DRIFTING LIGHT- WA VES. 79 



he found that only nine passed him in a minute, instead 

 of ten. 



Again, it is not difficult to see that if an observer were at 

 rest, and a body in the water, which by certain motions 

 produced waves, were approaching or receding from the 

 observer, the waves would come in faster in the former case, 

 slower in the latter, than if the body were at rest Suppose, 

 for instance, that some machinery at the bows of a ship 

 raised waves which, if the ship were at rest, would travel 

 along at the rate of ten a minute past the observer's station. 

 Then clearly, if the ship approached him, each successive 

 wave would have a shorter distance to travel, and so would 

 reach him sooner than it otherwise would have done. 

 Suppose, for instance, the ship travelled one-tenth as fast as 

 the waves, and consider ten waves proceeding from her 

 bows the first would have to travel a certain distance 

 before reaching the observer; the tenth, starting a minute 

 later, instead of having to travel the same distance, would 

 have to travel this distance diminished by the space ove'r 

 over which the ship had passed in one minute (which the 

 wave itself passes over in the tenth of a minute) ; instead, 

 then, of reaching the observer one minute after the other, it 

 would reach him nine-tenths of a minute after the first. 

 Thus it would seem to him as though the waves were 

 coming in faster than when the ship was at rest, in the 

 proportion of ten to nine, though in reality they would 

 be travelling at the same rate as before, only arriving in 

 quicker succession, because of the continual shortening of 

 the distance they had to travel, on account of the ship's 

 approach. If he knew precisely how fast they would arrive 

 if the ship were at rest, and determined precisely how fast 

 they did arrive, he would be able to determine at once 

 the rate of the ship's approach, at least the proportion 

 between her rate and the rate of the waves' motion. 

 Similarly if, owing to the ship's recession, the apparent rate 

 of the waves' motion were reduced, it is obvious that the 

 actual change in the wave motion would not be a difference 



