Distance

“ But it is not only the distance that reduces our power of seeing, but also the layers, or veils of atmosphere that hang between us and the object. We are sure of this on a foggy day, when the mist lies low over the country or city, and trees and tall buildings loom up like blurs, and everything beyond the distance of a few hundred paces is blotted from sight. ”

“ We come to these visionary altitudes, not to look at realities but at pictures. Distance is a famous hand with the brush. To omit details and to fill the canvas with atmosphere, these are the secrets of his art. ”

“ Thus they learn the sun’s distance precisely as a rifleman learns the distance of a line of soldiers when he has ascertained their apparent size—for only at a certain distance can an object of known size have a certain apparent size. ”

“ Now, one way whereby we estimate the distance of anything is by the number and extent of the intermediate objects: when therefore the moon is seen in the horizon, the variety of fields, houses, etc., together with the large prospect of the wide extended land or sea that lies between the eye and the utmost limb of the horizon, suggest unto the mind the idea of greater distance, and consequently magnify the appearance. ”

“ So little have we intuition of distance in itself that in the night, as we have said, a distance might become a thousand times greater without our being able to perceive it, if all other distances had undergone the same alteration. ”

“ Distance has the same effect on the mind as on the eye; and while we glide along the stream of time, whatever we leave behind us is always lessening, and that which we approach increasing in magnitude. ”

“ Distance does actually lend enchantment. The range beyond has always some attraction this one lacks. In truth, mountains are illusory objects, and, to the most matter-of-fact point of view, are something more than rock. ”

“ In measuring distance they are much more deficient than in computing numbers, having but one term which answers to fathom; when they speak of distances from place to place, they express it, like the Asiatics, by the time that is required to pass it. ”

“ And all these the great and good Creator is sustaining in life, and leading through life, and on to a yet higher and happier eternal life in heaven.
Try, now, to estimate the vastness of this universe; What, think you, is the distance of those stars? We must take for our instrument of measure, the speed of light:—nothing else will suffice, to give a conception of that distance. Light travels at the rate of 192,000 miles in one second of time, or nearly twelve millions of miles a minute. ”

“ There is a curious absence of the sense of distance, even of distance in cloudland, for the sky ends as abruptly as the sea at that severely drawn circumference and there is no vague merging of the seen into the unseen, which alone gives the imagination room for flight. ”

“ Given the distance through which a body falls in a vertical line from rest and given also the time of fall, it is required to find the time in which the same body will, later, traverse an equal distance chosen anywhere in the same vertical line. ”

“ As a knowledge of distance is relative, a keen perception on the part of the prophet revealed to him, as he beheld the birds soaring in air, that the journey to lands beyond the sea was no greater distance to those winged creatures than a few miles would be to him. ”

“ The variations in distance may amount to many millions of miles, but, even in extreme cases, the variation in the distance of the planet is only a small fraction—usually a very small fraction—of the total amount of that distance. ”

“ The continued bisection of our distance, though it gives us continually smaller distances, gives us always finite distances. If our original distance was an inch, we reach successively half an inch, a quarter of an inch, an eighth, a sixteenth, and so on; but every one of this infinite series of diminishing distances is finite. ”

“ Here then are three relations betwixt that distance, which conveys the idea of extension, and that other, which is not fill’d with any colour’d or solid object. The distant objects affect the senses in the same manner, whether separated by the one distance or the other; the second species of distance is found capable of receiving the first ”

“ Have the pupils learn what two places in the neighborhood are about one mile apart; in a city, how many blocks there are to a mile. Have pupils tell about their walks or drives, noting distance and time.
1. What we Mean by Distance.—It is not easy to find a place if we know only in what direction it is from us. We should know also how far away it is, or the distance we shall have to go before reaching it.
If we know only that the house of a friend is east of ours, we cannot tell just where it is. ”

“ If we suppose a person looking at a remote object—let us say a lighted window—from a distance which is quite half a mile, the distance between his eyes bears nearly the same relation to that of the light, that the distance between any two stations practically usable on the earth does to that of the sun. ”

“ We frequently perceive the distance of objects, by means of intervening or contiguous objects, whose di-stance or magnitude is otherwise known. When I perceive certain fields or tracts of ground to lie between me and an object, it is evident, that these may become signs of its distance. And although we have no particular information of the dimensions of such fields or tracts, yet their similitude to others which we know, suggests their dimensions. ”

“ The relative distance of objects is easiest determined by moving the eyes; all stationary objects then appear displaced in the opposite direction (as for example when we look out of the window of a railway car) and those nearest most rapidly; from the different apparent rates of movement we can tell which are farther and which nearer. ”

“ The Perceiving of Distance.—Unquestionably the eye comes to be our chief dependence in determining distance. Yet the muscle and joint senses give us our earliest knowledge of distance. The babe reaches for the moon simply because the eye does not tell it that the moon is out of reach. Only as the child reaches for its105 playthings, creeps or walks after them, and in a thousand ways uses its muscles and joints in measuring distance, does the perception of distance become dependable. ”

“ For example, the walls of a city, reared in a vast level plain, and descried at a distance, appear to be far nearer than the traveller will find them to be; again, when standing on the beach, we look at a ship in the distance, we are apt to think it closer to the shore than we should prove it to be were we to traverse the distance in a boat. ”

“ But this distance in no way represents the actual distance that a person has to trudge up the mountain, and then to trudge down again in order that he may get, matériellement et physiquement, from one side of it to the other. ”

“ If we rightly picture these conditions, which fairly represent those under which the astronomer has to determine the distance of the sun from the earth, we shall perceive that the wonder rather is that any idea of the sun's distance should be obtained at all, than that the estimates obtained should differ from each other, and that the best of them should err in measurable degree from the true distance. ”

“ Longer distances he expresses by terms such as the distance of the nearest jhum, the distance of the furthest jhum, the distance a mithan will wander during the day, the distance a man can travel before his mid-day meal, &c.—terms which, though well understood by the people, are a little perplexing to strangers. ”

“ Keeping the same scale as before, in which our inconceivable distance from the sun, 9213 millions of miles, was reduced to a dozen rods or so, and then setting out to visit our neighbors, if we are lucky enough to turn our steps to the nearest, we find before us a journey of nearly 9,000 miles. ”

“ If the distance from the centre of the earth to its surface, which is 4000 miles, be called 1, then 4000 miles from the earth would be called 2, or twice as far from the centre, and 8000 miles from the earth would be 3, and so on. ”

“ Distance or space, in its simple abstract conception, to avoid confusion, I call expansion, to distinguish it from extension, which by some is used to express this distance only as it is in the solid parts of matter, and so includes, or at least intimates, the idea of body : whereas the idea of pure distance includes no such thing. ”

“ Distance is one of these, and the first idea of distance is to be attained by what children find a delightful operation. A child walks at his usual pace; somebody measures and tells him the length of his pace, and then he measures the paces of his brothers and sisters. Then such a walk, such a distance, here and there, is solemnly paced, and a little sum follows--so many inches or feet covered by each pace equals so many yards in the whole distance. ”

“ The question is this:—Will you go a long distance with a powerful horse, or a small distance with a weak horse? If the distance in each case is proportioned to the power of the horse, then the amount of the distance does not matter. ”

“ For my soul, being a real being as well as my body, is certainly as capable of changing distance with any other body, or being, as body itself ; and so is capable of motion. And if a mathematician can consider a certain distance, or a change of that distance between two points, one may certainly conceive a distance, and a change of distance, between two spirits ; and so conceive their motion, their approach or removal, one from another. ”

“ It is all very well, he reflected, to talk of the pull altering with the distance, but how are we to measure distance from a large body like the Earth or the Sun? Are we to measure it from the nearest point of the Earth, or from its centre, or from some point in between? When the whole Earth is far away, it does not much matter: but when we are dropping a weight as Galileo did, from the top of a tower, as at T in Fig. 4, then part of the Earth near F, the foot of the tower, is pretty close to us, and we have just seen how enormous the pull is when we come close to the attracting body. ”

“ This distance of P D + D E H F D = P D + 6 P D nearly, = 7 P D altogether, which gives the length of road that the man must be prepared to travel over who can answer no other than the question A. Of course, P D may cut the path, but I am speaking of the extreme distance which the lost man may have to travel. ”

“ We shall fix the position of that spot by applying two factors, the distance that you traveled and the direction in which you were moving. The direction is given by the compass; and, as the horse seems to have kept up a remarkably even pace, we can take time as representing distance. You seem to have been traveling at about eight miles an hour, that is, roughly, a seventh of a mile in one minute. So if, on our chart, we take one inch as representing one minute, we shall be working with a scale of about seven inches to the mile. ”

“ Similarly, the attraction which the sun will exert on the earth is not only known at distances for which it has been observed, but at all distances, because it is known to vary as the inverse square of the distance. ”

“ They and He paint the future in perspective, and the distance, seen behind the foreground, seems nearer than it really is. The spectator does not know how many weary miles have to be traversed before the distant blue hills are to be reached, nor what deep gorges lie between. ”

“ When under special conditions we cannot form a fair idea of distance, when we can only judge things by the size of the angle or rather of the image formed in our eyes, we cannot avoid being deceived as to the size of these objects. Every one knows by experience how when we are travelling at night we take a bush near at hand for a great tree at a distance, and vice versa. ”

“ See also BACK RANGE, LEADING LINE, MAGNETIC RANGE, MULTIPLE RANGES. 2. Distance in a single direction or along a great circle. 3. The extreme distance at which an object or light can be seen is called VISUAL RANGE. When the extreme distance is limited by the curvature of the earth and the heights of the object and the observer, this is called geographic range; when the range of a light is limited only by its intensity, clearness of the atmosphere, and sensitiveness of the observer’s eyes, it is called luminous range. 4. The extreme distance at which a signal can be detected or used. ”

“ Nothing makes the earth seem so spacious as to have friends at a distance; they make the latitudes and longitudes. ”

“ But from a distance of 100 miles the diminutions of deviation are slower, when they are navigating toward the mainland, than at a distance of 80 miles, and at a distance of 80 miles than at 50: for the deviations change and are diminished rather more swiftly the more they approach and draw near land than when at a great distance off. ”

“ I may further observe, that owing to the rotundity of the earth, and the allowance to be made in every mile, it does not require that the clouds should be very far away to be partly below the horizon. When we place our eye on a level with the ground and look along a flat country, at ten miles’ distance a man must be seventy feet high for his head to be seen above the horizon ”

“ But the five following associated circumstances seem to have also some influence on our judgments concerning distance, in certain cases, and under certain limitations: the number of objects which intervene, the degree of distinctness in which the minute parts are seen, the degree of brightness, the inclination of the optic axes, and the conformation of the eye. It will appear from the sixty-second and sixty-third propositions that the two last are associates to each other in their proper degrees, since each depends on the distance of the object. ”