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Thanks Frank and Bill and any others for the replies -
The book actually includes the complete work of Sumner's with all the examples.
Bill, thanks for the effort and good suggestion that the 'log-rising' table is some 'proprietary' table which most likely forms a simplified method of solving the formula.(I'm guessing that the 100000 scaling factor rids of annoying decimal point during computation and is allowed for in the table)
The trigonometrical identities which you suggest also make more sense of things.
Frank, I will check out the links for the mathematics.
regards
Russell