or nourish prejudices and ostentation. The first books which gave him a relish for the study of philosophy, were those of Des Cartes; for though he afterwards followed opinions contrary to those of that philosopher, yet he admired him for his perspicuity. Mr. Locke also applied himself to the study of physic, in which the learned Sydenham allows that he made a very great progress; but he never took upon himself that profession. In 1664, he went to Germany, was secretary to Sir William Swan, envoy from the English court to the elector of Brandenburgh, but in less than a year returned to England, where he applied himself to the study of natural philosophy at Oxford, and there became acquainted with the lord Ashley, afterwards earl of Shaftes bury, who introduced him into the conver sation of the most learned men of that time, with whom he contracted a strict friend ship, which lasted as long as his life. In 1668, he attended the earl and countess of Northumberland into France. At his return to England, he lived with the lord Ashley, as he had done before, and took upon himself the care of his son's education. That nobleman being made lord chancellor of England, in 1672, appointed him secretary of the presentations, which place he held till the end of 1673, when the earl resigned the great seal. Mr. Locke was the same year made secretary to a commission of trade; but that commission being dissolved in December 1674, and finding him self threatened with a consumption, he went the next year to Montpellier, where he staid a considerable time, and there became acquainted with the lord Herbert, earl of Pembroke. Some time after, the earl of Shaftesbury being retired to Holland, Mr. Locke went to him there, and contracted an intimate friendship with Limborch, Le Clerc, and other learned men. He was then accused at court of having composed certain tracts against the government, printed in Holland, on which his place of student of Christ-church was taken from him, by a special order from king Charles II.; but these tracts were afterwards discovered to be written by another person. After the death of king Charles II. Mr. William Penn offered his interest to procure a pardon for him from king James II.; but Mr. Locke said he had no need of a pardon, since he had not been guilty of any crime. In 1687, the English envoy at the Hague demanded him, and 83 other persons, to be delivered up by the States-General, for being concerned in the duke of Monmouth's rebellion, though he held no correspondence with him. This obliged Mr. Locke to keep himself concealed for several months, till his innocence being known, he again appeared in public. In 1689, he returned to England, in the fleet which convoyed the princess of Orange. He might then have easily obtained a very considerable post;

but be contented himself with being one of the commissioners of appeals, worth 2001. per annum. About the same year, he was asked to go abroad, as envoy to the emperor, or any other court where the air would be most suitable to him; but he waved it on account of his ill state of health. In 1695, he was appointed one of the commissioners of trade and plantations, a place worth 10001. per annum, which he dis charged with great success till the year 1700, when he resigned, on account of his asthmatic disorder. After he had resigned his commission, he lived at Oates, in Essex, a country seat of Sir Francis Masham's, where he spent the remainder of his life in the study of the Scriptures, and died there the 28th of October, 1704, in the 73d year of his age. His writings will immortalize his name. The earl of Shaftesbury, author of the Characteristics, though in one place he speaks of Mr. Locke's philosophy with severity, yet observes, concerning his Essay on the Human Understanding, in general, "that it may qualify men as well for business and the world, as for the sciences and the university." Whoever is acquainted with the barbarous state of the philosophy of the human mind, when Mr. Locke undertook to pave the way to a clear notion of knowledge, and the proper methods of pursuing and advancing it, will be surprised at this great man's abilities; and plainly discover how much we are beholden to him for any considerable improvements that have been made since. His Discourses on Government, Letters on Toleration, and his Commentaries on some of St. Paul's Epistles, are justly held in the highest estimation.

LOCKED JAW. Trismus. A species of tetanus. See TETANUS.

LOCKER GOULAND'S, in botany. See TROLLIUS.

LOCKER. 8. (from lock.) Any thing that is closed with a lock; a drawer (Crusoe). LO'CKET. s. (loquet, French.) A smalt lock; any catch or spring to fasten a necklace, or other ornament (Hudibras).

LO'CKRAM. s. A sort of coarse linen (Shakspeare).

LOCRI, a town of Magna Græcia, in Italy, on the Adriatic, not far from Rhegium. It was founded by a Grecian colony, about 757 years. The inhabitants were called Locrenses (Virg.)

LOCRIS, a county of Greece, whose inhabitants are known by the name of Ozolæ, Epicnemidii, and Opuntii,

LO'CRON. 8. A kind of ranunculus. LOCOMOTION. s. (locus and motus, Lat.) Power of changing place (Brown).

LOCOMOTIVE. a. (locus and movco, Lat.) Changing place; having the power of removing or changing place (Derham).

LO'CULAMENT. In botany, the cell of a pericarp or fruit. Concameratio vacua pro seminum loco. Pericarpium uniloculare, bi

This motion the Greeks distinguished into two kinds: the one continued, covey, the other disjunct, disanuarien.

Instances of the first kind are in speak ing; of the second, in singing; and this they called melodic motion, or what was adapted to singing. Ptolemy, in like manner, divides sounds of unequal pitch, 42285 es, into continued and discrete, and says the first kind are improper, and the second proper, for harmony.

Aristides Quintilianus interposes a third kind of motion between the two here mentioned, such as that of a person reciting a poem.

Locus geometricus denotes a line, by which a local or indeterminate problem is solved. See LOCAL PROBLEM.

A locus is a line, any point of which may equally solve an indeterminate problem.

This, if a right line suffice for the construction of the equation, is called locus ad rectum; if a circle, locus ad circulum; if a parabola, locus ad parabolum; if an ellip sis, locus ad ellipsim; and so of the rest of

the conic sections.

The loci of such equations as are right lines, or circles, the ancients called plain or plane loci; and of those that are parabolas, hyperboles, &c. solid loci.

Apollonius of Perge wrote two books on Plane Loci, in which the object was "to find the conditions under which a point varying in its position, is yet confined to trace a straight line or a circle given in position.' These books are lost; but attempts have been made at resterations, by Schooten, Fermat, and R. Simson; the treatise De Loris Planis, of the latter-mentioned geometer, published at Glasgow, in 1749, is a very elegant work. We shall here specify some of t chief propositions relative to plane loci.

1. If a straight line, drawn through a given point to a straight line given in position, be divided in a given ratio, the locus of the point of section is a straight line given in position.

2. If a straight line drawn through a given point to the circumference of a given

circle, be divided in a given ratio, the locus of the point of section will also be the circumference of a given circle.

3. If through a given point two straight lines be drawn in a given ratio, and containing a given angle; if the one terminate in a given circumference, the other will also terminate in a given circumference.

4. The middle point of a given straight line which is placed between two lines that include a right angle, lies in the circumference of a given circle.

5. If a straight line drawn from a given point to a straight line given in position, contain a given rectangle, the locus of its point of section will be a given circle.

6. If two straight lines in a given ratio, and containing a given angle, terminate in two diverging lines which are given in position, the locus of their vertex will be likewise a straight line given in position.

7. If from two given points there be drawn two straight lines, of whose squares the difference is given, the locus of their point of concourse will be a straight line given in position. In other words, if the base of a triangle, and the difference of the squares of the two other sides be given, the vertex of the triangle will fall in a right line given in position.

8. If from two given points there be drawn two straight lines in a given unequal ratio, the locus.of their point of concourse is a given circle: if the ratio be one of equality, the locus is a right line given in position.

9. If from given points there be drawn straight lines, whose squares are together equal to a given space, their point of concourse will terminate in the circumference of a a given circle.

10. If the base and vertical angle of a plane triangle be given, the vertex will fall in a given circle.

11. If in any triangle the base be given, and the sum of the squares of the two other sides, the locus of the vertex is a given circle.

12. If right lines be drawn from a given point, to cut a given circle, and from the points of intersection there be taken, upon these lines (on either side), lines in a constant given ratio to the distance between the respective points of intersection and the given point; the locus of the points so determined will be a circle.

13. If two circles cut each other, and through either point of intersection a right line be drawn, cutting both the circles, then, if a right line be always taken thereon, from one of those points, in a given ratio to the part intercepted between the circles, the locus of the points so determined will be a circle.

14. If two circles cut each other, and through either intersection a right line be drawn, cutting both the circles, then, if a right line be always taken thereon, from

one of those points, in a given ratio to the part between the other point and intersection, the locus of the points so determined will be a circle.

15. If triangles be inscribed in a given segment of a circle, and from the vertex, on either side (produced if necessary) there be taken (either way) a right line always in a constant ratio to either of the sides, or to their sum, or difference, the loci of the points so determined will be circles.

16. If a triangle be inscribed in a given segment of a circle, and lines be drawn from the vertex of the triangle to the vertices of the opposite segments, and parts he taken either way thereon, from the vertex of the triangle, in any constant ratio to either of the sides, the loci of the points so determined will be circles. Also, if those points be taken on the lines drawn to the vertex of the given seg ment in any constant ratio to the difference of the sides of the triangle; or on the lines drawn to the vertex of the opposite segment, in any constant ratio to their sums, the loci of the points so determined will be circles.

Wolfius, and most other moderns after him, divide the loci very commodiously into

α

y= +c; in the line AP (Pl. 99. fig. 1.) take AB-a, and draw BE-b, AD-c, parallel to PM. On the same side AP, draw the line AE of an indefinite length towards E, and the indefinite straight line DM parallel to AE : the line DM is the locus of the aforesaid equation, or formula; for if the line MP be drawn from any point M thereof parallel to QA, the triangles ABE, APF, will be similar; and

To find the locus of the third form, y=

The better to conceive the nature of the locus, suppose two unknown and variable right lines AP, PM, (Pl. 93. figs. 11, 12.) making any given angle APM, with each other; the one whereof, as AP, we call x, having a fixed origin in the point A, and extending itself in definitely along a right line given in position; the other PM, which we call y, continually changing its position, but always parallel to itself; and moreover an equation only contain

ing these two unknown quantities x and y, mixed with known ones, which expresses the relation of every variable quantity AP (x) to its correspondent variable quantity PM (y): the line passing through the extremities of all the values of y, i. e. through all the points M, is called a geometrical locus, in general, and the locus of that equation in particular.

All equations, whose loci are of the first order, may be reduced to some one of the four following formula:

b x

a

c, proceed thus. Assume AB=a, (P). 99. fig. 2.) and draw the right lines BE-6, ADc, parallel to PM, the one on one side AP, and the other on the other side; and through the points A, E, draw the right line AE of an indefinite length towards E, and through the point D, the line DM parallel to AE: the indefinite right line GM shall be the locus sought; for we shall have always PM

(y)=PF (*)—FM (c).

Lastly, to find the locus of the fourth for

b x

a

mula, y=c -; in AP, (Pl. 99. fig. 3.) take AB-a, and draw BE=b, AD=C, parallel to PM, the one on one side AP, and the other on the other side; and through the points A, E, draw the line AE indefinitely towards E, and through the point D draw the line DM parallel to AE. Then DG shall be the locus sought; for if the line MP be drawn from any point M thereof, parallel to AQ; we shall have always PM (y)=FM

(c)—PF (*).

Hence it appears, that all the loci of the first degree are straight lines; which may be easily found, because all their equations may be reduced to some one of the foregoing formulæ.