SOLIDITY
, in Physics, a property of matter or body, by which it excludes every other body from that place which is possessed by itself.
Solidity in this sense is a property common to all bodies, whether solid or fluid. It is usually called impenetrability; but Solidity expresses it better, as carrying with it somewhat more of positive than the other, which is a negative idea.
The idea of Solidity, Mr. Locke observes, arises from the resistance we find one body makes to the entrance of another into its own place. Solidity, he adds, seems the most extensive property of body, as being that by which we conceive it to fill space; it is distinguished from mere space, by this latter not being capable of resistance or motion.
It is distinguished from hardness, which is only a firm cohesion of the solid parts.
The difficulty of changing situation gives no more Solidity to the hardest body than to the softest; nor is the hardest diamond properly a jot more solid than water. By this we distinguish the idea of the extension of body, from that of the extension of space: that of body is the continuity or cohesion of solid, separable, moveable parts; that of space the continuity os unsolid, inseparable, immoveable parts.
The Cartesians however will, by all means, deduce Solidity, or as they call it impenetrability, from the nature of extension; they contend, that the idea of the former is contained in that of the latter; and hence they argue against a vacuum. Thus, say they, one cubic foot of extension cannot be added to another without having two cubic feet of extension; for each has in itself all that is required to constitute that magnitude. And hence they conclude, that every part of space is solid, or impenetrable, as of its own nature it excludes all others. But the conclusion is false, and the instance they give follows from this, that the parts of space are immoveable, not from their being impenetrable or solid. See Matter.
Solidity is also used for hardness, or firmness; as opposed to fluidity; viz, when body is considered either as fluid or solid, or hard or firm.
Solidity, in Geometry, denotes the quantity of space contained in a solid body, or occupied by it; called also the solid content, or the cubical content; for all solids are measured by cubes, whose sides are inches, or feet, or yards, &c; and hence the Solidity of a body is said to be so many cubic inches, feet, yards, &c, as will fill its capacity or space, or another of an equal magnitude.
The Solidity of a cube, parallelopipedon, cylinder, or any other prismatic body, i. e. one whose parallel sections are all equal and similar throughout, is found by multiplying the base by the height or perpendicular altitude. And of any cone or other pyramid, the Solidity is equal to one-third part of the same prism, because any pyramid is equal to the 3d part of its circumscribing prism. Also, because a sphere or globe may be considered as made up of an infinite number of pyramids, whose bases form the surface of the globe, and their vertices all meet in the centre, or having their common altitude equal to the radius of the globe; therefore the solid content of it is equal to onethird part of the product of its radius and surface. For the Solidity of other figures, see each figure separately.
The foregoing rules are such as are derived from common geometry. But there are in nature numberless other forms, which require the aid of other methods and principles, as follows.
Of the Solidity of Bodies formed by a Plane revolving about any Axis, either within or without the Body.— Concerning such bodies, there is a remarkable property or relation between their Solidity and the path or line described by the centre of gravity of the revolving plane; viz, the Solidity of the body generated, whether by a whole revolution, or only a part of one, is always equal to the product arising from the generating plane drawn into the path or line described by its centre of gravity, during its motion in describing the body. And this rule holds true for figures generated by all sorts of motion whatever, whether rotatory, or direct or parallel, or irregularly zigzag, &c, provided the generating plane vary not, but continue the same throughout. And the same law holds true also for all surfaces any how generated by the motion of a right line. This is called the Centrobaric method. See my Mensuration, sect. 3, part 4, pa. 501, 2d edit.
Of the Solidity of Bodies by the Method of Fluxions. —This method applies very advantageously in all cases also in which a body is conceived to be generated by the revolution of a plane figure about an axis, or, which is much the same thing, by the parallel motion of a circle, gradually expanding and contracting itself, according to the nature of the generating plane. And this method is particularly useful for the solids generated by any curvilineal plane figures. Thus, let the plane AED revolve about the axis AD; then it will generate the solid ABFEC. But as every ordinate DE, per- | pendicular to the axis AD, de- scribes a circle BCEF in the revolution, therefore the same solid may be conceived as generated by a circle BCEF, gradually expanding itself larger and larger, and moving perpendicularly along the axis AD. Consequently the area of that circle being drawn into the fluxion of the axis, will produce the fluxion of the solid; and therefore the fluent, when taken, will give the Solidity of that body. That is, AD X circle BCF, (whose radius is DE, or diameter BE) is the fluxion of the Solidity.
Hence then, putting ; because cy2 is equal to the area of the circle BCF; therefore cy2x. is the fluxion of the solid. Consequently if the value of either y2 or x. be found in terms of each other, from the given equation expressing the nature of the curve, and that value be substituted for it in the fluxional expression cy2x., the fluent of the resulting quantity, being taken, will be the required Solidity of the body.
For Ex. Suppose the figure of a parabolic conoid, generated by the rotation of the common parabola ADE about its axis AD. In this case, the equation of the curve of the parabola is , where p denotes the parameter of the axis. Substituting therefore px instead of y2, in the fluxion cy2x., it becomes cpxx.; and the fluent of this is for the Solidity; that is, half the product of the base of the solid drawn into its altitude; for cy2 is the area of the circular base BCF, and x is the altitude. And so on for other such figures. See the content of each solid under its proper article.
For the Solidity of Irregular Solids, or such as cannot be considered as generated by some regular motion or description; they must either be considered as cut or divided into several parts of known forms, as prisms, or pyramids, or wedges, &c, and the contents of these parts found separately. Or, in the case of the smaller bodies, of forms so irregular as not to be easily divided in that way, put them into some hollow regular vessel, as a hollow cylinder or parallelopipedon, &c; then pour in water or sand so as it may fill the vessel just up to the top of the inclosed irregular body, noting the height it rises to; then take out the body, and note the height the fluid again stands at; the difference of these two heights is to be considered as the altitude of a prism of the same base and form as the hollow vessel; and consequently the product of that altitude and base will be the accurate Solidity of the immerged body, be it ever so irregular.
