Cecil, W5DXP wrote:
"In such problems we are often most interested in the ratio of power in
the reflected wave to that in the incident wave, and the ratio is given
by the square of the magnitude of [rho] as can be shown by considering
the Poynting vectors:"

Terman agrees. On page 98 of his 1955 opus, Terman shows the value of
[rho] vs. SWR.

On page 97 Terman writes:
"This definition of standing-wave ratio is sometimes called the voltage
standing-wave ratio (VSWR) to distinguish it from the standing-wave
ratio expressed as a power ratio which is (Emax/Emin)squared."

Best regards, Richard Harrison, KB5WZI