# Michelson-Morley Experiment: A.P. French's book on Special Relativity

I am doing a self-study of A.P. French's book on Special relativity and I am stuck at the Michelson-Morley experiment. I am having a few difficulties in the derivation in the book,

1. On page 54, it is mentioned that the ether wind and light add up using vector addition and that the resultant velocity relative to the interferometer is given by $$\sqrt{c^2 - v^2}$$. I do not understand this since if the ether wind is parallel to the horizontal arm, shouldn't the velocity along the vertical arm remain independent of the ether wind speed? Am I missing something here?
2. On page 64, there is a remark that the MM experiment shows the null result for any random orientation of the arm relative to the horizontal. However, when I try to follow the steps for the usual MM experiment, my equations does not solve the equation $$t_1-t_2 = \frac{2(l_{10} - l_{20})/c}{\sqrt{1 - \frac{v^2}{c^2}}}$$ derived earlier in the literature. Did anybody solve this? If requested, I will post my solution here for better clarity.