Firstly, I found the RHF expansion of $\Phi_2$ and $\Phi_3$ is not symmetric at equation (4.29). Then I expand $\Phi_2$ by myself, the results showed it's $ \Phi_2 = (\chi_A\chi_A-\chi_B\chi_B)(\alpha\beta-\beta\alpha) - (\chi_A\chi_B-\chi_B\chi_A)(\alpha\beta+\beta\alpha) $ Moreover, even with t...

I understand that a common convention is to report the uncertainty of an analogue instrument as plus or minus half of the smallest scale division. By this logic, a measuring cylinder with $\pu{0.5 mL}$ graduations has an uncertainty of $\pu{\pm 0.25 mL}$. Because the measurement should also be re...