All my working life I have used Morse tapers without giving them a second thought, but having decided to 3D print a rack for my lathe tools I wanted to make holes match 2 and 3 Morse so a quick Google for the tables and I find every single taper is a slightly different angle?? 2M has an angle of 1.4307 3M has an angle of 1.4377.
I was baffled as to way this should be so a bit of googling and the answer appears to be that Stephen Morse (who to my surprise was an American) came up with his taper in 1864, he had two sets of master gauges made, one set he kept the other was sent to the bureau of standards in Washington DC and accepted as the national standard. Because machining accuracy wasn't that good in those days we end up with this raft of different angles.
I was baffled as to way this should be so a bit of googling and the answer appears to be that Stephen Morse (who to my surprise was an American) came up with his taper in 1864, he had two sets of master gauges made, one set he kept the other was sent to the bureau of standards in Washington DC and accepted as the national standard. Because machining accuracy wasn't that good in those days we end up with this raft of different angles.