Re: 1638 Letter from Oughtred to Allen

Tom and Lu Wetmore

On Jun 14, 2021, at 1:30 AM, Andreas Poschinger <andreas.poschinger@...> wrote:

Hi Tom,

thanks for clarification. I actually believe that Oughtred describes a slide rule or better sliding sticks here, even if we don't know how it should look like, but I believe that also Oughtred did not really know how they looked like:

"I would gladly see one of them when it is finished: wich yet I never have done."

I can only say maybe. The device in question is a cross staff with log lines. Whether both the staff and the transverse had the same log lines is open to question. I believe the quote only means Oughtred has not yet seen what Allen has done on the device so far. With a single set of log lines the cross staff is usable with compasses. These log lines were all two decades long, making this possible.

This is only one piece of communication between Oughtred and Allen about this device. This letter comes after Allen has already etched some scales. Allen had sent Oughtred impressions of those scales by inking the scales and 'printing' them on paper. Oughtred is sending instructions for follow on work. So we are seeing the cross staff through a small window in the middle of its development. I want to reexamine that printing to see if the log lines are already on it. If they are I think we could assume that the staff already had the log lines and Oughtred is adding them to the transverse. But if so it seems he would have instructed Allen to make them the exact length of the scales on the staff. Since the transverse is shorter than the staff this instruction would be very important.

On the open question whether he described sliding sticks, I interpret this from these sentences:

"The lines of Numbers, Sines, & Tangentes, are to be set on the transversarie, ..." (... where he tells as that these were on Gunters staff)

"The divisions of the line of Latitudes, and of the line of 100 aequal 
parts, on the fourth side of the staffe, must not be sett to the edges (as the –a–
other divisions were) but in the midle, close together..."

This isn't enough for me. I want this cross staff to be usable as a two rod slide rule, but I don't think there is enough evidence here.

So question what are the other divisions? Further for what does he need on both, staff and transversary, 100000 equal parts? Delamain also explains the 100000 equal parts in his I believe it was the 1632 edition respectively addition and there they are used to find the logarithms on the scales out of a 5 or even 6 digit table.

This could imply logarithmic lines, or it could mean that he is helping Allen compute etching locations for other scales by computing locations as parts of 100000. Though I agree this seems most applicable to log lines.

Well, it may not be 90% and even not 70% that he describes here a slide rule respectively sliding sticks, but what would be the novelty of this instrument? And for what that the pinnacles can be easily removed if not for sliding in parallel? So this makes the 90% more likely for me.

As I say, I want this cross staff to be used in this way, and the letter is suggestive of it, but I don't see it as conclusive.

My point somehow is, that under normal circumstances given the dates of publication Delamain has priority, and only due to Oughtreds attacks on Delamain it is taken from him, even after finding his book, including his layout it was not rectified. Delamain refers to Gunter as his teacher, so that at least for me it is likely that when Gunter died Delamain looked for somebody to whom he could speek - as what we could call nowadays "peer reviewer", and Oughtred was this guy. Oughtred for my taste did not want a peer relation but wanted a teacher-student connection to Delamain (maybe being also "theological father"), but obviously Delamain not.

I don't believe this. Have you read Forster's "The Circles of Proportion and Horizontal Instrument, Both Invented and the uses of both written in Latin by Mr. W. O. [William Oughtred], Translated into English and set forth for he publique by William Forster"? In the forward of this book Forster describes his visit with Oughtred in 1630, and that at that time Oughtred showed him both linear and circular slide rules that he had had in his work room for years, and his instructions, written in Latin, for using them, were fully developed by then. For me this puts the invention of the slide rule well back into the 1620s in Oughtred's back room. This is a second source that gives Oughtred priority. I know you believe that priority should go to the person who publishes first, but I am not as firm on that point.

Why should we clarify about history of ST scale, as long as the invention of the sliderule itself, respectively the insight of its usefulness is awarded to somebody who does not proof his priority with one technical detail but with mere attacks and as long as the priority of somebody is taken away from somebody who tried to describe each detail, so that every manufacturer and everybody can create copies of it? Unfortunaltely the problem of the Grammelogia for my understanding were its many scales. In times of manual division it did cost most likely some three times as much as Oughtreds dialrule which explains that none is found anymore.

I believe Oughtred deserves priority. I am not swayed by Delamain. But I concede that there is not enough evidence to prove the inventor. This argument seems similar to the one about who wrote Shakespeare's plays. Maybe we can never know, but we can appreciate that such masterpieces of the English language exist.

Tom Wetmore

Best regards


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