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From my reading of �Surveying� W. Norman Thomas, London, 1926., it
seems that the easiest method of locating the meridian accurately
using a theodolite is to take equal altitudes of a circumpolar star.
This does not require accurate timing of the observations, or
knowledge of the latitude. Nor does it require spherical trigonometry,
so even innumerates like me can manage.

If the sun is used, allowance has to be made for the fact that its
centre cannot be located, though correction for semi-diameter can be
eliminated by observing one limb in the morning and the other in the
afternoon.However, with the sun, the time interval between the two
observations must be recorded to allow for any changes in the sun�s
declination and the calculations get messy(i.e. difficult for me).
Refraction is perhaps also less liable to change during the night.

So, on to the stars. In places, I have paraphrased Thomas.

The time interval between the two observations should be as long as
possible so that the rate of change in altitude is relatively high and
the change in azimuth relatively low.

�The instrument is set up at O, the cross wires directed at
R(reference point, which might be a visible part of a distant street
lamp nowadays) and the readings of the two horizontal scales recorded.
The telescope is then directed to the star, which is in position S1,
say, and exact coincidence obtained. The vertical angle a1 is
recorded, and also the values of the angle ROS1 from both horizontal
scales.

�The �face� of the instrument is then changed , the telecope
redirected to R, both horizontal scales read, and after an interval
of, say, 15 to 20 minutes, the same star is again bisected with the
cross hairs, and the horizontal angle ROS2 and the vertical angle a2
recorded.

�[An alternative method of procedure , which is perhpas preferable, is
� instead of bisecting the star, and adopting whatever reading a1
results � to set the vertical scale at a suitable definite value for
the angle a1, e.g. at an even minute, and to follow the star with the
telescope until it makes its own contact  with the horizontal wire.
The instrument is then clamped, the intersection of the crosswires
moved laterally to bisect the star accurately, and the horizontal
angles read. Similarly, the star would be allowed to make its own
contact at a definite angle for a2]

�After culmination, the path of the star is again observed in the
telescope, until it is found that at S3 it has returned to the same
altitude a2. The approximate time can easily be predicted. The angle
ROS3 is then observed on both horizontal scales.

�The face of the instrument is changed to its original face, R
intersected, the vertical circle vernier adjusted to read a1, and the
star observed in the telescope until it coincides exactly with the
intersection of the cross wires, when the angle ROS4 is recorded.

�The values of the vertical angles, a1 and a2 are not used further,
but the azimuth of R, i.e. the angle ROP, is computed as the mean of
the eight readings of the horizontal angles to S1, S2, S3 and S4.

�Unless unavoidable, the altitudes a1 and a2 should not be very small,
as refraction is then uncertain.�

With a vernier thedolite reading to 10�, the probable error �...should
not greatly exceed +/- 8�, say.� (for a single set of face left and
face right readings). The uncertainty should be much less for a modern
single seconds instrument.

 Bill Morris

On Apr 22, 7:30�am, Geoffrey Kolbe 
wrote:
> With the recent discussion on the abolition of the leap-second and the
> problems of Delta T, I have been pondering the possibility of measuring
> Delta T myself.
>
> The transit telescope was invented by that Danish polymath genius Ole
> Roemer in about 1675 and quickly adopted by Greenwich and then by all the
> world's observatories as a means to determine time. So, this seems a good
> way to go. But the main problem would be setting the telescope up so that
> it was aligned to the meridian. With a transit theodolite - which is
> essentially a portable alt-az telescope - one can easily time the moment a
> star or the sun transits the vertical cross wire in the telescope. �Using
> the calculated azimuth of the sun or star for that moment, it is easy to
> correct the plate azimuth of the theodolite and swing it around to the
> meridian. But, since I want to use the telescope to measure time, I would
> prefer to find some other way to set it up which did not involve the use of
> absolute time.
>
> It seems that in England, there was a flurry of interest in small transit
> telescopes in the late 19th century as country gentlemen and the newly rich
> industrialists needed some way to determine the time in their country
> estates. To this end, a book called "A Treatise on the Transit Instrument
> as Applied to the Determination of Time" was written in 1882 by Latimer
> Clark. Unfortunately, although Google books tantalizingly lists the
> contents of the book, it does not seem to be available.
>
> There are a couple of ways that I can think of. First would be use Polaris,
> of course. But given that a transit telescope looks South, it may be
> inconvenient to use Polaris - especially at these high latitudes
> (Scotland). Second would be to time the transits of two stars of preferably
> similar SHA but greatly differing declination. Only if the telescope is
> aligned to the meridian will the difference in transit times be correct.
>
> Can anyone come up with any other ways to align a transit telescope to the
> meridian, which does not involve the use of absolute time?
>
> Geoffrey Kolbe
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