Radius

“ A sphere with earth as its centre, and a radius of one minute of light’s flight, would contain 21 billions of earths; a sphere whose radius was nine minutes would contain 15,310 billions of earths, one of an hour’s radius 4,500 trillions, one of a day’s 62 quintillions, a week’s 20 sextillions, a month’s 1675 sextillions, and a year’s radius of the flight of light three octillions. ”

“ The solid angle subtended at a given point by a closed curve is measured by the area of a spherical surface whose centre is the given point and whose radius is unity, the outline of which is traced by the intersection of the radius vector with the sphere as it traces the closed curve. ”

“ If the radius of the active surface is large compared with the distance of the plate A from it, the intensity of the radiation is approximately uniform over the opening in the plate A, and falls off with the distance x traversed according to an exponential law. ”

“ A circulating medium of constantly-increasing radius, appears indispensably necessary for the purpose of conveying solar matter through the regions of space, and for the maintaining all planetary motion in the same uniform direction. ”

“ Since rays proceeding from the extremity of the diameter, are reflected to making two-thirds of and that all points of the object are equally distant from the centre, it will readily be seen that the image of the portion of sphere represented by is a corresponding portion of sphere, having its radius one-third of that of the mirror. ”

“ If one part of a conducting body be a sphere of small radius, the electric fluid upon the surface of this sphere will, it appears by calculation, be more dense, and tend to escape more energetically, in proportion as the radius of the sphere is smaller; and, therefore, if we consider a point as part of the surface of a sphere of imperceptible radius, it follows from the theory that the effort of the fluid to escape at that place will be enormous ”

“ Now, it will require but little reflection to perceive that to move the earth in a circle with a radius of a little more than 2,000 miles, and the moon in a circle with a radius of nearly 240,000 miles, would require equal forces. ”

“ If fire is indicated by + 0-, the air then corresponds to the-, the water to +, the earth to the 0. The earth is therefore the Identical, water the Indifferent, air the Different; or the first the centre, the second the radius, the last the periphery of the general globe or of fire. The earth is naught but an accumulation of points. If radii occur in it, it happens only because all points have not place in the middle point. ”

“ Since Point and Plane represent in the realm of geometrical concepts what in outer nature we find in the form of the gravity-levity polarity, we may expect to meet Radius and Sphere as actual formative elements in nature, wherever gravity and levity interact in one way or another. ”

“ This the author calls the equation of the wave-surface or surface of ray-velocities. It has the form of the equation of FresneUs wave-surface, expressed in terms of the direction-cosines and reciprocal of the radius vector, and if are the direction-cosines of the ray, and the velocity of light in vacuo divided by the so-called ray-velocity in the crystal the equation will express Fresnel's law. ”

“ If we assume that there is no loss of energy in the transmitting medium, then the whole amount of radiant energy passing in one second across any closed surface completely surrounding the source of light must be the same whatever the size or form of the surface. Imagine for simplicity a point source of light, or its equivalent, a uniformly radiating spherical surface with the point at its centre, and draw round this point a spherical surface of unit radius. ”

“ Radiation. The passage of light or heat in rays, or straight lines; these being projected from every luminous, or heated point, in all directions.
Radius. The distance from the centre of a circle, to its circumference; or one half of its diameter. In the plural denominated radii.
Rainbow. An appearance in the atmosphere, occasioned by the decomposition of solar light, in its refraction, and reflection, in passing through drops of rain. The bow can be seen, only when the sun is near the horizon, when the back is turned towards it, and there is a shower in the opposite direction. ”

“ Having collected these Elements or Requisites, the following part of the work may be very much facilitated by means of a good Sector, with the use of which the reader should be so well acquainted, as to know how to open it to any given Radius, as far as it will go; and to take off the Chord or Sine of any Arc of that Radius. This is done by first taking the extent of the given Radius in your Compasses, and then opening the Sector so as the distance cross-wise between the ends of the lines of Sines or Chords at S or C, from Leg to Leg of the Sector, may be equal to that extent ”

“ Every point is equidistant from a fixed point within the surface; this point is the “centre,” the constant distance the “radius,” and any line through the centre and intersecting the sphere is a “diameter.” All sections of the sphere are necessarily circles; if the cutting plane contains the centre, the section is said to be “meridional,” the curve of intersection is a “great circle,” and the solid cut off a “hemisphere.” If the plane does not contain the centre, the curve of intersection is a “small circle,” and the solid cut off is a “segment.” ”

“ And universally, if the greatest altitude CV of the body be called T, and the radius of the curvature which the orbit VPK has in V, that is, the radius of a circle equally curve, be called R, and the centripetal force with which a body may revolve in any immovable trajectory VPK at the place K be called , and in other places P be indefinitely stiled X ”

“ If, for example, the radius shortens 5 miles, each great circle must on the average be compressed, wrinkled, or otherwise distorted to the extent of about 31 miles, or, in reversed application, if the mountain foldings on any great circle together show a shortening of 100 miles, the appropriate radial shortening is 16 miles. ”

“ We want to talk about how fast the area changes, and we represent that by A. The area changes when the radius is swinging, and it is the component of velocity at right angles to the radius, times the radius, that tells us how fast the area changes. ”

“ We do not now enter into the proof, but it is sufficiently obvious that a sphere of which the radius is the geometric mean between the greatest and least radii of curvature at each point will to a large extent osculate the surface, so that a portion of the surface in the neighbourhood of the point will, generally speaking, have the same curvature as the sphere. ”

“ Since objects in equilibrium, such as rigid objects, electrons and atoms, all adjust themselves to the radius of curvature of the universe, it is only natural that results of greatest simplicity should be obtained when we select this radius or some definite fraction thereof as a gauge at every point. ”

“ That the region of greatest density, and the position of the interior surface of the shell, may be expressed with very approximate accuracy as follows:—The former must be at 0·7939 of the mean radius of the earth, and the latter at 0·5479 of the same; both counted from the centre.
(6) That if the earth is a hollow sphere, the same must be the case with all the major planets and their satellites, the sun, and all the suns, or stars, that are seen in the heavens; and that their interior proportions and form must be in much the same ratios to their radii as those we have found for the earth. ”

“ The Radius Vector is the imaginary straight line joining the centres of the sun and the earth or planet. While the First Law shows us the kind of path which a planet takes in revolving round the sun, the Second Law describes how the velocity of the planet varies in different parts of its orbit. ”

“ If the ratio of to is zero or unity, the system of surfaces becomes one system of meridian planes, one system of right cones having a common axis, and a system of concentric spherical surfaces of which the radius is inversely proportional to . ”

“ If the illuminating surface is a very small [AU 3] sphere of radius R, which oscillates according to the law for the rotation angle
around the X-axis, then, at the distance from the center of the sphere, the propagated rotations ψ are given by [2] [AU 4]
where
is set. ”

“ If we now make the inner surface coincide with that of the electrified sphere, and make the radius of the other infinite, becomes , the potential of the sphere, and becomes zero, so that the whole work done in the surrounding medium is . ”

“ Earth's orbital radius does in our views of the immensity of
space. ”

“ It is thence inferred, that a stratum occupying the entire surface of the sphere of which the earth’s distance from the sun is the radius, and consisting of three layers of flame, each 1/1000th of an inch in thickness, each possessing a brightness equal to that of such an electric light, and all three embraced within a thickness of 1/40th of an inch, would give an amount of illumination equal in quantity and intensity to that of the sun at the distance of 95 millions of miles from his centre. ”

“ For spheres of different sizes, the greatest increase in mass varies as the cube of the radius; hence the ratio of this increase to the whole mass of the sphere is constant for all spheres of the same material ”

“ Let us examine the case in which the particle is placed at a distance from a curved stratum of the substance, whose principal radii of curvature are and . Let (fig. 2) be the particle and a normal to the surface. Let the plane of the paper be a normal section of the surface of the stratum at the point , making an angle with the section whose radius of curvature is . ”

“ Also the motion of the planet in its orbit was such that equal areas were described about the Sun by the radius vector of the planet in equal times.—Kepler, Astronomia Nova αἰτολογητός (Prague) , 1609. ”

“ A radius, or half diameter of a column, is called a Mod- ule, which, when once ascertained,determines the height of the frieze, cornice, shaft, &c. These modules are each divided into twelve equal parts in the Tuscan and Dorick orders, and into eighteen in the Ionick and Co- rinthian. ”

“ Electricity ranks in eternal antagonism to magnetism.
33
SPHERE, HEAT, CHEMISTRY.
140. The line and surface are density, the representation of time and space; they have therefore like these originated out of nothing, namely, out of the point. The sphere is the expanded nothing. Nothing thus extended, or nothing posited, becomes a something, viz. line, surface, density, polarity. The line is a long nothing, the surface a hollow nothing, the sphere a dense nothing; in short, the something is a nothing which has received only predicates. All things are nothings with different forms. ”

“ In every twenty-four hours, by the earth's rotation, the line drawn from the body at right angles to the earth coincides successively with all the radii of a circle, and in the course of six months the place of that circle varies by nearly two hundred millions of miles; yet in all these changes of the earth's position, the line in which bodies tend to fall continues to be directed toward it: which proves that terrestrial gravity is directed to the earth, and not, as was once fancied by some, to a fixed point of space. ”

“ 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. ”

“ Accordingly, a body hanging by a line, which over a level surface would be drawn by the earth's attraction into a direction with reference to its point of suspension, the prolongation of the line of which would pass through the center of the earth—that is, would be perpendicular, or plumb—would be attracted and turned away from the perpendicular by a mass like a mountain in the neighborhood. ”

“ The angle A D B, contained between the incident ray and the normal, is termed the angle of incidence; and the angle C B D, contained between the corresponding reflected ray and the normal, is called the angle of reflection. The reflection of light by polished surfaces, as in this case, is governed by two laws: 1. The incident ray, the normal, and the reflected ray, are always in the same plane; and, 2. The angle of incidence is always equal to the angle of reflection. ”

“ You know full well that the condition of the outer sphere is, as I have described it, a bleak, turbulent surface, the roof of the earth on which man exists, as a creeping parasite does on a rind of fruit, exposed to the fury of the ever-present earth storms.
"The central circle, or medial sphere, the shell, or layer of gravitation, lies conformably to the outer configuration of the globe, about seven hundred miles towards its center. It stretches beneath the outer circle (sphere) as a transparent sheet, a shell of energy, the center of gravitation. ”

“ Seeing that the foregoing reasoning forces us to look upon the earth as a hollow sphere, or shell, in which the whole of the matter composing it is divided into two equal parts, attracted outwards and inwards by each other to a common plane, or region of meeting, we shall divide its whole volume into two equal parts radially, that is, one comprising a half from the surface inwards, and the other a half from the centre [170] outwards—that is to say, each one containing one-half of the whole volume of the earth. ”