[EMAIL PROTECTED] wrote: > > Hi everyone: > > I am working on a dial with a large declination similar to the one on page > 99 of Waugh's book but lat.40.17, long. 76.43, and faces S. 84.6 W. I am > having trouble > understanding completely the meaning on page 146 on the difference in > longitude so > I can plot the points for the lines of declination. > What is the meaning of the sentence " The difference in longitude tells us > that the dial would be horizontal at a longitude 28.0d father east ( since > the decl. is east) or > at a long. 44.8dW" ?? > What would be the longitude of the horizontal dial for my west dial? > My dial height will be 1.7 inch which is suppose to be 23.2 inches from > the dial center. My SD=49.7, SH=4.1, DL=86.5 > I still like using the calculator so I understand the math. I do not know > if I am using the right altitude. I though I understood this.! > > Thanks in advance. > > Ken Clark
Hi Ken, Assume you have a vertical dial, facing south on latitude +40 (northern lat.) and longitude +75 (west long.). Move this dial in the southern direction till it will be horizontal. You than have moved the dial 90 degrees ( it was a vertical dial) across a great circle and you are at latitude -50. (southern lat.), but still on the same longitude line. Now assume you have a vertical dial at lat. + 40 and long. +75, which faces to south west. So its declination is 45 degrees. Move this dial in the south west direction across a great circle till it is horizontal. You also moved 90 degrees across a great circle and you are now at latitude -32.80 but no longer at the same longitude line. The difference in longitude is 57.27 degrees, so you are at 75 + 57.27 = 132.27 west. The dial now can be calculated as an horizontal dial for this new latitude but remember that for the hourlines you have to correct for longtide with 57.27 degrees. With your real dial: lat +40.17 inclination 90 ( vertical dial) declination +84.6 The new lat is : -4.12 ( that is southern lat). This also is the height of the style. The diff in long is : 86.51, so you arrived at 76.43 + 86.51 = 162.94 west longitude. The substyle makes an angle with the vertical line of 49.7 degrees. In formulae for the height of the style v and for the diff. in long ts for any plane : sin v = sin lat .cos i - cos d .cos lat .sin i tan ts = sin i .sin d / ( cos lat .cos i + sin lat .sin i .cos d ) i is inclination of the dial d is declination of the dial. ts has to be corrected for the right quadrant, v needs no correction. Let me know if this explains your question. Fer J. de Vries Netherlands.
