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THE POPULAR SCIENCE MONTHLY.— SUPPLEMENT. 



may be compared to a wave-tossed sea, only that, 

 instead of a wave-tossed surface, there is wave- 

 tossed space." At every point, through every 

 point, along every line, athwart every line, myri- 

 ads of light-waves are at all times rushing with 

 the inconceivable velocity just mentioned. It is 

 from such waves that we have learned all we 

 know about the universe outside our own earth. 

 They bring to our shores news from other worlds, 

 though the news is not always easy to decipher. 



Now, seeing that we are thus immersed in an 

 ocean, athwart which infinite series of waves are 

 continually rushing, and, moreover, that we our- 

 selves, and every one of the bodies whence the 

 the waves proceed either directly or after reflec- 

 tion, are traveling with enormous velocity through 

 this ocean, the idea naturally presents itself that 

 we may learn something about these motions (as 

 well as about the bodies themselves whence they 

 proceed), by studying the aspect of the waves 

 which flow in upon us in all directions. Suppose 

 a strong swimmer who knew that, were he at 

 rest, a certain series of waves would cross him at 

 a particular rate — ten, for instance, in a minute — 

 were to notice that, when he was swimming di- 

 rectly facing them, eleven passed him in a minute 

 — he would be able at once to compare his rate 

 of swimming with the rate of the waves' motion. 

 He would know that while ten waves had passed 

 him on account of the waves' motion, he had by 

 his own motion caused yet another wave to pass 

 him, or, in other words, had traversed the dis- 

 tance from one wave-crest to the next. Thus he 

 would know that his rate was one-tenth that 

 of the waves. Similarly if, traveling the same 

 way as the waves, he found that only nine passed 

 him in a minute, instead often. Again, it is not 

 difficult to see that, if an observer were at rest, 

 and a body in the water, which by certain mo- 

 tions produced waves, were approaching or re- 

 ceding from the observer, the waves would come 

 ii faster in the former case, slower in the latter, 

 than if the body were at rest. Suppose, for in- 

 stance, 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 traveled 

 one-tenth as fast as the waves, and consider ten 

 waves proceeding from her bows — the first 

 would have to travel a certain distance be- 

 fore reaching the observer; the tenth, starling 



a minute later, instead of having to travel the 

 same distance, would have to travel this distance 

 diminished by the space 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 in 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 

 traveling at the same rate as before, only arriv- 

 ing in quicker succession, because of the contin- 

 ual 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 

 wave's 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 of 

 rate ; but, in the case of the approaching ship, 

 the breadth from crest to crest would be reduced, 

 while in the case of a receding ship the distance 

 from crest to crest would be increased. 



If the above explanation should still seem to 

 require closer attention than the general reader 

 may be disposed to give, the following, suggested 

 by a friend of mine — a very skillful mathematician 

 — will be found still simpler: Suppose a stream 

 to flow quite uniformly, and that at one place 

 on its banks an observer is stationed, while at an- 

 other higher up a person throws corks into the 

 water at regular intervals, say ten corks per min- 

 ute : then these will float down and pass the 

 other observer, wherever he may be, at the rate 

 of ten per minute, if the cork-thrower is at rest. 

 But if he saunters either up-stream or down-stream, 

 the corks will no longer float past the other at the 

 exact rate of ten per minute. If the thrower is 

 sauntering down-stream, then, between throwing 

 any cork and the next, he has walked a certain 

 way down, and the tenth cork, instead of having 

 to travel the same distance as the first before 

 reaching the observer, has a shorter distance to 

 travel, and so reaches that observer sooner. Or, 

 in fact, which some may find easier to see, this 

 cork will be nearer to the first cork than it would 

 have been if the thrower had remained still. The 

 corks will lie at equal distances from each other, 

 but these equal distances will be less than they 

 would have been if the observer had been at 



