Why is $r$ used to denote correlation?

Why was the symbol $$r$$ chosen to denote Pearson's product moment correlation?

• The question has been motivated by a comment of @IsabellaGhement in this thread. Hint: there is a paper by Karl Pearson called "Notes on the History of Correlation" (1920). Perhaps it contains an answer? – Richard Hardy Sep 22 '18 at 19:56
• The population correlation is often denoted $\rho$ so using $r$ for the sample correlation maintains an alphabetical parallel (link). This probably doesn't fully answer your question so I'll just leave this as a comment. – SecretAgentMan Sep 22 '18 at 19:58
• I'm still curious to see a good answer to this question...after my weak comment, your question still remains. I have half a mind to delete my comment and wait for a good answer. – SecretAgentMan Sep 22 '18 at 20:06
• Then the question may reduce to why $\rho$ is used for population correlation. Maybe a simple as observing that correlations are defined as ratios. – BruceET Sep 22 '18 at 21:08

The title of Galton's R. I. lecture was Typical Laws of Heredity in Man. Here for the first time appears a numerical measure $$r$$ of what is termed 'reversion' and which Galton later termed 'regression'. This $$r$$ is the source of our symbol for the correlation coefficient.
Reversion is expressed by a fractional coefficient of the deviation, which we will write $$r$$. In the "reverted" parentages (a phrase whose meaning and object have already been explained) $$y = \frac{1}{r c \sqrt{\pi}} \cdot e ^{- \frac{x^2}{r^2c^2}}$$ In short, the population, of which each unit is a reverted parentage, follows the law of deviation, and has modulus, which we will write $$c_2$$, equal to $$r c_1$$.