σ = \sqrt{\frac{∑_{i=0}^{N} (v_{i} − v̄)^{2}}{N}}

(luminosity)^{A} (size)^{B} (velocity dispersion)^{C} = constant

2 ∗ (kinetic energy) + (potential energy) = 0 2K + U = 0

K = −\frac{1}{2}U

U = −\frac{GMm}{R}

K = \frac{1}{2}mv^{2}

v^{2} = \frac{GM}{R}

if M ∝ L → v^{2} ∝ L v^{2}R = 2GM

σ^{2} = K (\frac{M}{R})

σ^{2} ∝ \frac{L}{R}

L = μ (πR^{2}) → R ∝ L^{1/2} L ∝ σ^{4} (luminosity)^{A} = \frac{constant}{(size)^{B} (velocity dispersion)^{C}}