Mass

“ 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. ”

“ First, the measure of gravity at its surface; this attractive force we know, by the increase of our own muscular force, must of course be considerably less than that at the surface of the earth. Secondly, its mass, that is, the quantity of its matter. ”

“ 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. ”

“ Mass meant monotony. But the differentiating energy and impetus encroached further and further, passing from the great to the small, pushing into the mass whose members no longer wanted to be mass, herd, but men. ”

“ It may fairly be doubted whether anything is gained by this particular definition of mass, but the really important step was the distinct recognition of mass as a property of bodies, of fundamental importance in dynamical questions, and capable of measurement. ”

“ 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. ”

“ Is there any such a thing as an absolute solid, or a body that has no degree of fluidity, the particles or parts of which will admit of no change of their relative positions, no movement upon each other without fracture of the mass? ”

“ If we take, for example, the laws of motion and the law of universal gravitation, we can express in a few lines, that which, when developed, represents and explains an innumerable mass of natural phenomena. ”

“ Will a given body have the same measure of mass when that mass is estimated in units of and in units of ? And will the mass of a body depend on the direction of its motion by means of which that mass is measured? ”

“ The attraction of gravitation, which is a property belonging to all known bodies, is measured by the mass, or amount of matter, in a body. It also varies with the distance between the attracting and attracted bodies. We know, by means which I shall not attempt to describe here, the mass both of the earth and of the moon. ”

“ Thus you understand that all matter is attractive, from the smallest particle to the largest mass; and that bodies attract each other with a force proportional to the quantity of matter they contain.
Emily. I do not perceive any difference between the attraction of cohesion and that of gravitation; is it not because every particle of matter is endowed with an attractive power, that large bodies consisting of a great number of particles, are so strongly attractive? ”

“ We have thus two kinds of mass, neither of which quite fulfils the old ideal. The mass as measured by an observer who is in motion relative to the body in question is a relative quantity, and has no physical significance as a property of the body. The “proper mass” is a genuine property of the body, not dependent upon the observer; but it, also, is not strictly constant. As we shall see shortly, the notion of mass becomes absorbed into the notion of energy; it represents, so to speak, the energy which the body expends internally, as opposed to that which it displays to the outer world. ”

“ Experience teaches that all the changes to which matter is subject are but variations of form, and that amid these variations there is an unvarying constant—the mass or quantity of matter. The constancy of the mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation nor corruption, can add to, or detract from, the weight of a body subjected to experiment. ”

“ For the purpose of general illustration the reader is asked to conceive a mass of heterogeneous matter, concentrated round a given point in space, forming a single body. This mass is assumed to be assembled and to obtain its coherent form in virtue of that universal and inherent property of matter, namely, gravitative or central attraction. ”

“ What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It is, replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?
These difficulties are inextricable.
When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. ”

“ In descriptive astronomy the mass of the sun or that of the earth is sometimes taken as a unit, but in the dynamical theory of astronomy the unit of mass is deduced from the units of time and length, combined with the fact of universal gravitation. ”

“ Now, as the manner in which we consider the given mass as composed of various substances is in some degree arbitrary, so that the energy may be considered as a function of various different sets of variables expressing quantities of component substances, it might seem that the above definition does not fix the value of the potential of any substance in the given mass, until we have fixed the manner in which the mass is to be considered as composed. ”

“ Now, the mass, or the quantity of matter in a body, is a numerical quantity; for it consists of a number of primitive units, independent of one another for their essence and for their existence, and therefore absolute in regard to their substantial being. Consequently, every mass of matter has an absolute value corresponding to the number of absolute [pg 788] units it contains; and thus every mass of matter is “an absolute constant of mass.” ”

“ 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. ”

“ There, though the weight of a given mass of matter is different from what it is with us, it is nevertheless determined by the law that determines here—the law of gravitation. There energy is indestructible, and is measured as it is measured among us, by work. Then is there any boundary that we can assign to natural law—is it not omnipresent, universal? ”

“ Familiar cases can readily be found of the perception of the mass of bodies, independently of their tendency to fall towards the earth. The mass of any portion of matter is found to be permanent under chemical and other changes, and this fact adds to its importance as a physical quantity. The study of the structure of atoms has suggested a connexion of mass with electrical phenomena which implies its dependence on motion ”

“ Such a mass, if exposed to constant temperature and pressure, would be in neutral equilibrium. A point in the developable surfaces represents a mass of which the matter is divided between two coexisting phases, which are represented by the extremities of the line in the figure passing through that point. A point in the primitive surface represents of course a homogeneous mass. ”

“ Mass would mean inter attraction holding together final particles, if there were final particles. Then, until final particles be discovered, only one term of this expression survives, or mass is attraction. ”

“ In the preceding chapter we gained a new insight into the relationship between mass and force. We have come to see that our concept of force is grounded on empirical observation in no less a degree than is usually assumed for our concept of number, or size, or position, provided we do not confine ourselves to non-stereoscopic, colourless vision for the forming of our scientific world-picture, but allow other senses to contribute to it. ”

“ To these ideas Newton added the very important and difficult conception of mass.
If we are comparing two different bodies of the same material but of different sizes, we are accustomed to think of the larger one as heavier than the other. In the same way we readily think of a ball of lead as being heavier than a ball of wood of the same size. ”

“ I have endeavored, thus far, to show that there are no absolute constants of mass; that both the hypothesis of corpuscular "atoms" and that of "centres of force" are growths of a confusion of the intellect which mistakes conceptual elements of matter for real elements ”

“ With this knowledge of the nature of the mass of the globe, the modes of combination of the several ingredients of the mass, and the properties under certain physical conditions of these ingredients existing separately, one of two conclusions must be adopted by the human mind. ”

“ Already this simple observation - as such made by means of the sense of movement and therefore outside the frontiers of the onlooker-consciousness - tells us that mass is nothing but a particular manifestation of force. ”

“ The law of masses may be extended to as great masses as those for which observation proves it (for example the mass of Jupiter) , by making the diameters of the bars of the supposed cage atoms constituting heavy bodies, small enough. ”

“ If we wish to speak of the continuous matter present at any particular point of space and time, we must use the term density. Density multiplied by volume in space gives us mass or, what appears to be the same thing, energy. ”

“ Conceive the synthesis of both, and you have matter as a fluxional antecedent, which, in the very act of formation, passes into body by its gravity, and yet in all bodies it still remains as their mass, which, being exclusively calculable under the law of gravitation, gives rise, as we before observed, to the science of statics, most improperly called celestial mechanics. ”

“ Thus originated the idea of matter, in which was grouped all that was sensibly connected with mass, and continued with it, such as weight, volume, chemical properties, etc., and the physical law of the conservation of mass passed into the metaphysical axiom of the conservation of matter. ”

“ A force which belongs to individual atoms, is independent of chemical and physical conditions, and cannot be altered or destroyed by any known means, must be closely related to the fundamental nature of the atoms. One of the most essential parts in our concept of matter is mass, and the force of gravitation of an atom is proportional to its mass. Mass and gravitation stand, therefore, either as co-effects of the same cause or as cause and effect. ”

“ The student should observe that the two terms mass and weight are not synonymous; mass is defined above as the quantity of matter contained in a body, while weight is the force with which the earth attracts that body, and in accordance with the law of gravitation its weight depends upon its distance from the center of the earth, while its mass is quite independent of its position with respect to the earth. ”

“ It has been found that every body attracts very other body with a force directly proportionate to its mass. Thus we see that, if every particle in a mass exerts its attractive influence, the more particles a body contains the greater will be the attraction. ”

“ Mass, which used to be regarded as the most indubitable of physical quantities, is now generally believed to vary according to velocity, and to be, in fact, a vector quantity which at a given moment is different in different directions. The detailed conclusions deduced from the supposed constancy of mass for such motions as used to be studied in physics will remain very nearly exact, and therefore over the field of the older investigations very little modification of the older results is required. ”

“ But the palpable fact, on the contrary, is that the greater the quantity, the lighter the mass is and the quicker its upward movement: and, similarly, in the reverse movement from above downward, the small mass will move quicker and the large slower. ”

“ Further investigation brought him to the unfolding of this general law of gravitation: "Every body in nature attracts every other body with a force directly as its mass, and inversely as the square of its distance." ”

“ So that if matter were separated from the energetic phenomena by means of which it is revealed to us—weight or energy of position, impenetrability or energy of volume, chemical properties or chemical energies, mass or capacity for kinetic energy—the very idea of matter would vanish. ”

“ In the case of a velocity 99 per cent, of that of light, the mass is increased about seven-fold, and the kinetic energy in the same proportion. The energy of the -particles, owing to their greater mass, is even more than that of the -particles. ”

“ "Give us matter, and a little motion, and we will construct the universe. It is not enough that we should have matter, we must also have a single impulse, one shove to launch the mass, [206] and generate the harmony of the centrifugal and centripetal [515] forces. ”

“ A second illustration may be given by the concepts of mass and weight. As a result of Newton’s discoveries, the weight of a body was realised to be relative, since its value varied with the proximity and distribution of matter. ”

“ The essential property of matter is its mass and its inertia. Mass remains constant everywhere and always, it even remains when a chemical transformation changes all observable properties of matter, and has apparently created an entirely new body. ”