John Carmichael wrote: "It seems as though the only practical use for a bead-in-hole is on the alidade of an equatorial heliochronometer Since for it to work properly, as John Davis pointed out, it must always be perpendicular to the suns rays."
A noon mark (possibly with an analemma) would be another possible use I think. The +/- 23 1/2 degree change from equinox to solstice should not cause too much trouble. Perhaps one should make the hole very slightly elongated (along the polar axis) to allow for this? An unrelated question: does anyone know of a sundial designed to show sunrise or sunset in quite another, distant, place? Presumably it is just necessary to construct a plane passing through the nodus of the dial and parallel to the plane of the horizon at the other place, and mark the line where it intersects the surface of the dial? I should go away and work out the formula, which I suppose must equate to an Italian or Babylonian hour line on an inclining declining dial with the inclination and declination corresponding to the lat./long. difference? Thinking about this gives me an obvious explanation of why Italian and Babylonian hours as shown by a pin gnomon on a flat dial are marked by straight lines, (which always used to surprise me), as taking a plane through the gnomon tip and parallel to that of the horizon for somewhere on the same latitude but the relevant number of hours East or West in longitude, that plane intersects the dial plane with a straight line, and the shadow crossing that line is a notification of the Sun's rising or setting either that number of hours ago or in that number of hours time in the other place. Perhaps others may find this a helpful idea? Andrew James N 51 04' W 01 18' -----Original Message----- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: 07 June 2002 16:50 To: sundial@rrz.uni-koeln.de Subject: Re: Shadow Sharpener Again It seems as though the only practical use for a bead-in-hole is on the alidade of an equatorial heliochronometer Since for it to work properly, as John Davis pointed out, it must always be perpendicular to the suns rays. It seems Patrick's excellent instructions on how to calculate its dimensions and focal length would come in very handy if you were designing an equatorial heliochronometer. John John L. Carmichael Jr. Sundial Sculptures 925 E. Foothills Dr. Tucson Arizona 85718 USA Tel: 520-696-1709 Email: [EMAIL PROTECTED] Website: <http://www.sundialsculptures.com> ----- Original Message ----- From: "Patrick Powers" <[EMAIL PROTECTED]> To: <sundial@rrz.uni-koeln.de> Sent: Thursday, June 06, 2002 3:14 PM Subject: Re: Shadow Sharpener Again > Message text written by INTERNET:sundial@rrz.uni-koeln.de > > >John said: ...but do you think your formula could help determine the > optimum > size of the gap between the bead and hole of a bead-in-hole sharpener?< > > Yes it can help but it's not the same! Strictly the process is different > but the formula used as I suggested (where you place the pin hole at > distance f for a hole of diameter D) instead gives the MAXIMUM distance of > the pinspeck device from the screen or image. You should actually choose a > distance that is substantially less than that given by the formula if you > want a pinspeck device to work. > > The formula I sent for the pinhole gives the details for a specific optical > situation that lies between two other forms of so called imaging which > happens to be the best for the purposes of a pin hole camera (or shadow > sharpener). Art is right that image formation is not achieved in the same > way as it is in a lens but if you choose to define focusing as 'a means by > which points in an object can be proportionately and spatially translated > into corresponding points of an image' then the pinhole and the lens do the > same thing - and you can consequently still talk of things like focal > length too. That's why I (like some people in the literature) do use the > same terms for both. But you do have to realise that it's not the same... > > The pinspeck - that's the 'bead-in-hole' device - operates somewhat > differently. Here the bright points in an object cast shadows of the > pinspeck itself (that's the bead) onto the screen or floor and it is these > points of shadow that you see. It therefore looks like a negative image. > Here the key things are: > > 1. That the bead must itself be large enough to cast a shadow at the > distance it is from the screen. > 2. The distance of the screen from the bead has to be less than (s^2)/L if > the effect is not to be marred by other optical effects like diffraction.. > So the formula gives a distance that you must be well within. > 3. The thing needs light to work so it doesn't work well in half light and > being placed in a penumbra effectively switches it off. > > Also if you are that close then the image size is usually too small and > indistinct even in good light. > > Because, with a pinspeck, every other point than the one causing a shadow > also illuminates the rest of the screen the contrast of the resulting > negative image is very poor - much less than that of the positive image > obtained with a pin hole. The pinspeck 'camera' does however have a > greater light gathering capacity than the pinhole so it can be useful for > imaging simple objects. That is why it is used (or used to be used) for > setting up X-ray tubes etc. However I would imagine that it would be near > useless when you take it into shadow because the contrast would vanish. > Having said all this I must confess to never having properly experimented > with a pinspeck device so I really ought to shut up at this stage!! Theory > is all very well, but.....! Maybe others who have tried this device can > comment? > > Have I confused you or is that of any help? > > (Sorry about the strange use of ^ to indicate a number raised to a power > (as in 2^3=8) - it's something that comes from computer programming but > it's very convenient when trying to write formulae in e-mails!! Some > people use two asterisks for the same thing (as in 2**3=8) too) > > Patrick > > > > > ------------------------------------------------------------------------- > E-Mail: [EMAIL PROTECTED] > Web: http://ourworld.compuserve.com/homepages/Patrick_Powers/ > Lat: N 51d. 49m. 09s: Long: W 00d. 21m. 53s > > - > - -
