. Which is the best direction to choose? We shall probably all agree that it will be either directly up and down stream, or directly across it, and we may confine attention to these two directions. First suppose an oarsman
starts straight across stream. To keep straight he must set his boat at an angle to the stream. If he reaches his 4 mile limit in an hour, the stream has been virtually carrying him down 3 miles in a direction at right angles to his course: and the well-known relation between the sides of a right-angled triangle tells us that he has effectively pulled 5 miles in the hour. It will take him similarly an hour to come back, and the total journey will involve an effective pull of 10 miles.
Now suppose another oarsman,
, of equal skill elects to row up stream. In two hours he could pull 10 miles if there were no stream; but since meantime the stream has pulled him back 6 miles by "direct action" he will have only just reached the 4 mile limit from the start, and has still his return journey to go. No doubt he will accomplish this pretty quickly with the stream to help him, but his antagonist has already got home before he begins the return. We might have let him do his quick journey down stream first, but it is easy to see that this would gain him no ultimate advantage.
Michelson and Morley sent two rays of light on two journeys similar to those of the oarsmen
and