Re: What equipment set up is needed to measure the parallax angle of Sirius?

Luckily, I have a textbook, Lessons in Astronomy by Charles A. Young, that 
was published in 1898, which was only about 30 years after the first 
successful measurement of parallax.  Because the determination of a star's 
parallax was a major technical acheivement of the time, the book goes into 
some detail about the methods and equipment used.

The determination of the parallax of stars had been attempted over and over 
again from the time of Tycho Brahe down, but without success.  Apparently, 
at one point this lack of success was an argument against the motion of the 
Earth around the Sun.  These old astronomers understood that if the Earth 
moved, then we should see some of the stars move.  Another explanation was 
that all of the stars are the same distance away from the Earth.  Of course 
we now know that neither is the case.  Stars are at different distances from 
the Earth, but they are so far away that their movement against the 
background is so minute that it can only be detected with the most sensitive 
techniques.  In 1838, Bessel determined the parallax of 61 Cygni and the 
next year Henderson determined the parallax of Alpha Centauri.

Two methods can be used, the absolute and the differential.  In the absolute 
method, it is necessary to make extremely accurate measurements of a star's 
right ascension and declination with meridian circle at different times 
through the course of an entire year.  If there is no parallax (the star is 
too far away), then all of these points will be the same.  If the star has a 
parallax, then they will show, when plotted on a chart, an apparent annual 
orbital motion of the star in a little ellipse, the major axis of which is 
twice the star's annual parallax.  Theoretically, this should work and this 
was the method used by Henderson.  Unfortunately, the equipment must be so 
precise and without any error, that actually gaining any useful data is 
almost impossible.

The differential method, which is what most astronomers of the time used, 
requires one to measure the difference in arc between two stars over the 
course of the year.  The problem with this method is that it is quite likely 
that both stars may have a parallax and it will not be possible to gain an 
absolute value.  Also, it is difficult to look at a star and tell which is 
nearer and which is closer.  But, today we have all this information.  You 
can find a star that is nearby that has a large parallax and then use 
another star which has no parallax and use that star for your comparison.

The two pieces of equipment that can be used are the heliometer and the wire 
micrometer.  The heliometer was used by Bessel, but unfortunately the book 
doesn't discuss exactly what a heliometer is or how it was used.  The wire 
micrometer is a pair of parallel spider threads, one or both of which can be 
moved with a fine screw with a graduated head, so that the distance between 
the two 'wires' can be varied at pleasure, and then "read off" by looking at 
the micrometer head.  This will only give accurate readings within a minute 
or two of arc.  If the arc is greater than that, then the heliometer must be 
used.  But, it doesn't say exactly how.

I hope this helped.  All in all I can say that it will be a very difficult 
and frustrating task.  But, if you can get it to work, then you will have 
really accomplished something.

[Moderator's note:  You can find writeups of early parallax measurements in many 
issues of "The Astrophysical Journal" or "Monthly Notices of the Royal 
Astronomical Society" from the late 1800s and early 1900s as well.  Good luck!]