Physical quantity

“ You will soon learn that the volume of all bodies is constantly changing in correspondence with the changes in the pressure exerted by other bodies, but more especially in correspondence with the changes of temperature to which they are subjected; while the weight of the same body, at the same point on the earth’s surface, never alters. Hence we may take the weight of a body as a measure of the quantity of matter which it contains ”

“ In the definition of the potentials etc., the energy of a homogeneous mass was considered as a function of its entropy, its volume, and the quantities of the various substances composing it. Then the potential for one of these substances was defined as the differential coefficient of the energy taken with respect to the variable expressing the quantity of that substance. ”

“ Definition.—If to any homogeneous mass we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered. ”

“ He is thus led to recognize a classification of quantities on a new principle, according to which the physical nature of the quantity is subordinated to its mathematical form. ”

“ Matter may be defined as that which occupies space and possesses weight. Like energy, matter may be changed oftentimes from one form into another; and since in these transformations all the other physical properties of a substance save weight are likely to change, the inquiry arises, Does the weight also change? Much careful experimenting has shown that it does not. The weight of the products formed in any change in matter always equals the weight of the substances undergoing change. ”

“ You are mistaken, my dear; equal weight must contain equal quantities of matter; and when we wish to know what is the relative quantity of caloric, 130 which substances of various kinds are capable of containing under the same temperature, we must compare equal weights, and not equal bulks of those substances. Bodies of the same weight may undoubtedly be of very different dimensions; but that does not change their real quantity of matter. A pound of feathers does not contain one atom more than a pound of lead. ”

“ In cases of materialisation, dense physical matter, probably chiefly in the form of gases or liquids, is frequently borrowed from the body of the medium, who actually decreases temporarily in size and weight ”

“ The accumulation of matter, however, and its relative quantity, are rendered sensible by weight; for weight is proportionate to the quantity of matter, as regards the parts of a tangible substance, but spirit and its quantity of matter are not to be computed by weight, which spirit rather diminishes than augments. ”

“ Hence the rate at which the energy of the corpuscles is spent in order to maintain the gravitating property of a single pound is at least millions of millions of foot-pounds per second. What becomes of this enormous quantity of energy ? ”

“ It may be added that, as the volume, entropy, and energy of a body are equal to the sums of the volumes, entropies, and energies of its parts, if the surface should be constructed for bodies differing in quantity but not in kind of matter, the different surfaces thus formed would be similar to one another, their linear dimensions being proportional to the quantities of matter. ”

“ It is amazing to find a theory so plainly at variance with elementary physical laws accepted by eminent men. What would be the result if we had to bear upon the surface of the body a pressure of 15,000 kilogrammes, and if every variation of the barometer added or subtracted from this sum one or two hundred kilogrammes? ”

“ That the weight of a given lump of matter is not a constant but a dependent quantity may be seen from a number of considerations. Its weight in vacuo, for instance, is different from its weight in air, and this latter differs considerably from its weight in water or in oil. ”

“ It is required to find the amount by which the volume of the body can be diminished, using for that purpose, according to the conditions, only the force derived from the body itself. The conditions require that the energy of the body shall not be altered nor its entropy diminished. Hence the quantity sought is represented by the distance of the point representing the initial state from the surface of dissipated energy, measured parallel to the axis of volume. ”

“ Porosity.—The volume of a body is the quantity of space included within its external surfaces. The mass of a body, is the collection of atoms or material particles of which it consists. Two atoms or particles are said to be in contact, when they have approached each other until arrested by their mutual impenetrability. If the component particles of a body were in contact, the volume would be completely occupied by the mass. But this is not the case. We shall presently prove, that the component particles of no known substance are in absolute contact. ”

“ And since it seems reasonable to suppose that a large quantity of matter, moving slowly, possesses as much motion as a small quantity moving faster, 'mass' has been held to express 'quantity of matter.' It is further demonstrable that, at any given time and place, the relative mass of any two bodies is expressed by the ratio of their weights. ”

“ And, moreover, chemistry aided by physics has concluded that the properties of a body "are dependent on the variations of the energy of the body, and not on its total value," and therefore that "it is unnecessary, even if it were possible, to form any estimate of the energy of the body in its standard state." ”

“ But inasmuch as the effect of the attractive influence of the earth, or the weight of the liquid, increases with the quantity we use, while on the other hand the surface-tension, or its own moulding molecular force, remains precisely the same, we should, if we use a large quantity of liquid, expect the weight to be the particular force which determined its shape; and if we employ a small mass of liquid, then the surface-tension, growing proportionately greater, would become the more important. ”

“ Now we choose mass as a unit of measure of the quantity of material; and we are justified in doing so, because experiments have shown that material, confined in a closed space, does not appreciably alter its mass. The mass is proportional to the weight, generally measured as [Pg 234] the force exerted at some definite latitude on the earth’s surface, tending to pull the body towards the centre of the earth. ”

“ By the above mode of reasoning, together with the conclusions drawn from our experience of bodies consisting of an immense number of molecules, the result has been arrived at that the availability of a given amount of energy is determined on a physical basis, and is dependent on the infinite number of particles of which every tangible mass must be composed. ”

“ The exact investigation of material changes called chemistry rests on the statement that mass, and mass is practically measured by weight, is the one property of what we call matter, the determination whereof enables us to decide whether a change is a combination, or coalescence, of different things, or a separation of one thing into parts. That any part of a material system can be removed without the weight of the portion which remains being less than the original weight of the whole system, is unthinkable, in the present state of our knowledge of material changes. ”

“ And nothing that man has been able to do has affected the weight of a given quantity of either of these gases. So far as we know, elementary bodies retain their weight under all 73circumstances, and can be traced by it whatever shape they may take. ”

“ What kind of a quantity is that which now weighs more, and now weighs less, so to speak? But this apparent deviation from the method of determination commonly used in practical life, that by weight, is, closely considered, an agreement. On a high mountain a heavy mass also is less powerfully attracted to the earth than at the level of the sea, and if it is permitted us in our determinations to neglect the consideration of level, it is only because the comparison of a body with fixed conventional weights is invariably effected at the same level. ”

“ But if some of the components of the solid are only possible components (see page 64) of the fluid, is incapable of positive values, as the quantity of the solid cannot be increased, and it is sufficient for equilibrium that To express- condition (383) in a form independent of the state of reference, we may use , etc., to denote the densities of energy, of entropy, and of the several component substances in the variable state of the solid. We shall obtain, on dividing the equation by , It will be remembered that the summation relates to the several components of the solid. ”

“ It will be observed that denotes the excess of the energy of the actual mass which occupies the total volume which we have considered over that energy which it would have, if on each side of the surface the density of energy had the same uniform value quite up to that surface which it has at a sensible distance from it ”

“ The potential for any substance in any homogeneous mass is equal to the work required to bring a unit of the substance by a reversible process from a state in which and the temperature is the same as that of the given mass into combination with this mass, which at the close of the process must have the same volume and temperature as at first, and which is supposed so large as not to be sensibly altered in any part. ”

“ While the factors of kinetic and of gravitational energy, velocity and momentum, on the one hand, and force and distance, on the other, are simply related to each other, the capacity factors of other forms of energy—surface, in the case of surface-energy; volume, in the case of volume-energy; entropy for heat; electric capacity when electric charges are being conveyed by means of ions; atomic weight, when chemical energy is being gained or lost—all these are simply connected with the fundamental chemical capacity, atomic weight or mass. ”

“ Suppose the medium to be pressed by an incumbent weight after the manner of our air; and let A be the height of a homogeneous medium, whose weight is equal to the incumbent weight, and whose density is the same with the density of the compressed medium in which the pulses are propagated. ”

“ It became, then, highly probable, for a number of reasons, that what we called the mass of a body at rest was itself due to the contained energy of the body. In a general way, therefore, a body, when heated or electrified or compressed, would increase in mass. ”

“ Let us now seek the complete value of the variation of the energy of a system of heterogeneous fluid masses, in which the influence of gravity and of the surfaces of discontinuity shall be included, and deduce from it the conditions of internal equilibrium for such a system. ”

“ It is, however, a necessary condition of success in calculating the course of events, that there should be some quantitative identity which remains unaffected in the various processes of physical change, and it is chiefly in the special forms of the quantitative constancy of Mass and Energy that we seem at present able to give definite expression to this a priori postulate of mechanical construction. ”

“ For all substances the specific gravity is used in various tests for the purpose of distinguishing bodies from each other, the same substance being found, under the equal conditions of temperature, &c., to retain its peculiar proportional weight or density. ”

“ It is evident, however, that the relation between the volume, pressure, and temperature affords a less complete knowledge of the properties of the body than the relation between the volume, entropy, and energy. ”

“ The numerical value of a potential depends not only upon the system of units employed, but also upon the arbitrary constants involved in the definition of the energy and entropy of the substance to which the potential relates, or, it may be, of the elementary substances of which that substance is formed. ”

“ Where lies the limit to such a prospect? As the body contracts, its density must increase, until it either becomes a liquid, or a solid, or, at any rate, until it ceases to obey the laws of a purely gaseous body which we have supposed. ”

“ Whereas the physicist of to-day holds that the chemical energy of such an element as carbon, the elasticity of a coiled spring or of a confined body of gas, and the quality we call temperature, all denote real activities, nevertheless? the lifting of a weight, into which any of these activities can bo readily transformed, is not represented by motion at all, but by an ultimate and unnamed something else. ”

“ We thus represent energy to ourselves as taking different forms—mechanical, electrical, calorific, and chemical—capable of changing one into the other, but in such a way that the quantitative value always remains the same. ”