An ill-balanced load also exaggerates " plunging," and if the period of oscillation of the load happens to agree with the changes of contour or other inequalities of the track vibrations of a dangerous character, giving rise to so-called " sinuous " motion, may occur.
Given that inequalities in income are likely to grow, how I can I contend that we will see an end of poverty?
- Diurnal inequalities such as those of Tables II.
The amount of slack varies in different cases between 3 and Do per cent., but some is always allowed, so that the cable may easily adapt itself to inequalities of the bottom and may be more readily lifted for repairs.
But even here the hopefulness as regards a future life, in which the inequalities of the present would be rectified, compensated for the gloomy fatalism with which the present was 1 The earliest example given in the New English Dictionary is in S.
The floors of both crypts have sunk considerably and are often under water; this settlement accounts for the inequalities of the pavement.
More than a modicum of rusticity is needed as a protection to a man who attempts such colossal reforms. This necessity had its consequences in the disquieting inequalities of Wagner's early work, and the undeniable egotism that embittered his fiery nature throughout his life; while the cut-and-dried system of culture of later Wagnerian discipleship has revenged him in a specially sacerdotal type of tradition, which makes progress even in the study of his works impossible except through revolt.
From a mining settlement the city grew as the inequalities of the site permitted.
The result is an approximation, for inequalities of the ground bounded by the two contours have not been considered.
The tough but flexible coarse grey paper (German Fliesspapier), upon which on the Continent specimens are commonly fixed by gummed strips of the same, is less hygroscopic than ordinary cartridge paper, but has the disadvantage of affording harbourage in the inequalities of its surface to a minute insect, Atropos pulsatoria, which commits great havoc in damp specimens, and which, even if noticed, cannot be dislodged without difficulty.
On the other hand, there is recognition of the inequalities and miseries of life (Job; Ecclus.
Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.
The final achievement of Lagrange in this direction was the extension of the method of the variation of arbitrary constants, successfully used by him in the investigation of periodical as well as of secular inequalities, to any system whatever of mutually interacting bodies.'
Of these the most conspicuous was offered by the opposite inequalities of Jupiter and Saturn, which the emulous efforts of L.
The theory of inequalities is closely connected with that of maxima and minima, and therefore seems to come properly under this head.
Mention may also be made of his chapter on inequalities, in which he proves that the arithmetic mean is always greater than the geometric mean.
The actual formation of On account of inequalities in the atmosphere giving a variable refraction, the light from a star would be irregularly distributed over a screen.
His contemporary Domenico Guglielmini (1655-1710), who was inspector of the rivers and canals at Bologna, had ascribed this diminution of velocity in rivers to transverse motions arising from inequalities in their bottom.
The problem of the stresses in rarefied gaseous media arising from inequalities of temperature, which is thereby opened out, involves some of the most delicate considerations in molecular physics.
The inequalities of the geoid in no case exceed 300 ft.
Mohn has shown how the inequalities of what he terms the densitysurface can be found from the salinity and temperature; and he calculates that the level of the Skagerrak should be about 2 ft.
Still there are everywhere gentle inequalities on the smoothest ocean floor which give to its greater features a distinct relief.
The work was continued - with some inequalities, but always in the same spirit - until the suppression of the Society of Jesus in 1773.
This shape is most suitable for planing uneven timber, as inequalities are "hooked off" by the curved blade.
Inequalities of the required sort in the returns of the eclipses would ensue; moreover, their duration should concomitantly vary with the varying distance from periastron at the times of their occurrence.
Iii.) pointed out that the compressions and extensions in sound waves in air alternate so rapidly that there is no time for the temperature inequalities produced by them to spread.
Again, rapidly changing forces, due to the moving parts of the engine which are unbalanced vertically, act on the bridge; and, lastly, inequalities of level at the rail ends give rise to shocks.
This view of existence as an endless and concomitant sowing and reaping is accepted by learned and unlearned alike as accounting for those inequalities in human life which might otherwise lead men to doubt the justice of God.
But the detached and piecemeal way in which the revision had been carried out naturally caused certain inequalities in the execution of the work.
Although his search among documents was undoubtedly wide, its results are by no means always accurate, and his admirers themselves admit great inequalities of style in him.
With the renewal of uplift by which the earlier cycle of erosion was interrupted and the present cycle introduced, inequalities of surface due to renewed faulting were again introduced; these still appear as cliffs, of more nearly rectilinear front than the retreating escarpments formed in the previous cycle.
C. Huygens, in his De Circuli Magnitudine Inventa, 1654, proved the propositions of Snell, giving at the same time a number of other interesting theorems, for example, two inequalities which may be written as follows 8 - chd B }- 4 chd Bsin a (chd 0-sin >chd 8+3 (chd 0-sin 0).
The reason is that the sum of the solar and lunar inequalities, which are compensated in the whole period, may amount in certain cases to io, and thereby cause the new moon to arrive on the second day before or after its mean time.
The great variety of conditions under which the sediments and limestones were formed naturally produced corresponding inequalities in the thickness.
Will be found, besides his masterly report on the observatory, a general theory of secular inequalities, in which the development of the disturbing function was carried further than had previously been attempted.
The, chief uncertainty in applying this method appears to have arisen from variations of temperature at different parts of the surface, due to inequalities in the heating or cooling effect of the stream of water flowing over the surfaces.
The stuff taken out of the conductor should be employed in making up its banks or correcting inequalities in the meadow.
In depth may be obtained and inequalities of 3 ft.
He soon, however, returned to literary interests, moved towards them by the sudden success of Tennyson; and in 1844 he published a small volume of Poems, which was not without individuality, but marred by inequalities of workmanship. It was widely criticized, both in praise and blame; and Patmore, distressed at its reception, bought up the remainder of the edition and caused it to be destroyed.
Determined by the inequalities of surface of the overlying mantle of sedimentary material, they would be wholly independent of the geological structure of the rocks lying.
The great inequalities observed in the different vintages and the exceptionally fine character of the wines in good years are, generally, due to the same cause, namely, to the geographical position of the vineyards.
The phenomenon, which depends upon the inequalities of the moon's limb, was so vividly described by him as to attract an unprecedented amount of attention to the totality of the 8th of July 1842, observed by Baily himself at Pavia.
But the surface-tension, acting on a cylindric column of liquid whose length exceeds the limit of stability, begins to produce enlargements and contractions in the stream as soon as the liquid has left the orifice, and these inequalities in the figure of the column go on increasing till it is broken up into elongated fragments.
Even the incumbent of a parish is in law a " corporation sole," his benefice a freehold; and until the establishment in 1836, by act of parliament, of the Ecclesiastical Commissioners nothing could be done to adjust the inequalities in the emoluments of the clergy resulting from the natural rise and fall of the value of property in various parts of the country.
It may be expedient for balancing taxation and roughly redressing palpable inequalities, and may be adopted for that purpose and no other.
In 1755 Euler had been elected a foreign member of the Academy of Sciences at Paris, and some time afterwards the academical prize was adjudged to three of his memoirs Concerning the Inequalities in the Motions of the Planets.
Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit.
Among these subjects were the transit of Mercury, the Aurora Borealis, the figure of the earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, various problems of spherical trigonometry, &c. In 1742 he was consulted, with other men of science, by the pope, Benedict XIV., as to the best means of securing the stability of the dome of St Peter's, Rome, in which a crack had been discovered.
If 1 be the mean longitude of the planet whose motion we are considering, and 1' that of the attracting planet affecting it, the periodic inequalities of the elements as well as of the co-ordinates of the attracted planet, may be represented by an infinite series of terms like the following: a sin (l' - l)+b sin (2l' - l)+c sin (l'- 2l)+&c.
The most interesting kind of periodic inequalities are those known as " terms of long period."
It was especially adapted to the tracing out of " secular inequalities," or those depending upon changes in the orbital elements of the bodies affected by them, and hence progressing indefinitely with time; and by its means, accordingly, the mechanical stability of the solar system was splendidly demonstrated through the successive efforts of Lagrange and Laplace.
Before Newton the problem was that of devising empirical curves to formally represent the observed inequalities in the motion of the moon around the earth.
If we put g for the moon's anomaly or distance from the perigee, and D for its elongation from the sun, the inequalities in question as now known are 6.29° sin g (equation of centre) +1.27° sin (2D-g) (evection).
He found that, although the two inequalities found by Hipparchus and Ptolemy correctly represented the moon's longitude near conjunction and opposition, and also at the quadratures, it left a large outstanding error at the octants, that is when the moon was 45° or 135° on either side of the sun.
Although Tycho Brahe was an original discoverer of this inequality, through whom it became known, Joseph Bertrand of Paris claimed the discovery for Abu 'l-Wefa, an Arabian astronomer, and made it appear that the latter really detected inequalities in the moon's motion which we now know to have been the variation.
We may conclude the ancient history of the lunar theory by saying that the only real progress from Hipparchus to Newton consisted in the more exact determination of the mean motions of the moon, its perigee and its line of nodes, and in the discovery of three inequalities, the representation of which required geometrical constructions increasing in complexity with every step.
During the twenty years following he devoted a large part of his energies to the numerical computation of the lunar inequalities, the redetermination of the elements of motion, and the preparation of new tables for computing the moon's position.
It was therefore necessary that the numerical inequalities should be again determined by an entirely different method.
The mean motion of the moon round the earth is then invariable, the longitude containing no inequalities of longer period than that of the moon's node, 18.6 y.
While inequalities still exist around the world for women, the tide of history is flowing inexorably in favor of women's rights.
It is thus customary in calculating diurnal inequalities either to take no account of days on which there is an appreciable rainfall, or else to form separate tables for " dry " or " fine " days and for " all " days.
Hansen of two new inequalities in the moon's motion.
On the one hand he may make the line follow the natural inequalities of the ground as nearly as may be, avoiding the elevations and depressions by curves; or on the other he may aim at making it as nearly straight and level as possible by taking it through the elevations in cuttings or tunnels and across the depressions on embankments or bridges.
He favoured the idea of a future life as being necessary to set right the mistakes and inequalities of the present.