I would say from each quarter (of the udder). I've worked in a dairy before, and the term for each teat and the surrounding tissue on a cow's udder is known as a quarter, as there are of course four of them. Goats have only two teats on their udders and different milking units are needed for them. Sometimes it may be necessary not to milk a quarter as much or not at all for one reason or another, so I can see where this invention would be very useful.