deletions | additions       diff --git a/Based_on_our_tilde_chi__.tex b/Based_on_our_tilde_chi__.tex  index 9411298..21b8782 100644  --- a/Based_on_our_tilde_chi__.tex  +++ b/Based_on_our_tilde_chi__.tex 
...
In addition to the uncertainty coming from the measurements, the fit of the data points might also result in some uncertainties. In order to see whether our fits in Figure \ref{fig:directmethoddata} and Figure \ref{fig:VB} are reliable or not, we calculated the $\tilde{\chi}^2$ for those fits.  Based on our $\tilde{\chi}^2$ values, calculation,  we can conclude that our obtained Verdet constants are obtained from accurate fits from our data. \\  For the direct fit method, we obtained a $\tilde{\chi}^2=1.150$ for the fit of our data with no field applied，and $\tilde{\chi}^2=1.206$ for the fit of our data with a magnetic field applied.  For the slope fit  method, we obtained a $\tilde{\chi}^2=1.02$. $\tilde{\chi}^2=1.018$.\\  As a $\tilde{\chi}^2\approx1$ indicates a good fit, we can conclude that our value of $21.095\pm 0.003\frac{radians}{T \cdot m}$ was obtained from a line which fits our data well.Likewise, for the direct fit method, $\tilde{\chi}^2=1.15$ for the fit of our data with no field applied， and $\tilde{\chi}^2=1.21$ for the fit of our data with a magnetic field applied.  Therefore, we can assume that our curves fit our data well, giving us reasonable results. %The issues that had the most impact on our data occurred with the lock-in method. We initially took data for currents that were much too high for our solenoid, causing possible temperature effects in our data. We also saturated the lock-in amplifier without realizing it. For future experiments, even more accuracy could be achieved by measuring in smaller angle increments around the angle that was found to be most sensitive. It would also be interesting to test the methods we have used here using a material with a much smaller Verdet constant.  %Furthermore, had we had more time and not had to retake our data due to the temperature effects on the solenoid, we could have measured the Verdet constant for different materials.