NIP:
Looking around the www and after consulting a number of beery books, there seems to be some disagreement on the size of the imperial beer measure known as the "nip".
The following describe a nip as a quarter of a pint of beer*:
Whereas these describe the nip as a third of a pint of beer (which is still a legal measure): Brian Glover - CAMRA Dictionary of Beer
Perhaps as the following site indicates, there is more than one usage: " nip of beer is 1/4 pint (the same as a gill, 4 fluid ounces or about 117.7 milliliters) or sometimes 1/3 pint (189.4 milliliters)."
STICK:
A more regional measure seems to be the "stick" or 1/3 of a pint. The term "stick" appears to be restricted to the Birmingham area. This is confirmed by two people who've I heard use it - Dr Carl Chinn and one of our CAMRA branch members, both B'ham born and bred. The "stick" was popular with licensees who chose it when being bought a drink.
nb: The beer nip is completely different measure from the spirit (eg whisky) nip.
*A gill is 5 fl oz or a quarter of a pint