Massiveness

“ Consequently gravitation is proportional to the volume, while the pressure of light is proportional to the surface of the body acted upon. Now the mass, or volume, of any body varies as the cube of its diameter, and the surface only as the square. If, then, we have two bodies, one of which has twice the diameter of the other, the mass of the second will be eight times less than that of the first, but the surface will be only four times less. If the second has only one-third the diameter of the first, then its mass will be twenty-seven times less, but its surface only nine times less. ”

“ 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. ”

“ Let us further assume that, owing to the attraction of some immense stellar body, this huge mass has what we would call a weight corresponding to that which a plate of the same material would have at the surface of the earth, and let it be required to calculate the length of the side of a square plate of the same material and thickness and which shall be exactly equal to the circular plate. ”

“ When an object, in which magnitude is a desirable attribute, leaves an impression, on a practised eye, of less magnitude than it really possesses, we should place objects beside it, of whose magnitude we can satisfy ourselves, of larger size than that which we are accustomed to; for, by finding these large objects in precisely the proportion to the grand object, to which we are accustomed, while we know their actual size to be one to which we are not accustomed, we become aware of the true magnitude of the principal feature. ”

“ It is only when one or both of the masses m', m'' are very great that the force of gravity becomes large, and the weight of bodies at the [Pg 56] surface of the earth is considerable because of the great quantity of matter which goes to make up the earth. Many of the heavenly bodies are much more massive than the earth, as the mathematical astronomers have found by applying the law of gravitation to determine numerically their masses, or, in more popular language, to "weigh" them. ”

“ The size alone would have been enough to mark it as having come from outside this solar system. Yet without bulkheads, without bracing, the mass of it loomed as one incredibly vast and far-spreading room—an engineering feat to stagger man's imagination. ”

“ The general rule by which we are to determine the size is, to select the largest mass which will not overwhelm any object of fine form, within two hundred yards of it; and, if it does not do this, we may be quite sure it is not too large for the distant features: for it is one of Nature's most beautiful adaptations, that she is never out of proportion with herself; that is, the minor details of scenery of the first class bear exactly the proportion to the same species of detail in scenery of the second class, that the large features of the first bear to the large features of the second. ”

“ Nor is it indeed only the mass of the globe which is concerned in the matter. It will easily be seen that the diameter of the body must enter as a significant element. Suppose that there were two globes equal in mass, but that in one the materials were of a lighter specific gravity than in the other, and that consequently the globes were of unequal dimensions. ”

“ It is of enormous dimensions and almost unbelievable mass and consists of one billion spheres of unimagined beauty and superb grandeur, but the true magnitude of this vast creation is really beyond the understanding grasp of the human mind. ”

“ 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 her mass were larger or less than it is, the weight of all living and lifeless things on her surface would no longer be the same; but absolute weight is one of the primary elements of organic construction. ”

“ If we desire to conceive gravitation as a force of measurable intensity, we must employ masses immensely more ponderous than those 50lb. weights. Imagine a pair of globes, each composed of 417,000 tons of cast iron, and each, if solid, being about 53 yards in diameter. ”

“ Thanks to the investigations of modern philosophers, we are enabled to magnify objects to 2,000 times their diameter with perfect distinctness; that is to say, the surface of the object appears to occupy 4,000,000 times its natural extent. Under such a power a hair would appear about six inches thick, a fine needle would look like a street post, and a grain of sand like a mass of rock. ”

“ From what has already been demonstrated, you can plainly see the impossibility of increasing the size of structures to vast dimensions either in art or in nature; likewise the impossibility of building ships, palaces, or temples of enormous size in such a way that their oars, yards, beams, iron-bolts, and, in short, all their other parts will hold together; nor can nature produce trees of extraordinary size because the branches would break down under their own weight ”

“ When the sun reached out to earth it must have had a diameter of nearly 200 million miles, but having now contracted to a diameter of less than one million of miles, should it not have a density ten times greater than earth’s, instead of one so much less? ”

“ Now give the giant of the twentieth globe above us the 607 decimal places, and, when he has measured the diameter of his globe with accuracy worthy of his size, let him calculate the circumference of his equator from the 607 places. Bring the little philosopher from the twentieth globe below us with his very best microscope, and set him to see the small error which the giant must make. He will not succeed, unless his microscopes be much better for his size than ours are for ours. ”

“ In architecture, the greatness of the mass sometimes imposes, even where the structure is barbarous; but, in sculpture, the mass becomes an intolerable enormity, where it is not highly executed and imagined ”

“ In astronomical calculations we have first to learn the mass of our earth. Experiment informs us that the density of our hardest rock is not above 2·8; but from the enormous pressure to which matter must be subjected, at great depths from the surface, the weight of the superincumbent mass constantly increasing, it is quite certain that the earth’s density must be far more than this. Maskelyne determined the attraction of large masses by a plummet and line on the mountain Schehallion. ”

“ 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. ”

“ Hence the law of gravitation may be thus expressed: “The mutual attraction of two bodies increases in the same proportion as their masses are increased, and as the square of their distance is decreased; and it decreases in proportion as their masses are decreased, and as the square of their distance is increased.” ”

“ 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. ”

“ The physical equilibrium which exists in the balanced “seesaw” of our childhood and the optical balance which is the result of the proper adjustment of masses within the confining edges of a design are similar, in that each is an equalizing of forces of attraction. In the former the force is gravity; in the latter, the attraction to the eye, which varies with the size and tone of the mass. ”

“ Of the great moving masses which compose our own system, from the sun—1,000,000 times larger than the earth—to the little asteroids—250 miles in diameter—and from these down to the meteorites of a few pounds in weight, which strike the earth, we have become quite familiar, while spectrum analysis has carried us a long way toward the conclusion that there is a unity in the material composition of the universe. ”

“ Slower—slower—and in moments more the vast mass of its towering cylindrical buildings, ablaze with outlining lights, was coming into view, with midmost among them the greatest of all, the huge mass of the World Government building. ”

“ 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. ”

“ 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. ”

“ All the particles, big and little, are - 8 - known to be revolving about the central mass, much as the earth revolves about the sun. The little white lumps, or knots, in the filmy skein are supposed to be worlds in the making. Being larger than the other particles, they draw the smaller to them, according to the same law of gravitation which makes every unsupported thing on earth fall to the ground, because the earth is so much bigger than anything there is on it. ”

“ But the proportion of the resistance to the weight is augmented, when either the specific gravity is made less, the magnitude remaining equal, or when the density of the medium is made greater, or when, by diminishing the magnitude, the resistance becomes diminished in a less ratio than the weight. ”

“ If the butcher, with his spring-balance and a ham, could fly to all the planets, one after the other, weigh the ham on each, and come back to report the results to an astronomer, the latter could immediately compute the weight of each planet of known diameter, as compared with that of the earth. In applying this principle to the heavenly bodies, we at once meet a difficulty that looks insurmountable. You cannot get up to the heavenly bodies to do your weighing; how then will you measure their pull? I must begin the answer to this question by explaining a nice point in exact science. ”

“ 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." ”

“ Decompose all heavy bodies into equal masses so small as to allow them to be treated without sensible error as attractive particles are treated in those theories of gravitation in which no hypothesis is made as to its cause. In such a small mass the effects of unequal distance and position of its particles relative to those of the mass which is conceived to attract it, and to be attracted by it, may be neglected. Such masses will have a diameter no more than one one-hundred-thousandth as great as the mutual distance of the two masses under examination. ”

“ The central mass—the sun—should rotate on his axis in less time than any of the planets revolve about him in their orbits. 9. The primary planets should revolve on their axes in less time than any of their satellites revolve around them; and 10. The central mass, left after the process of genesis was completed, should contain a much larger quantity of matter than the sum of the masses separated. ”

“ Yet in fact, how is a hundred millions of miles a great distance? how is a hundred millions of times a great ratio? Not in itself: this greatness is no quality of the numbers which can be proved like their mathematical properties; on the contrary, all that absolutely belongs to number, space, and ratio, must, we know demonstrably, be equally true of the largest and the smallest. ”

“ 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. ”

“ 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. ”