1. bel scale

In the early 1920's in order to quantfy the degree of signal loss along telephony cables Bell Laboratories came up with the bel (B) scale, named after Alexander Graham Bell - this scale was simply a logarithmic comparison of two signal powers (one at the start of a cable and one at the end). The definition was:

(2.1)

Where L denotes the relative difference between the two powers P₂ and P₁ on a logarithmic scale.

2. decibel scale

However, this bel scale was found to be too coarse so the scale was modified to give the decibel scale where individual steps on the scale are one-tenth the size of those on the bel scale. The decibel scale is given by:

(2.2)

Where L again denotes the relative difference between the two powers P₂ and P₁ on a logarithmic scale.