This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
Taps for watch screw threads may be made from needles, but probably they would not last long. A tap should be made from the best steel; therefore get a length of tool steel wire of the correct size. From this cut off a suitable length, say 1 1/2 in. Soften it by heating to a dull red and allowing it to cool slowly. Hold it in a pin-vice and, resting it on a piece of boxwood, file it to a gentle taper until the end just enters the hole in a screw-plate; the wire may then be screwed into the latter, plenty of oil being used. When it goes hard, turn it back half a turn, then forward three-quarters of a turn, back half a turn again, and so on, advancing slowly until a full thread is cut for a sufficient distance. Then file three flats upon it for the whole length of the thread, tapering the flats to the end, where they should meet in a knife edge and show only half a full thread. Harden the tap by heating to a red colour aud plunging in cold water. Brighten one flat and heat it over a flame until it is of a pale straw colour. This renders it less brittle, and is called "tempering." Then carefully smooth all three flats on an oilstone so as to leave good cutting edges.
Finally, file some nicks in the soft end to indicate the number of the hole in the screw-plate to which it belongs.
 
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