Volume

“ You quickly thrust aside, one by one, or by the half-dozen, all the volumes which are not green, cloth-bound, thin duodecimos, without so much as glancing at them. Your special volume is quickly found among hundreds of volumes, and your faculty of memory and intuition has saved you perhaps a quarter of an hour of valuable time, which, without that faculty, might have been wasted in search. ”

“ What is the use of giving, for instance, an unestablished, and perhaps preposterous, notion of corporeal quantity to him who has as yet to learn what is the essential composition of bodies? Is a student prepared to realize the true nature of the quantity of mass, or of the quantity of volume, who has never yet explored either the mysterious attributes of formal continuity or the intimate constitution of material substance? ”

“ For instance, the scientific unit of volume is always the cube whose side is the unit of length. If the unit of length varies, the unit of volume will vary as its third power, and the unit of volume is said to be of three dimensions with respect to the unit of length. ”

“ The volume of a substance is proportional to its weight, and inversely proportional to its density, and therefore by dividing the amount by weight of each substance entering into the composition of a compound by its density in the gaseous or vaporous state we shall obtain factors which will be in the same proportion as the volumes of the substances entering into the composition of the compound. ”

“ Volumes are always most accurately defined by their weight of water, as weighing can be more accurately done than measuring. If the volume is hollow, it may be filled with water and closed with a sheet of plate glass, or if solid the body may be weighed in water and out, the difference giving the weight of its volume of water. ”

“ Volucrine, vol′ū-krin, adj. pertaining to birds, bird-like. [L. volucris, a bird—volāre, to fly.]
Volume, vol′ūm, n. a roll or scroll, which was the form of ancient books: a book, whether complete in itself or part of a work: a rounded mass, convolution: cubical content: a quantity: dimensions: fullness of voice.—v.i. to swell.—adj. Vol′umed, having the form of a volume or roll: of volume or bulk.—ns. Volumenom′eter, an instrument for measuring the volume of a solid body by the quantity of fluid it displaces; Vol′umēter, an instrument for measuring the volumes of gases.—adjs. ”

“ It is certain, in fact, that when we wish to consider separately a certain portion of indefinite space, conceived as gaseous, we mentally solidify its exterior envelope, so that a line and a surface are habitually, to our minds, just as solid as a volume. ”

“ The first type is always used for accurate purposes. Units of surface are always directly related to standards of length, without any separate standards. Volume is either determined by the lineal dimensions of a space or a solid, or, for accurate purposes, by the mass of water contained in a volume at a given temperature, which again is measured either by liquid measure, or, more accurately, by weight. ”

“ The statical energy of an infinitesimal element of volume may be represented by where is a quadratic function of the components of displacement Since for that element of volume may be regarded as linear functions of and diff. coeff., we may regard as a quadratic function of and diff, coeff., or as a linear function of the seventy-eight squares and products of these quantities. ”

“ A three-dimensional locus of event-particles which is the common portion of the boundary of two adjoined events will be called a ‘solid.’ A solid may or may not lie completely in one moment. A solid which does not lie in one moment will be called ‘vagrant.’ A solid which does lie in one moment will be called a volume. A volume may be defined as the locus of the event-particles in which a moment intersects an event, provided that the two do intersect. The intersection of a moment and an event will evidently consist of those event-particles which are covered by the moment and lie in the event. ”

“ General Remarks In the various names of weights and measures there are many general-utility words which offer no difficulty in the sphere of those who use them habitually, yet which are sometimes puzzling to others, while they are interesting to the student of semantics. They form a chapter in the history of weights and measures, itself a volume in the history of the human mind. ”

“ Each is entirely independent of the other. Bodies having very different volumes may have the same figure; and in like manner bodies differing in figure may have the same volume. The figure of a body is what in popular language is called its shape or form. The volume of a body is that which is commonly called its size. ”

“ So that if the volume of any body, whether atom, planet, satellite or sun, be doubled, its attractive power remains the same, simply because the mass of the whole body remains the same. Mass, we are told by mathematicians, is equal to the volume multiplied by the density, and whenever we increase the volume of a body we decrease the density, the total mass of the body remaining the same. ”

“ If any plane figure revolves about an external axis in its plane, the volume of the solid generated by the revolution is equal to the product of the area of the figure and the distance travelled by the centroid of the figure. ”

“ In our experience, a finite mass of matter occupies a volume and not a point. Evidently therefore the laws should be stated in an integral form, involving at certain points of the exposition greater elaboration of statement. ”

“ A material object expresses the spatial distribution of a quantity of 'material,' when the quantity is absolutely extensive.
59.3 The volume-density, at a time in the -space of a time-system , of the distribution of any absolutely extensive quantity possessed by a material object is calculated by the ordinary mathematical formula. Consider any event-particle occupying the -point at the -time . Let be the measure of a volume in the -space which contains ; and let ′ be the extensive component of located in , if there be such an extensive component. ”

“ My volume hath that mark of honour which no other volume in my collection hath, & vy diligently and carefully I continued the same until that most hapie restoration & coronation of his most gratious majestie King Charle ye 2d, whom God long preserve.
“Geo. Thomason.”
The volume bears the “honours” of its mischance. There are a great number of stains on the edges of the leaves—some more than an inch in depth. The accident must have happened on the road in the king’s flight, from the marks of the mud. ”

“ Arbitrary Scales.—An arbitrary scale can be constructed by selecting any physical property of a substance which varies regularly with the temperature, such as the volume of a liquid, or the pressure or density of a gas, or the electrical resistance of a metal. ”

“ To apprehend a surface is to apprehend a surface of a volume. To apprehend a volume is to apprehend a volume bounded by a surface. To apprehend a universal is to apprehend it [Pg 132] as the universal of an individual, and vice versa. ”

“ But whoever has once realized the fact that the dimensions of bodies are not continuous lines of matter, but intervals, or relations, in space, will agree that such dimensions do not inhere in the matter, but are extrinsic relations between material terms distinctly ubicated. What is called the volume of a body is nothing but the resultant of a system of relations in space. ”

“ We may, for instance, .choose a certain length, a certain volume, a certain mass, a certain force or power as our units of length, volume, mass, force or power, which have no simple or direct relation to each other. ”

“ I dare say I am compelled, unconsciously compelled, now to write volume after volume, as in past years I was compelled to go to sea voyage after voyage. Leaves must follow upon each other as leagues used to follow in the days gone by, on and on to the appointed end, which, being Truth itself, is One—one for all men and for all occupations. ”

“ Size is the measure, and he assumes that size means volume, and that volume means power. Hence, a man with a large head must have more brains than a man with a small head, and the more brains he has, the greater his power, other things being equal. ”

“ It is a general observation in physics that a given portion of matter is of constant mass, however its354 pressure, volume, temperature and other conditions may vary. In particular, the mass of a given portion of matter always equals the product of its mean density and volume, since density is defined as the amount of mass in the unit volume. ”

“ It is also convenient to regard as coming under mensuration the consideration of certain derived magnitudes, such as the moment of a plane figure with regard to a straight line in its plane, the calculation of which involves formulae which are closely related to formulae for determining areas and volumes. ”

“ That is, the sum of the products of the volumes of the masses by their pressures, diminished by the sum of the products of the areas of the surfaces of discontinuity by their tensions, must be a maximum. ”

“ It may also be remarked that most generally, in order that bodies may penetrate one another with more facility, we are obliged to imagine the interior of the volumes to be hollow, which renders still more sensible the impropriety of the word solid. ”

“ A column of the type used in printing the catalogue weighs ten pounds, so that supposing the work, when through the press, to consist of 600 volumes averaging 250 columns each, a million and a half pounds' weight of type will have been employed. ”

“ Example (3) . A cone having height and radius of base has volume . If its height remains constant, while changes, the ratio of change of volume, with respect to radius, is different from ratio of change of volume with respect to height which would occur if the height were varied and the radius kept constant, for
The variation when both the radius and the height change is given by . ”

“ Size, on the other hand, and its alteration regarded merely as size, is for the qualitative determination, when it is unable to assert itself in terms of measure, an indifferent determination. That is to say, measure is quantity, precisely in so far as it can give to itself an aspect which qualifies it, and thereby a qualitative determination is united to the purely quantitative one. ”

“ Work the problem properly, and the result must be what you require. All the parts are equal to the whole; the greater includes the less; and of several equal parts all are alike: and these propositions are not more true than is the answer I have given to your query; therefore allow me to hope that you will, in consideration of the accuracy of my analysis, find the perpendicular of your pocket, subtract from its base any circle whose circumference is a known quantity, and place it within the superficies of my hand. ”

“ And because whatsoever is real here, or there, or in any place, has dimensions, that is to say, magnitude; that which hath magnitude, whether it be visible or invisible, finite or infinite, is called by all the learned a body. ”

“ Previous measures have been represented by monosyllables, as grain, dram, gross, ounce, pound, stone, ton. Where a word is often repeated, in the hurry of business, it is instinctively abridged. We shall not err, if we profit by this experience, and seek to reduce the new nomenclature to its smallest proportions.
Twelve words only are required by this system. Learning these, you learn all. There are five designating the different units of length, surface, solid capacity, liquid capacity, and weight. ”

“ You see it fails you at the very moment you want it. When we measure our lances against one another, we can express their comparative length by saying that one measures three and the other four spaces,—a space being merely an imaginary measure ”

“ I use no figure of speech when I say that we may now buy our books in bulk. I saw, only this morning, the advertisement of a large dry goods “emporium” (’tis laces and literature now) wherein is announced for sale the bound volumes of a popular magazine. “Over eight pounds of the choicest reading, bound in the usual style—olive green.” ”

“ Why need I volumes, if one word suffice? ”

“ In every country the scale is generally expressed by the ratio of some fraction or multiple of the smallest to the largest national units of length, but sometimes by the fraction which indicates the ratio of the length of a line on the paper to that of the correspond- ing line on the ground. ”

“ Common addition will be easily understood by a child who distinctly perceives that the perpendicular columns, or places in which figures are written, may distinguish their value under various different denominations, as gallons, furlongs, shillings, &c. ”

“ Extended quantities, such as lines, surfaces and solids, besides what they have in common with all other quantities, have this peculiar, that their parts have a particular place and disposition among themselves: a line may not only bear any assignable proportion to another, in length or magnitude, but lines of the same length may vary in the disposition of their parts; one may be straight, another may be part of a curve of any kind or dimension, of which there is an endless variety. ”

“ A scale might be formed, graduated according to the degrees of a combined ratio of intensity, duration, connexion, periods of recurrence, and utility, which would be the standard, according to which all ideas might be measured, and an uninterrupted chain of nicely shadowed distinctions would be observed, from the faintest impression on the senses, to the most distinct combination of those impressions; from the simplest of those combinations, to that mass of knowledge which, including our own nature, constitutes what we call the universe. ”