Precipice

“ He wanted no explanation, for they were standing at the edge of a precipice, gazing down at another huge glacier, which glittered in the rays of the morning sun—a vast chaos of ice whose cracks and shadows were of a vivid blue; and as they gazed up towards the point where it suddenly curved round an immense buttress, there beyond, peak after peak, as far as eye could reach, stood out in the clear air, and all seeming to rise out of the fields and beds of snow which clung around them and filled every ravine and chasm running up from their feet. ”

“ Now, observe, if the precipices which we have just been describing had been broken when their substance was in a hard state, there appears no reason why any connexion should be apparent between the energy of undulation and these broken rocks. ”

“ I have climbed mountain after mountain, and still I behold peaks soaring far above, crowned with the snow that never melts. I stand upon beetling cliffs, and look into chasms that yawn beneath, sleeping in the silence of desolation. Great fragments have fallen into them, and lie piled one upon another. Others hang threatening over, as if waiting for some concussion of the atmosphere to hurl them from their balance. Dark precipices frown me into fear, and my head reels with a dizzy faintness. I hold by the pine-tree shaft, or the angle of the firmer rock. ”

“ The weight upon my spirit was sensibly lightened as I plunged yet deeper in the ravine of Arve. The immense mountains and precipices that overhung me on every side, the sound of the river raging among the rocks, and the dashing of the waterfalls around spoke of a power mighty as Omnipotence—and I ceased to fear or to bend before any being less almighty than that which had created and ruled the elements, here displayed in their most terrific guise. ”

“ The highest and youngest of all the lakes lie nestled in glacier wombs. At first sight, they seem pictures of pure bloodless desolation, miniature arctic seas, bound in perpetual ice and snow, and overshadowed by harsh, gloomy, crumbling precipices. ”

“ Why the concurrence of every favorable condition is requisite for success in such inquiries may be readily comprehended. The object in view is to discern, singly, sparkling points, small as the point of a needle, and close as the particles of a handful of sand; so that it needs but the smallest unsteadiness in the air, or imperfection in the shape of the reflecting surface, to scatter the light of each point, to merge them into each other, and present them as one mass. ”

“ In a wood-apple there are seeds, pulp and the shell. When I take the pulp, I leave out the seeds and the shell; but when I speak of the weight of the wood-apple, the weight of the pulp alone would not be equal to it. You will have to weigh the pulp, seeds, shell and everything. That which has pulp has also seeds and shell. Similarly, that which is the Absolute has also all phenomena. Therefore I take both the Absolute Reality and the phenomenal reality. I do not blow away the phenomenal world by calling it a dream, because then the weight will be less. ”

“ A scale might be formed, graduated according to the degrees of a combined ratio of intensity, duration, connexion, periods of recurrence, and utility, which would be the standard, according to which all ideas might be measured, and an uninterrupted chain of nicely shadowed distinctions would be observed, from the faintest impression on the senses, to the most distinct combination of those impressions; from the simplest of those combinations, to that mass of knowledge which, including our own nature, constitutes what we call the universe. ”

“ A natural extension of either of the methods already described will give us a series of surfaces in which every one is the surface, or every one the surface for a body of constant composition, the proportion of the components varying as we pass from one surface to another. But for a simultaneous view of the properties which are exhibited by compounds of two or three components without change of temperature or pressure, we may more advantageously make one or both of the quantities or constant in each surface. ”

“ Degrees are of two kinds, discrete and continuous. Discrete degrees are related to each other as end, cause, and effect. Continuous degrees consist in the gradual increase of some quality of the same discrete degree of substance. The increase of light from the faintest indications to the most intense brightness; the change from cold to intense heat; all the variations of matter from soft to hard, fine to gross, dense to rare, weakness to strength, are examples of continuous degrees. ”

“ Reflexion.—When rays of light fall upon a plane surface, as the flat surface of the mirror, a greater or less number of them are reflected, and this according to a definite law, by which the angle of incidence, or that formed by the incident ray with the perpendicular, is equal to the angle of reflexion, or that formed by the reflected ray with the same. ”

“ By Density and Rarity, I understand a property of a transparent body, that does either more or less refract a Ray of light (coming obliquely upon its superficies out of a third medium) toward its perpendicular: As I call Glass a more dense body then Water, and Water a more rare body then Glass, because of the refractions (more or less deflecting towards the perpendicular) that are made in them, of a Ray of light out of the Air that has the same inclination upon either of their superficies. ”

“ There is great Difference between changing the Substance, and only covering the Surface of a Body. These Petrifactions, as they are called, being no other than Precipitations of Matter too heavy to be longer sustained in the Water; and which, being very fine, adapts itself to every Prominence and Cavity of the Body it settles upon, and exactly assumes its Shape. ”

“ And now we will look again at a verse in the Book of Job, which tells us something very wonderful about the inside of this great globe of ours, upon the fair outside of which we live and move. You would never have thought it possible that such a great ball could be weighed. But by weighing and measuring—not with scales and weights, you may be sure, but by clever ways which are known to learned philosophers—it has been found out that our earth is very, very heavy. ”

“ 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. ”

“ I saw, methought, a pair of golden scales hanging by a chain in the same metal over the table that stood before me; when, on a sudden, there were great heaps of weights thrown down on each side of them. I found upon examining these weights, they showed the value of everything that is in esteem among men. I made an essay of them, by putting the weight of wisdom in one scale, and that of riches in another, upon which the latter, to show its comparative lightness, immediately "flew up and kicked the beam." ”

“ As we do to-day, so the alchemists did before us; they used the words fire and water to express different ideas.
Such terms as hardness, softness, coldness, toughness, and the like, are employed for the purpose of bringing together into one point of view different things which are alike in, at least, one respect. Hard things may differ in size, weight, shape, colour, texture, &c. A soft thing may weigh the same as a hard thing; both may have the same colour or the same size, or be at the same temperature, and so on. ”

“ 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. ”

“ 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. ”

“ I say that the attractive force of the whole solid, in the recess from its plane superficies, will decrease in the ratio of a power whose side is the distance of the corpuscle from the plane, and its index less by 3 than the index of the power of the distances. ”

“ The expression for the superficial tension is most readily found with the aid of the idea of superficial energy, introduced into the subject by Gauss. Since the tension is constant, the work that must be done to extend the surface by one unit of area measures the tension, and the work required for the generation of any surface is the product of the tension and the area. ”

“ What is a solid? It is the union of three dimensions. If sight can give us the idea of surfaces which consist of two, why not also of solids which consist of three dimensions? This one reflection is enough to show that it has been denied without reason; but I shall not stop with this, but shall prove, by the most rigorous observation, and the analysis of its phenomena, that sight can give us the idea of a solid. ”

“ Bodies, therefore, consisting but of one kind of substance, as wood, stone, or lead, and whose densities are consequently uniform, must stand more firmly, and be more difficult to overset, than bodies composed of a variety of substances, of different densities, which may throw the centre of gravity on one side. ”

“ A three-dimensional locus of event-particles which is the common portion of the boundary of two adjoined events will be called a ‘solid.’ A solid may or may not lie completely in one moment. A solid which does not lie in one moment will be called ‘vagrant.’ A solid which does lie in one moment will be called a volume. A volume may be defined as the locus of the event-particles in which a moment intersects an event, provided that the two do intersect. The intersection of a moment and an event will evidently consist of those event-particles which are covered by the moment and lie in the event. ”

“ As we next proceed to the study of inorganic nature, measure retires, as it were, into the background; at least we often find the quantitative and qualitative characteristics showing indifference to each other. Thus the quality of a rock or a river is not tied to a definite magnitude. ”

“ The degree in which these qualities of the earths prevail must determine the proportions of the mixture; which it is impossible here to point out for every particular case, but which may be learnt by a little practice. Some easy methods will be described, by which any one may make a trial of the qualities of his earth. ”

“ Continuous degrees are related like the degrees of the waning of a light from its bright blaze to darkness, or like the degrees of the decrease of vision from objects in the light to those in the shade, or like degrees of purity in the atmosphere from bottom to top. ”

“ Thus, if one should say that there is such an accumulation of matter in a given quantity of gold, that it would require twenty-one times the quantity in dimension of spirits of wine, to make up the same quantity of matter, it would not be far from the truth. ”

“ The exact distance of two signal poles, the position of a star at a certain hour, the expansion of a metal for a certain increase of temperature, all the numerous coefficients and other constants of physics and chemistry are given us as average values which only approximate to a high degree of constancy. ”

“ In general, therefore, if by the positive side of a surface for which is constant we understand the side on which has the greater value, we may say that denotes the component parallel to of the force exerted by the matter on the positive side of a surface for which is constant upon the matter on the negative side of that surface per unit of the surface measured in the state of reference. ”

“ The fundamental equation of a surface which gives the value of the tension in terms of the temperature and potentials seems best adapted to the purposes of theoretical discussion, especially when the number of components is large or undetermined. ”

“ Extended quantities, such as lines, surfaces and solids, besides what they have in common with all other quantities, have this peculiar, that their parts have a particular place and disposition among themselves: a line may not only bear any assignable proportion to another, in length or magnitude, but lines of the same length may vary in the disposition of their parts; one may be straight, another may be part of a curve of any kind or dimension, of which there is an endless variety. ”

“ Evidently, if chemical action be caused by a material medium, then an animal or a steam-engine lifting a weight is an instance (again) of motion coming from a material substance, and going back to it in a circle at the same time. ”

“ If any plane figure revolves about an external axis in its plane, the volume of the solid generated by the revolution is equal to the product of the area of the figure and the distance travelled by the centroid of the figure. ”

“ We deal with a compound or two-sided phenomenon—mental on one side, physical on the other; there is a definite correspondence in degree, although a difference of nature, between the two sides; and the physical side is itself in full correlation with the recognized physical forces of the world. ”

“ Surfaces and Curves in which the Composition of the Body represented is Variable and its Temperature and Pressure are Constant.
When there are three components, the position of a point in the plane may indicate the composition of a body most simply, perhaps, as follows. The body is supposed to be composed of the quantities of the substances , the value of being unity. ”

“ And when decay or tire shall once more consign them to the earth, or to the atmosphere, the same Elements will enter on some further department, of their perpetual ministration, in the economy of the material world. ”

“ Let’s see from what you would define a mirror—from a surface per se, in quantum est superficies, or from a substance that forms the surface, or from the substance upon which the surface rests, the raw material, modified by the attribute ‘surface,’ since it is clear that, surface being an accidental property of bodies, it cannot exist without substance. ”