Center of mass

“ Thus is suggested finally the law of gravitation in its most general form: every particle of matter attracts every other particle with a force proportional to the mass of each, and inversely proportional to the square of the distance between them. ”

“ 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. ”

“ If I put them into a bottle I collect them together as one mass, and philosophers have discovered that there is a certain point in the middle of the whole collection of shots that may be considered as the one point in which all their gravitating power is centred, and that point they call the centre of gravity; it is not at all a bad name, and rather a short one—the centre of gravity. ”

“ If the attraction of the earth upon two bodies of equal mass but of different substance were different, the resultant of the attractive and centrifugal forces would point in a different direction for each body. ”

“ 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. ”

“ As a fact of observation, gravitation is always found to be a property of gross tangible matter, with its tensions mathematically directed to the mass-centers, and in quantity always directly proportioned to the number of material molecules, agreeably to the first and second propositions. ”

“ We find universally distributed in nature the sensation of the mechanical stimulus of gravitation, the most comprehensive statement of which is given in Newton's law of gravity. According to this fundamental and all-ruling law, any two particles of matter are attracted in direct proportion to their mass and inverse proportion to the square of their distance. ”

“ It has been shown by Newton, that if any mass of matter be distributed in a uniform sphere, or in uniform concentric spherical shells, the total attraction on a point without the sphere, will be the same as if the whole mass were collected in that single point, the centre. ”

“ The philosophy of the fact is simply this--while a body revolves on its axis, the component particles of its mass move in circles, the centres of which are placed in the axis; a centrifugal force therefore is generated, which is resisted by the cohesion of the parts of the mass, and this tendency of each particle to fly off is expended in exciting a pressure upon the axis ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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." ”

“ On the other hand, when a body is situated in the gravitational field of the earth, the gravitational force which acts upon it and which is commonly known as the weight of the body not only depends on the mass of the earth but likewise varies with the mass of the body. ”

“ This force is called the attraction of gravitation. A large body possesses more attractive force than a small one, in proportion to the mass, or quantity of matter, that it contains. The 71earth, being extremely large, holds all bodies on its surface with a force proportionate to its great mass. This explains why we possess what we call weight, which is simply the effect of the attraction of the earth upon our bodies. A large body is heavier, or drawn with more force by the earth, than a small one (composed of the same kind of matter) , because it has a greater 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? ”

“ 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. ”

“ Multiplying the number of units of density of a portion of matter, by the number of units of space occupied by it, we arrive at the quantity of matter, or, as it is usually called, the unit of mass, as indicated by the inertia and gravity it possesses. To proceed in the most simple manner, the unit of mass ought to be that of a cubic unit of matter of the standard density ”

“ 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. ”

“ Considered in the most general way, we may define matter as a complex of gravitational, kinetic and chemical energies, which are found to cling together in the same space. Of these energies the capacity factors, namely, weight, mass and elements, are conservative as described, while the intensity factors, potential, velocity and affinity, may change in wide limits. To explain why we find these energies constantly combined one with another, we only have to think of a mass without gravity or a ponderable body without mass. ”

“ 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. ”

“ While the force of gravity usually brings balancing masses to a horizontal alignment, optical balance may bring the masses in a design into equilibrium on any desired line, horizontal, vertical, or diagonal.
The attraction which a mass possesses varies directly with its size and tone. Thus a mass of four square inches, solid black, will be twice as strong in attraction value as a mass of two square inches, solid black. ”

“ Slowly setting around common centres, however, in anticipation of Sir Isaac Newton's gravitative theories, the fluid haze gradually collected into suns and stars, whose light and heat is presumably due to the clashing together of their component atoms as they fall perpetually towards the central mass. ”

“ It will be obvious that in the case of a nebulous mass, whose matter is unequally distributed, that in such a case several sub-centres of gravity would be elected, that is to say, each patch of nebulous matter would have its own centre of gravity ”

“ In this way both the unit of force and the unit of mass are made to depend on the value of the force of gravity, which varies from place to place, so that statements involving these quantities are not complete without a knowledge of the force of gravity in the places where these statements were found to be true. ”

“ 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. ”

“ 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. ”

“ On the contrary, we believe that the facts admit of an interpretation quite consistent with the hypothesis of Laplace.
There are three possible causes of unlike specific gravities in the members of our Solar System:—1. Differences between the kinds of matter or matters composing them. 2. Differences between the quantities of matter; for, other things equal, the mutual gravitation of atoms will make a large mass denser than a small one. 3. Differences between the structures: the masses being either solid or liquid throughout, or having central cavities filled with elastic aeriform substance. ”

“ By the earth’s attraction, all the particles which compose the mass of a body are solicited by equal forces in parallel directions downwards. If these component particles were placed in mere juxtaposition, without any mechanical connection, the force impressed on any one of them could in nowise affect the others, and the mass would, in such a case, be contemplated as an aggregation of small particles of matter, each urged by an independent force. ”

“ It does not appear, at first sight, that the law by which the force is related to the distance, will be the same for the particles as it is for the masses; and, in reality, it 413 is not so, except in special cases. And, again, in the instance of any effect produced by the force of a body, how are we to know whether the force resides in the whole mass as a unit, or in the separate particles? We may reason, as Newton does,45 that the rule which proves gravity to belong universally to the planets, proves it also to belong to their parts ”

“ "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. ”

“ Seen dynamically, and from the aspect of the universe as an interrelated whole, all aggregations of mass are the manifestation of certain dynamic conditions within the universe, and what appears to us as a change of the state of motion of such a mass is nothing but a change in the dynamic relationship between this particular aggregation and the rest of the world. ”

“ 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. ”

“ Gaining a rapidly-increasing preponderance as the gravitative force does during the closing stages of concentration, the centrifugal force cannot, in ordinary cases, cause the leaving behind of rings when the mass has become dense. ”