CENTER. 



MUtaifiipg a single head of flowers ; they 

 have u strong odour, so as to be very of- 

 fensive 10 many people ; they are purple, 

 \vime, or flesh-coloured ; there is also a 

 variety with tistula flowers, and another 

 \viui fringed flowers ; but these degene- 

 rate in a few years, however carefully the 

 seeds may be saved. 



CENTER, in carpentry, an arch fram- 

 ed of wood, upon which a stone or brick 

 arch is turned. 



CE'HTER, or CENTRE, in geometry, a 

 point equally distant from the extremities 

 ot a line figure, or body. 



CENTER of a circle, a point in the mid- 

 dle of a circle, or circular figure, from 

 which all lines drawn to the circumfe- 

 rence are equal. 



CENTER o/'a conic section, a point where- 

 in the diameters intersect each other. In 

 the ellipsis, this point is within the fi- 

 gure ; and in the hyperbola, without. 



CENTER oj a curve of the higher kind, the 

 point wher. two diameters concur. When 

 all the diameters concur in the same 

 point, Sir Isaac Newton calls it the gene- 

 ral cenier. 



CENTER of an ellipsis, the point where 

 the transverse and conjugate diameters 

 intersect each other. 



CENTER of gravitation and attraction, in 

 physics, thai point to which the revolving 

 planet or comet is impelled or attracted 

 by the impetus of gravity. 



CEJSTKK of gravity, in mechanics, that 

 point about winch all the parls of a body 

 do, in any situation, exactly balance each 

 other. Hence, 1. If a body be suspended 

 by this point as the center of motion, it 

 will remain at rest in any position indiffe- 

 rently. 2. If a body be suspended in any 

 other point, it can rest only in two posi- 

 tions, viz. when the said center of gravi- 

 ty is exactly above or below the point of 

 suspension. 3. When the center of gra- 

 vity is supported, the whole body is 

 kept from failing. 4. Because this point 

 has a constant endeavour to descend to 

 the center of the earth ; therefore, 5. 

 "When the point is at liberty to descend, 

 the whole body must also descend, ei- 

 ther by sliding, rolling, or tumbling 

 down. 6. The center of gravity in regu- 

 lar uniform and homogeneal bodies, as 

 squares, circles, &c. is the middle point 

 in a line connecting any two opposite 

 points or angles ; wherefore, if such a 

 line be bisected, the point of section will 

 be the center of gravity. 



To find the center of gravity of a tri- 

 angle. LetBG (Plate 111. Miscell. fig. 

 1,) bisect the base A C of the triangle 

 A B C, it will also bisect every other line. 



D E drawn parallel to the base, conse- 

 quently the center of gravity of the tri- 

 angle will be found somewhere in the 

 line B G. The area of the triangle may 

 be considered as consisting of an infinite 

 number of indefinitely small parallelo- 

 grams, D, E, b, a, each of which is to be 

 considered as a weight, and also as the 

 fluxion of the area of the triangle, and so 

 may be expressed by 2 y x, (putting B F 

 = x, and F E = y} if this fluxionary 

 weight be multiplied by its velocity x, 

 we shall have 2 y x x for its momentum. 

 Now put B G = a and A C = b, then 

 B G (a) : A C (b) :: B F (#) : D E = 



= 2 y, therefore the fluxion of the 

 weight 2 y x = X *; and the fluxion of 

 : , whence 

 divided 



the momenta 2 y x x = 

 the fluent of the latter, viz. 



by the fluent of the former, viz. -^ will 



2 

 give x for the distance of the point 



3 



from B in the fine B F, which has a velo- 

 city equal to the mean velocity of all the 

 particles in the triangle D B E, and is 

 therefore its center of gravity. Conse- 

 quently the centre of gravity of any tri- 

 angle A B C, is distant from the vertex 

 B 2 B G, a right line drawn from the an- 

 gle B bisecting the base AC. And since 

 the section of a superficial or hollow r cone 

 is a triangle, and circles have the same 

 ratio as their diameters, it follows that the 

 circle, whose plane passes through the 

 center of gravity of the cone, is .2 of the 

 length of the side distant from the vertex 

 of the said cone. 



To find the center of gravity of a solid 

 cone. As the cone consists of an infinite 

 number of circular areas, which may be 

 considered as so many weights, the cen- 

 ter of gravity may be found as before, by 

 putting B E == x (fig. 2.) B G = a, the 

 circular area D F E = y, and A G C = b ; 

 and from the nature of the cone, a 1 : x 3 - 



ion of the weights ; and y x x -. 



=x fluxion of the momenta, whence the 



fluent of the latter, viz. - -, divided by 



the fluent of the former 



will give 



