Well, contrary to some of the info here there WERE established standards for threads in 1910, and in fact way before that!
To find out which, if any, applies to your machine, the easiest way is to see if you can work out where the machine was made! If it's a British machine the threads will probably be BSW (British Standard Whitworth) or BSF (British Standard Fine).
If it's a US machine they will be National Coarse or National Fine.
Bear in mind though, that standards change, and some formerly popular forms become less used. Back then different thread pitches were often used for 'heavy' nuts or square nuts, which don't get used in that size of nut now.
Bear in mind also, that the U.S. adopted Unified threads in the 1950's. Although they are 'similar' to the old National series, there are some changes. The 'Numbered' threads on the old series included a far greater range than on the new, and these often cause confusion if found by the unwary!
The only way to be sure is to get a selection of bolts, and keep trying till you get a fit! You'll probably get the right size easily, but will need a bit of a fiddle to find the correct pitch!
Once you've discovered the correct thread, the only way to re cut it, is to use a Tap in a tap wrench. You can get both for little money from firms such as MSC.