![178
Before trying to explain the process by which he reached his results it
may be well to give his own account of the discovery of Neptune by a
similar method:
[39]
“Neptune has proved a planet of surprises. Though its orbital
revolution is performed direct, its rotation apparently takes place
backward, in a plane tilted about 35° to its orbital course. Its satellite
certainly travels in this retrograde manner. Then its appearance is
unexpectedly bright, while its spectrum shows bands which as yet,
for the most part, defy explanation, though they state positively the
vast amount of its atmosphere and its very peculiar constitution. But
first and not least of its surprises was its discovery,—a set of
surprises, in fact. For after owing recognition to one of the most
brilliant mathematical triumphs, it turned out not to be the planet
expected.
“‘Neptune is much nearer the Sun than it ought to be,’ is the
authoritative way in which a popular historian puts the intruding
planet in its place. For the planet failed to justify theory by not
fulfilling Bode’s law, which Leverrier and Adams, in pointing out the
disturber of Uranus, assumed ‘as they could do no otherwise.’ Though
not strictly correct, as not only did both geometers do otherwise, but
neither did otherwise enough, the quotation may serve to bring
Bode’s law into court, as it was at the bottom of one of the
strangest and most generally misunderstood chapters in
celestial mechanics.
“Very soon after Uranus was recognized as a planet, approximate
ephemerides of its motion resulted in showing that it had several
times previously been recorded as a fixed star. Bode himself
discovered the first of these records, one by Mayer in 1756, and Bode
and others found another made by Flamsteed in 1690. These
observations enabled an elliptic orbit to be calculated which satisfied
them all. Subsequently others were detected. Lemonnier discovered
that he had himself not discovered it several times, cataloguing it as
a fixed star. Flamsteed was spared a like mortification by being dead.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-30-320.jpg)
![180
started with Bouvard’s work, with the result of finding it very much
the reverse of good. The farther he went, the more errors he found,
until he was obliged to cast it aside entirely and recompute these
perturbations himself. The catalogue of Bouvard’s errors he gave
must have been an eye-opener generally, and it speaks for the ability
and precision with which Leverrier conducted his investigation that
neither Airy, Bessel, nor Adams had detected these errors, with the
exception of one term noticed by Bessel and subsequently by Adams.
[40]
The result of this recalculation of his was to show the more
clearly that the irregularities in the motion of Uranus could not
be explained except by the existence of another planet
exterior to him. He next set himself to locate this body. Influenced by
Bode’s law, he began by assuming it to lie at twice Uranus’ distance
from the Sun, and, expressing the observed discrepancies in
longitude in equations, comprising the perturbations and possible
errors in the elements of Uranus, proceeded to solve them. He could
get no rational solution. He then gave the distance and the extreme
observations a certain elasticity, and by this means was able to find a
position for the disturber which sufficiently satisfied the conditions of
the problem. Leverrier’s first memoir on the subject was presented to
the French Academy on November 10, 1845, that giving the place of
the disturbing planet on June 1, 1846. There is no evidence that the
slightest search in consequence was made by anybody, with the
possible exception of the Naval Observatory at Washington. On
August 31 he presented his third paper, giving an orbit, mass, and
more precise place for the unknown. Still no search followed. Taking
advantage of the acknowledging of a memoir, Leverrier, in September,
wrote to Dr. Galle in Berlin asking him to look for the planet. The
letter reached Galle on the 23rd, and that very night he found a
planet showing a disk just as Leverrier had foretold, and within 55′ of
its predicted place.
“The planet had scarcely been found when, on October 1, a letter
from Sir John Herschel appeared in the London Athenaeum
announcing that a young Cambridge graduate, Mr. J. C. Adams, had
been engaged on the same investigation as Leverrier, and with similar](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-32-320.jpg)
![181
182
results. This was the first public announcement of Mr. Adams’ labors.
It then appeared that he had started as early as 1843, and had
communicated his results to Airy in October, 1845, a year
before. Into the sad set of circumstances which prevented the
brilliant young mathematician from reaping the fruit of what might
have been his discovery, we need not go. It reflected no credit on
any one concerned except Adams, who throughout his life maintained
a dignified silence. Suffice it to say that Adams had found a place for
the unknown within a few degrees of Leverrier’s; that he had
communicated these results to Airy; that Airy had not considered
them significant until Leverrier had published an almost identical
place; that then Challis, the head of the Cambridge Observatory, had
set to work to search for the planet but so routinely that he had
actually mapped it several times without finding that he had done so,
when word arrived of its discovery by Galle.
“But now came an even more interesting chapter in this whole
strange story. Mr. Walker at Washington and Dr. Petersen of Altona
independently came to the conclusion from a provisional circular orbit
for the newcomer that Lalande had catalogued in the vicinity of its
path. They therefore set to work to find out if any Lalande stars were
missing. Dr. Petersen compared a chart directly with the heavens to
the finding a star absent, which his calculations showed was about
where Neptune should have been at the time. Walker found that
Lalande could only have swept in the neighborhood of Neptune on
the 8th and 10th of May, 1795. By assuming different eccentricities
for Neptune’s orbit under two hypotheses for the place of its
perihelion, he found a star catalogued on the latter date which
sufficiently satisfied his computations. He predicted that on searching
the sky this star would be found missing. On the next fine
evening Professor Hubbard looked for it, and the star was
gone. It had been Neptune.
[41]
“This discovery enabled elliptic elements to be computed for it, when
the surprising fact appeared that it was not moving in anything
approaching the orbit either Leverrier or Adams had assigned.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-33-320.jpg)
![Instead of a mean distance of 36 astronomical units or more, the
stranger was only at 30. The result so disconcerted Leverrier that he
declared that ‘the small eccentricity which appeared to result from Mr.
Walker’s computations would be incompatible with the nature of the
perturbations of the planet Herschel,’ as he called Uranus. In other
words, he expressly denied that Neptune was his planet. For the
newcomer proceeded to follow the path Walker had computed. This
was strikingly confirmed by Mauvais’ discovering that Lalande had
observed the star on the 8th of May as well as on the 10th, but
because the two places did not agree, he had rejected the first
observation, and marked the second as doubtful, thus carefully
avoiding a discovery that actually knocked at his door.
“Meanwhile Peirce had made a remarkable contribution to the whole
subject. In a series of profound papers presented to the American
Academy, he went into the matter more generally than either of the
discoverers, to the startling conclusion ‘that the planet Neptune is not
the planet to which geometrical analysis had directed the telescope,
and that its discovery by Galle must be regarded as a happy
accident.’
[42]
He first proved this by showing that Leverrier’s two
fundamental propositions,—](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-34-320.jpg)
![183
184
“1. That the disturber’s mean distance must be between 35
and 37.9 astronomical units;
“2. That its mean longitude for January 1, 1800, must have been
between 243° and 252°,—were incompatible with Neptune. Either
alone might be reconciled with the observations, but not both.
“In justification of his assertion that the discovery was a happy
accident, he showed that three solutions of the problem Leverrier
had set himself were possible, all equally complete and decidedly
different from each other, the positions of the supposed planet being
120° apart. Had Leverrier and Adams fallen upon either of the outer
two, Neptune would not have been discovered.
[43]
“He next showed that at 35.3 astronomical units, an important
change takes place in the character of the perturbations because of
the commensurability of period of a planet revolving there with that
of Uranus. In consequence of which, a planet inside of this limit
might equally account for the observed perturbations with the one
outside of it supposed by Leverrier. This Neptune actually did. From
not considering wide enough limits, Leverrier had found one
solution, Neptune fulfilled the other.
[44]
And Bode’s law was
responsible for this. Had Bode’s law not been taken originally as
basis for the disturber’s distance, those two great geometers,
Leverrier and Adams, might have looked inside.
“This more general solution, as Peirce was careful to state, does not
detract from the honor due either to Leverrier or to Adams. Their
masterly calculations, the difficulty of which no one who has not had
some experience of the subject can appreciate, remain as an
imperishable monument to both, as does also Peirce’s to
him.”](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-35-320.jpg)
![187
reducing the residuals to a minimum—that is, would come nearest to
accounting for them. In fact, supposing that the unknown planet
would be about the distance from the Sun indicated by Bode’s law,
the limits within which he assumed trial distances were narrow, and,
as it proved, wholly beyond the place where it was found. This
method, which in its general outline Percival followed, consisted
therefore of a process of trial and error for the distance (with the
mean motion) and for the place of X in its orbit (ε). For the other
three elements (e, ῶ and m) he used in the various solutions 24 to
37 equations drawn from the residuals of Uranus at different dates,
and expressed in terms of ε. He did this in order to have several
corroborative calculations, and to discover which of them accorded
most closely with the perturbations observed.
We have seen that in 1908-09 Percival was inquiring about the exact
residuals of Uranus, and he must have been at work on them soon
afterwards, for on December 1, 1910, he writes to Mr. Lampland that
Miss Williams, his head computer, and he have been puzzling away
over that trans-Neptunian planet, have constructed the curve of
perturbations, but find some strange things, looking as if
Leverrier’s later theory of Uranus were not exact. This work
had been done by Leverrier’s methods “but with extensions in the
number and character of the terms calculated in the perturbation in
order to render it more complete.” Though uncertain of his results,
he asks Mr. Lampland, in April 1911, to look for the planet. But he
was by no means himself convinced that his data were accurate, and
he computed all over again with the residuals given by Gaillot, which
he considered more accurate than Leverrier’s in regard to the
masses, and therefore the attractions, of the known planets
concerned. Incidentally he remarks at this point in his Memoir,
[45]
in
speaking of works on celestial mechanics, that “after excellent
analytical solutions, values of the quantities involved are introduced
on the basis apparently of the respect due to age. Nautical Almanacs
abet the practice by never publishing, consciously, contemporary
values of astronomic constants; thus avoiding committal to doubtful](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-38-320.jpg)
![196
CHAPTER XX
PLUTO FOUND
[46]
Percival had long intended that his Observatory should be
permanent, and that his work, especially on the planets, should be
forever carried on there with an adequate foundation. Save for an
income to his wife during her lifetime, he therefore left his whole
fortune in a trust modeled on the lines of the Lowell Institute in
Boston, created eighty years earlier by his kinsman John Lowell, Jr.
The will provides for a single trustee who appoints his own
successor; the first being his cousin Guy Lowell, the next the present
trustee, Percival’s nephew, Roger Lowell Putnam. Dr. V. M. Slipher
and Mr. C. O. Lampland, who have been at the Observatory from an
early time, are the astronomers in charge, carrying on the founder’s
principles of constantly enlarging the field of study, and using for the
purpose the best instrumental equipment to be procured.
Of course the search was continued for the planet X, but without
success, and for a time almost without hope, not only because its
body is too small to show a disk, but also by reason of the multitude
of stars of like size in that crowded part of the heavens, the Milky
Way, where it is extremely difficult to detect one that has
moved. It was as if out of many thousand pins thrown upon
the floor one were slightly moved and someone were asked to find
which it was. Mere visual observation was clearly futile, for no man
could record the positions of all the points of light from one night to
another. The only way to conduct a systematic search was through
an enduring record, that is by taking photographs of the probable
sections of the sky, and comparing two of the same section taken a
few days apart to discover a point of light that had changed its place](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-45-320.jpg)
![197
—no simple matter when more than one hundred thousand stars
showed upon a single plate. This process Percival tried, but although
his hopes were often raised by finding bodies that moved, they
proved to be asteroids hitherto unknown,
[47]
and the X sought so
long did not appear.
[48]
Percival had felt the need of a new photographic telescope of
considerable light power and a wider field, and an attempt was
made to borrow such an instrument, for use while one was being
manufactured, but in vain. Then came the war when optical glass for
large lenses could not be obtained, and before it was over Percival
had died. After his death Guy Lowell, the trustee, took up the
project, but also died too soon to carry it out. At last in 1929 the
lens needed was obtained, the instrument completed in the
workshop of the Observatory, and the search renewed in March with
much better prospects. Photographs of section after section of the
region where X was expected to be were taken and examined by a
Blink comparator. This is a device whereby two photographs of
slightly different dates could be seen through a microscope at
the same time as if superposed. But with all the improvement
in apparatus months of labor revealed nothing.
After nearly a year of photographing, and comparing plates, Mr.
Clyde W. Tombaugh, a young man brought up on a farm but with a
natural love of astronomy, was working in this search at Flagstaff,
when he suddenly found, on two plates taken January 23 and 29,
1930, a body that had moved in a way to indicate, not an asteroid,
but something vastly farther off. It was followed, and appeared night
after night in the path expected for X at about the distance from the
sun Percival had predicted. Before giving out any information it was
watched for seven weeks, until there could be no doubt from its
movements that it was a planet far beyond Neptune, and was
following very closely the track which his calculations had foretold.
Then, on his birthday, March 13, the news was given to the world.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-46-320.jpg)
![199
perturbations were small the resulting elements of the orbit could at
best be rather rough approximations, the actual accordance is all
that could be demanded by a severe critic.
“Even so, the table does not tell the whole story. Figure 1
[49]
shows
the actual and the predicted orbits, the real positions of the planet at
intervals from 1781 to 1989, and the positions resulting from
Lowell’s calculations. It appears at once that the predicted positions
of the orbit and of the planet upon it were nearest right during the
19th century and the early part of the 20th, while at earlier
and later dates the error rapidly increased. Now this
(speaking broadly) is just the interval covered by the observations
from which the influence of the planet’s attraction could be
determined and, therefore, the interval in which calculation could
find the position of the planet itself with the least uncertainty.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-48-320.jpg)
![200
Predicted and Actual Orbits of PLUTO
“In the writer’s judgment this test is conclusive.”
[50]
Later observations, and computations of the orbit of Pluto, do
not vary very much from those that Professor Russell had
when he wrote. Two of the most typical—giving more elements—are
as follows:
Predicted Nicholson and
Mayall
F. Zagar
Period 282 years 249.2 248.9
Eccentricity 0.202 0.2461 0.2472](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-49-320.jpg)
![201
Longitude of
perihelion
204.9 222° 23′ 20″ .17 222° 29′ 39″
.4
Perihelion passage 1991.2 1889.75 1888.4
Inclination about
10°
17° 6′ 58″ .4 17° 6′ 50″ .8
Semi-major axis 43. 39.60 39.58
Perihelion distance 34.31 29.86 29.80
Aphelion distance 51.69 49.35 49.36
Except for the eccentricity, and the inclination which he declared it
impossible to calculate, these results have proved as near as, with
the uncertainty of his data, he could have expected; and in regard to
the position of the planet in its orbit it will be recalled that he found
two solutions on opposite sides, both of which would account almost
wholly for the residuals of Uranus. The one that came nearest to
doing so he had regarded as the least probable because it placed
the planet in a part of the sky that had been much searched without
finding it; but it was there that Pluto appeared—a striking proof of
his rigorous analytic method.
But the question of its mass has raised serious doubts whether Pluto
can have caused the perturbations of Uranus from which he
predicted its presence, for if it has no significant mass the whole
basis of the calculation falls to the ground, and there has been found
a body travelling, by a marvellous coincidence, in such an
orbit that, if large enough, it would produce the perturbations
but does not do so.
[51]
Now as there is no visible satellite to gauge
its attraction, and as it will be long before Pluto in its eccentric orbit
approaches Neptune or Uranus closely enough to measure
accurately by that means, the mass cannot yet be determined with
certainty. What is needed are measures of position of the highest
possible accuracy of Neptune and Uranus, long continued and
homogeneous.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-50-320.jpg)
![202
The reasons for the doubt about adequate mass are two.
[52]
One
that with the largest telescopes it shows no visible disk, and must
therefore be very small in size, and hence in mass unless its density
is much greater, or its albedo far less, than those of any other known
planet. The other substantially that the orbits of Uranus and
Neptune can be, and are more naturally, explained by assuming
appropriate elements therefor, without the intervention of Pluto’s
disturbing force. This is precisely what Percival stated in discussing
the correctness of the residuals—that it was always possible to
account for the motions of a planet, whose normal orbit about the
sun is not definitely ascertained, by throwing any observed
divergencies either on errors in the supposed orbit, or upon
perturbations by an unknown body.
The conditions here are quite unlike those at the discovery of
Neptune, for there the existence of the perturbations was
clear, because fairly large, and the orbit predicted was wrong
because of an error in the distance assumed; and the question was
whether the presence of Neptune in the direction predicted, though
in a different orbit, was an accident, or inevitable. Here the predicted
orbit is substantially the actual one, adequate to account for the
perturbations of Uranus if such really exist, and the question is
whether they do or not. If not the discovery of Pluto is a mere
unexplained coincidence which has no connection with the
prediction. Whether among recognized uncertainties it is more
rational to suppose a very high density, and very low albedo, with
corresponding perturbations of Uranus and Neptune, whose orbits
are still imperfectly known, or to conclude that a planet, which would
account for these things if dense enough, revolves in fact in the
appropriate path, a mere ghost of itself—a phantom but not a force
—one who is not an astronomer must leave to the professionals.](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-51-320.jpg)
![APPENDIX I
Professor Henry Norris Russell’s later views on the size of Pluto
(written to the Biographer and printed with the writer’s consent).
Later investigations have revealed a very curious situation. When
once the elements of Pluto’s orbit are known, the calculation of the
perturbations which it produces on another planet, such as Neptune,
are greatly simplified. But the problem of finding Pluto’s mass from
observations of Neptune is still none too easy, for the perturbations
affect the calculated values of the elements of Neptune’s orbit, and
are thus “entangled” with them in an intricate fashion.
Nicholson and Mayall, in 1930, attacked the problem, and found that
the perturbations of Neptune by Pluto, throughout the interval from
its discovery to the present, were almost exactly similar to the
effects which would have been produced by certain small changes in
the elements of Neptune’s orbit, so that, from these observations
alone, it would have been quite impossible to detect Pluto’s
influence. Outside this interval of time, the effects of the
perturbations steadily diverge from those of the spurious changes in
the orbit, but we cannot go into the future to observe them, and all
we have in the past is two rather inaccurate observations made in
1795 by Lalande.
[53]
If the average of these two discordant
observations is taken as it stands, Pluto’s mass comes out 0.9 times
that of the Earth, and this determination is entitled to very little
weight.
Uranus is farther from Pluto, and its perturbations are smaller; but it
has been accurately observed over one and a half revolutions, as
against half a revolution for Neptune, and this greatly favors the](https://image.slidesharecdn.com/43024-250406014342-34fcb446/85/Sourcebook-for-research-in-music-Crabtree-53-320.jpg)
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- 11. SOURCEBOOK FOR RESEARCH IN MUSIC PHILLIP D. CRABTREE AND DONALD H. FOSTER INDIANA UNIVERSITY PRESS BLOOMINGTON & INDIANAPOLIS
- 12. Copyright © 1993 by Phillip D. Crabtree and Donald H. Foster All rights reserved No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, without permission in writing from the publisher. The Association of American University Presses' Resolution on Permissions constitutes the only exception to this prohibition. The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984. ©T“ Manufactured in the United States of America Library of Congress Cataloging-in-Publication Data Crabtree, Phillip. Sourcebook for research in music / Phillip D. Crabtree and Donald H. Foster, p. cm. Includes indexes. ISBN 0-253-31476-3 (cloth : alk. paper) 1. Music—Bibliography. 2. Music—History and criticism— Bibliography 3. Bibliography—Bibliography—Music. I. Foster, Donald H. II. Title. III. Title: Source book for research in music. ML113.C68 1993 016.7—dc20 1 2 3 4 5 97 96 95 94 93 92-32038
- 13. Preface xi Contents 1. Introductory Materials 1 Common Bibliographical Terms 1 German Bibliographical Terms 8 French Bibliographical Terms 12 Library of Congress Music Classification 14 2. Basic Bibliographical Tools for Research in Music 21 Music Literature Sources 22 Current Writings about Music 22 Periodicals 23 Periodical Articles 24 Bibliographic Databases 25 Music Dictionaries and Encyclopedias 26 Festschriften 27 Monographs in Series 27 Congress Reports 27 Dissertations 28 Biographies of Musicians 29 Garland Composer Resource Manuals 30 Other Bibliographies of Music Literature Sources 31 Directories and Catalogs of Institutions 32 Libraries 32 Library and Union Catalogs 33 American 33 European 34 International 34 Musical Instrument Collections 36 Schools of Music 36 International Music Guides 37 Music Sources 38 Primary Sources of Early Music: Manuscripts and Prints 38 General 38 American 40 Editions of Music 40 Thematic Catalogues 42 158119
- 14. VI Contents Catalogues of Librettos 42 Discographies 43 Bibliographies of Discographies 43 Guides to Currently Available Recordings 44 Specialized Discographies 44 Classical and Opera 44 Gregorian Chant and Early Music 45 American Music 45 Conductors 45 Women Composers 45 Ethnomusicology 46 Jazz 46 Selected General Bibliographies 46 3. Area Bibliographies and Other Reference Sources 48 Musicology 48 The History of Musicology 49 Comprehensive Overviews 50 Selected Discussions of the Discipline in Chronological Order 51 Discussions of Musicology in the United States in Chronological Order 52 Music Historiography 53 Miscellaneous Sources 53 Bibliographic Database 54 Ethnomusicology 54 General Sources 55 Classic Presentations of the Field 55 Works about Ethnomusicology as a Field of Research 56 Surveys of World Music 56 Instruments 57 Selected Monographs and Studies 57 Examplars of Ethnomusicological Method 57 General Works about Individual Cultures or Cultural Areas 58 Bibliographies and Other Reference Guides 60 Performance Practice 60 General Treatments 62 Studies Specific to an Era 62 Examples of More Specialized Discussions 62 Discussions of the Performance Practice Movement 64 Guides for Performers 65
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- 16. Contents vii Studies of Historical Interest 67 Editions of Selected Primary Sources 68 Anthologies 69 Bibliographies of the Literature 69 Music Theory 69 The History of Theory 71 General Issues of Style and Analysis 72 Twentieth-Century Theories of Tonal Music 73 Theories of Tonality and Tonal Music 73 Schenkerian Analysis 74 Twentieth-Century Theories of Nontonal Music 75 Atonality, Serialism, and Set Theory 75 Modality and Octatonicism 75 Microtonality 76 Musical Time: Theories of Rhythm and Meter 76 Theories of Musical Timbre 76 Aesthetics and Semiotics of Music 77 Texts of Theoretical Treatises 78 Bibliographies and Guides to the Literature 78 Music Education 80 The History of Music Education 81 Research Methodology 81 General Reference Sources 82 Research Overviews 82 Bibliographies, Directories, and Indexes 83 Bibliographies in Other Selected Areas 85 African-American Music 85 American Music 86 Dance 87 Jazz 88 Women in Music 89 Dictionaries and Encyclopedias of Music 90 General Dictionaries and Encyclopedias 90 Of Historical Interest 93 Biographical Dictionaries and Encyclopedias 93 International 94 North American 95 English 96 Of Historical Interest 96 Dictionaries of Terms 96 Individual Subject Areas 98 Of Historical Interest 98 Specialized Dictionaries and Encyclopedias 99
- 17. viii Contents Musical Instruments and Makers 100 General 100 Of Historical Interest 100 Strings 100 Winds 101 Percussion 101 Keyboard 101 Opera 101 Sacred Music 102 Jazz 103 Musical Themes and Compositional Devices Miscellaneous Sources 104 The New Harvard Dictionary of Music: Articles of General Interest 104 Research in Music 105 Music History, Style Periods, and Trends 105 Countries, Cities, and Musical Centers 105 General Music Theory 106 Musical Forms and Genres 106 Performance and Performance Practice 106 The Music Profession 107 5. Sources Treating the History of Music 108 Historical Surveys of Western Music 108 Miscellaneous Sources 110 Of Historical Interest 110 Histories in Series 110 Of Historical Interest 115 Single-Volume Studies in English of Historical Periods 116 Medieval, Renaissance 116 Baroque, Classic, Romantic 117 Twentieth Century 117 Miscellaneous Sources 118 Histories of American Music 118 English-Language Sources on Musical Genres and Forms 119 Vocal 120 Solo Song 120 Cantata 121 Dramatic Music 121 Surveys and General Studies 121 Studies by Country 122 Czech Republic 122 England 122
- 18. Contents ix France 123 Germany and Austria 123 Italy 123 Libretto Studies 124 Secular Part Song 124 Sacred Music 124 Oratorio, Passion, and Requiem 126 Surveys of Choral Music 127 Instrumental 127 Symphonic Music 127 Chamber Music 128 Keyboard Music 129 Sonata 130 Fugue 130 Miscellaneous Sources 131 Chronologies and Outlines 131 General and Comprehensive 131 Twentieth Century 133 American 133 Biographies of Composers in English 133 Series of Composers' Biographies in English 143 Collections of Excerpts from Primary Sources on Music 147 Histories of Musical Instruments 148 Pictorial Sources on Music History 149 General 150 Instruments and Ensembles 150 6. Current Research Journals in Music 152 Musicology 153 Bibliography 153 Historical Musicology 153 Limited to a Country and/or Period 154 Limited to a Single Composer 155 Iconography 155 Performance Practice 156 Ethnomusicology 156 Music Theory and New Music 157 Performing Instrument, Medium, or Genre 157 Music Education 158 Other Journals 159 7. Editions of Music 160 Sources in English on Music Notation and Editing 160 General Sources 161 Editing Early Music 162
- 19. x Contents New Notation 163 Historical Sets and Monuments of Music 163 Limited to an Era 164 Limited to a Region 165 Limited to an Era and a Region 166 Limited to a Medium or Genre 167 Instrumental Ensemble 167 Keyboard 168 Lute/Guitar 168 Vocal 168 Limited to a Medium or Genre and to a Region 168 Without Specific Limitations 169 Composers' Complete Works and Catalogues 170 Anthologies of Music 180 General 180 Limited to an Era 182 Limited to a Medium or Genre 183 Limited to a Medium or Genre and to a Region 184 Comprehensive Multivolume Set 185 8. Miscellaneous Sources 188 Manuals of Style and Other Aids to Research, Writing, and Publication 188 General Aids to Research 189 Computer Aids to Music Research 190 General Manuals of Style and Other Guides to English 191 Guides to Writing about Music 192 Guides to the Publication Process 193 Miscellaneous 194 The Music Industry 194 General Sources 194 Careers in Music 195 Performing Arts, Competitions, and Festivals 196 Musical Instrument Makers 197 Music Publishing and Copyright 197 Music Recording and Production 198 Grant Support for the Arts 199 Arts Management 199 Periodicals and Periodical Database 200 Indexes 202 Index of Authors, Editors, Compilers, and Translators 202 Index of Titles 214
- 20. Preface This book is intended as an introductory reference source of varied information, largely bibliographical, pertaining to research in the field of music. It has come largely out of the authors' years of experience in teaching Introduction to Graduate Study and Senior Research, two courses in music bibliography, research, and writing at the College-Conservatory of Music, University of Cincinnati, and it may function as a text in such courses, as well as in any mu¬ sic research class or seminar, graduate or upper-class undergradu¬ ate. If so used, it is not necessarily meant to be followed page by page from beginning to end, but adapted in accordance with the needs and emphases of different instructors and schools or individ¬ uals using the book. Its use is by no means limited to the classroom; it may also serve as a guide to current important sources in music for music researchers, faculty members, librarians, performing and teaching musicians, and musical amateurs. The Sourcebook for Research in Music consists of seven chapters of bibliographies, each of a different type of source, preceded by a chapter of introductory materials regarding research in music. The bibliographies are usually divided into subcategories in order to avoid the confusion of long, undifferentiated lists of variously re¬ lated items. The organization of the book is evident in the detailed table of contents, with all of the subheadings included, which should facilitate fairly rapid access to particular categories or types of sources. Furthermore, there are collective annotations through¬ out the book that introduce and identify specific items within the bibliographies they precede, often singling out sources of particular importance or distinguishing between different ones; where appro¬ priate, cross references are made to items appearing elsewhere in the book. Finally, there are two indexes: the first of authors, edi¬ tors, compilers, and translators; the second of titles of books, arti¬ cles, and series. The past decade or so has witnessed an extraordinary expan¬ sion of the materials of music, and the field is growing ever more
- 21. xii Preface rapidly. It has become a herculean task to try to keep up with the many effort-saving sources that are constantly becoming available. Thus, in the interest of practicality and usefulness, emphasis has been placed on the more recent and up-to-date ones rather than on those of more purely historical or musicological interest, and on English-language sources rather than on those in foreign lan¬ guages. Certain major early sources have occasionally been in¬ cluded, usually under the heading "Of Historical Interest," and some of the bibliographies include more recent sources in other lan¬ guages as well, chiefly German and French, when considered to be of particular importance. (Brief lists of bibliographical terms in these languages have been provided in chapter 1 to assist further in confronting such sources.) Some of the bibliographies—in particu¬ lar the "Basic Bibliographical Tools for Research in Music" in chap¬ ter 2—are meant to provide the means of direct access to materials of research; others emphasize the basic or current representative sources of significance. In other words, in the bibliographies and other materials that follow, the guiding principle, to one extent or another, is selectivity rather than comprehensiveness, as detailed in the chapter introductions and collective annotations throughout. We have not tried to cover every conceivable area in which re¬ search might be conducted in music. For exhaustive lists of sources in areas such as, for example, the literature of specific instruments and performing ensembles, the music of individual countries throughout the world, popular music, and folk music, the reader should consult Vincent H. Duckies and Michael A. Keller, Music Reference and Research Materials: An Annotated Bibliography, 4th ed., rev.; and Guy A. Marco, ed.. Information on Music: A Handbook of Ref¬ erence Sources in European Languages (both listed on p. 32 below). Three sources. The New Grove Dictionary of Music and Musicians, The New Harvard Dictionary of Music, and, to a lesser extent. Die Musik in Geschichte und Gegenwart, are cited fairly often throughout these pages, so they are given in abbreviated form whenever they occur (full citations appear in chapter 4 below on pp. 93, 97, and 92 respectively). The stylistic and bibliographical format followed throughout is the one specified in Kate L. Turabian's A Manual for Writers of Term Papers, Theses, and Dissertations, 5th ed. (listed on p. 192 below). We have made a few adaptations, the most important of which are: (1) In the case of sources in second or later editions, or of translations of sources published earlier, the date of the original edition is also given (e.g., "First published in 1963"). (2) In the interest of simplic¬ ity, information about reprint and microform editions is usually omitted, the main exceptions being those instances in which some-
- 22. Preface xiii thing new has been added in the reprint, such as a list of correc¬ tions or a new preface. (3) Normally, when more than one city and/ or publishing firm is listed in a source, only one of each is cited here, the city usually being the one where the principal headquar¬ ters is located. (4) Ordinarily, complicated or frequently changing publication information in serial publications, e.g., in the case of sets and monuments of music, has been abbreviated. For complete publication data related to music editions, see Hill and Stephens' recent Collected Editions, Historical Series and Sets, and Monuments of Music: A Bibliography (listed on p. 41 below). We wish to extend our thanks to the following persons whose expertise and assistance have helped in various ways in the prep¬ aration of this book: Charles Benner, J. Bunker Clark, Carl Dahl- gren, Karen Faaborg, Warren George, Lewis B. Hilton, Roland Jackson, David Lasocki, Michael Luebbe, bruce d. mcclung, Sever- ine Neff, Bruno Nettl, Edward Nowacki, Karin Pendle, Lewis Pe¬ terman, Jennifer Stasack, Jennifer Thomas, J. Randall Wheaton, Lizabeth Wing, and Robert Zierolf; and to Robert Johnson and his staff at the Gorno Memorial Music Library of the University of Cin¬ cinnati: Paul Cauthen, Sharon Downing, Ollie Meyer, Mark Pal- kovic, and Rebecca Willingham. Finally, we are grateful to E. Eugene Helm, Jon Piersol, and Ruth Watanabe for their initial en¬ couragement in this project. University of Cincinnati June 1992
- 26. Visit https://ebookmass.com today to explore a vast collection of ebooks across various genres, available in popular formats like PDF, EPUB, and MOBI, fully compatible with all devices. Enjoy a seamless reading experience and effortlessly download high- quality materials in just a few simple steps. Plus, don’t miss out on exciting offers that let you access a wealth of knowledge at the best prices!
- 27. Exploring the Variety of Random Documents with Different Content
- 28. 175 176 how he did so after his marriage in 1908. He went with Mrs. Lowell again in the spring of 1910, giving lectures before the Société Astronomique in Paris, and the Royal Institution in London, and once more, two years later, when we find him entertained and speaking before several scientific bodies in both Paris and London. That autumn he was confined to the house by illness; and although he improved and went to Flagstaff in March, he writes of himself in August 1913 as “personally still on the retired list.” In the spring it was thought wise for him to take another vacation abroad; and since his wife was recovering from an operation he went alone. He saw his old friends in France and England and enjoyed their hospitality; but he did not feel well, and save for showing at the Bureau des Longitudes “some of our latest discoveries” he seems to have made no addresses. He sailed back on the Mauretania on August 1, just before England declared war, and four days later she was instructed to run to Halifax, which she did, reaching it the following day. That was destined to be his last voyage, for although he seemed well again he was working above his strength. His time in these years was divided between Flagstaff, where his days and nights were spent in observing and calculating, and Boston, where the alternative was between calculations and business. He was always busy and when one summer he hired a house at Marblehead near to his cousins Mr. and Mrs. Guy Lowell he would frequently drop in to see them; and was charming when he did so; but could not spare the time to take a meal there, and never stayed more than five minutes.
- 29. 177 CHAPTER XIX THE SEARCH FOR A TRANS- NEPTUNIAN PLANET We must now return to the last paragraph of his “Memoir on the Origin of the Planets,” where he suggests the probable distance of a body beyond Neptune. In fact he had long been interested in its existence and whereabouts. By 1905 his calculations had given him so much encouragement that the Observatory began to search for the outer planet, which he then expected would be like Neptune, low in density, large and bright, and therefore much more easily detected than it turned out to be. But the photographs taken in 1906, with a well planned routine search the next year revealed nothing, and he became distrustful of the data on which he was working. In March 1908, one finds in his letter-books from the office in Boston the first of a series of letters to Mr. William T. Garrigan of the Naval Observatory and Nautical Almanack about the residuals of Uranus— that is the residue in the perturbations of its normal orbit not accounted for by those due to the known planets. He suggests including later data than had hitherto been done; asks what elements other astronomers had taken into account in estimating the residuals; points out that for different periods they are made up on different theories in the publications of Greenwich Observatory, and that some curious facts appear from them. About his own calculation he writes on December 28, 1908: “The results so far are both interesting and promising.” He was hard at work on the calculations for such a planet, based upon the residuals of Uranus, and assisted by a corps of computers, with Miss Elizabeth Williams, now Mrs. George Hall Hamilton of the Observatory at Mandeville, Jamaica, at their head.
- 30. 178 Before trying to explain the process by which he reached his results it may be well to give his own account of the discovery of Neptune by a similar method: [39] “Neptune has proved a planet of surprises. Though its orbital revolution is performed direct, its rotation apparently takes place backward, in a plane tilted about 35° to its orbital course. Its satellite certainly travels in this retrograde manner. Then its appearance is unexpectedly bright, while its spectrum shows bands which as yet, for the most part, defy explanation, though they state positively the vast amount of its atmosphere and its very peculiar constitution. But first and not least of its surprises was its discovery,—a set of surprises, in fact. For after owing recognition to one of the most brilliant mathematical triumphs, it turned out not to be the planet expected. “‘Neptune is much nearer the Sun than it ought to be,’ is the authoritative way in which a popular historian puts the intruding planet in its place. For the planet failed to justify theory by not fulfilling Bode’s law, which Leverrier and Adams, in pointing out the disturber of Uranus, assumed ‘as they could do no otherwise.’ Though not strictly correct, as not only did both geometers do otherwise, but neither did otherwise enough, the quotation may serve to bring Bode’s law into court, as it was at the bottom of one of the strangest and most generally misunderstood chapters in celestial mechanics. “Very soon after Uranus was recognized as a planet, approximate ephemerides of its motion resulted in showing that it had several times previously been recorded as a fixed star. Bode himself discovered the first of these records, one by Mayer in 1756, and Bode and others found another made by Flamsteed in 1690. These observations enabled an elliptic orbit to be calculated which satisfied them all. Subsequently others were detected. Lemonnier discovered that he had himself not discovered it several times, cataloguing it as a fixed star. Flamsteed was spared a like mortification by being dead.
- 31. 179 For both these observers had recorded it two or more nights running, from which it would seem almost incredible not to have suspected its character from its change of place. “Sixteen of these pre-discovery observations were found (there are now nineteen known), which with those made upon it since gave a series running back a hundred and thirty years, when Alexis Bouvard prepared his tables of the planet, the best up to that time, published in 1821. In doing so, however, he stated that he had been unable to find any orbit which would satisfy both the new and the old observations. He therefore rejected the old as untrustworthy, forgetting that they had been satisfied thirty years before, and based his tables solely on the new, leaving it to posterity, he said, to decide whether the old observations were faulty or whether some unknown influence had acted on the planet. He had hardly made this invidious distinction against the accuracy of the ancient observers when his own tables began to be out and grew seriously more so, so that within eleven years they quite failed to represent the planet. “The discrepancies between theory and observation attracted the attention of the astronomic world, and the idea of another planet began to be in the air. The great Bessel was the first to state definitely his conviction in a popular lecture at Königsberg in 1840, and thereupon encouraged his talented assistant Flemming to begin reductions looking to its locating. Unfortunately, in the midst of his labors Flemming died, and shortly after Bessel himself, who had taken up the matter after Flemming’s death. “Somewhat later Arago, then head of the Paris observatory, who had also been impressed with the existence of such a planet, requested one of his assistants, a remarkable young mathematician named Leverrier, to undertake its investigation. Leverrier, who had already evidenced his marked ability in celestial mechanics, proceeded to grapple with the problem in the most thorough manner. He began by looking into the perturbations of Uranus by Jupiter and Saturn. He
- 32. 180 started with Bouvard’s work, with the result of finding it very much the reverse of good. The farther he went, the more errors he found, until he was obliged to cast it aside entirely and recompute these perturbations himself. The catalogue of Bouvard’s errors he gave must have been an eye-opener generally, and it speaks for the ability and precision with which Leverrier conducted his investigation that neither Airy, Bessel, nor Adams had detected these errors, with the exception of one term noticed by Bessel and subsequently by Adams. [40] The result of this recalculation of his was to show the more clearly that the irregularities in the motion of Uranus could not be explained except by the existence of another planet exterior to him. He next set himself to locate this body. Influenced by Bode’s law, he began by assuming it to lie at twice Uranus’ distance from the Sun, and, expressing the observed discrepancies in longitude in equations, comprising the perturbations and possible errors in the elements of Uranus, proceeded to solve them. He could get no rational solution. He then gave the distance and the extreme observations a certain elasticity, and by this means was able to find a position for the disturber which sufficiently satisfied the conditions of the problem. Leverrier’s first memoir on the subject was presented to the French Academy on November 10, 1845, that giving the place of the disturbing planet on June 1, 1846. There is no evidence that the slightest search in consequence was made by anybody, with the possible exception of the Naval Observatory at Washington. On August 31 he presented his third paper, giving an orbit, mass, and more precise place for the unknown. Still no search followed. Taking advantage of the acknowledging of a memoir, Leverrier, in September, wrote to Dr. Galle in Berlin asking him to look for the planet. The letter reached Galle on the 23rd, and that very night he found a planet showing a disk just as Leverrier had foretold, and within 55′ of its predicted place. “The planet had scarcely been found when, on October 1, a letter from Sir John Herschel appeared in the London Athenaeum announcing that a young Cambridge graduate, Mr. J. C. Adams, had been engaged on the same investigation as Leverrier, and with similar
- 33. 181 182 results. This was the first public announcement of Mr. Adams’ labors. It then appeared that he had started as early as 1843, and had communicated his results to Airy in October, 1845, a year before. Into the sad set of circumstances which prevented the brilliant young mathematician from reaping the fruit of what might have been his discovery, we need not go. It reflected no credit on any one concerned except Adams, who throughout his life maintained a dignified silence. Suffice it to say that Adams had found a place for the unknown within a few degrees of Leverrier’s; that he had communicated these results to Airy; that Airy had not considered them significant until Leverrier had published an almost identical place; that then Challis, the head of the Cambridge Observatory, had set to work to search for the planet but so routinely that he had actually mapped it several times without finding that he had done so, when word arrived of its discovery by Galle. “But now came an even more interesting chapter in this whole strange story. Mr. Walker at Washington and Dr. Petersen of Altona independently came to the conclusion from a provisional circular orbit for the newcomer that Lalande had catalogued in the vicinity of its path. They therefore set to work to find out if any Lalande stars were missing. Dr. Petersen compared a chart directly with the heavens to the finding a star absent, which his calculations showed was about where Neptune should have been at the time. Walker found that Lalande could only have swept in the neighborhood of Neptune on the 8th and 10th of May, 1795. By assuming different eccentricities for Neptune’s orbit under two hypotheses for the place of its perihelion, he found a star catalogued on the latter date which sufficiently satisfied his computations. He predicted that on searching the sky this star would be found missing. On the next fine evening Professor Hubbard looked for it, and the star was gone. It had been Neptune. [41] “This discovery enabled elliptic elements to be computed for it, when the surprising fact appeared that it was not moving in anything approaching the orbit either Leverrier or Adams had assigned.
- 34. Instead of a mean distance of 36 astronomical units or more, the stranger was only at 30. The result so disconcerted Leverrier that he declared that ‘the small eccentricity which appeared to result from Mr. Walker’s computations would be incompatible with the nature of the perturbations of the planet Herschel,’ as he called Uranus. In other words, he expressly denied that Neptune was his planet. For the newcomer proceeded to follow the path Walker had computed. This was strikingly confirmed by Mauvais’ discovering that Lalande had observed the star on the 8th of May as well as on the 10th, but because the two places did not agree, he had rejected the first observation, and marked the second as doubtful, thus carefully avoiding a discovery that actually knocked at his door. “Meanwhile Peirce had made a remarkable contribution to the whole subject. In a series of profound papers presented to the American Academy, he went into the matter more generally than either of the discoverers, to the startling conclusion ‘that the planet Neptune is not the planet to which geometrical analysis had directed the telescope, and that its discovery by Galle must be regarded as a happy accident.’ [42] He first proved this by showing that Leverrier’s two fundamental propositions,—
- 35. 183 184 “1. That the disturber’s mean distance must be between 35 and 37.9 astronomical units; “2. That its mean longitude for January 1, 1800, must have been between 243° and 252°,—were incompatible with Neptune. Either alone might be reconciled with the observations, but not both. “In justification of his assertion that the discovery was a happy accident, he showed that three solutions of the problem Leverrier had set himself were possible, all equally complete and decidedly different from each other, the positions of the supposed planet being 120° apart. Had Leverrier and Adams fallen upon either of the outer two, Neptune would not have been discovered. [43] “He next showed that at 35.3 astronomical units, an important change takes place in the character of the perturbations because of the commensurability of period of a planet revolving there with that of Uranus. In consequence of which, a planet inside of this limit might equally account for the observed perturbations with the one outside of it supposed by Leverrier. This Neptune actually did. From not considering wide enough limits, Leverrier had found one solution, Neptune fulfilled the other. [44] And Bode’s law was responsible for this. Had Bode’s law not been taken originally as basis for the disturber’s distance, those two great geometers, Leverrier and Adams, might have looked inside. “This more general solution, as Peirce was careful to state, does not detract from the honor due either to Leverrier or to Adams. Their masterly calculations, the difficulty of which no one who has not had some experience of the subject can appreciate, remain as an imperishable monument to both, as does also Peirce’s to him.”
- 36. 185 The facts, that is what was done and written, are of course correct; but the conclusions drawn from them are highly controversial to the present day. The calculations for finding an unknown planet by the perturbations it causes in the orbit of another are extremely difficult, the more so when the data are small and uncertain. For Percival they were very small because Neptune,—nearest to the unknown body,—had been discovered so short a time that its true orbit, apart from the disturbances therein caused by other planets, was by no means certain. In fact Percival tried to analyze its residuals, but they yielded no rational result. This left only what could be gleaned from Uranus after deducting the perturbations caused by Neptune, and that was small indeed. In 1845, when the calculations were made which revealed that planet, “the outstanding irregularities of Uranus had reached the relatively huge sum of 133″. To-day its residuals do not exceed 4.5″ at any point of its path.” Then there are uncertainties depending on errors of observation, which may be estimated by the method of least squares of the differences between contemporary observations. Moreover there is the uncertainty that comes from not knowing how much of the observed motion is to be attributed to a normal orbit regulated by the Sun, and how much to the other planets, including the unknown. Its true motion under these influences can be ascertained only by observing it for a long time, and by taking periods sufficiently far apart to distinguish the continuing effects of the known bodies from those that flow from an unknown source. This was the ingenious method devised by Leverrier as a basis for his calculations, and he thereby got his residuals caused by the unknown planet in a form that could be handled. Finally there was the uncertainty whether the residual perturbations, however accurately determined, were caused by one or more outer bodies. Of this Percival was, of course, well aware, and in fact, in his study of the comets associated with Jupiter he had pointed out that
- 37. 186 there probably was a planet far beyond the one for which he was now in search. But, as no one has ever been able to devise a formula for the mutual attraction of three bodies, he could calculate only for a single body that would account as nearly as possible for the whole of the residuals. Thus he knew that his work was an approximation; near enough, he hoped, to lead to the discovery of the unknown. The various elements in the longitude of a planet’s orbit, that is in the plane of the ecliptic, that are affected by and affect another, are: a—The length of its major, or longest, axis. n—Its mean motion, which depends on the distance from the Sun. ε—The longitude at a given time, that is its place in its orbit. e—The eccentricity of its orbit, that is how far it is from a circle. ῶ—The place of its perihelion, that is the position of its nearest approach to the Sun. (These last two determine the shape of the ellipse, and the direction of its longer axis with respect to that of the other planet.) m—Its mass. Now formulas, or series of equations, that express the perturbations caused by one planet in the orbit of another must contain all these elements, because all of them affect the result. But there are too many of them for a direct solution. Therefore Leverrier assumed a distance of the unknown planet from the Sun, and with it the mean motion which is proportional to that distance; worked out from the residuals of Uranus at various dates a series of equations in terms of the place of the unknown in its orbit; and then found what place therein at a given time would give results
- 38. 187 reducing the residuals to a minimum—that is, would come nearest to accounting for them. In fact, supposing that the unknown planet would be about the distance from the Sun indicated by Bode’s law, the limits within which he assumed trial distances were narrow, and, as it proved, wholly beyond the place where it was found. This method, which in its general outline Percival followed, consisted therefore of a process of trial and error for the distance (with the mean motion) and for the place of X in its orbit (ε). For the other three elements (e, ῶ and m) he used in the various solutions 24 to 37 equations drawn from the residuals of Uranus at different dates, and expressed in terms of ε. He did this in order to have several corroborative calculations, and to discover which of them accorded most closely with the perturbations observed. We have seen that in 1908-09 Percival was inquiring about the exact residuals of Uranus, and he must have been at work on them soon afterwards, for on December 1, 1910, he writes to Mr. Lampland that Miss Williams, his head computer, and he have been puzzling away over that trans-Neptunian planet, have constructed the curve of perturbations, but find some strange things, looking as if Leverrier’s later theory of Uranus were not exact. This work had been done by Leverrier’s methods “but with extensions in the number and character of the terms calculated in the perturbation in order to render it more complete.” Though uncertain of his results, he asks Mr. Lampland, in April 1911, to look for the planet. But he was by no means himself convinced that his data were accurate, and he computed all over again with the residuals given by Gaillot, which he considered more accurate than Leverrier’s in regard to the masses, and therefore the attractions, of the known planets concerned. Incidentally he remarks at this point in his Memoir, [45] in speaking of works on celestial mechanics, that “after excellent analytical solutions, values of the quantities involved are introduced on the basis apparently of the respect due to age. Nautical Almanacs abet the practice by never publishing, consciously, contemporary values of astronomic constants; thus avoiding committal to doubtful
- 39. 188 results by the simple expedient of not printing anything not known to be wrong.” His result for X, as he called the planet he was seeking, computed by Gaillot’s residuals, differed from that found in using Leverrier’s figures by some forty degrees to the East, and on July 8 he telegraphs Mr. Lampland to look there. These telegrams to Mr. Lampland continue at short intervals for a long time with constant revisions and extensions in the calculations; and, as he notes, every new move takes weeks in the doing; but all without finding planet X. Perhaps it was this disappointment that led him to make the even more gigantic calculation printed in the Memoir, where he says: “In the present case, it seemed advisable to pursue the subject in a different way, longer and more laborious than these earlier methods, but also more certain and exact: that by a true least-square method throughout. When this was done, a result substantially differing from the preliminary one was the outcome. It both shifted the minimum and bettered the solution. In consequence, the whole work was done de novo in this more rigorous way, with results which proved its value.” Then follow many pages of transformations which, as the guide books say of mountain climbing, no one should undertake unless he is sure of his feet and has a perfectly steady head. But anyone can see that, even in the same plane, the aggregate attractions of one planet on another, pulling eventually from all possible relative positions in their respective elliptical orbits with a force inversely as the square of the ever-changing distance, must form a highly complex problem. Nor, when for one of them the distance, velocity, mass, position and shape of orbit are wholly unknown, so that all these things must be represented by symbols, will anyone be surprised if the relations of the two bodies are expressed by lines of these, following one another by regiments over the pages. In fact the Memoir is printed for those who are thoroughly familiar with this kind of solitaire.
- 40. 189 For the first trial and error Percival assumed the distance of X from the Sun to be 47.5 planetary units (the distance of the Earth from the Sun being the unit), as that seemed on analogy a probable, though by no means a certain, distance. With this as a basis, and with the actual observations of Uranus brought to the nearest accuracy by the method of least-squares of errors, he finds the eccentricity, the place of the perihelion and the mass of X in terms of its position in its orbit. Then he computes the results for about every ten degrees all the way round the orbit, and finds two positions, almost opposite, near 0° and near 180°, which reduce the residuals to a minimum—that is which most nearly account for the perturbations. Each of these thirty tried positions involved a vast amount of computation, but more still was to come. Finally, to be sure that he had covered the ground and left no loophole for X to escape, he tried, beside the 47.5 he had already used, a series of other possible distances from the Sun,—40.5, 42.5, 45, 51.25 units,—each of them requiring every computation to be done over again. But the result was satisfactory, for it showed that the residuals were most nearly accounted for by a distance not far from 45 units (or a little less if the planet was at the opposite side of its orbit), and that the residuals increased for a distance greater or less than this. But still he was not satisfied, and for greater security he took up terms of the second and third order—very difficult to deal with—but found that they made no substantial difference in the result. So much for the longitude of X (that is its orbit and position in the plane of the ecliptic) but that was not all, for its orbit might not lie in that plane but might be inclined to it, and like all the other planets he supposed it more or less so—more he surmised. Although he made some calculations on the subject he did not feel that any result obtained would be reliable, and if the longitude were near enough he thought the planet could be found. He says:
- 41. 190 191 “To determine the inclination of the orbit of the unknown from the residuals in latitude of Uranus has proved as inconclusive as Leverrier found the like attempt in the case of Neptune. “The cause of failure lies, it would seem, in the fact that the elements of X enter into the observational equations for the latitude. Not only e and ῶ are thus initially affected but ε as well. Hence as these are doubtful from the longitude results, we can get from the latitude ones only doubtfulness to the second power.” Nevertheless he makes some calculations on the subject which, however, prove unsatisfactory. Such in outline was his method of calculating the probable orbit and position in the sky of the trans-Neptunian planet; an herculean labor carried out with infinite pains, and attaining, not absolute definiteness, but results from the varying solutions sufficiently alike to warrant the belief in a close approximation. In dealing with what he calls the credentials for the acceptance of his results, he points out that one of his solutions for X in which he has much confidence, reduces the squares of the residuals to be accounted for by ninety per cent., and in the case of some of the others almost to nothing. Yet he had no illusions about the uncertainty of the result, for in the conclusions of the Memoir he says: “But that the investigation opens our eyes to the pitfalls of the past does not on that account render us blind to those of the present. To begin with, the curves of the solutions show that a proper change in the errors of observation would quite alter the minimum point for either the different mean distances or the mean longitudes. A slight increase of the actual errors over the most probable ones, such as it by no means strains human capacity for error to suppose, would suffice entirely to change the most probable distance of the disturber and its longitude at the epoch. Indeed the imposing ‘probable error’ of a set of observations imposes on no one familiar with observation, the actual errors committed, due to systematic causes, always far exceeding it.
- 42. 192 “In the next place the solutions themselves tell us of alternatives between which they leave us in doubt to decide. If we go by residuals alone, we should choose those solutions which have their mean longitudes at the epoch in the neighborhood of 0°, since the residuals are there the smallest. But on the other hand this would place the unknown now and for many decades back in a part of the sky which has been most assiduously scanned, while the solutions with ε around 180° lead us to one nearly inaccessible to most observatories, and, therefore, preferable for planetary hiding. Between the elements of the two, there is not much to choose, all agreeing pretty well with one another. “Owing to the inexactitude of our data, then, we cannot regard our results with the complacency of completeness we should like.” The bulk of the computations for the trans-Neptunian planet were finished by the spring of 1914, and in April he sent to Flagstaff from Boston, where the work had been done, two of the assistant computers. The final Memoir he read to the American Academy of Arts and Sciences on January 13, 1915; and printed in the spring as a publication of the Observatory. Naturally he was deeply anxious to see the fruit from such colossal labor. In July, 1913, he had written to Mr. Lampland: “Generally speaking what fields have you taken? Is there nothing suspicious?” and in May, 1914, “Don’t hesitate to startle me with a telegram ‘FOUND.’” Again, in August, he writes to Dr. Slipher: “I feel sadly of course that nothing has been reported about X, but I suppose the bad weather and Mrs. Lampland’s condition may somewhat explain it”; and to Mr. Lampland in December: “I am giving my work before the Academy on January 13. It would be thoughtful of you to announce the actual discovery at the same time.” Through the banter one can see the craving to find the long-sought planet, and the grief at the baffling of his hopes. That X was not found was the sharpest disappointment of his life.
- 43. 193 If so much labor without tangible result gave little satisfaction, there was still less glory won by a vast calculation that did not prove itself correct. Curiously enough, he always enjoyed more recognition among astronomers in Europe than in America; for here, as a highly distinguished member of the craft recently remarked, he did not belong to the guild. He was fond of calling himself an amateur—by which he meant one who worked without remuneration—and of noting how many of the great contributors to science were in that category. The guild here was not readily hospitable to those who had not been trained in the regular treadmill; and it had been shocked by his audacity in proclaiming a discovery of intelligent handiwork on Mars. So for the most part he remained to the end of his life an amateur in this country; though what would have been said had he succeeded in producing, by rigorous calculation, an unknown planet far beyond the orbit of Neptune, it is interesting to conjecture, but difficult to know, for the younger generation of astronomers had not then come upon the stage nor the older ones outlived their prejudice. The last eighteen months of his life were spent as usual partly at Flagstaff, where he was adding to the buildings, partly in Boston, and in lecturing. In May, 1916, he writes to Sig. Rigano of “Scientia” that he has not time to write an article for his Review, and adds: “Eventually I hope to publish a work on each planet—the whole connected together—but the end not yet.” Fortunately he did not know how near it was. In May he lectured at Toronto; and in the autumn in the Northwest on Mars and other planets, at Washington State and Reed Colleges, and the universities of Idaho, Washington, Oregon and California. These set forth his latest views, often including much that had been discovered at Flagstaff and elsewhere since his earlier books were published; for his mind was far from closed to change of opinion on newly discovered evidence. It was something of a triumphal procession at these institutions; but it was too much.
- 44. 194 195 More exhausted than he was himself aware, he returned to Flagstaff eager about a new investigation he had been planning on Jupiter’s satellites. It will be recalled that he had found the exact position of the gap in Saturn’s rings accounted for if the inner layers of the planet rotated faster and therefore were more oblate than the visible gaseous surface. Now the innermost satellite of Jupiter (the Vth) was farther off than the simple relation between distance and period should make it, a difference that might be explained if in Jupiter, as in Saturn, the molten inner core were more oblate than the outer gaseous envelope. To ascertain this the distance of the satellite V. must be determined exactly, and with Mr. E. C. Slipher he was busy in doing so night after night through that of November 11th. But he was overstrained, and the next day, November 12, 1916, not long after his return to Flagstaff, an attack of apoplexy brought to a sudden close his intensely active life. Before he became unconscious he said that he always knew it would come thus, but not so soon. He lies buried in a mausoleum built by his widow close to the dome where his work was done.
- 45. 196 CHAPTER XX PLUTO FOUND [46] Percival had long intended that his Observatory should be permanent, and that his work, especially on the planets, should be forever carried on there with an adequate foundation. Save for an income to his wife during her lifetime, he therefore left his whole fortune in a trust modeled on the lines of the Lowell Institute in Boston, created eighty years earlier by his kinsman John Lowell, Jr. The will provides for a single trustee who appoints his own successor; the first being his cousin Guy Lowell, the next the present trustee, Percival’s nephew, Roger Lowell Putnam. Dr. V. M. Slipher and Mr. C. O. Lampland, who have been at the Observatory from an early time, are the astronomers in charge, carrying on the founder’s principles of constantly enlarging the field of study, and using for the purpose the best instrumental equipment to be procured. Of course the search was continued for the planet X, but without success, and for a time almost without hope, not only because its body is too small to show a disk, but also by reason of the multitude of stars of like size in that crowded part of the heavens, the Milky Way, where it is extremely difficult to detect one that has moved. It was as if out of many thousand pins thrown upon the floor one were slightly moved and someone were asked to find which it was. Mere visual observation was clearly futile, for no man could record the positions of all the points of light from one night to another. The only way to conduct a systematic search was through an enduring record, that is by taking photographs of the probable sections of the sky, and comparing two of the same section taken a few days apart to discover a point of light that had changed its place
- 46. 197 —no simple matter when more than one hundred thousand stars showed upon a single plate. This process Percival tried, but although his hopes were often raised by finding bodies that moved, they proved to be asteroids hitherto unknown, [47] and the X sought so long did not appear. [48] Percival had felt the need of a new photographic telescope of considerable light power and a wider field, and an attempt was made to borrow such an instrument, for use while one was being manufactured, but in vain. Then came the war when optical glass for large lenses could not be obtained, and before it was over Percival had died. After his death Guy Lowell, the trustee, took up the project, but also died too soon to carry it out. At last in 1929 the lens needed was obtained, the instrument completed in the workshop of the Observatory, and the search renewed in March with much better prospects. Photographs of section after section of the region where X was expected to be were taken and examined by a Blink comparator. This is a device whereby two photographs of slightly different dates could be seen through a microscope at the same time as if superposed. But with all the improvement in apparatus months of labor revealed nothing. After nearly a year of photographing, and comparing plates, Mr. Clyde W. Tombaugh, a young man brought up on a farm but with a natural love of astronomy, was working in this search at Flagstaff, when he suddenly found, on two plates taken January 23 and 29, 1930, a body that had moved in a way to indicate, not an asteroid, but something vastly farther off. It was followed, and appeared night after night in the path expected for X at about the distance from the sun Percival had predicted. Before giving out any information it was watched for seven weeks, until there could be no doubt from its movements that it was a planet far beyond Neptune, and was following very closely the track which his calculations had foretold. Then, on his birthday, March 13, the news was given to the world.
- 47. 198 Recalling Percival’s own statement: “Owing to the inexactitude of our data, then, we cannot regard our results with the complacency of completeness we should like,” one inquires eagerly how nearly the actual elements in the orbit of the newly found planet agree with those he calculated. To this an answer was given by Professor Henry Norris Russell of Princeton, the leading astronomer in this country, in an article in the Scientific American for December, 1930. He wrote as follows: “The orbit, now that we know it, is found to be so similar to that which Lowell predicted from his calculations fifteen years ago that it is quite incredible that the agreement can be due to accident. Setting prediction and fact side by side we have the following table of characteristics: Predicted Actual Period 282 years 249.17 Eccentricity 0.202 0.254 Longitude of perihelion 205° 202° 30′ Perihelion passage 1991.2 1989.16 Inclination about 10° 17° 9′ Longitude of node not predicted 109° 22′ “Lowell saw in advance that the perturbations of the latitudes of Uranus and Neptune (from which alone the position of the orbit plane of the unknown planet could be calculated) were too small to give a reliable result and contented himself with the prophecy that the inclination, like the eccentricity, would be considerable. For the other four independent elements of the orbit, which are those that Lowell actually undertook to determine by his calculations, the agreement is good in all cases, the greatest discrepancy being in the period, which is notoriously difficult to determine by computations of this sort. In view of Lowell’s explicit statement that since the
- 48. 199 perturbations were small the resulting elements of the orbit could at best be rather rough approximations, the actual accordance is all that could be demanded by a severe critic. “Even so, the table does not tell the whole story. Figure 1 [49] shows the actual and the predicted orbits, the real positions of the planet at intervals from 1781 to 1989, and the positions resulting from Lowell’s calculations. It appears at once that the predicted positions of the orbit and of the planet upon it were nearest right during the 19th century and the early part of the 20th, while at earlier and later dates the error rapidly increased. Now this (speaking broadly) is just the interval covered by the observations from which the influence of the planet’s attraction could be determined and, therefore, the interval in which calculation could find the position of the planet itself with the least uncertainty.
- 49. 200 Predicted and Actual Orbits of PLUTO “In the writer’s judgment this test is conclusive.” [50] Later observations, and computations of the orbit of Pluto, do not vary very much from those that Professor Russell had when he wrote. Two of the most typical—giving more elements—are as follows: Predicted Nicholson and Mayall F. Zagar Period 282 years 249.2 248.9 Eccentricity 0.202 0.2461 0.2472
- 50. 201 Longitude of perihelion 204.9 222° 23′ 20″ .17 222° 29′ 39″ .4 Perihelion passage 1991.2 1889.75 1888.4 Inclination about 10° 17° 6′ 58″ .4 17° 6′ 50″ .8 Semi-major axis 43. 39.60 39.58 Perihelion distance 34.31 29.86 29.80 Aphelion distance 51.69 49.35 49.36 Except for the eccentricity, and the inclination which he declared it impossible to calculate, these results have proved as near as, with the uncertainty of his data, he could have expected; and in regard to the position of the planet in its orbit it will be recalled that he found two solutions on opposite sides, both of which would account almost wholly for the residuals of Uranus. The one that came nearest to doing so he had regarded as the least probable because it placed the planet in a part of the sky that had been much searched without finding it; but it was there that Pluto appeared—a striking proof of his rigorous analytic method. But the question of its mass has raised serious doubts whether Pluto can have caused the perturbations of Uranus from which he predicted its presence, for if it has no significant mass the whole basis of the calculation falls to the ground, and there has been found a body travelling, by a marvellous coincidence, in such an orbit that, if large enough, it would produce the perturbations but does not do so. [51] Now as there is no visible satellite to gauge its attraction, and as it will be long before Pluto in its eccentric orbit approaches Neptune or Uranus closely enough to measure accurately by that means, the mass cannot yet be determined with certainty. What is needed are measures of position of the highest possible accuracy of Neptune and Uranus, long continued and homogeneous.
- 51. 202 The reasons for the doubt about adequate mass are two. [52] One that with the largest telescopes it shows no visible disk, and must therefore be very small in size, and hence in mass unless its density is much greater, or its albedo far less, than those of any other known planet. The other substantially that the orbits of Uranus and Neptune can be, and are more naturally, explained by assuming appropriate elements therefor, without the intervention of Pluto’s disturbing force. This is precisely what Percival stated in discussing the correctness of the residuals—that it was always possible to account for the motions of a planet, whose normal orbit about the sun is not definitely ascertained, by throwing any observed divergencies either on errors in the supposed orbit, or upon perturbations by an unknown body. The conditions here are quite unlike those at the discovery of Neptune, for there the existence of the perturbations was clear, because fairly large, and the orbit predicted was wrong because of an error in the distance assumed; and the question was whether the presence of Neptune in the direction predicted, though in a different orbit, was an accident, or inevitable. Here the predicted orbit is substantially the actual one, adequate to account for the perturbations of Uranus if such really exist, and the question is whether they do or not. If not the discovery of Pluto is a mere unexplained coincidence which has no connection with the prediction. Whether among recognized uncertainties it is more rational to suppose a very high density, and very low albedo, with corresponding perturbations of Uranus and Neptune, whose orbits are still imperfectly known, or to conclude that a planet, which would account for these things if dense enough, revolves in fact in the appropriate path, a mere ghost of itself—a phantom but not a force —one who is not an astronomer must leave to the professionals.
- 52. 203 In the case of both Neptune and Pluto the calculation was certainly a marvellous mathematical feat, and in accord with the usual practice whereby the discoverer of a new celestial body is entitled to propose its name the observers at Flagstaff selected from many suggestions that of “Pluto” with the symbol ; and henceforth astronomers will be reminded of Percival Lowell, by the planet he found but never saw.
- 53. APPENDIX I Professor Henry Norris Russell’s later views on the size of Pluto (written to the Biographer and printed with the writer’s consent). Later investigations have revealed a very curious situation. When once the elements of Pluto’s orbit are known, the calculation of the perturbations which it produces on another planet, such as Neptune, are greatly simplified. But the problem of finding Pluto’s mass from observations of Neptune is still none too easy, for the perturbations affect the calculated values of the elements of Neptune’s orbit, and are thus “entangled” with them in an intricate fashion. Nicholson and Mayall, in 1930, attacked the problem, and found that the perturbations of Neptune by Pluto, throughout the interval from its discovery to the present, were almost exactly similar to the effects which would have been produced by certain small changes in the elements of Neptune’s orbit, so that, from these observations alone, it would have been quite impossible to detect Pluto’s influence. Outside this interval of time, the effects of the perturbations steadily diverge from those of the spurious changes in the orbit, but we cannot go into the future to observe them, and all we have in the past is two rather inaccurate observations made in 1795 by Lalande. [53] If the average of these two discordant observations is taken as it stands, Pluto’s mass comes out 0.9 times that of the Earth, and this determination is entitled to very little weight. Uranus is farther from Pluto, and its perturbations are smaller; but it has been accurately observed over one and a half revolutions, as against half a revolution for Neptune, and this greatly favors the
- 54. 204 separation of the perturbations from changes in the assumed orbital elements. Professor E. W. Brown—the most distinguished living student of the subject—concludes from a careful investigation that the observations of Uranus show that Pluto’s mass cannot exceed one-half of the Earth’s and may be much less. In his latest work a great part of the complication is removed by a curiously simple device. Take the sum of the residuals of Uranus at any two dates separated by one-third of its period, and subtract from this the residual at the middle date. Brown proves—very simply —that the troublesome effect of uncertainties in the eccentricity and perihelion of the disturbed planet will be completely removed from the resulting series of numbers, leaving the perturbations much easier to detect. The curve which expresses their effects, though changed in shape, can easily be calculated. Applying this method to the longitude of Uranus, he finds, beside the casual errors of observation, certain deviations; but these change far more rapidly than perturbations due to Pluto could possibly do, and presumably arise from small errors in calculating the perturbations produced by Neptune. When these are accurately re-calculated, a minute effect of Pluto’s attraction may perhaps be revealed, but Brown concludes that “another century of accurate observations appears to be necessary for a determination which shall have a probable error less than a quarter of the Earth’s mass.” The conclusion that Pluto’s mass is small is confirmed by its brightness. Its visual magnitude is 14.9—just equal to that which Neptune’s satellite Triton would have if brought to the same distance. (Since Pluto’s perihelion distance is less than that of Neptune, this experiment is one which Nature actually performs at times.) Now Nicholson’s observations show that the mass of Triton is between 0.06 and 0.09 times the Earth’s. It is highly probable that Pluto’s mass is about the same—in which case the perturbations which it produces, even on Neptune, will be barely perceptible, so long as observations have their present degree of accuracy.
- 55. 205 The value of seven times the Earth’s mass, derived in Percival Lowell’s earlier calculations, must have been influenced by some error. His mathematical methods were completely sound—on Professor Brown’s excellent authority—and the orbit of Planet X which he computed resembled so closely that of the actual Pluto that no serious discordance could arise from the difference. But, in this case also, the result obtained for the mass of the perturbing planet depended essentially on the few early observations of Uranus as a star, made before its discovery as a planet, and long before the introduction of modern methods of precise observation. Errors in these are solely responsible for the inaccuracy in the results of the analytical solution. The question arises, if Percival Lowell’s results were vitiated in this way by errors made by others more than a century before his birth, why is there an actual planet moving in an orbit which is so uncannily like the one he predicted? There seems no escape from the conclusion that this is a matter of chance. That so close a set of chance coincidences should occur is almost incredible; but the evidence assembled by Brown permits of no other conclusion. Other equally remarkable coincidences have occurred in scientific experience. A cipher cable-gram transmitting to the Lick Observatory the place of a comet discovered in Europe was garbled in transmission, and when decoded gave an erroneous position in the heavens. Close to this position that evening another undiscovered comet was found. More recently a slight discrepancy between determinations of the atomic weight of hydrogen by the mass-spectrograph and by chemical means led to a successful search for a heavy isotype of hydrogen. Later and more precise work with the mass-spectrograph showed that the discrepancy had at first been much over-estimated. Had this error not been made, heavy hydrogen might not yet have been discovered. Like this later error, the inaccuracy in the ancient observations, which led to an over-estimate of the mass and brightness of Pluto,
- 56. 206 was a fortunate one for science. In any event, the initial credit for the discovery of Pluto justly belongs to Percival Lowell. His analytical methods were sound; his profound enthusiasm stimulated the search, and, even after his death, was the inspiration of the campaign which resulted in its discovery at the Observatory which he had founded.
- 57. APPENDIX II THE LOWELL OBSERVATORY by Professor Henry Norris Russell The Observatory at Flagstaff is Percival Lowell’s creation. The material support which he gave it, both during his lifetime and by endowment, represents but a small part of his connection with it. He chose the site, which in its combination of excellent observing conditions and the amenities of everyday life, is still unsurpassed. He selected the permanent members of the staff and provided for the successor to the Directorship after his death. Last, but not least, he inspired a tradition of intense interest in the problems of the universe, and independent and original thought in attacking them, which survives unimpaired. On a numerical basis—whether in number of staff, size of instruments, or annual budget—the Lowell Observatory takes a fairly modest rank in comparison with some great American foundations. But throughout its history it has produced a long and brilliant series of important discoveries and observations notable especially for originality of conception and technical skill. Percival Lowell’s own work has been fully described; it remains to summarize briefly that of the men whom he chose as his colleagues, presenting it according to its subject, rather than in chronological order. The photography of the planets has been pursued for thirty years, mainly by the assiduous work of E. C. Slipher, and the resulting collections are unrivalled. Only a small amount of this store has been published or described in print, but among its successes may be noted the first photographs of the canals of Mars, and the
- 58. 207 demonstration by this impersonal method of the seasonal changes in the dark areas, and of the occasional appearance of clouds. It is a commonplace that any astronomer who wants photographs of the planets for any illustrative purpose instinctively applies to his friends in Flagstaff, and is not likely to be disappointed. The discovery of Pluto, and incidentally of many hundreds of asteroids, has already been described. An important series of measurements of the radiation from the planets was made at Flagstaff in 1921 and 1922 by Dr. W. W. Coblentz of the Bureau of Standards and Dr. C. O. Lampland. Using the 40-inch reflector, and the vacuum thermocouples which the former had developed, and employed in measurements of stellar radiation at the Lick Observatory, and working with and without a water-cell (which transmits most of the heat carried by the sunlight reflected from a planet, but stops practically all of that radiated from its own surface), they found that the true “planetary heat” from Jupiter was so small that its surface must be very cold, probably below -100° Centigrade, while that from Mars was considerable, indicating a relatively high temperature. Both conclusions have been fully confirmed by later work. Spectroscopic observation has been equally successful. In 1912 Lowell and Slipher (V. M.) successfully attacked the difficult problem of the rotation of Uranus. One side of a rotating planet is approaching us, the other receding. If its image is thrown on a spectroscope, so that its equatorial regions fall upon the slit, the lines of the spectrum will be shifted toward the violet on one edge, and the red on the other, and will cross it at a slant instead of at right angles. This method had long before been applied to Jupiter and to Saturn and its rings, but Uranus is so faint as to discourage previous observation. Nevertheless, with the 24-inch reflector, and a single-prism spectrograph, seven satisfactory plates were obtained, with an average exposure of 2½ hours, every one of which showed a definite rotation effect. The mean result indicated that Uranus
- 59. 208 rotates in 10¾ hours, with motion retrograde, as in the case of his satellites. This result was confirmed five years latter by Leon Campbell at Harvard, who observed regular variations in the planet’s brightness with substantially the same period. It has been known since the early days of the spectroscope that the major planets exhibit in their spectra bands produced by absorption by the gases of their atmospheres, and that these bands are strongest in the outer planets. Photographs showing this were first made by V. M. Slipher at the Lowell Observatory in 1902. To get adequate spectrograms of Neptune required exposures of 14 and 21 hours—occupying the available parts of the clear nights of a week. The results well repaid the effort. The bands which appear faintly in Jupiter are very strong in Uranus, and enormous in Neptune’s spectrum, cutting out great portions of the red and yellow, and accounting for the well-known greenish color of the planet. Only one band in the red was present in Jupiter alone. For a quarter of a century after this discovery those bands remained one of the most perplexing riddles of astrophysics. The conviction gradually grew that they must be due to some familiar gases, but the first hint of their origin was obtained by Wildt in 1932, who showed that one band in Jupiter was produced by ammonia gas, and another probably by methane. These conclusions were confirmed by Dunham in the following year, but the general solution of the problem was reserved for Slipher and Adel, who, in 1934, announced that the whole series of unidentified bands were due to methane. The reason why they had not been identified sooner is that it requires an enormous thickness of gas to produce them. A tube 45 meters long, containing methane at 40 atmospheres pressure, produces bands comparable to those in the spectra of Saturn. The far heavier bands in Neptune indicate an atmosphere equivalent to a layer 25 miles thick at standard atmospheric pressure. The fainter bands though not yet observed in the laboratory, have been conclusively identified by the theory of band-spectra. Ammonia shows only in Jupiter and faintly in Saturn; the gas is doubtless
- 60. 209 liquefied or solidified at the very low temperatures of the outer planets. The earth’s own atmosphere has also been the subject of discovery at Flagstaff. The light of a clear moonless sky does not come entirely from the stars and planets; about one-third of it originates in the upper air, and shows a spectrum of bright lines and bands. The familiar auroral line is the most conspicuous of these, but V. M. Slipher, making long exposures with instruments of remarkably great light-gathering power, has recently detected a large number of other bands, in the deep red and even the infra-red. Were our eyes strongly sensitive to these wave-lengths, the midnight skies would appear ruddy. Just as the first rays of the rising sun strike the upper layers of the atmosphere many miles above the surface, new emission bands appear in the spectrum—to be drowned out soon afterwards by the twilight reflected from the lower and denser layers; and the reverse process is observable after sunset. The origin of these remarkable and wholly unexpected radiations is not yet determined. The spectrograph of the Observatory was also employed in observations of stars, and again led to unexpected discoveries. In 1908, while observing the spectroscopic binary Beta Scorpii, V. M. Slipher found that the K line of calcium was sharp on his plates, while all the others were broad and diffuse. Moreover, while the broad lines shifted in position as the bright star moved in its orbit, the narrow line remained stationery. Hartmann, in 1904, had observed a similar line in the spectra of Delta Orionis, and suggested that it was absorbed in a cloud of gas somewhere between the sun and the star. Slipher, extending his observations to other parts of the heavens, found that such stationery calcium lines were very generally present (in spectra of such types that they were not masked by heavier lines arising in the stars themselves), and made
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