THE FIRST AND THE LAST CATASTROPHE. 279 



showing that the i-ates of vibration of all these molecules of sodium all 

 over the universe, so far as we know, are as near as possible alike. 

 That implies a similarity of molecular structure, which is a great deal 

 more delicate than mere test of weight. You may weigh two fiddles 

 until you are tired, and you will never find out whether they are in 

 tune ; tlie one test is a great deal more delicate than the other. Let 

 us see how delicate this test is. Lord Rayleigh has remarked that 

 there is a natural limit for the precise position of a given line in the 

 spectrum, and for this i-eason. If a body which is emitting a sound 

 comes toward you, you will find that the pitch of the sound is altered. 

 Suppose that omnibuses run every ten minutes in the streets, and you 

 walk in a direction opposite to that in which they are coming, you 

 will obviously pass more omnibuses in an hour than if you walked in 

 an opposite direction. If a body emitting light is coming toward 

 you, you will find more waves in a certain direction than if it was 

 going from you ; consequently, if you are approaching a body emit- 

 ting light, the light will come quicker, the vibration will be of shorter 

 duration, and the light will be higher up in the spectrum it will be 

 more blue. If you are going away from the body, then the rate is 

 slower, the light is lower down on the spectrum. By means of varia- 

 tions in the positions of certain known lines of that character, the 

 actual rate of approach of certain fixed stars to the earth has been 

 measured, and the rate of going away of certain other fixed stars has 

 also been measured. Suppose we have a gas which is glowing in a 

 state of incandescence, all the molecules are giving out light at a cer- 

 tain specified rate of vibration ; but some of these are coming toward 

 us at a rate much greater than seventeen miles a minute, because the 

 temperature is higher when the gas is glowing, and others are also 

 going away at a much higher rate than that. The consequence is, 

 that instead of having one sharply-defined line on the spectrum, in- 

 stead of having light of exactly one bright color, we have light which 

 varies between certain limits. 



If the actual rate of the vibration of the molecules of the gas were 

 marked down upon the spectrum, we should not get that single bright 

 line there, but we should get a bright band overlapping it on every 

 side. Lord Rayleigh calculated that, in the most favorable circum- 

 stances, the breadth of this band would not be less than one-hundredth 

 of the distance between the sodium-lines. It is precisely upon that 

 experiment that the ev'idence of the exact similarity of molecules 

 rests. We see, therefore, from the nature of the experiment, that we 

 should get exactly the same results if the rate of vibration of all the 

 molecules was not exactly equal, but varied within certain very small 

 limits. If, for example, the rates of vibration varied in the same way 

 as the heads of different men, then we should get very much what we 

 get now from the experiment. From these two sources of evidence, 

 then, the evidence of their being of the same weight and degree of 



