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The boundary between Quebec and New York was set at the 45th parallel in 1763; around 1766 Governor Moore of New York began writing about starting a survey of that line, apparently in an attempt to head off the sorts of problems being experienced along New York's other, more-populous borders.
Samuel Holland, the first Surveyor General of Quebec, had proposed a survey of all the British lands in North America in 1762 though it wasn't approved until 1764 (the same year as his appointment to Surveyor General). Holland was focused on tasks outside Quebec, like surveying the Atlantic coast, so he appointed John Collins the Deputy Surveyor General, tasking him with surveys inside Quebec. The map of the boundary along the 45th parallel completed by Collins was probably performed at Holland's request (p14).
In February 1771 New York province approved a budget to send a New York representative to take part in the survey. Thomas Valentine ended up with the job in early 1772, after the first two or three surveyors from New York begged off with various illnesses. Valentine's involvement also ended early due to illness (he died before the survey was completed), and CJ Sauthier participated in the end of the survey on behalf of New York.
It may be interesting to know that Valentine reported, after meeting up with Collins, that the surveying expedition consisted of 20 men in addition to Collins and Valentine.