Why Does Rotating the Michelson-Morley Apparatus Change the Time Delay?

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BareFootKing
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I am having difficulty understanding why when the apparatus in the figure on page 448 (http://web.physics.ucsb.edu/~phys22/K%20and%20K%20Sections/KK_Chapter11.pdf ) is rotated 90 degrees the time delay is twice what it was before. When I think about I immediately think it would be the same since the two are merely switching the positions.


It discuses it on page 449. The last paragraph. I didn't understand the reason as to why.
 
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