Page:Cyclopaedia, Chambers - Supplement, Volume 2.djvu/538

 SPR

SPORTS, In the cuftoms of Flanders, were in great vogue through Flanders and the Low-Countries, fome centuries ago. Every city had a fokmnity or" this kind peculiar to it- felf : thus Bruges had that called the Forejisr ; Valenciennes the Prhice of Pleafantry, and the Prince of the Horfe-comb ; Cambray the King of Ribaldry ; and Bouchain the Provofi of Sots. Lille, one of the richeft towns in Flanders, was not behind hand with its neighbours in celebrating ftoffs, by the magnificence and diversions whereof, to draw together a vaft concourfe of people from all parts. One of the chief of thefe diver! ifements was called the King of the Spinet, Roy (TEpinette ; which was celebrated with a great deal of pomp and ihew. See HifL Acad. Infcript. Tom. 4. p. 452, feq,

SPOT (Cycl.) — Spot, in ornithology, the name of a particu- lar fpecies of pigeon, called by Moore the columba jnaculata. It is of the fize of a (mall common pigeon, and was brought over to England from Holland. This fpecies has always a fpot upon its head, juft above its beak, from whence it has its name. The feathers of the tail are always of the fame colour with tin's fpot, and the reft of the body is all white. The fpot and tail are black in fome, red in others, and yel- low in others. They look very beautiful when they fpread their tails and fly, and are a diftincT: fpecies, as they always produce young ones of their own marks. Mosre's Columb. p. 44.

SPRING, (Cycl.) in mecanics, is ufed to fignify a body of any fhape, perfectly elaftic.

Length of a Spuing may, according to its etymology, fignify the length of any elaftic body, but it is particularly ufed by Dr. jurin to fignify the greateft length to which a fpring can be forced inwards, or drawn outwards, without preju- dice to its elafticity. He obferves this would be the whole length, were the fpring confidered as a mathematical line ; but in a material fpring, is the difference between the wholi length, when the fpring is in its natural fituation, or the fituation it will reft in when not difturbed by any external force, and the length or fpace it takes up when wholly compreiTed and clofed, or when drawn out.

Strength, ox force of a Spring, is ufed for the leaft force or weight, which, when the fpring is wholly comprefTed or clofed, will reftrain it from unbending itfelf. Hence alfo the force of a fpring bent, or partly clofed, is ufed for the leaft force or weight, which, when the fpring is bent thro' any fpace lefs than its whole length, will confine it to the ftate it is then in, without fuffering it to unbend any farther.

The theory of fprings is founded on this principle, ut tenjio, fie vis ; that is, if a fpring be forced or bent inwards, or drawn outwards, or anyway removed from its natural 1 fitua- tion, its refiftance is proportional to the fpace by which it is removed from that fituation.

This principle was verified by the experiments of Dr. Hook b , and fince him by thofe of others, particularly by the accu- rate hand of Mr. George Graham.— [ b Le&ures de potentia rejlitutiva, 1678.]

For the better in elligence of this principle, on which the whole theory of fprings depends, fuppofc a fpring C L rett- ing with the end L againft any immoveable fupport, but otherwife lying in its natural fituation, and at full liberty ; then if this fpring be prefled inwards by any force p, or from C towards L, through the fpace of one inch, and can be there detained by that force p, the refiftance of the fpring, and the force p, exaclly counterbalancing one another j then will the force 2 p bend the fpring through the fpace of two inches, 3 p through three inches, 4 p through four inches, &c. The fpace CI (Fig. 2.) through which the fpring is bent, _ or by which its end C is removed from its natural fituation, being always proportional to the force which will bend it fo far, and will detain it fo bent.

SPR

c /

And if one end L be fattened to an immoveable fupport, (F' g- 3-) and the other end C be drawn outwards to /, and be there detained from returning back by any force p, the fpace C /, through which it is fo drawn outwards, will be always proportional to the force p, which is able to detain it in that fituation.

And the fame principle holds in all cafes, where the fpring is of any form whatsoever, and is in any manner whatfoever forcibly removed from its natural fituation. It may be here obferved, that the fpring, or elaftic force of the air, is a power of a different nature, and governed by different laws from that of a material fpring. For fuppofing the IjheL C (Fig. I.) to reprefent a cylindrical volume of air,

wbich by compreffion is reduced to L /, (Fig. 2.) or by di- latation is extended to L /, (Fig. 3.) its elaftic force will be reciprocally as LI; whereas die force, or refiftance of a fpring, will be directly as C /.

This principle being premifed, Dr. Jurin gives us a general theorem concerning the act ion of a body ftriking on one end of & fpring, while the other end is fuppofed to reft againft an immoveable fupport. And left any abjection lhould be formed againft the poffibility of an immoveable fupport, fince any. body, how great foever, may be moved out of its place by the leaft force, he obferves, that the objection may eafily be removed. Thus, if the fpring L M "be fuppofed continued to N, fo that N ]L LN = LM, if a body

ewA/^Wvw^ Al m ; witn any ve]oci ty

in the direction M L, (hikes one end of the fpring, and a body N, at the fame time, with an equal velocity, and a contrary direction, N L (hikes the other end N of the continued fpring, the point L, the end of the firft fuppofed fpring will be im- moveable.

Thecrem. IS a. fpring of the ftrength P, and the length C L, lying at full liberty upon an horizontal plane, reft with one end L againft an immoveable fupport ; and a body of the weight M, moving with the velocity V, in the di- reaion of the axis of the fpring, ftrike directly on the other end C, and thereby force the fpring inwards, or bend it through any fpace C B ; and a middle proportional C G be 'taken between the line

r r M

and 2 a, a

being the height to which a heavy body would af- cend in vacuo with the velocity V ; and upon the radius R =z C G be erect- ed the qu ad rant of a circle G.FA: then, i°. When the fpring n bent through any right line of rhat quadrant, as vi the body M, is to be C B, the velocity v of the original velocity V, as the co-

BF R

fine to the radius; that is, v = V x

2 n. The time t of bending the fpring through the fame fine

C B, is to T the time of a heavy body's afcending in vacuo

with the velocity V, as the correfponding arch to 2 a ; that

t. G I is, / = T x.

2 a

The doctor gives a demonflration of this theorem, and de- duces a great many curious corollaries from it. Thefe he divides into three claffes. The firft contains fuch corolla- ries as are of more particular ufe when the fpring is wholly clofed, before the motion of the body ceafes. The fecond comprehends thofe relating to the cafe, when the motion of the body ceafes before the fpring is wholly clofed. And ' ......

The third, in cafe the motion of the body ceafes at the in- ftant that the fpring is wholly clofed.

We (hall mention fome of the laft ciafs, as the moft fimple ; having firft premifed, that P = ftrength of the fpring, L = its length, V = the initial velocity of the body clofing the fpring, M r= its mafs, t = time fpent by the body in clof- ing the fpring, A = height from which a heavy body will fall in vacuo in a fecond of time, a =z the height to which a body would afcend in vacuo with the velocity V, C = the velocity gained by the fall, m = the circumference of a circle, whofe diameter is 1, Then,

l°. If the motion of the body ftriking the fpring ceafe, when it is wholly clofed, the initial velocity V is equal to

C ^aMA-

initial velocity V is proportional to ,/

PL

equal to

2°. The

3 . If P L be given, either in the fame or in different fprings, the initial velocity V is reciprocally as ^M. 4°. The produd of the initial velocity, and the time fpent in clofing the fpring, or V t is equal to 1" x ?i£L aI1 d

A A

is proportional to L the length of the fpring. 5°. The initial quantity of motion, or M V,

6". MV is proportional to ,/PLM, or to P t. And if P L be given, either in the fame or different fprings, M V is as j/M.

p 7 . If— be given, either in the fame or in different fprings,

the initial quantity of motion is as the length of the fpring into the time of bending it.

8°. If a quantity of motion M V bend a fpring through

its whole length, and be confirmed thereby, no other

1 quantity