Question concerning tapers to degrees

Gang, Recently had to bore a taper (for a homemade battery terminal I'm making for an auto battery) and got involved in trying to determine
the angle (in degrees) that I would have to set the compound on my lathe. In looking through the Machinery Handbook, "Rule: Divide the taper in inches per foot by 24, find the angle corresponding to the quotient, in a table of tangents, and double this angle". Example : taper of 1-1/2 inches per foot, divided by 24 = .0625. The angle whose tangent is .0625 = 3 degrees 35 minutes nearly, then 3 degrees 35 minutes multiplied by 2 results in 7 degrees 10 minutes. Now, I realize the last part (multiplying by two) is dropped for turning on the lathe as I don't need the included angle - only the angle from the centerline of the part.... but my question is "Who came up with the number _24_ ? ? Is this some mystical number that just works or is there actually a relationship? Thanks. (btw, the bored holes came out perfect). Ken.
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<Ken Sterling> wrote: "Who came up with the number _24_ ? ? Is this some mystical number that just works or is there actually a relationship?" ^^^^^^^^^^^^^ The tangent of an angle has to be dimensionless, inches/inch or feet/foot, etc. So you divide by 12 to change from inches per foot. Then you divide by two to get the half-angle, so it becomes division by 24.
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Ken wrote:

1/2 '/"
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I'm sorry - I must really be dense (plus I never had higher math) but I'm just not getting it.....I had a little algebra, no trig, no geometry and no calc....so maybe I just need to do a little studying to understand.... Please forgive my ignorance. Ken.
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There are 12 inches in a foot. Dividing a taper expressed in inches per foot (included angle) will give you taper in inches per inch (included angle). But you want half of this for the compound on your lathe as it generates the included angle automatically. So divide by two again. 2 x 12 = 24.
Now you have the taper in inches per inch from the centreline (half the included taper).
Now you can apply your trig to turn this taper into degrees using tangents.
There's no magic about the number 24. It's just twice the number of inches in a foot.
If you had a taper expressed in mm per metre your magic number would be 2000.
If you had a taper expressed in barleycorns per inch your magic number would be 6.
If you had a taper expressed in feet per fathom your magic number would be 12.
If you had a taper expressed in furlongs per mile your magic number would be 16.
Shall I continue :)
Dave Baker - Puma Race Engines (www.pumaracing.co.uk) I'm not at all sure why women like men. We're argumentative, childish, unsociable and extremely unappealing naked. I'm quite grateful they do though.
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THANK YOU!!!! This explanation made more sense to me... I appreciate your efforts. Ken.
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