly in these equatorial forests, and it is very difficult to do so even at this short distance.

The water is not brought to the surface, but is carried over long distances by an underground channel or drain, which is constructed by sinking shafts at intervals along the required course and connecting the shafts by tunnelling.

Nearly one hundred and fifty years ago Pallas had his attention arrested by the existence of the salt lakes and dry saline deposits on the steppes to the east of the Caspian, and at great distances from its shores, and by the presence in the same localities of shells of the same marine fauna as that which now inhabits that sea, and he suggested the obvious explanation that those regions must formerly have been covered by the waters of the sea.

The actual tempera ture of the metal itself can then be observed by inserting thermometers or thermo-couples at measured distances from the centre.

This gives an average value of the conductivity over the range, but it is better to observe the temperatures at three distances, and to assume k to be a linear function of the temperature, in which case the solution of the equation is still very simple, namely, 0+Ze6 2 =a log r+b, (3) where e is the temperature-coefficient of the conductivity.

The chief difficulty in this method lay in determining the effective distances of the bulbs of the thermometers from the axis of the cylinder, and in ensuring uniformity of flow of heat along different radii.

The Perfect kept it wrapped up in a bag of pure white cloth, tied round the neck, and sent it long distances to regions which through persecution they could not enter.

The calculated horizontal distances of this arc varied between 5 and 24 km.

Vicentini of Padua, will yield excellent diagrams of the gentle undulations of earthquakes which have originated at great distances, but for local disturbances, even if the bob of the pendulum acts as a steady point, the highly multiplied displacements are usually too great to be recorded.

There was also a very considerable caravan trade in native goods which the industrious Hausa population carried for great distances through the western and central states of the Sudan.

All the troops present in the surprise fight when the Dervish force was destroyed at Firket in June 1896 had covered long distances, and one battalion (the 10th Sudanese) accomplished 90 m.

The Oscillatoriaceae are capable of a peculiar oscillatory movement, which has earned for them their name, and which enables them to move through considerable distances.

When such plants are detached they are enabled to float for great distances, and the great Sargasso Sea of the North Atlantic Ocean is probably only renewed by the constant addition of plants detached from the shores of the Caribbean Sea and Gulf of Mexico.

They present a hypha-like appearance, running longitudinally for considerable distances.

In the case of the freshwater algae, however, belonging to the Chlorophyceae and Cyanophyceae, although they required to be immersed during the vegetative period, the reproductive cells are often capable of resisting a considerable degree of desiccation, and in this condition are dispersed through great distances by various agencies.

Their northwestern margin for the most part springs boldly above the fields and moorlands of the Central Plain, and its boundary for long distances continues remarkably straight.

The summits of the western range form a line of noteworthy regularity, but those of the eastern form a broken irregular line of varying distances from the first.

Both are navigable for considerable distances.

It may be defined as a section of a right circular cone by a plane parallel to a tangent plane to the cone, or as the locus of a point which moves .so that its distances from a fixed point and a fixed line are equal.

Sometimes the passage is the conjoint work of many bees whose cells are grouped along it at convenient distances apart.

The Berbers are keen traders too, and, after the harvest, hawk small goods, travelling great distances.

It is less near the sea, where for long distances there is no fall at all.

He fitted the lenses in a tube, in order to adjust and preserve their relative distances, and thus constructed his first telescope.

The Zenith Telescope The zenith telescope is an instrument generally employed to measure the difference between two nearly equal and opposite zenith distances.

In practice the vertical circle is adjusted once for all, so that when the levels k and l are in the centre of their run, the verniers read true zenith distances.

A pair of stars of known declination are selected such that their zenith distances, when on the meridian, are nearly equal and opposite, and whose right ascensions differ by five or ten minutes of time.

Suppose now, for the moment, that the readings of the levels k and l are identical in both observations, we have then, in the difference between the micrometer readings north and south, a measure of the difference of the two zenith distances expressed in terms of the micrometer screw; and, if the "` value of one revolution of the micrometer screw" is known in seconds of arc we have for the resulting latitude FIG.

In the spring two caverns were excavated in the ice at distances of about 5 and 12 m.

Distances and .Parallaxes of the Stars.-As the earth traverses annually its path around the sun, and passes from one part of its orbit to another, the direction in which a fixed star is seen changes.

A unit of length, which is often used in measuring stellar distances, is the light year or distance that light travels in a year; it is rather less than six billion miles.

Although the parallaxes hitherto measured have added greatly to our general knowledge of stellar distances and absolute luminosities of stars, a collection of results derived by various observers choosing specially selected stars is not suitable for statistical discussion.

Fortunately the study of proper motions teaches us with some degree of certainty something of the general mean distances and distribution of these more distant stars, though it cannot tell us the distances of individual stars.

There is another method of determining stellar distances, which is applicable to a few double stars.

There is also clear evidence that the mean distances of both drifts from us are very approximately the same.

It is studded with villages, interspersed at greater distances with commercial towns.

Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

It is expressed by the statement that the proportionate distances of the several planets from the sun may be represented by adding 4 to each term of the series; o, 3, 6, 12, 24, &c. The irregularity will be noticed of the first term, which should be 12 instead of o.

Thus we see at once why the shadows cast by the sun or moon are in general so much less sharp than those cast by the electric arc. For, practically, at moderate distances the arc appears as a mere luminous point.

The most important naval station of the United 1 Small masses of water made to fall great distances and the use of turbines are important features of such plants.

Some do not flow directly to the sea; others find their way to the coast through deep rocky gorges, or are mere torrents; and a few only are navigable for boats for short distances from their mouths.

For many years such characterizations as "Wilderness City," "Capital of Miserable Huts," "City of Streets without Houses," "City of Magnificent Distances" and "A I1udhole almost Equal to the Great Serbonian Bog" were common.

The problem of determining the possible configurations of equilibrium of a system of particles subject to extraneous forces which are known functions of the positions of the particles, and to internal forces which are known functions of the distances of the pairs of particles between which they act, is in general determinate For if n be the number of particles, the 3n conditions of equilibrium (three for each particle) are equal in number to the 351 Cartesian (or other) co-ordinates of the particles, which are to be found.

For if we have an assemblage of particles whose mutual distances are small compared with the dimensions of the earth, the forces of gravity on them constitute a system of sensibly parallel forces, sensibly proportional to the respective masses.

If now the assemblage be brought into any other position relative to the earth, without alteration of the mutual distances, this is equivalent to a rotation of the directions of the forces relatively to the assemblage, the ratios of the forces remaining unaltered.

The mass-centre is accordingly that point the mean square of whose distances from the several particles is least.

This, theorem, also due to Lagrange, enables us to express the mean square of the distances of the particles from the centre of mass in terms of the masses and mutual distances.

In the case of a rigid body we must suppose that those forces adjust themselves so as to preserve the mutual distances of the various particles unaltered.

If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.

The motion being assumed to be small, the tensions of the two strings may be taken to have their statical values Mgb/(a+b), Mga/(a+b), where a, b are the distances of G from the two threads.

Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

This is the principle of the modification of motion by the lever, which consists of a rigid body turning about a fixed axis called a fulcrum, and having two points at the same or different distances from that axis, and in the same or different directions, one of which receives motion and the other transmits motion, modified in direction and velocity according to the above law.

That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.

The line of intersection of the planes perpendicular to the paths of the two connected points at a given instant is the instantaneous axis of the link at that instant; and the velocities of the connected points are directly as their distances from that axis.

Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.

The sheets were severed by knives placed on the cylinders, and when cut were carried by grippers and tapes; and delivery was made by means of automatic metal fingers fixed upon endless belts at such distances apart as to seize each sheet in succession as it left the last printing cylinder.

If then two experiments are made, first with the upper plate connected to earth, and secondly, connected to the object being tested, we get an expression for the potential V of this conductor in the form V=A(d' - d), where d and d' are the distances of the fixed and movable plates from one another in the two cases, and A is some constant.

Parallel to this is a second movable plate A, the distances between the two being measurable by means of a screw.

If the gold-leaf is unelectrified, it is not acted upon by the two plates placed at equal distances on either side of it, but if its potential is raised or lowered it is attracted by one disk and repelled by the other, and the displacement becomes a measure of its potential.

These violent shocks are usually limited to comparatively small districts, though the vibrations may be felt at long distances from the centre of disturbance.

All these rules are valid, inasmuch as the thicknesses and distances of the lenses are not to be taken into account.

The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small.

If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colours, and the system is said to be in " stable achromatism."

Long distances are calculated in farsakhs, a farsakh being equal to 6000 zar.

It distances perhaps every other German university in the extent to which it carries out what are popularly regarded as the characteristics of German student-life - duelling and the passion for Freiheit.

These rivers are navigable for short distances, but in general rapids or cataracts mark their middle courses.

The former results from distance; but distances, or dimensions, are straight lines, i.e.

It is to be observed that, while these early speculators ascribe the phenomena to attraction, they do not distinctly assert that this attraction is sensible only at insensible distances, and that for all distances which we can directly measure the force is altogether insensible.

But for those who wish to study the molecular constitution of bodies it is necessary to study the effect of forces which are sensible only at insensible distances; and Laplace has furnished us with an example of the method of this study which has never been surpassed.

This process, which we have followed as it takes place on an individual portion of the falling liquid, goes through its several phases at different distances from the orifice, so that if we examine different portions of the stream as it descends, we shall find next the orifice the unbroken column, then a series of contractions and enlargements, then elongated drops, then flattened drops, and so on till the drops become spherical.

Extremely local contacts of the liquids, while opposed by capillary tension which tends to keep the surfaces flat, are thus favoured by the electrical forces, which moreover at the small distances in question act with exaggerated power.

If we place the base of the filament in each case on a base line in the order of the successive times of observation recorded, and at distances apart proportional to the intervals of time (8.30, 10.0, 10.30, 11.40, and so on) and erect the straightened-out filaments, the proportional length of each of which is here given for each period, a line joining the tips of the filaments gives the curve of growth.

In the particular case when the radii are in the ratio of I to 3 the epicycloid (curve a) will consist of three cusps external to the circle and placed at equal distances along its circumference.

He traced the influence of induction to surprising distances, magnetizing needles in the lower story of a house through several intervening floors by means of electrical discharges in the upper story, and also by the secondary current in a wire 220 ft.

The range of the Caucasus, like that of the Pyrenees, maintains for considerable distances a high average elevation, and is not cleft by deep trenches, forming natural passes across the range, such as are common in the Alps.

The rivers which go down from the central Caucasus northwards have considerably longer courses than those on the south side of the range, partly as a consequence of the gentler versant and partly also because of the great distances to which the steppes extend across which they make their way to the sea.

With the exception of a few riverine tribes, such as the Wagenia who are fishers only, all are agriculturists and the majority keen traders, going long distances to buy and sell goods, but there are marked differences among them corresponding to their environment.

The atmosphere on the plateaus is exceedingly clear, so that objects are easily recognizable at great distances.

Slicing stations established at distances of from 12 to 25 m.

To prove this, it will be sufficient to mention that an exceedingly small deficiency in the transparency of the free aether would be sufficient to prevent the light of the fixed stars from reaching the earth, since their distances are so immense.

The entries in the table on following page express the reduction of intensity for different wave-lengths X, when the slit is set at distances yXradius from the centre of the disk.

Both the San Jorge and Nechi are navigable for considerable distances.

In 1 The distances given after the names of rivers indicate the length of the river valleys, including those of the main upper branch.

Many of the great towns had already secured such sites within moderate distances, and had constructed reservoirs of considerable size, when, in 1879, 1880 and 1892 respectively, Manchester, Liverpool and Birmingham obtained statutory powers to draw water from relatively great distances, viz.

The Glacial striae, and the dislocated rocks - moved a few inches or feet from their places, and others, at greater distances, turned over, and beginning to assume the sub-angular form of Glacial boulders - were found precisely as the glacier, receding from the bar, and giving place to the ancient lake, had left them, covered and preserved by sand and gravel washed from the terminal morain.

The distances between drains he showed must be regulated by the greater or less retentiveness of the ground operated upon, and gave io to 40 ft.

The salt-springs attracted the first permanent settlers to the site of Lincoln in 1856, and settlers and freighters came long distances to reduce the brine or to scrape up the dry-weather surface deposits.

Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.

Halley only communicated to Newton the fact " that Hooke had some pretensions to the invention of the rule for the decrease of gravity being reciprocally as the squares of the distances from the centre," acknowledging at the same time that, though Newton had the notion from him, " yet the demonstration of the curves generated thereby belonged wholly to Newton."

That in one of my papers writ (I cannot say in what year, but I am sure some time before I had any correspondence with Mr Oldenburg, and that's above fifteen years ago), the proportion of the forces of the planets from the sun, reciprocally duplicate of their distances from him, is expressed, and the proportion of our gravity to the moon's conatus recedendi a centro terrae is calculated, though not accurately enough.

For as Kepler knew the orb to be not circular but oval, and guessed it to be elliptical, so Mr Hooke, without knowing what I have found out since his letters to me, can know no more, but that the proportion was duplicate quam proxime at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre, whereas Kepler guessed right at the ellipsis.

On clearing the land south of the Cape the waters of the Agulhas current meet those of the west wind drift of the Southern Ocean, and mingle with them in such a manner as to produce, by interdigitation, alternate strips of warm and cold water, which are met with at great distances south-west and south of the Cape.

But in measuring a distance we may find that it is " between " two distances differing by a unit of the lowest denomination used, and a subdivision of this unit follows naturally.

In the wet season, it overflows the country far and wide, sometimes to a breadth of 20 m., for long distances, and for 400 m.

Occasionally, for long distances, it divides into two main streams with inland, lateral channels, all connected by a complicated system of natural canals, cutting the low, flat igapo lands, which are never more than 15 ft.

Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is constant, &c., &c.

These probably afford the principal means by which wild animals are able to become aware of the presence of other members of the species, even at great distances.

The Cetacea, however, are by no means limited to the ocean, or even to salt water, some entering large rivers for considerable distances, and others being exclusively fluviatile.

Slow in their movements, and feeding on vegetable substances, they are confined to the neighbourhood of rivers, estuaries or coasts, although there is a possibility of accidental transport by currents across considerable distances.

In the area of the square stood the Milion, whence distances from Constantinople were measured, and a lofty column which bore the equestrian statue of Justinian the Great.

The production of wheat, with the use of wheat bread, has increased enormously since the extension of railways has made possible the transportation of grain for great distances (see Grain Trade).

The distances across wheat fields are so great that even horseback communication is too slow.

Sometimes there is another church and small settlement in the upper valley, to which, once or twice in a summer, the Lapps come from great distances to attend service.

In several places there are traces of shells; and sometimes skeletal remains of whales and walruses, as well as ancient driftwood, have been discovered at tolerable distances from the present coast.

But although these sometimes wander to distances considerably beyond the orbit of Neptune, it is probable that the extent of the void which separates our system from the nearest star is hundreds of times the distance of the farthest point to which a comet ever recedes.

In the language of algebra putting m l, m2, m 3, &c. for the masses of the bodies, r1.2 r1.3 r2.3, &c. for their mutual distances apart; vi, v 2, v 3, &c., for the velocities with which they are moving at any moment; these quantities will continually satisfy the equation orbit, appear as arbitrary constants, introduced by the process of integration.

This being ascertained by one or more stars near it, may be used to determine by direct measurements the polar distances of other bodies.

It states that the squares of the periods of circulation round the sun of the several planets are in the same ratio as the cubes of their mean distances.

Yet another remarkable feature comprises bright streaks, branching out in various directions and through long distances from a few central points, especially that known as Tycho.

Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically.

Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the perpendiculars from the foci on any tangent always lie on the auxiliary circle, and the product of these perpendiculars is constant, and equal to the product of the distances of a focus from the two vertices.

More valid instances of the anticipation of modern discoveries may be found in his prevision that a small annual parallax would eventually be found for some of the fixed stars, and that extra-Saturnian planets would at some future time be ascertained to exist, and in his conviction that light travels with a measurable, although, in relation to terrestrial distances, infinite velocity.

On the south the principal streams, after cutting their way through the highest zone at right angles to the general direction of the range, become involved half-way to the plains in great longitudinal folds, from which they make their escape only after traversing long distances without finding an outlet.

One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the directrix) are in constant ratio.

The definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two fixed points is constant); such definitions and other special properties are treated in the articles Ellipse, Hyperbola and Parabola.

Objects at different distances, however, are not seen distinctly simultaneously, but in succession.

This is effected by the power of accommodation of the eye, which can so alter the focal length of its crystalline lens that images of objects at different distances can be produced rapidly and distinctly one after another upon the retina.

Another way of correcting this system is to alter the distances.

A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used.

It is surrounded by a wall, strengthened by square towers at distances of 18-20 steps, probably dating in its present condition from medieval Mahommedan times.

For these reasons the principal gathering places of fine pure clays are deep, still lakes, and the sea bottom at considerable distances from the shore.

The salt is highly prized and is exported to great distances.

Westien made use of two Chevalier-Briicke's simple microscopes with their long working distances in order to form an instrument in which the curvature of the image was not entirely avoided.

Most stations had one of the Guardians—or Naturals—capable of Traveling great distances the way he did, by using magic to slip through space and time and end up elsewhere.

Tiyan's lands were shallow but extended for great distances along the coast.

They disintegrate asteroids and aliens alike and are particularly renowned for their pin-point accuracy even over extraordinary distances.

Many have impairments as a result of repeated beatings and being made to carry heavy loads for long distances.

Longer training distances also dampened systolic and diastolic blood pressure in a pretty consistent manner.

Even at the distances from the Sun involved, a small brown dwarf among the comets could provide a habitable environment on its moons.

Experiments have shown that some British garden bumblebees can return to a nest from distances over 6km.

Thus the user can measure bond lengths, interatomic distances, angles between bonds and planes; create centroids and more.

This leads to gross errors in size constancy, particularly at far viewing distances.

And its now clear that whatever industry claims, there are no safe distances between GM and non-GM crops.

The separation distances for the FSEs have been set to ensure that cross-pollination is a maximum of 1% .

Distances in the Himalayas, we found, can be extremely deceptive.

Long distance travel providers will need to respond to the increasingly demanding business traveler who is traveling further distances for longer periods of time.

We design distorted diffraction gratings that simulate the effects of long propagation distances in a short instrument.

The hunted animal can be chased for long distances by hunts, maybe for ten or more miles.

This was 80 times the separation distances used for crop trials of GM oilseed rape in the UK.

The system also allows for driving shorter distances with just electrical power and therefore zero emissions.

Quick explosive bounds over distances of 30 to 60 meters are very beneficial toward speed endurance training.

Vehicles wishing to travel over great distances within the city will usually take the expressways in order to save on travel time.

They use fuzzy logic to compute distances between features.

The line-of-site hardware is capable of transmitting at rates Industries slovakia calls of up to 1.25 Gbps at distances of up to 8 miles.

Their presence in wild bird reservoirs, especially those species known to migrate long distances, are potentially of high significance.

Women of these villages have to walk long distances to fetch water.

And nearly half of those questioned cited that their companies were reliant on key staff commuting long distances to work.

Well, I spend most of my day with headphones on, and I drive long distances.

The routine calculates the square symmetric matrix of distances between each atom and every other atom currently selected.

It is also a land in which the sea is seemingly omnipresent, and in which changes in scenery occur over relatively short distances.

Trigonometric parallax is used to measure the distances of the nearby stars.

His reasoning was correct, but even Tycho's marvelous instruments were not accurate enough to register stellar parallax given the vast distances involved.

These are acute sense organs which can detect female pheromones on the air from astonishing distances.

Races including portages are held over 4, 8 and 12 miles with some special events and internationals over longer distances!

Clip cited reports of criminals using hand-helds to steal anti-theft car passcodes that are transmitted by infrared radio waves over short distances.

Thus the great distances were covered and soon all were enjoying repose on the desired shore.

At larger distances also arrivals caused by multiple P-wave reverberations inside the whole crust with a group velocity around 5.8 km/s.

Thus skeletal elements which have been transported distances along river beds or streams will appear similar to those from heavily reworked deposits.

Pigs, probably not covering such long distances, wore knitted woolen socks with leather soles.

This enables the specimen to be moved by distances of the order of the interatomic spacing.

They also throw the javelin, using hunting spears that are flung huge distances through the bush.

Both Sarah and her sister Mary Lovell became very stout in middle age and found it an effort to walk even short distances.

The small sweeper was more flexible, for shorter striking distances.