May S, 1S65.] 



♦ KNOWLEDGE • 



399 



for 65 sec3., by which tiiue the first wave has reached a point 100 

 yards distant from him, and a total of 3l!0 waves have passed him, 

 thus giving a distribution of 360 waves within the 100 yards, which 

 shows each wave to be l-300th part of llX) yards, or 10 in. in breadth. 

 This is quite right. But suppose the observer, during the 05 sees., 

 instead of standing still, to be unconsciously carried a distance of 

 20 yards, say, in the same direction as the waves are travelling, 

 and supposing the waves to be travelling at exactly the same speed 

 as in the first observation, tben the first wave, at the expirutitin 

 of the 05 sees., will have reached the 100 yards distance from the 

 starting-point, and obviously the 300th wave will have just passed 

 the starting-post as before; but not passed the observer this 

 time, because he has travelled 20 yards away from the .starting- 

 point in the same direction as the waves, and, as this is one-fifth 

 of the 100 yards, it is clear that only four-fifths, or 2SS, of tlie 

 300 waves can possibly have passed the observer, and these 2S8 

 will be all the waves that will be distributed over the remaining 

 four-fifths, or 80 yards of the distance, thus showing each wave to 

 be l-28Sth part of 80 yards, or 10 in. in breadth, just the sama 

 breadth as shown by the first observation, and not 8 in., as you 

 make it when your observer is travelling in the same directicm 

 as the waves. Then, again, suppose the observer during the 

 65 sees., instead of standing still, to bo unconscioush- carried 

 20 yards from the starting-point in a direction opposite to 

 that of the waves' motion; and supposing again that the waves 

 are travelling at exactly the same speed as before, then at the 

 expiration of the 65 sees, the first wave will have reached the 100 

 yards distance from the starting-point, and obviously the 300th 

 wave will again have just passed the starting-point and also passed 

 the observer as well this time, but clearly, in addition to these 300, 

 72 other waves must also have passed him, because he has travelled 

 20 yards, which is equal to one-fifth of the original distance, farther 

 back than the starting-point, and so an extra number of waves, 

 equal to one-fifth of the original number, must also have passed 

 him, thus giving a total of 432 waves distributed over the total 

 distance of 120 yards now in question, which shows each wave to 

 be l-432nd part of 120 yards, or 10 in. in breadth, just the same 

 breadth as sbown by my first and second observations, and not 

 12 in. as you make it when your observer is travelling in the 

 opposite direction to the waves. Thus, it is clear that the fact of 

 the observer moving in either direction, at the time of making the 

 obsctrations, does not alter the breadth of the waves in the 

 slightest degree, neither does it alter the speed at which the 

 waves are actually travelling along the surface of the water, 

 but it does alter the speed at which thej' pass the oljserver, 

 or, in other words, the number which pass him in a given time; for 

 in the first observation, when he stood still, 360 waves passed him 

 in the 65 sees., while in my second example, when the observer was 

 moving twenty yards in the same direction as the waves, only 288 

 passed him in the 65 sees., and in my third example, when moving 

 twenty yards in the opposite direction, -132 passed him in the same 

 time. And so with light waves. Supposing a star to be sending 

 na light waves of a certain breadth, the fact of us approaching that 

 star, and so travelling in an opposite direction to the light waves, 

 will not make the waves broader, as your example, quoted here- 

 with, would show ; but will simply cause us to receive them more 

 quickly than if we were standing still ; and similarly our recession 

 from the star, and so travelling in the same direction as the light 

 waves will not make the waves narrower, as your example would 

 show, but will simply cause ns to receive them less quickly, 

 according to the speed at which we are moving. Just as when you 

 see a highwayman in the road coming towards you, if you stand 

 still he will reach your pockets in a certain time ; but if you move 

 towards him (a very unlikely thing, I suppose) he will reach 

 them much more quickly, and, on the other hand, if you run away 

 from him he will get at them much less quickly, according to the 

 speed at which you run away ; and so you do not, by your move- 

 ments, alter the size of the highwayman at all, but you do alter 

 the speed at which he reaches you. And so, whatever change 

 there may be in the spectrum of a star, according as we are 

 approaching or receding from it, I do not see that it can be caused 

 by any narrowing or widening of the wave lengths (or breadths) of 

 its light, but by the greater or less speed at which the waves enter 

 the spectroscope, according as we are approaching or receding from 

 the star. 



Even supposing your examples in the paragraph in question to 

 be correct, the paragraph contains a blank contradiction of the 

 examples, for in your examples you show, in the first place, that 

 when the observer is standing still counting the passing waves the 

 result gives to each wave a breadth of 10 inches ; then, when he 

 moves in the opposite direction to the waves, you get a result 

 showing them to be 12 inches broad, which is 2 inches hroaiJer, and 

 when he moves in the same direction as the vaves, you get the 

 breadth 8 inches, which is 2 inches narrower, and yet, near the 



bottom of the paragraph, is this sentence, " If it (the truck with 

 ob.servur) moves in a direction oppoxite to that in which the waves 

 travel, they appear narrower (sic) ; if it travel with thoni, thoy appear 

 broader than they really are." You would, no doubt, notice that 1 

 indicated those mistakes by a query (?) and correction within 

 ])arentheses in tho places wIkm-o they occur in the paragraph as 

 <luoted in full at comnionconicnt of this letter. How you managed 

 to overlook such a contradi(Uion so far as to allow it to bo printed 

 both in the Cornhill for 1803 and in " Tho Sun," 1 am at a loss to 

 understand, and can only account for it on this theory, that the 

 statements in tho latter scntenco of your paragrapli, quoted above, 

 aro nearer the truth than your examples thoniRelves, because, when 

 an observer is moving in an opposite direction to tho waves, a 

 greater number of them pass him in any given time than when 

 standing still, and thus at first sight they appear narrower, as 

 stated in the sentence (and not 2 in. broader, as your examjilo 

 shows), though not narrower in reality, as I have proved by my 

 example. And similarly, wlien moving in the same direction as 

 the waves, a less number pass him in any given timo that when 

 standing still, and so thoy appear broader, as stated in tlio sentence 

 (and not 2 in. narrower, as your example shows), though they aro 

 not broaler in reality, as 1 have provcil by my example. There- 

 fore, it is clearly the results you obtain from your moving observer 

 which are wrong. 



Now 1 have tried my best to make myself plain, and hope 1 have 

 succeeded, and that you will receive this letter in the spirit in 

 which it is written — that of pure good will— for I greatly admire 

 your wonderful talents both as a lecturer and writer, and it is only 

 a sense of grief at finding such a mistake in the book in question 

 which impels me to write this letter. — With every good wish, I beg 

 to subscribe myself as usual, E.xcelsior. 



[I am altogether grateful to "Excelsior" for the care with 

 which he has explained my supposed mistake in the passage he has 

 quoted ; and although ho is mistaken, as I shall show, in attribu- 

 ting error to me in this place, yet it is clear that, as he has failed 

 in catching my meaning, I failed in my purpose, which was to 

 make my meaning clear. The article from which he quotes, 

 written in 1803 for the Cornhill Mariazine, was the first matter I 

 ever wrote for publication. Possibly this may account for its 

 being not so clear (it would seem) as I meant to make it if I could. 

 It was, however, written with great care ; I should hardly expect 

 to be believed if I were to tell how long I was at work upon it ; 

 and I had thought better of it than I fear I must now do— regarding 

 it simply as a piece of explanatory writing. I can only say, with 

 " Excelsior," that I had tried my best to make myself plain, and 

 hoped I had succeeded. 



In tho first place, I must admit that I c.aunot see anything in 

 the passage suggesting that I supposed, or wanted my readers to 

 suppose, that the breadth of waves in a canal would be altered by 

 the movements of a truck on the canal bank. It may have been, 

 possibly, the conviction that no one would imagine me to mean 

 this (in wkatever other way I might fail to make my meaning 

 clear) which prevented me from definitely saying that the waves 

 would not really be altered, let the observer career as he might 

 along the side of the canal. 



Perhaps the following abstract of my reasoning in the quoted 

 passage will set " Excelsior's" misgivings at rest : — ■ 



The real breadth of the waves is suppo.sed to be unknown to the 

 observer; only the details of tho observation, as recorded, are 

 available for forming an opinion. I point out, then, in my explana- 

 tion, that 



1. If the observer is, as he supposes, at rest, tho real breadth of 

 each wave is 10 in. 



2. If he is moving unconsciously in a direction contrary to that 

 of the waves at the stated rate, their real breadth is not 10 in., as 

 he mistakenly infers, but 12 in. ; in other words, he supposes them 

 to be narrower than they really are— 10 in., his estimate, being less 

 than 12 in., the real breadth. 



3. If he is moving, unconsciously, in the same direction as the 

 waves, at the stated rate, their real breadth is not 10 in., as he 

 mistakenly infers, but 8 in. ; in other words, he supposes them to 

 be broader than they really are— 10 in., his estimate, being greater 

 than 8 in., the real breadth. 



The measurement of the breadth of canal waves is not a matter 

 of much interest ; but the matter illustrated by this supposed ex- 

 periment is exceedingly interesting. When we are approaching or 

 receding from a source of sound waves, the breadth of the waves 

 is not altered, but our appreciation of their breadth is altered, in 

 other words the tone is changed — made higher if we are approach- 

 ing, lower if we are receding. For, observe, the tone we hear is 

 not the breadth of the waves, but indicates our appreciation of 

 their breadth. .So with light. If wo are receding from or ap- 

 proaching a source of light, we form a wrong estimate of the light's 



