Is there an algorithm for solar eclipse duration?

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Some helpful resources ?

Amateur Astronomy pocket skyguide
  If the umbra passes across Earth, an umbral, or total, solar eclipse occurs. Only people within the umbra see totality; those outside see a penumbral eclipse or no eclipse at all. Both Moon and Earth are moving, so the tip of the umbra moves across the surface of Earth, tracing out the eclipse path. The shadow moves eastward at about 1600 km per hour. The duration of totality is determined by the size of the shadow and the geometry of how it hits the surface of Earth. The maximum length is about 7½ minutes.

Observational Astronomy for amateurs
   Anyone interested in the computation of eclipses should refer to B.3.26.
…
3.26  M.DAVIDSON, the Computation of Total Solar Eclipses (J.B.A.A., 49, No. 8, 299).

Monthly Notices of the Royal Astronomical Society
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ps: attachment is MOST helpful