Massa

“ The shadows of the early winter morning were grey and sombre; a pale sunshine coming through them faintly touched a gigantic caryatide in Carrara marble at his side. In that splendid age when the prince and the noble, sheathing their swords in moments of repose, turned to the arts alike for pleasure and for glory, the lords of Massa had summoned painters of Florence to decorate and ennoble this place that was now forgotten and going to decay on the solitary mountain side, as so many other palaces and castles fade and fall, all over Italy, burying their stories with them. ”

“ ALEXANDRE-PHILIPPE-REGNIER DE MASSA MARQUIS DE MASSA, soldier, composer, and French dramatist, was born in Paris, December 5, 1831. He selected the military career and received a commission in the cavalry after leaving the school of St. Cyr. He served in the Imperial Guards, took part in the Italian and Franco-German Wars and was promoted Chief of Squadron, Fifth Regiment, Chasseurs a Cheval, September 10, 1871. Having tendered his resignation from active service, he was appointed a lieutenant-colonel in the territorial army February 3, 1880. He has been decorated with the Legion of Honor. ”

“ It is characteristic of these phases that we cannot alter the values of in any real mass in such a phase, while the volume of the mass as well as its matter remain unchanged, without diminishing the energy or increasing the entropy of some other system. Hence, if the mass is large, its equilibrium can be but slightly disturbed by the action of any small body, or by a single electric spark, or by any cause which is not in some way proportioned to the effect to be produced. ”

“ When the masses are unequal the point is at unequal distances from the centers of the masses. These unequal distances have the same ratio as the masses themselves, but the larger mass is always the shorter distance from the point. If 1 pound is to balance 4 [Pg 26] pounds it is obvious that the 1-pound mass must be 4 times as far from the point of balance as the 4-pound mass.
Fig. 13. Mass of 4 units balanced by 1 unit.
Hence, to balance two masses in a rectangle, the point of balance will be found by proportion, placing it [Pg 27] on a line which divides the rectangle into parts of 2 to 3. ”

“ For determining the state of a given mass when in equilibrium and having a given volume and given energy or entropy, the condition of equilibrium affords an additional equation corresponding to each of the independent relations between the n component substances. But the equations which express our knowledge of the matter in the given mass will be correspondingly diminished, being in number, like the equations of condition relating to the quantities of the component substances, which may be derived from the former by differentiation. ”

“ Or, when one of three contiguous masses can be formed out of the other two, it is necessary for equilibrium that the value of for any quantity of the first mass should be equal to the sum of the values of for such quantities of the second and third masses as together contain the same matter. ”

“ If this is true, if energy and mass are synonymous, if mass is merely energy, it follows that free energy must possess the property of mass. As a matter of fact, light, for instance, has mass. Careful experiments have shown that when a ray of light strikes a material object, it exerts upon it a pressure which has been measured. Light has mass; therefore it has weight, like all masses. When we come to consider the new form given by Einstein to the problem of gravitation, we shall see a further and beautiful proof that light has weight. ”

“ We know that if the bodies in the scale-pans were formed, one of brass and the other of iron, and there were a magnet concealed under the table on which the operator placed his balance, the masses would not be equal when there was equilibrium. But that the law is true, and that, accordingly, weight is a true measure of mass, follows with the highest probability from the third of Kepler's laws, and was proved experimentally by Newton, by experiments with pendulums. ”

“ 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. ”

“ If we also know the total energy of the given mass, or its total entropy, we will have as many equations as there are independent variables.
But if any of the substances are only possible components of some parts of the given mass, the variation of the quantity of such a substance in such a part cannot have a negative value, so that the general condition of equilibrium (15) does not require that the potential for that substance in that part should be equal to the potential for the same substance in the parts of which it is an actual component, but only that it shall not be less. ”

“ The extreme delicacy and exactness of the measurement work done upon the standards was illustrated by saying that when two of the standard kilogrammes were balanced against two similar masses, if one of the masses on one side of the balance was placed on top of the other mass, the balance would be destroyed. In other words, raising the mass of one kilogramme through less than two inches made a difference in the attraction of the earth readily observed. ”

“ If, then, the value of the expression (133) for the mass considered is less when it is in the given condition than when it is in any other, the energy of the mass in its given condition must be less than in any other condition in which it has the same entropy and volume. The given condition is therefore stable. (See page 57.)
Again, if it is possible to assign such values to the constants in (133) that the value of the expression shall be zero for the given fluid mass, and shall not be negative for any phase of the same components, the given condition will be evidently not unstable. ”

“ A part of the total energy which belongs to the matter in the vicinity of the separating surface, relates to pairs of particles which are on different sides of the surface, and such energy is not in the nature of things referable to either mass by itself. Yet, to avoid the necessity of taking separate account of such energy, it will often be convenient to include it in the energies which we refer to the separate masses. When there is no break in the homogeneity at the surface, it is natural to treat the energy as distributed with a uniform density. ”

“ It is not correct to define mass by the introduction of the idea of weight, because the mass of a body is something independent of the existence of the earth, whereas weight is produced by the attraction of the earth. It is true that weight is a convenient means of measuring mass, but this is only a consequence of the property of gravity which the experiment proves, namely, that the attraction of gravity for a body is proportional to its mass. ”

“ But Einstein has revolutionized the conception of mass, as well as all the other elementary conceptions of physics. Mass is now absorbed into energy, and the mass of a body is not by any means always constant. [10] A system of electrons and hydrogen nuclei may have different amounts of energy in different [Pg 130] arrangements; when the system passes from an arrangement with more energy to one with less, the energy it loses is radiated into the surrounding medium, in the sort of way with which we became familiar when we were considering the spectrum of hydrogen. ”

“ 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. ”

“ Bodies attract each other in direct proportion to their masses and in inverse proportion to the square of their distances. What does that mean? We saw that the mass of a body varies with its velocity. When, for instance, we introduce the mass of our planet into calculations which involve Newton’s law, what precisely do we mean? Do we mean the mass which the earth would have if it did not revolve round the sun? Or do we mean the larger mass which it has in virtue of its motion? This motion, however, is not always of the same speed, because the earth travels in an ellipse, not a circle. ”

“ 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 ”

“ A small mass, or a simple line or accent, may be made to balance a very much greater mass. The greater part of a canvas may be one mass, and be balanced by quite a small spot. But leverage must come in to help. Somewhere in the picture will be the point of support, the fulcrum. And the large mass and the small one will have an obvious relation with reference to that point. Or the element of apparent density will come in. The large mass will be the least dense, the small [Pg 181] one the most dense, and the equilibrium is established. ”

“ So it was natural to assume that the mass of the body at rest was due to its contained or bound energy, which would be released were the body to disintegrate into nothingness. The formula connecting this energy of constitution of the body with its mass was obtained from the mathematical expression of the mass, and it was found that in C.G.S. units the contained energy was equal to the mass multiplied by the square of the velocity of light. ”

“ The weight of a body is proportional to its mass, that is if the weights of a number of substances are equal the masses will be equal, whatever the substances may be. This result was verified to a considerable degree of approximation by Newton by means of experiments with pendulums; later, in 1830 Bessel by a very extensive and accurate series of experiments, also made on pendulums, showed that the ratio of mass to weight was certainly to one part in 60,000 the same for all the substances examined by him, these included brass, silver, iron, lead, copper, ivory, water. ”

“ 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. ”

“ 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 ”

“ That mass has more than once passed in a few years from one extreme to the other, and back again. Sometimes it has changed sides, merely because it was tired of supporting the same men, sometimes because it was dismayed by its own excesses, sometimes because it had expected impossibilities, and had been disappointed. But whenever it has leaned with its whole weight in either direction, that weight has, for the time, been irresistible. ”

“ When the body consists of a compound of two different homogeneous states, the point which represents the compound state will be at the center of gravity of masses proportioned to the masses of the parts of the body in the two different states and placed at the points of the primitive surface which represent these two states (i.e., which represent the volume, entropy, and energy of the body, if its whole mass were supposed succesively in the two homogeneous states which occur in its parts.) ”

“ 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. ”

“ If m is 10 and E is 10, then a mass of 2m gives an energy of 102, a mass of 3m yields an energy of 103', a mass of 4m gives an energy of 104, or 10,000, a mass of 5m gives an energy of 105 or 100,000. While the mass increases in an arithmetical progression of 10, the mass energy grows in a geometrical progression of 10. Briefly stated, the mass grows as the logarithm of mass-energy.
A knowledge of the subconscious and of the laws of suggestibility are of vital consequence in Social Psychology in general and in Social Pathology in particular. ”

“ And similarly with mechanical forces, the unhesitating assumption is that if one unit of force acting in a given direction produces a certain result, two units will produce twice the result. Every process of measurement in a physical experiment takes this for granted; as we see in one of the simplest of them—the process of weighing. If a measured quantity of metal, gravitating towards the Earth, counterbalances a quantity of some other substance, the truth postulated in every act {301} of weighing is, that any multiple of such weight will counterbalance an equi-multiple of such substance. ”