Range

“ The proportion may be far to seek at times, but the proportion is there. Man’s farms about the lower Alps, his summer pastures aloft, have their relation to the whole construction of the range; and the range is great because it is great in regard to the village lodged in a steep valley in the foot hills. The relation of flower and fruit to his hands and mouth, to his capacity and senses (I am dealing with size, and nothing else) , is a very commonplace of our conditions in the world. The arm of man is sufficient to dig just as deep as the harvest is to be sown. ”

“ In endowing me with passions and faculties Nature has been horribly niggardly. The full range of human potentialities is in any case distressingly limited; my range is a limitation within a limitation. ”

“ Completion of Table of Differences.—If no values of u outside the range within which we have to interpolate are given, the series of differences will be incomplete at both ends. It may be continued in each direction by treating as constant the extreme difference of the highest order involved; and central-difference formulae can then be employed uniformly throughout the whole range. ”

“ He takes the widest possible range, but from that very range he has his choice of the greatest variety and aptitude of materials. He brings together images the most alike, but placed at the greatest distance from each other ”

“ Range′-find′er, an instrument for determining the range of an object by sight.—n.pl. Range′-lights, lights placed in line, usually at or near a lighthouse, so as to direct the course of a ship through a channel: lights on board ship so placed as to give a ready indication of changes of course to other vessels.—n. ”

“ Look at a plant in the midst of its range! Why does it not double or quadruple its numbers? We know that it can perfectly well withstand a little more heat or cold, dampness or dryness, for elsewhere it ranges into slightly hotter or colder, damper or drier districts. In this case we can clearly see that if we wish in imagination to give the plant the power of increasing in numbers, we should have to give it some advantage over its competitors, or over the animals which prey on it. ”

“ But since all evils, like all goods, partake of latitude and altitude, and according to latitude have their genera, and according to altitude their degrees, therefore, in order that adulteries may be known as to each dimension, they shall first be arranged into their genera, and afterwards into their degrees ”

“ Far beyond the keenest of human vision is its range of sight. If the light is good, this sensitive plate of glass will have recorded and discerned a thousand uplifted faces as perfectly as the human eye perceives the features of a single countenance. Every expression of joy or sorrow, every peculiarity of dress or attitude, the leaves of a forest or the grass by the wayside, will have been seen and delineated and retained perfectly in far less than the briefest possible twinkling of a human eye. ”

“ The elevation of the piece is the angle its axis (produced) makes with the horizon, and the axis itself is called the direction.
10. The horizontal distance to which a mortar, elevated to a given angle, and loaded with a given quantity of powder, throws a shell of a given weight, is called the range of that mortar, with that charge and elevation.
11. The inclination of a plane is the angle it makes with the horizon either above or below. ”

“ They amicably laid it down, that there was a just and geometrical arrangement and proportion of the several parts of the human frame to its several destinations, offices, and functions, which could not be transgressed but within certain limits—that nature, though she sported——she sported within a certain circle;—and they could not agree about the diameter of it. ”

“ "Something hidden. Go and find it. Go and look behind the Ranges—
"Something lost behind the Ranges. Lost and waiting for you. ”

“ In the measurements of areas, size of fields and gardens, width of ponds, or heights of trees and hills, the pupil has numerical facts from which he judges of other forms and areas; as forests, marshes, plains, the width of rivers and lakes, the heights of mountains and cliffs, or length of rivers and mountain ranges.
Also in the measuring of the deposition of silt in small streams, he may judge of the quantity that large rivers like the Mississippi or Nile must carry; and from measuring the yearly growth of vegetation in his own climate, he judges what might be the growth in other climates. ”

“ Where is the girl so angelic as not to feel a slight curiosity to know how she shall look in a new and strange costume? Mary bent over the rock, where a little pool of water lay in a brown hollow above the fluctuations of the tide, dark and still, like a mirror,—and saw a fair face, with a white shell above the forehead and drooping wreaths of green seaweed in the silken hair; and a faint blush and smile rose on the cheek, giving the last finish to the picture. ”

“ 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. ”

“ Then you see nothing strange and solemn in this wonderful stream? nothing in the weird civilization crouching at the feet, vainly looking to the head of its master hidden in the clouds? nothing in the echoing footsteps of nations passing down its banks to their destiny? ”

“ There are natural measures, nearly the same everywhere, such as a man's pace, the length of his arm, or his height. When the child is calculating the height of the story of a house, his tutor may serve as a unit of measure. In estimating the altitude of a steeple, he may compare it with that of the neighboring houses. If he wants to know how many leagues there are in a given journey, let him reckon the number of hours spent in making it on foot. ”

“ 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. ”

“ But at night, when our own star is hidden, our vision ranges into the depths of creation, and we behold them sparkling with a multitude of other suns. With so simple an aid as that of an opera-glass, we penetrate still deeper into the profundities of space, and thousands more of these strange, far-away suns come into sight. ”

“ It is said in the Bible that God has ordered all things according to weight, number and measure. Omnia in pondere et numero et mensura disposuit Deus. Weight is equilibrium, number is quantity, measure is proportion—these three, and these are the eternal or divine basis of the science of Nature. Here now is the formula of equilibrium: Harmony results from the analogy of contraries. Number is the scale of analogies, the proportion of which is measure. The entire occult philosophy of the Zohar might be termed the science of equilibrium. ”

“ The visions continue as brilliantly as ever: I think I see them better in a room lighted by fire than in a dark room. I have seen thick glorious fields of jewels which spring into forms like flowers beneath my view and then seem to turn into gorgeous butterfly-like forms. When I speak my voice seems strange to me and certainly sounds hoarse. ”

“ A measurement is a comparison. We measure the length of a lot by comparing it with the standard of length, the yard or foot. We measure a farm by comparing its area with the standard unit of surface measure, the acre, square rod, or square yard.
In every measurement we must first have an accepted standard unit. The history of units of measurement is a very interesting one, and its difficulty arises from the fact that no two things in nature are the same. ”

“ 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." ”

“ The progression from pre-word to notation, and in our days from literacy to illiteracy is paralleled by the progression of scale. Numbers as such-how many people in a given area, how many people interacting in a particular practical experience, the longevity of people under given circumstances, the mortality rate, family size-are almost meaningless. Only when relations among numbers and circumstances can be established is some meaningful inference possible. Scale is the expression of relations. ”

“ The Level.—Every piece of work should be square and level, except when it is of a curved form, and then it should be reduced to the principles of the circle or ellipse. The level is used in putting up posts, palings, or work of any kind in an upright position. ”

“ Why, the height of a man, in nine cases out of ten, can be told from the length of his stride. It is a simple calculation enough, though there is no use my boring you with figures. I had this fellow's stride both on the clay outside and on the dust within. Then I had a way of checking my calculation. When a man writes on a wall, his instinct leads him to write about the level of his own eyes. Now that writing was just over six feet from the ground. ”

“ By exercising the class in this manner, not to exceed half an hour a day, they would, at the end of the first quarter, judge of each other's height, of the height of persons generally, of the length of various objects, of the size of buildings, and of the dimensions of yards, gardens, and fields, with greater accuracy than the average of adult persons, as was tested by actual measurement in some instances where there was a disagreement in opinion. ”

“ If we were to call a foot measure a yard, and were then to say that all cloth measured by it became thereby stretched to three times its length, relatively to a true yard-stick, we should simply make ourselves ridiculous. ”

“ In the pure frosty air the stars seem splintered and multiplied indefinitely, and the brighter ones shine with a splendor of light and color unknown to the denizen of the smoky city, whose eyes are dulled and blinded by the glare of street-lights. There one may detect the delicate shade of green that lurks in the imperial blaze of Sirius, the beautiful rose-red light of Aldebaran, the rich orange hue of Betelgeuse, the blue-white radiance of Rigel, and the pearly luster of Capella. ”

“ Consequently, Nature herself supplies us with an ascending scale or Alphabet of angles for half a degree up to 60°, specimens of which are placed in every Elementary School throughout the land. Owing to occasional retrogressions, to still more frequent moral and intellectual stagnation, and to the extraordinary fecundity of the Criminal and Vagabond Classes, there is always a vast superfluity of individuals of the half degree and single degree class, and a fair abundance of Specimens up to 10°. ”

“ There are two general classes of degrees; continuous degrees, and discrete degrees. One may be best understood in contrast with the other. Continuous degrees of any thing exist on the same plane. They may be thought of as degrees of latitude. Discrete degrees exist on different planes. They may be conceived of as degrees of altitude. Continuous degrees are like degrees from hard to soft, from gross to subtile, or from dense to rare, and the like. ”

“ The times of descent along planes of different length, slope and height bear to one another a ratio which is equal to the product of the ratio of the lengths by the square root of the inverse ratio of their heights. ”

“ The size of the farm is another of those questions on which there is endless debate and to which no general answer can be given. There are, however, certain rather definite principles which may help in settling an individual problem. ”

“ Contenting ourselves, however, with our own small value-scale, as we needs must, and assuming it to be adequate, the most important thing to consider is the value-key of our picture. Assuming the whole scale of values from the deepest black to the purest white to be represented by the number 100, the question arises as to what proportion of this number we shall use in the particular work which we are proposing to execute. ”

“ It is actually a fact, proven many times, that those estimates should be divided by two in order to get near the measured truth! The "four hundred yards if it's an inch!" becomes two hundred--and even two hundred yards at living game in natural surroundings is a long and creditable shot. ”

“ He says: "There is an overpowering feeling of predominance in case of the large and I must judge for them. The large space covered seems an important factor. The longer I reflect upon the relative numbers the more numerous seem the larger, that is, they appear to increase over the small after the exposure. It is hard to give judgments of equal in most cases."
C. The Factor of Form. The material consisted of a group of circles, each of the same size as in former material; and a group of squares, each approximately equal to a circle of the other group. ”

“ 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. ”