Note 42 — Chapter V · ToC

If c be the depth of the focus, a the intensity at unit distance from the focus, and y the intensity on the surface at distance x from the epicentre, then

y = a / (c² + x²)

The inclination of the curve at any point is given by

dy / dx = -2ax / (c² + x²)²,

and this is a maximum when

d²y / dx² or (3x² - c²) / (c² + x²)³

is zero, which is satisfied when c = x √3