deletions | additions       diff --git a/begin_centering_textbf_Abstract_end__.tex b/begin_centering_textbf_Abstract_end__.tex  index f111418..c9c4265 100644  --- a/begin_centering_textbf_Abstract_end__.tex  +++ b/begin_centering_textbf_Abstract_end__.tex 
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\textbf{Abstract}  \end{centering}  \begin{centering}  \par We performed spectroscopy on the $5^{2}S_{1/2}$ → $5^{2}P_{3/2}$ transition of rubidium 85 and rubidium 87. Using Doppler spectroscopy, we found the energies of the transition of the F=2 excited state of the $5^{2}S_{1/2}$ state of rubidium 85 to the $5^{2}P_{3/2}$ state, the F=3 excited state of the $5^{2}S_{1/2}$ state of rubidium 85 to the $5^{2}P_{3/2}$ state, the F=1 excited state of the $5^{2}S_{1/2}$ state of rubidium 87 to the $5^{2}P_{3/2}$ state, and the F=2 excited state of the $5^{2}S_{1/2}$ state of rubidium 87 to the $5^{2}P_{3/2}$ state. Our results were not quite consistent with theory within uncertainty, but there are many possible reasons for this slight discrepancy. Using saturation absorption spectroscopy, we were able to resolve the hyperfine structure of each of the previously mentioned energy levels. One major contribution to our Our  results again were  not being quite  consistent with theory theory, but that  is likely mainly due to the fact  that we modeled our frequency scan as linear but it is not actually linear. \end{centering}