Quartz Question

A question has been asked on another group which I was expected to know
the definitive answer (they know I have an interest in horology).

The question has never even crossed my mind so I have no thoughts!

It is said that when the battery in a quartz watch is close to 'dying'
the watch will 'speed up' - Why?

The original questioner also stated that "We all know it happens" so it
seems to be taken for granted but i have never seen or heard any
reference to ths 'phenomenon'.

One response said the reason would be :

". . . . a change in the parametric capacitance of the oscillator
circuit due to the drop in bias voltage pulling the crystal's resonant
frequency slightly higher than normal."

Your comments would be most appreciated.

JG
.