Fer, Here is, I think, the message Mac mentioned.
Bill ---------- Forwarded Message ---------- From: "fer j. de vries", INTERNET:[EMAIL PROTECTED] TO: "Shadow Maker", INTERNET:[EMAIL PROTECTED] "sundial", INTERNET:sundial@rrz.uni-koeln.de DATE: 3/26/01 7:21 AM RE: Re: Reclining/Declining Hello Robert, Calculating the angles for the hourlines isn't complicated if the dial is translated to an equivalent horizontal sundial. Start to calculate 3 angles: sin v = sin phi . cos i - cos d . cos phi . sin i v is the style height and also the equivalent latitude where the dial is horizontal sin b = cos phi . sin d / cos v b is the angle of the substyle, relative to the line of greatest slope. With v and b it is known where the polestyle will be. tan ts = sin i . sin d / ( cos phi . cos i + sin phi . sin i . cos d ) ts is the hourangle at what time the shadow of the style falls on the substyle. Use ts as a longitude correction to calculate the horizontal dial at latitude v. Use the usual formula for an horizontal dial tan z = tan t . sin v in which t is corrected for longitude ts. z is the angle of the wanted hourline relative to the ( known ) substyle. Correct values for b , ts and z to the right quadranr if necessary. I think this is the easiest way to do the job. Best wishes and happy dialing, Fer Fer J. de Vries [EMAIL PROTECTED] http://www.iae.nl/users/ferdv/ Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: Shadow Maker <[EMAIL PROTECTED]> To: <sundial@rrz.uni-koeln.de> Sent: Friday, March 23, 2001 6:58 PM Subject: Reclining/Declining > I have built some horizonal, vertical and vertical/declining dials and I am > now ready to build a reclining/declining dial, that will compensate for > standard time (that part is easy). > > I have read what Mayall/Mayall, Waugh and Rohr have written about the > layout process. I would prefer to use the trig formulas for SD, SH and > HourAngles because I can use them in a PostScript file that will render the > dial face and print out the values of all of the angles. Rohr does show the > formulas for SD and SH but, like the others, he recommends a graphic layout > method instead of a computational method > for the hour line angles. I was hoping that all of the trig formulas would > be available, but can't find them. Waugh says that older editions of the > Encyclopedia Britannica had all the trig formulas but dropped them a hundred > years ago. > > Can anyone help? > > Robert Hough > [EMAIL PROTECTED] > > _________________________________________________________________ > Get your FREE download of MSN Explorer at http://explorer.msn.com > ----------------------- Internet Header -------------------------------- Sender: [EMAIL PROTECTED] Received: from mail1.rrz.Uni-Koeln.DE (mail1.rrz.Uni-Koeln.DE [134.95.100.208]) by sphmgaaf.compuserve.com (8.9.3/8.9.3/SUN-1.9) with ESMTP id HAA01682; Mon, 26 Mar 2001 07:21:40 -0500 (EST) Received: (from [EMAIL PROTECTED]) by mail1.rrz.Uni-Koeln.DE (8.9.3/8.9.3) id OAA23861 for sundial-out; Mon, 26 Mar 2001 14:19:54 +0200 (MET DST) Received: from mail.iae.nl ([EMAIL PROTECTED] [212.61.26.34]) by mail1.rrz.Uni-Koeln.DE (8.9.3/8.9.3) with ESMTP id OAA23854 for <sundial@rrz.uni-koeln.de>; Mon, 26 Mar 2001 14:19:53 +0200 (MET DST) Received: from z0k5w2 (pm17d117.iae.nl [212.61.3.117]) by mail.iae.nl (Postfix) with SMTP id 0137120F48; Sun, 25 Mar 2001 16:54:08 +0200 (CEST) Message-ID: <[EMAIL PROTECTED]> From: "fer j. de vries" <[EMAIL PROTECTED]> To: "sundial" <sundial@rrz.uni-koeln.de>, "Shadow Maker" <[EMAIL PROTECTED]> References: <[EMAIL PROTECTED]> Subject: Re: Reclining/Declining Date: Sun, 25 Mar 2001 15:21:58 +0200 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 5.00.2615.200 X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 Sender: [EMAIL PROTECTED] Precedence: bulk