
\section{Introduction}

As you may have learned in class, the Hertzsprung-Russell Diagram, or the 
``HR diagram'', is one of the most important tools used by astronomers: it 
helps us determine both the ages of star clusters and their distances. In 
your Astronomy 110 textbooks the type of HR diagram that you will normally 
encounter plots the Luminosity of a star (in solar luminosity units,
L$_{\rm Sun}$) versus 
its temperature (or spectral type). An example is shown here:

\begin{figure}[h]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/HRDiag.eps}
\end{figure}

The positions of the various main types of stars are labeled in this HR 
diagram. The Sun has a temperature of 5,800 K, and a luminosity of 1 L$_{\rm 
Sun}$. The 
Sun is a main sequence ``G'' star. All stars cooler than the Sun are plotted to 
the right of the Sun in this diagram. Cool main sequence stars (with spectral 
types of K and M) are plotted to the lower right of the Sun. Hotter main 
sequence stars (O, B, A, and F stars) are plotted to the upper left of the 
Sun's position. As the Sun runs out of hydrogen fuel in its center, it will 
become a red giant star--a star that is cooler than the Sun, but 100$\times$ 
more 
luminous. Red giants are plotted to the upper right of the Sun's position. As 
the Sun runs out of all of its fuel, it sheds its atmosphere and ends its days 
as a white dwarf. White dwarfs are hotter, and much less luminous than the 
Sun, so they are plotted to the lower left of the Sun's position in the HR 
diagram.

The HR diagrams for clusters can be very different depending on their ages. In 
the following examples, we show the HR diagram of a hypothetical cluster of 
stars at a variety of different ages. When the star cluster is very young, 
only the hottest stars have made it to the main sequence. In the HR diagram 
below, the G, K, and M stars (stars that have temperatures below 6,000 K) are 
still not on the main sequence, while those stars hotter than 7,000 K (O, B, 
A, and F stars) are already fusing hydrogen into helium at their cores:

\begin{figure}[h]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/1myr.eps}
\end{figure}

In the next HR diagram, we see a much older cluster of stars (100 million 
years = 100 Myr). In this older cluster, some of the hottest and most massive 
stars (the O and B stars) have evolved into red supergiants. The position of 
the ``main sequence turn off'' allows us to estimate the age of a cluster. 

\begin{figure}[h]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/100myr.eps}
\end{figure}

In the final HR diagram we have a much older cluster (10 billion years old = 
10 Gyr), now stars with one solar mass are becoming red giants, and we say the 
main sequence turn-off is at spectral type G (T = 5,500 K).

\begin{figure}[!ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/10gyr.eps}
\end{figure}


Some white dwarfs (produced by evolved A and F stars) now exist in the 
cluster. Thus, the HR diagram for a cluster of stars is useful for determining 
its age.


\section{Magnitudes and Color Index}

While the HR diagrams presented in your class lectures or textbook allow us to 
provide a very nice description of the evolution of stars and star clusters, 
astronomers do 
not actually directly measure either the temperatures or luminosities of stars. 
Remember that luminosity is a measure the total amount of energy that a star 
emits. For the Sun it is 10$^{\rm 26}$ Watts. But how much energy appears to be coming 
from an object depends on how far away that object is. Thus, to determine a 
star's luminosity requires you to know its distance. For example, the two 
brightest stars in the constellation Orion (see the ``Constellation Highlight''
for February in the back of this lab book), the red supergiant Betelgeuse and 
the blue supergiant Rigel, appear to have about the same brightness. But Rigel 
is six more times luminous than Betelgeuse--Rigel just happens to be further 
away, 
so it appears to have the same brightness even though it is pumping out much 
more energy than Betelgeuse. The ``Dog star'' Sirius, located to the southeast 
of Orion, is the brightest star in the sky and appears to be about 5 times 
brighter than either Betelgeuse or Rigel. But in fact, Sirius is a nearby star, 
and actually only emits 22$\times$ the luminosity of the Sun, or about 
1/2000$^{\rm th}$ the luminosity of Rigel!

Therefore, without a distance, it is impossible to determine a star's 
luminosity--and remember that it is very difficult to measure the distance to a 
star. We can, however, measure the relative luminosity of two (or more) stars 
if they are at the same distance: for example if they are both in a cluster of 
stars. If two stars are at the same distance, then the difference in their 
apparent brightness is a measurement of the true differences in their 
luminosities. To measure the apparent brightness of a star, astronomers use 
the ancient unit of ``magnitude''. This system was first developed by the Greek 
astronomer Hipparcos ({\it ca.} 190 to 120 BC). Hipparcos called the brightest 
stars ``stars of the first magnitude''. The next brightest were called ``stars 
of the second magnitude''. His system progressed all the way down to ``stars 
of the sixth magnitude'', the faintest stars you can see with the naked eye 
from a dark location. 

Astronomers adopted this system and made it more rigorous by defining a five 
magnitude difference to be exactly equal to a factor of 100 in brightness. 
That is, a first magnitude star is 100X brighter than a sixth magnitude star.  
If you are good with mathematics, you will find that a difference of one 
magnitude turns out to be a factor of 2.5 (2.5 $\times$ 2.5 $\times$ 2.5
$\times$ 2.5 $\times$ 2.5 = 100, we say that the fifth root of 100 = 
100$^{1/5}$ = 2.5). Besides this peculiar step size, it is also important to 
note that the magnitude system is upside down: usually when we talk about 
something being bigger, faster, or heavier, the quantity being measured 
increases with size (a car going 100 mph is going faster than one going 
50 mph, etc.). In the magnitude system, the brighter the object, the smaller 
its magnitude! For example, Rigel has an apparent magnitude of 0.2, while the 
star Sirius (which appears to be 4.5 times brighter than Rigel) has a 
magnitude of $-$1.43. 

Even though they are a bit screwy, and cause much confusion among Astronomy 
110 students, astronomers use magnitudes because of their long history and 
tradition. So, when astronomers measure the brightness of a star, they measure 
its apparent magnitude. How bright that star appears to be on the magnitude 
scale. Usually, astronomers will measure the brightness of a star in a variety 
of different color filters to allow them to determine its temperature. This 
technique, called ``multi-wavelength photometry'', is simply the measurement of 
how much light is detected on Earth at a specific set of wavelengths from a 
star of interest. Most astronomers use a system of five filters, one each for 
the ultraviolet region (the ``U filter''), the blue region (the ``B filter''), the 
visual (``V'', or green) region, the yellow-red region (``R''), and the 
near-infrared region (``I''). Generally, when doing real research, astronomers 
measure the apparent magnitude of a star in more than one filter. [Note: 
because the name of the filter can some times get confused with spectral 
types, filter names will be {\it italicized} to eliminate any possible 
confusion.]

To determine the temperature of a star, measurements of the apparent 
brightness in at least two filters is necessary. The difference between these 
two measurements is called the ``color index''. For example, the apparent 
magnitude in the {\it B} filter minus the apparent magnitude in the {\it V}
filter, ($B - V$), is one example of a color index (it is also the main color 
index used by astronomers to measure the temperature of stars, but 
any two of the standard filters can be used to construct a color index). Let us 
take Polaris (the ``North Star'') as an example. Its apparent {\it B} magnitude 
is 2.59, and its apparent {\it V} magnitude is 2.00, so the color index for 
Polaris is ($B - V$) = 2.59 $-$ 2.00 = 0.59. In Table 12.1, we list the 
($B - V$) color index for main sequence stars. We see that Polaris has the 
color of a G star.

In Table 12.1, we see that O and B stars have negative ($B - V$) color indices. 
We say that O and B stars are ``Blue'', because they emit more light in the 
{\it B} filter than in the {\it V} filter. We say that K and M stars are very 
red, as they emit much more {\it V} light than {\it B} light (and
even more light in the {\it R} and {\it I} filters!). A-stars emit the 
same amount of light at {\it B} and {\it V}, while F and G stars emit slightly 
more light at {\it V} than at {\it B} . With this type of information, we can 
now figure out the spectral types, and hence temperatures of stars by using 
photometry.

\begin{table}
\label{table:index}
\begin{center}
\caption{The ($B - V$) Color Index for Main Sequence Stars}
\begin{tabular}{|c|c|c|c|}\hline
Spectra Type & ($B - V$) & Spectral Type &($B - V$)\\
\hline
O and B Stars&$-$0.40 to $-$0.06&G Stars&0.59 to 0.76\\
\hline
A Stars&0.00 to 0.20&K Stars&0.82 to 1.32\\
\hline
F Stars&0.31 to 0.54&M Stars&1.41 to 2.00\\
\hline
\end{tabular}
\end{center}
\end{table}

\section{The Color-Magnitude HR Diagram}

To construct HR diagrams of star clusters, astronomers measure the apparent 
brightness of stars in two different color filters, and then plot the data 
into a ``Color-Magnitude'' diagram, plotting the apparent {\it V} magnitude 
versus the color index ($B - V$) as shown below. This following figure shows 
a color-magnitude diagram for a globular cluster. You might remember from class 
(or will soon be told!) that globular clusters are old, and that the low mass 
stars are evolving off the main sequence and 
becoming red giants. The main sequence turnoff for this globular cluster is at 
a color index of about ($B - V$) = 0.4, the color of F stars. An F star has a 
mass of about 1.5 M$_{\rm Sun}$, thus stars with masses near 1.5 M$_{\rm Sun}$ 
are evolving off the main sequence to become red giants, so this globular 
cluster is about 7 billion years old.


\begin{figure}[!ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/m15cm.eps}
\end{figure}

\section{The Color-Magnitude Diagram for the Pleiades}

In today's lab, you and your lab partners will construct a color magnitude 
diagram for the Pleiades star cluster. The Pleiades, sometimes known as the 
``Seven Sisters'' (see the constellation highlight for January at the back of
this lab manual), is a star cluster located in the wintertime constellation of 
Taurus, 
and can be seen with the naked eye. A wide-angle photograph of the Pleiades is 
shown below. Many people confuse the Pleiades with the Little Dipper because 
the brightest stars form a small dipper-like shape.

\begin{figure}[!ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{HRLAB/m45aj.eps}
\end{figure}

As you will find out, the Pleiades is a relatively young group of stars. We 
will be using photographs of the Pleiades taken using two different color 
filters to construct a Color-Magnitude diagram. If you look closely at the 
photograph of the Pleiades, you will notice that the brighter stars are larger 
in size than the fainter stars. Note: you are not seeing the actual disks
of the stars in these photographs. Brighter stars appear bigger on photographs
because more light from them is detected by the photograph. As the light
from the stars accumulates, it spreads out. Think of a pile of sand.
As you add sand to a pile, it develops a conical, pyramid shape. The addition
of more sand to the pile raises the height of the sand pile, but the {\it
base} of the sand pile has to spread more to support this height.
The same thing happens on a photograph. The more light there is, the
larger the spread in the {\it image} of the star. In reality, {\it all}
of the stars in the sky are much to far away to be seen as little disks (like 
those we see for the planets in our solar system) when viewed/imaged through 
{\it any existing telescope}.  We would
need to have a space-based telescope with a mirror 1.5 miles across to 
actually be able to see the stars in the Pleiades as little, resolved disks! 
[However, there are some special techniques astronomers have developed to
actually measure the diameters of stars. Ask your TA about them if you
are curious.]

Thus, we can use the sizes of the stars on a photograph to figure out
how bright they are, we simply 
have to measure their diameters! A special tool, called
a ``dynameter'', is used
to measure sizes of circles. You will be given a clear 
plastic dynameter in class. A replica of this dynameter is shown here:

\begin{figure}[!ht]
\centering
\leavevmode
\epsfysize=0.16\textheight
\epsfbox{HRLAB/dynameter.eps}
\end{figure}

As demonstrated, a dynameter allows you to measure the diameter of a star 
image by simply sliding the dynameter along until the edges of the star just 
touch the lines. In the example above, the star image is 2.8 mm in diameter. 
On the following two pages are digitized scans of two photographs of the 
Pleiades taken through {\it B} and {\it V} filters. These photographs were digitized to 
allow us to put in an X-Y scale so that you can keep track of which star is 
which in the two different photographs. You should be able to compare the 
digitized photographs with the actual photo shown above and see that most of 
the brighter stars are on all three images.
\clearpage
\begin{figure}[!ht]
\begin{center}
\centering
%\leavevmode
\setlength{\abovecaptionskip}{0pt}
\setlength{\belowcaptionskip}{10pt}
\includegraphics[scale=0.8]{HRLAB/hrlabB.eps}
\end{center}
%\epsfysize=0.8\textheight
%\epsfbox{hrlabV.eps}
\caption{This is not the right figure for use in this lab--manually insert
the correct one here.}
\end{figure}
\clearpage
\begin{figure}[!ht]
\begin{center}
\centering
\setlength{\abovecaptionskip}{0pt}
\setlength{\belowcaptionskip}{10pt}
\includegraphics[scale=0.8]{HRLAB/hrlabV.eps}
%\leavevmode
%\epsfysize=0.8\textheight
%\epsfbox{hrlabV.eps}
\caption{This is not the right figure for use in this lab--manually insert
correct one here.}
\end{center}
\end{figure}
\clearpage
\subsection{Procedure}

The first task for this lab is to collect your data. What you need to do for 
this lab is to measure the diameters of ten of the 63 stars on both digitized 
photographs. At the end of this lab there is a data table that has the final
data for 53 of the 63 stars. It is missing the information for ten of the
stars (\#'s 7, 8, 13, 18, 30, 39, 53, 55, 61, and 63). You must collect the
data for these ten stars.  

{\bf Task \#1:} First, identify the stars with the missing data on {\it both} of the 
digitized photographs (use their X,Y positions to do this). Then measure
their diameters of these ten stars on both photographs using the dynameter. 
Write the V and B diameters into the appropriate spaces within the data table.
[Note: You will probably not be able to measure the diameters to the same
precision as shown for the other stars in the data table. Those diameters were 
measured using a computer. Do the best you can---make several measurements of each star
and average the results.]
({\bf 15 points})
~ ~\\

\subsection{Converting Diameters to Magnitudes}

Obviously, the diameter you measure of a star on a photograph has no obvious 
link to its actual magnitude. For example, we could blow the photograph up, or 
shrink it down. The diameters of the stars would change, but the relative
change in size between stars of different brightnesses would stay the same. To
turn diameters into magnitudes requires us to ``calibrate'' the two 
photographs. For example, the brightest star in the Pleiades, ``Alcyone'' (star
\#35), has 
a {\it V} magnitude of 2.92, and has a {\it V} diameter of 4.4 mm. We have used 
this star to calibrate our data.  
Once you have completed measuring the diameters of the stars, you must convert 
those diameters (in millimeters) into {\it V} magnitudes and ($B - V$) color 
index. To do so, requires you to use the following two equations:

\begin{center}
    {\it V}(mag) =  $-$2.95$\times$(V mm) + 15.9              (Eq. \# 1)\\

~~\\
and \\
~~\\
     ($B - V$) =  $-$1.0$\times$(B mm $-$  V mm) + 0.1         (Eq. \#2)
\end{center}

These equations might seem confusing to you because of the negative number in 
front of the diameters. But if you remember, the brighter the star, the 
smaller its magnitude. Brighter stars appear bigger, so bigger diameters mean 
smaller magnitudes! That is why there is a negative sign. Using the example of 
Alcyone, its {\it V} diameter is 4.4 mm and it has a {\it B} diameter of 4.7 
mm. Putting the {\it V} diameter into equation \#1 gives: {\it V} (mag) =  
$-$2.95$\times$(4.4 mm) + 15.9 = $-$13.0 + 15.9 = 2.9. So, the {\it V} magnitude 
of Alcyone is correct: {\it V} = 2.9, and we have calibrated the photograph. Its color index can be found using Eq. 
\#2: ($B - V$) = $-$ 1.0$\times$(4.7 $-$ 4.4) + 0.1 = $-$1.0$\times$(0.4) + 
0.1 = $-$0.20. Alcyone is a B star!

~ ~ \\

{\bf Task \#2:} Convert all of the {\it B} and {\it V} diameters into {\it V}
magnitudes and ($B - V$) color index, entering them into the proper column in 
your data table. Use any of the other stars in the table to see how 
it is done. Make sure all students in your group have complete tables
with all of the data entered. {\bf (15 points)} 

\subsection{Constructing a Color-Magnitude Diagram}

The collection of the data is now complete. In 
this lab you are getting exactly the same kind of experience in ``reducing 
data'' that real astronomers do. Aren't you glad you didn't have to
measure the diameters of all 63 stars? Obtaining and reducing data can be very 
tedious, tiring, or even 
boring. But it is an essential part of the scientific process. Because of the 
possibility of mis-measurement of the star diameters, a real astronomer doing 
this lab would probably measure all of the star diameters at least three times 
to insure that they had not made any errors. Today, we will assume you did 
everything exactly right, but we will provide a check shortly.

Now we want to finally get to the goal of the lab: constructing a 
Color-Magnitude diagram. In this portion of the lab, we will be plotting the 
{\it V} magnitudes vs. the ($B - V$) color index. On the following page is a 
blank grid that has {\it V} magnitude on the Y axis, and the ($B - V$) color 
index on the X axis. Now we want to plot your data onto this blank 
Color-Magnitude diagram to closely examine what kind of stars are in the 
Pleiades.

~ ~\\
{\bf Task \#3:} For each star in your table, plot its position where the ($B - V$) 
color index is the X coordinate, and the {\it V} magnitude is the Y coordinate.
Note that some stars will have very similar magnitudes and colors because
they are the same types of star. When this happens, 
simply plot them as close together as possible, making sure they are slightly 
separated for clarity. All students must complete their own Color-Magnitude
diagram. ({\bf 15 points})

\begin{figure}[!ht]
\begin{center}
\centering
\setlength{\abovecaptionskip}{0pt}
\setlength{\belowcaptionskip}{10pt}
\includegraphics[scale=0.8]{HRLAB/emptyhrdiag.eps}
%\leavevmode
%\epsfysize=0.8\textheight
%\epsfbox{hrlabV.eps}
\caption{The Color-Magnitude Diagram for the Pleiades}
\end{center}
\end{figure}

{\bf Error checking:} All of your stars should fit within the boundaries of the
Color-Magnitude diagram! If not, go back and re-measure the problem star(s) to 
see if you have 
made an error in the {\it B} or {\it V} diameter or in the calculations.

\section{Results}

If you have done everything correctly, you should now have a Color-Magnitude 
diagram in which your plotted stars trace out the main sequence for the 
Pleiades. Use your Color-Magnitude diagram to answer the following questions:

\begin{flushleft}
1. Are there more B stars in the Pleiades, or more K stars? ({\bf 5 points})

~\\

2. Given that the Sun is a main sequence G star, draw an ``X'' to mark the spot 
where the Sun would be in your Color-Magnitude diagram for the Pleiades 
({\bf 5 points})

~\\

3. The faintest stars that the human eye can see on a clear, dark night is 
{\it V = 6.0}. If the Sun was located in the Pleiades, could you see it with 
the naked eye? ({\bf 5 points})

~\\

4. Are there any red giants or supergiants in the Pleiades? What does this 
tell you about the age of the Pleiades? ({\bf 5 points})

~\\

\end{flushleft}
\clearpage
\section{Summary (35 points)} 


Please summarize the important concepts of this lab.

\begin{itemize}
\item{Describe how an HR diagram is constructed.}
\item{If you have plotted your HR Diagram for the Pleiades correctly,
you will notice that the faint, red stars seem to have a spread when
compared to the brighter, bluer stars. Why do you think this occurs? How might
you change your observing or measuring procedure to fix this problem? [Hint:
is it harder or easier to measure big diameters vs. small diameters?]}
\item{Why are HR diagrams important to astronomers?}  
\end{itemize}

\noindent
Use complete sentences, and proofread your lab before handing it in.

\section{Possible Quiz Questions}

\begin{flushleft}

1. What is a magnitude?  Which star is brighter, a star with V = -2.0, or one 
with V = 7.0?

~\\
2. In an HR Diagram, what are the two quantities that are plotted?

~\\
3. What are the properties of a white dwarf?

~\\
4. What are the properties of a red giant?

~\\
5. What is a Color Index, and what does it tell you about a star?

\section{Extra Credit (ask your TA for permission before attempting, 5 points)}

White dwarfs are 100$\times$ less luminous than the Sun, but are hot, and 
have a negative color index ($B - V$) =  $-$0.2. Given that a factor of 100 = 
5 magnitudes, is it possible to plot the positions of white dwarfs on your 
Color-Magnitude diagram for the Pleiades? 

\end{flushleft}
\clearpage
\begin{table}
\begin{center}
\caption{Data Table}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\# &X&Y &V(mm) &B(mm) &V(mag) &($B - V$) \\
\hline
01 & 157.00 & 832.00 & 3.10 & 2.89 & 6.76 & 0.31\\
\hline
02 & 157.61 & 832.20 & 2.49 & 2.00 & 8.50 & 0.59\\
\hline
03 & 178.33 & 821.70 & 2.37 & 1.70 & 8.91 & 0.77\\
\hline
04 & 183.40 & 830.51 & 2.32 & 1.60 & 9.06 & 0.82\\
\hline
05 & 190.53 & 818.94 & 2.24 & 1.52 & 9.29 & 0.82\\
\hline
06 & 190.62 & 834.99 & 2.23 & 1.52 & 9.32 & 0.81\\
\hline
07 &192.98  &865.44  &  &  &  & \\
\hline
08 &197.37  &754.50  &  &  &  & \\
\hline
09 &202.78  &696.35  &2.23  &1.46  &9.32  &0.87\\
\hline
10 & 203.87 & 810.57 & 2.36 & 1.72 & 8.94 & 0.74\\
\hline
11 & 210.57 & 789.29 & 2.32 & 1.62 & 9.06 & 0.80\\
\hline
12 & 212.22 & 693.49 & 2.48 & 1.97 & 8.58 & 0.61\\
\hline
13 & 233.44 &830.40  &  &  &  & \\
\hline
14 & 234.34 & 759.27 & 2.35 & 1.57 & 8.97 & 0.88\\
\hline
15 & 235.50 & 751.74 & 2.40 & 1.85 & 8.82 & 0.65\\
\hline
16 & 246.00 & 807.00 & 3.26 & 3.07 & 6.28 & 0.29\\
\hline
17 & 252.95 & 795.24 & 2.75 & 2.35 & 7.78 & 0.50\\
\hline
18 &254.95  &688.02  &  &  & & \\
\hline
19 & 259.60 & 730.54 & 2.39 & 1.74 & 8.85 & 0.75\\
\hline
20 & 260.00 & 795.00 & 2.35 & 1.77 & 8.97 & 0.68\\
\hline
21 & 265.00 & 792.00 & 2.24 & 1.48 & 9.29 & 0.86\\
\hline
22 & 265.00 & 831.00 & 2.95 & 2.65 & 7.20 & 0.40\\
\hline
23 & 266.66 & 831.82 & 2.20 & 1.36 & 9.41 & 0.94\\
\hline
24 & 269.27 & 731.47 & 2.18 & 1.33 & 9.47 & 0.95\\
\hline
25 & 270.00 & 789.00 & 2.31 & 1.62 & 9.09 & 0.79\\
\hline
26 & 274.00 & 790.00 & 2.32 & 1.70 & 9.06 & 0.72\\
\hline
27 & 276.28 & 836.35 & 2.50 & 1.98 & 8.53 & 0.62\\
\hline
28 & 277.19 & 811.96 & 2.22 & 1.55 & 9.35 & 0.77\\
\hline
29 & 283.00 & 792.00 & 2.35 & 1.75 & 8.97 & 0.70\\
\hline
30 &285.00  &774.00  & &  & & \\
\hline
31 & 288.00 & 786.00 & 2.20 & 1.42 & 9.41 & 0.88\\
\hline
32 & 289.50 & 852.50 & 2.18 & 1.54 & 9.47 & 0.74\\
\hline
33 & 291.00 & 822.00 & 4.24 & 4.46 & 3.39 & $-$0.12\\
\hline
34 & 297.00 & 822.00 & 3.46 & 3.38 & 5.69 & 0.18\\
\hline
35 & 298.00 & 793.00 & 4.40 & 4.70 & 2.92 & $-$0.20\\
\hline
36 & 299.00 & 749.00 & 4.09 & 4.23 & 3.83 & $-$0.04\\
\hline
37 & 304.00 & 773.00 & 2.39 & 1.79 & 8.85 & 0.70\\
\hline
38 & 308.00 & 777.00 & 2.31 & 1.67 & 9.09 & 0.74\\
\hline
39 & 310.00 &794.04  &  &  &  & \\
\hline
40 & 312.00 & 748.00 & 3.35 & 3.20 & 6.02 & 0.25\\
\hline
\end{tabular}
\end{center}
\end{table}
\clearpage
\begin{table}
\begin{center}
\caption{Data Table (cont.)}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\# &X&Y &V(mm) &B(mm) &V(mag) &($B - V$) \\
\hline
41 & 316.46 & 832.35 & 2.52 & 2.01 & 8.47 & 0.61\\
\hline
42 & 317.00 & 766.00 & 3.93 & 4.00 & 4.31 & 0.03\\
\hline
43 & 319.14 & 731.31 & 2.38 & 1.81 & 8.88 & 0.67\\
\hline
44 & 320.29 & 742.55 & 2.17 & 1.46 & 9.50 & 0.81\\
\hline
45 & 322.43 & 819.50 & 2.17 & 1.52 & 9.50 & 0.75\\
\hline
46 & 325.00 & 756.00 & 3.62 & 3.57 & 5.22 & 0.15\\
\hline
47 & 327.00 & 787.00 & 2.20 & 1.47 & 9.41 & 0.83\\
\hline
48 & 327.80 & 841.25 & 2.34 & 1.68 & 8.99 & 0.76\\
\hline
49 & 329.00 & 771.00 & 2.87 & 2.52 & 7.43 & 0.45\\
\hline
50 & 332.00 & 794.00 & 2.62 & 2.14 & 8.17 & 0.58\\
\hline
51 & 335.13 & 732.56 & 2.28 & 1.54 & 9.17 & 0.84\\
\hline
52 & 347.41 & 654.23 & 2.15 & 1.43 & 9.55 & 0.82\\
\hline
53 & 352.00 &756.00  &  &  &  & \\
\hline
54 & 359.05 & 685.95 & 2.35 & 1.70 & 8.97 & 0.75\\
\hline
55 &361.00  &807.00  &  &  &  & \\
\hline
56 & 368.31 & 692.12 & 2.35 & 1.69 & 8.96 & 0.76\\
\hline
57 & 375.90 & 729.41 & 2.20 & 1.50 & 9.41 & 0.80\\
\hline
58 & 375.90 & 729.41 & 2.36 & 1.73 & 8.94 & 0.73\\
\hline
59 & 386.00 & 813.00 & 2.37 & 1.72 & 8.91 & 0.75\\
\hline
60 & 387.50 & 683.69 & 2.20 & 1.54 & 9.41 & 0.76\\
\hline
61 &397.48  &769.11  &  &  &  & \\
\hline
62 & 410.49 & 839.98 & 2.34 & 1.62 & 8.99 & 0.82\\
\hline
63 &420.52  &720.04  &  &  &  & \\
\hline
\end{tabular}
\end{center}
\end{table}
\clearpage
