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Any line cuts off equal distances between the curve and the asymptotes.

71This pumping action results in an extremely rapid circulation of the heating agent, enabling long distances to be traversed without much loss of heat.

60Most 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.

35An important property is: the difference of the focal distances of any point on the curve equals the transverse axis.

20The 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.

20Two brightly lit, massive bronze chandeliers dangled at even distances across the ceiling.

21He looked away and turned his back to her, stance guarded as he paced short distances back and forth, like a caged panther.

21Eusebius in his Onomasticon uses it as a central point from which the distances of other towns are measured.

21µcxp6s, small, i tthrpov, a measure), an instrument generally applied to telescopes and microscopes for measuring small angular distances with the former or the dimensions of small objects with the latter.

21These 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.

21Above these distances they are mere mountain torrents.

21Above these distances they are mere mountain torrents.

21At Greenwich, Oxford and several other observatories, instead of measuring the distances of the star's image from the opposite sides of the 5 mm.

10The tangent at any point bisects the angle between the focal distances of the point, and the normal is equally inclined to the focal distances.

10The 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.

10At Greenwich, Oxford and several other observatories, instead of measuring the distances of the star's image from the opposite sides of the 5 mm.

10(3) Sunday and Wednesday of each week are appointed as the chief market days and to that end a sufficient number of troops will be stationed along the highroads on Tuesdays and Saturdays at such distances from the town as to protect the carts.

11It was impossible first because--as experience shows that a three-mile movement of columns on a battlefield never coincides with the plans--the probability of Chichagov, Kutuzov, and Wittgenstein effecting a junction on time at an appointed place was so remote as to be tantamount to impossibility, as in fact thought Kutuzov, who when he received the plan remarked that diversions planned over great distances do not yield the desired results.

11But even then, at moments of weakness as he had accounted them, his mind had penetrated to those distances and he had there seen the same pettiness, worldliness, and senselessness.

11rate irrespective of distance had not justified itself, and that for any but very short distances the tariff was " utterly unremunerative " notwithstanding a very large increase in volume of business.

12That 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.

00Owing 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.

00It 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.

00through such long distances.

00for a like message over distances from ioo to 200 miles; 2s.

00In 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.

00The 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.

00In 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.

00This only answers, however, for telephoning musical sounds to short distances.

00Pupin 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.

00The capacity of camels for travelling long distances without water - owing to special structural modifications in the stomach - is familiar to all.

00There are, however, considerable reductions for distances over 93 m., on a scale increasing in proportion to the distance.

00The first of these is wind: it cannot be doubted that small seeds can be swept up like dust and transported to considerable distances.

00Birds are even more effective than wind in transporting seeds to long distances.

00particulars arising from comparing one part with another "; but under this head the questions discussed were longitude, the situation and distances of places, and navigation.

00The 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.

00In 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.

00Others are navigable only for short distances by steamers of light draught.

00A 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.

00They 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.

00year, and the continuous frost of winter is favourable to F the transportation of fish for great distances.

00So 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.

00For 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.

00In 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.

00In 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.

00Over 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.

00an hour, are reached, and sustained for shorter or longer distances every day by express trains whose average speed between any two stoppingplaces is very much less.

00On 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.

00The other, or central, pair of tracks is for trains making stops at longer distances.

00At 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.

00The 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.

00The 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.

00west of that river (south of the city); and the outer works, approximately paralleling the inner line, at distances of from 2 to 3 m.

00In 1879, at Kilburn, the competition was of railway waggons to convey perishable goods long distances at low temperatures.

00The 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.

00ANTONINI ITINERARIUM, a valuable register, still extant, of the stations and distances along the various roads of the Roman empire, seemingly based on official documents, which were probably those of the survey organized by Julius Caesar, and carried out under Augustus.

00Plans of attack were sketched: routes were traced: distances were measured; and finally in 1163 there came the impulse from within which turned these plans into action.

00Among these lavas is the "pipe" amygdaloid of which many blocks have been transported great distances down the Vaal river.

00Many 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.

00In 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.

00These orthodromic distances are of course shorter than those measured along a loxodromic line, which intersects all parallels at the same angle.

00These 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.

00Distances 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.

00On 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.

00Other 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.

00In 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.

00The 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.

00These 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.

00It 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.

00On 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.

00Both 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.

00Owing to the distances over which they are carried and the bad organization of trade, all manufactured articles are exceedingly dear, especially in the east.

00be immediately derived, because the ratios of distances in the solar system are known with the last degree of of precision.

00By 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.

00The results were: Transit of 1874: Distances; par.

00Distances; =8-873".

00The 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.

00At 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.

00The 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.

00The celluloid sheet is laid upon the squared paper, and in plotting a curve horizontal distances are reckoned from the proper demagnetization line instead of from the vertical axis.

00Mangrove 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.

00The former reach the coastal plain over long and gradual descents, and are navigable for considerable distances.

00The latter descend from the plateau much nearer the coast, and are in most cases navigable for short distances only.

00Brazil 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.

00Thence the railway is continued to Johannesburg, &c. The distances from Durban to the places mentioned by this route are: Johannesburg, 483 m.; Pretoria 511 m.; Kimberley, 793 m.; Bulawayo, 1508 m.; Delagoa Bay, 860 m.

00The most important are: (I) To express the time of describing an elliptic arc under the Newtonian law of gravitation in terms of the focal distances of the initial and final points, and the length of the chord joining them.

00The principle of this system is to offer cheap fares and relatively low tariffs for greater distances, and to promote, therefore, long-distance travelling.

00Laplace 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.

00The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

00In virtue of (4) the difference of the optical distances to A and B is f Sµ ds (along Bo.

00In different gratings the lengths of the spectra and their distances from the axis were inversely proportional to the grating interval, while with a given grating the distances of the various spectra from the axis were as i, 2, 3, &c. To Fraunhofer we owe the first accurate measurements of wave-lengths, and the method of separating the overlapping spectra by a prism dispersing in the perpendicular direction.

00In order to find the difference of optical distances between the courses QAQ', QPQ', we have to express QP-QA, PQ'-AQ'.

00The following table gives the distances from that city to other places in South Africa' :- Besides the lines enumerated the other railways of importance are: (I) A line from Johannesburg eastward via Springs and Breyten to Machadodorp on the Pretoria-Delagoa Bay railway.

00Land went up in value, and farms, many of them at comparatively remote distances from the goldfields, were sold at enormously enhanced prices.

00The 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.

00The 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.

00in diameter may be carried long distances underground with the use of little more than an equal volume of water.

00per minute, and the distances preferably but a few hundred feet.

00Mine 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%.

00Locomotive haulage is applicable to large mines, where trains of cars are hauled long distances on flat or undulating roads of moderate gradients.

00The 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.

00That 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.

00- Employ the elliptic coordinates n,, and -=n+Vi, such that z=cch?, cchncos,y=cshnsin-; (1) then the curves for which n and are constant are confocal ellipses and hyperbolas, and -d(n,) =c 2 (ch 2 n - cost) = 2c 2 (ch2n-cos2) = r i r 2 = OD 2, (2) if OD is the semi-diameter conjugate to OP, and ri, r 2 the focal distances, rl,r2 = c (ch n cos 0; r 2 = x2 +y2 = c 2 (ch 2 n - sin20 = 1c 2 (ch 2 7 7 +cos 2?).

00Thus 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.

00The 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.

00They 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.

00This 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.

00The 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.

00Brushwood 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.

00gravis, heavy), in physical science, that mutual action between masses of matter by virtue of which every such mass tends toward every other with a force varying directly as the product of the masses and inversely as the square of their distances apart.

00It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.

00But 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.

00To the eastward numerous spurs extend for varying distances into the great plain of the Amazons.

00Where, 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.

00Japanese 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.

00Shadows 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.

00It is the point from which all distances in Japan are measured.

00For constant charges and distances the mechanical force is inversely as the dielectric constant.

00The 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.

00The 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.

003), and describe through it as centre a cone of small solid angle dw cutting out of the enclosing surface in two small areas dS and dS' at distances x and x'.

00The distances by rail from Johannesburg to the following seaports are: Lourengo Marques, 364 m.; Durban, 483 m.; East London, 6S9 m.; Port Elizabeth, 714 m.; Cape Town, 957 m.

00Migrants proceeding long distances generally go by preference to one of the great cities of commerce or industry.

00So 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.

00The 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.

00Newton 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.

00By 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.

004) that Bessel had indicated, by notes in his handbooks, the following points which should be kept in mind in the construction of future heliometers: (I) The segments should move in cylindrical slides; b (2) the screw should be protected from dust; 6 (3) the zero of the position circle should not be so liable to change; 7 (4) the distance of the optical centres of the segments should not change in different position angles or otherwise; 8 (5) the points of the micrometer screws should rest on ivory plates; 9 (6) there should be an apparatus for changing the screen.'° Wilhelm Struve, in describing the Pulkowa heliometer,' 1 made The distances of the optical centres of the segments from the eye-piece are in this method as I; secant of the angle under measurement.

00Bessel confined his measures to distances considerably less than I °.

00© 0 easy and convenient in use, and yielding results of very high accuracy in measuring distances.

00(2) That an additional motion intermediate between the quick and slow motion in position angle was necessary, because, whilst the slow motion provided by Repsolds was admirably adapted for adjusting the pointings in position angle, it was too slow for causing the images to "cross through " each other in the process of measuring distances.

00Of 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.

00through a series of vertical pipes closed at the bottom, contained in boreholes arranged at equal distances apart around the space to be frozen, and carried down to a short distance below the bottom of the ground to be secured.

00The 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.

00The 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.

00For smaller distances the force is an attraction for one distance and a repulsion for another, according to some law not yet discovered.

00That the distances traversed by the molecules of a solid are very small in extent is shown by innumerable facts of everyday observation, as for instance, the fact that the surface of a finely-carved metal (such as a plate used for steel engraving) will retain its exact shape for centuries, or again, the fact that when a metal body is coated with gold-leaf the molecules of the gold remain on its surface indefinitely: if they moved through.

00any but the smallest distances they would soon become mixed with the molecules of the baser metal and diffused through its interior.

00In 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.

00It 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.

00A 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.

00However, 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.

00The 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.

00His only extant work is a short treatise (with a commentary by Pappus) On the Magnitudes and Distances of the Sun and Moon.

00His method of estimating the relative lunar and solar distances is geometrically correct, though the instrumental means at his command rendered his data erroneous.

00of distances between points) as belonging to geometry or trigonometry; while the measurement of curved lengths, except in certain special cases, involves the use of the integral calculus.

00(iii) Another special case is that in which the distances MN, NP, PQ,.

00there are entered the distances AN, AP, AQ,.

00The 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.

00In 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),.

00i g h oo hsuvii where T is the area of a trapezette whose ordinates at successive distances h are o, Ali' (x i), (Al +A4), g 5' (x2), (Az +A 2 + ...

00In 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.

00All the flowers of each triplet are fertile as in (ii.), but the rows are not arranged regularly at equal distances round the rachis.

00The Anatolian troops, ever the bulk of Ottoman armed strength, had to be conveyed great distances by inadequate means of transportation.

00The 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.

00Regnault used two different distances, viz.

00§ 68 c), consists of a wheel carrying several soft-iron armatures fixed at equal distances Rayleigh's round its circumference.

00us imagine it to form half a wave-length of the extended train Zgahbkc, on an indefinitely extended stretched string, the values of y at equal distances from A (or from B) being equal and opposite.

00The 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.

00Similar 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.

00Transverse girders are hung from the chains at distances of 18 ft.

00The most ordinary type of staging consists of timber piles at nearly equal distances of 20 ft.

00When the headway is great or the river deep, timberbraced piers or clusters of piles at distances of 50 ft.

00In the case of a series of travelling loads at fixed distances apart passing over the girder from the left, let W1, W 2 (fig.

0048), at distances x and x+a from the left abutment, be their resultants on either side of C. Then the reaction at B is WIx/1+W2(x+a)/l.

00Let W 1, W2, W3 traverse the girder from the left at fixed distances a, b.

00The 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.

00of travelling loads at fixed distances, let PI, P2, P3,.

00be the loads which at the moment considered are at distances m l, m 2,

00Set off these distances along AB and let Y1, y2,.

00at distances m l, m 21

00The 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.

00The 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.

00It 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.

00They 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.

00For 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.

00During the voyage he experimented upon the determination of longitude by lunar distances, and ultimately effected the introduction of the method into navigation (q.v.).

00In 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.

00The 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.

00Long 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.

00The 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.

00The rivers of the Pacific coast have no navigable channels worth mentioning, but many on the Gulf coast are navigable for considerable distances.

00The 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.

00The 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.

00He 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.

00This extraordinary production is memorable as having announced the discovery of the "third law" - that of the sesquiplicate ratio between the planetary periods and distances.

00But 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.

00De Sectione Determinata resolved the problem: Given two, three or four points on a straight line, to find another point on it such that its distances from the given points satisfy the condition that the square on one or the rectangle contained by two has to the square on the remaining one or the rectangle contained by the remaining two, or to the rectangle contained by the remaining one and another given straight line, a given ratio.

00As 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.

00Appended 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.

00He 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.

00The announcement of the first discoveries made through the application of spectroscopy, then called spectrum analysis, appealed to the imagination of the scientific world because it revealed a method of investigating the chemical nature of substances independently of their distances: a new science was thus created, inasmuch as chemical analysis could =rT?

00From the measured distances of the diffraction bands the width of the slit may be easily deduced.

00The distances between the two first lines is A, and is small compared with the frequency itself, which is B.

00A 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.

00Preston 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.

00If 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.

00In all observed cases the distances are multiples of some number which itself is a sub-mutiple of a.

00It accordingly comments on the Sphaerica of Theodosius, the Moving Sphere of Autolycus, Theodosius's book on Day and Night, the treatise of Aristarchus On the Size and Distances of the Sun and Moon, and Euclid's Optics and Phaenomena.

00The value of the constants P and Q can be obtained by making deflexion experiments at three distances.

00Thus 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.

00In autumn the withered weeds are torn up by the wind and driven immense distances.

00At 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.

00Halos are at definite distances (22° and 46 °) from the sun, and are coloured red on the inside, being due to refraction; coronae closely surround the sun at variable distances, and are coloured red on the outside, being due to diffraction.

00These angular;distances are attained only when the sun is on the horizon, and they increase as it rises.

00Immediately 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.

00Lastly, in a practical point of view: Thales furnished the first example of an application of theoretical geometry to practice,' and laid the foundation of an important branch of the same - the measurement of heights and distances.

00Within 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.

00Owing 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.

00During winter, grafts may be conveyed long distances, if carefully packed.

00The 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.

00The pins E, F rise out of the back of the fixed plates A and C, at unequal distances from the axis.

00Many 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.

001), in which vertical distances represent temperatures and horizontal ones the percentage of carbon in the iron, aids our study of these constituents of iron.

00Thus 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.

00The wheel carries a series of cups placed at equal distances around the circumference.

00At 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.

00The 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.

00Nearly 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.

00The actual tempera ture of the metal itself can then be observed by inserting thermometers or thermo-couples at measured distances from the centre.

00(2) If k is constant the solution is evidently B =a log r+b, where a= and b and k are determined from the known values of the temperatures observed at any two distances from the axis.

00This 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.

00The 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.

002 were varied by taking three different periods, 60, 90 and 120 minutes, and two distances, 6 in.

00for distances exceeding 93 m.

00The 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.

00The calculated horizontal distances of this arc varied between 5 and 24 km.

00have been violent, to such distances that their move ments are no longer perceptible.

00Vicentini 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.

00There 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.

00All 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.

00Fo~r setting out a mastaba with sloping sides, on an irregular foundation at different levels, hollow corner walls were built outside the place of each corner; the distances of the faces at the above-ground level were marked on the inner faces of the walls; the above-ground level was also marked; then sloping lines at the intended angle of the face were drawn downward from the ground-level measures, and each face was set out so as to MALLETS - 2

00The Oscillatoriaceae are capable of a peculiar oscillatory movement, which has earned for them their name, and which enables them to move through considerable distances.

00When 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.

00They present a hypha-like appearance, running longitudinally for considerable distances.

00In 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.

00Their 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.

00The 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.

00Both are navigable for considerable distances.

00It 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.

00If the chlorine is made to act on cream of lime, care being taken that the temperature does not rise above 35° and that the chlorine is not in excess, a solution is obtained containing a mixture of calcium chloride and hypochlorite which is a very convenient agent for bleachers, but which does not bear the expense of carriage over long distances.

00Sometimes the passage is the conjoint work of many bees whose cells are grouped along it at convenient distances apart.

00The Berbers are keen traders too, and, after the harvest, hawk small goods, travelling great distances.

00It is less near the sea, where for long distances there is no fall at all.

00He fitted the lenses in a tube, in order to adjust and preserve their relative distances, and thus constructed his first telescope.

00The Zenith Telescope The zenith telescope is an instrument generally employed to measure the difference between two nearly equal and opposite zenith distances.

00In 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.

00A 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.

00Suppose 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.

00In the spring two caverns were excavated in the ice at distances of about 5 and 12 m.

00The agreement is too close to be dismissed as a mere coincidence, and it is confirmed by a corresponding agreement of their radial motions determined by the spectroscope; and yet, seeing that a and Ursae Majoris are 19° apart, these two stars must be distant from each other at least one-third of the distance of each from the sun; thus the members of this singular group are separated by the ordinary stellar distances, and probably each has neighbours, not belonging to the system, which are closer to it than the other four stars of the group. Further, E.

00Distances 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.

00A 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.

00Although 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.

00Fortunately 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.

00There is another method of determining stellar distances, which is applicable to a few double stars.

00There is also clear evidence that the mean distances of both drifts from us are very approximately the same.

00It is studded with villages, interspersed at greater distances with commercial towns.

00Newton 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).

00It 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.

00Thus 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.

00When the eclipse is total, there is a real geometrical shadow - very small compared with the penumbra (for the apparent diameters of the sun and moon are nearly equal, but their distances are as 370: I); when the eclipse is annular, the shadow is all penumbra.

00The 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.

00Some 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.

00For 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.

00The 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.

00For 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.

00If 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.

00~ Three-dimensional Kinematics of a Rigid Body.The position of a rigid body is determined when we know the positions of three points A, B, C of it which are not colljnear, for the position of any other point P is then determined by the three distances PA, PB, PC. The nine co-ordinates (Cartesian or other) of A, B, C are subject to the three relations which express the invariability of the distances BC, CA, AB, and are therefote equivalent to six independent quantities.

00be the perpendicular distances of the particles from any fixed plane, the sum ~(mh2) is the quadratic moment with respect to the plane.

00/n be the perpendicular distances from any given axis, the sum ~(mp2) is the quadratic moment with respect to the axis; it is also called the moment of inertia about the axis.

00r,~ be the distances from a fixed point, the sum ~(mr2) is the quadratic moment with respect to that point (or pole).

00If we divide any of the above quadratic moments by the total mass ~(m), the result is called the mean square of the distances of the particles from the respective plane, axis or pole.

00and expresses that the mean square of the distances of the particles from 0 exceeds the mean square of the distances from G by 0G2.

00The mass-centre is accordingly that point the mean square of whose distances from the several particles is least.

00This, 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.

00where x, x are any two corresponding distances; e.g.

00they may be the initial distances, both particles being supposed to start from rest.

00where ri, rf are the distances of mi, rni from their mass-centre G.

00In 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.

00If 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.

00The 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.

00Relations 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.

00This 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.

00That 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.

00of 39 it appears that the angular velocityratio of a pair of wheels is the inverse ratio of the distances of the point of contact from the Centres respectively.

00To find the length of the path of contact on either side of the pitch-point I, it is to be observed that the distance between the fronts of two successive teeth, as measured along PiIPi, is less than the pitch in the ratio of cos obliquity: I; and consequently that, if distances equal to the pitch be marked off either way from I towards P~ and Pi respectively, as the extremities of the path of contact, and if, according to Principle IV.

00The 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.

00moves at right angles to the central plane of its shaft and (ork, therefore the line of intersection of the central planes of the two forks at any instant is the instantaneous axis of the cross, and the velocity ratio of the points Ff, F2 (which, as the forks are equal, is also the angular velocity ratio of the shafts) is equal to the ratio of the distances of those points from that instantaneous axis.

00While the stroke of A is ACa, extending to equal distances on either side of C, and equal to twice the chord of the arc Dd, the stroke of B is only equal to twice the sagitta; and thus A is guided through a comparatively long stroke by the sliding of B through a comparatively short stroke, and by rotatory motions at the joints C, D, B.

00the ratio of the distances ab and ac is constant, and the angle baa E a is constant for all positions of the FIG H

00Now 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.

00Hence 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.

00Felix Savary (1797-1841) made some very curious observations in 1827 on the magnetization of steel needles placed at different distances from a wire conveying the discharge of a Leyden jar (Ann.

00The 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.

00If 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.

00Parallel to this is a second movable plate A, the distances between the two being measurable by means of a screw.

00If 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.

00These violent shocks are usually limited to comparatively small districts, though the vibrations may be felt at long distances from the centre of disturbance.

00the radii, thicknesses, refractive indices and distances between the lenses, was solved by L.

00All these rules are valid, inasmuch as the thicknesses and distances of the lenses are not to be taken into account.

00The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small.

00there are " chromatic differences " of the distances of intersection, of magnifications, and of monochromatic aberrations.

00These constants are determined by the data of the system (radii, thicknesses, distances, indices, &c., of the lenses); therefore their dependence on the refractive index, and consequently on the colour, are calculable (the formulae are given in Czapski-Eppenstein, G'rundziige der Theorie der optischen Instrumente (1903, p. 166).

00If 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."

00Long distances are calculated in farsakhs, a farsakh being equal to 6000 zar.

00It 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.

00These rivers are navigable for short distances, but in general rapids or cataracts mark their middle courses.

00City lima Thule Table of approximate distances „ rtoo ., 4200 1957 ..

00The former results from distance; but distances, or dimensions, are straight lines, i.e.

00p. 402) made experiments to determine the greatest distance at which the effect of these forces is sensible, and he found for various substances distances about the twenty-thousandth part of a millimetre.

00It 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.

00But 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.

00This 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.

00Extremely 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.

00parts the waters of the Gila and the Little Colorado, it often has an elevation of 1000 to 2000 ft., and the ascent is impracticable through long distances to the most daring climber.

00If 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.

00In 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.

00He 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.

00The 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.

00The 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.

00With 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.

00to the reign of the emperor Claudius (Gothicus); that both died on the same day; and that both were buried on the Via Flaminia, but at different distances from Rome.

00The atmosphere on the plateaus is exceedingly clear, so that objects are easily recognizable at great distances.

00Slicing stations established at distances of from 12 to 25 m.

00To 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.

00The 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.

00The chief term in the lunar longitude which introduces the ratio of the distances of the sun and moon from the earth explicitly is known as the parallactic inequality; by analysis of the observations P. H.

00Both the San Jorge and Nechi are navigable for considerable distances.

00In 1 The distances given after the names of rivers indicate the length of the river valleys, including those of the main upper branch.

00Many 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.

00The 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.

00The 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.

00If the length of the arms AC =BC =/,CD =a,SD=s, the angle of deviation of ° Z the balance from the horizontal =4), the weight of the beam alone G, the weight on one side = P, that on the other = P +Z, and lastly the weight of each scale with its appurtenances = Q then Zl tan:473 - 12 (P+Q)+Z la+G sj From this it is inferred that the deviation, and therefore the sensitive - ness, of the balance increases with the length of the beam, and de - creases as the distances, a and s, increase; also, that a heavy balance is, ceteris paribus, less sensitive than a light one, and that the sensitive - ness decreases continually the greater the weight put upon the scales.

00farther for very light draft vessels) and a few other coast streams for short distances.

00The 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.

00Johann 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.

00Newton, 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.

00Halley 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."

00That 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.

00For 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.

00On 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.

00But 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.

00In the wet season, it overflows the country far and wide, sometimes to a breadth of 20 m., for long distances, and for 400 m.

00Occasionally, 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.

00Similarly 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.

00These 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.

00The 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.

00Slow 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.

00Mundane distances become trivial when compared with the distance from the earth of the sun and still more of other heavenly bodies: hence we infer infinite space.

00In 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.

00The 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).

00The distances across wheat fields are so great that even horseback communication is too slow.

00Sometimes 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.

00In 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.

00But 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.

00In 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.

00When bodies revolve at different distances around a centre, their velocities must be such that the centrifugal force of each shall be balanced by the attraction of the central mass, and therefore vary inversely as the square of the v(m i v -+m 2 vz+

00This being ascertained by one or more stars near it, may be used to determine by direct measurements the polar distances of other bodies.

00It 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.

00Yet 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.

00vessels can now navigate the Iron Gates at all seasons of the year when the river is not closed by ice, whereas formerly at extreme low water, lasting generally for about three months in the late summer and autumn, through navigation was always at a standstill, and goods had to be landed and transported considerable distances by land.

00distances on the interior highlands before breaking through the outer ranges.

00eccentricity less than unity: this involves the notion of one directrix and one focus; (2) the ellipse is the locus of a point the sum of whose distances from two fixed points is constant: this involves the notion of two foci.

00Metrical 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.

00the square on the semi-major axis equals the rectangle contained by the distances of the focus and directrix from the centre; and 2a = SP+S'P, where P is any point on the curve, i.e.

00the sum of the focal distances of any point on the curve equals the major axis.

00Of 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.

00(a) Let AA', BB' be the axes intersecting at right angles in a point C. Take a strip of paper or rule and mark off from a point P, distances Pa and Pb equal respectively to CA and CB.

00(2) If the major axis and foci be given, there is a convenient mechanical construction based on the property that the sum of the focal distances of any point is constant and equal to the major axis.

00More 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.

00On 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.

00bee-keepers a movable frame which in its most im- stroth's respective distances left between the side-bars and hive walls on each side, and between the lower edge of the bottom-bars and the floor-board.

00One 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.

00The 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.

00Objects at different distances, however, are not seen distinctly simultaneously, but in succession.

00This 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.

00For especially large free working distances the corrections proposed by Chevalier and carried out by E.

00Another way of correcting this system is to alter the distances.

00A second method for diminishing the spherical aberration was to alter the distances of the single systems, a method still used.

00It 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.

00For these reasons the principal gathering places of fine pure clays are deep, still lakes, and the sea bottom at considerable distances from the shore.

00The salt is highly prized and is exported to great distances.

00Westien 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.

00Most stations had one of the Guardiansâ€”or Naturalsâ€”capable of Traveling great distances the way he did, by using magic to slip through space and time and end up elsewhere.

00Two brightly lit, massive bronze chandeliers dangled at even distances across the ceiling.

00He looked away and turned his back to her, stance guarded as he paced short distances back and forth, like a caged panther.

00Tiyan's lands were shallow but extended for great distances along the coast.

00accretion of material at these great distances progressed more slowly than material closer to the Sun.

00They disintegrate asteroids and aliens alike and are particularly renowned for their pin-point accuracy even over extraordinary distances.

00aquaplanend snow will seriously affect stopping distances and if heavy rain has fallen pilots should be aware of the aircraft's aquaplaning speed.

00arrowhead round consists of 36 arrows on unknown distances and 36 arrows on known distances.

00Many have impairments as a result of repeated beatings and being made to carry heavy loads for long distances.

00Longer training distances also dampened systolic and diastolic blood pressure in a pretty consistent manner.

00Even at the distances from the Sun involved, a small brown dwarf among the comets could provide a habitable environment on its moons.

00Experiments have shown that some British garden bumblebees can return to a nest from distances over 6km.

00catalytic converters on cars can reduce noxious emissions, they do not work on cold engines or for short distances.

00Thus the user can measure bond lengths, interatomic distances, angles between bonds and planes; create centroids and more.

00PASTORAL CARE The cathedral congregation is far flung, many members traveling considerable distances to attend.

00This leads to gross errors in size constancy, particularly at far viewing distances.

00And its now clear that whatever industry claims, there are no safe distances between GM and non-GM crops.

00The separation distances for the FSEs have been set to ensure that cross-pollination is a maximum of 1% .

00cutoff distances selected!

00Distances in the Himalayas, we found, can be extremely deceptive.

00Long distance travel providers will need to respond to the increasingly demanding business traveler who is traveling further distances for longer periods of time.

00detonators on the track in certain number combinations and distances.

00We design distorted diffraction gratings that simulate the effects of long propagation distances in a short instrument.

00He derived the distances from inverse square law of brightness: clusters farther away should appear dimmer.

00The hunted animal can be chased for long distances by hunts, maybe for ten or more miles.

00This was 80 times the separation distances used for crop trials of GM oilseed rape in the UK.

00You can usually find our runners at local races - ranging from 5km track sessions up to full marathon distances (& occasionally beyond!

00dragonflylass="ex">Adult dragonflies often fly long distances away from water in search of prey.

00The system also allows for driving shorter distances with just electrical power and therefore zero emissions.

00Quick explosive bounds over distances of 30 to 60 meters are very beneficial toward speed endurance training.

00Vehicles wishing to travel over great distances within the city will usually take the expressways in order to save on travel time.

00Achieve superior range with distances of up to 300 feet with automatic rate fallback.

00fuzzy logic to compute distances between features.

00They use fuzzy logic to compute distances between features.

00The 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.

00heliocentric distances between the planets with musical scales.

00Approach: Every wild animal has an inbuilt ' flee ' instinct triggered at various distances to your approach.

00inscriptions on the tombs, others started pacing out distances again.

00intergalactic distances, the quickest path is in fact a curve.

00interspersed with clean patches at varying distances.

00killer whale pod, which spends its summers in Washington state's San Juan Islands, covers tremendous distances.

00lactate tolerance session work relief was given, normally over set distances.

00leeway for patients who have traveled long distances at the discretion of the senior nurse on duty.

00lineal successor, carrying a similar bomb load over similar distances.

00linearity errors can be seen mainly with dished screens due to unequal horizontal and vertical distances.

00They use fuzzy logic to compute distances between features.

00long distances with precise step sizes.

00Their presence in wild bird reservoirs, especially those species known to migrate long distances, are potentially of high significance.

00Women of these villages have to walk long distances to fetch water.

00And nearly half of those questioned cited that their companies were reliant on key staff commuting long distances to work.

00Well, I spend most of my day with headphones on, and I drive long distances.

00long distances on currents of air.

00long distances in gas-guzzlers than half of and can cancel.

00long distanceS Adventure remains in the 2004 model range as the definitive bike for serious long-distance on and off-road riding.

00The routine calculates the square symmetric matrix of distances between each atom and every other atom currently selected.

00migrate over long distances in order to search for food.

00It is also a land in which the sea is seemingly omnipresent, and in which changes in scenery occur over relatively short distances.

00outcrossing distances.

00parallax given the vast distances involved.

00Trigonometric parallax is used to measure the distances of the nearby stars.

00His reasoning was correct, but even Tycho's marvelous instruments were not accurate enough to register stellar parallax given the vast distances involved.

00These are acute sense organs which can detect female pheromones on the air from astonishing distances.

00Races including portages are held over 4, 8 and 12 miles with some special events and internationals over longer distances!

00Clip cited reports of criminals using hand-helds to steal anti-theft car passcodes that are transmitted by infrared radio waves over short distances.

00Add wireless repeaters for distances up to 1.7 miles (2.7 km ).

00Thus the great distances were covered and soon all were enjoying repose on the desired shore.

00At larger distances also arrivals caused by multiple P-wave reverberations inside the whole crust with a group velocity around 5.8 km/s.

00Thus skeletal elements which have been transported distances along river beds or streams will appear similar to those from heavily reworked deposits.

00Jacob's Ladder: A ladder with missing rungs and big distances apart!

00sensible to consult your doctor before traveling long distances.

00separation distances used for crop trials of GM oilseed rape in the UK.

00Pigs, probably not covering such long distances, wore knitted woolen socks with leather soles.

00This enables the specimen to be moved by distances of the order of the interatomic spacing.

00They also throw the javelin, using hunting spears that are flung huge distances through the bush.

00stellar parallax given the vast distances involved.

00Both Sarah and her sister Mary Lovell became very stout in middle age and found it an effort to walk even short distances.

00subtended distances, lean, volume in ONE Compact Unit!

00The small sweeper was more flexible, for shorter striking distances.

00Secondly, by mapping the output of a focussed ultrasound transducer at various distances from the focus.

00transect sampling, distances of detected objects from the sampled points are recorded.

00transoceanic distances.

00He applied Alexandrian trigonometry to estimate the distances and sizes of the sun and moon, and also postulated a heliocentric universe.

00The use of these simple trigonometry is illustrated by the method of calculating distances on the Earth.

00At the great distances of the Oort Cloud, comets can be affected by the gentle gravitational tugs of nearby passing stars.

00Are you still doing it..and did you get any info on the best distances and courses to lay 1.20 in play... cheers uptrend.

00Lamps sited at these distances will provide, at the center of the beam, higher UVB in the D-UV range.

00By attaching chrome vanadium flexible rods, in 5 meter lengths, distances of up to 260 meters can be achieved.

00Global warming will have a pronounced effect on mountain ecosystems due to the altitudinal zonation which occurs in relatively short horizontal distances.

00"Tetrahedral co-ordinates" are a system of quadriplanar co-ordinates, the fundamental planes being the faces of a tetrahedron, and the co-ordinates the perpendicular distances of the point from the faces, a positive sign being given if the point be between the face and the opposite vertex, and a negative sign if not.

00Eusebius in his Onomasticon uses it as a central point from which the distances of other towns are measured.

00µcxp6s, small, i tthrpov, a measure), an instrument generally applied to telescopes and microscopes for measuring small angular distances with the former or the dimensions of small objects with the latter.

00These 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.

00The mutual distances of the intersecting wires he determined by counting, with the aid of a pendulum clock, the number of seconds required by an equatorial star to pass from web to web, while the telescope was adjusted so that the star ran parallel to the wires at right angles to those under investigation.

00Indeed, in those days, the difficulties attached to such measures, and to the measurement of distances with the filar micrometer, were exceedingly great, and must have taxed to the Utmost the skill and patience of the observer.

00To measure distances with the Fraunhofer micrometer, the position-circle is clamped at the true position-angle of the star, and the telescope is moved by its slow motions so that the component A of the star is bisected by the fixed wire; the other component B is then bisected by the web, which is moved by the graduated head S.

00on which rubs the block CD, which represents the female screw or bush, and moves between the points E and F, sometimes towards E, sometimes towards F, but having as often to measure short distances as long distances from the middle point of this range, and these as often towards E as towards F.

00That 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.

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

00The tangent at any point bisects the angle between the focal distances of the point, and the normal is equally inclined to the focal distances.

00Any line cuts off equal distances between the curve and the asymptotes.

00This pumping action results in an extremely rapid circulation of the heating agent, enabling long distances to be traversed without much loss of heat.

00Owing 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.

00Its prevailing aspect is characterized by flat and terraced hills, capped by desert sandstone, with stone-covered flats stretching over long distances.

00Since the time of these early experiments, various other modes of detecting the existence of electric waves have been found out in addition to the spark-gap which he first employed, and the results of his observations, the earliest interest of which was simply that they afforded a confirmation of an abstruse mathematical theory, have been applied to the practical purposes of signalling over considerable distances (see Telegraphy, Wireless).

00It 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.

00through such long distances.

00for a like message over distances from ioo to 200 miles; 2s.

00rate irrespective of distance had not justified itself, and that for any but very short distances the tariff was " utterly unremunerative " notwithstanding a very large increase in volume of business.

00In 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.

00In subsequent years numerous experiments were carried out by him in various parts of Great Britain, in some cases with circuits earthed at both ends, and in other cases with completely insulated circuits, which showed that conductive effects could be detected at distances of many miles, and also that inductive effects could take place even between circuits separated by solid earth and by considerable distances.

00The 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.

00In creating powerful electric waves for communication over long distances it is necessary to employ an alternating current transformer (see Transformers) supplied with alternating currents from a low frequency alternator D driven by an engine to charge the condenser (fig.

00In 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.

00There is no doubt that the transmission of articulate sounds and speech over long distances without wires by means of electric waves is not only possible as an experimental feat but may perhaps come to be commercially employed.

00Nevertheless, transoceanic wireless telegraphy over long distances, such as those across the Atlantic and Pacific oceans, is a matter to be reckoned with in the future, but it remains to be seen whether the present means are sufficient to render possible communication to the antipodes.

00This only answers, however, for telephoning musical sounds to short distances.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.