, in Natural History, a fountain or source of water, rising out of the ground.

The most general and probable opinion among philosophers, on the formation of Springs, is, that they are owing to rain. The rain-water penetrates the earth till such time as it meets a clayey soil, or stratum; which proving a bottom sufficiently solid to sustain and stop its descent, it glides along it that way to which the earth declines, till, meeting with a place or aperture on the surface, through which it may escape, it forms a Spring, and perhaps the head of a stream or brook.

Now, that the rain is sufficient for this effect, appears from hence, that upon calculating the quantity of rain and snow which falls yearly on the tract of ground that is to furnish, for instance, the water of the Seine, it is found that this river does not take up above onesixth part of it.

Springs commonly rise at the bottom of mountains; the reason is, that mountains collect the most waters, and give them the greatest descent the same way. And if we sometimes see Springs on high grounds, and even on the tops of mountains, they must come from other remoter places, considerably higher, along beds of clay, or clayey ground, as in their natural channels. So that if there happen to be a valley between a mountain on whose top is a Spring, and the mountain which is to | furnish it with water, the Spring must be considered as water conducted from a reservoir of a certain height, through a subterraneous channel, to make a jet of an almost equal height.

As to the manner in which this water is collected, so as to form reservoirs for the different kinds of Springs, it seems to be this: the tops of mountains usually abound with cavities and subterraneous caverns, formed by nature to serve as reservoirs; and their pointed summits, which seem to pierce the clouds, stop those vapours which float in the atmosphere; which being thus condensed, they precipitate in water, and by their gravity and fluidity easily penetrate through beds of sand and the lighter earth, till they become stopped in their descent by the denser strata, such as beds of clay, stone, &c, where they form a bason or cavern, and working a passage horizontally, or a little declining, they issue out at the sides of the mountains. Many of these Springs discharge water, which running down between the ridges of hills, unite their streams, and form rivulets or brooks, and many of these uniting again on the plain, become a river.

The perpetuity of divers Springs, always yielding the same quantity of water, equally when the least rain or vapour is afforded as when they are the greatest, furnish, in the opinion of some, considerable objections to the universality or sufficiency of the theory above. Dr. Derham mentions a Spring in his own parish of Upminster, which he could never perceive by his eye was diminished in the greatest droughts, even when all the ponds in the country, as well as an adjoining brook, had been dry for several months together; nor ever to be increased in the most rainy seasons, excepting perhaps for a few hours, or at most for a day, from sudden and violent rains. Had this Spring, he thought, derived its origin from rain or vapours, there would be found an increase and decrease of its water corresponding to those of its causes; as we actually find in such temporary Springs, as have undoubtedly their rise from rain and vapour.

Some naturalists therefore have recourse to the sea, and derive the origin of Springs immediately from thence. But how the sea-water should be raised up to the surface of the earth, and even to the tops of the mountains, is a difficulty, in the solution of which they cannot agree. Some fancy a kind of hollow subterranean rocks to receive the watery vapours raised from channels communicating with the sea, by means of an internal fire, and to act the part of alembics, in freeing them from their saline particles, as well as condensing and converting them into water. This kind of subterranean laboratory, serving for the distillation of seawater, was the invention of Des Cartes: see his Princip. part 4, § 64. Others, as De la Hire &c (Mem. de l'Acad. 1703) set aside the alembics, and think it enough that there be large subterranean reservoirs of water at the height of the sea, from whence the warmth of the bottom of the earth, &c, may raise vapours; which pervade not only the intervals and fissures of the strata, but the bodies of the strata themselves, and at length arrive near the surface; where, being condensed by the cold, they glide along on the first bed of clay they meet with, till they issue forth by some aperture in the ground. De la Hire adds, that the salts of stones and minerals may contribute to the de- taining and fixing the vapours, and converting them into water. Farther, it is urged by some, that there is a still more natural and easy way of exhibiting the rise of the sea-water up into mountains &c, viz, by putting a little heap of sand, or ashes, or the like, into a bason of water; in which case the sand &c will represent the dry land, or an island; and the bason of water, the sea about it. Here, say they, the water in the bason will rise to the top of the heap, or nearly so, in the same manner, and from the same principle, as the waters of the sea, lakes, &c, rise in the hills. The principle of ascent in both is accordingly supposed to be the same with that of the ascent of liquids in capillary tubes, or between contiguous planes, or in a tube filled with ashes; all which are now generally accounted for by the doctrine of attraction.

Against this last theory, Perrault and others have urged several unanswerable objections. It supposes a variety of subterranean passages and caverns, communicating with the sea, and a complicated apparatus of alembics, with heat and cold, &c, of the existence of all which we have no sort of proof. Besides, the water that is supposed to ascend from the depths of the sea, or from subterranean canals proceeding from it, through the porous parts of the earth, as it rises in capillary tubes, ascends to no great height, and in much too small a quantity to furnish springs with water, as Perrault has sufficiently shewn. And though the sand and earth through which the water ascends may acquire some saline particles from it, they are nevertheless incapable of rendering it so fresh as the water of our fountains is generally found to be. Not to add, that in process of time the saline particles of which the water is deprived, either by subterranean distillation or filtration, must clog and obstruct those canals and alembics, by which it is supposed to be conveyed to our Springs, and the sea must likewise gradually lose a considerable quantity of its salt.

Different sorts of Springs. Springs are either such as run continually, called perennial; or such as run only for a time, and at certain seasons of the year, and therefore called temporary Springs. Others again are called intermitting Springs, because they flow and then stop, aud flow and stop again; and reciprocating Springs, whose waters rise and fall, or flow and ebb, by regular intervals.

In order to account for these differences in Springs, let ABCDE (fig. 2, pl. 27) represent the declivity of a hill, along which the rain descends; passing through the fissures or channels BF, CG, DH, and LK, into the cavity or reservoir FGHKMI; from this cavity let there be a narrow drain or duct KE, which discharges the water at E. As the capacity of the reservoir is supposed to be large in proportion to that of the drain, it will furnish a constant supply of water to the spring at E. But if the reservoir FGHKMI be small, and the drain large, the water contained in the former, unless it is supplied by rain, will be wholly discharged by the latter, and the Spring will become dry: and so it will continue, even though it rains, till the water has had time to penetrate through the earth, or to pass through the channels into the reservoir; and the time necessary for furnishing a new supply to the drain KE will depend on the size of the fissures, the na- | ture of the soil, and the depth of the cavity with which it communicates. Hence it may happen, that the Spring at E may remain dry for a considerable time, and even while it rains; but when the water has found its way into the cavity of the hill, the Spring will begin to run. Springs of this kind, it is evident, may be dry in wet weather, especially if the duct KE be not exactly level with the bottom of the cavity in the hill, and discharge water in dry weather; and the intermissions of the Spring may continue several days. But if we suppose XOP to represent another cavity, supplied with water by the channel NO, as well as by fissures and clefts in the rock, and by the draining of the adjacent earth; and another channel STV, communicating with the bottom of it at S, ascending to T, and terminating on the surface at V, in the form of a siphon; this disposition of the internal cavities of the earth, which we may reasonably suppose that nature has formed in a variety of places, will serve to explain the principle of reciprocating Springs; for it is plain, that the cavity XOP must be supplied with water to the height QPT, before it can pass over the bend of the channel at T, and then it will flow through the longer leg of the siphon TV, and be discharged at the end V, which is lower than S. Now if the channel STV be considerably larger than NO, by which the water is principally conveyed into the reservoir XOP, the reservoir will be emptied of its water by the siphon; and when the water descends below its orifice S, the air will drive the remaining water out of the channel STV, and the Spring will cease to flow. But in time the water in the reservoir will again rise to the height QPT, and be discharged at V as before. It is easy to conceive, that the diameters of the channels NO and STV may be so proportioned to one ancther, as to afford an intermission and renewal of the Spring V at regular intervals. Thus, if NO communicates with a well supplied by the tide, during the time of flow, the quantity of water conveyed by it into the cavity XOP may be sufficient to fill it up to QPT; and STV may be of such a size as to empty it, during the time of ebb. It is easy to apply this reasoning to more complicated cases, where several reservoirs and siphons communicating with each other, may supply Springs with circumstances of greater variety. See Musschenbroek's Introd. ad Phil. Nat. tom. ii. pa. 1010. Desagu. Exp. Phil. vol. ii, pa. 173, &c.

We shall here observe, that Desaguliers calls those reciprocating Springs which flow constantly, but with a stream subject to increase and decrease; and thus he distinguishes them from intermitting Springs, which flow or stop alternately.

It is said that in the diocese of Paderborn, in Westphalia, there is a Spring which disappears after twentyfour hours, and always returns at the end of six hours with a great noise, and with so much force, as to turn three mills, not far from its source. It is called the Bolderborn, or boisterous Spring. Phil. Trans. num. 7, pa. 127.

There are many Springs of an extraordinary nature in our own country, which it is needless to recite, as they are explicable by the general principles already illustrated.


, Ver, in Astronomy and Cosmography, denotes one of the seasons of the year; commencing, in the northern parts of the earth, on the day the sun enters the first degree of Aries, which is about the 21st day of March, and ending when the sun enters Cancer, at the summer solstice, about the 21st of June; Spring ending when the summer begins.

Or, more strictly and generally, for any part of the earth, or on either side of the equator, the Spring season begins when the meridian altitude of the sun, being on the increase, is at a medium between the greatest and least; and ends when the meridian altitude is at the greatest. Or the Spring is the season, or time, from the moment of the sun's crossing the equator till he rise to the greatest height above it.

Elater Spring, in Physics, denotes a natural faculty, or endeavour, of certain bodies, to return to their first state, after having been violently put out of the same by compressing, or bending them, or the like.

This faculty is usually called by philosophers, elastic force, or elasticity.


, in Mechanics, is used to signify a body of any shape, perfectly elastic.

Elasticity of a Spring. See Elasticity.

Length of a Spring, may, from its etymology, signify the length of any elastic body; but it is particularly used by Dr. Jurin to signify the greatest length to which a Spring can be forced inwards, or drawn outwards, without prejudice to its elasticity. He observes, this would be the whole length, were the Spring considered as a mathematical line; but in a material Spring, it is the difference between the whole length, when the Spring is in its natural situation, or the situation it will rest in when not disturbed by any external force, and the length or space it takes up when wholly compressed and closed, or when drawn out.

Strength or Force of a Spring, is used for the force or weight which, when the Spring is wholly compressed or closed, will just prevent it from unbending itself. Also the Force of a Spring partly bent or closed, is the force or weight which is just sufficient to keep the Spring in that state, by preventing it from unbending itself any farther.

The theory of Springs is founded on this principle, ut intensio, sic vis; that is, the intensity is as the compressing force; or if a Spring be any way forced or put out of its natural situation, its resistance is proportional to the space by which it is removed from that situation. This principle has been verified by the experiments of Dr. Hook, and since him by those of others, particularly by the accurate hand of Mr. George Graham. Lectures De Potentia Restitutiva, 1678.

For elucidating this principle, on which the whole theory of Springs depends, suppose a Spring CL, resting at L against any immoveable support, but otherwise lying in its natural situation, and at full liberty. Then if this Spring be pressed inwards by any force p, or from C towards L, through the space of one inch, and can be there detained by that force p, the resistance of the Spring, and the force p, exactly counterbalancing each other; then will the double force 2p bend the Spring through the space of 2 inches, and the triple force 3p through 3 inches, and the quadruple force 4p through 4 inches, and so on. The space CL through which the Spring is bent, or by which its end C is removed from its natural situation, being al- | ways proportional to the force which will bend it so far, and will just detain it when so bent. On the other hand, if the end C be drawn outwards to any place l, and be there detained from returning back by any force p, the space Cl, through which it is so drawn outwards, will be also proportional to the force p, which is just able to retain it in that situation.

It may here be observed, that the Spring of the air, or its elastic force, is a power of a different nature, and governed by different laws, from that of a palpable rigid Spring. For supposing the line LC to represent a cylindrical volume of air, which by compression is reduced to Ll, or by dilatation is extended to Ll, its elastic force will be reciprocally as Ll or Ll; whereas the force or resistance of a Spring is directly as Cl or Cl.

This principle being premised, Dr. Jurin lays down a general theorem concerning the action of a body striking on one end of a Spring, while the other end is supposed to rest against an immoveable support.

Thus, if a Spring of the strength P, and the length CL, lying at full liberty upon an horizontal plane, rest with one end L against an immoveable support; and a body of the weight M, moving with the velocity V, in the direction of the axis of the Spring, strike directly on the other end C, and so force the Spring inwards, or bend it through any space CB; and if a mean proportional CG be taken between (M/P) X CL and 2a, where a denotes the height to which a body would ascend in vacuo with the velocity V; and farther, if upon the radius R = CG be described the quadrant of a circle GFA: then,

1. When the Spring is bent through the right sine CB of any arc GF, the velocity v of the body M is to the original velocity V, as the cosine BF is to the radius CG; that is v : V :: BF : CG, or .

2. The time t of bending the Spring through the same sine CB, is to T, the time of a heavy body's ascending in vacuo with the velocity V, as the corre- sponding arc is to 2a; that is t : T :: GF : 2a, or .

The doctor gives a demonstration of this theorem, and deduces a great many curious corollaries from it. These he divides into three classes. The first contains such corollaries as are of more particular use when the Spring is wholly closed before the motion of the body ceases: the second comprehends those relating to the case, when the motion of the body ceases before the Spring is wholly closed: and the third when the motion of the body ceases at the instant that the Spring is wholly closed.

We shall here mention some of the last class, as being the most simple; having first premised, that P = the strength of the Spring, L = its length, V = the initial velocity of the body closing the Spring, M = its mass, t = time spent by the body in closing the Spring, A = height from which a heavy body will fall in vacuo in a second of time, a = the height to which a body would ascend in vacuo with the velocity V, C = the velocity gained by the fall, m = the circumference of a circle, whose diameter is 1. Then, the motion of the striking body ceasing when the Spring is wholly closed, it will be,

1. .

2. .

3. the first momentum.

4. If a quantity of motion MV bend a Spring through its whole length, and be destroyed by it; no other quantity of motion equal to the former, as nM X (V/n), will close the same Spring, and be wholly destroyed by it.

5. But a quantity of motion, greater or less than MV, in any given ratio, may close the same Spring, and be wholly destroyed in closing it; and the time spent in closing the Spring will be respectively greater or less, in the same given ratio.

6. The initial vis viva, or MV2 is = (C2PL)/(2A); and 2aM = PL; also the initial vis viva is as the rectangle under the length and strength of the Spring, that is, MV2 is as PL.

7. If the vis viva MV2 bend a Spring through its whole length, and be destroyed in closing it; any other vis viva, equal to the former, as n2M X (V2/n2), will close the same Spring, and be destroyed by it.

8. But the time of closing the Spring by the vis viva n2M X (V2/n2), will be to the time of closing it by the vis viva MV2, as n to 1.

9. If the vis viva MV2 be wholly consumed in closing a Spring, of the length L, and strength P; then the | vis viva n2MV2 will be sufficient to close, 1st, Either a Spring of the length L and strength n2P. 2d, Or a Spring of the length nL and strength nP. 3d, Or of the length n2L and strength P. 4th, Or, if n be a whole number, the number n2 of Springs, each of the length L and strength P.—It may be added, that it appears from hence, that the number of similar and equal Springs a given body in motion can wholly close, is always proportional to the squares of the velocity of that body. And it is from this principle that the chief argument, to prove that the force of a body in motion is as the square of its velocity, is deduced. See Force.

The theorem given above, and its corollaries, will equally hold good, if the Spring be supposed to have been at first bent through a certain space, and by unbending itself to press upon a body at rest, and thus to drive that body before it, during the time of its expansion: only V, instead of being the initial velocity with which the body struck the Spring, will now be the final velocity with which the body parts from the Spring when totally expanded.

It may also be observed, that the theorem, &c, will equally hold good, if the Spring, instead of being pressed inward, be drawn outward by the action of the body. The like may be said, if the Spring be supposed to have been already drawn outward to a certain length, and in restoring itself draw the body after it. And lastly, the theorem extends to a Spring of any form whatever, provided L be the greatest length it can be extended to from its natural situation, and P the force which will confine it to that length. See Philos. Trans. num. 472, sect. 10, or vol. 43, art. 10.

Spring is more particularly used, in the Mechanic Arts, for a piece of tempered steel, put into various machines to give them motion, by the endeavour it makes to unbend itself.

In watches, it is a fine piece of well-beaten steel, coiled up in a cylindrical case, or frame; which by stretching itself forth, gives motion to the wheels, &c.

Spring Arbor, in a Watch, is that part in the middle of the Spring-box, about which the Spring is wound or turned, and to which it is hooked at one end.

Spring Box, in a Watch, is the cylindrical case, or frame, containing within it the Spring of the watch.

Spring-Compasses. See Compasses.

Spring of the Air, or its elastic force. See Air, and Elastioity.

Spring-Tides, are the higher tides, about the times of the new and full moon. See Tide.


, or Elastic Body. See Elastic Body.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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