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The method of measuring the mo- lestial motions by its means, described tion of very swiftly-travelling bodies by the method, in words which I shall presnoting changes in the light-waves which ently quote, in the number of Fraser's reach us from them-one of the most re- Magazine for January, 1868, two months markable methods of observation ever before the earliest enunciation of its nayet devised by man-has recently been ture by the physicists just named. placed upon its trial, so to speak, with It will be well briefly to describe the results exceedingly satisfactory to the principle of this interesting method, bestudents of science who had accepted the fore considering the attack to which it facts established by it. The method will has been recently subjected, and its trinot be unfamiliar to many readers of umphant acquittal from defects charged these pages. The principle involved was against it. This brief description will first noted by M. Doppler, but not in a not only be useful to those readers who form which promised any useful results. chance not to be acquainted with the The method actually applied appears to method, but may serve to remove objechave occurred simultaneously to several tions which suggest themselves, I notice, persons, as well theorists as observers. to many who !have had the principle of Thus Secchi claimed in March, 1868, to the method imperfectly explained to have applied it, though unsuccessfully; them. Huggins in April, 1868, described his Light travels from every self-luminous successful use of the method. I myself, body in waves which sweep through the wholly unaware that either of these ob- ether of space at the rate of 185,000 miles servers was endeavoring to measure ce- per second. As I have elsewhere pointed New SERIES.- Vol. XXVI., No. 3

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out, “the whole of that region of space of a ship raised waves which, if the ship over which astronomers have extended were at rest, would travel along at the their survey, and doubtless a region many rate of ten a minute past the observer's millions of millions of times more ex- station. Then clearly, if the ship aptended, may be compared to a wave- proached him, each successive wave tossed sea, only that instead of a wave- would have a shorter distance to travel, tossed surface, there is wave-tossed and so would reach him sooner than it space.” At every point, through every otherwise would have done. Suppose, point, along every line, athwart every for instance, the ship travelled one-tenth line, myriads of light-waves are at all as fast as the waves, and consider ten times rushing with the inconceivable ve- waves proceeding from her bows-the locity just mentioned. It is from such first would have to travel a certain diswaves that we have learned all we know tance before reaching the observer; the about the universe outside our own earth. tenth, starting a minute later, instead of They bring to our shores news from other having to travel the same distance, would worlds, though the news is not always have to travel this distance diminished easy to decipher.

by the space over which the ship had Now, seeing that we are thus immersed passed in one minute (which the wave in an ocean, athwart which infinite series itself passes over in the tenth of a minof waves are continually rushing, and ute); instead, then, of reaching the obmoreover that we ourselves, and every server one minute after the other, it one of the bodies whence the waves pro- would reach him in nine-tenths of a ceed either directly or after reflection, minute after the first. Thus it would are travelling with enormous velocity seem to him as though the waves through this ocean, the idea naturally were coming in faster than when the presents itself that we may learn some- ship was at rest, in the proportion of thing about these motions (as well as ten to nine, though in reality they would about the bodies themselves whence they be travelling at the same rate as beproceed), by studying the aspect of the fore, only arriving in quicker succeswaves which flow in upon us in all direc- sion, because of the continual shortening tions. Suppose a strong swimmer who of the distance they had to travel, on acknew that, were he at rest, a certain se- count of the ship's approach. If he ries of waves would cross him at a par- knew precisely how fast they would articular rate-ten, for instance, in a minute rive if the ship were at rest, and deter-were to notice that when he was swim- mined precisely how fast they did arrive, ming directly facing them, eleven passed he would be able to determine at once him in a minute-he would be able at the rate of the ship's approach, at least once to compare his rate of swimming with the proportion between rate and the the rate of the waves' motion. He rate of the waves' motion. Similarly if, would know that while ten waves had owing to the ship's recession, the apparpassed him on account of the waves' mo- ent rate of the waves' motion were retion, he had by his own motion caused duced, it is obvious that the actual yet another wave to pass him, or in other change in the wave motion would not be words, had traversed the distance from a difference of rate; but, in the case of one wave-crest to the next. Thus he the approaching ship, the breadth from would know that his rate was one-tenth crest to crest would be reduced, while in that of the waves. Similarly if, travels the case of a receding ship the distance ling the same way as the waves, he found from crest to crest would be increased. that only nine passed him in a minute, If the above explanation should still instead of ten. Again, it is not difficult seem to require closer attention than the to see that if an observer were at rest, general reader may be disposed to give, and a body in the water, which by cer- the following, suggested by a friend of tain motions produced waves, were ap

mine-a very skilful mathematicianproaching or receding from the observer, will be found still simpler: Suppose a the waves would come in faster in the stream to flow quite uniformly, and that former case, slower in the latter, than if at one place on its banks an observer is the body were at rest. Suppose, for in- stationed, while at another higher up a stance, that some machinery at the bows person throws corks into the water at regular intervals, say ten corks per min- travel onwards like the water-waves or ute; then these will float down and pass the corks of the preceding illustrations. the other observer, wherever he may be, If the body which emits them is rapidly at the rate of ten per minute, if the cork- approaching us the waves are set closer thrower is at rest. But if he saunters together or narrowed, whereas if the either up stream or down stream, the body is receding they are thrown farther corks will no longer float past the other apart or broadened. And if we can in at the exact rate of ten per minute. If any way recognize such narrowing or the thrower is sauntering down stream, broadening of the light-waves, we know then between throwing any cork and the just as certainly that the source of light next, he has walked a certain way down, is approaching us or receding from us as and the tenth cork, instead of having to the case may be, as our observer in the travel the same distance as the first be- second illustration would know from the fore reaching the observer, has a shorter distance between the corks whether his distance to travel, and so reaches that friend, the cork-thrower, was drawing observer sooner. Or, in fact, which near to him or travelling away from him. some may find easier to see, this cork But it may be convenient to give anwill be nearer to the first cork than it other illustration, drawn from waves would have been if the thrower had re- which, like those of light, are not themmained still. The corks will lie at equal selves discernible by our senses—I refer distances from each other, but these equal to those aerial waves of compression and distances will be less than they would rarefaction which produce what we call have been if the observer had been at sound. These waves are not only in rest. If, on the contrary, the cork- this respect better suited than waterthrower saunters up stream, the corks waves to illustrate our subject, but also will be somewhat farther apart than if he because they travel in all directions. had remained at rest. And supposing through aerial space, not merely along a. the observer to know beforehand that surface. The waves which produce a. the corks wouid be thrown in at the rate certain note, that is, which excite in our of ten a minute, he would know, if they minds, through the auditory nerve, the passed him at a greater rate than ten a impression corresponding to a certain minute (or, in other words, at a less dis- tone, have a definite length. So long as tance from each other than the stream the observer, and a source of sound. traversed in the tenth of a minute), that vibrating in one particular period, rethe cork-thrower was travelling down- main both in the same place, the note stream or approaching him; whereas if is unchanged in tone, though it may fewer than ten a minute passed him, he grow louder or fainter according as the would know that the cork-thrower was vibrations increase or diminish in amplitravelling away from him, or up-stream. tude. But if the source of sound is ap-But also, if the cork-thrower were at proaching the hearer, the waves rest, and the observer moved up-stream thrown closer together and the sound is. -that is, towards him—the corks would rendered more acute (the longer waves. pass him at a greater rate than ten a giving the deeper sound); and, on the minute; whereas if the observer were other hand, if the source of sound is retravelling down-stream, or from the ceding from the hearer, the waves are thrower, they would pass him at a slower thrown farther apart and the sound is. rate. If both were moving, it is easily rendered graver. The rationale of these: seen that if their movement brought changes is precisely the same as that of them nearer together, the number of the changes described in the preceding, corks passing the observer per minute illustrations. It might, perhaps, appear would be increased, whereas if their that in so saying we were dismissing the movements set them farther apart, the illustration from sound, at least as an innumber passing him per minute would dependent one, because we are explainbe diminished.

ing the illustration by preceding illustraThese illustrations, derived from the tions. But in reality, while there is abmotions of water, suffice in reality for solutely nothing new to be said respectour purpose. The waves which are ing the increase and diminution of disemitted by luminous bodies in space tances (as between the waves and corks

are

of the preceding illustration), the illus- periment theoretically more exact but tration from sound has the immense ad- practically unsatisfactory. As it rushes vantage of admitting readily of experi- past instead of through him, there is a mental tests. It is necessary only that brief time during which the rate of apthe rate of approach or recession should proach is rapidly being reduced to bear an appreciable proportion to the nothing, followed by a similarly brief rate at which sound travels. For waves time during which the rate of recession are shortened or lengthened by approach gradually increases from nothing up to or recession by an amount which bears the actual rate of the engines' velocities to the entire length of the wave the same added together. proportion which the rate of approach Where a bell is sounded on the enor recession bears to the rate of the gine, as in America, the effect is better wave's advance. Now it is not very recognized, as I had repeated occasion difficult to obtain rates of approach or to notice during my travels in that counrecession fairly comparable with the ve- try. Probably this is because the tone locity of sound,-about 364 yards per of a bell is in any case much more clearsecond. An express train at full speed ly recognized than the tone of a railway travels, let us say, about 1,800 yards per whistle. The change of tone as a clangminute, or 30 yards per second. Such ing bell is carried swiftly past (by the a velocity would suffice to reduce all the combined motions of both trains) is not sound-waves proceeding from a bell or at all of such a nature as to require close whistle upon the engine, by about one attention for its detection. twelfth part, for an observer at rest on a However, the apparent variation of station-platform approached by the en- sound produced by rapid approach or gine. On the contrary, after the engine recession has been tested by exact experhad passed him, the sound-waves pro- iments. On a railway uniting Utrecht ceeding from the same bell cr whistle and Maarsen were placed," the late would be lengthened by one-twelfth. Professor Nichol wrote, “ at intervals of The difference between the two tones something upwards of a thousand yards, would be almost exactly three semitones. three groups of musicians, who remained If the hearer, instead of being on a motionless during the requisite period. platform, were in a train carried .past Another musician on the railway soundthe other at the same rate, the differ- ed at intervals one uniform note; and ence between the tone of the bell in its effects on the ears of the stationary approaching and its tone in receding musicians have been fully published. would be about three tones. It would From these, certainly—from the recordnot be at all difficult so to arrange mat- ed changes between grave and the more ters, that while two bells were sound- acute, and vice versa —confirming, even ing the same note-Mi, let us say—one numerically, what the relative velocities

one engine the other on the might have enabled one to predict, it apother, a traveller by one should hear his pears justifiable to conclude that the own engine's bell, the bell of the ap- general theory is correct; and that the proaching engine, and the bell of the note of any sound may be greatly modisame engine receding, as the three notes fied, if not wholly changed, by the veloc-Do-Mi-Sol, whose wave-lengths are ity of the individual hearing it," or, as the numbers 15, 12, and 10. We he should have added, by the velocity of have here differences very easily to be the source of sound : perhaps more correcognized even by those who are not rect than either, is the statement that musicians. Every one who travels much the note may be altered by the apby train must have noticed how the tone proach or recession of the source of of a whistle changes as the engine sound- sound, whether that be caused by the ing it travels past. The change is not motion of the sounding body or of the quite sharp, but very rapid, because the hearer himself, or of both. other engine does not approach with a It is difficult, indeed, to understand certain velocity up to a definite moment how doubt can exist in the mind of any and then recede with the same velocity. one competent to form an opinion on the It could only do this by rushing through matter, though, as we shall presently see, the hearer, which would render the ex- some students of science and one or two

bell on

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