Spirits used to be commonly served in 25ml measures, which are one unit of alcohol, many pubs and bars now serve 35ml or 50ml measures. Large wine glasses hold 250ml, which is one third of a bottle. It means there can be nearly three units or more in just one glass.
"Parts" are imprecise measurement units: "1 part" is any equal part of the total volume. It could be 1 ounce for a single cocktail, 1 cup for a punch, or any other measurement.