Aggregate

“ Growth, which is increase of bulk, is simply the absorption of diffuse gaseous or liquid materials, which may theoretically be regarded as having originally belonged to the aggregate in its most widely diffused condition. Development, which is increase of structure, is the same process which all aggregates undergo in their transition from the homogeneous and indefinite toward the heterogeneous and definite, under the laws of segregation and the multiplication of effects. Finally, equilibration in organic aggregates is distinct and universal. ”

“ An aggregate of ten bricks, for instance, has no character as a whole beyond the mere fact of being thought of in one mental act. It has not even a collective weight until you put your ten bricks into the same cart, or on the same scale-pan, and then they have ceased to be a mere aggregate in the very moment of exerting pressure upon the same surface, and have become a true material system. ”

“ When we desire to classify, it is necessary to contemplate entire groups of strata in the aggregate; but if we wish to understand the mode of their formation, and to explain their origin, we must think only of the minute subdivisions of which each mass is composed. We must bear in mind how many thin leaf-like seams of matter, each containing the remains of myriads of testacea and plants, frequently enter into the composition of a single stratum, and how vast a succession of these strata unite to form a single group! ”

“ Sometimes none of the coarse aggregates readily available are sufficiently durable or uniform for the wearing surface of the concrete road, but a suitable aggregate may be obtained at relatively high price by shipping considerable distances. ”

“ Respecting the structural state simultaneously reached, it must obviously be one presenting an arrangement of forces that counterbalance all the forces to which the aggregate is subject. So long as there remains a residual force in any direction—be it excess of a force exercised by the aggregate on its environment, or of a force exercised by its environment on the aggregate, equilibrium does not exist ”

“ Whence we found it to follow that the final structural arrangements, must be such as will meet all the forces acting on the aggregate, by equivalent antagonist forces. What is the implication in the case of organic aggregates; the equilibrium of which is a moving one? We have seen that the maintenance of such a moving equilibrium, requires the habitual genesis of internal forces corresponding in number, directions, and amounts to the external incident forces—as many inner functions, single or combined, as there are single or combined outer actions to be met. ”

“ If an infinite aggregate of points does not extend to an infinite distance, there must be at least one point a, which has the property that the points of the aggregate which are in the neighbourhood of a for any number h, however small, themselves constitute an infinite aggregate, and then the point a is called a “limiting point” of the aggregate; it may or may not be a point of the aggregate. An aggregate of points is “perfect” when all its points are limiting points of it, and all its limiting points are points of it ”

“ The totality of entities which lend themselves to a given type of order, form a collection, or an aggregate; and if the order of a given aggregate is to be unambiguous, the members of this aggregate must be uniquely determined, and must be mutually exclusive: they must be what we shall later denote by the term elements of the aggregate. Externality and ‘elementarity’ are only different consequences of the same relation, which we denote by the term extension, and which thus together with the relation of order, will constitute the basis of our definition of space and time. ”

“ This numerical excess increases rapidly with each successive increase in the original aggregate, so that if we apply the same reasoning to an infinite aggregate, the aggregate of partial aggregates becomes an infinity of a higher order. This is expressed by saying that the infinite aggregate of partial aggregates has a greater potentiality than the infinity of the elements of the original aggregate.
So we see that the one infinity is, in popular language, much more comprehensive, more powerful than the other. ”

“ The most important truth which can be called in to aid us in this difficulty and apparent confusion of phenomena is that of the perpetual competitive operation of both the forces of evolution and of dissolution. Both these influences are at all times and in all kinds of aggregates simultaneously at work. The history of every aggregate is that of its struggle with these opposite contending influences. The final equilibration implies this. It is the establishment of equilibrium between just these forces. In the evolution of a star the forces of dissolution are mostly within the aggregate. ”

“ In subordination to the different amounts and kinds of forces to which its different parts are exposed, every individual organic aggregate, like all other aggregates, tends to pass from its original indistinct simplicity towards a more distinct complexity. ”

“ And the fact which we have here particularly to observe, is, that as a corollary from the general law of equilibration above set forth, the evolution of every aggregate must go on until this equilibrium mobile is established; since, as we have seen, an excess of force which the aggregate possesses in any direction, must eventually be expended in overcoming resistances to change in that 448direction: leaving behind only those movements which compensate each other, and so form a moving equilibrium. ”

“ The aggregate by no means should be uniform in size. Fragments of different dimensions are most essential, so that the smaller material may fill up the interstices of the larger. It is not infrequently stipulated by engineers that no individual fragment shall be more than 4 inches across, and the material is often specified to pass through a ring 1 1/2 to 2 inches in diameter. ”

“ We know that an organism develops, much like a world, out of an homogeneous and diffused state of its elements. Throughout its course the organic aggregate behaves like other aggregates. From the imperceptible it becomes perceptible. From the diffuse it becomes concentrated. From the indefinite it becomes definite. From the homogeneous it becomes heterogeneous. From the unstable it approaches the stable condition. Segregation, which is the selective process, is more marked in the organic than in the inorganic aggregate. ”

“ If this force is such that in expending itself it disturbs beyond rectification the balance of the organic processes, then the aggregate is disintegrated or decomposed. But if it does not overthrow that moving equilibrium constituting the life of the aggregate, then the aggregate continues in that modified form produced by the expenditure of the force. Thus, by direct equilibration, continually furthered by indirect equilibration, there must arise this distinction between the outer part adapted to meet outer forces, and the inner part adapted to meet inner forces. ”

“ Fine Aggregate.—The fine aggregate is generally natural sand, but a mixture of natural sand and stone screenings is sometimes employed. The fine aggregate of whatever character must be clean, free from organic matter and sand, must contain no appreciable amount of mica, feldspar, alkali, shale or similar deleterious substances and not exceed two and one-half per cent of clay and silt. The sand is of such a range of sizes that all will pass the one-fourth-inch sieve and that not exceeding about five per cent will pass the 100-mesh sieve. ”

“ Though here, in the augmentation of mass, we see a progress towards the evolution of a higher type, we have as yet none of that definiteness required to constitute a compound unit, or true aggregate of the second order. Another kind of obscuration of the morphological units, is brought about by their more complete coalescence into the form of some structure made by their union. ”

“ Similarly when mechanical force is expended on any aggregate, either by collision, continued pressure, or tension, the amounts of strain distributed throughout the mass are manifestly unlike for unlike positions. But to say the different parts of an aggregate receive different quantities of any incident force, is to say that their states are modified by it in different degrees—is to say that if they were before homogeneous in their relations they must be rendered to a proportionate extent heterogeneous ”

“ Spencer holds that this can be done. For any finite aggregate, being unequally exposed to surrounding forces, will become more diverse in structure, every differentiated part will become the parent of further differences; at the same time, dissimilar units in the aggregate tend to separate, and those which are similar, to cluster together ("segregation") ; and this subdivision and dissipation of forces, so long as there are any forces unbalanced by opposite forces, must end at last in rest ”

“ The factors of the first class are those which tend directly to change an organic aggregate, in common with every other aggregate, from that more simple form which is not in equilibrium with incident forces, to that more complex form which is in equilibrium with them. We have to mark how, in correspondence with the universal law that the uniform lapses into the multiform, and the less multiform into the more multiform, the parts of each organism are ever becoming further differentiated ”

“ The absolute limits to size for the aggregate, however, are determinable by a number of considerations, not the least important of which is the magnitude and bulk of the work in which it is to be employed. The particles of sand should also be of varying degrees of coarseness. A fine, dust-like sand is objectionable; its minute subdivision prevents complete contact with the cement on all its faces. ”

“ Measuring Materials.—In considering the methods employed for measuring aggregates, emphasis should be placed on the futility of rigid requirements for the aggregates, both as regards quality and range of sizes, if the materials are carelessly proportioned at the mixer. If even reasonably near uniform wearing qualities are to be secured throughout the entire area of the concrete road surface, successive batches of concrete must be alike, and [Pg 102] to insure that, the aggregates including the water in each batch of concrete must be mixed in exactly the same proportions. ”

“ For beams and lintels, a light aggregate, such as coke breeze from gasworks, is permissible, especially when the work is designed to receive nails. On the other hand, for retaining walls, the heaviest possible aggregate is desirable on the ground of stability. ”

“ It is seldom that aggregate larger than will pass a 3-in. ring is used and this only in very massive work. The more usual size is 21⁄2 ins. For reinforced concrete 11⁄4 ins. is about the maximum size allowed and in building work 1-in. aggregate is most commonly used. Same constructors use no aggregate larger than 3⁄4 in. in reinforced building work, and others require that for that portion of the concrete coming directly in contact with the reinforcement the aggregate shall not exceed 1⁄4 to 1⁄2 in. ”

“ It may be noted that it is not unreasonable to argue that the density of a continuum is necessarily greater than the density of any disconnected aggregate: certainly of any assemblage whose particles are actually composed of the material of the continuum. ”

“ A domain which consists of all the real numbers which exceed some fixed number may be described as an “interval unlimited towards the right”; similarly we may have an interval” unlimited towards the left.”
In more complicated cases we must have some rule or process for assigning the aggregate of numbers which constitute the domain of a variable. The methods of definition of particular types of aggregates, and the theorems relating to them, form a branch of analysis called the “theory of aggregates” (Mengenlehre, Théorie des ensembles, Theory of sets of points) . ”

“ Most of the objects which surround us, whether organic or inorganic, are known to consist of a great number of elementary parts of the same size and form which are aggregated in definite ways to form the general mass which each such object presents. These particles, which are alike for all parts of the same object or species of object, are unlike for different objects. Each object is an aggregate of elements of the same species, and these elements are the units of aggregation. All aggregates which have been thus far resolved into these units have confirmed this law. ”

“ Manifestly, if two or more kinds of units contained in any aggregate, are united by powerful affinities, an incident force, failing to destroy their cohesions, will not cause such various re-arrangements as it would, could it produce new chemical combinations as well as new mechanical adjustments. On the other hand, chemical affinities that are easily overcome, must be favourable to multiplied re-arrangements of the units. ”

“ For the liquid state is a state in which the units become so far free from mutual restraints, that incident forces can change their relative positions very readily. Thus we have reason to conclude that an aggregate of units which, though in the main similar to one another, have minor differences, must be more unstable than an aggregate of homogeneous units. The one will yield to disturbing forces which the other successfully resists. ”

“ To add or unite, as, a person, to an association.
It is many times hard to discern to which of the two sorts, the good or the bad, a man ought to be aggregated. Wollaston.
3. To amount in the aggregate to; as, ten loads, aggregating five hundred bushels. [Colloq.]
Syn. — To heap up; accumulate; pile; collect.
AGGREGATE
Ag"gre*gate, n.
1. A mass, assemblage, or sum of particulars; as, a house is an aggregate of stone, brick, timber, etc.
In an aggregate the particulars are less intimately mixed than in a
compound. ”