First crack at an a priori calculation of DM scale for USGS maps:
Let a = original dpi of scan
scale = 1:24000 = 1/s so s = 24000
fpi = s/12 so fpi = 2000
Let l = the original size of the map, whatever it is.
Now, download the map file. The original dpi is not stated so the
default becomes 72. The original size of the map is magnified so that
l' = a/72
The downloaded map is much larger. The new scale s of the downloaded map
then becomes less so that
s' = s*(72/a)
The fpi is always the scale divided by 12 so
fpi' = s'/12 = (s/12)*(72/a) = 2000*(72/a)
Thus, if the original dpi was 250, the downloaded scale becomes 576 fpi.
And, if the original dpi was 300, the downloaded scale becomes 480 fpi.
So, my original map must have been scanned at 300 dpi.
Comments or corrections appreciated.