CEN 



CEN 



,q/ magnitude, of any homoge- 

 neal body, the same with the center of 

 gravity. 



CENTER of motion, that point which 

 remains* at rest, while all the other 

 pi.rts o( a body move about it And this 

 is the same in uniform bodies of the 

 s-iiDc- matter throughout, as the center of 

 gnu ity. 



CENTER of oscillation, that point in a 

 pendulum, in which, if the weight of the 

 several parts thereof were collected, 

 each vibration would be performed in 

 the same time as when those weights 

 are separate. This is the point from 

 whence the length of a pendulum is 

 measured, which, in our latitude, in a 

 pendulum that swings seconds, is 39 

 inches and _* 



The center of suspension is the point 

 on which the pendulum hangs. 



Jl general rule for finding the center of 

 oscillation. If several bodies be fixed to an 

 inflexible rod suspended on a point, and 

 each body be multiplied by the square of 

 its distance from the point of suspension, 

 and then each body be multiplied by its 

 distance from the same point, and all the 

 former products, when added together, 

 be divided by all the latter products add- 

 ed together, the quotient which shall 

 arise from thence will be the distance of 

 the center of oscillation of these bodies 

 from the said point. 



Thus if C F (fig. 8) be a rod on which 

 are fixed the bodies A, 15, D, &c. at the 

 several points A, B, D, &c. and if the body 

 A be multiplied by the square of the dis- 

 tance C A, and B be multiplied by the 

 square of the distance. C B, and so on for 

 the rest ; and then if the body A be mul- 

 tiplied by the distance C A, and B be 

 multiplied by the distance C B, and so on 

 for the rest; and if the sum of the pro- 

 ducts arising in the former case be divid- 

 ed by the sum of those which arise in the 

 latter, the quotient will give C Q the dis- 

 tance of the center of oscillation of the 

 bodies A, B, D, &c. from the point C. 

 To determine the center of oscillation of 

 the rectangle R I H S (fig. 9) suspended 

 on the middle point A of the side R I, and 

 oscillating about its axis R I. Let R I = 

 S H = a, A P = x, then will P p = dx 

 and the element or the area, consequently 

 one weight = ad x and its momentum 

 a x d x. Wherr fore sax z dx:saxdx 

 = JL a #3 : $ a x- = 2 Xf indefinitely ex- 

 presses the distance of the center of os- 

 cillation fram the axis of oscillation in the 

 segment R C D I. If then for x be sub- 

 stituted the altitude of the whole rec- 



tangle R S = b, the distance of the cen- 

 ter of oscillation from the axis will be 

 found = -| 



The center of oscillation in an equila- 

 teral triangle S A H oscillating about its 

 axis R 1, parallel to the base S H, is found 

 at a distance from the vertex A equal to 

 | A Ethe altitude of the triangle. 



The center of oscillation in an equila- 

 teral triangle S A H oscillating about its 

 base S H, is found at a distance from the 

 vertex A = A E. 



For the centers of oscillation of para- 

 bolas and curves of the like kind oscillat- 

 ing about their axes parallel to their bases, 

 they are found as follows. In the apol- 

 lonian parabola, the distance of the cen- 

 ter of oscillation from the axis = * 

 AE. 



In the cubical paraboloid, the distance 

 of the center from the axis _7 A E. In a 

 biquadratic paraboloid, the distance of the 

 center from the axis = _?_ A E. 



CENTER of percussion, in a moving body, 

 that point wherein the striking force is 

 greatest, or that point, with which, if the 

 body strikes against any obstacle, no 

 shock shall be felt at the point of suspen- 

 sion. 



The center of percussion, when the 

 striking body revolves round a fixed 

 point, is the same with the center of os- 

 cillation, and consequently may be deter- 

 mined by the same rule. 



Hence a stick of a cylindrical figure, 

 supposing the center of motion at the 

 hand, will strike the greatest blow at a 

 distance about two-thirds of its length 

 from the hand. 



The center of percussion is the same 

 with the center of gravity, if all the 

 parts of the striking body be carried 

 with a parallel motion, or with the same 

 celerity. 



CENTER of a parallelogram, or polygon, 

 the point in which its diagonals inter- 

 sect. 



CENTER of a sphere, a point in the mid- 

 dle, from which all lines drawn to the 

 surface are equal. Hermes Trismegistus 

 defines God an intellectual sphere, whose 

 center is every where, and circumference 

 no where. 



CENTINEL, or CENTRT, in military 

 language, is a private soldier, from the 

 guard posted upon any spot of ground, to 

 stand and watch carefully for the security 

 of the said guard, or of any body of troops, 

 or post, and to prevent any surprise from 

 the enemy. All centinels are to be very vi- 



