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Zoological Literature for 1866, by Dr. Albsrt C. L. G. Guntbxr: Chambers's
Encyelopedia : Notices of New Works and Proceedings of Societies, 144.



NUMBEE XXXT.

Page.
Abt. XIV. — On Mineralogioal Nomenclature; by Jamss D. Dana.

No. I. On Systom in Mineralogical Nomenclature, - * 145
XY. — ObeefTatioBs and Experiments on li?iDg Organisms in

heated water ; by Jeffries Wtm AN, - - - - 152

XVI. — Remarks on Prof. Geinitz's views respecting the Upper Pa-

leoBoic rocks and fossils of Southeastern Nebraska ; by F. B.

Meek, - » 170

XYII. — Description of an apparatus for collecting and wasbiog

precipitates in test tubes; by M. MgDonau^ - - - 188
Xym. — ^On certain Lecture Experiments, and on a new form of

Eudiometer ; by JoBiAB P. CooKB, Jr., - - - 189

XIX. — Crystallographie Examination of some American Cblorites ;

by JosiAH P. Cooke, Jr., 201

XX. — Contributions to Chemistry from the Laboratory of the

Lawrence Scientific School — No. 3 ; by Wolcott Oibbs, - 207
XXL — ^Note on the action of peroxyd of manganese upon urio

. add ; by C. GiLBBBT Wheeler, 218



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XXIL— GoDtribotioiit (rom tlie Sheffield Ubontory of Tele Col-
lege. No. XY. Obeenratioiie on the natiTeHiydratee of Iron ;
by Oeoboe J. Brubh, with analyses of Tnrgite by Chablxs
a RODMAV, 219

XXm.— On a new Test for Hyposulphites; by M. Cabbt Lka, - 222

XXIV. — Contribnlions to Chemistry from the Laboratory of the
Lawrence Scientific School. No. 4. — On a new mineral from
Bockport, Mass. ; by W. J. Kvowltov, .... 224

XXV. — On the Subdifisions of the Cretaceous rocks of California ;

by Wm. M. Gabb, 226

XXVL — Oo a new apparatus for technical analysis ef Petroleum

and kindred substances; by S. F. Pxckham, ... 230

XXVIL— Notes on the Grass Valley Gold-mining District ; by

Prof. B. SiLLiMAV, 286

XXVIIL— The Action of Sunlight on Glass ; by Thomas GArrau), 244

XXIX. — Crystallogenic and Crystallographic Contributions; by
Jambs D. Daha.— IV. On a connection between Crystalline
form and Chemical constitution^ with some inferences there-
from. — Supplement, 262

XXX. — Formic versus Carbonous acid ; by Georgb F. Barkkb, - 263

XXXL — Observations on Skylight Polarization in Nebraska dur-
ing the month of July, 1867 ; by Edward O. Chasb, - - 265

BCIENTIFIO DTTELLIGENCB.

ChtmiHry and Phytiet.'^Otk the tyotheiis of organic seldB, Cabtos, 266. — On tbe
action of heat upon bensol and analogous hydrocarbons, Bbbthxlot, 266.— On
the acids of the lactic series, Fbamklaitd and Doppa, 268.— ThaUic add, E. Cais-
TAM/Eir, 269.— The Aew Chemical Calculus of Sir BDrjAimr Baorni, 870.

Mineralogy and ^M^y.— Notice of volume IV of the Paleontology of New York,
278.— On the Paleontology of Victoria, South Australia, by Fudekiok MoCot,
279.— Note by F. B. Meek to his Review of Prof. Geinitz in r^ard to Nebraska
foBsils, 282.- Note on the Corundophilite of Cheater, Mass.: Note on the opti-
cal characters of different micaceous minerals called Margarite, by Mr. DbsCloi-
SBAUZ, 288.- Eosoon Oanadense in Finland : Qeological obsenrations in Colo-
rado : Geological Surrey of Nebraska, 284.

i^o^ony.— Manual of the Botany of the Northern United States, mcluding the dis-
trict East of the Mississippi and North Carolina and Tennessee, arranged accord-
ing to the natural system, by Asa Geat, 284.

^•^onomy.— Recent Obsenrations and Remarks of Hofrath Schwabs regarding
Sun-spots and other Solar Phenomena, 287.— On a Meteor ef July 18th, 1867,
by Daniil Kibxwood, 288.



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COKTEIVTS. VU

liiteillaneom SeimUific InMigmoej^B^tn^uohM on Oon-oottun. Second memoir.
Od the Stabilitj of Gan-eotton, by F. iu Abu, F.R.S., etc^ 288.— Scientific party
for Sitka: American Aasociation for the Advancement of Science, 291.

06tftMity.— Jeremiah Day, 291.— E. J. Pickett, 292.— Faraday, 298.

liUeellaMoui Bihliography, — Annals of the Aetronomical Obeerratory of Harrard
College, 298.— The Chemical Kevs, and Jonmal of Phyaical Science, 294.— A
Treatise on Astronomy, Spherical and Physical, ete., by Wiixiam A. KoftTOH,
M.A., etc : Elements of Chemistry, Theoretical and Practical, by Wzluam Ai^
Lszf MiLLBE, M.D., etc.: A Popular Treatise on Oems in reference to their sci*
entific yalue, etc, by Dr. L. Fedohtwamgib: Annual of the National Academy
of Sciences for 1866 : Memoirs of the Boston Society of Natural History, 295.
— ^Transactions of the American Entomological Society, 296.

Fkoeeedings of Soeietiee, 296.



NUMBER XXXn.

Page*
Art. XXXn. AddresB of Gborob Bentham, President, read at

the ADniTersary meeting of the Linnean Society on Friday,

May 24, 1867, 297

XXXIIL The Action of Sanlight on Glass ; by Thomas Gatfield, 816
XXXrV. Remarks on Prof. Geinitz^s views respecting the Upper
Paleozoic rocks and fossils of Southeastern Nebraska ; by

F.B.Meek, 827

XXXV. Indian Summer; by Joseph EWiLLBT, - - - 840
XXXVL A method of determining the amount of Protozyd of
Iron in Silicatee not soluble in the ordinary mineral acids ;

by JosiAH P. Cooks, Jr., 847

XXXVII. The Parks of Colorado, 861

XXXVm. Contributions to the Mineralogy of Nova Scotia ; by

O. C. Marsh. — No. 1. Ledererite identical with Gmelinite, 862
XXXIX. Notes on Fossils recently obtained from the Laurentian
Rocks of Canada, and on objections to the organic nature of
Eozoon ; by J. W. Dawson and W. B. Carpenter, - - 867
XL. Reply to Mr. Gabb on the Cretaceous rocks of California ;

by T. A. Conrad, - 876

XLI. Geographical Notices, 377

XLH On normal and derived acids ; by George F. Barker, - 884
XLIIE Crystallogenic and Crystallographio Contributions; by
Jambs D. Dana. On the Feldspar group of Minerals : sup-
plementary to Art. XXIX : On the Chemical Formulas of the

Silicates, 898

XLIV. On certain points in the theory of Atomicities ; by Wol-

oottGibbs, 409



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vm coiffTsins.



BOiWXtlflO nmLLICKKOX.



Chemist/ry and i%9ii^.-^-0& a new oiasB of homologaee of Ofanhydrio add, A.
W. HorMiiKN, 416. — On the aame sutject: On certain hydrpoarbonB contained
in coal-tar, Bebthxlot, 418.

Mineralogy and <3Mtvy* - Note on the genua PalflMUsiB, Haima, 1860 s=(Spheiio-
poterium, M. & W., 1866X F. B. Mbse, 419.

Botany arid Zoology, — Monographia Sallcum, auctore TSf, J. ANDEBasoN, 420. —
Flora BrasilienslB of Mabtius: Lois de la Komendature, redig^B et oommen-
tdes par M. Alph. BbCandolls: Sur les Affinit^B de la Flora da Japan avec
celles de I'Asie et de TAmerique du Nord, 421. — ^Tall trees in Australia, 422. —
Beport on the disastrous effects of the destruction of Forest Trees now going
on so rapidly in Wisconsin, I. A. Lapham, etc. : Annates Musei Botanid Lug-
duni Batavi edidit F. A. G. Miqttxl, 424.— Synopsis of the spedes of Starfishes,
in the British Museum, by John Edwabd Grat, 426.

A^^onomy.— -Discoyery of new planet (93) : Discovery of new planet (94), Wat-
son: Shooting Stars in August, 1867, 426. — Meteoric Astronomy, a treatise on
Shooting Stars, eta, Daniel SjBrwooD, 428. — On Meteors in the Southern
Hemisphere, E. Heis and GaoBaB Neumatbb: Stemschnuppen und Kometen,
Oabl yon Littbow, 429.

MiaceUaneoua Scientific /nieS^ancs.— Ascent of Mt Hood in Oregon, and deter-
mination of its height, 429. — American Association for the Advancement of
Sdence, 431.— National Academy of Sdences, 436.->-Mineralogic^ Nomenolar
tuie: British Association: Walker Prizes of the Boston Sodety of Natural
History, 436.

Misc^neoua BiHUography.^^The Mechanical Theory of Heat with its application
to the Steam Engine, eta, by R. Olaxtsiub: Condition and doings of the Boston
Sodety of Natural History: The Culture demanded by Modem Iiife, 437.— On
the distribution of temperature in the lower regions of the earth's atmosphere,
by Prof. Henbt Hbnnbbst : Die Chemie der austrodmenden Oele, Ihre Ber-
eitung und ihre technische Anwendung m KQnsten und Gewerben, von G. J.
Muldbb, 438.



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THE

AMERICAN

JOURNAL OF SCIENCE AND ARTS.

[SECOND 8 SBIE8.]



Art. I. — On Perfect Harmony in Music, the Double Diatonic Scale,
and an Enharmonic Key^ Board for Organs, Pianofortes, etc,;
by Hbnry Ward Poole, of South Danvers, Mass.

1. Seventeen years ago I published in this Journal* a theory
of Perfect Intonation in music, with a description of an organ
made to obtain this result, which had then just been completed.
The organ was provided with pedals and mechanism by which
the large number of pipes necessary for perfect tuning could be
played by the common key-board. It was supposed that all
music, for the moment, was in some key or scale. This scale the
organist could prepare by putting down a single pedal, which
had the effect of uniting the twelve finger-keys of each octave
with twelve valves, ana disconnecting all the others. As the

* music passed into other scales, by modulation, and other less
marked transitions, the player, by touching the pedal of the new
scale, made the changes of sounds required. In the present
paper, I shall describe a new key-board in which all the sounds

\ contained in the organ are represented, and placed within con-
trol of the organist, without aid from pedals or any interior
mechanism ; and which is practicable for any extent of modula-
tion, or number of notes in the octave. It is uniform in all keys,
and the same succession of melodies or harmonies is fingered the
same in every signature. The pedal-base is also provided for
by an appropriate key -board. 1 shall also treat of the scale
heretofore unnoticed by theorists, to which I have given the
name of Double Diatonicy\ together with other matters bearing
upon the theory and practice of perfect harmony.

* VoL iz, Jin., Mar^ 1850. f See the Mathematical Monthly, ii, 16, 1859.

▲h. Jour. Sgi.— Sbcozid Sxrim , Vol. XLIV, No. 180.— Jult* 1807.
1



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2 H. W, Poole on Perfect Harmony, etc,

2. In my former article in tbis Journal it was maintained that
the Prime Seventh with the ratio 4 : 7 was harmonious, admis-
sible and used in music, although this, so far as I have seen,
was asserted for the first time.* It is clearly evident that this
element enters into music of all kinds, and that the diatonic
scale must contain it, or that there must be tioo diatonic scales :
which latter supposition is most correct. If onljr fifths and
thirds are admitted in forming a diatonic scale it will naturally
be made of the common chords of three roots, namely, the
tonic or key-note, the dominant or fifth above, and the subdom-
inant or fifth below. This I have distinguished as the triple
diatonic acale^ whidh has three intervals in the ratio of 8 : 9,
9 : 10, and 15 : 16. The notes are represented by the syllables
Do, Re, Mi, etc., which always bear the same relation to the
key-note and to each other. Thus, Do to Re is always as 8 : 9
or a major tone. Re to Mi as 9 : 10 or a minor tone. Mi to Fa as
15 : 16 or a diatonic semitone. No exception is admitted in this
rule. Considering the key-note to make 4:8 vibrations in a given
time, we have the

Triple Diatonic Scale. Do to Do.

Common chords on Do, Sol and Fa.

Do Re Mi Fa Sol La Si Do
Re), vibrations, 48 54 60 64 72 80 90 96

First. Second. Third. Fourth. Fifth. Sixth Seventh. OctBTe.

Intervals, 8:9 9:1015:16 8:9 9:10 8 : 9 15 : 16

8. But if the ear prefers — and it often does prefer — the sub-
dominant harmony may be suppressed, and the fourth of the
scale, Fa, and the sixth. La, may be replaced by the perfect
seventh and ninth of the dominant harmony; so that if we still
take Z)o as a starting point or first of the scale, we require a
new Fa and La, for which formerly there have been no names.
But the perfect seventh, or flat sevent/i as it is called, is already
in solmization sung as Si^, taking the sound of Se — pronounced
by the Italian rules as are all these syllables, and like the Eng-
lish tHiy — and no other name is needed. Below Si therefore we
take /%, and take as first of a scale the Fa already given. Then
wo have the

Double Diatonic Scale. Fa to Fa.

Common chord on Fa, chord of *1 and 9 on Do.
Fa
Rel. ?ibrations, 32
or 48

First

Intervals, 8 :

* The Oerman ** Jahrbuch ** of Liebig and Eopp, in a disttriminatiDi; review of
my article in tbia Journal in 1860, specified this declaration.



Sol


Ll


Sb


Do


Re


Mi Fa


36


40


42


48


64


60 64


54


60


63


n


81


90 96


Second.


Third.


Fourtii.


Fifth.


Blxth.


Seventh. Octave.


9 9:


10 20


:21 7


8 8


9 9


10 16:16



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H. W. Poole on Perfect Harmony, etc. 3

4 The reasons for taking the key-note on Fa will appear on
consideration, but for the present the reader will recollect that
if the flat seventh of the natural key is taken — ^for example B^
with the common chord of C — the ear req^uires a resolution on
the chord of F or Fa^ which is the controlling note.

6. To sing this soEde is easy, provided the intervals of the
triple scale are well fixed by their syllables ; and it only remains
to learn the intervals Za to &, 20 : 21, and Se to Do^ 7 : 8, which
are easily recognized on hearing the harmony which should ac-
company a lesson in singing. In the last scale are five different
intervals in place of the three of the first scale, by which more
variety is secured.

6. These two scales contain all that belongs to the major
kevs; the additional notes required to complete the minor keys
will be considered afterwards, as well as those called *' acciden-
tals," which are borrowed from related scales. The notation
generally employed in music is practically correct, and, without
changing the letters or sharps and flats, scales may be noted so
that the exact sounds shall be indicated. In all times a singer
must know or feel the pitch of each note, if he would sing it
correctly. If be has learned the intervals by solmization, in
the only rational way, or by always giving the same intervals to
the same succession of syllables, and if he knows by the written
music what intervals are called for, he will give them equally
well in the key of C or in C#, or on the dozen diflFerent pitches
which can be given between these two sounds. But when we
are to deal with fixed sounds, as is necessary when constructing
an instrument, or when two fixed instruments may have to play
together, it is necessary to know and express the exact sounds
required. If the note be C, it will not ao to use that which is
the key-note of the natural scale for the third of four flats,
which is a comma lower, nor for the perfect seventh of D, two
sharps, which is lower still. I formerlv indicated this distinc-
tion by a numerical index, but the following system presents
advantages.

7. Every key-note is marked as usual, but with a Boman cap-
ital ; every major third to these key-notes with Boman lower
case, and every perfect seventh with a Gothic capital. The sec-
ond, fourth and fifth of the trip>le diatonic scale, oeing key-notes
in other scales, and in the series of key-notes, each a fifth one
from another, are accordingly in Boman capitals. So the sixth
and seventh of the same scale are thirds of other keys, and
marked in letters of the lower case. The two diatonic scales
will then be represented thus in the natural key.

Triple diatonic, ODeFGabO
Do Re mi Fa Sol la si Do

Double diatonic, CDeFGAbC
Fa Sol la se Do Rb mi Fa



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4 H. TV. Poole on Perfect Harmony^ etc,

8. Macb that is carious and interesting concerning this
double diatonic scale could be shown, did the character of this
article admit, and were it practicable to give musical examples
from the masters. It would be seen that the most beautiful,
varied and ornate compositions are made from the elements it
contains. It has the capacity in certain styles of music of using
with much grace accidentals, or chromatics, as they are called ;
for example, the ^, the regular leading note to Zfo, and the Soli^
diatonic semitone below Za, or the leading note to the relative
minor; th^se chromatics always ascending diatonic semitone
(15 : 16) to the notes above. Especially is the ^, or major
seveuth, used with Z)o, making the ratio of 8 : 16, if it is to be
considered as claiming to be attended to as concordant, or as
otherwise than as a passing note of a melody. But when per-
fectly tuned it is heard in harmony, especially with the mi and
Sol with which it is sounded. An examplie will be given to
illustrate this. First, it may be mentioned that besides the three
series of notes — key-notes, thirds and sevenths — another series is
used, that of the dominant's thirds in the minor scales, the lead-
ing notes to the relative minor's key-note. This in each key is
Solif^^ and is tuned a major third above mi; and m% Sol^ and si
form a major common chord (4:5: 6), These notes are ex-
pressed in italic letters of the lower-case. The example being
the double diatonic scale of G, in one sharp, I shall give this
scale with the accidentals introduced in the following melody
from Rossini's ' II Barbiere di Seviglia.* The air will be remem-
bered as appearing in the accompaniment to the song or recita-
tive (for it IS all on one note, D or Do, the part which this ac-
companies), in which Figaro describes his place of business,
{Numero quindici^ etc.), and afterward is the air sung by Alma-
viva when he has a prospect of seeing Rosina, while at the same
time Figaro sings in joy at the sound of his patron's gold.

Double Diatonic Scale in G, with accidentals.




Ahj olied'a • mo- re U flam > ma ■en-to, oan-zia do gl«-lM-lo, a
Sisurmony of the aoeompanimaU.

G - - - D with the Vth - - O

9. Although it is convenient to consider a special strain of
music as being in a definite key or scale, and to consider the
notes which are sometimes prone to introduce themselves as
'* accidentalSi" and in a manner extraneous, yet the truth is that



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jff. W. Poole on Perfect Harmony^ etc, 5

all such intruders have the excuse of being relatives, with the
right of entrance, under certain rules, which the great masters
understand. Among the related notes in the scale in G, last
given, are C and e, or the fourth and sixth of the double dia-
tonic on the same key-note, G. These are introduced in a pass-
ing manner, as in the cadence — a familiar example is found in the
Oh I dolce concento* of Mozart — where the subdominant harmony,
not before heard, comes in just before the final dominant and
tonic chords. In the example given from Eossini, the third
note of the third measure may be 0, as well as c — Fa of the
triple scale, as well as /% of the double. In the fifth measure
the fourth note mav be the same C, and the sixth note may be e,
the sixth or la of the triple scale of G. But the following note
on the same degree in the sixth measure is clearly and neces-
sarily £, Be, or the ninth of the chord of the seventh on D. So
the third note of the first measure may be e. The enhar-
monic change from e to E, a rise of a comma, is often required,
is very beautiful, and I have proved that it can readily be
made for my singers, who know this change of a comma as
well as others know the tone or semitone, will give it, even
without accompaniment, with perfect accuracy, as proved by the
harmony afterward applied as a test. All this variety within
the limits of musical laws — which only forbid what is disor-
derlv, complicated, or what the ear will not distinguish — adds
to the pleasure of music, and it is the exact rendering of all
the melodies and harmonies which gives the charm to a good
singer. When acutely perceptive of such accuracy, I had the
good fortune to listen to Alboni on all the occasions when it
was possible to do so. I thought her then, and still am of the
opinion, that she was the best singer I have ever heard. It is
certain that she had a wonderful exactness in executing what-
ever she undertook. There was no "temperament" in Aer scales,
and what the strictest theory requires in intonation she under-
stood and gave. She sang music whose analysis would alarm a
student with its apparent difficulties ; but the delighted auditors
perceived only a delicious and " easy " flow of melody.

10. Fortunately, the greater part of the difficulties in the
higher class of melodies are overcome by the unconscious or
instinctive talent of the singers. The accompaniment of such
melodies is not difficult, and the harmonies attending make clear
what the melody must be. No instrument will ever compete
with the voice in its peculiar department, but may surpass it in
that which it is fitted for. Neither voices nor instruments sepa-
rately can produce the highest effects in music ; those will be
attained by the combination of the two. Improvement in the

* GeneraUy so called. It is the air in Mozart's ll Flavio Magico, " Oh I eata
armonia,'* From ibis is taken the song " Away with melaacholy."



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6 H. W. Poole on Perfect Harmony^ etc.

instruments which accompany will be followed by better vocal
music.

11. For understanding what is to follow, I would have.it
borne in mind, that I consider that all musical ratios derived
from the primes 3, 5, and 7 are appreciable by the ear, and may
be used in all their combinations and transpositions into differ-
ent keys, which is already done in a senes of perfect fifths.
The next prime, the eleventh, does not present sufficient claims
to be admitted to the musical canon, except under regulations
which as yet I would not undertake to define. I can tune it,
and can perceive that it yields harmony so far as to give coinci-
dences in its vibrations with the other prime chords, the fifth,
ik^ third and the seventh. It is not impossible, when a great
refinement is made in music, and the sense highly cultivated,
that this class of novel sounds may be introduced and appreci-
ated. But except under such conditions, and without the most
exact intonation, the eleventh would fail to give any effect other
dian incomprehensible discord. It might be admissible in the
harmonic stops of an organ — those called mixtures, sesquialtras,
etc. — ^but only under a system of perfect harmony.

12. For a practical instrument i would provide five series of
sounds— a series signifying that each sound is a fifth from that
which precedes, and that which follows it. These five series,
Arranged in the order of their importance, are as follows, the
Dotes of each series being marked with the letter and sharp or
flat in common use, but in a distinctive type for each series :

Series I. Key-Notes. Roman capitals, A, B.

*» II. Thirds (major^ to key-notes, series I, Roman lower-case, a, b.
" III. Perfect sevenths to key-notes, " I, Gbthic capitals, A, B.

(These constitute the major scales.)
*' IV. Dominant thirds (major), in the minor

mode, being major thirds to^ II, Italic lower-case, a, 5.
«< V. Dominant sevenths, in the minor mode,

being perfect sevenths to II, Gothic lower-case, a, b.

(These two last complete the minor mode.)

IS. This being understood, it will be known that the same
letter in the same type is always the same sound, and its rela-
tion evident; that the same letter in Boman lower-case is a
comma lower than the same in capitals, and a quarter (0*256) of
a comma higher than the seventh in Gothic capitals. A letter of
the III series, in Italics, is two commas below the same in the
I series, or one comma below that of the 11. The sevenths of
the V are one comma below those of the III ; the lower-case
letter indicating this difference below the capital.

14. Among the names which have to be remembered as ad-
vocates of perfect harmony and just ideas in music, perhaps the
first in modern times is that of Gen. T. PerJbnet Tnompson of



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H. W. Poole on Perfect Harmony, etc. 7

London. My first knowledge of his valuable services came
during the preparation of the second part of my article in this
Journal (in March, 1850), by an allusion in the Westminster
Beview to an enharmonic organ which he had just brought out
in London. This led to the reading of his spirited articles on
music and other subjects in the Westminster Review, and to the
seeking his acquaintance, which, through a considerable corre-
spondence, I have had the good fortune to make. I have also
received his ^^ Theory and Practice of Just Intonation^^ and '*.Z?tf-
acription and use of the Enharmonic Organ^^ of his invention,



Online LibraryJohn AlmonThe American journal of science and arts → online text (page 51 of 102)