Gravity is what keeps everything from floating around.
The gravity in his voice made her afraid of what was to come.
The gravity of the situation encompassed Jackson, his breath became shallow.
If it weren't for gravity, life on earth would be impossible.
His strength and warmth pierced her body, somehow easing the gravity of her world.
Tina's youngest son tried his hardest to fly like a superhero, but gravity would not permit it.
The perception of direction or the influence of gravity presents greater difficulty, as we have no clear idea of the form which the force of gravity takes.
She was pressed against the ceiling despite the gravity controller in the pod.
He explained this to her with as much gravity as if she had asked him to do it.
Such a unit is independent of gravity or of any other quantity which varies with the locality.
It was impossible for any section of the Italians to mistake the gravity of his access to power.
The most difficult part of space travel for the team was adjusting to the change in gravity.
The downward pull of gravity suffices to bring about the fall of such material, but the path it will follow and the distance it will travel before coming to rest depend upon the land form.
In practical matters Pierre unexpectedly felt within himself a center of gravity he had previously lacked.
In spite of the gravity of the charges formulated against many prominent men, the report merely deplored and disapproved of their conduct, without proposing penal proceedings.
By using a formula that takes into account the acceleration of gravity, you can calculate the time it takes for an object to fall to the ground.
Its specific gravity is 0.8009 (o C.).
"There may be signs soon of deterioration, Deidre," he said with gravity.
Its specific gravity is about 9; it is sparingly soluble in water, but readily dissolves in acids and molten alkalis.
Red lead or triplumbic tetroxide, Pb304, is a scarlet crystalline powder of specific gravity 8.6-9.1, obtained by roasting very finely divided pure massicot or lead carbonate; the brightness of the colour depends in a great measure on the roasting.
In considering the forces that produce derailment the total mass of the vehicle or locomotive may be supposed to be concentrated at its centre of gravity.
The restoring force exerted by gravity acts in a vertical line from the centre of gravity; and the length of its lever arm is the horizontal distance between this vertical line and the outer rail.
The wagons are pushed by an engine at their rear up one slope of an artificial mound, and as they run down the other slope by gravity are switched into the desired siding.
It has many advantages for heavy high-speed service, namely, large and well-proportioned boiler, practically unlimited grate area, fire-box of favourable proportions for firing, fairly low centre of gravity, short coupling-rods, and, finally, a combination of the safe and smooth riding qualities of the fourcoupled bogie type, with great steaming capacity and moderate axle loads.
He made use of the expression F =Wg=27r12+HI, where W is the weight in grammes per square centimetre of sectional area, and g is the intensity of gravity which was taken as.
He had not attempted to include in his calculations the orbital variations of the disturbing bodies; but Lagrange, by the happy artifice of transferring the origin of coordinates from the centre of the sun to the centre of gravity of the sun and planets, obtained a simplification of the formulae, by which the same analysis was rendered equally applicable to each of the planets severally.
The centre of gravity in Hebrew religion was shifted from ceremonial observance and local sacra to righteous conduct.
In Germany, the punishment for blasphemy is imprisonment varying from one day to three years, according to the gravity of the offence.
As a lecturer, he was inferior in charm and eloquence to Brown and Stewart; the latter says that "silent and respectful attention" was accorded to the "simplicity and perspicuity of his style" and "the gravity and authority of his character."
This liquid is concentrated in vacuum pans to a specific gravity of 40° to 44° B., a small quantity of sodium bisulphite solution being added to bleach it, to prevent fermentation, and to inhibit browning.
Assuming as an axiom that the centre of gravity of any number of interdependent bodies cannot rise higher than the point from which it fell, he arrived, by anticipating in the particular case the general principle of the conservation of vis viva, at correct although not strictly demonstrated conclusions.
The fifth method consists in observing the displacement in the direction of the sun, or of one of the nearer planets, due to the motion of the earth round the common centre of gravity of the earth and moon.
In a refined form this method is often employed for measuring the intensity of a magnetic field at a given place, just as the intensity of gravity at different parts of the earth is deduced from observations of the rate at which a pendulum of known length vibrates.
If a magnetized needle were supported so that it could move freely'about its centre of gravity it would not generally settle with its axis in a horizontal position, but would come to rest with its north-seeking pole either higher or lower than its centre.
For the practical observation of this phenomenon it is usual to employ a needle which can turn freely in the plane of the magnetic meridian upon a horizontal axis passing through the centre of gravity of the needle.
The effect slammed her downwards, and the pod spun out of control, head over tail, shaking as it fought gravity.
The amount of superelevation required to prevent derailment at a curve can be calculated under perfect running conditions, given the radius of curvature, the weight of the vehicle, the height of the centre of gravity, the distance between the rails, and the speed; but great experience 1 See The Times Engineering Supplement (August 22, 1906), p. 265.
Sometimes, as on the Central London railway, the acceleration of gravity is also utilized; the different stations stand, as it were, on the top of a hill, so that outgoing trains are aided at the start by having a slope to run down, while incoming ones are checked by the rising gradient they encounter.
The residues from petroleum distillation have been shown to contain very dense solids and liquids of high specific gravity, having a large proportion of carbon and possessed of remarkable fluorescent properties.
I wouldn't throw down the gauntlet with him, Gerry said with gravity.
The specific gravity is 11 352 for ingot, and from 11.354 to II '365 for sheet lead (water of 4°C. = 1).
Petroleum spirit is tested for specific gravity, range of boilingpoints, and results of fractional distillation.
To illuminating oil or kerosene a series of tests is applied in order that the colour, odour, specific gravity and flash-point or fire-test may be recorded.
In the testing of mineral lubricating oils the viscosity, flash-point, cold-test," and specific gravity are the characters of chief importance.
Yet one must remember, in justice to Alexius, the gravity of the problem by which he was confronted; nor was the conduct of the crusaders themselves such that he could readily make them his brethren in arms.
Such an instrument is called a soft-iron gravity ammeter.
the above-described gravity type can be employed with certain restrictions for the measurement of alternating currents.
In the use of ammeters in which the control is the gravity of a weight, such as the Kelvin ampere balances and other instruments, it should be noted that the scale reading or indication of the instrument will vary with the latitude and with the height of the instrument above the mean sea-level.
For this reason a thin bar suspended at its centre of gravity between a pair of magnetic poles will, if paramagnetic, set itself along the line joining the poles, where the field is strongest, and if diamagnetic, transversely to the line.
Since the difference between the acceleration of gravity at the pole and at the equator is about 2%, the correction for latitude will be quite sensible in an instrument which might be used at various times in high and low latitudes.
If G is the acceleration of gravity at the equator and g that at any latitude X, then g= G(IFoï¿½o0513 sin 2 X).
In the case of an instrument with gravity control, the FIG.
In this he showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolution.
When perfectly pure, carbon bisulphide is a colourless, somewhat pleasant smelling, highly refractive liquid, of specific gravity 1 2661 (18°/4°) (J.
This solution is allowed to stand for some time (in order that any calcium sulphate and basic ferric sulphate may separate), and is then evaporated until ferrous sulphate crystallizes on cooling; it is then drawn off and evaporated until it attains a specific gravity of 1.40.
As obtained by the reduction of the chloride, it is a steel grey powder of specific gravity 7 06.
The central plains, which have the most fertile soil, and from the geographical conditions of the country form its centre of gravity, are occupied almost exclusively by the Magyars, the most numerous and the dominant race.
Its specific gravity has the high value 18.7; its specific heat is 0.02765, which, according to Dulong and Petit's law, corresponds to U = 240: It melts at bright redness.
The extent of the operations and the gravity of the situation now began to be felt in England; every available man was called up from the reserves, and the war office made what at the time appeared to be adequate provision for the waste which it was seen would occur.
But meantime the mobile enemy, whose original flank had been turned, had gathered at the new centre of gravity, and the upshot of several days' fighting was the retreat of the British.
Seldom has it happened, since the discovery of the law of gravity, that so profound an impression has been made upon the scientific world at large as by the revelation of the part played by germ-life in nature; seldom has any discovery been fraught with such momentous issues in so many spheres of science and industry.
The size, shape and design of the cars depend on the size of the mine passage and of the hoisting compartments of the shafts; on whether the cars are to be trammed by hand or hauled in trains; whether they are loaded by shovel or by gravity from a chute; and whether they are to be hoisted to the surface or used only for underground transport.
Mine cars are sometimes run long distances, singly or in trains, over roads which are given sufficient grade to impart considerable speed by gravity, say from I to 21%.
Near the top and bottom of hoisting shafts the tracks are usually graded to permit the cars to be run to and from the shaft by gravity.
Gravity or self-acting planes are for lowering loaded cars, one or more at a time, from a higher to a lower level.
It melts at 26° to 27° C. and has a specific gravity of 1.88 (15°C.).
Here he was, in total control, independent of outside power—only his arms and legs and gravity.
One somewhat similar phenomenon, differing in a few respects, marks the relation of the plant to the attraction of gravity.
There is every reason to believe that plants are as irritable to varying external conditions as they are to light or to gravity.
One of the earliest and best known of such " gravity " yards is that at Edgehill, near Liverpool, on the London & North-Western railway, which was established in 1873.
The specific gravity of crude petroleum appears to range from 771 to 1.06, and the flash point from below o° to 370°F.
The " cracking " process, whereby a considerable quantity of the oil which is intermediate between kerosene and lubricating oil is converted into hydrocarbons of lower specific gravity and boiling-point suitable for illuminating purposes, is one of great scientific and technical interest.
In the routine examination of crude petroleum it is customary to determine the specific gravity, and the amount of water and earthy matter in suspension; the oil is also frequently subjected to a process of fractional distillation in order to ascertain whether there has been any addition of distilled products or residue.
The needle is balanced so that gravity compels it to take a certain position in which the fragment of iron occupies a position in the centre of the field of the coil where it is weakest.
Lord Roberts's plan was first to concentrate to his left, taking every measure to induce the Boers to believe that the original scheme of invasion by the centre would now be resumed, and in this purpose he succeeded so well that his field army with the necessary transport for a cross-country march was assembled between the Orange and the Modder without serious mishap. Cronje at the new centre of gravity was not reinforced, all available Boers drawing down towards Colesberg.
Of the impurities of the ore the wolframite (tungstate of iron and manganese) is the most troublesome, because on account of its high specific gravity it cannot be washed away as gangue.
The specific gravity of cast tin is 7.29, of rolled tin 7.299, and of electrically deposited tin 7.143 to 7.178.
It is a colourless fuming liquid of specific gravity 2.269 at o°; it freezes at - 33° C., and boils at I13.9°.
Dropsical liquids are usually pale yellow or greenish, limpid, with a saltish taste and alkaline reaction, and a specific gravity ranging from 1005 to 1024.
The resultant of a parallel projection of any system of forces is the projection of their resultant; and the centre of gravity of a parallel projection of a solid is the projection of the centre of gravity of the first solid.
An engine plane is an inclined road, up which loaded cars are hauled by a stationary engine and rope, the empty cars running down by gravity, dragging the rope after them.
The range of the specific gravity of glasses from 2.5 to 5.0 illustrates the effect of modified compositions.
Lumps of glass of approximately the right weight are chosen, and are heated to a temperature just sufficient to soften the glass, when the lumps are caused to assume the shape of moulds made of iron or fireclay either by the natural flow of the softened glass under gravity, or by pressure from suitable tools or presses.
The product is a crystalline solid of specific gravity 2.34, and melts at about 1430° C. See also German Patent 108817 for the production of crystallized silicon from silica and carborundum.
The specific gravity of the amorphous form is 2.35 (Vigouroux), that of the crystalline variety varying, according to the method of preparation, from 2.004 to 2.493.
Diethylcarbonate, CO(OC2H5)2, is a colourless liquid, which boils at 225.8° C.; its specific gravity is 0.978 (20°) [H.
It boils at 93.1° C., and has a specific gravity of 1.144 (15° C.).
substances having high specific gravity, malleability, opacity, and especially a peculiar lustre, the term "metal" became generic for all substances with these properties.
In former times a high specific gravity used to be quoted as one of the characters of the genus; but this no longer holds, since we now know a series of metals lighter than water.
Thus, for instance, chemically pure iron in the ingot has the specific gravity 7.844; when it is rolled out into thin sheet, the value falls to 7.6; when drawn into thin wire, to 7.75.
Its specific gravity is o 899 at o° C. It is very slightly soluble in water, more soluble in alcohol, and completely miscible with ether, acetic acid and carbon disulphide.
- In a fluid at rest under gravity the pressure is the same at any two points in the same horizontal plane; in other words, a surface of equal pressure is a horizontal plane.
As gravity and the fluid pressure on the sides of the prism act at right angles to AB, the equilibrium requires the equality of thrust on the ends A and B; and as the areas are equal, the pressure must be equal at A and B; and so the pressure is the same at all points in the same horizontal plane.
- The free surface of a liquid at rest under gravity is a horizontal plane.
- In a homogeneous liquid at rest under gravity the pressure increases uniformly with the depth.
- A body immersed in a fluid is buoyed up by a force equal to the weight of the liquid displaced, acting vertically upward through the centre of gravity of the displaced liquid.
For if the body is removed, and replaced by the fluid as at first, this fluid is in equilibrium under its own weight and the thrust of the surrounding fluid, which must be equal and opposite, and the surrounding fluid acts in the same manner when the body replaces the displaced fluid again; so that the resultant thrust of the fluid acts vertically upward through the centre of gravity of the fluid displaced, and is equal to the weight.
When the body is floating freely like a ship, the equilibrium of this liquid thrust with the weight of the ship requires that the weight of water displaced is equal to the weight of the ship and the two centres of gravity are in the same vertical line.
It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid (I) (2) "F r an Minim ' 'i n or weight of liquid displaced is W-W, so that the specific gravity (S.G.), defined as the ratio of the weight of a body to the weight of an equal volume of water, is W/(W-W').
The resultant vertical thrust on any portion of a curved surface exposed to the pressure of a fluid at rest under gravity is the weight of fluid cut out by vertical lines drawn round the boundary of the curved surface.
As an example of the general equations, take the simplest case of a uniform field of gravity, with Oz directed vertically downward; employing the gravitation unit of force, 1 dp i dp t dp dp/dz = p = pzn (4) z n+I pz 1 /n p-p n-H ?t), (5) supposing p and p to vanish together.
For a homogeneous liquid at rest under gravity, p is proportional to the depth below the surface, i.e.
In the steady motion under no force of such a body in medium, the centre of gravity describes a helix, while the axis escribes a cone round the direction of motion of the centre of ravity, and the couple causing precession is due to the dislacement of the medium.
192, resembling the trochoidal curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.
The pans are provided with steam worms to keep the mass hot as required, and with mechanical stirrers to keep it in movement and thoroughly mixed with the water and sweet water which are added to the sugar to obtain a solution of the specific gravity desired.
It is a clear, strongly refractive liquid, which has a pleasant odour; it boils at 144° and has a specific gravity of o 925 at o°.
The hardness is 2, and the specific gravity 2 I.
The specific gravity of zinc cannot be expected to be perfectly constant; according to Karsten, that of pure ingot is 6.915, and rises to 7.191 after rolling.
The product has a brilliant white fracture, a specific gravity of 4.87, very friable, but harder than quartz or steel.
The pure salt is dissolved in hot water and decomposed with ammonia to produce a slightly ammoniacal hydrated oxide; this, when ignited in platinum, leaves pure TiO 2 in the form of brownish lumps, the specific gravity of which varies from 3.9 to 4.25, according to the temperature at which it was kept in igniting.
It is a silver-white ductile metal (of specific gravity 2.54) which melts at 8000.
Thus far Latin literature, of which the predominant characteristics are dignity, gravity and fervour of feeling, seemed likely to become a mere vehicle of amusement adapted to all classes of the people in their holiday mood.
The quantity of alcohol present in an aqueous solution is determined by a comparison of its specific gravity with standard tables, or directly by the use of an alcoholometer, which is a hydrometer graduated so as to read per cents by weight (degrees according to Richter) or volume per cents (degrees according to Tralles).
In the United Kingdom "proof spirit" is defined as having a specific gravity at 51° of 12/13 (.
The reader should, however, notice that what is generally called electric force is the analogue in electricity of the so-called acceleration of gravity in mechanics, whilst electrification or quantity_of electricity is analogous to mass.
The path described by it when removed from the action of gravity and all other physical forces is called a line of electric force.
Newton and Dr Samuel Clarke is laid open, 1732; Glory or Gravity, 1733; The Religion of Satan, or Antichrist Delineated, 1736.
The specific gravity of gold obtained by precipitation from solution by ferrous sulphate is from 19.55 to 20.72.
The specific gravity of cast gold varies from 18.29 to 19.37, and by compression between dies the specific gravity may be raised from 19.37 to 19.41; by annealing, however, the previous density is to some extent recovered, as it is then found to be 19.40.
According to Chenevix, the alloy composed of equal parts of the two metals is grey, is less ductile than its constituent metals and has the specific gravity i i.
The operation may be conducted in vessels of glass or platinum, and each pound of granulated metal is treated with a pound and a quarter of nitric acid of specific gravity 1.32.
When not tarnished, the mineral has a silver-white colour with a tinge of red, and the lustre is metallic. Hardness 2-21; specific gravity 9-70-9.83.
The slight variations in specific gravity are due to the presence of small amounts of arsenic, sulphur or tellurium, or to enclosed impurities.
2 9, p. 2 94), its specific gravity is 9.7 81 43; Roberts and Wrightson give the specific gravity of solid bismuth as 9.82, and of molten bismuth as to 055.
If, therefore, the walls of the enclosure held the gas that is directly in contact with them, this equilibrium would be the actual state of affairs; and it would follow from the principle of Archimedes that, when extraneous forces such as gravity are not considered, the gas would exert no resultant force on any body immersed in it.
densus, thick), in physics, the mass or quantity of matter contained in unit volume of any substance: this is the absolute density; the term relative density or specific gravity denotes the ratio of the mass of a certain volume of a substance to the mass of the same volume of some standard substance.
The specific gravity bottle may be used to determine the relative density of a solid which is available in small fragments, and is insoluble in the standard liquid.
The method involves three operations: - (1) weighing the solid in air (W), (2) weighing the specific gravity bottle full of liquid (W 1), (3) weighing the bottle containing the solid and filled up with liquid (W2).
Some balances are provided with a "specific gravity pan," i.e.
Tellurium is a brittle silvery-white element of specific gravity 6.27.
An amor phous form is obtained when tellurium is precipitated from its solutions by sulphur dioxide, this variety having a specific gravity 6.015.
5, p. iv.) he found that the index error of the scale changed systematically in different position angles by quantities which were independent of the direction of gravity relative to the position angle under measurement, but which depended solely on the direction of the measured position angle relative to a fixed radius of the object-glass.
But the method is not available if the separation is to be measured by screws; it is found, in that case, that the direction of the final motion of turning of the screw must always be such as to produce motion of the segment against gravity, otherwise the " loss of time " is apt to be variable.
It melts between 2250° and 2300°, its specific heat is 0.0365, coefficient of expansion o 0000079, and specific gravity 16.64.
The intensity of gravity at the surface of the sea far from land has been measured on several occasions.
Besides the determination of salinity by titration of the chlorides, the method of determination by the specific gravity of the sea-water is still often used.
In the laboratory the specific gravity is determined in a pyknometer by actual weighing, and on board ship by the use of an areometer or hydrometer.
Three types of areometer are in use: (I) the ordinary hydrometer of invariable weight with a direct reading scale, a set of from five to ten being necessary to cover the range of specific gravity from 1 000 to 1.031 so as to take account of sea-water of all possible salinities; (2) the " Challenger " type of areometer designed by J.
In all areometer work it is necessary to ascertain the temperature of the water sample under examination with great exactness, as the volume of the areometer as well as the specific gravity of the water varies with temperature.
Sorensen, carried out a careful investigation of the relation between the amount of chlorine, the total salinity and the specific gravity of sea-water of different strengths including an entirely new determination of the thermal expansion of sea-water.
The relations between the various conditions are set forth in the following equations where 0-o signifies the specific gravity of the sea-water in question at o° C., the standard at 4° being taken as 1000, S the salinity and Cl the chlorine, both expressed in parts by weight per mille.
The temperature of maximum density of sea-water of any specific gravity was found by Knudsen to be given with sufficient accuracy for all practical purposes by the formula 0 = 3.950.2660 -0, where 0 is the temperature of maximum density in degrees centigrade.
The compressibility is in itself very small, but so great in its effect on the density of deep water in situ that the specific gravity (0 0 /4°) at 2000 fathoms increases by o 017 and at 3000 fathoms by o 026.
In other words, water which has a specific gravity of 1 0280 at the surface would at the same temperature have a specific gravity of 1 0450 at 2000 and I 0540 at 3000 fathoms. If the whole mass of water in the ocean were relieved from pressure its volume would expand from 319 million cub.
As a rule, the density increases with the amount of carbon, but in some instances a very high specific gravity is due to intermixed earthy matters, which are always denser than even the densest form of coal substance.
The specific gravity is low when not brought up by an excessive amount of earthy matter.
Each impinging molecule exerts an impulsive pressure equal to mu on the boundary before the component of velocity of its centre of gravity normal to the boundary is reduced to zero.
The hardness is 51-6, and the specific gravity 5.9-6.2.
Pure methyl alcohol is a colourless mobile liquid, boiling at 66°-67°, and having a specific gravity of 0 8142 at o° C. It has a burning taste, and generally a spirituous odour, but when absolutely pure it is said to be odourless.
Methyl bromide is a liquid, specific gravity I 73, boiling point 13°; methyl iodide has a specific gravity of 2.19, and boils at 43°.
In a vacuum, the projectile acted on by the force of projection begins to fall under the action of gravity immediately it leaves the bore, and under the combined action of these two forces the path of the projectile is a parabola.
It passes over equal spaces in equal times, but falls with an accelerating velocity according to the formula h = zgt 2, where h is the height fallen through, g the force of gravity, and t the time of flight.
Its specific gravity is 21.3-22.48 (Deville and Debray) and its specific heat is 0.03113 (Regnault).
The crystals look like antimony, and are brittle, and so hard as to scratch glass and rubies; their specific gravity is 4.25.
They are inspired also by a fervid and steadfast glow of spirit and reveal a gentleness and humanity of sentiment blended with the severe gravity of the original Roman character.
The centroid is sometimes called the centre of volume, centre of area, or centre of arc. The proof of the existence of the centroid of a figure is the same as the proof of the existence of the centre of gravity of a body.
The theorems are of use, not only for finding the volumes or areas of solids or surfaces of revolution, but also, conversely, for finding centroids or centres of gravity.
Algol, in fact, travels at the rate of 26.3 miles a second round the centre of gravity of the system which it forms with an invisible companion, while the two together approach the sun with an unvarying speed of 2.3 miles per second.
If it is always on it only acts as if the value of gravity were increased, and does not help to maintain or check the vibration, but merely to shorten the period.
This, and the movements of the 4th Army, which had set its face towards Haicheng and no longer seemed to be part of a threat on Liao-Yang, led to the idea being entertained at Kuropatkin's headquarters that the centre of gravity was shifting to the south.
If it revolves about a vertical axis d its centre of gravity must always lie in that axis; if it rolls the centre of gravity must always lie over the e abutment.
The bed of the river is too far below the surrounding country to permit the use of its waters for irrigation purposes by the usual gravity methods.
Its specific gravity is 1 54, and after remelting 1 56; after distillation it is 1.52.
Ammonia is a colourless gas possessing a characteristic pungent smell and a strongly alkaline reaction; it is lighter than air, its specific gravity being oï¿½589 (air =1).
Fluorine is a pale greenish-yellow gas with a very sharp smell; its specific gravity is 1.265.
The tasks, almost infinite in number, confronting the new State were of great gravity.
But in the ensuing anarchic period both cities were utterly ruined, and the centre of political gravity was transferred from Great Poland to Little Poland, where Cracow, singularly favoured by her position, soon became the capital of the monarchy, and one of the wealthiest cities in Europe.
He is described by Fuller as "low of stature, little in bulk, cheerful in countenance (wherein gravity and quickness were all compounded), of a sharp and piercing eye, clear judgment and (abating the influence of age) term memory."
The specific gravity is 0.9735 at 13.5° (Baumhauer).
Several hydrates are known: 2NaOH 7H 2 O is obtained as large monoclinic crystals by' cooling a solution of specific gravity 1.365 to -8'; Pickering (Journ.
The specific gravity of milk ordinarily ranges from i 029 to 1.033, very seldom reaching 1 035 or falling so low as 1.027.
The shot is supposed to move horizontally, and the curving effect of gravity is ignored.
8 and 9, in a curve showing the relation between p and D the gravimetric density, which is the specific gravity of the P lb of powder when filling the volume C, cub.
G.) of the powder filling a given volume in a state of gas, and the specific gravity of the separate solid grain or cord of powder.
The specific gravity is 2.2, that of diamond is 3.5.
It is a colourless, odourless gas of specific gravity 0.967 (air = I).
Its specific gravity is 1.529 (air = I).
having two components revolving about their common centre of gravity - and the first to have its orbit calculated.
The latter work contains elaborate investigations in regard to the centre of gravity, and it is remarkable also for the employment of the principle of virtual velocities.
gravity of 1.200 at about 20° C. Brass case removed.
For the sulphate of copper solution, take 16.5 parts by weight of pure crystals of copper sulphate (CuSO 4 50H 2) and dissolve in 83.5 parts by weight of water; the resulting solution should have a specific gravity of 1.
Its specific gravity is o 865; hence it is the lightest metal known except lithium.
The latter begin to oxidize before the ley has come up to the traditional strength of specific gravity 1.333 when cold, while nickel is not attacked so long as the percentage of real KHO is short of 60.
Solid caustic potash forms an opaque, white, stone-like mass of dense granular fracture; specific gravity 2'1.
The salt crystallizes in cubes of specific gravity 1.995; it melts at about 800° and volatilizes at a bright red heat.
But the importance of these modifications is something more than the doubt which they have thrown on WH's theories: they have really shifted the centre of gravity of the textual problem.
Though he was not a good teacher, his influence both on his pupils and on those few intimate friends for whom alone he relaxed the gravity of his manner was profound, and, little as he-was known to the white inhabitants of Lexington, he was revered by the slaves, to whom he showed uniform kindness, and for whose moral instruction he worked unceasingly.
The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity.
in height; the specific gravity of mercury being now taken as 13.5950, after Volkmann and Marek, and at the normal intensity followed under this pressure.
The value of this intensity is equal to that of the force of gravity at the Bureau International, Paris (at the level of the Bureau), divided by 1.000332; a co-efficient which allows for theoretical reduction to the latitude 45° and to the level of the sea.
Specific gravity bottles are also adjusted at 60° F., the figures indicating specific gravities being quotients obtained by dividing in each instance the weight of the solid or liquid by the weight of an equal bulk of water, both taken at 60 F.
An important character, and one by which the mineral may always be recognized, is the perfect cubical cleavage, on which the lustre is brilliant and metallic. The colour of the mineral and of its streak is lead-grey; it is opaque; the hardness is 2 2 and the specific gravity 7.5.
Its specific gravity varies from I 054 to I 057.
Herschel, who discovered that many of them formed systems of two stars revolving round their common centre of gravity.
Its specific gravity is 4.94 8 (1 7°14°).
In the former case the control is generally due to gravity, the plates being so balanced on the knife edge that they tend to take up a certain fixed position from which they are constrained when the electric forces come into play, their displacement relatively to the fixed plates being shown on a scale and thus indicating the P. D.
He clearly perceived the significant analogy between terrestrial gravity and the force exerted in the solar system, and by the ingenious device of a circular pendulum illustrated the composite character of the planetary movements.
Formic acid is a colourless, sharp-smelling liquid, which crystallizes at 0° C., melts at 8.6° C. and boils at 100.8° C. Its specific gravity is 1.22 (20°/4°).
distant, by a gravity system which cost $5,000,000; and the city has an intercepting sewer system.
long have been resorted to, provided with a steel eye at the top and a ring near the centre of gravity to enable them to be worked (fig.
The oil has been chemically analysed and found to be a fish-oil, and to possess nearly all the qualities of that obtained from the liver of the cod, with a lighter specific gravity.
When a body floats in a fluid under the action of gravity, the weight of the body is equal to that of the fluid which it displaces.
2) "After having made several fruitless trials with ivory, because it imbibes spirituous liquors, and thereby alters its gravity, he (Mr Clarke) at last made a copper hydrometer, represented in fig.
In comparing the densities of different liquids, it is clear that this instrument is precisely equivalent to that of Fahrenheit, and must be employed in the same manner, weights being placed in the top scale only until the hydrometer sinks to the mark on the wire, when the specific gravity of the liquid will be proportional to the weight of the instrument together with the weights in the scale.
The hydrometer therefore displaced woo grains of distilled water at 60°F.and hence the specific gravity of any other liquid was at once indicated FIG.
Without the extra 5 grammes the instrument weighs about 20 grammes, and therefore floats in a liquid of specific gravity 8.
Proof spirit is defined in the United States as a mixture of alcohol and water which contains equal volumes of alcohol and water at 60° F., the alcohol having a specific gravity of 0.7939 at 60° as compared with water at its maximum density.
The specific gravity of proof spirit is 0.93353 at 60°; and 100 volumes of the mixture is made from 50 volumes of absolute alcohol and 53.71 volumes of water.
The instrument is provided with a sliding rule, with scales corresponding to the several weights, which indicate the specific gravity corresponding to the several divisions of the hydrometer scale compared with water at 55° F.
The specific gravity of any sample of spirits thus determined, when multiplied by ten, gives the weight in pounds per imperial gallon, and the weight of any bulk of spirits divided by this number gives its volume at once in imperial gallons.
The scale is so arranged that the reading multiplied by 5 and added to 1000 gives the specific gravity with reference to water as 1000.
Wohler reduced the sesquioxide by zinc, and obtained a shining green powder of specific gravity 6.81, which tarnished in air and dissolved in hydrochloric acid and warm dilute sulphuric acid, but was unacted upon by concentrated nitric acid.
In the amorphous state it is a dull green, almost infusible powder, but as obtained from chromium oxychloride it is deposited in the form of dark green hexagonal crystals of specific gravity 5 2.
Again, suddenly altering the centre of gravity, Wellington invested Badajoz in the middle of March.
treats principally of mechanics, the properties of the centre of gravity, and some mechanical powers.
Its specific gravity is 1.0636 (-8° C.), and it boils at 179 1° C. (751 3mm).
(c) Wren and Huygens further proved that the law of equal action and reaction, already experimentally established by the former, is deducible from the conservation of the velocity of the common centre of gravity, which is the same as the common velocity of the bodies, that is, deducible from the fact that their common centre of gravity does not change its state of motion or rest by the actions of the bodies between themselves; and they further extended the law to bodies, qua elastic.
(e) Newton in the Principia, repeating and correcting Wren's experiments on collision, and adding further instances from attractive forces of magnetism and gravity, induced the third law of motion as a general law of all forces.
Withdraw this foundation of bodies as inter-resisting forces causing one another in collision to form a joint mass with a common velocity but without penetration, and the evidence of the third law disappears; for in the case of attractive forces we know nothing of their modus operandi except by the analogy of the collision of inter-resisting bodies, which makes us believe that something similar, we know not what, takes place in gravity, magnetism, electricity, &c. Now, Mach, though he occasionally drops hints that the discovery of the law of collision comes first, yet never explains the process of development from it to the third law of motion.
The needle is peculiarly poised, with its point of suspension a little below its centre of gravity, and is exceedingly sensitive; it is seldom more than an inch in length, and is less than a line in thickness.
The chancellor never realized the gravity of the onslaught which, with his Kulturkampf, he was making upon the conscience and liberty of his Catholic fellow citizens.
The socialistic idea, with which the " Democratie Chretienne " had identified itself both in France and Belgium, regards numbers as the centre of gravity of the whole state organism.
, 3' of Gravity.
He attained correct views as to the character of centrifugal force in connexion with Galileo's theory; and, when the fact of the variation of gravity (Galileo's acceleration) in different latitudes first became known from the results of pendulum experiments, he at once perceived the possibility of connecting such a variation with the fact of the earth's diurnal rotation relatively to the stars.
At the same time he thought of the possibility of terrestrial gravity extending to the moon, and made a calculation with regard to it.
Some years later he succeeded in showing that Kepler's elliptic orbit for planetary motion agreed with the assumed law of attraction; he also completed the co-ordination with terrestrial gravity by his investigation of the attractions of homogeneous spherical bodies.
On the whole, however, what may be called the speculative centre of gravity of Great Britain's export business in cotton goods is not in Manchester but abroad.
distant; but this was only a gravity road down which cars loaded with coal descended by their own gravity and up which the empty cars were drawn by mules.
In his memoir of 1785 he writes: "As far as the experiments hitherto published extend, we scarcely know more of the phlogisticated part of our atmosphere than that it is not diminished by lime-water, caustic alkalies, or nitrous air; that it is unfit to support fire or maintain life in animals; and that its specific gravity is not much less than that of common air; so that, though the nitrous acid, by being united to phlogiston, is converted into air possessed of these properties, and consequently, though it was reasonable to suppose, that part at least of the phlogisticated air of the atmosphere consists of this acid united to phlogiston, yet it may fairly be doubted whether the whole is of this kind, or whether there are not in reality many different substances confounded together by us under the name of phlogisticated air.
Its hardness is rather above 5, and its specific gravity varies from 3.5 to 4.
His success in winning the prize of a thousand crowns offered for a dissertation on the cause of gravity by the Academy of Sciences of Paris secured his return to his native land in 1731.
Nitric acid is a colourless strongly fuming liquid, having a specific gravity of 1.50394 (24.2° C.) (V.
The acid solidifies when strongly cooled, the solid melting at - 47° C. Concentrated nitric acid forms with water a constant boiling mixture which boils at 120.5° C., contains 68% of acid and possesses a specific gravity of 1.414 (15.5° C.).
Thus at 55° C. it is passive to an acid of specific gravity 1.42, and at 31° C. to an acid of specific gravity.
with a solution of sodium hydroxide having the specific gravity 1ï¿½ 4 5.
The filtrate, now containing roughly two molecules of alumina to one of soda, is concentrated to the original gravity of 1.45, and employed instead of fresh caustic for the attack of more bauxite; the precipitate is then collected, washed till free from soda, dried and ignited at about looo C. to convert it into a crystalline oxide which is less hygroscopic than the former amorphous variety.
The molten metal has a specific gravity of 2 ï¿½ S4, that of molten cryolite saturated with alumina is 2.3 5, and that of the fluoride Al 2 F 6 2NaF saturated with alumina 1.97.
The specific gravity of cast metal is 2.583, and of rolled 2.688 at 4° C. It melts at 626° C. (freezingpoint 654.5 Heycock and Neville).
Heating by hot water may be said to depend, in part, on the influence of gravity on water being to some extent overcome by heating in a boiler.
Its specific gravity is 96, a little less than that of water, and it dissolves freely in alcohol, ether and glacial acetic acid.
Chloroform solidifies in the cold and then melts at - 62° C.; it boils at 61.2° C., and has a specific gravity I.
Its hardness is about 6, and its specific gravity 4 9 to 5.2, being rather more than that of marcasite.
Its specific gravity is 5.2, and its hardness 5.5 to 6.5.
Its specific gravity is 5.3 and its hardness 5.5 to 6.5.
Its streak is yellowish-black, its specific gravity 3.6 to 4.0, and its hardness 5 to 5.5.
Its specific gravity is 3.7 to 3.9, and its hardness 3.5 to 4.5.
Its specific gravity is 4.83 to 5.2, its hardness 6 to 6.5.
Thus some 1700 tons of materials are charged daily into each of these furnaces without being shovelled at all, running by gravity from bin to bucket and from bucket to furnace, and being hoisted and charged into the furnace by a single engineer below, without any assistance or supervision at the furnacetop.
Fortunately its embrittling effect on cast iron is very much less than on steel, so that the upper limit or greatest tolerable proportion of phosphorus, instead of being o.10 or better 0.08% as in the case of rail steel, may be put at 0.50% in case of machinery castings even if they are exposed to moderate shocks; at 1.60% for gas and water mains in spite of the gravity of the disasters which extreme brittleness here might cause; and even higher for castings which are not exposed to shock, and are so thin that the iron of which they are made must needs be very fluid.
Pure hydrogen is a tasteless, colourless and odourless gas of specific gravity 0.06947 (air= i) (Lord Rayleigh, Proc. Roy.
Berthelot, Comptes rendus, 1878, 86, P. 71) The anhydrous hydrogen peroxide obtained by Wolffenstein boils at 84-85°C. (68 mm.); its specific gravity is 1.4996 (I.
It is a colourless highly volatile and inflammable liquid, having at 20° C. a specific gravity of 0.65.
The specific gravity ranges from 3.56 to 3.50, generally about 3.52.
The electrical resistance is about that of ordinary glass, and is diminished by one-half during exposure by Rntgen rays; the dielectric constant (16) is greater than that which should correspond to the specific gravity.
Carbonado or " black diamond," found in Bahia (also recently in Minas Geraes), is a black material with a minutely crystalline structure somewhat porous, opaque, resembling charcoal in appearance, devoid of cleavage, rather harder than diamond, but of less specific gravity; it sometimes displays a rude cubic crystalline form.
Among other American improvements were: an efficient fire department, a sewer system whereby the sewage by means of pumps is discharged into the bay more than a mile from the shore; a system of gravity waterworks (1908) whereby the city's water supply is taken from the Mariquina river about 23 m.
In specific gravity it ranges between 0.9112 and 0.9117 in the raw state, and from 0.9127 to 0.9136 when refined; the solidifying point is from - 4° to - 6° C.
In the northern section, which receives the copious volumes brought down by the Volga, Ural and Terek, the salinity is so slight (only 0.0075% in the surface layers) that the water is quite drinkable, its specific gravity being not higher than 1.0016.
The specific gravity is 40, and the hardness 4.
Its specific gravity is 6.1545, and it melts at 810°.
The unfailing freshness and charm of the contrast between the importance, the gravity, in some cases the dry and abstruse nature, of their subjects, and the lightness, sometimes almost approaching levity in its special sense, of the manner in which these subjects are attacked is a triumph of literary art of which no familiarity dims the splendour, and which no lapse of time can ever impair.
Pascal solved the hitherto refractory problem of the general quadrature of the cycloid, and proposed and solved a variety of others relating to the centre of gravity of the curve and its segments, and to the volume and centre of gravity of solids of revolution generated in various ways by means of it.
Owing to the difficulty and expense of securing water from running streams by gravity systems, a great variety of methods were developed of pumping water by windmills, gasoline or hot-air engines, and steam.
The total acreage supplied by such means was probably less than 1% of that watered by gravity systems.
It is a malleable metal, of specific gravity 1.64 (Nilson and Pettersson) and a specific heat of 0.4079.
of the German problem; with his accustomed calculated bluntness he had more than once openly asserted that this problem could only be settled by Austria ceasing to influence the German courts and transferring her centre of gravity towards Budapest; with equal bluntness he told the committee on the budget, on the 30th of September 1862, that the problem could not be solved by parliamentary decrees, but only by blood and iron.
It is rather softer and less dense than crystallized quartz, its hardness being about 6.5 and its specific gravity 2.6, the difference being probably due to the presence of a small amount of opaline silica between the fibres.
The acid is an oily liquid of unpleasant smell, and solidifies at - 19° C.; it boils at 162.3° C., and has a specific gravity of o 9746 (o° C.).
It is a liquid of somewhat unpleasant smell, boiling at 155.5° C. Its specific gravity is o 9697 (0°).
With the enormous extension of Greek territory a great shifting took place in the old centres of gravity.
Its centres of gravity to some extent shifted.
In Aeolis, of course, the centre of gravity moved to the Attalid capital, Pergamum.
(ga 2 /2b); or if the height of the centre of gravity of a column like a gravestone above the base on which it rests is y, and x is the horizontal distance of this centre from the edge over which it has turned, then the acceleration or suddenness of motion which caused its overthrow is measured, as pointed out by C. D.
This cylinder, which is suspended from a stand rigidly attached to the earth, has a vertical hole in its centre extending from its upper surface to its centre of gravity, and to the bottom of this well a light rod is fixed.
Baring, who, realizing soon afterwards the gravity of the situation, telegraphed on the 16th of March: It has now become of the utmost importance not only to open the road between Suakin and Berber, but to come to terms with the tribes between Berber and Khartum.
Belisarius was sent against him, but with forces too small for the gravity of the situation.
Primarily but a slight deposit is formed (none until the concentration arrives at specific gravity 1.0509), this deposit consisting for the most part of calcium carbonate and ferric oxide.
This goes on till a density of 1.1315 is attained, when hydrated calcium sulphate begins to deposit, and continues till specific gravity 1.2646 is reached.
At specific gravity 1.2461 a Up to the time then that the water became concentrated to specific gravity 1.218 only 0.150 of deposit had formed, and that chiefly composed of lime and iron, but between specific gravity I 218 and 1.313 there is deposited a mixture of Of this about 95% is sodium chloride.
The mother-liquor now falls to a specific gravity of 1.3082 to 1.2965, and yields a very mixed deposit of magnesium bromide and chloride, potassium chloride and magnesium sulphate, with the double magnesium and potassium sulphate, corresponding to the kainite of Stassfurt.
There is also deposited a double magnesium and potassium chloride, similar to the carnallite of Stassfurt, and finally the mother-liquor, which has now again risen to specific gravity 1.3374, contains only pure magnesium chloride.
Antioch became the capital and court-city of the western Seleucid empire under Antiochus I., its counterpart in the east being Seleucia-on-Tigris; but its paramount importance dates from the battle of Ancyra (240 B.C.), which shifted the Seleucid centre of gravity from Asia Minor, and led indirectly to the rise of Pergamum.
The quality of Portland cement is ascertained by its analysis and by determining its specific gravity, fineness, mechanical strength Tesfing.
Its specific gravity is 11.86.
The specific gravity of this "horn" thallium is 7.02.
The ordinate of the dotted curve which contains its "centre of gravity" has, of course, for its abscissa the "mean" number of glands; the maximum ordinate of the curve is, however, at 2.98, or sensibly at 3 glands, showing what Pearson has called the "modal" number of glands, or the number occurring most frequently.
It is somewhat heavier than air, its specific gravity being 1.10523 (A.
It is a dark coloured powder of specific gravity 5.09.
Nevertheless these two insignificant works, as points to hold and lines to defend on an otherwise featureless battlefield, became the centres of gravity of the battle.
One general conclusion arrived at both by Bauschinger and Johnson was that the strength is much affected by the specific gravity of the timber.
The metal has somewhat the appearance of iron, and has a specific gravity of 6.628, which, after melting, is increased to 6.728.
Its specific gravity is 6.739, and its specific heat 0.0877.
It is a red infusible mass of specific gravity 5.1, and is slowly decomposed by warm water.
It is a white powder of specific gravity 3.912, easily soluble in cold water.
His mind, however, was also busy with the momentous problem of gravity.
17) be a section of the polar axis; it is then easy to adjust the weight P attached to its lower end so that the centre of gravity X of the whole moving parts of the instrument shall be in the vertical (V V) of a line passing through the apex of the hollowed flange p q at q, which flange forms part of the polar axis.
The difficulties of relief friction could probably be best overcome by a large hollow cylinder concentric with the polar axis fixed near the centre of gravity of the whole instrument and floated in mercury, on the plan adopted in the Mount Wilson 60-in.
The specific gravity of the solid form is 5.956 (24.5° C.), of the liquid 6 069, whilst the specific heats of the two varieties are, for the solid form 0.079 (12-23° C.) and for the liquid 0.082 (106-119°) [M.
system of expression in ergs per gramme-degree-centigrade, or " calorie," is the most appropriate, as being independent of the value of gravity.
Its specific gravity varies according to the method employed for its preparation, the extreme values being 8.279 and 9.25.
Erdmann, again, has invented an induction from particular predicates to a totality of predicates which he calls " erganzende Induction, " giving as an example, " This body has the colour, extensibility and specific gravity of magnesium; therefore it is magnesium."
Acceleration of gravity.
It is a silvery white metal which melts at 38.5° C. and has a specific gravity of I 52.
Resentment, however, incited him to personal revenge on the Californian government, and an ambition that clearly saw the gravity of the crisis prompted him to improve it unscrupulously for his own advancement, leaving his The government to support or disavow him according as P1 war should come or not.
The colour is iron-black and the lustre metallic; hardness 6, specific gravity 5.2.
Hardness 4; specific gravity 4.2.
They afford 60% of a colourless or pale-yellow, sweettasting, non-drying oil, which has a specific gravity of 0.92 nearly, becomes solid at - 19° C. (Cloez), and consists approximately of carbon 77, and hydrogen and oxygen each 11.5%.
The upper stratum is struck at a depth of 600 to 700 ft., and yields a natural liquid fuel of heavy specific gravity.
The magnet is in equilibrium under the influence of the couple VM due to the vertical component V, and the couple due to the fact that the centre of gravity is slightly on one side of the knife-edge.
The chief difficulty with this form of instrument is that it is very sensitive to changes of temperature, for such changes not only alter M but also in general cause the centre of gravity of the system to be displaced with reference to the knife-edge.
In the Eschenhagen form of vertical force balance two deflecting magnets are used to partly neutralize the vertical component, so that the centre of gravity is almost exactly over the support.
The strongest aqueous solution of hydrochloric acid at 15° C. contains 42.9% of the acid, and has a specific gravity of 1.212.
This solid, on redistillation, gives the pure acid, which is a liquid boiling at 39° C. (under a pressure of 56 mm.) and of specific gravity 1.764 0,2').
The relations between this force P, the gravity W of the body, and the reaction S of the plane are then determined by a triangle of forces HKL.
Let G be the centrc of gravity (~ 11), and let AG=a, GB=b.
It contains the theory of the centre of gravity as ordinarily understood.
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.
We can hence derive the theory of the centre of gravity, as in 4.
If the system be subject to gravity, the corresponding part of the virtual work can be calculated from the displacement of the centre of gravity.
., respectively, the virtual work of gravity is W~ozi + W2zl +.
.l (~) =(Wi+W2+ ...)&s, where ~ is the depth of the centre of gravity (see 8 (14) and 11 (6)).
This expression is the same as if the whole mass were concentrated at the centre of gravity, and displaced with this point.
An important conclusion is that in any displacement of a system of bodies in equilibrium, such that the virtual work of all forces except gravity may be ignored, the depth of the centre of gravity is stationary.
The question as to stability of equilibrium belongs essentially to kinetics; but we may state by anticipation that in cases where gravity is the only force which does work, the equilibrium of a body or system of bodies is stable only if the depth of the centre of gravity be a maximum.
For equilibrium, the altitude of the centre of gravity G must be stationary; hence G must lie in the same vertical line with the point of contact J of the two curves.
Is cos 4,, the vertical through the new position of G will fall to the left of J and gravity will tend to restore the body to its former position.
Again, take the case of a string under gravity, in contact with a smooth curve in a vertical plane.
In the case of a chain hanging freely under gravity it is usually convenient to formulate the conditions of equilibrium of a finite portion PQ.
It is a classical problem in the calculus of variations to deduce the equation (9) from the condition that the depth of the centre of gravity of a, chain of given length hanging I I between fixed points must be catenary; it determines the scale of the curve, all cate } stationary (~ 9).
The vertical through the centre of gravity of the arc AP (see fig.
This contains the theory of the centre of gravity (~ 4, 9).
We may take it as an experimental result, although the best evidence is indirect, that a particle falling freely under gravity experiences a constant acceleration which at the same place is the same for all bodies.
We infer that on our reckoning the force of gravity on a mass m is to be measured by mg, the momentum produced per second when this force acts alone.
If c be the statical increase of length which is produced by the gravity of the mass M, we have Kc=Mg, and the period is 2 ~r~t(c/g).
If the inclination of the string to the vertical does not exceed a few degrees, the vertical displacement of the particle is of the second order, so that the vertical acceleration may be neglected, and the tension of the string may be equated to the gravity mg of the particle.
Hence if 1 be the length of the string, and x the horizontal displacement of the bob from the equilibrium position, the horizontal component of gravity is mgx/l, whence The motion is therefore simple-harmonic, of period r= 27ri/(l/g).
For example, the path of a particle projected anyhow under gravity will obviously be confined to the vertical plane through the initial direction of motion.
Take, for example, the case of a particle moving on a smooth curve in a vertical plane, under the action of gravity and the pressure R of the curve.
In the motion of a projectile under gravity the hodograph is a vertical line described with constant velocity.
In the case of a particle oscillating under gravity on a smooth cycloid from rest at the cusp the hotlograph is a circle through the pole, described with constant velocity.
Again, the mass-centre~ ~f a chain oi particles connected by strings, projected anyhow under gravity, will describe a parabola.
gravity) have zero moment about G, w will be constant.
A compound pendulum is a body of any form which is free to rotate about a fixed horizontal axis, the only extraneous force (other than the pressures of the axis) being that of gravity.
where 0 is the angle which the plane containing the axis and the centre of gravity G makes with the vertical, and h is the distance of G from the axis.
Thus a M circular disk projected under gravity in a vertical plane spins Fic. 7~.
Thus the centre of a sphere rolling under gravity on a plane of inclination a describes a parabola with an acceleration g sin a/(I+C/Ma)
When the gravity of the rolling sphere is to be taken into account the preceding method is not in general convenient, unless the whole motion of G is small.
The absence of g from the latter expressior indicates that the circumstances of the rapid precession are verb nearly those of a free Eulerian rotation (~ 19), gravity playing only a subordinate part.
As regards the most general motion of a spherical pendulum, it is obvious that a particle moving under gravity on a smooth sphere cannot pass through the highest or lowest point unless it describes a vertical circle.
Of this kind is the weight of any piece in the mechanism whose centre of gravity alternately rises and falls; for during the rise of the centre of gravity that weight acts as a resistance, and energy is employed in lifting it to an amount expressed by the product of the weight into the vertical height of its rise; and during the fall of the centre of gravity the weight acts as an effort, and exerts in assisting to perform the work of the machine an amount of energy exactly equal to that which had previously been employed in lifting it.
Other forces besides gravity may be used as reciprocating forces for storing and restoring energyfor example, the elasticity of a spring or of a mass of air.
Centrifugal Force of a Rotating BodyThe centrifugal force exerted by a rotating body on its axis of rotation is the same in magnitude as if the mass of the body were concentrated at its centre of gravity, and acts in a plane passing through the axis of rotation and the centre of gravity of the body.
If the axis of rotation traverses the centre of gravity of the body, the centrifugal force exerted on that axis is nothing.
It is essential to the steady motion of every rapidly rotating piece in a machine that its axis of rotation should not merely traverse its centre of gravity, but should be a permanent axis; for otherwise the centrifugal couples will increass friction, produce oscillation of the shaft and tend to make it leave its bearings.
In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.
* Centrifugal Whirling of Shafts.When a system of revolv ing masses is balanced so that the conditions of the preceding sectiol are fulfilled, the centre of gravity of the system lies on the axis o revolution.
If there is the slightest displacement of the centre o gravity of the system from the axis of revolution a force acts on th shaft tending to deflect it, and varies as the deflexion and as th square of the speed.
To take a simple case, suppose a shaft supported on two bearings to carry a disk of weight W at its centre, I and let the centre of gravity of the disk be at a distance e from the axis of rotation, this small distance being due to imperfections of material or faulty construction.
Let da be the deviation of angular velocity to be produced in the interval dt, and I the moment of the inertia of the body about an axis through its centre of gravity; then 1/8Id(&) = Iada is the variation of the bodys actual energy.
through its centre of gravity.
133) let the required deviation be a rotation of the bod3 BB about an axis 0, not traversing the centre of gravity G, di being, as before, the deviation of angular velocity to be produced in the interval dl.
i25.* To find the moment of inertia of a body about an axis through 1?s ceetre of gravity experimentally.Suspenc~ the body from any conveniently selected axis 0 (fig.
134) be any link moving in any manner in a plane, and let G be its centre of gravity.
Then its motion may be analysed into (I) a translation of its centre of gravity; and (2) a rotation about an axis through its centre of gravity perpendicular to its plane of motion.
Let a be the acceleration of be the angular acceleration about the axis through the Centre of gravity; then the K I1~~ the centre of gravity and let A
force required to produce the - translation of the centre of - gravity is F =Wa/g, and the - couple required to produce the - angular acceleration about the Centre of gravity is M = IA/g, FiG.
W and I being respectively the weight and the moment of inertia of the link about the axis through the Centre of gravity.
Og is then the acceleration of the centre of gravity and the force F can therefore be immediately calculated.
Hence the magnitude F and the position of F relatively to the centre of gravity of the link, necessary to give rise to the couple M, are known, and this force is therefore the resultant force required.
I35, so that the centre of gravity G is not in the line joining them.
Through G, the centre of gravity of the rod, draw Gg parallel to the line of stroke, thus dividing the image at g in the proportion that the connecting rod is divided by G.
Hence Og represents the acceleration of the centre of gravity and, the weight of the connecting J.
The motion of the common centre of gravity of the two bodies is unchanged by the collision.
The loss of energy consists of a certain proportion of that part of the actual energy of the bodies which is due to their motion relatively to their common centre of gravity.
Commercial linseed oil has a peculiar, rather disagreeable sharp taste and smell; its specific gravity is given as varying from 0.928 to 0.953, and it solidifies at about - 27°.
Except by smell, by change of specific gravity, and by deterioration of drying properties, these adulterations are difficult to detect.
To say that it displaced the centre of gravity in politics and commerce, substituting the ocean for the Mediterranean, dethroning Italy from her seat of central importance in traffic, depressing the eastern and elevating the western powers of Europe, opening a path for Anglo-Saxon expansiveness, forcing philosophers and statesmen to regard the Occidental nations as a single group in counterpoise to other groups of nations, the European community as one unit correlated to other units of humanity upon this planet, is truth enough to vindicate the vast significance of these discoveries.
at the beginning of July when the berries have attained to an appreciable size - the specific gravity of the juice is very low; it contains very little sugar, but a good deal of acid, chiefly free tartaric acid and malic acid.
He determined the specific gravity of these gases with reference to common air, investigated the extent to which they are absorbed by various liquids, and noted that common air containing one part in nine by volume of fixed air is no longer able to support combustion, and that the air produced by fermentation and putrefaction has properties identical with those of fixed air obtained from marble.
The whole family seems, indeed, to have worn a character of austerity and dignity, and when Millet's father finally decided to test the vocation of his son as an artist, it was with a gravity and authority which recalls the patriarchal households of Calvinist France.
Its specific gravity varies between 8.91 and 8.95, according to the treatment to which it may have been subjected; J.
Ordinary commercial copper is somewhat porous and has a specific gravity ranging from 8.2 to 8.5.
Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.
The most important improvements in connexion with electrometers are due, however, to Lord Kelvin, who introduced the guard plate and used gravity or the torsion of a wire as a means for evaluating the electrical forces.
If W is the weight required to depress the attracted disk into the same sighted position when the plates are unelectrified and g is the acceleration of gravity, then the difference of potentials of the conductors tested is expressed by the formula V - V'=(d - d') /87 W where S denotes the area of the attracted disk.
If, in an unsharp image, a patch of light corresponds to an object point, the " centre of gravity " of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g.
But the gravity of the situation renders it unlikely that he would delay for any length of time in writing to counteract the intrigues of his opponents; to judge from allusions like those in i.
of Salamis and Plataea definitely shattered the offensive powe of the empire; that the centre of gravity in the worlds history had shifted from Susa and Babylon to the Aegean Sea; and that the Persians were conscious that in spite of all their courage they were henceforward in the presence of an enemy, superior in arms as well as in intellect, whom they could not hope to subdue by their own strength.
The chloride crystallizes in colourless rhombic tables of specific gravity 3.9 and is readily soluble in water, but is almost insoluble in concentrated hydrochloric acid and in absolute alcohol.
It crystallizes in octahedra, having a specific gravity of 3.2, and melts at 597° C. (T.
Barium carbonate, BaCO 31 occurs rather widely distributed as witherite, and may be prepared by the addition of barium chloride to a hot solution of ammonium carbonate, when it is precipitated as a dense white powder of specific gravity 4.3; almost insoluble in water.
The same hydrate can be prepared by dissolving borax in water until the solution has a specific gravity of 1.246 and then allowing the solution to cool.
Clarke answered his unknown opponent with a gravity and care that showed his high opinion of the metaphysical acuteness displayed in the objections, and published the correspondence in later editions'of the Demonstration.
Hardness 3-31-, specific gravity 6-65-6-72.
Its specific gravity varies from 6.7 to 6.86; it melts at 432° C. (Dalton), and boils between 1090 -1600 C. (T.
It has a specific gravity of 5.78 and always contains some unaltered antimony trichloride (from 6 to 20%, G.
Similar phenomena are exhibited in the electrolysis of solutions of antimony tribromide and tri-iodide, the product obtained from the tribromide having a specific gravity of 5.4, and containing 18-20% of antimony tribromide, whilst that from the tri-iodide has a specific gravity of 5.2-5.8 and contains about 22% of hydriodic acid and antimony tri-iodide.
It is a nonvolatile white powder, and has a specific gravity of 6.6952; it is insoluble in water and almost so in acids - concentrated hydrochloric acid dissolving a small quantity.
It is a pale yellow powder (of specific gravity 6.5), which on being heated strongly gives up oxygen and forms the tetroxide.
The tri-iodide forms red-coloured crystals of specific gravity 4.848 (26°), melting at 165° to 167° C. and boiling at 401° C. By the action of water they give oxybromides and oxyiodides SbOBr, Sb 4 O 5 Br 21 SbOI.
There were to be found the most contradictory qualities in perfect agreement with each other - gravity and courtliness, earnestness and gaiety, the man of learning, the noble and the bishop. But all centred in an air of high-bred dignity, of graceful, polished seemliness and wit - it cost an effort to turn away one's eyes.
The result of this pressure if unopposed is to cause this stratum to spread itself over the surface of the solid as a drop of water is observed to do when placed on a clean horizontal glass plate, and this even when gravity opposes the action, as when the drop is placed on the under surface of the plate.
It consists of three parts, the first depending on the action of gravity, the second on the mutual action between the particles of the fluid, and the third on the action between the particles of the fluid and the particles of a solid or fluid in contact with it.
Plateau (Statique experimentale et theorique des liquides), who made elaborate study of the phenomena of surfacetension, adopted the following method of getting rid of the effects of gravity.
If, however, it were negative, the displacement of the liquids which tends to enlarge the surface of contact would be aided by the molecular forces, so that the liquids, if not kept separate by gravity, would at length become thoroughly mixed.
The upper surface of this column is not level, so that the height of the column cannot be directly measured, but let us assume that h is the mean height of the column, that is to say, the height of a column of equal weight, but with a flat top. Then if r is the radius of the tube at the top of the column, the volume of the suspended column is 717 2 12, and its weight is 7rpgr 2 h, when p is its density and g the intensity of gravity.
We Will Assume That When, As In Most Cases, Viscosity Maybe Neglected, The Mass (M) Of A Drop Depends Only Upon The Density (V), The Capillary Tension (T), The Acceleration Of Gravity (G), And The Linear Dimension Of The Tube (A).
If, as is sometimes stated, the tension of a vertical film were absolutely the same throughout, the middle parts would of necessity fall with the acceleration of gravity.
But the liquid after it leaves the vessel is subject to no forces except gravity, the pressure of the air, and its own surface-tension.
Of these gravity has no effect on the form of the stream except in drawing asunder its parts in a vertical direction, because the lower parts are moving faster than the upper parts.
In this case drops which break away with different velocities are carried under the action of gravity into different paths; and thus under ordinary circumstances a jet is apparently resolved into a " sheaf," or bundle of jets all lying in one vertical plane.
This pressure must be added to the pressure due to gravity gpy.
Hence the waves will be propagated as if the intensity of gravity had been 4?r2 T f =g +:2 p instead of g.
for irrigation, and develop also an electric power sufficient to pump underground water for an additional 50,000 acres at the lowest estimate' of lands lying too high for supply by gravity.
Corps occupied the plain from opposite Novak to Kikuricani, with its centre of gravity on the Prilep road.'
Its specific gravity is about 3.2.
The specific gravity of the syrup should be 1'33.
Acetone is a colourless mobile liquid of pleasant smell, boiling at 56.53°C., and has a specific gravity 0.819 (0 deg.
In dealing with the early stages of the Protestant revolt in Germany Adrian did not fully recognize the gravity of the situation.
The hardness of the crystallized haematite is about 6, and the specific gravity 5.2.
Its specific gravity, according to G.
I 2.3 3'9 9.5 The same observer established the following relation between fineness p and specific gravity of alloys containing from 375 to 875 of silver per 1000: - sp. gr.
With the fall of water there is an increase in the specific gravity, which in 1850 was 1.17, and in September 1901 was I 179; in 1850 the proportion of solids by weight was 22.282%, in September 1901 it was 25.221; at the earlier of these dates the solids in a litre of water weighed 260.69 grams, at the latter date 302'122 grams. The exact cause of this cyclic variation is unknown: the low level of 1906 is usually regarded as the result of extensive irrigation and ploughing in the surrounding country, which have robbed the lake, in part, of its normal supply of water.
His style ranges from the brilliancy of his youth to the sternness and sombre gravity of age, passing almost to poetic expression in its epigrammatic terseness.
Blaise Pascal determined the area of the section made by any line parallel to the base and the volumes and centres of gravity of the solids generated by revolving the curve about its axis and base.
Sir Christopher Wren, the famous architect, determined the length of the arc and its centre of gravity, and Pierre Fermat deduced the surface of the spindle generated by its revolution.
The plane of the ecliptic is that plane in or near which the centre of gravity of the earth and moon.
Owing to the action of the planets, especially Venus and Jupiter, on the earth, the centre of gravity of the earth and moon deviates by a yet minuter amount, generally one or two tenths of a second, from the plane of the ecliptic proper.
They also decrease the specific gravity, so that the grain is more readily carried by the wind, especially when, as in Briza, the glume has a large surface compared with the size of the grain, or when, as in H olcus, empty glumes also take part; in Canary grass (Phalaris) the large empty glumes bear a membranous wing on the keel.