Page:Cyclopaedia, Chambers - Volume 2.djvu/110

 LOC

among the Apothecaries. The Latins call it LinBus, and the Greek $Hhiyp& t by reafon the manner of taking it is by licking. There are various kinds of Laches. See Ec- legma.

LOCHIA, or Lodes, the Evacuations confequent on the Delivery of a Woman in Child-bed. As foon as the Vtertts is eafed of its Load, its Fibres, as alfo thofe of the Peritonseum, Mufcles of the Abdomen, £S?c. which had been extremely diftendcd during the laft Period of Geftation, begin to contract themfelves and their Veflels 5 particularly the Uterus, which by this means expels the .Blood amafs'd in it. At firft, pure Blood is evacuated, and in confiderable quantities; afterwards it is diluted, and comes out more fparingly 5 at length it becomes vifcid, pale, i$c. Thcfe are called the Laches.

LOCK, a little Inllrument ufed for the fhutting of Doors, Chefts, &c. The Lack is reckon'd the Mailer- piece in Smithery; a great deal of Art and Delicacy being required in contriving and varying the Wards, Springs, Bolts, £i?c. and adjulting them to the Places where they are to be ufed, and the various Occafions of tiling them.

From the various Structure of Lacks, accommodated to their different Intentions, they acquire various Names. Thofe placed on outer Doors are called Stack-Lacks; thofe on Chamber-Doors, Spring-Loch; thofe on Trunks, Tnmk-Loch, Tad Lacks, Sic. Of thefe, the Spring-lack is the moft confiderable, both for its Frequency and the Cu- rioftty of its Structure. Its principal Parts are, the Main- Plate, the Cover Plate, and the Pin-hole : To the Main- Plate belong the Key-hole, Top-hook, Crofs-wards, .Bolt, Bolt-toe or Bolt-nab, Drawback Spring, Tumbler, Pin of the Tumbler, and the Staples; to the Cover- Plate belong the Pin, Main-ward, Crofs-ward, Step-ward or Dap-ward; to the Pin-hole belong the Hook-ward, Main Crofs-ward, Shank, the Pot, or Bread, Bow-ward, and Bit. See Smithery.

LOCULAMENTA, flriflly fignifies little Pockets; and thence the Term is made ufe of in Botany, to ex- prefs thofe little diftinct Cells, or Partitions, within the common Capjula Seminalis of any Plant : as thofe within the Seeds of Poppies, &c.

LOCUS, or the Place of any Body, is rightly diftin- guifhed into Abfolute and Relative; and fo ought Space to be accounted. The Locus slbfoluuts, or Trimarius, of any Body, is that part of the abfolute and immovable Space, or extended Capacity to receive all Bodies, which this individual one takes up. Locus Relativus, or Secundaria, is that apparent and fenfible Place, in which a Body is determined to be placed by ourfelves, and with relation to other adjoining or contiguous Bodies. The Locus Jp- f tains is a Term in Optics : fee apparent Tlace of any Ob- jell. It is alfo, in Aftronomy that Place, in which any Planet or Star appears, when view'd from an Eye at the fenfible Horizon.

LOCUS GEOMETRICUS, a Line by which an In- determinate Problem is folved. This, if a right Line fuffice for the Conftruction of the Equation, is called Lo- cus ad ReBum; if a Circle, Locus ad Circulum; if a Para- bola, Locus adTarabolam j if an Ellipfis, Locus ad Ellipjin 5 and fo of the reft of the Conic Sections.

The Loci of fuch Equations as are Right Lines or Cir- cles, the Antients call'd Tla'm Loci; and of thofe that are Parabolas, Hyperbolas, S?c. Solid Loci. Wolfius, and othersof the Moderns, divide the Loci more commodioufly into Orders; according to the Number of Dimcnfions to whici. the Indeterminate Quantities rife. Thus it will be a Normofthe firft Order if the Equation x~ay.c. A ioctu of the fecond or quadrate Order, if y' = ax, or y = «_x, Stc. A Loa.s of the third or cubic Order, if y' = a*%, orj'=(jxix', £jc.

The better to conceive the Nature of the Locus, fup- pofe two unknown and variable right Lines A P, PM, (■frfr 3>4- Plate Analysis _) making any given Angle A P M with each other; the one whereof, as A P, we call x, having a fixed Origin in the Point A, and extending itfelf indefinitely along a right Line given in Pofition; the other P M, which we call y, con- tinually changing its Pofition, but always parallel to it- felf. An Equation only containing thefe two unknown Quantities x and y, mix'd with known ones, which ex- preffes the Relation of every variable Quantity A P (x) to its correfpondent variable Quantity PM(j) : the Line paffing thro' the Extremities of all the Values of y, i. e. thro' all the Points M, is called a Geometrical Locus, in ge- neral, and the Locus of that Equation in particular.

All Equations whofe Loci are of the firft Order, may be reduced to fome one of the four following Formula's : h x h x bx

1. y - —. i.y = 7 + c. 5. y = --'. 4-

bx

y=zc— — Where the unknown Quantity^' is lup-

(4^)

LOG

pored always to be freed from Fraflions, and the Frac> tton that multiplies the other unknown Quantity x, to be

reduced to this Expreffion -, and all the known Terms' to this c. Thei-ocw of the firft Formula being already determined :

To find that of the fecond, y =3 r- "5 in the

a Line A P, (fig. 5.) take A B = a, and draw B E =5, A D = c, parallel to P M. On the fame fide A P draw the Line A E of an indefinite length towards E and the indefinite {trait Line D M parallel to A E. I fay, the Line D M is the Locus of the aforefaid' E- quation or Formula; for if the Line M P be drawn from any Point M thereof parallel to A Q, the Tri- angles ABE, APF, will be fimilar : and" therefore

ABO): BE(J)!: AP( 8 ):PF= -; and confe-

a

quently P M (y) = P F (— ) + F M 0).

bx To find the Locus of the third Form v = — — c pro-

a r

ceed thus. Affutne A B =a, (Fig. «.) and draw the right Lines BE=Z>, A D =c, parallel to PM, the one on one fide A P, and the other on the other fide 3 and thro' the Points A, E, draw the right Line A E of an indefinite length towards E, and thro' the Point D the Line D M parallel to A E : I fay, the indefinite right Line G M fhall be the Locus fought; for we ihall have always

PM(yJ = PF f—"^ -PJIft).

Laftly To find the £»„„ f the f ourtn Formula. b x y = c ——> in A P ( F 'S- 70 tike A B =f«, and draw

B E = b, A D = c, parallel to P M, the one oh one, fide A P, and the other on the other; and thro' the Points A, E, draw the Line A E indefinitely towards E, and thro' the Point D draw the Line D M parallel to A E. I fay, D G fhall be the Locus fought; for if the Line M P be drawn from any Point M thereof parallel to A 6, then we

fhall have always P M (y) sa F M (c) — P F (-O

Hence it appears, that all the Lad of the firft Degree are flrait Lines, which may be eafily found, becaufe all their Equations may be reduced to fome one of the fore- going Formula's.

All Loci of the fecond Degree are Conic Sections, viz. either the Parabola, the Circle, Ellipfis, or Hyperbo- la; if an Equation therefore be given, whofe Locks is of the fecond Degree, and it be required to draw the Conic Section, which is the Locus thereof J firft draw a Parabola, Ellipfis, and Hyperbola; fo, as that the Equations expreffing the Natures thereof, may be as compound as poffible : In order to get general Equa- tions or Formula's, by examining the peculiar Pro- perties whereof, we may know which of thefe Formu- la's the given Equation ought to have regard to; that is, which of the Conic Sections will be the Locus of the propofed Equation. This known, compare all the Terms of the propofed Equation with the Terms of the general Formula of that Conic Section which you have found will be the Locus of the given Equation; by which means you will find how to draw the Section which is the Locus of the Equation given.

For example, let A P (x) P M (y), be unknown and variable ftrait Lines, (Fig. 8.) and let m,n,p,r,s, be given right Lines : In the Line A P take A B =: m, and draw B E = 11, AD=r, parallel to PM, and thro' the Point A draw AE=e, and thro' the Point D the indefinite right Line D G parallel to A E. In DG take DC=>, and with C G as a Diameter, having its Ordinates parallel to P M, and the L'ne C-H =», as the Parameter, defcribe a Parabola C M : then the Portion theteof included in the Angle PAD will be the Locus of the following general Formula.

— ep

+ p:

For if from any Point M of that Portion there be drawn the right Line M P, making any Angle A P M with M P; the Triangles ABE, APF, fhall 'be fimilar, therefore

ABC»: AE(<0 :: A P (V) :AF or DG = - . And

m

Cccecc ^g