The ratios of specific heats found for argon, air and carbon dioxide were found using Cl\'{e}ment and Desormes' method to be $1.57 \pm 0.03$, $1.38 \pm 0.01$ and $1.31 \pm 0.02$ respectively. These values of $\gamma$ were $3\sigma$, $2\sigma$ and $1\sigma$ away from their respective accepted values of 1.668, 1.403 and 1.304. All three linear fits were found to pass through the origin to within 1$\sigma$ for argon and air, and to within 2$\sigma$ for $CO_2$. The residual plots for air and carbon dioxide had an acceptable number of values falling outside of the 1$\sigma$ region, but for argon, almost half the values were outside one standard deviation from the model. Also, the fact that the ratio for Argon is so much lower is most likely due to a systematic error of not waiting long enough for the pressure to stabilize before taking measurements. For air, it's harder to explain since equilibrium was reached much faster and therefore harder to miss. Considering that the error there is smaller than the other two though, the Taylor approximation could be starting to play a role there. Graphing the pressure level at constant intervals and graphing it in order to precisely see the plateau would have helped in getting rid of the systematics, and using one more term of the Taylor expension would have also been necessary for higher precisions.

As for R\"{u}chardt's method, the value for the ratio of specific heat of air was found to be $1.39 \pm 0.01$ which is within one standard deviation of the accepted value of 1.403. Here, since we were only able to obtain 4 to 6 oscillation with our apparatus was 7, most of the error comes from the human reflex in starting and stopping the stopwatch, which was assumed to be 100ms. The error is therefore smaller on the runs with more oscillations, which is why a weighted mean was talked. To improve, we would need longer tubes in which we could get more oscillations and also an electronic system for starting and stopping the timer to get rid of the human error. The error here is still as large as the one on the $\gamma$ for air obtained by Cl\'{e}ment and Desormes' method, which agrees with this value to within one standard deviation.