Dimensions Sentence Examples

The dimensions of this trade are shown in Table XIV.

Lastly, what are "dimensions" ?

In order to permit a comparison of crystal forms, from which we hope to gain an insight into the prevailing molecular conditions, it is necessary that some unit of crystal dimensions must be chosen.

This tree acquires large dimensions, the trunk being often from 4 to 6 ft.

The lakes of Central Italy, which are comparatively of trifling dimensions, belong to a wholly different class.

Several globes of unusual dimensions were produced in the course of last century.

Changes of Dimensions attending Magnetization.

She suggests herself that she can know them better than we do, because she can get the true dimensions and appreciate more immediately the solid nature of a sculptured figure.

Kutuzov was occupying a nobleman's castle of modest dimensions near Ostralitz.

Nearly all the cable companies possess their own steamers, of sufficient dimensions and specially equipped for making ordinary repairs; but for exceptional cases, where a considerable quantity of new cable may have to be inserted, it may be necessary to charter the services of one of the larger vessels owned by a cable-manufacturing company, at a certain sum per day, which may well reach £200 to £300.

The figure and dimensions of the Mafhema- earth are the first of these.

The leading dimensions of a few locomotives typical of English, American and European practice are given in Table Xxii.

The observed facts as to polarization are thus readily explained, and the general law connecting the intensity of the scattered light with the wave-length follows almost as easily from considerations of dimensions.

This naturally Asie led to a contraband trade of considerable dimensions.

There are still many magneto exchanges in existence, but when new exchanges are erected only the very smallest are equipped for magneto working, that system having succumbed to the common battery one in the case of all equipments of moderate and large dimensions.

The neighbouring lake of Chiusi is of similar character, but much smaller dimensions.

The study of existing Algae, that is of plants that have continued to live in water, shows that under these conditions no high degree of organization has been reached, though some of them have attained gigantic dimensions.

In 1840 the finest cloth that could be made of the above dimensions weighed about 1600 grains, and was worth Do.

On the northern side Cimon completed the wall of Themistocles at both ends and added to its height; the ground behind was levelled up on this side also, the platform of the Acropolis thus receiving its present shape and dimensions.

Without resorting to this exaggeration, Mommsen can speak with perfect truth of the " enormous space occupied by the burial vaults of Christian Rome, not surpassed even by the cloacae or sewers of Republican Rome," but the data are too vague to warrant any attempt to define their dimensions.

Its dimensions are given as 300 cubits long, 50 cubits broad and 30 cubits high (cubit =18-22 in.).

Yarns, textile goods and weaving industries generally have not attained any great dimensions, but there are large jute-spinning mills and factories for cotton-wool and cotton driving - belts.

As soon as the output of plantation rubber of constant composition has reached much larger dimensions it is probable that the manufacturer will be able to dispense with washing.

The technical value of caoutchouc chiefly depends on the extent to which it is capable of being stretched without breaking, and the extent to which it at once returns to its original dimensions.

The following table gives the dimensions of some well-known American lead-furnaces.

The dimensions of a piece of iron, for example, its elasticity, its thermo-electric power and its electric conductivity are all changed under the influence of magnetism.

The standard rod and the test specimen, which must be of the same dimensions, are placed side by side within two magnetizing coils, and each pair of adjacent ends is joined by a short rectangular block or " yoke " of soft iron.

But when exceptionally strong fields are desired, the use of a coil is limited by the heating effect of the magnetizing current, the quantity of heat generated per unit of time in a coil of given dimensions increasing as the square of the magnetic field produced in its interior.

Changes Of Dimensions Attending Magnetization It is well known that the form of a piece of ferromagnetic metal is in general slightly changed by magnetization.

Thomson (Applications of Dynamics to Physics and Chemistry, 47) that on dynamical principles there must be a reciprocal relation between the changes of dimensions produced by magnetization and the changes of magnetization attending mechanical strain.

The method indeed fails for equations of an order above the fourth, because it then involves the solution of an equation of higher dimensions than they proposed.

It was his just boast to have transformed mechanics (defined by him as a "geometry of four dimensions") into a branch of analysis, and to have exhibited the so-called mechanical "principles" as simple results of the calculus.

A fine belfry (12th, 13th and 15th centuries) commanding the town is built on the terrace, beneath which are hollowed in the rock the oratory and hermitage of St Emilion, and adjoining them an ancient monolithic church of considerable dimensions.

Its extreme dimensions are 2629 m.

This is sometimes called the number of homogeneous products of r dimensions formed out of n letters; i.e.

If we consider for the present only the primary plane of symmetry, the figure is reduced to two dimensions.

In theoretical investigations these problems are usually treated as of two dimensions only, everything being referred to the plane passing through the luminous point and perpendicular to the diffracting edges, supposed to be straight and parallel.

Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?

Problems not limited to two dimensions, such for example as the shadow of a circular disk, present great difficulties, and have not hitherto been treated by a rigorous method; but there is no reason to suppose that Fresnel's results would be departed from materially.

The plan of campaign which found favour with the Boers, when they determined to put their differences with Great Britain to the test by the ordeal of the sword, was to attack all the principal British towns adjacent to their own borders; at the same time to despatch a field army of the necessary dimensions to invade and reduce Natal, where the largest British garrison existed.

A valuable historical source, though of small dimensions, is the Chronicle of Edessa, which gives a record of events from 132-131 B.C. to A.D.

He found by patient inquiry that several physical features and the dimensions of certain bones or bony structures in the body remain practically constant during adult life.

The whole of the information is easily contained in one cabinet of very ordinary dimensions, and most ingeniously contrived so as to make the most of the space and facilitate the search.

Albert Nyanza has indeed shrunk in its dimensions during the comparatively few years it has been known to Europeans.

After this the need of fortifying Londinium must have been apparent, and a walled city of small dimensions arose soon after the defeat of the British queen.

Roach Smith pointed out that the enclosure indicated above gives dimensions far greater than those of any other town in Britain.

Slow-speed fans are sometimes of large dimensions, up to 30 and even 45 ft.

Its dimensions are 300 X400 ft.

Further, all the subsequent processes of cutting, moulding and annealing become increasingly difficult, owing to the greatly increased risk of breakage arising from either external injury or internal strain, as the dimensions of the individual piece of glass increase.

Thus the dimensions of the largest glass tanks greatly exceed those of the largest steel furnaces; glass furnaces containing up to 250 tons of molten sible to work glass-tanks continuously for many months together; on the other hand, glass is not readily freed from foreign bodies that may become admixed with it, so that the absence of detachable particles is much more essential in glass than in steel melting.

The size of cylinder which can be produced in this way depends chiefly upon the dimensions of the working platform and the weight which a man is able to handle freely.

Molten glass is spread upon a large iron plate of the required shape and dimensions.

Each cell is of suitable dimensions to turn out a slab of sugar about 14 in.

For eight months of the year the Jumna shrinks to the dimensions of a mere rivulet, meandering through a waste of sand.

The meteors, whatever their dimensions, must have motions around the sun in obedience to the law of gravitation in the same manner as planets and comets - that is, in conic sections of which the sun is always at one focus.

At the time of its greatest dimensions the volcano was perhaps twice as high as it is now.

The northern islandYezocontains seven, and there are as many more in the main and southern islands, to say nothing of flat lands of minor dimensions.

In actual wealth of blossom or dimensions of forest trees the Japanese islands cannot claim any special distinction.

Spiders abound, from a giant species to one of the minutest dimensions, and the tree-bug is always ready to make a destructive lodgment in any sickly tree-stem.

The difference between this process and ordinary inlaying is that for sumi-zogan the design to be inlaid is fully chiselled out of an independent block of metal with sides sloping so as to be broader at the base than at the top. The object which is to receive the decoration is then channelled in dimensions corresponding to those of the design block, and the latter having been fixed in the channels, the surface is ground and polished until an intimate union is obtained between the inlaid design and the metal forming its field.

But if the Japanese sculptor adopted such standards in working for foreign patrons, his market would be reduced to very narrow dimensions.

The building, sometimes of huge dimensions, is invariably surrounded by a raised gallery, reached by a flight of steps in the centre of the approach front, the balustrade of which is a continuation of the gallery railing.

When the temple is of very large dimensions an interior peristyle of pillars is introduced tc assist in supporting the roof, and in such cases each pillar carrim profuse bracketing corresponding to that of the cornice.

Arras of large dimensions, showing remarkable workmanship and grand combinations of colors, is now manufactured in KiOto, the product of years of patient toil on the part of weaver and designer alike.

Up to that time there had been little demand for enamels of large dimensions, but when the foreign market called for vases, censers, plaques and such things, no difficulty was found in supplying them.

The industry was threatened with extinction, and would certainly have dwindled to insignificant dimensions had not a few earnest artists, working in the face of many difficulties and discouragements, succeeded in striking out new lines and establishing new standar4s for excellence.

This capacity is then a function of the geometrical dimensions of the conductor, and can be mathematically determined in certain cases.

A rectangular trough of boards, whose dimensions depend chiefly on the size of the planks available, is set up on the higher part of the ground at one side of the claim to be worked, upon trestles or piers of rough stone-work, at such an inclination that the stream may carry off all but the largest stones, which are kept back by a grating of boards about 2 in.

The largest timber tree is the mvule, which attains vast dimensions, its trunk supplying the natives with the dug-out canoes with which they navigate the lake.

Scarcely inferior in beauty of design and execution, though of more moderate dimensions, is the tomb of the saint Abdullah Ansari, in the same neighbourhood.

But at high exhaustions the free path becomes comparable with the dimensions of the glass bulb, and this equalization proceeds slowly.

Its dimensions are similar to those of the former instrument.

By the adoption of more refined methods of construction, especially in the shape of the intake and discharge passages for the air and the forms of the fan blades, the efficiency of the ventilating fan has been greatly increased so that the dimensions can be much reduced and a higher rate of speed adopted.

The great size and weight of such drums are also disadvantages, as giving rather unmanageable dimensions in a very deep pit.

The most valuable of these are the egg and stove sizes, which are broken to the proper dimensions for household use, the larger lumps being unfit for burning in open fire-places.

On the other hand, the atom itself has no parts or dimensions.

Apart from speculation, the first definite evidence for the molecular structure of matter occurs when it is found that certain physical phenomena change their whole nature as soon as we deal with matter of which the linear dimensions are less than a certain amount.

This leads to an interpretation of the fact that a change of dimensions usually attends a change in the temperature of a substance.

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

In the same way, in the case of a figure in three dimensions, analytical geometry is concerned with the form of the surface, while analytical mensuration is concerned with the figure as a whole.

The reduction in thickness of the bars is accompanied by a slight increase in their width and a very great increase in their length, so that it is generally necessary to cut partly rolled bars into two parts to keep them of convenient dimensions.

It had a continuous fringe of covered halls of various dimensions and shapes, once richly adorned with statues and columnar screens.

Immediately above this fixed plate, and almost in contact with it, is another of the same dimensions, and furnished with the same number, n, of openings similarly placed, but passing obliquely through in an opposite direction from those in the fixed plate, the one set being inclined to the left, the other to the right.

The energy of this fork with a given amplitude of vibration could be calculated from its dimensions and elasticity, and the amplitude was observed by measuring with a microscope the line into which the image of a starch grain on the prong was drawn by the vibration.

The velocity of a disturbance along such a bar, and its modes of vibration, depend therefore on the elastic properties of the material and the dimensions of the bar.

When girders form the superstructure, the resultant pressure on the piers or abutments is vertical, and the dimensions of these are simply regulated by the sufficiency to bear this vertical load.

The first investigates mathematical facts relating to the earth as a whole, its figure, dimensions, motions, their measurement, &c. The second part considers the earth as affected by the sun and stars, climates, seasons, the difference of apparent time at different places, variations in the length of the day, &c. The third part treats briefly of the actual divisions of_the surface of the earth, their relative positions, globe and map-construction, longitude, navigation, &c. Varenius, with the materials at his command, dealt with the subject in a truly philosophic spirit; and his work long held its position as the best treatise in existence on scientific and comparative geography.

It remained for the third influence to complete the work begun and to develop systematic nursing to its present dimensions.

It is safer to give it the more reasonable dimensions of Caesar, and to accept the verdict of later commentators that it never extended west of the Scheldt.

This result is inconsistent with the aether remaining at rest, unless we assume that the dimensions of the moving system depend, though to an extent so small as to be not otherwise detectable, on its orientation with regard to the aether that is streaming through it.

That date may therefore be reckoned as that of the foundation of the coaltar colour industry, which has since attained such important dimensions - in Germany, however, rather than in England, the country where it originated.

In 1615 he planned and carried into practice a new method of finding the dimensions of the earth, by determining the distance of one point on its surface from the parallel of another, by means of a triangulation.

The moas ranged in size from that of a turkey to truly colossal dimensions, the giant being Dinornis maximus, which, with a tibial length of 39 in., stood with its small head about 12 ft.

Poland was now reduced to one-third of her original dimensions, with a population of about three and a half millions.

There are, first, the Books; then, the Collection; then, the Sacred Volume, complete as such in idea, though not as yet complete in its actual contents; and, lastly, the Sacred Volume in its full dimensions, as it has come down to us.

The chapels of the colleges at Oxford and Cambridge are sometimes of large dimensions and architecturally of great importance, that of Christ Church being actually the cathedral of Oxford; among others may be mentioned the chapel of Merton College, and the new chapel of Exeter College, both in Oxford, and the chapel of King's College, Cambridge, which is roofed over with perhaps the finest fan-vault in England.

This unit is also recorded by cubit lengths scratched on a tomb at Beni Hasan (44), and by dimensions of the tomb of Ramessu IV.

The foot of 11.6 appears probably first in the prehistoric and early Greek remains, and is certainly found in Etrurian tomb dimensions as 11.59 (25).

With the object of reaching fainter stars, Professor Pickering constructed another instrument of larger dimensions, and with this more than a million observations have been made.

In two families motile articulated rods occur; in Triarthridae they probably simply expand the dimensions of the body in adaptation to life at the surface; or as a protection against being swallowed by their smaller foes.

To the home government the purely military problem, although assuming larger dimensions and more difficulties, still seemed to admit of a simple solution, namely, to strike hard where the rebellion was most active and capable of the longest resistance.

He was associated with Sir William Fairbairn in an important series of experiments on cast iron, and his help was sought by Robert Stephenson in regard to the forms and dimensions of the tubes for the Britannia bridge.

Great emphasis has been laid on the agreement of a tetrapolis, formed by Nineveh, Khorsabad, Calah and Keramlis, with the dimensions given by Diodorus and with the phrase " an exceeding great city of three days' journey ."

The duration of the Pleistocene lakes was, however, brief as compared with the time since the dislocation of the faulted blocks, as is shown by the small dimensions of the lacustrine beaches compared to the great volume of the ravine-heading fans on which the beaches often lie.

The lode was an ore channel of great dimensions included within volcanic rocks of Tertiary age, themselves broken through pre-existing strata of Triassic age, and exhibited some of the features of a fissure vein, combined in part with those of a contact deposit and in part with those of a segregated vein.

We may form some idea of its enormous dimensions from the fact recorded, that when, A.D.

The church, the ground-plan of which bears a remarkable resemblance to that of Lincoln Cathedral, was of vast dimensions.

The western entrance was approached by an ante-church, or narthex (B), itself an aisled church of no mean dimensions, flanked by two towers, rising from a stately flight of steps bearing a large stone cross.

The chief conclusions of astronomers concerning the .spherical figure and dimensions of the earth, its relation to the heavenly bodies, and the great circles of the globe - the equator, the ecliptic and the tropics - were considered as well established.

The woollen trade once promised to reach considerable dimensions, but towards the end of the 18th century was superseded by the linen (for which flax came to be largely grown); and when this in turn collapsed before the products of the mills of Dundee, Dunfermline and Glasgow, straw-plaiting was taken up, though only to be killed in due time by the competition of the south.

These organs are characteristic of all Lamellibranchs; they do not vary except in size, being sometimes drawn out to streamer-like dimensions.

Special mention may be made of Megamys, from the caves of Brazil, which, while apparently allied to the living viscacha, attained dimensions approximating to those of a hippopotamus.

Leaving the consideration of radical changes of a vibrating system out of account for the present, the minor differences which have been observed in the appearances of spectra under different sparking conditions are probably to a large extent due to differences in the quantities of material examined, though temperature must alter the violence of the impact and there is a possible effect due to a difference in the impact according as the vibrating system collides with an electron or with a body of atomic dimensions.

According to him, whatever inferences we make, certain or uncertain, are mere economies of thought, adapting ideas to sensations, and filling out the gaps of experience by ideas; whatever we infer, whether bodies, or molecules, or atoms, or space of more than three dimensions, are all without distinction equally provisional conceptions, things of thought; and " bodies or things are compendious mental symbols for groups of sensations - symbols which do not exist outside thought."

Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.

Originally it is thought to have been the measure of a day's ploughing, in which case the dimensions given above would scarcely be reached.

If so the normal dimensions of the acre may very well have been quite different.

But for its university Bonn would be a place of comparatively little importance, its trade and commerce being of moderate dimensions.

For export the dimensions are commonly 32 or 36 in.

Extending in longitudinal dimensions 257 ft., it is FIG.

The dimensions of the buildings at Sheen are stated to have been remarkably large.

Where the cultivation of large specimens has to be carried on, a span-roofed house of greater height and larger dimensions may sometimes prove useful; but space for this class of plants may generally be secured in a house of the smaller elevation, simply by lowering or removing altogether the staging erected for smaller plants, and allowing the larger ones to stand on or nearer the floor.

The latter may in certain cases attain large dimensions, and even undergo cell-divisions in their interior, resulting in the development of true tissues.

It is an irregular building in Gothic style, with a high pointed roof, and flanked by four towers of unequal dimensions.

This is found in the Borinage district near Mons and in the neighbourhood of Liege, but the working of an entirely new coal-field, which promises to attain vast dimensions, was commenced in 1906 in the Campine district of the province of Limburg.

Whatever may be the truth about the origin of the kingdom, and it is by no means impossible that the invasion really proceeded from a different quarter, we need not doubt that its dimensions were largely increased under Ceawlin.

A small office was first taken on a second floor in Essex Street, Strand; but this had soon to be abandoned, as the dimensions of the League rapidly increased.

In their conceptions a single social imperfection assumed such portentous dimensions that it seemed to overcloud the whole heaven and threaten the world with ruin.

In all cases the dimensions of the leaf are enlarged by interstitial growth of its parts.

This condition can generally be satisfied with sufficient approximation with plates of reasonable dimensions.

If the dimensions of the bar are suitably chosen, the distribution of temperature is always very nearly parabolic, so that it is not necessary to determine the value of the critical current C 2 = hpllaRo very accurately, as the correction for external loss is a small percentage in any case.

Its dimensions should be capable of carrying off the whole water used so quickly as to prevent the least stagnation, and discharge it into the river.

The Civil War gradually grew to dimensions beyond all expectation.

The jute manufacture, the principal centres of which are Berlin, Bonn, Brunswick and Hamburg, has of late attained considerable dimensions.

If an auroral arc represented a definite selfluminous portion of space of small transverse dimensions at a uniform height above the ground, its height could be accurately determined by observations made with theodolites at the two ends of a measured base, provided the base were not too short compared to the height.

If after a heavy earthquake we find bodies that have been projected or overturned, then by observing the distance of projection, and the height through which they have fallen, or their dimensions, we can 5.

Within this is hung loosely a second tube of much smaller dimensions so as to leave an annular space between the two.

Even among Bangiaceae the carpospores arise from the fertilized cell by division, while in all other Rhodophyceae the oospore, as it may be called, gives rise to a filamentous structure, varying greatly in its dimensions, epiphytic, and to a large extent parasitic upon the egg-bearing parent plant, and in the end giving rise to carpospores in the terminal cells of certain branches.

In 1511 was completed another famous painting, multitudinous in the number of its figures though of very moderate dimensions, the "Adoration of the Trinity by all the Saints," a subject commissioned for a chapel dedicated to All Saints in an almshouse for decayed tradesmen at Nuremberg, and now at the Imperial Gallery at Vienna.

Besides such fine single woodcuts as the "Mass of St Gregory," the "St Christopher," the "St Jerome," and two Holy Families of 1511, Darer published in the same year the most numerous and popularly conceived of all his woodcut series, that known from the dimensions of its thirty-seven subjects as the "Little Passion" on wood; and in the next year, 1512, a set of fifteen small copper-engravings on the same theme, the "Little Passion" on copper.

A preorbital vacuity of such dimensions as to exclude the lachrymal bone from articulation with the nasal.

The majority of the palace buildings are, in ground-plan, quadrangular, with all the rooms opening on to a central court; and the whole reached its present size simply by the gradual addition of new quadrangles, designed on the same principle, though varying in dimensions, and connected with each other by smaller rooms and passages.

It is chiefly remarkable for its finely preserved fortifications constructed of tetrahedral and polygonal blocks of local limestone well jointed, with maximum dimensions of about 3 by i z ft.; the outer circuit of the city wall measures about 22 m.

If a statue was to be cast, the figure was first roughly modelled in clay - only rather smaller in all its dimensions than the future bronze; all over this a skin of wax was laid, and worked by the sculptor with modelling tools to the required form and finish.

In all work done in thick plates the dimensions marked out must have reference to the final shape of the article.

Generally the dimensions are taken as in the middle of the plate, but they may be on the inside or outside according to circumstances.

If an object has to be beaten into concave form from a flat thin sheet, the outer portions must be hammered until they occupy smaller dimensions than on the flat sheet.

The weak chlorine from the Deacon process cannot be treated in this manner, as chambers of impossibly large dimensions would be required.

The reflecting telescope became the only available tool of the astronomer when great light grasp was requisite, as the difficulty of procuring disks of glass (especially of flint glass) of suitable purity and homogeneity limited the dimensions of the achromatic telescope.

Telescopes of such dimensions can be conveniently directed to any object by the circles without the observer being under the necessity to climb a special ladder.

But a floor, however heavy, suspended by three wire ropes and properly balanced over large, well-mounted pulleys, requires an amount of energy to work it which does not exceed that required to operate a platform of moderate dimensions, and there is a freedom, a safety and a facility of working with a complete floor which no partial platform can give.

The instrument is thus a theodolite, although, compared with its other dimensions, feeble as an apparatus for the measurement of absolute altitudes and azimuths, although capable of determining these co-ordinates with considerable precision.

The dimensions of the Algol system have been calculated, with the result that Algol appears to have'a diameter of 1,000,000 m.

Whilst there is thus no well-defined lower limit to the dimensions of systems of two stars, on the other hand we cannot set any superior limit either to the number of stars which shall form a system or to the dimensions of that system.

By means of the spectroscope it is possible to determine the relative orbital velocity of the two components, and this when compared with the period fixes the absolute dimensions of the orbit; the apparent dimensions of the orbit being known from visual observations the distance can then be found.

The cells inhabited by prisoners (and separate cellular confinement was now very general) were of different dimensions - variously lighted, warmed and ventilated.

It consists of three stages, connected by numerous exterior staircases and decreasing in dimensions as they rise, culminating in the sanctuary, a great central tower pyramidal in form.

Hamilton, still keeping prominently before him as his great object the invention of a method applicable to space of three dimensions, proceeded to study the properties of triplets of the form x+iy+jz, by which he proposed to represent the directed line in space whose projections on the co-ordinate axes are x, y, z.

Another peculiarity of the males is the presence of a huge throat-sac or pouch on the front of the throat and chest, which may extend even to the arm-pits; although present in females, it does not reach nearly the same dimensions in that sex.

In all, about sixty kinds of timber of marketable quality are furnished in more or less profusion, but the difficulty of extraction, even in the regions situated in close proximity to the large waterways, renders it improbable that the timber trade of Borneo will attain to any very great dimensions until other and easier sources of supply have become exhausted.

Its exact dimensions are unknown; they probably coincided with those of the old diocese of Worcester, the early bishops of which bore the title "Episcopus Hwicciorum."

For the present we confine ourselves to the consideration of displacements in two dimensions, so that the body is adequately represented by a thin lamina or plate.

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

A general criterion for the case of a rigid body movable in two dimensions, with one degree of freedom, can be obtained as follows.

For investigations relating to the equilibrium of a string in three dimensions we must refer to the textbooks.

This is perhaps the most suitable place for a few remarks 011 the theory of dimensions.

In any general dynamical equation the dimensions of each term in the fundamental units must be the same, for a change of units would otherwise alter the various terms in different ratios.

The theory of dimensions often enables us to forecast, to some extent, the manner in which the magnitudes involved in any particular problem will enter into the result.

For it can only depend on the mass m of the bob, the length 1 of the string, and the value of g at the place in question; and the above expression is the only combination of these symbols whose dimensions are those of a time, simply.

Proceeding to the general motion of a rigid body in two dimensions we may take as the three co-ordinates of the body the rectangular Cartesian co-ordinates x, y of the mass-centre G and the angle C through which the body has turned from some standard position.

Conditions of Stiffness and Strength.After the arrangement of the pieces of a structure and the size and figure of their joints or surfaces of contact have been determined so as to fulfil the conditions of stabilityconditions which depend mainly on the position and direction of the resultant or total load on each piece, and the relative magnitude of the loads on the different piecesthe dimensions of each piece singly have to be adjusted so as to fulfil the conditions of stiffness and strengthconditions which depend not only on the absolute magnitude of the load on each piece, and of the resistances by which it is balanced, but also on the mode of distribution of the load over the piece, and of the resistances over the joints.

The foi-m and arrangement of the pieces of the frame depend upon the arrangement and the motions of the mechanism; the dimensions of the pieces of the frame required in order to give it stability and strength are determined from the pressures applied to it by means of the mechanism.

Motions ClassedIn problems of mechanism, each solid piece of the machine is supposed to be so stiff and strong as not to undergo any sensible change of figure or dimensions by the forces applied to ita supposition which is realized in practice if the machine is skilfully designed.

Rather the Iliad is itself a single lay which has grown with the growth of poetical art to the dimensions of an epic.

The temple, which usually stands in the middle of a court, is as a rule a building of very moderate dimensions, consisting either of a single square chamber, surmounted by a pyramidal structure, or of a chamber for the linga and a small vestibule.

The dimensions of the various chambers included in Luray Cavern cannot easily be stated, on account of the great irregularity of their outlines.

The Gothic parish church (c. 1400) incorporates remains of a cathedral of vast dimensions.

He advocated peace, and his influence carried the day, thus removing a difficulty which, though apparently of minor dimensions, might have changed the whole course of Japan's modern history.

The red pine of Canada and New England (so called from the colour of its bark), P. resinosa, is a tree of considerable size, sometimes attaining the dimensions of P. sylvestris.

It is found in Kumaon and Bhotan and on some of the Nepal ranges, but does not grow in the moist climate of the Sikkim Himalayas; it is found at a height of 7000 to 12,000 ft., and attains large dimensions; the wood is highly resinous, and is said to be durable; great quantities of a white clear turpentine exude from the branches when injured.

The tree abounds in some sandy districts, but more generally occurs singly or in small groups dispersed through the woods, attaining its greatest dimensions in light soils.

The population is largely nomadic. The fact that so many as 15,000 camels have been counted in the Bolan Pass during one month of the annual Brahui migration indicates the dimensions which the movement assumes.

The dimensions of the glaciers on the outer Himalaya, where, as before remarked, the valleys descend rapidly to lower levels, are fairly comparable with those of Alpine glaciers, though frequently much exceeding them in length8 or io m.

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

On the one hand, soul is corporeal, else it would have no real existence, would be incapable of extension in three dimensions (and therefore of equable diffusion all over the body), incapable of holding the body together, as the Stoics contended that it does, herein presenting a sharp contrast to the Epicurean tenet that it is the body which confines and shelters the light vagrant atoms of soul.

In May 1907 there was a street-car strike of large dimensions.

He did not, however, enter into the explanation of particular phenomena, as this had been done already by Laplace, but he pointed out to physicists the advantages of the method of Segner and Gay Lussac, afterwards carried out by Quincke, of measuring the dimensions of large drops of mercury on a horizontal or slightly concave surface, and those of large bubbles of air in transparent liquids resting against the under side of a horizontal plate of a substance wetted by the liquid.

Since e is a line of insensible magnitude compared with the dimensions of the mass of liquid and the principal radii of curvature of its surface, the volume of the shell whose surface is S and thickness will be and that of the interior space will be V - SE.

The method already given for the investigation of the surface-tension of a liquid, all whose dimensions are sensible, fails in the case of a liquid film such as a soap-bubble.

If the thickness of the film is greater than 2E, there will be a stratum of thickness c-2E in the middle of the film, within which the values of p and x will be pc and In the two strata on either side of this the law, according to which p and x depend on the depth, will be the same as in a liquid mass of large dimensions.

The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

Taking the case where the motion is strictly in two dimensions, we may write as the polar equation of the surface at time t r =a cos nB cos pt, (4) where p is given by p2 = (n3_ n)..

Ciliary movements, which undoubtedly contribute in bringing the surface into contact with larger supplies of oxygen and other fluids in unity of time, are not so rapid or so extensive when compared with other standards than the apparent dimensions of the microscopic field.

For the most part the surface of the state is gently undulating and at a slight elevation above the lakes, but low marsh lands are common to many sections; the north part of the lower peninsula is occupied by a plateau of considerable dimensions, and the north-west part of the upper peninsula is rugged with hills and mountains.

Here and there along the course of the western rivers are found lagoons, sometimes of considerable dimensions.

Those apparent inconsistencies in the dimensions of the body and wings are readily explained by the greater muscular development of the heavy-bodied, small-winged insects, birds and bats, and the increased power and rapidity with which the wings in them are made to oscillate.

That no fixed relation exists between the area of the wings and the size and weight of the body to be elevated is evident on comparing the dimensions of the wings and bodies of the several orders of insects, bats and birds.

It is usually the case that the secondary caustic is easier to determine than the caustic, and hence, when determined, it affords a ready means for deducing, the primary caustic. It may be shown by geometrical considerations that the secondary caustic is a curve similar to the first positive pedal of the reflecting curve, of twice the linear dimensions, with respect to the luminous point.

The fruits do not usually exceed in size the dimensions of a hen's or of a swan's egg, but that of P. macrocarpa is a gourd-like oblong fruit attaining a weight of 7 to 8 lb.

Like most of the lesser apartments, it is lined with white Italian marble, and in spite of its enormous dimensions the roof is unsupported by pillars.

East Chicago covers an area whose greatest dimensions are 4 by 31 m.

The dimensions of the exterior piers ceased to control the height of the building, which was limited alone by the possibility of securing adequate foundations, and by a consideration of the amount of floor space which could be devoted without too great loss to a system of passenger lifts of sufficient capacity to afford speedy access to all parts of the building.

All abutting joints in riveted work are faced to exact lengths and absolutely at right angles to the axis of the piece, and are spliced by scarf plates of proper dimensions adequately secured by rivets.

These dimensions are very slightly lessened in the choir.

Of course we are unable to say whether such a region is an actuality in the sun, on the earth it is an exception and transient, but the greater the dimensions of the body the more probable is its occurrence.

His attempt to carve a principality for his son out of Moldavia, which Poland regarded as her vassal, led to the outbreak in 1651 of a third war between subject and suzerain, which speedily assumed the dignity and the dimensions of a crusade.

The sand, which is nominally the filter, has interstices about thirty times as wide as the largest dimensions of the larger microbes; and the reason why these, and, still more, why organisms which were individually invisible under any magnifying power, and could only be detected as colonies, were arrested, was not understood.

The dimensions of the nave depend to a large extent on the method of keying or otherwise securing the pulley to the shaft.

The dimensions of the pulleys are generally so arranged that the return motion of the lathe spindle is faster than the forward motion.

In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by solving the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a.

P Bullarium of Benedict XIV., officially published by him in 1747; further, the Bullarium is a compilation arranged in chronological order, and its dimensions make it rather unwieldy.

Both contain occasional state papers, and not very trustworthy reports of parliamentary proceedings., The publication of debates was not authorized till the last quarter of the century; parliamentary papers begin earlier, but only slowly attain their present portentous dimensions.

Trilinear and Tangential Co-ordinates.---The Geometrie descriptive, by Gaspard Monge, was written in the year 1794 or 1 795 (7th edition, Paris, 1847), and in it we have stated, in piano with regard to the circle, and in three dimensions with regard to a surface of the second order, the fundamental theorem of reciprocal polars, viz.

When the aquatic members of the class are taken into consideration, the maximum dimensions are vastly greater, Sibbald's rorqual attaining a length of fully 80 ft., and being probably the bulkiest and heaviest animal that has ever existed.

The fate of the reptilian quadrate bone (which is reduced to very small dimensions in the Anomodontia) has been referred to in an earlier section of the present article, where some mention has also been made of the disappearance in mammals of the hinder elements of the reptilian lower jaw, so as to leave the single bone (dentary) of each half of this part of the skeleton in mammals.

These plants, which appear to have grown in swampy soil, thus attained the dimensions of considerable trees.

In1784-1785he enlarged the villa into the mansion-house with its present dimensions by building an addition at each end, erected several of the out-buildings, and adorned the grounds, all according to his own plans and specifications.

The largest horns are found in the Galla cattle, in which they attain enormous dimensions.

For the dimensions of units see Units, Dimensions Of.

A tablet copied by George Smith gives us interesting details as to the plan and dimensions of this famous temple of Bel; a plan based on these will be found in Hommel's Grundriss der Geographie and Geschichte des alten Orients, p. 321.

The field we have defined is divisible into at least two parts, that of Astronomy proper, or " Astrometry," which treats of the motions, mutual relations and dimensions of the heavenly bodies; and that of Astrophysics, which treats of their physical constitution.

Such a body can be made known to us only when in the neighbourhood of an incandescent body; and even then, unless its mass or its dimensions are considerable, it will evade all the scrutiny of our science.

In one, the bodies are regarded as material particles, no account being taken of their dimensions.

It will be seen that the reasoning applies to the case of any one body or system of bodies, the dimensions of which are not regarded as infinitely small compared with the distance of the attracting body.

The exhaustive ascertainment of stellar parallaxes, combined with the visible facts of stellar distribution, would enable us to build a perfect plan of the universe in three dimensions.

His hair is black and frizzly, worn generally in a mop, often of large dimensions, but sometimes worked into plaits with grease or mud.

Previous to 1836, most of the coal worked in the parish was consumed locally, chiefly in the ironworks, but in that year the working of steam coal for export was begun, pits were sunk in rapid succession, and the coal trade, which at least since 1875 has been the chief support of the town, soon reached huge dimensions.

In places, as at Lere and Bifara, it widens into lake-like dimensions.

Becquerel that the intensity of the effect depended on the thermoelectric power of the junction and was independent of its form or dimensions.

Lydia never again shrank back into its original dimensions.

Its light is so faint and diffuse that it is impossible to assign dimensions to it, except to say it covers a region of several degrees in extent.

They are generally to be found within the town or village precincts, and are of much smaller dimensions than caravanserais.

The angle under which the object appears depends upon the distance and size of the object, or, in other words, the size of the image on the retina is determined by the distance and the dimensions of the object.

With the .orthogonal arrangement for illuminating and observing the beam of light traverses an extremely fine slit through a well-corrected system, whose optic axis is perpendicular to the axis of the microscope; the system reduces the dimensions of the beam to about 2 to 4 in the focal plane of the objective.

These are the dimensions necessary for determining the magnification of the microscope, viz.

Hall, built originally about 1682 as the mansion of the son of Frederick Philipse (1626-1702), the lord of Philipsburgh, and enlarged to its present dimensions in 1745, is of some historic interest.

The Calamarieae, now known to have been the chief Palaeozoic representatives of the Horsetail stock, attained the dimensions of trees, reaching, according to Grand' Eury, a height of from 30 to 60 metres, and showed in all respects a higher and more varied organization than their recent successors.

Broadly speaking, the Palaeozoic Lycopods, whatever their dimensions, show a general agreement in habit and structure with our living forms, though often attaining a much higher grade of organization.

Lyelli - in England, Germany, Portugal, Japan and elsewhere, differing still less in dimensions from modern species.

It cannot be demanded that the objective accusative of religious experiences occupy the spatial dimensions, since being spatial entails having sensory qualities.

The heritage Criteria of nations in Bloom judging is a complex amalgam of built, natural, cultural and social dimensions of a community.

Image A byte or integer array of either two or three dimensions, containing the image to be written.

It was a two-seat reconnaissance float biplane of very small overall dimensions designed to be folded and carried in the confines of a submarine.

A set of dimensions is produced for each detected calcification.

The pieces of the reptile are preserved in three dimensions inside a series of limestone concretions.

Whilst retaining classic two-door coupe dimensions, the unique Freestyle Door System does away with the need for center pillars.

The connector side of the router looks almost cramped due to the small dimensions.

F Attainment of intended learning outcomes appreciably deficient in critical respects, lacking secure basis in relevant factual and analytical dimensions.

Special emphasis is put on geographical and spatial dimensions of firm demography.

Here, the mathematical derivation, which involves matrix algebra, will be followed first, in two dimensions to make things easier.

The definition of a determinant in all dimensions will be given in detail, together with applications and techniques for calculating determinants.

For this reason, the course will seek to explore specific dimensions of world cinema in terms of historical and social contexts of production.

This must be of a material which is opaque to thermal infra-red; the approximate dimensions are 13mm length by 5mm diameter.

The voxel dimensions for the 6 datasets are and hence we consider SUSAN filtering with.

Images can by limited by color, animation and pixel dimensions.

The wheel at each corner design maximizes the interior dimensions and allows the Getz to offer generous accommodation despite its relatively diminutive size.

Right panel shows a disjunction for two categories having adjacent ranges for two different dimensions.

Of cathedral-like dimensions, used in their time as a refuge, a medieval dungeon and church, and smugglers ' hideout.

The work will develop fibers with optimal dimensions and solubility for cell growth do deliver genetically modified muscle cells to treat muscular dystrophy.

The guidance highlights five key dimensions of a SACRE's work and provides exemplification of good practice.

Mach suggesting more than 3 dimensions to make things explicable.

This is significant because the theoretical underpinning is often geometric in nature and such systems lend themselves to representation in three dimensions.

Dimensions 7'3 " x 12 " £ 59.99 JRC Cocoon holdall - 12ft fully padded holdall.

Dimensions 6'9 " x 8 " (206 x 22cm) £ 17.99 Shakespeare Rod holdall - A holdall for the specialist carp angler.

Research fields include small-scale hydropower, wind, solar, wave, and bioenergy as well as social dimensions of energy use.

They found themselves in a chamber of large dimensions, with several choked inlets.

Four working groups then focused on climatology, coastal zone ecosystems and land use, ocean-atmosphere interactions, and human dimensions.

The three dimensions are not necessarily equal, but the sampling interval is the same in each direction.

The MBTI® is a self-report inventory with four psychological dimensions, energizing, attending, deciding and living.

The computational cost of refining these n-m guesses will rapidly become large as the dimensions of the space increase.

The requirements for testing using the cylindrical mandrel are the same as the conical mandrel in terms of dimensions.

And because these drawings are derived automatically from the 3D model, there is no need to check dimensions.

When using oblique the side of the object you are looking at is drawn in two dimensions, i.e. flat.

They were a form of whiff, with roughly the same dimensions, fitted with sliding seats and full outriggers.

They bulge outwards like grapefruit segments, giving two dimensions the appearance of three.

Mark on all dimensions of the garden including all planters.

Later parts of the module will assume familiarity with elementary material on vectors in 2 and 3 dimensions including scalar and vector products.

They use sine, cosine and tangent in right-angled triangles when solving problems in two dimensions.

Quick Size Guide Below is a sizing chart to better help you choose the snowboard with the right dimensions for you.

Space has three dimensions, and time has one, so space-time is four-dimensional, but the four components are discrete.

Possibilities include supersymmetry (SUSY) as well as models which posit the existence of spatial dimensions beyond our normal experience.

The scale is sumptuous, the dimensions breath taking.

They explore how to create images that will be viewed in two dimensions, but actually look three-dimensional.

Mixed gear/chain valve timing drive with the two gears (one per timing chain) located in the crankcase to reduce cylinder head dimensions.

It helps to give the toolmaker the dimensions in the form that he will actually use them.

Casting - up to about 25kg and 2ft x 2ft x 1ft (60cm x 60cm x 30cm) overall dimensions is easily do-able.

It is equally evident that i varies as T, and therefore that it must be proportional to T/Xr, T being of three dimensions in space.

From the general theory (see Interference Of Light, § 8), or by the method of dimensions, it is easy to prove that in the latter case the intensity varies as A2, instead of A-4.

Subsequent visits to Winchester inspired Henry with the idea of rebuilding Eton church on cathedral dimensions.

The ruins of the retrenched northern portion of Kublai's great rampart are still prominent along their whole extent, so that there is no room for question as to the position or true dimensions of the Cambaluc of the middle ages; and it is most probable, indeed it is almost a necessity, that the present palace stands on the lines of Kublai's palace.

The detached building, formerly the stables, is converted into a fine concert hall; it is lighted by a vast glazed dome approaching that of St Paul's cathedral, London, in dimensions.

The Cowthorpe oak, standing (a ruin) near Wetherby in Yorkshire, at the same height measures 382 ft., and seems to have been of no smaller dimensions when described by Evelyn two centuries ago; like most of the giant oaks of Britain, it is of the pedunculate variety.

Out of a portion of the ancient markets a hotel-deville of modest dimensions has been constructed, and in the hospital of St Jean are a few pictures.

General geography was divided into - (I) the Absolute part, dealing with the form, dimensions, position and substance of the earth, the distribution of land and water, mountains, woods and deserts, hydrography (including all the waters of the earth) and the atmosphere; (2) the Relative part, including the celestial properties, i.e.

They should be of ample dimensions to accommodate the traffic - the British Board of Trade requires them to be not less than 6 ft.

After the exodus, which perhaps took place about 1300 B.C., they moved northwards again and founded a state of modest dimensions, which attained a short-lived unity under Solomon, but succumbed to internal dissensions and to the attacks of Assyria and Babylon.

Eleazar Albin between 1738 and 1740 produced a Natural History of Birds in three volumes of more modest dimensions; but he seems to have been ignorant of ornithology, and his coloured plates are greatly inferior to Catesby's.

Joule also made experiments upon iron wires under tension, and drew the erroneous inference (which has been often quoted as if it were a demonstrated fact) that under a certain critical tension (differing for different specimens of iron but independent of the magnetizing force) magnetization would produce no effect whatever upon the dimensions of the wire.

Serious students in Portugal and abroad welcomed the book as an historical work of the first rank, for its evidence of careful research, its able marshalling of facts, its learning and its painful accuracy, while the sculptural simplicity of the style and the correctness of the diction have made it a Portuguese classic. The first volume, however, gave rise to a celebrated controversy, because Herculano had reduced the famous battle of Ourique, which was supposed to have seen the birth of the Portuguese monarchy, to the dimensions of a mere skirmish, and denied the apparition of Christ to King Affonso, a fable first circulated in the 15th century.

But if its dimensions be much less than the half wave-length, it can only be seen as a whole, and its parts cannot be distinctly separated, although in cases near the border line some inference may be possible, founded upon experience of what appearances are presented in various cases.

During the first twenty-five years of the Meiji era, the Owari potters sought to compensate the technical and artistic defects of their pieces by giving them magnificent dimensions; but at the Tokyo industrial exhibition (1891) they were able to contribute some specimens showing decorative, plastic and graving skill of no mean order.

With three component metals the complete diagram giving the variations in any property must be in three dimensions, although by the use of contour lines the essential facts can be represented in a plane diagram.

The dimensions of a capacity in electrostatic measure is a length (see Physical Units).

One result of this damming up has been to submerge the Silver Strand and to curtail the dimensions of Ellen's Isle.

When early in the 16th century the Spaniards found their way from the West India Islands to this part of the mainland of America, they discovered not rude and simple tribes like the islanders of the Antilles, but nations with armies, official administrators, courts of justice, high agriculture and mechanical arts, and, what struck the white men especially, stone buildings whose architecture and sculpture were often of dimensions and elaborateness to astonish the builders and sculptors of Europe.

But the dimensions of the several belts and the strength of the relief developed by their later erosion varies greatly along the system.

Nor are its dimensions (460 by 345 ft.) such as to place it in the first rank of structures of this class, nor are there any underground chambers below the arena, with devices for raising wild beasts, &c. But, as we learn from the case of their squabble with the people of Nuceria, the games celebrated in the amphitheatre on grand occasions would be visited by large numbers from the neighbouring towns.

We know nothing quantitatively of the radiations from a nebulous body; and it is quite possible that the loss of radiant energy in this early stage was very small; but it is at least as certain as any other physical inference that 17,000,000 years ago the earth itself was of its present dimensions, a comparatively old body with sea and living creatures upon it, and it is impossible to believe that the sun's radiations were wholly different; but, if they were not, they have been maintained from some other source than contraction.

The consequence of the ancient evaporation, by which the great Pleistocene lake was reduced to its present modest dimensions, and of the ceaseless modern daily evaporation, is the impregnation of the waters of the lake with salts and other mineral substances to a remarkable degree.

Many redshift surveys are being undertaken to gain an understanding of the geometry of the Universe in three spatial dimensions.

Luckily the two Redwoods planted in Grosvenor Park will not attain such astounding dimensions, but may nevertheless develop into very large specimens.

The straps have some flexibility, but the new haft must be shaved down to the same dimensions as the old one.

Some are compacted into little balls so that only the strings poke out into the four space-time dimensions we observe.

In the past this has focussed on the construction of perturbative, semi-realistic models of softly broken N=1 supergravity models in four dimensions.

For this reason, language can no more transcend duality than paintings or photographs upon a flat surface can go beyond two dimensions.

The book was born out of a workshop organized by the US National Research Council 's Committee on the Human Dimensions of Global Change.

Measure the dimensions of the space the clothes dryer will occupy before you start shopping.

You also need to know the dimensions of the space where you are putting the washing machines.

Select the right dimensions for your portfolio, depending upon the nature and size of your artwork.