NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Star-star distances for arc error
From: Gary LaPook
Date: 2009 Jun 29, 10:18 -0700
From: Gary LaPook
Date: 2009 Jun 29, 10:18 -0700
Douglas wrote: "I think, for what it is worth, this is either a simple 'slip-up' when he wrote the specification; or more likely to my mind, he was meaning the scale is derived from the basic function of log cosines; and I think this was done deliberately to link with the given formulae in the patent itself which only uses cosines being mentioned." But he could have written out the formulas in his patent application to mirror the actual scales as I have pointed out in my previoius posts so I still don't know why he didn't. I guess we will never know. BTW, soes anybody know what ever became of Captain Bygrave after he invented the slide rule? gl On Jun 29, 8:35�am,wrote: > Dear Brad, > > Many thanks �for the comments, which I agree with totally, as both versions come to the same result with the same operations so it is a non sequitur - either logically is correct. > > What is more interesting to query is why Bygrave did not specify in his patent more accurately? that is the fascinating thing to ponder I think. > > It is clear he had a perfectly good working model of the 'system' all sorted out in exquisite detail, �and even gives a diagram/picture of the device and it's scales with numbers, and the operation sequence on the outer sliding cursor sleeve. � > So why did he say:- > "... an inner cylinder of log tangents....... > and an outer cylinder of log cosines ......" > > I think, for what it is worth, this is either a simple 'slip-up' when he wrote the specification; �or more likely to my mind, �he was meaning the scale is derived from the basic function of log cosines; and I think this was done deliberately to link with the given formulae in the patent itself which only uses cosines being mentioned. > > As one finds with the device itself though, he uses the slide-rule operation of division when a multiply is needed, and vice versa to facilitate the operations required for the sight reduction purpose. This therefore needs an invesrse function for one of them. (Choose which you think - log Cotan or log Cosecant - same thing when used in the operations of this device). > > I believe he was _fully_ aware of what he wrote, but did so with what is now, to us, an apparent anomaly, � only to illustrate for the purposes of the patent requirements the _principle_ of the device; and he just kept to himself the detail of the actual nitty-gritty mechanics of it. �The patent requirements had been fulfilled �in describing the principles and were accepted. That was that.. but leaving us to now speculate as to his thought processes in what amounts to historical archeology I suppose. > Fascinating. > > Douglas Denny. > Chichester. �England. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---