ARE THERE ANY FIXED STARS? 
363 
The simplest illustration we have of wave-motion is in the 
material waves which traverse the surface of water. Now 
here, be it noticed, we must not think of such waves as roll in 
upon the shores of the sea, but of the true waves which traverse 
the surface of open seas. In such waves there is not as there 
appears to be a rapid transmission of matter, but a simple os- 
cillation of the particles of the water. Suppose there are long 
rollers sweeping over the face of the ocean. Then we should 
call the distance from the crest of one roller to the crest of 
another the wave-length ; the difference of altitude between the 
crests of the rollers and the bottom of the “ trough ” between 
them would be the wave-height, or wave-amplitude as it is 
sometimes termed; and the rate at which the rollers travel 
would be the velocity of transmission, I mention these points, 
so tha.t in dealing with other waves which we are unable to 
recognise as visible entities, the significance of the terms we 
shall have to make use of may be understood by a reference to 
the familiar relations of the ocean-rollers. 
Now, suppose we wish to determine the wave-length of a roll- 
ing sea, what are the methods which would suggest themselves ? 
If we could measure a line extending from crest to crest at any 
moment, we should, of course, know the wave-length ; but fail- 
ing (as might well happen) such a means as this, it is obvious 
that our resource must be to determine first the velocity of the 
waves, and secondl}^ the number which pass in a given time. 
Suppose the first point gained (say by noticing the time which a 
particular roller occupies in travelling between two ships a mile 
apart), and, for convenience of illustration, let us imagine that 
the ascertained velocity of the rollers is 500 yards per minute. 
Now, suppose that an observer, counting the waves which pass 
the side of his ship, notices that 10 pass each minute. Then 
he knows at once that in that time the first which passed has 
travelled to a distance of 500 yards; and as all the 10 are dis- 
tributed over that distance, each must be 50 yards in length, if 
the ship has not moved in the interval. But if the ship has 
moved, there is a difference. For supposing the ship to have 
moved in the same direction as the waves, and at the rate of 
100 yards per minute, then the crest of the first wave is only 
400 yards off instead of 500, and the wave-length is but 
40 yards. In other words, the true length is less by 10 yards 
than the length which would be arrived at on the supposition 
that the ship is at rest. On the contrary, if the ship is moving 
at the same rate against the waves, the true distance of the first 
wave-crest is 600 yards, the true wave-length 60 yards ; and 
the effect of the ship’s motion is to cause an apparent increase 
of 10 yards in the wave-lengths. 
