A computer program Is described for the calculation of tb.9 zeroes of the associated Legendre functions, Pnm and their derivatives, for the calculation of the extrema of Pnm and also the Integral between pairs of successive zeroes. The program has been run for all n,m from (0,0) to (20,20) and selected cases beyonu that for n up to 40. Up to (20,20), the program (written In double precision) retains nearly full accuracy, and indications are that up to (40,40) there is still sufficient precision (4-5 decimal digits for a 54-blt man¬tissa) for estimation of various bounds and errors involved in geopotential modal-ling, the purpose for which the program was written.
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