The mostly likely candidate country is the US, because Americans are notorious for not thinking they ever need to specify a country. But the date doesn't work for America, either. The first milk "bottle" in America (the Lester Milk Jar, whose lid was held in place as a screw cap), wasn't patented until 29 January 1878 (18 days after the alleged first delivery), and no one is sure that it ever even actually saw use. The first viable milk bottles were patented by the Warren Glass Company in 1880. Nevertheless, it's clear [see the New York Times excerpt below] that bottled milk delivery was starting to happen in America by October 1878; and by 1880, was making enough headway for sellers of milk the old "milk can and dipper" way to be fighting back with dirty tricks.
World Milk Day, as declared by the United Nation's Food and Agricultural Organisation (FAO) in 2001, is 1 June. The FAO also declared, as of 2000, that World School Milk Day is 28th September.
School Milk Week in the UK is the 2nd week of October each year.
Harvard Milk Days are held in Harvard, Illinois on the first weekend in June. The festival started in 1942. From 1945 to 1983, they elected a Queen. Today, they choose instead a Dairy Princess.
In northern Pakistan, the Kalash people celebrate a milk day during their spring festival (called "Joshi").
[1] It is repeated in a great many places that this first delivery was done in New York City by either an Alexander Campbell or by the New York Dairy Company. Sadly, a search by Practically Edible of the New York Times from 1870 to 1880 didn't turn up evidence of either name being involved in the dairy business in New York City at that time.
History
"Difficulty of Selling Pure Milk: The mode of delivering milk in Paris, in sealed bottles, of standard quantity and quality, with the date marked upon the bottles is one familiar to traveled Americans, but one that has not been imitated here until very recently...." Credited to the New York Times. In Burlington Weekly Hawkeye. Burlington, Iowa. 19 October 1878. Page 7.
The following letter to the New York Times in 1880 presents a glimpse into the battle between those milkmen delivering milk the old way -- out of large milk containers dishing it out to the customer with a dipper, versus those trying to upset the milkwaggon by delivering it in sealed bottles:
"To the Editor of the New York Times:
I noticed in a recent issue of THE TIMES an article with reference to the supply of pure milk in cities, and referring to the method of delivering the same in sealed bottles. It is a subject in which I am much interested, as I am in this way serving families in New York with the milk produced on my farm, and, having considerable experience in the business, I would like to state briefly, for the benefit of your City readers, some serious obstacles to their being served with pure, fresh milk, which it is in their power to remove.
Incredible though it may seem, I say what I know to be a fact when I assert that it is impossible to serve many of the best families in the City with pure milk, except at a loss to the farmer or the dealer who may deliver it. The source of the trouble lies in the almost universal corruption prevalent with the servants employed in these families, by which the farmer, in order to retain their custom, must submit to continuous exacting fees, which he cannot afford to do, but which the dishonest dealer can and is willing to do. A customer is secured for the farmer
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