In 1889 George Eastman introduced a thin transparent celluloid film for his Kodak camera which had previously used a paper roll film.
Laurie Dickson, the Scottish born engineer who was working on the development of moving pictures at the Edison workshop in Orange, New Jersey, saw a demonstration of the new film and realised that this was just what he needed to further his experiments.
The roll film was 2 3/4" wide, supplied in 50 foot lengths and unperforated. After experimenting with narrow widths slit from the roll, Dickson eventually ended up slitting the film in half, 1 3/8" (35mm). He perforated both edges and worked to a frame size of 1" x 3/4" picture area spaced between four perforations.
Film 35mm in width with a 4 sprocket hole pull down is still the camera standard today although the 1" x 3/4" picture area has altered due to the placement of the optical sound track and variations in aspect ratio such as wide screen.
Edison tried to patent the perforations used for his Kinetoscope film. The matter was taken to court where the judge ruled against his claim on the ground that as they are used to facilitate the separation of leaves of paper from a toilet roll, perforations were not unique. Perhaps he would have been successful had he called them sprocket holes.
Some may claim that 1889 was the birth of 35mm cinema film, but I take it to be 1894 when it first made its public appearance in Kinetoscope parlours. 1889 was the year of conception leading to a five year pregnancy!
The use of millimetres to describe the width of motion picture film devised in the USA, a non-metric country, puzzles me. I can only assume that 35mm us easier to write and say than 1 3/8 inches!