8o PLEASANT WA YS IN SCIENCE. 



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 

 skilful 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 another higher 

 up a person throws corks into the water at regular intervals, 

 say ten corks per minute ; then these will float down and 

 pass the other observer, wherever he may be, at the rate 01 

 ten per minute, if the cork-thrower is at rest But if he 

 saunters either up-stream or down-stream, the corks will nc 

 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 rest. If, on the contrary, the cork-thrower saunters 

 up-stream, the corks will be somewhat further apart than if 

 he had remained at rest And supposing the observer to 

 know beforehand that the corks would be thrown in at the 

 tate of ten a minute, he would know, if they passed him at a 

 greater rate than ten a minute (or, in other words, at a less 

 distance from each other than the stream traversed in the 

 tenth of a minute), that the cork-thrower was travelling 

 down-stream or approaching him ; whereas, if fewer than ten 

 a minute passed him, he would know that the cork-thrower 

 was travelling away from him, or up-stream. But also, if the 



