Circumference, or PERIPHERY — Chambers's Encyclopaedia

Circumference, or PERIPHERY, the curve which incloses a circle, ellipse, oval, cardioid, or other plane figure. In figures bounded by straight lines, as the triangle, square, and polygon, the term perimeter is employed to designate the sum of all the bounding lines taken together. The length of the circumference depends partly on the nature of the curve; thus, that of the Circle (q.v.) = $2\pi r = \pi d$ ; and that of the Ellipse (q.v.)

= 2\pi a \left\{ 1 - \left(\frac{1}{2}\right)^2 e^2 - \left(\frac{1.3}{2.4}\right)^2 e^4 - \left(\frac{1.3.5}{2.4.6}\right)^2 e^6 - \&c. \right\}

where $a$ is the semi-axis major, and $e$ the eccentricity.