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Willis' Sight Reduction Method

Edward J. Willis, in his "The Mathematics of Navigation" 1921, (available via Google Books), describes a method of sight reduction using "Creele's Tables" (also on Google Books). On page 17, Willis makes some 'bold' statements about the difficulties of using logs and equations recast to facilitate the use of logs. He outlines the use of Creele's multiplication tables and seems to say that tremendous insight is gained into understanding by direct observation of the magnitude and signs of all the terms.

In my opinion, he has a real dilemma. Those who want answers, want robust, quick, easy, simple rule based methods and most likely don't care at all about 'insight'. On the other hand, those who might appreciate insight, are probably familiar enough with logs, haversines, and spherical trigonometry that there isn't much insight added by his method. Another problem is, having acquired a hard copy of Creele's, it takes a fair number of table entries to actually execute his method. Not to mention the need to have in addition, a five place trig table to look up the sines and cosines you're about to use Creele's to multiply. It seems to me, that while I've got the trig table open to the needed angle it would be pretty darn simple to slide my finger over and take out the log instead of the natural. And I don't see how Creele's even comes close to simple addition of the logs! (Having tried it, although admittedly not a significant number of times.)

In spite of the above, it has been an interesting and entertaining adventure to acquire and understand the use of Creele's. Based on the number of editions and translations, it seems to have been a fairly widely used tool in the days before calculators, particularly if a large number of significant figures is needed. I also have Wilkenson's Multi-Divi tables which provide a similar capability.

Attached is a little spread sheet which attempts to automate and reproduce the use of Creele's. The data is from the example on page 18 of Willis, and reproduces his result. No guarantees that there are not still errors to be found. Willis was from Richmond, Virginia. The University of Virginia at Charlottesville holds an interesting collection of his works and manuscripts which I have seen.

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