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TRANSACTIONS
mt OF
m. VASSAR BROTHERS INSTITUTE,
“an AND ITS

SCIENTIFIC SECTION.
POUGHKEEPSIE, N. Y.
41884-1885.
: VOL, Il. PART I.
eee ee ee eee

PUBLISHING COMMITTEE:

LEROY C. COOLEY, WILLIAM B. DWIGHT,
F CHARLES L. BRISTOL.

qAaOMlae FS tA
=< 4

x NOV 24 1988 =
is Ry:

Na MOn ae muse

CONTENTS OF VOLUME III.

PART TI.

Minutes of Regular Meetings,
Annual Meeting, May 5, 1885,

Treasurer

Curator’s

Librarian’
Secretary’

Board of

’s Report,
Report,

s Report,
s Report,
Trustees,

Officers of the Institute,

The Jolly B

PART II.

Officers of the Scientific Section—1884-85, ;
The Evolution of Science—LeRoy C. Cooley, Ph.D., :
The Just Claims of Natural Science—Prof. W. B. earth
The Genealogy of the Vertebrata, as learned }

from Paleontology—Prof. E. D. Cope
Some Changes in the Habits of Birds—James M. DeGarmo, Ph.D.,
Note on the ‘‘ Downy Woodpecker”
Sand and Kaolin from Decaying Quartzite—Prof. W. B. Divieht,
Balance—LeRoy C. Cooley, Ph.D., .
The Peculiar Structure of Clark’s Clay Beds—Prof. W. B. Diiene 8&6
An Empirical Study of Gyrating Bodies—C. B. Warring, Ph.D.,
Recent Celestial Phenomena—Prof,. Maria Mitchell, :

On Sun Spots—Miss Mary Whitney, .

Chairman’s Annual Report—Prof. W. B. Bente
Officers of the Scientific Section—1885-86,
Van Duzer and Townsend Mines—Corrigenda,

aS er

EXC

Du iPLIC, ATE

PRANGE —~

—George Tremper,

—

5
7
7
8
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Nt BOARD OF TRUSTEES.
1884-1885,

JoHN Guy VASSAR,

S. M. BucKINGHAM,
JOACHIM ELMENDORF,
WILLIAM B. Dwieut,
CHARLES N. ARNOLD,
LeRoy C. Coouny,

Wu. G. STEVENSON,
EDWARD ELLSWORTH,
Henry V.. PELTON,
CHARLES B. HERRICK,
A. P. Van Grxson,
FRANK L. Moore.

1885-1886.

JOHN Guy VASSAR,
S. M. BucKINGHAM,
JOACHIM ELMENDORE,
WitiiaMm B. Dwicut,
CuHar_es N. ARNOLD,
LeRoy C. Coonry,

Wm. G. STEVENSON,
EpwarpD ELSworth,
Henry V. PELTON,
CHARLES B. HERRICK,
A. P. VAN GTESON,
WILLIAM T. REYNOLDS,

OFFICERS OF THE INSTITUTE.
1884-1885.

LeRoy C. Coonxry, Ph.D.,

Rev. Henry L. ZIEGENFUSS,

Wm. G. StEvENsoN, M.D.,
EDWARD Exsworth, KEsq.,

Pror. WILLIAM B. Dwicut,

ProF. HENRY VAN INGEN,
FRANK L. Moors, C.E.,

President.

Vice President.
Secretary.
Treasurer.
Curator.

Art Director.
Librarian.

1885-1886.

Wm. G. Stevenson, M.D.,
Henry V. PELTON, Esq.,

Mr. CHARLES L. BRISTOL,
EDWARD ELSWortTH, EsqQ.,

Pro¥r. WILLIAM B. Dwieut,

Pror. HENRy VAN INGEN,
IrvinG ELTING, Esq.,

President.

Vice President.
Secretary.
Treasurer.
Curator.

Art Director.
Librarian.

TRANSACTIONS

OF
VASSAR BROTHERS INSTITUTE,
1884-1885.

OCTOBER 7, 1884A—TWENTIETH REGULAR MERTING.

LeRoy C. Cooley, Ph. D., president, in the chair ;
twenty-six members and one hundred guests present.

The president gave his inaugural address, entitled
“The Evolution of Science.’’ (Dr. Cooley’s address is
published in full in part 11. of this volume).

Mr. H. M. Curtis and Mr. E. P. Carpenter were elected
active members.

OCTOBER 21, 1884—TWENTY-FIRST REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair ,
twenty-four members and seventy: four guests present.

Prof. Wiliam B. Dwight, chairman of the Scientific
Section, gave an address entitled ‘‘The Just Claims of
Natural Science.”’ (Prof. Dwight’s address is published in
full in part ii. of this volume).

Mr. E. N. Howell, Mr. G. M. Hine, Rev. Howard B.
Grose, Rev. W. Spaulding, Mr. C. C. Gaines, Mr. F. B.
Warring and Mr. C. L. Bristol were elected active
members.

OCTOBER 28, 1884—TWENTY-SECOND REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair ;
eighteen members and fifty guests present.

6 TRANSACTIONS

Mr. Henry V. Pelton, chairman of the Literary Section,
gave an address entitled ‘* Social Questions.’’

Prof. Manuel J. Drennan and Harry F. Parker, M.D.,
were elected active members.

DECEMBER 2, 1884—TWENTY-THIRD REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair ;

twenty-six members and two hundred and seventy-five
guests present.

Mr. Clarence Cook, of New York, gave an address
entitled ‘‘ Artists and Artisans.’ For this interesting
address a cordial vote of thanks was extended by the
Institute to the speaker.

JANUARY 6, 1885—TWENTY-FOURTH REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair;
twenty-one members and sixty-five guests present.

A. P. Van Gieson, D.D., chairman of the Art Section,
gave an address entitled ‘‘ Art and Beauty.”

JANUARY 27, 1885—TWENTY-FIFTH REGULAR MEETING.

President Cooley in the chair ; twenty-eight members
and two hundred guests present.

Prof. Edward JD. Cope, of Philadelphia, gave an ad-
dress entitled ‘‘The Genealogy of the Vertebrata, as
learned from Paleontology.’ The subject was amply
illustrated by large and accurate drawings, by charts and
the blackboard.

On motion, a vote of thanks was given to Prof. Cope
for his learned and interesting address.

(Prof. Cope’s address is published in part ii. of this
volume).

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the heavy-line tee.

VASSAR BROTHERS INSTITUTE. 7

MARCH 3. 1885—TWENTY-SIXTH REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair; many
members and a large number of guests present.

Prof. Henry Van Ingen gave an address entitled
‘¢Three Centuries of Painting from Chimabue to Raph-
ael,’? which was beautifully illustrated by projections
on the screen of copies of the most typical paintings of
the best masters during that period.

APRIL 6, 1885—TWENTY-SEVENTH REGULAR MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair ; four-
teen members and seventy-five guests present.

James M. De Garmo, Ph.D., gave an address entitled
‘*A Study of the Sun.’ It was very fully illustrated
by projections of a large number of well chosen pictures.

Mr. 8. W. Ford was elected an honorary member, and
Lucy M. Hall, M.D., was elected an active member.

MAY 5, 1885—FOURTH ANNUAL MEETING.

LeRoy C. Cooley, Ph.D., president, in the chair ;
twenty-two members present.

The minutes of regular meetings were read and
approved.

The committee on museum and library gave an item-
ized report of expenditures for the museum and library
amounting to $15.25.

A. P. VanGieson, D.D., president of the board of
trustees, made a general report of the condition of the
property of the Institute.

Mr. Edward Elsworth, treasurer, rendered a full re-
port of receipts and expenditures for the fiscal year end-
ing May 5, 1885, showing a balance in the treasury of
$832.74. The following is an abstract :

8 CURATOR’S ANNUAL REPORT.

Balance in treasury May 6, 1884....... (ace eaeee eee ene . $509 16

Maralreceipts during the year.(j.). «eee eine dels eae er ene 1,968 24
“ito he} Renan a Ane een neon renin coe cman on ond oll od Go $2,477 40

Total disbursements during the year..................---..- 1,644 66

Prof.

William B. Dwight, curator of the museum,

presented a report as follows :

The

museum has been increased by the following

donations during the season of 1884-1885:

From Mr. C. N. Arnold—One coral, and one hundred and thirty speci-
mens of North American ferns.

‘¢ Mr. A. Innis—One tropical snake—chilabothwist inornatus.
“Dr. Junghans—One beetle from Japan, and one tapeworm.

oe Mr

. J.C. Pumpelly—Two geodes from Keokuk, lowa.

“ Mr. William Ward—One echinoderm.

“é Mr
Se we IN la

. W. Hanlon—One specimen of peat from Ireland.
F. L. Moore—a cord showing the circumference of a big tree

at Mariposa, California.
«Mr. W. B. Styles—One concretionary nodule of iron, Lawton, Mich.

ee Dr

. W. G. Stevenson—One tarantula, two specimens of sponge

e

from Nassau, N. P., one banded water-snake—platenis cati-
caudatus—South Atlantic ; one wngatia vepsadnia, Port Paix,
Hayti; seven specimens of crabs, Nantucket, Mass., (one of
carcinus irroratus, six of gelasimus fugnax); two slugs—limaa
agrestis— Poughkeepsie ; one spider—epeira diadema—Pough-
keepsie ; eight craw-fishes—astacus bartoni—Poughkeepsie ;
three lizards, one brain each of the shad—clupea sapidissma—
Hudson River, of the screech owl—scops asio—of the blue jay
—cyanurus cristatus—of the large-eared owl—osio otus— of the
red-winged starling—agelaeus phoeniceus—of the pigeon-hawk
—faleo colrun barius—and of the flying-squirrel—sciuropterus
volucella.

Mr. W. B. Dwight—various specimens of sand, gravel, clay, and

concretionary material illustrative of the peculiar formation of
Clark’s clay beds near Newburgh.

The following articles have been added to the museum

during

the year by purchase:

One hawk—buteo lineatus.

One king

fisher—ceryle alcyon.

One purple grackle—quis calis purpureus.

VASSAR BROTHERS INSTITUTE. 9

One egg of the emeu, Holland.

One porcupine fish—diodon hystrix, West Indies.

One sea feather—gorgonia sp. ?

One yellow coral, one sponge, West Indies.

Two echinoderms, one triton, one unnamed sea-shell from the West

Indies.

Considerable progress has been made in naming, ar-
ranging and catalogueing the specimens. For the latter
purpose a set of large and substantial books has been
prepared. This labor is, however, a task of much magni-
tude, and a large part of it Hes yetin the future. Ithas
been found necessary to manipulate all of the mounted
specimens with much care, in such a way as to stop the
ravages of insects which were destroying them.

It has been impossible for your curator to do much
more personally than to attend to the naming of speci-
mens. For the rest of the work above mentioned, the
society is indebted to the very able and dilligent services
of the assistant curator, Dr. Stevenson.

Mr. Frank L. Moore, librarian, reported as follows :

The library has been augmented during the past year
by the receipt of 170 pamphlets and 57 bound volumes.
The individual contributors of the year are Messrs. H.
L Ziegenfuss, J. H. Ketcham, J. I. Platt, E. P. Carpen-
ter, T. A. Leister, George Corlies, EK. Osborn, Dr. Bockée,
Thomas Newbold and Mrs. Whitehouse. The pub-
lications that have been received from various scientific
societies and state departments will be reported by the
secretary.

The shelving has been handsomely extended during
the past year. They are now lettered and numbered
after the most approved methods, and the books are ju-
diciously distributed and located thereon. The card
system, adopted a year ago, iscompleted, and every book
is accessible by the easiest methods of search.

The secretary, W. G. Stevenson, M.D., presented the
following annual report:

10 _ SECRETARY’S ANNUAL REPORT.

Mr. President and Members of Vassar Brothers In-
stitute: Observing the requirements of our rules, your
secretary has the honor to present his fourth annual re-
port in relation to the work and progress of the oa
for the year ending this date.

During the year one member, Mr. John Sleight, has
died, and the names of twenty-three members have been
taken from the roll by resignations or because of arrear-
age in annual dues. Six gentlemen and one lady have
been elected, and have qualified as active members.
The present membership is one hundred nineteen.

The following addresses were given before the Institute
during the season of 1884—85 :

1884.
October 7%. ‘* The Evolution of Science.”

L. C. Cooley, Ph.D., president of the Institute.
October 21. ‘‘ The Just Claims of Natural Science.”

Prof. W. B. Dwight, chairman of Scientific Section.
October 28. ‘‘ Social Questions.”

Henry V. Pelton, Esq., chairman of ene: Section.
December 2. ‘‘ Artist and Artizan.”..Mr. Clarence Cook, of New York.
1885.

January 6. ‘‘ Art and Beauty.”
A. P. Van Gieson, D. De chairman of Art Section.

January 27. ‘‘The Genealogy of the Vertebrata, as learned from

Paleontology.”...Prof. E. D. Cope, of Philadelphia.
March 3. ‘‘Three Centuries of Painting.”....Prof. H. von Ingen.
April 6; “A Study of the Sunt 7.7%. 5: James M. DeGarmo, Ph.D.

Your secretary desires, in a special manner to express,
1 ee public way, the cordial thanks of the Institute to
Clarence Cook and to Prof. E. D. Cope for the
ue and interesting addresses they so kindly and
generously gave before us.
The average number of members present at the meet-
ings was twenty-two, and of guests one hundred twenty.
During the year volume ii., containing the transactions
and scientific papers of the Institute and its Scientific
Section from May 1, 1883, to May 6, 1884, has been is-

VASSAR BROTHERS INSTITUTE. sha

sued, and distributed to various scientific and philosophi-
cal societies, journals, individuals and public libraries.
The volume, of one hundred sixty-six pages, contains,
beside official reports and abstracts of addresses, the
following papers in full:
lirantoumal NGdieSSHe sam sieimicrs/see cle sae es President, J. Elmendorf, D.D.
‘“The objects and duties of the Art Section.” ...... Prot. H. von Ingen.
‘* Specialization in Natural Science,”
‘** An Interesting Geological Locality,”
** Embryonic Forms of Limulus Polyphemus,”
‘*Geological Investigation in the vicinity of
Poughkeepsie,”
‘* Gyroscope,” Z ape
: : : ; -C. B. Warring, Ph.D.
‘* Uniformity of Climate in Past Ages,” © ee ae
SOM OUEM aa Ae.cralsr vistas as Saale chalecs v iteioe ace ielntc vege ee Maria Mitchell, LL.D.
‘*Compressibility of Gases,” }
‘““ A New Apparatus for Boyle’s Law,” H ae
Ds os - L. C. Cooley, Ph.D.
‘“ Ventilation for the Laboratory Table, poley Ey
** Device for Locking Laboratory Drawers,”
Snteliicencein) Buttertlies));.-5.....2..--..- Jas. M. DeGarmo, Ph.D.
‘* Carcharodon carcharias,”’ |
** Odontaspis littoralis,” | w.G
“Our Local Mammalian Fauna,” | ar
** List of our Local Birds.” J

Prot. W. B. Dwight.

a —~--—-—_~

—

Stevenson, M.D.

Your secretary is pleased to report that his corre-
spondence has enabled him to place many additional
names of societies and journals upon the exchange list
of the Institute. The following have already made
valuable contributions to our library.

American Philosophical Society, of Philadelphia.
Albany Institute, of Aibany, N. Y.

American Geographical Society, of New York.
American Monthly Microscopical Journal.
Academy of Sciences of St. Louis, Mo.

Academy of Natural Sciences of Philadelphia.
American Museum of Natural History, New York.
Bussey Institute, Mass.

Boston Society of Natural History, Boston, Mass.
Buffalo Society of Natural Science, Buffalo N. Y.
Bureau of Education, (Department of the Interior),

12 SECRETARY'S ANNUAL REPORT.

Bureau of Ethnolgy, (Department of the Interior).

Bureau of U.S. Geological Survey, (Department of the Interior).
Bureau of Statistics of Labor and Industries of New Jersey.
California Academy of Sciences.

Cornell University, Ithaca, N. Y.

Connecticut Academy of Arts and Sciences, New Haven, Conn.
Cincinnati Society of Natural Science, Cincinnati, Ohio.
Canadian Record and Natural History Society of Montreal.
Davenport Academy of Natural Science, Davenport, Iowa.
Department of the Interior.

Engineer Department of U.S. Army.

Library Company, Philadelphia.

Minnesota Academy of Natural Sciences, Minn.

Middlesex Institute, Mass.

Missouri Historical Society, St. Louis, Mo.

Magazine of American History.

New York Academy of Sciences, New York.

Natural History Society of Glasgow, Scotland.

Nova Scotian Institute of Natural Science, Halifax.

Newport Natural History Society, Newport, R. I.

New York Microscopical Society, New York.

Oberhessischen Gesellaschaft fur Natur-und Heilkunde, Giessen.
Peabody Academy of Sciences, Salem, Mass.

Psyche.

Portland Society of Natural History, Portland, Me.

Rochester Society of Natural Science, Rochester, N. Y.

Royal Society of Canada.

Sociedad Cientifica Argentina, Buenos Aires.

Société Impériale des Naturalistes de Moscou, Russia.
Smithsonian Institution.

Torrey Botanical Club, New York.

U.S. Fish Commission, Washington, D. C.

Wisconsin Natural History Society.

Wisconsin Academy of Sciences, Arts and Letters, Madison, Wis.
Vassar Miscellany, Vassar College.

Fifty-seven volumes of books, and one hundred seventy-
two pamphlets, mostly the transactions and papers of
scientific and philosophical societies, have been received
for the library. Valuable contributions have also been
made to the museum, the details of which appear in the
report of the curator.

The following papers were read before the Scientific
Section during the season of 1884—’85 :

1884.

December 3.

December 17.

1885.

January 28.

February 11.

February 25.

March Tale
March ale
March 25.

VASSAR BROTHERS INSTITUTE. 13

‘““The Gyroscope: what it does and the reason for its
peculiarities.” ‘‘The Top, Gyrostat, Gyrocycle and
Bohneuberger Machine; their rationale.”

C. B. Warring, Ph.D.

**Scraps from a Worker’s Note Book.”

James M. DeGarmo, Ph.D.

** Description of the Jolly Specific Gravity Balance, and
a simple device for overcoming an optical difficulty

AMPIbS USCH a staan ccrePie oboe slo wont etsts L. C. Cooley, Ph.D.
‘The Peculiar Structure of Clark’s Clay Beds near New-
[oreo INGA fost = meee eros a eracake Claes Prof. W. B. Dwight.

‘*‘The Gyroscope: various results and final studies.”
**Precession of the Equinoxes.” ‘‘ Frisi’s Law.”
C. B. Warring, Ph.D.
“* Recent Celestial Phenomena.”’.. Maria Mitchell, LL.D.
Pry ERTL SPO USathcrs) clates we aaa) aks = ae.s) ote Miss Mary Whitney.
“ Exhibition of a Collection of North American Ferns.
Mr. C. N. Arnold.

At the annual meeting of this Section C. B. Warring,
Ph.D., was elected chairman, and Mr. C. N. Arnold was
reélected recording secretary.

The following papers and discussions were given before
the Literary Section during the season of 1884~ 85.

1884.

November 11.

November 18.
November 25.
December 9.

December 16.
December 23.

1885.

January 13.
January 20.

January 27.
February 10.
February 17.

: ; Mr. Benson Van Vliet.
‘* Business Speculation”...... W. C. Albro, Esq
Fase) SEO 2 hia aa ccc) aah 20d ws spa ceo Rev. 8S. H. Synnott.
‘Concerning Pleasantness”........ Rev. C. W. Fritts

‘* The Effect of Amusements on National Character”
Rev. L. H. Squires.
Mr. Henry Bartlett.

“The Mexican! War? : i.) j 0s. Edward Elsworth, Esq.

‘Phe Isthmian? Canal”. 2.2.02 )4./. C. B. Herrick, Esq.

‘* How Science Aids Faith”..... Hon. John Thompson.
“The American Marine,

Its Past, ( Mr. L. F. Gardner.

Ve Future,” t Mr. A R. Haskin.

SOR OMS: 1a orl as ta he segtens «aes conte s F. B. Lown, Esq.

Sy NCO DhMASUISa ye Utter crcl yaentet ust Jp: R. E. Taylor, Esq.

** Education.” The American System of Education,
Mr, S. W. Buck,

aX
14 SECRETARY’S ANNUAL REPORT.
1885.

February 24. ‘‘ Rome” (Illustrated)............... James Nilan, D.D.

March 9. ‘* Dutch Village Communities on the Hudson River ”
Irving Elting, Esq.

March 16. ‘‘ Evolution in Literature”......... Mr. Wallace Bruce.

March 23.) Manis sPlacesiny Nawune yee Mr. Edward Burgess.

At the annual meeting of this section, Charles B.
Herrick, Esq., was elected chairman, and Mr. James H.
Hamill was reélected recording secretary.

The Art Section has held no meetings and made no
effort, during the past year, to organize the work which
was planned by it, and approved by the trustees over a
year ago. It is possible that there may be no ‘‘ public
demand ”’ which will justify any effort in this direction,
but your secretary begs to suggest that a proper concep-
tion of official duty should prompt the officers of this
Section to, at least, hold the regular meetings as instituted
by the by-laws, and thereby permit the Section itself to
determine as to the expediency of organizing its work.

There are several questions relating to the future policy
and work of the Institute which, in the opinion of the
secretary, demand careful consideration, and sugges-
tions thereon are not embodied in this report, for the
reason that a special committee has been appointed to
revise the by-laws, and it is not desirable to anticipate
in any way the work of this committee.

On surrendering the official trust, held since the Society
was incorporated, your secretary may be pardoned a
single personal allusion when he states that it has been
his endeavor—whether acting in an official or individual
capacity—to advance the interest of the Institute in all
ways and at all times, believing that thereby the educa-
tional object for which the Society was organized was
being promoted for the good of individuals, and for the
benefit and honor of our city.

That a moderate success, at least, has been attained
all are assured, and that still greater success may be

,

ii

i ;

.
VASSAR BROTHERS INSTITUTE. 15

attained there should be no doubt. All depends upon
the energy and faithfulness with which members do
their duty, and officials execute the trust reposed in
them.
For the many expressions of personal confidence, your
secretary desires to express his gratitude.
Respectfully submitted.

W. G. STEVENSON,
Secretary.

The following gentlemen were elected trustees of the
Institute for 1885-1886 :

JOHN Guy VaAssaR, WILLIAM G. STEVENSON,
S. M. BuckInGHaAM, EDWARD ELSworTH,
JOACHIM ELMENDORF, Henry V. PELton,
Witii1Am B. Dwieut, CHARLES B. HERRICK,
CuHaRues N. ARNOLD, A. P. Van GIESON,
LERoy C. Coo.ry, WILLIAM T. REYNOLDS.

The following gentlemen were elected officers of the
Institute for 1885-1886 :

President, . : h Wm. G. STEVENSON, M.D.
Vice President, . Henry V. PELTON, Esa.
Secretary, ° . Mr. CHarues L. BRISTOL.
Treasurer.) EpWaArRD ELswortH, Esa.
Curator, ; . Pror. WiLiiAM B. Dwieur.
Librarian, . ; IrRvinG ELTiIne, Esa.

Art Director, : 5 Pror. HENRY von INGEN.

Sele EE PAPERS
PeNocA Re. BROTHERS INSTITUTE,
TRANSACTIONS

SCLENTLEIC SECTION.

ASKS —“[S5)—
VOL. II. PART II.

SCIENTIFIC SE CMION

1884-1885.

Pror. WiLuiAmM B. Dwicut,. Chairman.
Cuaries N. ARNOLD, ; - Secretary.

"
:

THE EVOLUTION OF SCIENCE.

AN ADDRESS DELIVERED BEFORE VASSAR
BROTHERS INSTITUTE,
OCTOBER 7, 1884.

BY LEROY C. COOLEY, Ph.D., PRESIDENT OF THE INSTITUTE.

Members of the Institute, Ladies and Gentlemen: In
discharging the duties of office, it is my privilege this
evening to inaugurate the work of the fourth year of the
Vassar Brothers Institute. The task is not a little diffi-
cult on account of the wide scope of the Institute, which
includes subjects so broad and so distinct as literature,
the fine arts, and science. I have felt some difficulty
also arising from the fact that, by a law of the Institute,
literature, art, and science, must each, through the chair-
man of its respective section, speak to you in the near
future for itself. It has not been easy to decide just
what line of thought I might with propriety ask you to
pursue with me on this anniversary occasion. And it is
not without considerable solicitude, therefore, that I pro-
ceed to offer some thoughts in regard to the very ancient
history—I may say the birth—of literature, art, and
science, confining myself, however, chiefly to the last.

But, first, let me call attention to the vital connection
which at present exists between these departments of hu-
man knowledge and the civilization of the world.

Literature, art, and science, on the one hand, the po-
litical, social, and religious condition of a people, on the
other, hold a mutual and most intimate relation. The
first represent the last as herbage represents the soil

which produces it; the last depend upon the first as the
fe}

20 THE EVOLUTION OF SCIENCE.

soil depends upon the dew, the rain, and the annual con-
tribution of falling leaves, which enrich it.

Literature, art, and science, make the most luxuriant
growth where wealth is the most abundant and most
widely diffused, where government is strongest and most
liberal, and where religion is most pervading and spirit-
ual. Poverty, anarchy, and irreligion, are to them what
the sands of the Sahara are to the flowers, the grains
and the grasses.

But, while literature, art, and science can thrive only
in civilized communities, they are at the same time, on
the other hand, the most powerful elements in modern
civilization. Just consider how large a part they play
in the affairs of life. Banish the libraries from our
homes and our schools; deprive our houses of their stat-
uary and paintings, and our public institutions of their
galleries of art; rob our commerce of steam and electric-
ity, our manufactories of chemical processes, and our
agricultural industries of scientific appliances, and how
barren and lifeless would be our political and social
condition.

From such considerations it would seem that neither
of these two sets of factors in civilization could exist
without the other. Nevertheless, if, prompted by the
spirit of modern philosophy, we probe antiquity, we find
that, in the beginning, this mutual dependence did not
exist ; that these two sets of elements were introduced
at different periods in human development; and that
law and religion—not literature and art—came first and
are most fundamental. This is the testimony of the
records.

The light of history, as we look backward, becomes
more and more obscured, and yet not quite wholly ob-
secured, by the mists of legends. Wealso catch glimpses
of an almost prehistoric poetry. Think, for example, of

such bards as Eumolpus and Orpheus, antedating Homer
4

:
ae
an inl vr

vali
ind
Md
aa

LE ROY C. COOLEY. 21

by a period of unmeasured length. Now, we find that
the most ancient legends are simply the stories of still
more ancient heroes, whose exploits were performed in
the service of organized communities ; and that many
of those earliest poems are hymns which constituted a
part of a religious ritual.

Greek literature begins with Homer. But before this
beginning of what is distinctly recognized as literature,
the political condition of those almosf prebistoric peo-
ples had ripened into an elementary form of organization,
and their religious customs into a state requiring a dis-
tinct religious ritual. It would therefore appear that
the very earliest of Greek attempts toward literature
were the offspring of a somewhat highly developed social
condition of the ancient Helenes.

The histories of other ancient literatures, if we had
time to trace them, would lead us to the same conclusion
in regard to other peoples.

And, then, as to the fine arts—we speak of that group
of them which includes architecture, sculpture and
painting,—we find that the very early specimens, such as
are to be seen in Egyptian temples, Assyrian palaces,
and Etruscan tombs, bear witness to the already ad-
vanced social development of the people who produced
them.

But, clearest of all, is the illustration furnished by
physical science.

Science is not prehistoric to the same degree that
literature and art are. And the records show more
clearly that its beginnings were never made, except by
races which had already long passed the primitive stages
of political and social life.

Take astronomy, for example; for beyond a doubt
astronomy covers the most ancient observations. History
hesitates whether to assign its origin to the Chinese, to

the Chaldeans, or to the Egyptians ; but it does not hesi-
5

22 THE EVOLUTION OF SCIENCE.

tate to declare that China, Chaldea, and Egypt, which
divide with no other countries the reasonable claim to
be its birth place, were the seats of the most advanced
primeval governments.

Now, the character of the astronomy founded by these
peoples throws some light upon the order of their de-
velopment. It consisted of such phenomena as marked
the divisions of time—the year, the months, and the
days. And the knowledge acquired by observing these
phenomena was employed to regulate feasts, festivals,
and other periodic affairs, unknown everywhere, except
in organized communities.

The order of development seems to have been every-
where the same. First, the attainment of those favorable
conditions furnished by a more or less highly-organized
social life, and, afterwards, the introduction of the primi-
tive forms of literature, fine arts, and science.

If the doctrine of evolution be true then is civilization
the parent ; literature, art, and science, are its offspring.

Just how the introduction of these elements into hu-
man life was brought about, is a problem which philoso-
phers have not yet solved to the satisfaction of one an-
other. At this point even the theory of evolution halts.
For, while we may think that we recognize the germ of
literature in the gift of language, and of art in manual
dexterity, and while we may safely affirm that the em-
ployment of language and skill was the inevitable
prompting of the material wants of men, yet the su-
preme difficulty remains that we can not dignify the re-
sults of these first promptings with the names of litera-
ture and art. These terms should be reserved to describe
those forms of language and those products of the hand
which express thoughts and emotions such as are not
suggested by material wants nor by animal instinct.

Accordingly, we must seek the earliest germ of litera-
ture, not in the first sentence ever uttered, but in the

iS

LE ROW C2 COOLEY: 2B;

first sentence ever uttered to express anabstract thought ;
and of art, not in the first rade implement ever made, but
in the first product of the hand, however rude, which
symbolized a mental conception.

The fact is that the very soul of literature, art, and
science, is human thought. But thought is the pure
product of mind ; and, to quote the language of Sully,
the companion of Huxley, in the authorship of the ar-
ticle on ‘‘ Evolution,”’ in the Wew Britannica (vol. viii.,
p. 770), ‘‘ All the laws of physical evolution can never
help us to understand the first genesis of mind.”

The birth of literature, art, and science, can neither be
dated nor explained on mechanical principles. We must
start with the simple fact that the germs were brought
into being in the first mental acts by which language,
manual dexterity and sensation were employed to
minister to the intellectual wants of man.

From such puny germs to the robust literature, the
thrifty art, and the athletic science of the present day,
what a development! The process has been one of as
genuine evolution as ever occurred in the progress of
the world. It has gone step by step, through successive
changes in forms, and structures, and functions, from
simple to complex, from uniform to variable, from worse
to better, the higher not only following but depending
upon the lower. But this description, it will be noticed,
conforms exactly to the best modern definition of evolu-
tion. (Hne. Brit. vili., 746, 751). Indeed, the only ele-
ment Jacking in this description which is needed to com-
plete that definition is the assumption that the cause of
the progress is a property or an attribute of that which
is transformed. It will appear in the sequel whether we
may safely add this element also.

And to this end we have to consider, first, whether
what has been called the primary germs possessed within

themselves the elements of life and growth. And if not,
7

24 THE EVOLUTION OF SCIENCE.

then we have to discover what these elements are, and,
if possible, the origin of them.

Now, the gift of language, as the vehicle of abstract
thought, created the possibility of the evolution of litera-
ture, but it could not ensure it. So, likewise, the flexi-
bility of the human hand in obedience to the human
will, and the innate sympathy of the mind with nature,
only created the possibility of the development of art
and science. All these were like dead seeds. That some
spirit was needed to animate them is evident. The sim-
ple power to express a thought does not make a poet nor
a historian. A man may beable to carve an image or
sketch a figure, and yet be destitute of the ability to
become an artist. In addition to these fundamental
elements there must be a motive; and besides the motive
there must be the faculty to devise means to make it
effective. We shall find that an appropriate motive
and the faculty of invention are the elements of their
life and growth ; and no account of the evolution of lit-
erature, art and science can be complete which does not
define these elements, and at least attempt to give some
reasonable hyphothesis of their source.

But at this point the vastness of the subject confronts
us. Thus far it has been proper to speak of literature,
art and science together, because, in the earliest periods
of human history, the mental and mechanical operations
of men were not only limited but also blended. The
first step in the evolution was the introduction of lan-
guage, skill and observation ; and these came into man’s
possession at once, constituting a common stock of abil-
ity by which men accomplished their individual or trib-
al purposes. The second step in the progress was the
differentiation of these into the distinct germs of litera-
ture, art and science. This is the point which we have
already reached in this discussion.

And now three separate pathways open before us.
8

\
i

A | ale

LERON Cs) COOLEY. Q5

History offers itself as a guide. But to follow history
to the end, in either literature, art or science, would
overtask a single evening. I know not in which direc-
tion one could make the greatest distance, nor in which
his search would be most fruitful ; but, for obvious rea-
sons, I have chosen to consider

THE EVOLUTION OF SCIENCE.

In the outset, I must tell you what I understand
science to be. I regard it as something more than is im-
plied in the usual definition of it. One form of that de-
finition runs in this wise: ‘‘Science is knowledge duly
arranged and referred to general truths and principles,
on which it is founded and from which it is derived.’
(Webster). But I think that this definition represents
science very much as the instantaneous photograph rep-
resents the racehorse—all the lite, and motion, and
energy are left out. It portrays the science which is at
rest in books or in the memories of men, but not the
science which is abroad and active in the world. Science
is not static but dynamic. It isa thing which lives and
grows. It draws its nourishment from all material
sources ; it drops its fruits into all the activities of hu-
man life, and continually exhales new elements into the
atmosphere of human thought.

I therefore propose this definition: True science is a
living, growing organism, whose body is the aggregate
of knowledge pertaining to nature, whose spirit is the
love of truth for its own sake, and whose purpose is the
elevation of mankind. But this definition is truly de-
scriptive of only what may be called modern science—
of science dating from about the beginning of the seven-
teenth century. Down to that time science has been un-
dergoing a process of gradual development. It was not
simply growing, as science now grows, by imbibing new

facts and principles, but its body was only just becoming
9

26 THE EVOLUTION OF SCIENCE.

organized, while its spirit and purpose were gradually be-
ing defined. It is of its transformations during this
formative period that I wish to speak.

It is natural to suppose that the surpassing beauty of
the unclouded skies would earliest attract the eyes of
men ; and we may therefore beleve that the contact of
nature with the human mind began with the observation
of the stars. Asa matter of fact, we find in Babylonia
and Egypt, as well asin China, a great number of date-
less observations of an astronomical character, made
during a period reaching, according to chinese chronol-
ogy, {trom almost four thousand years before the Chris-
tian era. The emperor Fou Hi, who reigned twenty-
two hundred and fifty-eight years before Christ, is said
to have erected an observatory ; and, seen a little more
clearly in the mists of antiquity, is Tcheou Kong, who,
eleven hundred years before the advent of our Lord,
observed the altitude of the sun at the time of solstice.
This, by some authorities, is regarded as the first obser-
vation which can claim to have been made with any
degree of precision ; and therefore the first that has any
astronomical value.

The knowledge acquired by observation during this
ancient period, extending to within a half century of the
beginning of our era, consisted almost wholly of the
periods of the motions of the sun and moon. By means
of these periods, by the simplest arithmetical calcula-
tions, eclipses were foretold with some degree of success,
the lengths of the year and the month were fixed with
some approach to accuracy, and a calendar was con-
structed to regulate the national festiva!s. This was the
total outcome of all the centuries—a mass of observations
without the vestige of a principle to connect them, and
esteemed of value only so far as they ministered to the
necessities of national or religious life. Astronomy had

not yet become a living science. Nothing had been
10

Le BON. Ce COOLEN, 27

added to it for several centuries before the close of this
long period. The elements of life and growth were ab-
solutely wanting.

Astronomy as a living science began with the Greeks.
Thales, the father of it, was born six hundred and forty
years before the Christian era. From the small number
of isolated facts then known, astronomy in Greece grew
into a more and more extensive catalogue of observations
and hypotheses, until the illustrious Ptolemy, who lived
in the first century of our era, was able to construct, as
he did, a comprehensive theory of the universe.

Now, the Grecian skies were not unlike those of Egypt
or Chaldea. The same objects and similar changes were
presented to the eye, so that there were the same mate-
rials out of which to construct a science in all those coun-
tries. The success of the Greeks did not, therefore, arise
because of better material or better conditions for obser-
vation. But we have to ascribe their superior attain-
ments to the fact that they, in the observation of the
skies, were actuated by a far different and nobler motive.

Wefind that the Chaldean watched the periodic changes
of the moon and the aspects of the stars, prompted by the
vain desire to foretell his own future, and the Egyptian
that he might fix the times of his feasts and festivals ;
but the Grecian that he might learn the relations of the
heavenly bodies to one another and the causes of their
changes. 'The Chinese were content to observe the order
of the moon’s phases and the times of successive eclipses,
which, by simple inspection, would give them the rule
of the recurrence of these phenomena, while the Greeks
sought for the causes of these facts, and abated their
study only when they found an adequate explanation of
them in the phenomena of the sun’s light and the moon’s
motion around the earth.

The more ancient peoples gathered many facts in re-

gard to the movements of the sun and stars, but went no
tat

28 THE EVOLUTION OF SCIENCE.

further than the facts, never exercising upon them any
intellectual power beyond that which was called into ac-
tion by the simple effort to see and record them. The
Greeks, on the other hand, early transcended this effort
by trying to construct a distinct mental picture of the
mechanism of celestial motions. To what patient and
persistent watching of the stars, to what toilsome calcu-
lations, and to what repeated resort to mental invention,
were they impelled by their steady purpose to discover
the invisible methods of the complex motions of the
heavenly bodies !—how ingenious, and, as faras the facts
then known were concerned, how complete was the con-
ception of the theory of epycycles and excentrics which
was established by Hipparchus !

The body of science is made up of the facts of nature ;
but the life of it consistsin clear and appropriate ideas.
The Greeks imparted to astronomy this vital element.
They observed in order that they might know, and they
sought knowledge for the sake of truth itself.

That the admiration of truth, and the desire to possess
it for its own sake, is the principle of life in science, is
shown not only by the superiority of the Greek over the
more ancient astronomy, but also by the invariably
erowthless and degraded existence of science in the ab-
sence of it. The history of science shows, for example,
that astronomy when deprived of it was astrology ; that
alchemy when animated by it became chemistry ; and
that magic, by the entrance of this breath of life, was
transformed into natural philosophy. I will trace one
or two of these illustrations in detail.

Astronomy and astrology existed together in Chaldea
and Keypt long before the beginning of Greek history,
and both alike were founded upon the observations of
the skies. So far as these observations were employed
to detect facts, even if for no higher purpose than to con-

struct a calendar to regulate the recurrence of feasts and
12

~“

TER Oe Ol. COOLMY: 29

festivals, we may call the study of them astronomy.
But this was a very subordinate purpose of the early star-
gazers. A preposterous philosophy led them to allot to
the stars the moral control of the inhabitants of the
earth ; and that study of the heavens which was pur-
sued with a view to detect the system of this stellar in-
fluence, and secure the ability to forecast the destinies of
men and nations by it, was astrology. Astrology and
not astronomy was the chief pursuit in the most ancient
times of which we speak.

But at length a better period of the human mind
dawned in Greece. The study of stellar motions then be-
gan to counteract the study of stellar influences. Cicero
tells us that ‘‘ Eudoxus rejected the pretensions of the
Chaldeans :”’ and, itis certain that Aristarchus, Hippar-
chus and Ptolemy, among other successors of EKudoxus,
largely advanced in the real knowledge of the heavenly
bodies. Astronomy, and not astrology, was the chief
pursuit of the ancient Grecian student of the skies.

And yet during the later periods of ancient Greece,
when the minds of her philosophers had become specu-
lative and unstable ; when the professors who taught in
the famous schools of Athens and Alexandria no longer
tried to find out new facts for themselves, but were con-
tent to repeat the observations of Aristotle and Ptol-
emy ; when, in a word, the Greeks had lost their love
for discovery of truth—then the realities of astronomical
science were again overborne by the illusions of astrol-
ogy. ‘*For my own part,’’ says Tacitus, ‘‘I doubt but
certainly the majority of mankind cannot be weaned
from the opinion that, at the birth of each man, his
future destiny is fixed. Though some things may fall
out differently from their predictions by the ignorance of
those who profess the art; and that, thus, the art is
unjustly blamed, confirmed as it is by noted examples in

all ages.’ (Whewell Hist. Ind., Sec. I., 298). During
13

30 ‘THE EVOLUTION OF SCIENCE.

the reign of this belief there was, as: Ou show no
advance in astronomical science.

But after this long and barren period, when the revival
of learning began, in the sixteenth century, celestial
observations were renewed. During the early part of
the revival the astronomer and the astrologer were often
combined in the same person. Tycho Brahe, for exam-
ple, began as an astrologer ; so did Gassendi; and even
the great Kepler ‘‘spoke of astronomy as the wise
mother and astrology as the foolish daughter,’ adding
that the daughter was necessary to the life of the mother.
(Ene. Brit., 9th, I1., 741). The visionary notion of occult
influences lay in the minds of these men, side by side
with a true conception of mechanical causes ; and it was
only because their love of truth for its own sake sur-
passed their love of truth for the sake of what they con-
ceived to be its practical uses, that these energetic
students of nature finally became eminent astronomers
instead of famous astrologers.

Thenceforward, the unflinching attachment to the
study of nature for the sake of knowledge lifted as-
tronomy from rank to rank, until she stands the con-
fessed queen of sciences, beautiful in form, lovely in
character, and pure and powerful in influence over the
human intellect; while astrology, animated by no such
love of truth, declined even unto death.

The history of chemistry and alchemy furnishes, if
possible, a still better illustration. Both are alike
founded upon the incessant changes which abound in
nature. Decay, growth, melting, burning, the trans-
formation of water, earths and metals, by heat, and a
thousand other mutations in the nature of familiar ob-
jects have offered themselves for study in all periods of
human history. Whether the study of them should be
called chemistry or alchemy depends upon the motives
which have prompted it.

14

MRO CO. OOOMEY. i |

The alchemist could conceive nothing more supremely
to be desired than perennial youth; and next to this,
than happiness and power. He therefore watched the
changes occurring in his crucible and alembic, hoping to
discover the edivir vite, which should banish age, and
the philosopher’s stone, by which to manufacture gold.
To the chemist, on the other hand, some exact and real
knowledge of matter, some better understanding of the
nature of forces, some further insight into the mechanism
and some revelation of the thoughts which underlie the
mechanism of the world, are more to be desired than
gold or youth. He therefore directs and watches the
transformations of matter, animated with the desire to
discover and make known the truth.

If we consider some of the qualities of the alchemist
and of the chemist, we shall be the better able to
give due weight to the contrast of their motives. I know
not whether to regard the chemist or the alchemist as the
more industrious observer. As for facts, these in the
early times were the same for both, and both alike had
the power to reason well. M. Ferdinand Hofer illus-
trates this last thought as follows: ‘‘ Let us fancy our-
selves for a moment transported to the laboratory of one
of the great masters of sacred art, and watch as neophytes
some of his operations. First experiment: Sume com-
mon water is heated in an open vessel. The water boils
and changes to an aeriform body, leaving at the bottom
of the vessel a white earth in the form of powder. Con-
clusion: Water changes into air and earth. What ob-
jection could we (ora chemist), make to this inference
if we were wholly ignorant of the substances which
water holds in solution, and which are, after evaporation,
deposited at the bottom of the vessel. Another experi-
ment: Argentiferous lead is burned in cupels composed
of ashes or pulverized bones; the lead disappears, and

at the end of the operation there remains in the cupel a
15

32 THE EVOLUTION OF SCIENCE.

nugget of pure silver. Nothing was more natural than
to suppose that the lead was transformed into silver;
and to build on this and analogous facts the theory of the
transmutation of the metals, a theory which, later on, led
to the search for the philosopher’s stone.’ The alchem-
ists, therefore, were carried to fruitless conclusions, not
by anything wrong in their experiments or their logic ;
but their minds were driven in a wrong direction by a
false motive. They were not in search of truth ; we need
not wonder that they missed finding it.

Having thus pointed out the contrast in their motives,
we may next proceed to show that alchemy was a life-
less mass of chemical operations, while chemistry was a
living body of natural science.

Alchemy, according to M. Hofer, arose in the fourth
century of our era. It flourished twelve hundred years.
In the sixteenth century its transformation into real
chemistry began, and the last traces of it vanished less
than one hundred years ago.

There is an erroneous idea—I do not know how widely
it prevails—that alchemy ought to be credited with all
the chemical knowledge which had been acquired pre-
vious to the revival of learning in the sixteenth century.
The fact is, however, that a large part of this knowledge
is more ancient than alchemy; and the true value of
alchemy as a step toward chemistry is represented by
the residue.

From the ancients the alchemists inherited various

processes with the furnace and the blowpipe: methods
of extracting several metals from their ores; the art of
making colors, of enameling metals, of tanning hides, of
glassmaking, together with a knowledge of several val-
uable alloys, salts, and other chemical products. Now,
during the twelve hundred years of alchemy, these val-
uable arts were stationary. The sum of chemical

knowledge was enlarged during that interval only by
16

LE ROY C. COOLEY. 33

the discovery of some products, such as caustic soda,
nitric and sulphuric acids, and by the introduction of a
few chemical processes, such as distillation and _ filtra-
tion. But we find little definite knowledge of the com-
position of these isolated compounds; little fruitful ap-
plication of these processes ; no classification, no expla-
nation, no generalization, and hence no living science.
Alchemy was false, fruitless, dead.

Now, mark the occurrence of the first sign of vitality.
A new doctrine—the theory of the three elements—arose
to vanquish the speculation of Aristotle in regard to the
composition of matter, which had held possession of
men’s minds for nineteen hundred years. The father of
this new theory was Paracelsus (1493-1541); and Para-
celsus was the first of the alchemists to break away from
the ambition to transmute baser metals into gold. He,
great physician as he was, perceived in the materials of
alchemy powerful agents to benefit the human race by
curing or preventing disease.

This higher motive turned men’s minds into a new
channel. <A better study of the properties of bodies was
begun. Some insight into the composition of com-
pounds was acquired. Ideas of the relation of chemical
changes to chemical causes took root. And, as Para-
celsus was followed at considerable intervals, along the
sixteenth century, by Agricola, Sylvius, Boyle, Hooke,
Mayow, Becker, and Stahl, these new conceptions be-
came clearer and broader, until, within less than one
hundred years, they had developed into the first con-
sistent theory of the composition of bodies and of the
chemical changes which they undergo.

Nor is this all. Reading the history of that century «
little more carefully, we discover that long before the
end of it chemistry had not only rejected the false and
degrading motives of the alchemists, but it had also

outgrown the better ambition of Paracelsus. For, just
stg

34 THE EVOLUTION OF SCIENCE.

in the middle of the century, we find that Robert Boyle
was experimenting and writing vigorously against the
empiricism of the Paracelsians, and turning all the en-
ergies of chemical research toward the discovery of the
elements—not of medicines, but of matter itself. The
search after truth had supplanted the search after the
philosopher’s stone; the love of truth for its own sake
took the place of the love of truth for the sake of physi-
cal health and ease; and in less than half a century af-
terward, the dead mass of chemical Knowledge—the ac-
cumulation of ages—was transformed intoa living science.

All history, modern as well as ancient, would be found
to confirm the conclusion that the love of truth for its
own sake is the principle of life in science. There was
no science of nature before this spirit entered the body
of human knowledge ; there will again be none if ever
this spirit shall take its flight.

In addition to this element, there is another which
contributes especially to the growth of science. I refer
to the faculty of invention. Next to the love of truth,
which prompts investigation, that which contributes
most largely to its success is the power to invent hy-
potheses and the instrumental means to test their truth
by bringing them in direct contact with the facts of
nature.

For example: next to the astronomer himself the most
vital agent for the growth of astronomy is his observa-
tory. Let us consider its equipment. There are tele-
scopes, small and gigantic, with curved glasses, true
to the fraction of a hair, mounted on masonry as firm
as the native rock, and driven by mechanism whose
motions are as equable as the rotation of the earth.
There are circles for the measurement of angles, with
graduations, accurate to the last degree of refinement,
with clocks and cronographs, which mark the passing

moments with a precision corresponding with the pre-
1s

——

LE ROY C. COOLEY. 30

cision of celestial motions. These instruments suggest
the-modern methods by which facts are discovered and
theories tested.

But the ancient Greeks inherited none of these instru-
ments of precision. Their only observatory was an open
roof, and their only instrument was the naked eye. In
such absolute poverty of equipment, Greek astronomy
could be pursued, in the outset, only by the same crude
method which was practiced’ by the Chaldeans. Meas-
urements were impossible. The sun was said to bea foot
in breadth. The distances between stars were estimated
in cubits. In fact, all notions of size and distance and
velocities were necessarily inexact, as all judgments
must be when based upon unaided vision. Now, the
Greeks saw the worthlessness of such observations.
They apprehended the need of mathematical exactness ;
and to supply it they created a new method of obser-
vation, by inventing instruments of measurement.

We should, of course, expect these early inventions
to be, as we find they were, of the simplest form and
capable of yielding results far from accurate, as accuracy
is measured in modern times. There was the gnomon, for
example, which was little more than an upright staff.
And yet the Greek astronomer declared that Byzantium
and Marseilles were on the same parallel of latitude, be-
cause the shadows at those places have the same propor-
tions to the gnomon. Now, it was a long step toward
accuracy to abandon the simple eye-observations of the
altitude of the sun, and substitute therefor the measure-
ment of a shadow which represents that altitude, and
thereby compare the latitude of distant cities. The in-
vention of a thing so simple as the gnomon was a stride
in the early progress of science. A graduated circle was
soon afterward employed to divide the day into equal
portions ; and this was the prototype of the most refined

instruments of later days for the measurement of angles.
19

36 THE EVOLUTION OF SCIENCE.

Even by the Greeks themselves it was developed into
the quadrant, essentially the same as the modern instru-
ment with this name. Armils, to mark with precision
the time of the equinoxes and solstices, and the astro-
labe, for measurements referred to the ecliptic, were also
inventions of the early Greeks.

This introduction of the idea and the means of meas-
urement was the first step in the actual progress of
scientific astronomy. In fact, we may say that it was
the birth of the only philosophic, and, therefore, fruitful
method of attacking science in any of its provinces.

Without the instrumental means to make _ obser-
vations, and to measure phenomena, the knowledge of
nature can be nothing more than the common every-day
conceptions of things applied to the common and every-
day wants of life, inspiring nothing but vague if not
superstitious notions of the laws of nature. But by
the use of instruments the limitations of the organs of
sense are overstepped; their inaccuracies are detected
and corrected; the catalogue of facts is extended; the
weight and value of each is determined; and the judg-
ment is, in this way, furnished with appropriate data
out of which to construct and by which to test its hy-
potheses.

The sagacity of Thales led him to announce some new
truths, which, being destitute of instruments, he was not
able to demonstrate, nor to separate by a distinct line
from much that was false. But, in the course of time,
the dial, the astrolabe, the armil, and the quadrant, were
invented. Then came Hipparchus, sometimes called the
prince of Greek astronomers, who measured the obliquity
of the ecliptic; who determined the length of the year
to within twelve seconds of the truth; who discovered
the excentricity of the lunar and solar orbits, and the
inequality in the lengths of the solar day, which makes

it impossible for the best-regulated clock to keep true
20

ME ROM 6. COOL: 27

time as represented by the sun; who catalogued the
stars, discovered the precession of the equinoxes, caleu-
lated longitude by means of eclipses; who, in a word,
left, at his death, the mass of astronomical facts which
were afterwards elaborated by Ptolemy into a theory of
the solar system.

Now the instrumental method was the chiefest ele-
ment in this wonderful progress from Thales to Hip-
parchus. An invention is to science, sometimes, what
the relay is to the telegraphic message. When the im-
petus of the past is nearly exhausted a new instrument
lets in a fresh energy to impel it further. So the inven-
tion of the telescope was the starting point of modern as-
tronomy ; and so the invention of the spectroscope was
the opening of the gateway into celestial chemistry.

Scarcely can an original research be conducted in
modern science without the aid of mechanical invention.
New lines of thought exhaust the capacity of old instru-
ments, and discovery then pauses until new ones are made:
as when Crookes, investigating high vacua, reached the
limit of all the old appliances for exhausting air while
he was yet upon the very threshold of his problem, and
could go no further until he devised mechanical im-
provements in his air pump. The invention of the in-
strument is a step in the investigation as truly as is the
discovery of facts by the use of it or the induction based
upon the facts discovered.

Even in sciences which depend least upon the use of
instruments, the faculty of invention is in constant req-
uisition. Invention consists in combining old elements
into new forms adapted to supply a want or to fulfilla
purpose. But this definition will apply to thoughts as
well as to bodies of matter. A rearrangement of old
thoughts to form a new one, is as truly an invention as
the rearrangement of known mechanical principles to

produce a new device. A new arrangement of bodies
21

38 THE EVOLUTION OF SCIENCE.

according to the laws of mechanics to do a certain work,
is an instrument; a new arrangement of ideas according
to the laws of thought to explain or to discover a truth
of nature, is an hypothesis. Both are inventions. More-
over, the last is of a higher order of invention than the
first. Newton and Watt were both inventors. Looked
at from a scientific standpoint, Newton was the greater
inventor of the two, inasmuch as Newton’s theory of uni-
versal gravitation resulted from the combination of pure-
ly mental conceptions, while the steam engine of Watt
resulted from the contemplation of mechanical actions.

Likewise, as an element in the growth of science, the
invention of hypotheses outranks the invention of instru-
ments. The office of instruments is to establish facts;
but facts are only the material out of which science is
constructed. Facts may constitute Knowledge, but
knowledge must be suitably arranged and referred to
general principles in order to become science. The office
of an hypothesis is to group and explain the facts; and
it is by the invention and improvement of hypotheses
that a chaotic accumulation of instrumental observations
is transformed into an organized system subject to gen-
eral principles. Look, for example, at meteorology. It
is the most chaotic of the sciences, notwithstanding the
fact that it is the science which “gives the description
and explanation of the phenomena on which weather and
climate depend.’? We may well suppose that it is not
from any lack of interest in the subject that the science
of weather has remained undeveloped. Noris it from
any lack of instruments ; nor from any poverty of ob-
servations. There are thermometers which show atmos-
pheric changes in temperature to the fraction of a degree ;
barometers measuring changes in pressure down to the
five ten-thousandths of a pound to the square inch, and
instruments for the precise measure of moisture and elec-
tricity.

22

MER ONG Com OO Olub ye 39

These are to be found at every scientific center on the
globe, and observations with them have been continuous
for many years. The shelves of the libraries fairly groan
under the weight of their accumulation. And yet the
greatest achievement in meteorology is the modern sys-
tem of predicting the weather, not as eclipses by calcu-
lations based on established laws, but by means of elec-
tric signals, which simply outrun the atmospheric
changes.

The ingenuity of the meteorologist is baftled, not by
obstacles in the way of getting facts, but by the difficulty
experienced in conceiving a suitable hypothesis to explain
them. Astronomy waited long for its law of gravitation ;
chemistry for its atomic theory ; optics for the theory of
waves. Meteorology still waits fora Newton, a Dalton,
or a Huyghens, whose transcendent genius may be equal
to the task of inventing a theory which will reduce the
multitude of its observed facts to scientific order.

But I have already overstepped the lmit of time
properly allotted to this discussion, and must hasten to
its conclusions.

In the first place, science, when reduced to its ulti-
mate elements, consists of three, which may be desig-
nated respectively as a power, a motive, and a faculty.
There is the power of the mind to come into conscious
contact with nature through the senses ; there is the mo-
tive which prompts to observation, which is the love of
truth for its own sake; and there is the faculty of in-
vention.

In the second place, these elements came into human
life, one after the other, in the order named, the exist-
ence of each being a condition necessary to the intro-
duction of the next. ‘To this extent the birth of science
was an example of evolution.

In the third place, science, since its birth, has passed

along successive stages of development, from the simple
23

40) THE EVOLUTION OF SCIENCE.

to the complex, always differentiating and always ex-
panding, every step being made possible only by those
which had already been taken. And to this extent
‘the growth of science, even to the present day, has been
an evolution.

But in the fourth place, it remains for us to consider
whether the final term in the definition of materialistic
evolution, viz., that which assumes the cause of its de-
velopment to be a property or a tendency inherent in
the thing itself, is exemplified in the evolution of science.

Now we have already in this paper regarded the
power of conscious observation as a part of the original
equipment of the human mind, and need stop here only
to repeat our former quotation from Sully: ‘All the
laws of physical evolution cannot help us to understand
the first genesis of mind.”’

But in regard to the second element—the motive in
science,—we have also very briefly to say, that the love
of truth for its own sake is not prompted by the material
wants of men; that it does not arise from any political
or social necessity ; that it has no affinity with any ma-
terial object, nor is it the result of the collision of matter
with the organs of sense as the spark of fire is thrown
into being by the collision of flint and steel. The long-
ing after truth for its own sake is a purely intellectual
instinct; and as such it has had its birth quite inde-
pendent of physical causes, and unconditioned by the

facts of nature towards which it impells the human in-~

tellect.

And then the theory of evolution must explain the
origin of the third element—the power to construct ma-
chines and conceive hypotheses. But the ingenuity
which is displayed in invention can not be a property of
matter—it is a quality of mind. The genius exercised
in the construction of a theory can not be the offspring

of material combinations; it has nothing in common
24

THROW . COOmHY: 4]

with the products of sensation, and its parentage can
not be traced to either of these. Nor, is it akin to in-
stinct, for instinct is blind and unconscious, while genius
is quick-sighted and sensitive. Instinct never grows :
genius cannot be its offspring. The origin of the faculty
which constructs machines and theories must be sought
for outside and above all material combinations, me-
chanical laws, animal instincts, and the necessities of
primitive human life. We can find no clue to it in any
combination of facts, events, principles, or laws relating
to material things.

Hence, the birth and growth of science is an example
of evolution in so far as evolution is a progress from the
lowly and simple to the high and complex. It is an
evolution also in the relationship of successive steps,
each growing out of the preceding, as branch, and twig,
and flower, and fruit, inherit the same life and follow in
necessary succession. But it is not an example of evo-
lution, if by evolution we must mean a transformation,
the cause of which is imminent in that which is trans-
formed. Materialistic evolution here breaks down again.
I say again, because it breaks down once when it at-
tempts to pass from the lifeless to the living forms of
matter ; a second time, when from living forms it would
pass to conscious beings ; and a third time, when out of
consciousness it is asked to construct an intellect.

But, finally, there is extant a better than the material-
istic theory of evolution. I refer to that phase of evolu-
tion which invokes a principle higher than mechanical
forces to explain the progress of the world. This theory
the birth and growth of science fitly illustrates.

In the beginning there were nature and sensation. A
truth-loving and inventive intelligence is the higher and
independent principle which moulded them into the in-
fant form of science, and which has since determined

25

42 THE EVOLUTION OF SCIENCE.

and guided every step toward its present gigantic
attainments.

But the doctrine of evolution has been invoked to
explain the progress of all things. It is claimed that de-
velopmentiscontinuous. From inanimate matter through
living to sentient and reasoning beings, and thence
upward even into religion, philosophy and all else that
goes to make up civilization, it is claimed that there is
no break in the line of heredity. If this be so, then the
evolution of any one thing, as of science, must represent
the true character of the process in all its stages. And
if the evolution of science can be explained only by in-
voking the power of a principle which is superior to
science and independent of it, then is evolution nowhere
spontaneous. It must everywhere be determined by
something higher than the attributes of things. It is a
process which at every step must have been directed by
an independent and a supreme intelligence.

26

THE JUST CLAIMS OF NATURAL SCIENCE.

AN ADDRESS DELIVERED BEFORE VASSAR
BROTHERS INSTITUTE,
OCTOBER 14, 1884.

BY PROF. WILLIAM B. DWIGHT, CHAIRMAN OF THE SCIENTIFIC SECTION.

It is only within comparatively recent times that nat-
ural science has become sufficiently restricted to its
proper and independent work, so that by the nature and
extent of that work its claims upon society can be fairly
judged. The expression natural science is here intended
to cover the entire study of material nature in all its
departments. During earlier stages of human history
it has suffered, either by being too much involved with
other departments of human thought and industry, or
still worse, from being used, under the name of an honest
study of nature, to promote pursuits whose motives
were more or less sordid and unworthy.

The low estate of scientific study during those transi-
tional ages, and the steps by which it developed into the
free and noble science of to-day, were set before us last
week in a most learned, graphic, and philosophic way
by the honored president of this Institute. If you will
recall the points on that occasion so clearly brought to
your attention, there will be little need for me to say
more on this point than to give a few general statements
as to the difference between the work and status of nat-
ural science now from what these were in former days.

The great department of astronomy was for centuries
intermingled with the untruthful so-called science of as-

trology. This unholy alliance wrought constant injury,
27

44 THE JUST CLAIMS OF NATURAL SCIENCE.

not only directly to astronomy, but indirectly to scien-
tific study in general. After chemistry had made a fair
start in its grand career, the fog of alchemy, lurid with
gleams of false lights, rolled over it and long stifled its
energies and true progress.

The dishonest pursuit of chemistry and physics asa
means of influence in necromancy and in medical charla-
tanism, have at certain periods tended to hold up these
noble sciences to popular reproach.

At last, with the advancing centuries, the enlighten-
ment of civilization refused to tolerate anything under
the name of science that was not the honest study of
nature with the purpose solely of arriving at truth. Al-
chemy, astrology and necromancy continued, indeed,
their teaching and influence even into our own century ;
but the true and recognized scientific research of the world
was at last on a high plane of honesty—far above con-
tamination with such quackeries.

Yet it was not until it had passed through another
stage that it reached its highest plane of independent
thought. It was now in the main an honest, but it was
not yet a simple search after the facts and laws of mate-
rial nature. It was still mixed and entangled with
studies which, though noble and honest enough in them-
selves, were not in the sphere of natural science.

These foreign elements were mainly of three kinds:
First, the study and practice of medicine, or the healing
art, in its legitimate forms. Much of chemical experi-
mentation was turned entirely in this direction, in the
honest hope of controlling bodily disorders by a finished
system of chemical laws. But while attention was thus
distracted from higher chemical study, there was far less
gain than had been hoped in the line of medical practice.
The second element, commingled with scientific study,
was the intense desire to pursue it inordinately in those

lines where it bears directly on accumulation of material
28

WILLIAM B. DWIGHT. 45

wealth. This may be illustrated by noting how geo-
graphical science suffered when Martin Frobisher cut
short his scientific explorations in the arctic regions to
turn his second and third voyages into a commonplace
and barren search for gold. In the third piace, natural
science has been too much entangled with religious in-
struction and theologic dogmatism. Men had failed to
see that two separate lines of research for truth, as re-
gards the conditions and surroundings of men, if honest
and thorough, must necessarily, in the end, be har-
monious and consistent. They therefore too often
thought it necessary to harness religious and scientific
study tightly together, as one team, to drag behind them
a single chariot of human thought. But their mettle
and gait have proved quite too diverse to make the ex-
periment a successful one. It is found that, if they are
disposed each in independent harness, charging none the
less side by side over the battle-fields of human progress,
they will win more certain victories for men.

The science of this century is then, as never before,
both honest and simple. In reaching this point, as we
have seen, it has emancipated itself in two ways. First,
it has freed itself from everything with which it was
formerly involved which does not imply a thoroughly
honest seeking for natural laws. Secondly, it has sepa-
rated itself from entanglement with other lines of thought
which, though they may be in harmony with itself, and
equally honest, are not strictly scientific.

The first claim, then, which may be made for natural
science to-day, and the one which is the foundation for
all other claims is, that it is now itse/f—a single inde-
pendent, homogeneous unit, asasystem of human study.
Freed from heterogeneous entanglements, it now forms
a measurably well-defined field of thought. There is
really no absolutely sharp line of definition between any

of these great departments of human thought; it only
29

46 THE JUST CLAIMS OF NATURAL SCIENCE.

works mischief to attempt to draw such lines. Thus the
physical and metaphysical studies of organic life are as
closely and organically interlocked as are the actions
of the heart and lungs. Yet, for most purposes of prac-
tical work, that study of the material elements of nature
called natural science is well defined.

We may now weigh and measure its work by itself.
Whatever may have been the nature of the study in the
past, we may to-day value or undervalue it strictly on its
own merits.

The second claim which may fairly be made for science
to-day, is that, through its representatives in all nations,
it is doing an honest, faithful work. It might seem
that this point had already been covered by what has
previously been said. This is true only toa partial ex-
tent. What is now claimed comprehends much more
than anything previously advanced. What has already
been said in this regard has reference only to the general
professional definition, limits and nature of science
among the various departments of study in human prog-
ress. As a profession it claims to do only honest work.
But the question yet remains as to the actual practice in
the experience of scientific workers. Can it be also fairly
claimed that they are in the main carrying out the
honest professions of science? Are those who are the
leading exponents of science to-day carrying out its high
principles by showing themselves honest, unprejudiced
searchers after truth, and above such weak motives as
might impair the integrity of their work? Are scientific
men honestly carrying out the true and honest mission
of science ¢

We may claim, without hesitation, that they are.
After making due allowance for the elements of human
weakness, inherent in all human transactions, for the in-
evitable percentage, in all caliings, of narrow-minded,

prejudiced, or positively dishonest ones, the greater part
30

WILLIAM B. DWIGHT. 47

of scientists are animated by as true and honest motives
as those of any other body of professionals on earth,
the honored clergy not excepted.

Look at the great leaders of modern scientific research,
one by one, individual by individual, and no other con-
clusion will be possible. Darwin was the very soul of
honesty. Those great masters, respectively, in physical
and biological research, Tyndall and Huxley, possess no
element in their characters more potent than this; that
they are thoroughly honest, whether it be in statements
of facts or in the subsequent digestion of these facts,
and the evolving from them of hypotheses and laws. I
might cite, with the same results, a long list of the most
eminent scientists such as Helmholtz, J. R. Mayer, Pas-
teur, Carpenter, Dana, Cope, Cones, Hyatt and others.
Under the leadership of such men the unnumbered
scientists everywhere, working either independently, or
in universities or societies, are largely inspired by the
same spirit of honest research, often carried to the point
of great self-sacrifice.

Certainly any scientist in this age who allows himself
to be habitually swayed by motives not consistent with
honest research, or who labors chiefly to sustain pre-
conceived notions at any cost of principle, will soon be
found out—will soon lose the respect in his profession,
and entirely imperil his scientific influence and status.

Again, it may be justly claimed that science is now
doing probably more truly than ever before, a work
which is directly or indirectly of profound usefulness to
the world. This appears to be so obvious a fact, so com-
monplace a remark, that any explanation of it may seem
a useless waste of time. Yet there is probably no point
connected with the relations of science to the world so
little apprehended by any who have not given it special
thought than this very one—the nature and extent of the

useful work of natural science ; and it is probably due to
S31

48 THE JUST CLAIMS OF NATURAL SCIENCE.

misconceptions in this regard that this department of
human thought has never yet been assigned to its full,
proportionate share in the scholastic upbuilding of mind
and character. I ask your indulgence while I develop
this point a little further.

There are lying on the very surface of human action
and history, certain, and not a few, conspicuously useful
achievements of science which have won for her universal
applause. Men have not needed to look beneath this
brilliant surface of results to adjudge to science a use-
ful career. But because this superficial observation
seemed sufficient for the purpose, the judgment has been
generally a superficial one; there has been a popular
failure to search out and appreciate the underlying,
deeper, subtler and grander work which science has been
doing in the interests of the human mind. Hence, it fol-
lows that in the majority of cases the man who assents
most cheerfully to the usefulness of the study of natural
science knows the least about its real work and worth.
Could his eyes have been shaded from the dazzling bril-
liancy of these material achievements, which are ever
coming to the surface of things, so that he might have
been in some doubt as to the question—so that he would
have been constrained to look deeper into true scientific
work—he would have come into a far more adequate
comprehension of its value.

The truth is, that these conspicuous achievements are
for the most part its material successes, which it values
the least. They lie along that portion of the vast cir-
cumference of its action where it touches the material
interests of men so beneficently that mankind rises up
and calls it blessed ; but its deeper, nobler, more lasting
and comprehensive work, only one who looks into the
philosophy of its methods can see. It follows, also, that
to an ordinary observer, the failures of science in at-

tempting certain material successes, seem real failures;
32

WILLIAM B. DWIGHT. 49

whereas, the fact is, that it is often during those very
seasons of lack of popular economical success that she is
achieving some of her grandest results, in the accumula-
tion of observations, the formulating of natural laws and
the sharp discipline of mental habits.

Thus, during the last thirty or more years, experts in
electrical science have, until very lately, been utterly
baffled in any attempts to make the electric current
practicable in the lighting of streets and buildings. Yet,
during all those experiences of material economical re-
verses, the science was, all unknown to the popular in-
telligence, gaining some of its noblest victories, and win-
ning some of its most perpetual laurels in the field of
philosophic thought and the mastery of law. And now,
as we glance at the galaxies of electric lights which at
last brighten our streets and pubiic halls, we are looking
at only a small material offshoot from that long line of
intellectual achievements of many years.

This difference and disproportion between the super-
ficial and popular apprehension of a subject and its true
and deeper philosophy may, perhaps, be made more
clear by the following illustration:

Ask an ordinary observer as to the useful functions of
water. He will have no hesitation in enumerating its
obvious uses in promoting commerce through navigation,
in turning water-wheels, irrigating fields and quenching
thirst. But the physicist, whose knowledge of nature is
intimate, sees that these few palpable beneficencies are a
very small part of the true office and work of water. He
sees it pervading all nature through and through ; he sees
it to be an essential constituent of a large part of the
foundation-rocks of the earth ; he sees that without it
almost all natural organisms would be dead and
shrivelled ; that it is the great circulatory medium of the
solid yet porous globe; that it controls and modifies

every ray of light sent to our sphere ; and that it has been
33

5O THE JUST CLAIMS OF NATURAL SCIENCE.

the great chisel in the Supreme Architect’s hands, by
which have been cut out the grander economic, as well as
esthetic and romantic features of the continents.

How slight an acquaintance with all these functions
has the ordinary observer reached !

So, if you call for the popular apprehension as to the
great uses and results of science, you will have enu-
merated gunpowder and dynamite, steam and caloric
engines, the telescope, the telegraph and the telephone.

All these things are very well and very brilliant
results. They come within the honorable aims of
science, and are to be sought for and gloried in. But
they are, at best, the few inferior material results, and
are no true measure of its higher work.

What this higher work is I will try to indicate briefly,
as | comprehend it. It is purely an intellectual work,
seeking to be rational rather than empirical ; aiming only
indirectly at material achievements and wealth, but
directly at intellectual comprehension and command of
the facts, laws and powers of nature. In so far as it
accomplishes these objects the grand result is not merely
the acquisition of the principles which regulate the pro-
found system of nature, but the noble expansion of the
human mind, as it becomes by degrees capable of com-
prehending those laws in their intricacy and grandeur.
And, if it were possible for man, (which I suppose it is
not), to understand finally and thoroughly all this inter-
woven system of natural laws which regulate the world
and their organic and inorganic contents, he would have
taken a long step, intellectually, (I say it reverently),
toward attaining the vaster mind of Him who made
this system of laws.

The steps that scientists take in accomplishing their
higher work may be described as follows :

First, the patient, exact, constant observation and re-
34

WILLIAM B. DWIGHT. 51

cording of facts and their relations, including effects and
causes where they can be discovered.

Secondly, where causes are not known, forming reason-
able suppositions as to the causes which may produce
certain systems of known effects. Such suppositions
are called ‘‘hypotheses.’’ They are intended, by no
means, as specimens of ingenious conjecture, to lie upon
the shelf of record. They are, rather, to be used as the
basis of judicious and systematic experimentation, by
which the full truth may be finally reached and proved.

Thirdly, where the proper relations between known
causes and known effects are not certain, a supposition is
again made as to the proper adjustment of these causes
and effects. This is called ‘‘theory,’’ and is quite similar
in its use to the hypothesis.

Lastly, the scientist, either directly, by the orderly
grouping of facts, or if this be not possible, indirectly,
by experimentation under hy potheses or theories, arrives
atalaw. This is a key which will forever unlock cer-
tain doors in natural research ; and, once obtained, it
will stand for all time.

These four steps are the methods of research univer-
sally recognized and practiced by scientists. But two
of these, which are quite similar in most respects,—that
is ‘‘theory’’ and ‘‘ hypothesis’’—are very commonly
spoken of as of little use, or even as a matter of re-
proach, for science.

Even those well educated in other liberal professions
not infrequently belittle scientific research as being
largely a mere following of will-o’-the-wisp hypotheses
or vague guesses at the truth. And when one hypothe-
sis, followed for awhile, is supplanted by another, it
seems plain to such persons that science is aimlessly
wandering. Nothing can be more untrue; nothing can
be more unjust.

Theories and hypotheses in natural science are not idle
35

52 THE JUST CLAIMS OF NATURAL SCIENCE.

conjectures; they are the necessary and temporary
scaffolding by which, at last, the construction of the real
law is to be attained. The detective who, after looking
at all the minute facts, carefully frames an hypothesis by
which to explain them, is the one who, working on this,
or perhaps, subsequently, on some better framed hy-
pothesis, is going to unravel the mystery ; and thus
alone can he hope to unravel it.

Instead of being a reproach, the power to originate a
reasonable working hypothesis is a rare gift, and there-
fore a glory in scientific research ; while he who at last
comes through the workings and experiments with
theories and hypotheses into the establishment of natural
law, has placed the human mind on a higher plane of
intellectual culture.

Now these processes and these achievements of intel-
lectual victories are all the while taking place in scien-
tific research, whether the world knows it or not; and
whether inventive practical discoveries of economic value
to man result from them or not. They are the higher
results, adding continually to the intellectual mastery
of man, of which scientists have a right to be proud.
They are infinitely higher in quality than the material,
money-coining inventions that flow from them. As far
as the true merit of the achievement goes, I would rather
have. been the inventor of the ‘‘ nebular hypothesis,”’
with all the stimulus to thought and research which it
has inspired every since, than to have invented the
steam-engine. In the same view, I had rather have been
the discoverer of Ohm’s law of electric intensity, or of
Crooke’s theory of radiant matter, than even Pough-
keepsie’s justly honored citizen who, by the application
of such laws already established, elaborated the electric
telegraph.

Again, I may justly claim, as no small part of the use-

fulness of science, that it stimulates workers in other
36

WILLIAM B. DWIGHT. 53

fields. The example of long and patient investigation
of nature by ascertaining and carrying out her Jaws, has
prompted many a man who is not a scientist, to patient
experiments with material things which have often re-
sulted in advantage. It is true the process in such a
case is not at all scientific but empirical—the mere ex-
perimental collation of facts and things, under no guiding
principle ; but it has not been without its value. One of
the most important discoveries of the century—that of
vulcanized rubber—was made in just this way. It is
true, however, that Goodyear, who bravely carried on
for years these almost hopeless trials, occasionally was
enabled to make a short cut to the truth, through the
kindly suggestions of his firm friend, the great chemist,
Professor Benjamin Silliman.

It is also a stimulus, outside of scientific circles, not
only to experimentation, but to thought in fields of
literature and general philosophy. It provides subjects
and illustrations worthy of the highest skill of the ready
writer. Even to poetry it furnishes truthful facts of
eesthetic or romantic power which may serve the poet’s
purpose better than the creatures of mere fiction—the
dragons, unicorns, and maelstroms of past ages. In
Joseph Rodman Drake’s charming poem, ‘‘ The Culprit
Fay,’’ whose scene is laid upon the neighboring height
of Crow Nest, every flower and plant so deftly inwrought
into the legend is true to science, and had been located
by botanists on that very mountain slope. Also, the
‘*Kpie ofan Alp,’’? which has so recently awakened in-
terest in literary circles, is an apt proof of the extent to
which a close study of scientific subjects may furnish in-
spiration for the loftiest efforts of the poet.

Still, beyond all these influences is the fact that the
exact method of scientific study, and the evidence of
their excellent results, have given a needed stimulus to

the more general application of methods of scientific ex-
37

54 THE JUST CLAIMS OF NATURAL SCIENCE.

actness in other departments of human thought. Indeed
it may be safely asserted that this influence has been far
reaching and profound, modifying essentially the tone
of philosophic thought throughout the civilized world.
This point alone would be an ample subject for a treatise ;
but present limits permit but a passing allusion to it;
though it is one of the most important benefits of science.

Again, it may be confidently claimed that science is
yet pushing on with its full strength, in progressive
work. Its work is nowhere done; its powers are not
approaching exhaustion ; the time is yet unmeasurably
distant when, superannuated, it will be retired on half-
pay for what it has done but can do no longer.

It might appear that science had already approached
the final limits of its discoveries, and had well nigh used
up the material for new inventions. It has forced steam
and combustibles nearly to their utmost. in providing
motive power; it has wrested from magneto-electricity
the secrets which annihilate time, extend man’s nerves
of instant sensation quite around the globe, and provide
him at night with a radiant flow of miniature sunlight.
There seems to be little left that it can call upon this
mysterious agent to do. It has followed the thinning
current of life up to its primal driblets in protoplasmic
cells; beyond that, it would seem that it never can pass.
Is it not in danger of gliding soon into a Sargasso sea of
idleness, doomed to perpetual stagnation /

Such apprehensions are groundless. Nature in her
vastness 1s not soeasily probed. It would be more true to
say that science already perceives that it is on the very
verge of new discoveries of motive power, of electrical
conditions, laws and possibilities, of optical principles,
and, above all, of the relations of the forces of life to those
of chemistry and to dead matter.

Science was never more truly throbbing in every fibre

with the energy of hopeful action than she is to-day.
38

v

WILLIAM B. DWIGHT. 5

ay

And this not only because she is looking upon the past
with a glow of honest pride, but because she knows that
the greatest works are yet before her.

During the intense application of scientific workers in
the last three or four decades, there has been a ponder-
ous accumulation of facts. No thoughtful scientist ex-
pects these toremainas dry Statistics on shelves of record.
They will be digested as the work goes on—will serve as
the basis of new hypotheses and new laws. These, in
turn, shall prove new lines of scientific railways around
the globe, along which shall travel to all communities
treasures of practical discovery and invention.

I wouldalso deemit right to claim that science deserves
torank very high asa means of mental discipline ; proba-
bly as high as any department of study. The demands
which it makes upon the mind for careful observation—
nice discriminations of judgment, good memory of com-
parative facts, ability to reason well, and in framing of
theories and hypotheses—its demands on the imagina-
tive and inventive faculties—all these and other con.
siderations make it a good disciplinary medium. That
it does not yet hold its rightful share of influence in this
capacity is probably due largely to two causes: First,
that while classical and literary studies long ago reached
sufficient maturity to gain a well-established position in
academic culture, natural science has only, in more re-
cent years, become sufficiently well organized for the
purpose. Hence other departments have a superior
footho!d which it is hard to displace. The other reason
is that, from the very nature of scientific studies, the
question of the proper methods to be used to make them
efficient in general culture, is an exceedingly difficult
one, not yet fully solved.

Again, it may be truthfully claimed that science is not
necessarily either hostile or even cold towards religion ;

nay more, that in the main her attitude is not one of
39

56 THE JUST CLAIMS OF NATURAL SCIENCE.

irreverence, nor of disdain towards honest religious be-
lief. There are chiefly two considerations which doubt-
less lead many to believe otherwise. The first is the
fact that professional scientific work is now, as it was
not formerly, almost universally conducted independent-
ly of any purely religious teachings or views. But this
has been done not from any necessary hostility to religion,
but from the logical and practical necessity of the di-
vision of labor. The second consideration is that some
of the results of scientific thought seem antagonistic to
some religious views, and that scientists, as a class, seem
to care very little about this. This antagonism is gener-
ally only an apparent one, and is usually founded on a
misapprehension of what science really intends to set
forth.

Very few theologians take the pains to become
thoroughly acquainted with the meaning of the
scientific theories which they condemn, and those that
do generally cease from their apprehensions of any
lasting and serious antagonism. And the reason why
even religious scientists care very little about the ap-
parent antagonisms, is that they feel sure that two
honest and faithful lines of research for truth in one

ereat system of natural, physical, physiological and .

moral laws, must in the end prove harmonious. Mutual
errors will doubtless be corrected in time, and the truth
must and will prevail.

It is quite true that some scientists, inalignant towards
religion, have made science a tool with which to attack
it. But in this respect they are not at all representa-
tives of the main body of scientific men, however emi-

nent they may happen to be, and they should not be

treated as such.
Allow me to sustain the statement I have made, that
science to-day is not hostile to religious belief, by citing

the following words of high authority. They are from
40 ee

WILLIAM B. DWIGHT. 57

the address lateiy delivered at Montreal, before the
British Association for the Advancement of Science, by
its eminent president, Lord Rayleigh. He says: ‘‘ Many
excellent people are afraid of science, as tending towards
materialism. That such apprehension should exist is
not surprising ; for unfortunately there are writers speak-
ing in the name of science who have set themselves
to foster it. It is true that among scientific men, as in
other classes, crude views are to be met with as to the
deeper things of nature ; but that the life-long belief of
Newton, of Faraday and of Maxwell are inconsistent
with the scientific habit of mind, is a proposition which
I need not pause to refute.”

To the above words I may add afew of my own. I
am fully convinced that only a minor portion of the so-
called ‘‘ materialism ”’ of science is due to the scientists
who designedly, in the words of Lord Rayleigh, ‘‘ have
set themselves to foster’’ this spirit. I believe this
tendency to be chiefly due to an unfortunate habit into
which many scientists have fallen, who have no designed
sympathy with what is understood as ‘‘ materialism.’ I
refer to the habit of confining the province of natural
science as a specialism too rigidly and absolutely to the
physical side of natural objects. In the main this is
quite proper. Butin the many cases where the physical
and the psychical are so intimately co-ordinated that
one cannot be philosophically treated nor understood
without the other, this is insisting on unphilosophical
and injurious limits, to the inevitable falsity of the results.

But the remedy for this pseudo-materialism is within
the progress of scientific thought itself. There are evi-
dent signs that the needed reaction has already set in.
This reaction is well illustrated in the remarkable paper
entitled ‘‘ Catagenesis,’’ read recently before the Ameri-
can Association for the Advancement of Science, by Prof.

Edward D. Cope.
, 41

58 THE JUST CLAIMS OF NATURAL SCIENCE.

As I bring these thoughts to a close, I will only add
that science has a valid and a very strong claim on so-
ciety both for sympathy and support. Its material re-
sults, though only the indirect ends of its labors, fill the
whole civilized world with blessings and thrift. In its
higher aim to enlarge the intellectual scope of man, and
make him more thoroughly dominant over nature, by
more thoroughly comprehending her laws, it is deserving
of full appreciation and support.

But it is also deserving of a much better financial sup-
port in its researches than it has yet received. Original
research in science is generally very expensive. Those
who do geological, zodlogical, or botanical fieldwork in
original investigations, find it very costly in both time
and money. In all the above sciences, and yet more in
physics, chemistry, biology and astronomy, original re-
search in laboratory work requires very frequently in-
struments of precision; not only those in ordinary use
for instruction, but special forms made for each special
investigation. This involves great expense. Few scien-
tists possess independent fortunes; and hence, in our
country, original research is checked and burdened.
This has been a matter of very serious consideration in
scientific associations. Financial contributions, or en-
dowments for the especial work of original study, are
urgently needed. Such endowments may be made to
individuals eminent in such work, or to scientific socie-
ties, or to colleges. It is true that the great work of
colleges is instruction rather than research; yet the
presence, to a certain extent, of the work of research
gives a healthy tone and stimulus even to elementary
scientific study, otherwise not easily imparted. Such
endowments should be distinet from, and over and above
all endowments for buildings and for ordinary apparatus
for instruction.

In mathematical science, which, being abstract does not
42

WILLIAM B. DWIGHT. 59

necessitate expensive experimentation, our country has
been recently declared, on high authority, to lead the
world. When generous patrons shall be found to make
the needed provisions for copious research and experi-
mentation, it is not unlikely that our nation may soon be
able to claim the leadership also in other sciences.
Meanwhile, it will be best and profitable to make every
possible effort in original work with whatever means are
at our disposal. Let us diligently collect the .facts of
nature ; but if we would do the best work for science,
let us aim to do much more; to use and study these facts
so as to evolve from them general principles.

Lord Rayleigh, in the address above quoted, says very
justly: ‘‘Science is nothing without generalization.
Detached and ill-assorted facts are only raw material ;
and, in the absence of a theoretical solvent, have but
little nutritive value. At the present time, and in some
departments, the accumulation of material is so rapid
that there is danger of indigestion.”’

It is evident, therefore, that what the advancement of
Natural Science urgently needs, and has a right to de-
mand, is the very best use of our highest powers. In
return it will bestow upon us the most valuable results.
If not always material results, at least more or less of
a culture which, from its nature, is a priceless posses-
sion.

43

THE GENEALOGY OF THE VERTEBRATA AS
LEARNED FROM PALEONTOLOGY.

AN ADDRESS DELIVERED BEFORE THE
VASSAR BROTHERS INSTITUTE,
JANUARY 27, 1885.

BY PROF. EDWARD D. COPE.

A great deal of light has been happily thrown on the
question of the phylogeny of the Vertebrata, by the re-
cent work done in North American paleontology. The
lines of descent of many of the minor groups have been
positively determined, and the phylogenetic connections
of most of the primary divisions or classes have been
made out. The result of these investigations has been to
prove that the evolution of the Vertebrata has proceeded
not only on lines of acceleration, but, to a much greater
extent than has been heretofore suspected, on lines of
retardation.’ That is, that evolution has been not only
progressive, but at times retrogressive. This is entirely
in accord with the views derived by Dohrn from em-
bryology,” who, however, wrote only of the origin of the
Vertebrata as a whole and not of its divisions, excepting
only the Leptocardii and Marsipobranchii, that is, of the
sand lance and the lampreys and hags. The demonstra-
tion of such relations for the higher Vertebrata is now
done nearly for the first time.° -

1See Origin of Genera, E. D. Cope, Philadelphia, 1868, where these terms are introduced.
2 See Der Ursprung der Wirbelthiere u. d. Princip des Functionwechsels, Leipsic, 1875.
3On the Phylogeny of the Vertebrata, Cope, Amer. Naturalist, Dec., 1884. I here re-

mark that my researches have now, as I believe, disclosed the ancestry of the mammals, the

birds, the reptiles and the true fishes, or Teleostomi, including the special phylogenies of

the Batrachia and Reptilia, and some of the Mammalia. See the following references ;

American Naturalist, 1884, p. 1186 ; Proceedings Academy Philadelphia, 1867, p. 234; Pro-
ceedings American Philosoph. Society, 1884, p. 585 ; American Naturalist, 1884, p. 27; Pro-
ceedings American Association for the Advancement of Science, xix., 1871, p. 283 ; Proceed-
ings American Philosophical Society, 1882, p. 447: American Naturalist, 1884, pp. 261 and
1121 ; Report U. S. Geol. Survey W. of 100th Mer., G. M. Wheeler. 1877, iv., ii., p. 282.
Amer. Naturalist, Feb., March, and April, 1885.

Ce ms

EDWARD D. COPE. 61

Omitting from consideration the two classes above
mentioned, whose remains have not yet been certainly
found in a fossil state, there remain the following: the
Pisces, Batrachia, Reptilia, Aves and Mammalia.

The Mammalia have been traced to the theromorphous
reptiles by the Monotremata. The birds, some of them
at least, appear to have been derived from the Dinosau-
rian reptiles. The reptiles in their primary representa-
tive order, the Theromorpha, have been probably derived
from the embolomerous Batrachia. The Batrachia have
originated from the subclass of fishes, the Dipnoi, though
not from any known form. I have shown that the true
fishes or Teleostomi have descended from an order of
sharks,’ the Ichthyotomi, which possess characters of
the Dipnoi also. The origin of the sharks remains en-
tirely obscure, as does also that of the Pisces as a whole.
Dohrn believes the Marsipobranchii to have acquired its
present characters by a process of degeneration. The
origin of the Vertebrata is as yet entirely unknown,
Kowalevsky deriving them from the Ascidians, and
Semper from the Annelida.

The above results I have embodied in the following
phylogenetic diagram :

Aves Mammalia
Reptilia
( Teleostomi Batrachia
| |
Pisces + Selachii Ichthyotomi Dipnoi
too
Holocephali
Marsipobranchi
Leptocardii

1 Proceedings Am. Phil. Soc., 1884, p. 585.
45

62 THE GENEALOGY OF THE VERTEBRATA.

Accepting this phylogeny, it becomes possible to de-
termine the course of development, first, of the whole
series, and secondly of the contents of each class taken
by itself.

I. THE LINE OF THE UROCHORDA.

Embryological evidence leads us to anticipate that the
primitive Vertebrate possessed nothing representative of
the vertebrate skeleton beyond a chorda dorsalis. Above
this axis should lie the nervous chord, and below it the
nutritive and reproductive systems and their appendages.
Such a type we have in its simplest form in the Branchi-
ostoma, the representative of the division of the Acrania,
In the animals of this division the mouth and anus have
the usual vertebrate position, at opposite ends of the
body-cavity. The Tunicata (formerly referred to the
Mollusca) are now known to present a still more primi-
tive type of Vertebrata, to which the name of Urochorda
has been given. These curious, frequently sessile crea-
tures, have a vertebrate structure during the larval stage,
which they ultimately lose. They have the necessary
chorda, and nervous axis with a brain, and a cerebral
eye. They have at this time a tail, and are free-swim-
ming ; a peculiarity which few of them retain throughout
life (Appendicularia).' They differ from the Acrania in
the positions of the extremities of the alimentary canal.
The mouth ison the top of the anterior end of the animal,
and is supposed by some anatomists to represent an open
extremity of the pineal gland of other Vertebrata; while
the tract represented by this body, the third ventricle of
the brain, and pituitary body of the Craniata, are there.
mains of the primitive a@sophagus of the Urochorda.
The anus in the adult tunicates is either dorsal, or it
opens into the body cavity, as in the young larve. In
Appendicularia it is ventral (Gegenbaur).

1 See Lankester on Degeneration, Nature Series, 1880.

46

EDWARD D. COPE. 63

The history of the Tunicata cannot be traced by the
paleontologist as yet, owing to the absence of hard parts
in their structure. The evidence of embryology has,
however, convinced phylogenists that the ancestors of
this class resemble their larve, and that they have asa
whole undergone a remarkable degeneracy. They have
passed from an active, free life toa sessile one, and have
lost the characters which pertain to the life of verte-
brates generally. ;

It was to have been anticipated, however, that all of
these ancestral Tunicata did not undergo this degenera-
tive metamorphosis, for it is to such types that we must
look for the ancestors of the other Vertebrata, the Acra-
nia and the Craniata. And here paleontology steps in
and throws new light on the question. J have pointed
out briefly, in the American Naturalist,’ that a second
order must be added to the Urochorda, viz., the Anti-
archa, in which the anus presents the same position
as in the Acrania, at the posterior end of the body, while
an orifice of the upper surface represents the mouth of
the Tunicata. To this order is to be referred the family
of the Pterichithyide, of which the typical genus, Pter-
ichtys, is a well-known form of the Devonian period.
This genus retained its tail, which was the cause, in con-
nection with the presence of lateral fin-like appendages,
of its having been supposed to be a fish, by Agassiz,
Hugh Millerand others. It is possible that the American
Bothriolepis canadensis lost its tail, asin the majority of
Urochorda. The tunicate which approaches nearest to
the Antiarcha is the arctic Chelyosoma.

From the Antiarcha to the Acrania and Craniata, then,
the line is an ascending one.

Il. THE LINE OF THE PISCES.

The fishes form various series and subseries, and the

1 March number, 1885, under ‘‘ Geology and Paleontology.”

47

64 THE GENEALOGY OF THE VERTEBRATA.

tracing of all of them is not yet practicable owing to the
deficiency in our own knowledge of the earliest or ances-
tral forms. Thus the origins of the four subclasses,
Holocephali, Dipnoi, Elasmobranchii and Teleostomi, are
lost in the obscurity of the early Paleeozoic ages.

A comparison of the four subclasses just named shows
that they are related in pairs. The Holocephali and
Dipnoi have no distinct suspensory segment for the lower
jaw, while the Elasmobranchii and Teleostomi have
such a separate element. The latter therefore present
one step in the direction of complication beyond the
former, but whether the one type is descended from the
other, or whether both came from a common ancestor or
not, is unknown. If one type be derived from the other
it is not certain which is ancestor, and whether the pro-
cess has been one of advancement or retrogression. The
fauna of the Permian epoch throws some light on the
relations of these subclasses in other respects. The order
of the Ichthyotomi,' while belonging technically to the
Klasmobranchi, presents characters of both the Dipnoi
and the Teleostomi. It is so near to the Dipnoi in the
characters of the skull that nothing save the presence of
a free suspensor of the lower jaw prevents its entering
that subclass. It indicates that the one of these divisions
is descended from the other, or both from a common di-
vision which may well be the group Ichthyotomi itself.
In case the Elasmobranchi have descended from the Ich-
thyotomi, they have undergone degeneracy, as the Ich-
thyotomi have a higher degree of ossification and differ-
entiation of the bones of the skull. If they descended
from a purely cartilaginous type of Dipnoi, they have
advanced, in the addition of the free hyomandibular.
If the Dipnoi have descended from either division, they
have retrograded, in the loss of the free hyomandibular.
As regards the Teleostomi, we have a clear advance over

1See Paleontological Bulletin No, 38, E. D. Cope, 1884, p. 572, on the genus Didymodus.
48

EDWARD D. COPE. 65

the other subclasses in the presence of the maxillary
arch and the opercular apparatus.

Ill THE LINE OF THE BATRACHIA.

We know Batrachia first in the coal measures. They
reach a great development in the Permian epoch, and
are represented by large species in the Triassic period.
From that time they diminish in numbers, and at the
present day form an insignificant part of the vertebrate
fauna of the earth. The history of their succession is
told by a table of classification, such as I give below :

I. Supraoccipital, intercalary and supratemporal bones present.
Propodial bones distinct.

Vertebral centra, including atlas, segmented, one set of segments to-
PEMCESMpPHOLMUM a OMevaLC Miers c cers siaetets uo tetecye «cin cieye olor Rhachitomi.!
Vertebre segmented, the superior and inferior segments each complete,
LOVADUNAY=P ji) Cron), 1K) CeKElN ENKCldA Gs sooncoecddseodaucds Embolomeri.

Vertebral centra, including atlas, not segmented, one to each arch
Stegocephali.

II. Supraoccipital and supratemporal bones wanting. Frontal and
propodial bones distinct.
qa. An os intercalare.
A palatine arch and separate caudal vertebra... ............ Proteida.
aa No os interclare.
A maxillary arch: palatine arch imperfect ; nasals, premaxillaries and

Caudalnverte bras GIShiNGh 2 t2.ccc-. Cle occ sce aoce ee we oe sees Urodela.*
No maxillary or palatine arches ; nasals and premaxillary, also caudal
WEIN OZ CHE DTTC Tm obane aoe ep enn oe atm nmme araariee Trachystomata.

III. Supraoccipital, intercalare and supratemporal bones wanting.
Frontals and parietals connate ; propodial bones and caudal vertebrz
confluent.

Premaxillaries distinct from nasals; no palatine arch ; astragalus and
calcaneum elongate, forming a distinct segment of the limb. . Anwra.

The probable phylogeny of these orders as imperfectly
indicated by paleontology is as follows:
1 Includes the Eryopide.

2 Probably includes the Gymnophiona.
49

66 THE GENEALOGY OF THE VERTEBRATA.

Anura
. Urodela Trachystomata
Proteida
Stevan opiall
Embolomeri Rhachitomi
rier treet

An examination of the above tables shows that there
has been in the history of the Batrachian class a reduc-
tion in the number of the elements composing the skull,
both by loss and by fusion with each other. It also
shows that the vertebree have passed from a notochordal
state with segmented centra, to biconcave centra, and
finally to ball and socket centra, with a great reduction
of the caudal series. It is also the fact that the earlier
forms (those of the Permian epoch) show the most rep-
tilian characters of the tarsus and of the pelvis. The
later forms, the salamanders, show a more specialized
form of carpus and tarsus and of pelvis also. In the
latest forms, the Anura, the carpus and tarsus are re-
duced through loss of parts, except that the astragalus
and caleaneum are phenomenally elongate. We have
then, in the Batrachian series, a somewhat mixed kind
of change ; but it principally consists of concentration
and consolidation of parts. The question as to whether
this process is one of progression or retrogression may
be answered as follows : If degeneracy consists in ‘‘the
loss of parts without complementary addition of other
parts,’ then the Batrachian line is a degenerate one.
This is only partly true of the vertebral column, which
presents the most primitive characters in the early, Car-
boniferous, genera (Rhachitomi). If departure from the

1 Includes Trimerorhachide and Archegosauride.

50

EDWARD D. COPE. 67

nearest approximation to the Reptilia is degeneracy,
then the changes in this class come under that head.
The carpus, tarsus and scapular and pelvic arches of the
Rachitomi are more reptilian than are those of any
of their successors.

There are several groups which show especial marks
of degeneracy. Such are the reduced maxillary bones
and persistent gills of the Proteida; the absence of the
maxillary bones and the presence of gills in the Trachy-
stomata; the loss of a pair of legs and feebleness of the
remaining pair in the sirens ; and the extreme reduction
of the limbs in Amphiuma. Such I must also regard,
with Lankester, the persistent branchiz of the Siredons.
I may add that in the brain of the Proteid Necturus the
hemispheres are relatively larger than in the Anura,
which are at the end of the line.

It must be concluded, then, that in many respects,
the Batrachia have undergone degeneracy with the pas-
sage of time.

IV. THE REPTILIAN LINE.

As in the case of the Batrachia, the easiest way of ob-
taining a general view of the history of this class is by
throwing their principal structural characters into a
tabular form. As in the case of that class I commence
with the oldest forms and end with the latest in the or-
der of time, which, as usual, corresponds with the order
of structure. I except from this the first order, the
Ichthyopterygia, which we do not know prior to the
Triassic period 3!

A, Extremities not differentiated in form beyond proximal
segment.

I. Os quadratum immovably articulated to squamosal, etc.
Tubercular and capitular rib articulations present and distinct
1. Ichthyopterygia.
1Generally similar to the system published by me. Proceedings Amer. Ass, Ady. Science,

XIX, p. 238. See American Naturalist, March, 1885.
St

68 THE GENEALOGY OF THE VERTEBRATA.

AA, Elements of extremities differentiated.

II. Os quadratum immovably articulated ; capitular and tubercular
rib-articulations distinct. Archosauria.
Pubis and ischium united, and with little or no obturator foramen ; one
posterior cranial arch ; limbs ambulatory ; a procoracoid
2. Theromorpha.
Ischium and pubis distinct, the latter directed forwards, backwards or
downwards; two posterior cranial arches; limbs ambulatory ; no

PLOCOFACOIG ace sc ee~ 1 ainn7n o> slopes ave, See ee oy oN pe 3. Dinosauria.}
Ischium and pubis united; two postcranial arches; anterior limbs
WOLAM, 5-15 erste rs etecyers otis c ataie ie esate etre aoe oe oe Ne 4. Ornithosauria.

III. Os quadratum closely united to cranial arches ; but one rib-ar-
ticulation. Synaptosauria.

Distinct hyposternal and postabdominal bones ; ribs joining each two
vertebrz, and generally forming a carapace ; and posterior cranial
AUC IVS. sha coarse sterhas Sulehsveretciomep es elt beye ee wistrocnin were 5. Testudinata.

Hyposternal and postabdominal ones not distinct ; two posterior cranial
arches ; ribs attached to one vertebra ; asternum ; ? no procoracoid

6. Rhynchocephalia.

Hyposternal and postabdominal bones not distinct ; two posterior cranial

arches ; ribs attached to one centrum ; no sternum’ ; a procoracoid

7. Sauropterygia.

IV. Os quadratum attached only at the proximal extremity, and
more or less movable ; ribs with one head. Streptostylica’*.
Brain case membranous in front of prodtic bone; trabecula not per-

SESUOING so ose cs ei eho etalon Tale eevee are aiehve see SIEM CREE 8. Lacertilia.
Brain case with osseous walls anterior to prootic ; a scapular arch and
Sher OUI 6 seen sts be sinieeeie sepaeieies Wa ee eran 9. Pythonomorpha.

Brain case with osseous walls anterior to prootic ; no scapular arch nor
sternum ; trabecular grooves or sphenoid and presphenoid bones
10. Ophidia.

An inspection of the characters of these ten orders,

and their consideration in connection with their geologi-
cal history will give a definite idea as to the character of
their evolution. The history of the class, and therefore

the discussion of the question, is limited in time to the

1This definition includes the Crocodilia in the Dinosauria, as it is absolutely connected
with the typical Dinosaurs by the Opisthoccela (Sauropoda Marsh),
2 Episternum present.
3It is quite possible that the three divisions of this head form one natural order, the
Streptostylica, or Squamata.
52

EDWARD D. COPE. 69

period which elapsed since the Permian epoch inclusive,
for it is then that the Reptilia enter the field of our
knowledge. During this period but one order of reptiles
inhabited the earth, so far as now known, that of the
Theromorpha. The important character and role of this
type may be inferred from the fact that they are strac-
turally nearer to both the Batrachia and the Mammalia
than any other, but present characters which render it
probable that all the other reptiles, with possibly the ex-
ception of the Ichthyopterygia, derived their being from
them. The phylogeny may be thus expressed :

Dinosauria Testudinata Rhynchocephalia Lacertilia Ophidia
(Crocodilia) \ /

< Vi.

Pterosauria Pythonomorpha

Sauropterygia

Dinosauria

Ichthyopterygia Theromorpha

In the first place, this line departs with lapse of time
from the primitive and ancestral order, the Theromorpha,
in two respects. First in the loss of the capitular artic-
ulation Of the ribs, and second in the gradual elonga-
tion and final freedom of the suspensory bone of the
lower jaw (the os quadratum). Inso departing from the
Theromorpha, it also departs from the mammalian type.
The ribs assume the less perfect kind of attachment
which the mammals only exhibit in some of the whales,
and the articulation of the lower jaw loses in strength,
while it gains in extensibility, as is seen in the develop-
ment of the line of the eels among fishes. The end of
this series, the snakes, must therefore be said to be the
result of a process of creation by degeneration, and their

lack of scapular arch and fore limb and usual lack of
53

70 THE GENEALOGY OF THE VERTEBRATA.

pelvic arch and hind limb, are confirmatory evidence of
the truth of this view of the case.

Secondly, as regards the ossification of the anterior
part of the brain-case. This is deficient in some of the
Theromorpha, the ancestral order, which resemble in
this, asin many other things, the cotemporary Batrachia.
Some of them, however (Diadectide), have the brain
completely enclosed in front. The late orders mostly
have the anterior walls membranous, but in the strepto-
stylicate series at the end, the skull becomes entirely
closed in front. In this respect then the snakes may be
said to be the highest or most perfect order.

V. THE AVIAN LINE.

The paleontology of the birds not being well known,
our conclusions respecting the character of their evolu-
tion must be very incomplete. A few lines of succession
are, however, quite obvious, and some of them are clearly
lines of progress, and others are lines of retrogression.
The first bird we know at all completely, is the cele-
brated Archeopteryx of the Solenhofen slates of the
Jurassic period. Initselongate series of caudal vertebree
and the persistent digits of the anterior limbs, we have a
clear indication of the process of change which has pro-
duced the true birds, and we can see that it involves a
specialization of a very pronounced sort. . The later
forms described by Seeley and Marsh from the Creta-
ceous beds of England and North America, some of which
have biconcave vertebre,—all probably, the American
forms certainly, possessed teeth. This latter character
was evidently speedily lost, and others more character-
istic of the subclass became the field of developmental
change. The parts which subsequently attained especial
development are the wings and their appendages; the
feet and their envelopes, and the vocal organs. Taking

all things into consideration the greatest sum of progress
54

EDWARD D. COPE. ys!

has been made by the perching birds, whose feet have
become effective organs for grasping, whose vocal organs
are most perfect, and whose flight is generally good, and
often very good. Im these birds also the circulatory
system is most modified, in the loss of one of the carotid
arteries.

VI. THE MAMMALJAN LINE.

Discoveries in paleontology have so far invalidated
the accepted definitions of the orders of this class that it
is difficult to give a clearly cut analysis, especially from
the skeleton alone. The following scheme, therefore,
while it expresses the natural groupings and affinities,
is defective in that some of the definitions are not with-
out exceptions:

I. A large coracoid bone articulating with the sternum.
Marsupial bones ; fibula articulating with proximal end of astragalus
1. Monotremata.

Il. Coracoid a small process coéssified with the scapula.

a. Marsupial bones ; palate with perforations (vagina double ;
placenta and corpus callosum rudimental or wanting ; cere-
bral hemispheres small).

But one deciduous molar tooth....... ... Steed rarsster citer 2. Marsupialia.

aa. No marsupial bones; palate entire (one vagina; placenta
and corpus callosum well developed).

f8. Anterior limb reduced to more or less inflexible paddles,
posterior limbs wanting (Mutilata).
No elbow joint ; carpals discoid, and with the digits separated by car-

tilage ; lower jaw without ascending ramus............. 3. Cetacea.
An elbow joint; carpals and phalanges with normal articulations ;
lower jaw with ascending ramus....... ... cies SniEete GOS 4, Sirenia.

ff. Anterior limbs with flexible joints and distinct digits ;
ungual phalanges not compressed, and not acute at apex!
(Ungulata’).

y- Tarsal bones in linear series; carpals generally in linear
series.

1 Except the Hapalide.
2 Lamarck, Zoologie Philosophique, 1809,
55

We THE GENEALOGY OF THE VERTEBRATA.

Limbs ambulatory ; teeth with enamel.... ......... ...0. Taxeopoda',

yy. Tarsal series alternating ; carpel series linear.

Cuboid bone partly supporting navicular, not in contact with astra-
ALIAS te rahalre rs ato dn ateane Gaye sie See eanoe foheh evan: Sapna cic 6. Proboscidia.

VVY: Both tarsal and carpal series more or less alternating.
Os magnum not supporting scaphoides ; cuboid supporting astragalus ;
Superior molars trituberculan.-- 0m ecect. jen: caer ...7. Amblypoda.
Os magnum supporting scaphoides ; superior molars quadritubercular,’
8. Diplarthra,*
PPP. Anterior limbs with flexible joints. Ungual phalanges

compressed and pointed? (Unguiculata).

€. Teeth without enamel ; no incisors.
Limbs not volant ; hemispheres small, smooth............. 9. Hdentata.
€&. Teeth with enamel : incisors present.
No postglenoid process ; mandibular condyle round ; limbs not volant ;
hemispheres small, smooth.................. wi ec rees 2 LOb. OGemias
Limbs volant ; Hemispheres small, smooth............ 11. Chiroptera.
A postglenoid process ; mandibular condyle transverse ; limbs not vo-
lant ; no scapholunar bone ;° hemispheres small, smooth,
12. Bunotheria.*®
A postglenoid process ; limbs net volent, with a scapholunar bone ;
hemispheres larger, convoluted ........ anletendete jarctaha reve .138. Carnivora.

1 This order has the following suborders, whose association was made for the first time

in the American Naturalist for April, 1885.
Carpal series linear ; no intermedium ; fibula not interlocking with astragalus ; no ana-

pophyses ; incisors rooted ; hallnen ot opposabless 4 e-e ae sees Condylartha.
Carpal series linear; an intermedium ; fibula interlocking with astragalus; hallux not
VAM Gnasoh cnasocogesd -osdaednn coosecoo Caan ddboDeoac-augencaceoopemass TTyracoidea.
An intermedium ; fibula not interlocking ; anapophyses ; hallux opposable ; incisors grow-
ing from persistent pulps... ..--..-. --.-+-..-ese eee seen sere see cee . Daubentonioidea.
An intermedium; fibula not interlocking; anapophyses; hallux opposable; incisors
rooted ; carpus generally linear..............0. 0.2. esee seen eee oo ene eee QUAATUMGANG.

No intermedium ;* nor anapophyses ; carpal rows alternating ; incisors rooted

Anthropoidea.

The only difference between the Taxeopoda and the Bunotheria is in the unguliform
terminal phalanges of the former as compared with the clawed or unguiculate form in the
latter. The marmosets among the former division are, however, furnished with typical
claws.

Some may prefer to use the term Primates in place of Taxeopoda, and such may be the
better course.

2 Except Pantolestes.

3 This order includes the suborders Perissodactyla and Artiodactyla. It is the Ungulata
of some authors.

4 Except Mesonyx.

5 Except Erinaceus.

6 With the suborders Insectivora, Creodonta, Tzeniodonta and Tillodonta,

* Except in Pithecus and Hylobates.

56

EDWARD D. COPE. 73
Paleontology has cleared up the phylogeny of most
of these orders, but some of them remain as yet unex-
plained. This is the case with the Cetacea, the Sirenia
and the Taxeopoda. The last named order and the Mar-
supialia can be supposed with much probability to have
come off from the Monotremata, but there is as yet no
paleontological evidence to sustain the hypothesis. No
progress has been made in unraveling the phylogeny of
the Cetacea and Sirenia. The facts and hypotheses as to
the phylogeny of the Mammalia may be represented in
the following diagram :

Diplarthra Hyracoidea Insectivora Rodentia Chiroptera
Proboscidia \ Anthropoidea / Edentata | Carnivora

Tillodonta
Tzeniodonta | Creodonta

|
|
|
STS cea |

Amblypoda ' Cred umane

Cetacea a ae
Multituberculata
MS gm ear
Marsupialia
Monotremata

It will be readily seen from the above diagram that
the discovery of the Condylarthra was an important
event in the history of our knowledge of this subject.
This suborder of the Lower Eocene epoch stands to the
placental Mammalia in the same relation as the Thero-
morphous order does to the reptilian orders. It general-
izes the characteristics of them all, and is apparently the
parent stock of all, excepting perhaps the Cetacea. The
discovery of the extinct Bunotherian suborders united
together inseparably the clawed orders, excepting the

bats ; while the extinct order Amblypoda is the ancestor
57

74 THE GENEALOGY OF THE VERTEBRATA.

of the most specialized of the Ungulates, the odd and
even-toed Diplarthra.

The characters of the skeleton of the order Monotre-
mata shows that it is nearest of kin to the Reptilia, and
many subordinate characters point to the Theromorpha
as its ancestral source.' In the general characters the
Marsupialia naturally follow in a rising scale, as proven
by the increasing perfection of the reproductive system.
The Monodelphia follow with improvements in the repro-
ductive system and the brain, as indicated in the table
already given. The oldest monodelphia were, in respect
to the structure of the brain, much like the Marsupilia,
and some of the existing orders resemble them in some
parts of their brain-structure. Such are the Condylar-
thra and Amblypoda of extinct groups, and the Buno-
theria, Edentata, Rodentia and Chiroptera, recent and
extinct. The characters of the brains of Amblypoda
and some Creodonta are, in their superficial characters,
even inferior to existing marsupials. The divided uterus
of these recent forms also gives them the position next
to the Marsupialia. In the Carnivora, Hyracoidea and
Proboscidia a decided advance in both brain structure
and reproductive system is evident. The hemispheres
increase in size and they become convoluted. <A uterus
is formed and the testes become external, etc. In the
Quadrumana the culmination in these parts of the struc-
ture is reached, excepting only that in the lack of separ-
ation of the genital and urinary efferent ducts, the males
are inferior to those of many of the Artiodactyla. This
history displays a rising scale for the Mammalia.

Looking at the skeleton we observe the following suc-
cessional modifications :”

First, as to the feet, and (A) the digits. The Condy-

1 Proceedings American Philosoph. Society, 1884, p. 43.
2 See the evidence for evolution in the history of the extinct Mammalia. Proceeds. Amer.
Assoc. Ady. Science, 1883.

58

EDWARD D. COPE. ris)

larthra have five digits on both feet, and they are planti-
grade. This character is retained in their descendants
of the lines of Anthropoidea, Quadrumana and Hyra-
coidea, also in the Bunotheria, Edentata and most of the
Rodentia. In the Amblypoda and Proboscidia the palm
and heel are a little raised. In the Carnivora and. Di-
plarthra the heel is raised, often very high, above the
ground, and the number of toes is diminished, as is well
known, to two in the Artiodactyla and one in the Peris-
sodactyla. (B) The tarsus and carpus. In the Condy-
larthra the bones of the two series in the carpus and
tarsus are opposite each other, so as to form continuous
and separate longitudinal series of bones. This continues
to be the case in the Hyracoidea and many of the Quad-
rumana, but in the anthropoid apes and man the second
row is displaced inwards so as to alternate with a first
row, thus interrupting the series in the longitudinal di-
rection, and forming a stronger structure than that of
the Condylarthra. In the Bunotherian rodent and eden-
tate series, the tarsus continues to be without alternation,
as in the Condylarthra, and is generally identical in the
Carnivora. In the hoofed series proper it undergoes
change. In the Proboscidia the carpus continues linear,
while the tarsus alternates. In the Amblypoda the
tarsus alternates in another fashion, and the carpal bones
are on the inner side linear, and on the outer side alter-
nating. The complete interlocking by universal alterna-
tion of the two carpal series is only found in the Diplar-
thra. (C) As to the ankle-joint. In most of the Condy-
larthra it is a flat joint or not tongued or grooved. In
most of the Carnivora, in a few Rodentia, and in all Di-
plarthra, it is deeply tongued and grooved, forming a
more perfect and stronger joint than in the other orders,
where the surfaces of the tibia and astragalus are flat.
(D) In the highest forms of the Rodentia and Diplarthra

the fibula and ulna become more or less codssified with
59

76 THE GENEALOGY OF THE VERTEBRATA.

the tibia and radius, and their middle portions became
attenuated or disappear.

Secondly, as regards the vertebree. The mutual artic-
ulations (zygapophyses) in the Condylarthra are flat and
nearly horizontal. In higher forms, especially of the
ungulate series, they become curved, the posterior turn-
ing upwards and outwards, and the anterior embracing
them on theexternal side. In the higher Diplarthra this
curvature is followed by another curvature of the post-
zygapophysis upwards and outwards, so that the verti-
cal section of the face of this process is an 8. Thus is
formed a very close and secure joint, such as is nowhere
seen in any other Vertebrata.

Thirdly, as regards the dentition. Of the two types
of Monotremata, the Tachyglosside and the Platypodide,
the known genera of the former possess no teeth, and
the known genus of the latter possesses only a single
corneous epidermic grinder in each jaw. As the Thero-
morphous reptiles from which these are descended have
well developed teeth, their condition is evidently one of
degeneration, and we can look for well toothed forms of
Monotremata in the beds of the Triassic and Jurassic
periods. Perhaps some such are already known from
jaws and teeth. In the marsupial order we have a great
range of dental structure, which almost epitomizes that
of the Monodelph orders. The dentition of the car-
nivorous forms is creodont; that of the kangaroos is
perissodactyle, and that of the wombats is rodent.
Other forms repeat the Insectivora. I therefore con-
sider the placental series especially. I have already
shown that the greater number of the types of this series
have derived the characters of their molar teeth from
the stages of the following succession. First a simple
cone or reptilian crown, alternating with that of the
other jaw. Second, a cone with lateral denticles. Third,

the denticles to the inner side of the crown forming a
60

EDWARD D. COPE. |

three-sided prism, with tritubercular apex, which alter-
nates with that of the opposite jaw. Fourth, develop-
ment of a heel projecting from the posterior base of the
lower jaw, which meets the crown of the superior, form-
ing a tubercular-sectorial inferior molar. From this stage
the carnivorous and sectorial dentition is derived, the
tritubercular type being retained. Fifth, the develop-
ment of a posterior inner cusp of the superior molar and
the elevation of the heel of the inferior molar, with the
loss of the anterior inner cusp. Thus the molars become
quadritubercular, and opposite. This is the type of
many of the Taxeopoda, including the Quadrumana and
Insectivora as well as the inferior Diplarthra. The higher
Taxeopoda (Hyracoidea) and Diplarthra, add various
complexities. Thus the tubercles become flattened and
then concave, so as to form Vs in the section produced
by wearing ; or they are joined by cross-folds, forming
various patterns. In the Proboscidia the latter become
multiplied so as to produce numerous cross-crests.

The dentition of some of the Sirenia is like that of
some of the Ungulata, especially of the suilline group,
while in others the teeth consist of cylinders. In the
Cetacea the molars of the oldest (Hocene and Miocene)
types are but two-rooted and compressed, having much
the form of the premolars of other Mammalia. In exist-
ing forms a few have simple conical teeth, while in a
considerable number teeth are entirely wanting.

A review of the characters of the existing Mammalia as
compared with those of their extinct ancestors displays
a great deal of improvement in many ways, and but few
instances of retrogression. The succession in time of the
Monotremata, the Marsupialia, and the Monodelphia, is
a succession of advance in all the characters of the soft
parts and of the skeleton, which define them (see table of
classification). As to the monotremes themselves, it is

more than probable that the order has degenerated in
61

78 THE GENEALOGY OF THE VERTEBRATA.

some respects in producing the existing types. The
history of the Marsupialia is not made out, but the
earliest forms of which we know the skeleton, Poly-
mastodon (Cope) of the Lower Eocene, is as specialized
as the most specialized recent forms. The dentition of
the Jurassic forms, Plagiaulax, etc., is quite specialized
also, but not more so than that of the kangaroos. The
premolars are more specialized, the true molars less
specialized than in those animals.

Coming to the Monodelphia, the increase in the size
and complication of the brain, both of the cerebellum
and the hemispheres, is a remarkable evidence of
advance. But one retrogressive line in this respect is
known, viz., that of the order Amblypoda,’ where the
brain has become relatively smaller with the passage of
time. The successive changes in the structure of the feet
are all in one direction, viz., in the reduction of the
number of the toes, the elevation of the heel and the
creation of tongue and groove joints where plain surfaces
have previously existed. The diminution in the number
of toes might be regarded as a degeneracy, but the loss
is accompanied by a proportional gain in the size of the
toes that remain. In every respect the progressive
change of the feet is in advance. In the carpus and
tarsus we have a gradual rotation of the second row of
bones on the first, to the inner side. In the highest and
latest orders this process is most complete, and as it
results in a more perfect mechanical arrangement, the
change is clearly an advance. The same progressive
improvement is seen in the development of distinct
facets in the cubito-carpal articulation, and of a tongue
and groove (‘‘intertrochlear crest’’) in the elbow-joint.
In the verterbree the development of the interlocking
zy gapophysial articulations is a clear advance.

Progress is generally noticeable in the dental struc-

1 See American Naturalist, Jan., 1885, p. 55.
62

EDWARD D. COPE. 719
tures ; for unlike the marsupial line, the earliest denti-
tions are the most simple, and the later the more com-
plex. Some of the types retain the primitive trituber-
cular molars, as the Centetide, shrews and some lemurs,
and many Carnivora, but the quadritubercular and its
derivative forms are by far the most common type in the
recent fauna. The forms that produced the complicated
modifications in the Proboscidia and Diplarthra ap-
peared latest in time, and the most complex genera, Bos
and Equus, the latest of all. The extreme sectorial
modifications of the tritubercular type as seen in the
Hyeenide and the Felidee, are the latest of their line also.

Some cases of degeneracy are, however, apparent in
the monodelphous Mammalia. The loss of pelvis and
posterior limbs in the two mutilate orders is clearly a
degenerate character, since there can be no doubt but
that they have descended from forms with those parts of
the skeleton present. The reduction of flexibility seen
in the limbs of the Sirenia and the loss of this character
in the fore limbs of the Cetacea are features of degen-
eracy for the same reason. The teeth in both orders
have undergone degenerate evolution ; in the later and
existing forms of the Cetacea even to extinction. The
Edentata appear to have undergone degeneration. This
is chiefly apparent in the teeth, which are deprived of
enamel, and which are wanting from the premaxillary
bone. <A suborder of the Bunotheria, the Taeniodonta
of the Lower Eocene period, display a great reduction
of enamel on the molar teeth, so that in much worn ex-
amples it appears to be wanting. Its place is taken by
an extensive coat of cementum, as is seen in Edentata,
and the roots of the teeth are often undivided as in that
order. It is probable that the Edentata are the de-
scendants of the Tezeniodonta by a process of degeneracy.

Local or sporadic cases of degenerate loss of parts are

seen in various parts of the mammalian series, such as
63

80 TRANSACTIONS OF SCIENTIFIC SECTION.

toothless Mammalia wherever they occur. Such are
cases where the teeth become extremely simple, as in the
honey-eating marsupial Tarsipes, the carnivore Proteles,
the Pteropod bats, and the aye-aye. Also where teeth
are lost from the series, as in canine genus Dysodus, and
inman. The loss of the hallux and pollex without cor-
responding gain, in various genera, may be regarded in
the same light.

In conclusion, the progressive may be compared with
the retrogressive evolution of the Vertebrata, as follows :
In the earlier periods and with the lower forms, retro-
gressive evolution predominated. In the higher classes
progressive evolution has predominated. When wecon-

sider the history of the first class of vertebrates, the

Tunicata, in this respect, and compare it with that of the
last class, the Mammalia, the contrast is very great.

NOVEMBER 5, 1884—TWENTY-SEVENTH STATED MEETING.

Prof. W. B. Dwight, chairman, presiding ; many mem-
bers and guests present.

The first of a series of papers on the ‘‘ Gyroscope ”’
was read by C. B. Warring, Ph.D. Several forms of the
instrument were exhibited and many interesting experi-
ments were made, fully illustrating the theory of its ac-
tion.

NOVEMBER 19, 1884—TWENTY-EIGHTH STATED MEETING.

Prof. W. B. Dwight, chairman, presiding ; ten mem-
bers and several guests present.

A paper discussing the motions of the top, the gyrocy-
cle, the gyrostat, and the Bohnenberger machine, was
read by Dr. Warring. Many curious experiments were

made, illustrating the rationale cf these instruments.
64

VASSAR BROTHERS INSTITUTE. 81
DECEMBER 3, 1884—TWENTY-NINTH STATED MEETING.

Prof. W. B. Dwight, chairman, presiding; eleven
members and ten guests present.

The third paper in the series, on rotating bodies, was
read by Dr. Warring, presenting ‘‘ Frisi’s Law,’’ ‘‘ Pre-
cession of the Equinoxes,”’ and ‘‘ Various Results and
Final Studies.”’

Mr. Charles L. Bristol and H. F. Parker, M.D., were
elected members.

DECEMBER 17, 1884—THIRTIETH STATED MEETING.

Prof. W. B. Dwight, chairman, presiding ; nine mem-
bers and several guests present.
The following paper was read :

SOME CHANGES IN THE HABITS OF BIRDS.

BY JAMES M. DEGARMO, Pu.D.

We are accustomed to maintain that considerable
changes in the habits of animals require long reaches of
time, and great physical changes usually accompany or
precede them. But more careful and accurate observa-
tion has a tendency to show this opinion to be ill-
grounded in fact, and I am inclined to believe that much
modification may occur, in habit at least, in quite short
spaces of time.

Twenty years ago, the note of a wood-thrush was
not heard in the village where I live. In its habitat
away from the dwellings of man, the bird is shy, alert,
cautious, —avoiding the presence of man—emphatically
a wild bird. Several years ago, a wood-thrush appeared
in one of the large yards of the place, which yard was
densely wooded with large treesand some shrubbery. At
first its liquid notes were only heard in the still hours,
and in the most remote parts of the wood. But this shy-

ness has gradually left the birds, and they have not only
65

82 SOME CHANGES IN THE HABITS OF BIRDS.

soincreased in numbers that the note of a wood-thrush
isalmost as common as the cry of a robin, but the birds
are about as tame. Again and again have I seen them, at
noonday, hopping about on the piazza of a residence,
picking the crumbs thrown there by friendiy hands, and
doing it with the utmost disregard of several human
occupants of the other end of the piazza.

They still retire to secluded places for their nests, thus
exhibiting native tenacity to habits essential to the
preservation of their species. But here, as elsewhere,
the modification has begun in unimportant matters, —
apparently unimportant matters—while the apparently
essential features of its life are unchanged. But how
long before these non-essential habits will react upon
the essentials, and change them too? Let us look at it.

In their more remote dwelling place, these birds have
enemies, no doubt, enemies of their own _ personal
safety, enemies of their nests, and eggs, and unfledged
young. For avoiding these enemies most of their habits
are formed, especially that of nesting. In their remote
haunts they build on the ground, or in bushes where
old leaves only raise them from it. But as they ap-
proach the habitation of men, they meet a new enemy,
the prowling cat. This would at once necessitate a
change, and the birds seem to have made it, for all the
nests I have found were built at from three to five feet
from the ground, in well-guarded spots.

But still another change is manifestly likely to occur
from their more quiet and less alert habits in the vicinity
of dwellings, and the greater supply of food. » They
would naturally become more moderate in motions and
less agile, increase in size, and in general bulkiness of
appearance. Other changes might occur from leaving
the marshy vicinity of a stream, and taking up an abode
in a dry place—slight changes of food, and the manner

of securing it.
66

JAMES M. DEGARMO. 83

It is not at all difficult to see, in this way, how many
of the organized instincts of the bird may undergo slight
modifications, and these induce other modifications; and
so on, endlessly, till, from the sight changes from a
wild, marshy spot, to the dryer vicinity of man’s habi-
tation, such vital modifications might result as would
constitute a new species.

These hints suggest a most important field of observa-
tion for lovers of birds who have time to devote to their
study. The least fact pertaining to nests, food, size,
incubation, tameness, in short, every trifle, may be of
vast importance in the change. For instance, I found
the English sparrow, now unfortunately domesticated
among us, nesting this summer under a shelving rock,
far from any house or barn, in a lonely and secluded
spot. This would seem to be a new departure for the
sparrow, and one which may be fruitful in results,
especially for the ears of those who dislike the garrulous
and quarrelsome bird.

Another singular change is worthy of notice. When
the Sparrows first became domesticated in considerable
numbers, there was a perceptible diminution in the num-
bers of the robins (Turdus migratorius). Every battle
between the red-breast and the pugnacious sparrows
ended in the worsting of the larger bird. But, lately,
the issue is reversed, and the robins have regained their
lost ground. But it has entirely changed the style of
the battle—as, first, the sparrows were the aggressors,
fiercely attacking the robins, who stood upon the de-
fensive, fighting mostly with the beak. Time and ex-
perience have so modified this that the robin no longer
acts in defense, but is himself the assailant,—not with
his beak alone, but with wings, beak and claw,—fairly
overwhelming his smaller antagonist with the violence
of his onset.

In not a single instance this summer did I see a robin
67

84 TRANSACTIONS OF SOLENTIFIC SECTION.

suffer defeat. Once or twice the male sparrows attacked,
in numbers, a single male robin, but were demoralized
and routed by his vigorous onslaught, slashing right and
left among them.

In my own vicinity there has been a decided falling-
off in the annoyance of sparrows’ nests and sparrows’
quarrelsomeness till the departure of the robins in the
fall. Since then the chickadees have suffered at the
hands of the sparrows.

Simple facts like these show the importance of an ac-
curate and extended observation of the habits of birds.
Only let it be accurate, and not imaginary, that it may
be of service to the scientist.

An additional circumstance of importance is the
change in the papilio thoas, by its transplanting to the
northern latitudes. It has greatly increased the appar-
ent vigor of the butterfly ; and such a metamorphosis
has been made, that unskilled eyes have pronounced the
northern and southern specimens different species. The
northern specimens are heavier, stronger looking, coarser,
with markings more pronounced, and I doubt not that
in time the changes will be equivalent to a new species.

The following note was also read by Dr. De Garmo:

Rhinebeck, N. Y.
In the fall, 1883, I noticed a downy woodpecker
(Picus pubiscius) that had a hole nearly excavated in
an old limb of a maple tree. The entrance is nearly two
inches in diameter, and the body is large and roomy.
The woodpecker went there every night during the past
winter. It stored no food in it, but simply used it to

rest in over night, and for protection in storms.
Gro. TREMPER.

JANUARY 14, 1885—THIRTY-FIRST STATED MEETING.

Prof. W. B. Dwight, chairman, presiding ; eight mem-
bers and nineteen guests present.
6s

Sr

VASSAR BROTHERS INSTITUTE. §

Prof. Dwight spoke of the importance of study with
the microscope, and commended it to the attention of
members of the Section as a subject likely to yield in-
teresting and valuable results, even if pursued only
during leisure by those actively engaged in business or
the professions.

H. F. Parker, M.D., described the process of cutting
thin sections and exhibited the apparatus in use.

Prof. Dwight showed a large variety of interesting
slides, among which were beautiful specimens of sections
of pine needles mounted by Mrs. Dwight.

Hexagonal crystals of cold, deposited by electrolytic
action, were shown by L. C. Cooley.

A large number of beautiful slides were exhibited by
C. N. Arnold. Among these were many sections of both
recent and fossil woods, which revealed a remarkable
similarity in the texture of ancient and modern plants.

JANUARY 28, 1885—THIRTY-SECOND STATED MEETING.

Prof. W. B. Dwight, chairman, presiding ; fourteen
members and guests were present.

W. B. Dwight called attention to interesting observa-
tions made by Prof. James D. Dana in the American
Journal of Science tor December, 1884, on the formation
of loose quartz sand, and of Kaolin, from decaying quartz-
ite, in the town of Cheshire, Mass. The rock is original-
-ly a feldspathic quartzite. The decomposition of the
feldspar, which was abundantly disseminated through
the porous quartzite, furnished the material for the ad-
joining beds of pure white Kaolin; while the rock be-
came either very friable sandstone, easily broken up for
the use of glass factories, or else beds of loose sand.
The Kaolin derived from this source is quite free from
iron; while that derived from mica schist is generally
very impure from the iron in the mica.

Prof. Cooley spoke of the Jolly balance as an instru-
69

86 PECULIAR STRUCTURE OF CLARK’S CLAY-—BEDS.

ment of precision. In taking specific gravity, results
may be obtained which will be accurate to the second
place of decimals. The difficulty in reading the scale
arising from reflection from the surface of the mirror he
has entirely overcome by placing the back of the instru-
ment toward the window, and looking at thescale through
a hole one-fourth inch in diameter in a sheet of white
card board, held obliquely across the line of sight.

FEBRUARY 11, 1885—THIRTY-THIRD STATED MEETING.

Prof. W. B. Dwight in the chair ; eleven members and
seven guests present.
The following paper was read :

THE PECULIAR STRUCTURE OF CLARK’S CLAY-BEDS
NEAR NEWBURGH, N. Y.

BY PROF. W. B. DWIGHT.

The special clay-beds, whose peculiar features are the
subject of this paper, are a part of the enormous deposit
of clay and sand formed synchronously over a large
part of the Northern United States. This vast deposit,
of no small economic value, must not be confounded
with the great belt of plastic clays, of far greater
economic importance, which crosses New Jersey at the
latitude of Trenton, and which feeds one of the noblest
industries of that State.

The plastic clays of New Jersey belong to the earlier
cretaceous ; and they supply the more pure and valuable
combinations of clay and sand which are among the
choicer products of such deposits, such as fire-clays, and
stoneware and porcelain clays. But the more northern
deposit, which lines the banks of the Hudson River, is
much more recent, belonging to the Quaternary age ;
and its clays are, in general, fit only for red bricks and

tiles.
70

WILLIAM B. DWIGHT. 87

This Quaternary clay belongs to the fluvial and lacus-
trine formations of that period, which, in the language
of Prof. J. D. Dana, ‘‘appear to characterize all the
river valleys and lake-basins of the continent over the
drift latitudes and also, to a lesser extent, those still
farther south ; so that they may be said to have a con-
tinental distribution.”’

It is supposed to have been formed mainly during the
second or Champlain division of the Quaternary. The
elevated lands of our more northern latitudes, covered
by a vast southward-moving ice-cap, in the first or
glacial era, had sunk five hundred or one thousand feet.
It was an era of great floods, and expanded Jakes and
rivers. The debris of melting glaciers, and of decom-
posed and eroded rocks, was deposited—sometimes under
violent action of the waters, sometimes under gentler
currents—all along our great lakes, and all the water-
courses over this part of the continent. During the
earlier epochs of these great transportations of earthy
material, when the waters had not yet accumulated suf-
ficiently to re-arrange the drippings of the melting
glaciers, the deposits were unstratified and unsorted.
But when the increasing waters took up the droppings
of the glaciers, the material was at once redeposited in
successive layers of stratification, while the coarser and
finer portions were laid in somewhat separate courses.

Both banks of the Hudson, for the greater part, at
least, of its length, are lined with beds of clay thus
formed, and in many cases extending to quite a dis-
tance inland. During the following, or Terrace Period,
an elevation of land took place, which has lasted until
the present time. As the result of this elevation, the
diminishing waters have cut down their channels through
these deposits, also narrowing their banks during suc-
ceeding epochs ; thus leaving the successive terraces on
which the river cities repose.

Tee

88 PECULIAR STRUCTURE OF CLARK’S CLAY-BEDS.

Owing to this historic origin, the clay-beds should
rest upon the true glacial drift-deposits. Prof. Mather
has stated that this is everywhere the fact ; and the same
eminent geologist attributes the origin of the material
of the clay chiefly to the decomposition of the great slate
formations on the Hudson River. This is an essentially
different origin from that of Cretaceous clays of New
Jersey, which Prof. Cook, the state geologist, attributes
to the decomposition of feldspars in Azoic granite rocks.
These differences in origin are sufficient to account for
the great diversity in their respective economic values.

The thickness of this clay deposit is not generally over
one hundred feet, and frequently much less. But Prof.
Mather has stated that it is often two hundred feet deep
on the Hudson River. Along this river it is found in
two different layers, the blue and the gray. The blue
clay is always the lower and much the thicker of the
two. They are both generally calcareous, and, except
for local disturbance, horizontally stratified.

The usual nearly horizontal deposition is well shown
at the extensive clay beds at the Dutchess and Columbia
Junction, which are of blue clay and at least two miles
in leneth along the bank, and rising about sixty-five
feet above the river level. The material here is quite
free from sandy layers and very homogeneous. Through-
out its whole thickness there is a curious and perfectly

regular alternation between layers of clay about five or_

six inches thick and bands of layers of quite similar
material, of which each layer is about one quarter of an
inch thick. This clay is very adhesive and splits up
with perfect ease into quite thin and flexible slices, thus
presenting all the appearance of incipient shale which
has not quite reached the point of induration. It might
easily be mistaken for beds of shale which have become
softened by the elements.

Sand and gravel-beds were also prominent elements in
me

WILLIAM B. DWIGHT. 89

the deposits of the Quaternary, both contemporaneously
and alternately with the clays, and frequently entirely
overlying them, showing subsequent deposition.

Such being the general facts, we are prepared to note
the peculiar features of the particular deposits which
are the subject of this paper.

The locality of these deposits is now known as Clark’s
Dock Station, on the West Shore Railway, about three
miles northeasterly from Newburgh. The property is
owned by Mr. Leander Clark, Jr., formerly chief en-
gineer of the Newburgh City Water Works. It is
proper to say that my examination of the phenomena
of this locality was much facilitated by the kind assist-
ance of Mr. Clark, and by his own very intelligent obser-
vations. Iam especially indebted to him for statements
as to the original condition of those portions of the beds
which had been removed in the working

The clay-pits were originally three in number, lying
ina northeasterly and southwesterly line, parallel to the
trend of the Hudson River at this point, and very near
to it; in fact, in association with the sand and gravel
beds, forming its banks. Though closely contiguous,
they were not quite continuous—each had its own en-
tirely separate structure, but of a type identical in the
three beds.

The description of one, with a single additional state-
ment as toa peculiar feature belonging to the entire
series rather than to any portion of it, will cover the
structure of the entire group.

At the time of my visits, in 1881 and 1883, the two
most northerly beds had been entirely depleted of clay,
though a good part of the enveloping shells remained,
while the most southern and largest one was more than
half depleted.

I will therefore describe the latter clay-bed as I saw

it. It consisted of a mass of clay shaped like an in-
73

90 PECULIAR STRUCTURE OF CLARK’S CLAY-—BEDS.

verted truncated cone. The base of this cone was about
ninety or one hundred feet above the floor which formed
the lowest working level in the pit, and which was itself
about fifteen feet above the level of the Hudson River,
and also somewhat above the lowest portions of the clay.
Of this mass about twenty feet of the upper layers were
of gray clay; the rest was the blue variety. The ma-
terial was deposited mostly in concentric and frequent

Ke

By la] Weis
AALINNS

CAEN

CLARK’s CLAY-BEDs.

Fig. 1.—Vertical section through the south bed.

Fig. 2.—Diagrammatic view, as restored, of the three clay-beds with the vertical wall in
front of them.

Figs. 8 and .—Vertical sections through the clay-bed, vertical wall, and external gravel
beds, on the south and north sides, respectively, of the entrance (on the river side) into the
southern bed.

In the above figures, the clay-beds, for convenience, are made to appear higher propor-
tionally than they really are.

In all the figures the letters have the same reference: c., clay-beds ; s., fine sand imme-
diately surrounding the clay beds; w., the vertical wall; p., coarse, pebbly drift; 1
limestone strata in place, overhanging the clay deposits.

T14&

LS }

WILLIAM B. DWIGHT. 91

layers ; the outer and earlier ones being conformed to
the outlines of the conical mass, though they became
nearly level at the bottom ; the inner layers, however,
became less and less steep as the pit filled up, so that the
highest and most central ones were very shallow basins,
approximating to horizontality. Marked exceptions to
this regularity of deposit occurred at the lower part of
the mass, near the level of the floor above mentioned.
Here there were two or three mounds of clay, which, to-
gether, covered the greater part of the horizontal area
of the clay-bed at that level, and in which the various
layers formed inverted cups—precisely the reverse of the
position of the layers in the general mass. These
mounds were from ten to sixteen feet high (fig. 1).

This inverted cone (or conical basin, as we may call it,
if we regard rather the envelope of sand enclosing the
clay) has an elliptical cross-section of about eighty by
fifty feet at the lowest floor-level mentioned, and about
one hundred and fifty feet for its longest diameter (esti-
mated) at the top. The shorter diameter is parallel to
the course of the river at this point.

The clay is quite calcareous, and its layers are occa-
sionally separated by thin layers of very fine sand. A
few large boulders are found scattered through the clay
deposits, but there are no beds of gravel nor of coarse
pebbles within them. As the successive layers were un-
covered in the working of the pit, the fresh surfaces,
after a short exposure to the air and rain, soon became
superficially hardened in curious lamellar and nodulous
shapes; probably through the cementing agency of the
calcareous ingredients combining with the sand present.
This mass of clay everywhere rested upon or abutted
against fine sand, itself evidently stratified, or, more
commonly, the edges of the various clay-layers shaded
off into alternate layers of clay and fine calcareous sand
(s., figs. 1, 2, and 3).

75

92 PECULIAR STRUCTURE OF CLARK’S CLAY-—BEDS.

It is evident that this clay was deposited under very
different circumstances from those under which were
formed the principal horizontal deposits along the river,
like the typical one described at the Dutchess and Col-
umbia Junction. At Clark’s Dock there appears to have
been at first a deposit at least one hundred feet deep of
very fine sand stratified by the water. Subsequently,
by some change in the currents, whirlpools seem to have
been formed here, which, at first, were sufficiently violent
to excavate the conical basins in the sand ; then, as these
gyratory currents for some reason became far gentler in
their flow, clay was deposited in layers on the sloping
walls of these sand-basins ; as the currents became more
and more gentle the later layers became less concave,
and, at last, nearly horizontal.

But the most peculiar feature of the locality remains
to be described. Outside of both the inverted cone of
clay and a certain thickness of the containing shell of
sand, at the lower levels, at least, there was a distinct
and remarkable vertical wall (w., figs. 1, 2 and 8). It
was composed chiefly of very fine sand consolidated to a
rock by carbonate of lime, which is evident from its
effervescence with acids. This wall is sometimes single,
but sometimes double. This vertical wall appears to
enclose the clay-pit on its eastern or river-front, and to
pass closely around it on its southern side. It did not
appear, however, to follow the inward curve of the clay-_
bed on its northern side, but passed beyond its front to
the northward in such a direction, N. 70° E., as to form
a continuous front wall in a nearly straight line for all
three of the clay-beds on the east or river side. At the
time of my visits, the greater part of the northern exten-
sion of this wall, beyond the most southern bed, had
been either broken away or deeply covered up by the
working of the clay-beds. But Mr. Clark described to

me its original position, as above stated, and by careful
76

WILLIAM B. DWIGHT. 93

searching, I succeeded in tracing the remains of the wall
sufficiently to confirm his statement. The thickness of
the wall varies from one inch to two feet, the latter width
generally occuring only where the wall is double.

A very peculiar feature in the case is the fact that
almost everywhere the layers of very fine argillaceous
sand (sometimes alternating with layers of sandy clay)
which forms the enclosing envelope of the main clay-
beds (p. figs. 1, 2 and 3) were lying inside of the vertical
wall, while against the outside of it was everywhere a
mass of coarse sand gravel and pebbles, in stratified
deposits. This wall was everywhere, therefore, a dis-
tinct boundary between these two classes of deposits.
It should also be noted that as the wall was vertical,
while the exterior layers of the clay-beds sloped inwards,
the layers of fine sand within were of very little extent
near the top, but widened out rapidly near the bottom.
At the level of the working-floor there was more than
tive or six feet of sand. The outside drift was in a
series of mounds. The mound lying against this partic-
ular clay-bed was about forty feet high, or about half
the height of the mass of clay. The mutual relations of
these various portions was finely shown in the walls of
the one hundred and twenty foot passage-way, which
cut a vertical section through the whole, as shown in
figs. 3and 4. Fig. 1 represents a vertical section through
the mass of clay in a northerly and southerly direction.
Fig. 2 shows the position of the vertical wall with refer-
ence to the three clay-beds.

With regard to the particular form in which the clay
was deposited, the facts seem to me to show that in this
case there was originally (1) an extensive and deep de-
posit of fine argillaceous sand; (2) a series of conical
excavations in this sand-bank caused by whirlpools,
themselves occasioned by some changes in the shape of

the adjoining river-banks; (8) as the violence of these
77

94 PECULIAR STRUCTURE OF CLARK’S CLAY-—BEDS.

circular eddies abated, erosion ceased, and as they became
still more gentle, clay was deposited, its layers becoming
more and more horizontal with the constant lessening of
the force of the circular currents.

The difficult problem, however, in this case, is to ac-
count for the phenomena presented immediately outside
of the clay deposits; the sudden termination of the
containing beds of loose stratified sand in a vertical
plane, the occurrence of great beds of coarse, pebbly
drift immediately beyond the sand and bounded on the
inside by the same vertical plane ; also, the presence of
a wall of solidified material between these two. I can
find no report of any similar phenomena.

Any theory seeking to explain the formation of this
vertical wall should account for the following facts:

1. The existence of such a solid wall, either single or
double, in a vertical position between two high mounds
of loose shifting material.

2. The fact of the different character of these materials
inside and outside of the walls respectively.

3. The entire want of conformity between the inner lay-
ers of fine sand and the wall, giving the impression that
the method of deposition of the wall had resulted in
cutting them down vertically ; and, in striking contrast,
the evident disposition of the outer layers of stratified
gravel, (as seen in figs. 38 and 4), to conform to the verti-
cality of the wall as they approach it.

4. The fact that the inner surface of the wall is com-
paratively smooth, while the outside is very rough and
irregular.

5. The fact that at certain limited areas the coarse,
pebbly drift of the outside actually traverses the wall
and appears inside of it, and as a component in its own
structure.

6. The fact that the wall in some parts follows the out-

line of the upper edge of the single conical clay-bed
78

WILLIAM B. DWIGHT. 95

under discussion, while on the river-side it abandons the
individual contour, to extend along the common front of
the other two clay-beds.

I tind it very difficult to frame a theory which would
reasonably and sufficiently account for these very curious
facts. I will give two explanations which have occurred
to me, of which the second seems the preferable one.

On the first theory, the vertical wall may have been
formed as follows, while there was only a great con-
tinuous sand-bed outside of the clay to the east. Car-
bonated waters, holding calcium carbonate in solution,
may have been furnished from either of these two
sources: 1. The overhanging bluffs of Trenton and
Calciferous limestones, immediately adjoining the clay-
beds on the inner or west side. These limestones to-day
furnish streams in the immediate vicinity which deposit
large masses of calcareous tufa. 2. The clay itself
being exceedingly calcareous, its upper layer might have
furnished calcium carbonate to the flowing waters.
These waters, thus passing over the top of the imper-
meable clay beds toward their outer (eastern) rim,
would then have dropped over into the loose open sand
below, and, percolating easily through it, in a vertical
plane, it might have gradually cemented the sand grains
in its course into a wall. This wall, following the out-
line of the beds, was circular at the northern and southern
portions; but, as the three contiguous circular beds
were at that time probably united at the top, the wall
along their river front necessarily was formed in a
straight line. This is illustrated in fig. 4. Where the
descending sheet of carbonated waters found an obstruc-
tion, it split, forming a double wall. This must have
taken place during an elevation, when the whole mass
was above water. Subsequently, either by sinking of
the land, or the rise of the waters in floods, the great

mound of fine sand must have been re-stratified. That
79

96 PECULIAR STRUCTURE OF CLARK’S CLAY—BEDS.

within the strong wall was mostly undisturbed ; but
that without was changed to coarse sand and pebbles,
whose layers accommodated themselves to the wall, as
the facts show. Though this wall, solid as it was, could
not have held up the pressure of the inner sand, had
these changes taken place out of water, yet while under
water the pressure of the water without would have
gone far to relieve the strain. At some points of weak-
ness or incompletion, however, the coarse pebbles found
their way inside of the wall at its lower parts. Subse-
quently, the wall was completed across these pebbly
portions. The difference in smoothness between the
inner and outer surfaces of the wall may perhaps be ex-
plained by the difference in the coarseness of the material
on the two sides.

The only other possible explanation that has sug-
gested itself to me is that of a fault, by which the out-
side coarser material was forced up so as to cut the sand-
bank smoothly in a vertical plane. The carbonated wa-
ters, derived from sources stated above, falling along
this plane, thus determined, may have formed the wall
in question.

That such a fault is possible would appear from an ob-
servation made by Prof. Mather, Geol. of Ist Dist., N.
Y., (State Rep. p. 156), where he speaks of ‘‘a fault in
the clay and gravel-beds near Newburgh, where the clay
and sand, horizontally stratified. were separated by a
vertical line on the surface exposed, each abutting
against the other with little disturbance of either, and
covered by beds of coarse gravel, evidently deposited
after the fault had been formed. This locality was
where there had been no slide nor derangement of the
strata since the deposit of the gravel-beds, and where
no present causes could wash the gravel.”’ This locality
is ‘‘ half or three-quarters of a mile below Newburgh on

the shores of the Hudson.”’
80

WILLIAM B. DWIGHT. 97

The latter theory is simple and seems to me the more
acceptable, though the perfect verticality and smooth-
ness of the face of the sand, and the entire absence of
any disturbance of its stratification, seem difficult to rec-
oncile with the violent grinding motion of a fault.

FEBRUARY 25, 1885—THIRTY-FOURTH STATED MERTING.

Prof. W. B. Dwight, chairman, presiding; thirteen
members and guests present.

Prof. Dwight presented to the Museum five specimens
of materials from Clark’s clay-beds.

C. B. Warring, Ph.D., read a paper on precession and
nutation, completing his discussion of the motions of the
Gyroscope and other rotating bodies. The several parts
of this discussion are brought together in the following
paper :

AN EMPIRICAL STUDY OF GYRATING BODIES.

BY C. B. WARRING, Pa.D.

The Gyroscope, the Top, the Gyrostat, the Gyrocycle, Bohnenbergher
Machine, our Earth, Precession and Nutation, Gyrostatic Balance,
Gyrostatic Compass and Gyroscopic Pendulum. Illustrated by more
than fifty figures ‘* from life.”

GYRATING BODIES.

A gyrating body is a body revolving on an axis pass-
ing through its centre of gravity, and acted upon by a
continuous force’ tending to make it revolve on another
axis at right angles to the first. This second axis may,
or may not, pass through the centre of gravity.

Of such bodies the top is the best known example.
The gyroscope, the gyrostat, the gyrocycle, and the
Bohnenbergher machine, complete the list. The earth

1 ‘‘ Continuous force,” because as soon as the force ceases to act, gyrative peculiarities
cease, as will be shown hereafter. And, furthermore, in all the gyrating bodies in actual

operation, the force tending to make them revolve around a second axis is continuous.

SL

98 AN EMPIRICAL STUDY OF GYRATING BODIES.

is to be classed with the Bohnenbergher ; and precession
and nutation are problems in the mechanics of that
machine.

The top has been known from time immemorial. The
gyroscope came into prominent notice some thirty years
ago. It is perhaps an outgrowth of the Bohnenbergher,
as that is considerably the older. The gyrostat is a
modification of the gyroscope, first made by Sir William
Thomson. The gyrocycle is another modification of the
same instrument, invented and named by the writer of
this paper.

The literature of these bodies is meagre. Scattered
through the proceedings of various learned societies are
quite a number of papers relating to the gyroscope, but
scarcely any relating to the others.’ On examination it
will be found that these papers are, for the most part,
merely descriptive. The explanations offered are scant
and unsatisfactory. Going outside of ‘‘ proceedings,”’
we find a somewhat extensive discussion of the Bohnen-
bergher, and the gyroscope, in a lecture on ‘‘ Planetary
Disturbance,”’ by Prof. Snell, read before the Smith-
sonian Institution, 1855. There is quite an article in
the Hney. Brit., 9th ed. The explanation there given
and the mode of treatment are substantially identical
with that of General Barnard, published in the Amer.
Journ. Hd., vols. 3, 4, and 5, and afterwards republished
in the Amer. Journ. Science for 1857. A similar ex-
planation appears in Johnson's Cyclopedia. The last
of General Barnard’s papers includes a brief discussion
of the top. There is a somewhat extensive article upon
the gyroscope and gyrostat in Thomson & Tait’s Nat.
Phil. There is also one in the Hnglish Cyclopedia.

Frisi’s celebrated law was formulated with special
reference to precession, and will be treated of when we
come to that subject.

1 An incomplete list of such papers is given in Ency. Brit., 9th ed., article ‘‘Gyroscope.”

S22

F-

Cc. B. WARRING. 99

As to college text books, with few exceptions they ig-
nore the subject. Those that do speak of it devote
a limited space to the gyroscope, and, so far as I have
found, none to the other gyroscopic bodies.

In these papers I shall present the various phenomena
exhibited by these bodies, and offer what seems to me
their true explanation, fortifying each step by an ex-
perimental demonstration. How successful I shall be
is for others to decide. But, should my explanations
prove worthless, there will remain a somewhat large
residuum, independent of all theorizing, of what may,
in that case, be styled empirical laws and _ principles,
for each is the formulization of what these instruments
have actually done in my laboratory, and what they will
repeat before the Section.

Some of these phenomena are not only new, but are
fairly startling in their apparent contradiction of familiar
laws.

THE GYROSCOPE.

Although it is not the oldest of these machines, I shall
take up the gyroscope first, for a complete discussion
of this instrument will render the solution of the prob-
lems involved in the others a matter of comparatively
little difficulty.

The gyroscope, as usually made, consists of a heavily-
rimmed metal wheel, or disk, revolving freely in a ring,
as in fig. 1. In line with the axle is a projection, or Ing,
having in its under side a conical indention to receive
the point of a standard on which it rests with perfect
freedom to move in any direction. On the other end is
an inverted hook with its point in the vertical plane of
the axis, but a little above it.

The theoretical gyroscope of Gen. Barnard and others
is a solid of revolution with no supporting ring, and
moving around a fixed point situated in its axis of figure

at some distance from its centre of gravity. Such an
ss

100 AN EMPIRICAL STUDY OF GYRATING BODIES.

instrument has its nearest approach to realization in a
finely-pointed, truly-centered top. At present we shall
consider the gyroscope as all have seen it. The other
will come hereafter.

If the ring of fig. 1 be taken in the hand, or better
still, if it be held in the jaws of a vice (a small vice, such
as can be had for a dollar, we have found of very great
assistance if used to hold the gyroscope, when the ex-
perimenter is winding up the cord or drawing it out),
and a string be wound around one arm of the axle, and
then rapidly pulled—as boys sometimes spin a top—the

wheel will revolve with great rapidity. If, now, the .

gyroscope be placed with the lug on the point, the axis
being horizontal and the hand withdrawn, some curious
results will follow.

1. The unsupported end does not fall,.and, for a con-
siderable time, the axle seems to remain horizontal.

2. But, in fact, it begins at once to fall.

3. It also begins to revolve around the point of sup-
port in that direction in which the underside of the
wheel is moving.

4. The more rapid the wheel’s rotation, the slower the
horizontal movement and the fall, and vice versa.

IT remark, that henceforth, through the whole of these
papers, ‘‘ horizontal’’ will be used, for convenient brevi-
ty, in place of ‘‘apparently horizontal,’ or ‘‘ approxi-
mately horizontal,’ except where it might cause am-
biguity.

5. If Istop the horizontal movement by placing my
finger in its path the instrument instantly falls.

6. If, by any means, as, for example, by a string at-
tached to the hook of the free end, I stop the downward
movement the lateral ceases at the same instant.

7. If a weight be attached to the free end, the hori-
zontal and descending movement will both become more
rapid.

84

Cc. B. WARRING. 101

8. If, while the instrument is slowly revolving around
the fixed point, and standing out horizontally, as if by
some magic gravitation had ceased, it be placed upon
scales, the whole will weigh just the same as if the wheel
was at rest. The weight is in some way transferred from
the centre of gravity to the point of support.

The following is an interesting mode of showing this:

Put the standard in one pan of a pair of scales, and
counterpoise it so that its weight may be left out of con-
sideration. Place the gyroscope with one end on the
standard, and support the other by a thread from the
ceiling. Ifring and disk together weigh, for example,
two pounds, the scales, of course, will indicate a weight
of one pound. Whether the wheel is rotating, or not,
the scales will indicate one pound, and there will be no
horizontal movement. Now set the wheel in rapid
motion and then cut the string. The instrument does
not fall. Gyration’ at once commences, and the scales
indicate two pounds.

Let the lug be prolonged into an arm, as in fig. 2, with
a movable weight, w.” So long as the gyroscope is the
heavier, all the preceding phenomena can be produced
with this form. If, however, the weight is placed so
that neither side is the heavier, then there will be no
gyration. If the weight end is the heavier the gyration
re-commences, but goes backward and the wheel rises.
The arm is 11 inches long and graduated to 2 oz. or 4 oz.
notches, according as the weight is applied under the cen-
ter of the wheel or at the hook in the free end. The
screw, 8s, is of fine steel ending in a fine, hard, highly-
polished point, resting in a cup of polished, hard steel.

Mr. Wheatstone, in a paper read before the Royal So-

1Gyrate and gyration, as used in this paper indicate the lateral or horizontal movement
around the fixed point, while rotate and rotation have reference to the revolution of the
wheel on its axis.

2. The wheel of my instrument is 534 inches across, and weighs 3 lbs. The ring and arm
weigh 11b. 6 oz., and the weight, w, 1 lb. 12 oz.

85

102 AN EMPIRICAL STUDY OF GYRATING BODIES.

ciety, 1854, describes and gives a diagram of a gyro-
scope much like this. The conical support of my instru-
ment with the polished steel cup in which it rests is
ereatly superior to his arrangement, since it much more
nearly eliminates what may be called the horizontal
friction.

10. If while balanced on its fine point, the weight be-
ing placed so that the arm is horizontal, and the wheel
being at rest, the instrument is made to revolve rapidly
on the standard, it will continue in motion, until, after
some minutes, the friction and resistance of the air bring
it to rest. Evidently it possesses momentum, and, if
brought against an obstacle, would strike it a hard blow.
Now set the wheel in rapid motion, and attach a weight
to the free end by a thread a few inches long. It will
at once begin to revolve around the fixed point at a rate
proportional to the weight attached. When in full mo-
tion cut the thread with a match blaze. The gyration
will cease the instant the weight drops, as abruptly as if
the gyroscope had run against an obstacle, or as if it
had no momentum.

This is one of the new and singular effects of which
I spoke a little while ago.

To make this succeed most perfectly a few precautions
are necessary: After the instrument is balanced, the
wheel in operation, and the weight attached, raise the
gyroscope so that the axis is 10° or 15° above a hor-
izontal. Then let it go. Watch it as it slowly descends
and flash the thread (or ent it with sharp scissors) just
as the axis becomes horizontal. The stoppage of
forward movement will then be perfect.

11. If the ring is taken in the hand while the wheel is
in rapid motion, and an effort made to turn the instru-
ment in various directions, it will resist with surprising
force.

Perhaps nothing in the whole series of experiments,
86

C. B. WARRING. 103

except the last, excites so much surprise. The thing
seems to bealive. Somebody has compared the feeling
to that which would be produced by the squirming of a
serpent trying to escape from one’s hands. In fact, with
a large instrument, it will sometimes, by its unexpected
movements, throw itself out of the hands of an inexpe-
rienced holder.

12. If, while the gyroscope is balanced, as in fig. 2,
the wheel be set in rapid motion, the ring and arm will
remain at rest.

Now, attach a string at c, and pull downwards. The
instrument will move horizontally in the direction in
which the bottom of the wheel is going.

Pull the string upwards, the instrument will move in
the same direction as the top of the wheel.

Pull the string horizontally towards you, and at right
angles to the axle; the instrument goes vertically up-
wards.

Pull the string from you, but still horizontally ; the
instrument falls.

In each case, the resulting movement is at right angles
to the pull, continues while the pull lasts, and ceases
when the pull ceases.. In every case, however, there is
a small movement in the direction of the pull.

13. Sometimes the gyroscope stands out for many
seconds, as if in doubt whether to go up or down. Then
it begins slowly to rise, gyrating more and more rapidly
as it goes up, tillit reaches a vertical position, when both
wheel and ring spin around for a while likeatop. After
a short stay it begins to descend in widening circles.

The top-like spinning of the ring ceases as it leaves
the vertical, and in a few moments the instrument comes
to rest as it strikes the table.

This experiment is best performed as follows: Instead
of the standard, use a pane of glass laid flat on the table.

Set the wheel in motion. Place the gyroscope on the
S87

104 AN EMPIRICAL STUDY OF GYRATING BODIES.

glass, as in fig. 20, resting on the point of the hooked
end, and having the axle inclined about 60°.

N. B. If the point on the end of the gyroscope is
fine and sharp, and happens to be in line with the axis of
the shaft, the experiment will fail. The point should
be a little above the axis when held so that the latter is
horizontal. To this there is one very curious exception.

If, instead of a point, the instrument ends in a small
knob or sphere, so placed that the axis produced passes
through its center (or near to it) the actual point of sup-
port will be below the axis line, and yet the instrument
may rise to a vertical. If the experiment be tried and
succeeds, it will be found that in a few moments the
ring and wheel whirl around together, as if they were
one piece, as it were, a top; and, till this occurs, the
gyroscope will not rise.

The explanation is curiously different from that of the
gyroscope proper. It belongs to the theory of the top;
and, when that is understood, this will be found to pre-
sent no difficulty.

THEORIES OF THE GYROSCOPE.

A satisfactory explanation of the gyroscope must in-
clude not only all these phenomena, but any other that
it can be made to produce, and must make clear their
harmony with the long-known laws of motion.

Many attempts have been made to give such an ex-.
planation, but all—so far as I have seen them—more or
less unsatisfactory, and some quite absurd.

It was my intention to precede my discussion by a
somewhat extensive examination of the various theories
heretofore advanced ; but I find that this would occupy
too much space, with little benefit other than to show the
need of more thorough study of the problem.

I shall, however, speak of a few erroneous ideas em-

bodied in certain theories which have become popular-
ss

ye

CO. B. WARRING. 105

ized, or which are entitled to consideration on account
of the eminence of their authors.

One of the most common of these erroneous notions
is that there is an inherent power of resistance in the
rapidly rotating wheel. It will, however, be found on
trial that the slightest force is enough to turn the wheel
out of its plane of rotation, no matter how fast it re-
volves. A gyroscope, supported as in fig. 3 (where the
two cords are knotted at a, so as to prevent slipping),
will turnin azimuth without any sensible resistance ; even
the torsion of a thread will suffice to turn it.

There are several other modes of showing this lack

of ‘‘inherent resisting power.’’ Two of them will be
pointed out hereafter ; one when discussing the so-called
gyrostatic compass, and the other in the part of my
paper which treats of the gyroscopic pendulum.
_ Another erroneous explanation is found in Appleton’ s
Cyclopedia—‘*Gyroscope.’’ Weare there told that the
horizontal movement of this curious instrument is due
to gravity acting with the rotary motion on the descend-
ing side, and against it on the other, thus producing an
excess of force on one-half of the wheel, which pushes
it towards the weaker side.

To show how wrong this is, pass the standard in fig. 1
through asmall hole in the lug until stopped by a ring a
little below the point. Evidently, the instrument has
freedom to move in a horizontal plane, but not to go
downward. Now, set the wheel in rapid motion. It
makes no effort to go to the right or to the left; yet
gravity is all the time acting with the descending side
and against the ascending one.

The same thing can be proved in many other ways, all
giving the same result.

The most noted discussion of the gyroscope is that by
General Barnard. His article, with its two supplements,

is devoted to the higher mathematics of the subject, and,
89g

106 AN EMPIRICAL STUDY OF GYRATING BODIES.

hence, is for the most part outside of the limits of this
paper.

I shall confine myself to two or three of his conelu-
sions, which can be experimentally tested. On page
530, vol. iv., we read: ‘‘If the rotary motion remained
constant, . . . the deflecting force’ would be just
sufficient to lift the axis back to the original position.”
In another place’ he says: ‘‘The descent of the gyro-
scope is due only to the loss of rotary velocity.’? And
in yet another’: ‘‘ The axis (owing to the retarding in-
fluence of friction and the resistance of the air) slowly
falls.”

This is no slip of the pen, for he repeats it in many
places and forms, and evidently deems it an important
matter, as indeed it would be if true. As such, it enters
into his reasoning as to the path of the gyroscope in its
horizontal movement and elsewhere.

Sir William Thomson, when describing his ‘ gyro-
static balance”’ last summer, before the British Associa-
tion at Montreal, put forth substantially the same idea,
for he says: ‘‘ A ‘frictionless’ gyroscope, to wit, his
‘balance,’ if frictionless, would continue its up and
down motion forever.’’*

On this supposed persistency depends the force of his
empirical illustration of the kinetic theory of matter,
derived from the assumed action of his ‘‘ Gyrostatic
Balance.”’

The writer of the article ‘‘ Gyroscope” in the English
Cyclopedia, takes the same ground. Indeed, it seems

?)

1 This “‘ deflecting force ’’ he says on page 557, ‘‘is the sole agent in producing these para-
doxical etfects.’? Yet he admitted that ‘‘ the foregoing analysis ” (all of his high mathematics),
“while it has determined its value, has thrown no light upon its origin !’’ He naively
adds : ‘‘It may be well to attempt to inquire how this force is created !*” One would think
so in a work expressly to explain the Gyroscope. This he then attempts to do, but without
the help of any of the higher mathematics. How successful he is the reader must decide
for himself. It seems to me that he sees the truth dimly, ‘‘as in a glass darkly.”

2 Amer. Jour. Ed., vol. v., page 303.

3 Amer. Jour. Ed., vol. iv., page 530.

41 shall discuss this ‘‘ balance ’’ hereafter.

90

i

Cc. B. WARRING. 107

to be accepted by all writers upon the subject as beyond
question that ‘‘ the fall of the gyroscope is due only to
loss of rotary velocity.”’

But it is not true that, but for the loss of rotary veloci-
ty, the gyroscope would stay up forever.. As General
Barnard’s paper is before me, I shall speak especially of
that. At the same time, I add, that I know of no one
who disagrees with him.

In his statements which I have quoted, one is struck
by the implied assertion that the rate of rotation is of
no consequence, providing that it remains uniform. It
is true that elsewhere General Barnard says the rotation
must be very rapid ; but, in all cases, when speaking of
the cause of the descent which occurs, he uses sub-
stantially the same language: “If the rotary motion re-
mained constant, the reflecting force would be just suffi-
cient to lift the axis back to the original position ;”’ or
‘“the descent is due only to a loss of rotary velocity.”
How absurd this is, becomes evident when we reflect
that, if true, a gyroscope would stay up forever if it
turned on its axis only a small fraction of a revolution in
an hour, provided this rate continued without decrease.

But, undoubtedly General Barnard intended the speed
should continue uniformly very great. Then we have
this difficulty. One hundred times a second is very
great, while a fortiori one hundred and fifty is also
great. We have, consequently, the curious result that
a gyroscope revolving ‘‘uniformly”’ one hundred and
fifty times a second will stay up ‘‘forever,’’ and one re-
volving ‘‘uniformly,’’ one hundred and forty, or one
hundred and thirty, or one hundred and twenty, or one
hundred and ten, or one hundred times, will also stay
up ‘‘forever,’? but if the rate diminishes from one
hundred and fifty to one hundred and forty, or to one
hundred, the gyroscope wil! fall; while, if there had

91

108 AN EMPIRICAL STUDY OF GYRATING BODIES.

been no diminution, it would at any of these rates have
staid up ‘‘forever.”’

To say the least, the statement appears extraordinary,
one might say incredible, but for the high position of
General Barnard and his endorsement by Sir William
Thomson.

As this paper is an experimental study, we will see
what the gyroscope does when set going and left to
itself.

I take my instrument (fig. 2), set the weight so that
the axis is horizontal. I then wind up the string on
the axle, as usual, and set the wheel in motion. The
machine remains at rest. I attach at the hook end a
small weight. Gyration commences. Very slow it is,
but so far as we can see, accompanied by no fall. I set
an index (a wire pointer attached to a retort stand) to
the level of the hook as it sweeps by. When it comes
around again I notice that itis now below the index, and,
next time still lower, it is falling. I now attach a much
heavier weight—say thirty-two ounces—really sixty-four
ounces, since the hook is so far from the point of sup-
port. I must now release the gyroscope with some skill,
or the shock may throw it off the standard. Practice
has enabled me to do this very smoothly. At once the
gyration commences—this time quite rapidly —the fall
increases in equal ratio. Perhaps it may be thought the
increased speed is due to loss of rotational velocity, as
the wheel by this time has lost much of its original
motion. I therefore take off my heavy weight and restore
my light one, and again leave it to itself. The gyration
recommences, but, though a little more rapid than at the
first, it is very much slower than in the second case.
I again apply the heavy weight; the gyration and fall
become more rapid. I reduce the weight; they become
more slow. Yet the wheel of the gyroscope all this

time has been losing speed, for what it now has is the
92

C. B. WARRING. 109

residuum of what was imparted by the first pull of the
string.

I now vary the experiment. I set the wheel off witha
very moderate pull on the string. It revolves only four
or five times in a second. I attach my heavy weight.
Rapid gyration and rapid descent commence at once.
The latter does not need an index to showit. I now
wind the wheel up again, and give it the highest speed
I can.- It goes very fast. I let it out of my hand.
Gyration at once is seen, but I need the index to see
equally soon the descent. It is there, but is very slow.
The conditions may be varied in all possible ways, the
result is the same.

I formulate these results in this law. Increasing the
load, or the downward pull, diminishes the time of hori-
zontality, and, decreasing the load, increases that time.
The opposite is true of the velocity of rotation.

From all this we must conclude that the time of a gy-
roscope’s staying up varies inversely as the load, and,
directly as the velocity of the wheel on its axis; or in
mathematical symbols, we have h oc {, where h=time of
horizontality, and v=angular velocity of wheel, and
w=the load. As the two variables, v and w, are inde-
pendent of each other, h can become infinite only when
v is infinite, or when w is zero. Mere uniformity of ve-
locity cannot take the place of either of these. But,
uniformity of velocity is the highest effect capable of
being produced by absence of friction.

Hence, in a frictionless gyroscope with any finite ve-
locity, h will not *‘last forever ;” or, in other words, the
gyroscope will fall although all friction be removed.

It may, perhaps, be thought, the authority is so great
on that side, that, in some mysterious way, friction is,
nevertheless, the cause of the gyroscope’s not remain-
ing horizontal. I therefore inquired into the effect of

removing or neutralizing all the friction. This mani-
93

110 AN EMPIRICAL STUDY OF GYRATING BODIES.

fests itself (1) at the ends of the axle, and (2) at the
point of support and in the resistance of the air. The
sole effect of the first is to reduce the rate of rotation ;
consequently, if sufficient energy is constantly added to
replace what is lost in this way, this rotation will remain
constant.

This is accomplished by the electro-magnetic gyros-
copes invented by Mr. George M. Hopkins, of New York,
figured and described in the Scientific American, vol.
XXXVill, p. 335. This ingenious instrument gives a contin-
uous rotation which, for a short time, may be regarded
as uniform ; but, owing to the pressure of the connect-
ing wire against the standard, a disturbing element is in-
troduced, which greatly retards the gyroscope, and,
consequently, on the principle stated under the twelfth!
experiment, causes it to fall abnormally fast.

To obviate this, I devised the instrument shown in fig.
4, where it is represented as suspended from the ceiling
by a fine cord. From a to m there is metallic connection,
b and h being mercury cups, except at d and c, where the
electrical continuity is broken by short silk cords. These
compel the current to pass to the circular frame, and
thence around the magnet seen in the diagram. On the
opposide side, out of sight, is a current breaker, by
which the soft iron is made, and unmade, a magnet twice
in each revolution.

By this arrangement, the only resistance to horizontal
rotation comes from the torsion of the string. This is
easily obviated by twisting the string so that its torsion
is a slightly accelerating force, and therefore, so far as
it goes, tending to lift up the loaded end. The pins d
and g are in line as nearly as possible with the centre of
gravity. This arrangement gives great freedom of move-
ment vertically as well as horizontally. In line with the
axis are two hooks, one at each end, to which a weight

1 Retarding the gyroscope or pulling it backward causes it go down.

94

C. B. WARRING. LE

may be attached. All things being in readiness, connect
with the battery. The wheel of the gyroscope at once
begins to revolve, quickly reaching its maximum speed.
Attach at either end a moderate weight, gyration will
instantly commence.

In a very few seconds it will be evident that the loaded
end is descending. Now change the weight to the oppo-
site hook ; the same results will follow, varying a little in
the time, according as the torsion of the suspending
string acts with, or against, the gyration.

In every case (save where the torsion is too great, and
acts with the gyration) the loaded end falls.

The experiment need not occupy more than ten
seconds, and for that time even a bichromatic battery
may be regarded as sensibly constant.

I think, therefore, we may justly conclude that the
fall is not ‘‘ due to the retarding influence of friction and
the resistance of the air ;’ for all this influence is coun-
teracted by the magnet and the torsion of the string, and
yet the gyroscope falls.

The absurd results that would follow if General Bar-
nard’s statement, were correct, will become evident by a
little thought.

If the descent were due only to loss of rotary velocity,
then, as this loss is very gradual, and, in fact, almost
nothing, for, say one second, the power of the gyroscope
to resist a downward force for that time ought to be
almost infinite. During the next second a similar result
would follow, and so on. But, in fact, avery small force
overcomes the instrument’s staying up power.’

From all of which I deduce the following law :

A gyrating body tilts in the direction of the force
which tends to make it revolve around a second axis ;
and this tilting occurs whether the rotation is uniform

1 The nutation of the earth, as will be shown later, affords an example of a gyrating

body absolutely frictionless, which yields to the force pulling it.
95

112 AN EMPIRICAL STUDY OF GYRATING BODIES.

or decreasing, and whether the body is frictionless or
not.

THE EXPLANATIONS OFFERED BY COLLEGE TEXT BOOKS.

The few that mention the gyroscope confine them-
selves to showing, or attempting to show, that the rota-
tion of the wheel, combined with its downward motion,
under the action of gravity, results in a lateral move-
ment coinciding in direction with that of the under side
of the wheel.

That the lateral resultant does not account for the
staying-up of the instrument is evident from the follow-
ing :

It is a familiar principle, that, if the resultant of two
forces be replaced by an equal opposite force, the system
will be in equilibrium, and consequently at rest. If
this be attempted with the gyroscope, no single force
can be applied that will bring it to rest, except a verti-
cal one, and that is not the resultant claimed.

It is easy to try it. Attach a cord to the free end, and
hold it—the cord—in the horizontal plane in which the
instrument is moving. Pull back on the cord ; instead
of coming to rest, and staying at whatever point it hap-
pens to be, it will instantly fall. The same result will
occur even though the string is held above the plane so
as, to some extent, to lift the instrument.

A very brief trial will suffice to show that no single
force holds the gyroscope up.

Those who have any desire to see what is said in col-
lege text books, can turn to pp. 111-113, of Aimball s-
Olmstead s College Philosophy ; or to Pecks Mechanics
(with caleulus) pp. 230 to 235; or to Loomis’s Nat,
Philosophy, pp. 101 to 104; or to Brackelts Text Book
of Physics, 55-58. All have substantially the same
methods, and are open to the same objections.

Enough, I think, has been said to show the need of
96

Cc. B. WARRING. tS

further explanation. Should I add one more to the list
of failures I shall at least have the satisfaction of finding
myself in a company, goodly as to numbers, of whom
some occupy high positions in the world of science.

THE RATIONALE OF THE GYROSCOPE.

No new principle or occult force is concerned in any
of the phenomena presented by the gyrating bodies.

A few familiar laws will enable us to explain every-
thing :

1. A body moving in any direction will continue to
move in that direction notwithstanding other forces act
upon it which tend to send it in other directions.

2. Motion is not accelerated or retarded by forces per-
pendicular to it.

3. Action and re-action are equal.

If, for example, a body moving north ten feet in a
second, is acted upon by another force, sufficient to send
it east eight feet in a second, it will continue to go north
ten feet in a second, and, at the same time, it will go
east eight feet in a second, acting in reference to each
force as if the other did not exist.

It makes no difference how short the time in which
the force acts. If it produces a certain velocity, that ve-
locity remains unchanged in amount and direction till
the body meets a force not at right angles to its direction.

The second law may be illustrated by the case of two
balls on opposite ends of a rod supported on a friction-
less point, ina vacuum. If, insome way, they are made
to revolve, they will persist in circling around the point
forever. Every instant they are acted upon by a force
(the centripetal) at right angles to their direction, and yet
they are neither accelerated nor retarded by it.

The first question that arises when the gyroscope is in
operation is, why does it not fall at once, as other bodies

do? This solved, we can solve the rest.
97

114 AN EMPIRICAL STUDY OF GYRATING BODIES.

It will help us very much if we can get some certain
points in the wheel in which we can look steadily, see
how they behave; then, extending our view, we may
take in all. We will endeavor also to get rid of all
extraneous matter. Therefore, let us suppose the ring
laid aside, since it serves only to hold the axle of the
wheel. Suppose, also, that the axle rests without fric-
tion directly on the top of the standard ;—the other part
of the axle being now useless may be regarded as cut
off ;—and we will confine our attention toa single section
of the wheel, making in facta kind of tee-square, like
fig. 5. Its two extremities will be the two points desired.

I would strongly advise every one who wishes to un-
derstand the gyroscope, to take in his hand a common
tee-square, and to do with it whatever is said to be done
in the following discussion. One that will answer every
purpose can easily be made by nailing a narrow strip of
wood, ten or twelve inches long, across the end of another
piece of about half the length. Then, for the sake of
convenient reference to direction of motion, let the experi-
menter stand facing the north with, of course, his right
hand to the east and his left to the west. This arrange-
ment I shall suppose to continue all through these

papers. Fig. 6 shows such a tee-square, one end sup- .

ported on a standard, the leg horizontal and the arms

vertical. A p equals c p, so that A B subtends an arc of
GOs

The dotted lines, figs. 6 and 7, represent the tee-square

in its original position.

If, now, the free end—fig. 6—-be allowed to fall ever so
little, the point A will acquire a motion towards the
right, and the point Ba motion towards the left, repre-
sented by the arrows m and b.

Suppose, at this moment, and while yet moving, the

1 No such equality is really necessary, and it scarce ever occurs, but I. adopt it now. A
more general discussion will follow soon.

98

C. B. WARRING. 115
arms are instantly reversed, taking the position in fig. 7.
As the force necessary to reverse is at right angles to m
and b, it will neither increase nor diminish them. Con-
sequently A, when at the bottom, will continue to move
eastward, and B, which is now at the top, will continue
to move westward, each with unchanged velocity.
These motions tend to push A and B still, the first to
the right, and the other to the left, the effect of which is
to cause them to tend to go back to their first position—
a stress as it is called—and they would go back but for
reasons which I will try to explain.

Although A and B are now reversed, their downward
motion, x o and z y, is not thereby affected, and gravity,
too, continues to operate ; hence, b and m have two forces
to overcome before they can push the tee back to its start-
ing place. They are sufficient only for the one (o x and
ZY); they just neutralize that. Hence, A and B continue
to fall, but without the acceleration of falling bodies,
for in these acceleration is due to the velocity of the pre-
vious instant being joined to that of the present.’

A pendulum, when it has reached the bottom of its
arc, has absolutely no downward motion—no downward
momentum—to overcome ; the whole energy from its fall
is permitted to spend itself in lifting the bob against
gravitation to the height from which it fell.

But with the gyroscope the case is very different.
The whole energy of the fall is expended (after reversal)
in overcoming the downward momentum, leaving none
to act against the next instant’s pull of gravity.

It is as if a mass received successive impulses from
gravity, each of which carried it a small distance, and
then was neutralized by a counteracting force, which
was immediately followed by another equal impulse,
which in its turn was neutralized, and soon. The result

1. There is an acceleration due to the change in the inclination of the axis, as will be

shown further on.
99

116 AN EMPIRICAL STUDY OF GYRATING BODIES.

would be a slow, continuous motion without acceleration.

In this case, where the diameter of the wheel subtends
an are of 90°, taking the point of support as the centre,
it is not difficult to see that there will be no accelera-
tion; but it is not so clear in case the instrument is
differently proportioned, if, e. g., the wheel is very
small ; nor why the bare axle will not stay up.

There are various other questions that suggest them-
selves. I shall now, therefore, make the discussion so
general that all these may be included.

Let fig. 8 represent our tee-square with the lez PO
horizontal, and the arms vertical, and, for simplicity,
suppose the mass concentrated in the ends A and B. By
giving proper values to these, we can even make one
section represent the whole wheel. Let O be a fixed
point resting on the standard. Draw the lines O A and
OB. The initial movement of A falling in the vertical
plane A OB will be represented by the tang Ax.
Measure off any convenient distance, as Am, to represent
the force of gravity. It will be resolved into Ax and x
m, both being really applied at A. The latter, xm, be-
ing opposite to the line A O, and consequently expended
upon the fixed point O, may be neglected.

To find Ax, AOw+AOP or a=OAm+mAx. But
wOA =OAm.*.mAx=a.

From the triangle mx A, we have mA: Ax:1:
cos x Am or cos a.":Ax=cos amA ; or, taking Amas
unity, Ax =COSs a.

Suppose, now, our tee-square to be instantly reversed,
and that the time of the fall, A to x, was so short that
no sensible change occurred in the position of P, and,
for the present, suppose gravitation to cease. Fig. 9
will represent the new conditions.

The mass A continues to be affected by Ax, which, on
its part, is unaffected in amount and direction. The

100

Cc. B. WARRING. 147

same is true of Band of Bb. The new tangents will be
Be and Am.

By another resolution, we get the triangles Bbe and
Amx. From them we have Ax : Am = 1: cos m Ax, or
cos 2a ;‘ or, since Ax = cosa, we have cosa:mA=1:
cos 2a.

Hence, Am =cosacos2a. The other component, mx,
expends itself in pulling against O.

Another reversal gives Am: Am’=1:cos2a. Anda
third Am’: Am’ = 1: cos 2a, and so on.

We have therefore,

1st tang = cos a.
After 1st reversal—-2d tang = cos a cos 2a.

Gineeal *¢ =r — 8d tang = cos a cos’ 2a.
De esata < —4th tang = cos a cos’ 2a.
“ 4th ‘© —(n+1)th tang = cosa cos" 2a.

It will be seen that at each reversal, a part of the
effect produced by the one impulse of gravity is ex-
pended on the point O.

As in case of light reflected between parallel mirrors,
the intensity grows less and less, and gradually fades
away.

The above formula gives some curious results.

If the wheel is so large that 2a=90°, then the re-
mainder becomes 0 after the first reversal, for cos.2a (or
90°)=0; therefore, all the terms disappear except the
first, for in that cos 2a is not a factor.

That this is true is easily seen by the diagrams 10 and
11. When B, of fig. 10, comes to the top, B b (fig. 11),
which was perpendicular to O B, will keep its direction,
and hence will be perpendicular to A O, because the
latter is now in O B’s place; and as A OB is a right
angle, its direction will coincide with BO. Hence, the

1 To prove mAx = 2a; draw Ow parallel to Bb, and,of course, perpendicular to O A,
w OB (i. e., 90°— 2a) =OBb = Bbe. ... Bbc = 90°— 2a and b Bc = 2a.

But Bbe and mA x are similar, haying their sides perpendicular each to each, therefore,

m Ax is also equal to 2a.
nk @Jal

118 AN EMPIRICAL STUDY OF GYRATING BODIES.

whole of Bb will be expended upon O, while A x will
exhaust itself in pulling in the same point.

A yet more curious result follows when 2a is greater
than 90°, as in fig. 12. Cos 2a now becomes negative,
but its even powers are positive. Hence, for first revers-
al (see fig. 13), the new tangent tends to lift the instru-
ment; the second tends to depress it (see fig. 14), ete.

If 2a equals 180°, then cos a=0, and the whole series
disappears, as it ought. For, in this case, the whole
influence of gravity is expended on the supporting point,
which is then at the centre of gravity.

In this formula, too, we find why the stability dimin-
ishes as the diameter of the wheel grows less,—the dis-
tance from O to P remaining unchanged ; why, for ex-
ample, the axis without any wheel, however fast it re-
volves, falls as if it did not revolve at all. Fora and 2a
being almost zero, their cosine is very nearly unity.
Consequently, the series shows infinitely small diminu-
tion, and therefore only an infinitely small part of the
force of gravity is expended on the point of support.

We also find here the reason why a gyroscope whose
wheel has a heavy rim and a light centre, falls more
slowly than one with a wheel of uniform thickness ; and
this again, more slowly than one whose wheel has been
replaced by a sphere ; for the less the average distance
of the particles from the centre, the less the angle a-be-
comes, and consequently the more rapid the fall.

Thus far, I have limited myself to the consideration of
a single instant’s effect of gravity, and have traced it
out to extinction. In the next instant another impulse
is given, and so each instant thereafter.

To get the whole effect it is necessary to combine the
series.

As the instants are exceedingly brief, I have spoken
of the action of gravity as an impulse.

The series for each impulse wiil be as follows :

IOS

Cc. B. WARRING. 119

Impulses. 1st inst. 2d inst. 3d inst. 4th inst. 5th inst.
Ist. cosa : COS a Cos2a : cosacos?2a : cosacost2a : cosacos!2a : ete,
2d coS a : COS aCcos 2a : cosa cos? 2a : cos acos* 2a : etc.
3d COS & : COS & COS 2a : COS a cos? 2a : ete.
4th cosa : COS 4COS 2a : etc.
5th : cosa : etc.

The terms for any one instant are the same as the
terms of the first series up to that point.

The combined effect at the end of the fifth instant
equals the sum of five terms of the series. When ais
large, and, consequently, cos 2a very small, the series
converges rapidly. By the usual method of obtaining
the sum of a descending geometrical series, we find the
ultimate velocity to be equal to %., or <2" _.

This last is a convenient formula for those whose tables
give the versed sines, but for others, it should be changed
tO sSmza-

But this, it will be remembered, is to be multiplied by
Am, fig. 8, the velocity imparted by gravity to A during
the time, t, of one-quarter of a revolution. Calling this
velocity d, we have for the falling rate, q, of a gyroscope
in action, g = <4$%3; or, Since d varies as the time it is
falling, and that varies inversely as the angular velocity
of the wheel. w, we have q = zmequwzaw 3 OF, if we make
n = number of revolutions per second, we can write our
formula, q = s2mn: Hence, q varies inversely as n;
and, if n is infinite, q =:o: aresult which agrees with
a previous one, and with experiment, so far as experi-
ment is possible. Ifnis uniform, then qis uniform.

This is in accord with the result when discussing the
case in which the angle was only 45°. We have now
reached the same conclusion when a equals any angle.

It will be not without advantage to work out numeri-
cally a single example. We will take the most com-
mon of ali cases—that in which the angle a is less than
45°—let it be 40°.

Our series gives for the impulses :
108

120

Reversal.
1st

2d

3d

Ath

5th

AN EMPIRICAL

STUDY
1st inst. 2d inst.
0.766 0.183
0.'766
0.766 0.899

3d inst.
0.028
0.133
0.766

0.922

4th inst.

0.008
0.028
0:1383
0.766

0.925

OF GYRATING BODIES.

0.000,
0.003,
0.023,
0.138,
0.766,

?

0.926,

5th inst.

etc.
etc.
etc.
etc.
etc.
etc.
etc.

If we had included the 6th j instant, the teat would
have been 0.925, and the same ever ie. The effect in-
creases for a few terms by a constantly diminishing in-
crement, and then becomes constant.

The formula ££", gives the same final resuit in a
much shorter way, but does not exhibit so well the char-
acter of the series.

I will now apply this formula to certain crucial
conditions :

Suppose angle a=o.
is reduced to an

In other words, that the wheel
axle with weight, but no sensible

diameter: cos a=1; cos 2a=1; therefore the series be-
comes—-the impulses being numbered as before :
1st inst. 2d inst. 3d inst. 4th inst. 5th inst.

iL il 1 1 1 1 ete.
2 1 1 1 1 etc.
3 i 1 1 etc.
4 1 1 etc.
5 1 etc.

These series do not converge, and consequently they
give for each instant the old formula, V’=tv, where
V'=velocity after the instants, and v=velocity at the end
of the first instant.

Suppose angle a=45°. We have cos a=.71; cos 2a-0.
Therefore, the series become :

OF 0 0 0 0 0
0.71. 0 0 0 0
0.71. 0 0 0
Ore 0 0
0.71. 0 &e.
O01 3 ails ON ae a aO aiil ye Ted &e,

Cc. B. WARRING. 191

In other words, there is no increment whatever.
Total for any instant, = raicea sata i, age = 90 = af a 0.71 ;
ia 30";

Then we have %2.% 7", _

Let it be any angle between 45° and 90°; then, since,
in our series, every other term is negative, it may be
thought that, possibly, the sum of the negative terms
may exceed the sum of the positive, and hence, that the
gyroscope ought sometimes to rise.

The total effect at any instant has been shown to be
equal tO —.-aansa- AS a is less than 90°, cos a must al-
ways be positive, and the versed sin is always positive ;
hence the value of the fraction is always positive, and
in no case can there be an upward movement, as the re-
sult of the reversals’.

There is a case where the gyroscope actually rises to
a vertical, but it depends on another principle and other
conditions, which will be considered hereafter.

I have, thus far, considered only the case in which the
axis of the gyroscope is horizontal. If the inclination is
small no sensible error can arise from such neglect.

But suppose the inclination to be any angle b; I find
by a process similar to that already employed that the
total effect is Ss4iGaeva 3 Our previous formula multiplied
by the cosine of the inclination. The effect, therefore,
of the axis being above or below the horizontal is to
reduce the falling rate, since cos b is always less than
unity, save when 5 = 0°.

It follows that there is from this cause an increase of
rate of gyration as the axis approaches the horizontal,
and a decrease as it goes from it.”

We will now apply our results to the actual gyro-
scope, to see how its fall corresponds with our theory.

1The oscillations sometimes seen when a gyroscope is started, especially by unskillful
hands, are accidental, and have no influence in sustaining it.

2 The clearest and best experimental demonstration is afforded by the top in that series
of cases, hereafter considered, in which the inclination of the axis is alternately increased
and decreased, 105

122 AN EMPIRICAL STUDY OF GYRATING BODIES.

I think we may safely estimate the revolutions of a
gyroscope at twenty in a second, or forty reversals.
But the effective falling time is only half the time of a
reversal, since as soon as the arms of our tee pass the
horizontal, they begin to act in the opposite sense. We
have, then, to consider instants of only one-eightieth
of a second. A freely-falling body in that time would
acquire a velocity of one-eightieth of thirty-two feet, or
a little less than five inches per second. If angle a=40°
—about the average of gyroscopes—the falling rate
would be 0.925 of this, or about four and one-half inches
per second.

On trial, however, it will be found that the actual fall
of a gyroscope is very much less than this,’ in fact often
not exceeding one one-hundredth of an inch.

A higher rate of rotation would, of course, leave a
less residual velocity. Somewhere I have read that
someone’s gyroscope makes two hundred revolutions a
second. That would reduce the downward rate given by
the formula to a little less than one-half an inch per
second; but, even this is many times greater than the
actual rate even of a slow instrument—say one of twenty
revolutions per second like mine—and needs to be dis-
posed of.

The momentum of the ends of our tee-square, brought
by the reversals on alternate sides of the axis, suffices to
explain all the phenomena yet presented, and it will be
seen that it also suffices for all the phenomena discussed
in the rest of this paper. Also, in very many instances,
it has enabled me to say what the instrument would do
in new and untried conditions, and sometimes has led
to unexpected results which experiment verified. I con-
clude therefore that the force, or whatever it is, which
disposes of this residuum, must act in the same sense as

1In my instrument the weight of the ring is wholly got rid of by connterbalancing it.

L106

Cc. B. WARRING. Ie:

these reversals of momentum,' since it merely intensifies
their effect.

What this something is I hope soon to show; but, in
order to do so, we must first study the horizontal move-
ment, for in that, if lam not mistaken, lies the key to
the remaining mystery.

Returning to our tee-square, or, if you please, to our
section, e. g., in fig. 5, and standing in reference to it as
before, we see that when it falls any distance, however
small, the upper end acquires motion to the right, while
the lower goes to the left. Suppose that at this instant
the tee is rotated so that A goes from us. When the
arms reach a horizontal, A will still be going to the
right, and B to the left, as in the bird’s eye view (fig. 15),
and this means that the tee is caused to move in the
direction of the arrow m; in other words, around the
supporting point c, and in the same direction as that in
which the lower end moved from its vertical position.

As this tee differs in no respect from all other sections
of our gyroscope, we are entitled to conclude that each
of them will do the same thing. In this is the reason
why the gyroscope moves horizontally around the sup-
porting point, and why its direction coincides with that
of the under side of its wheel.

It is true that the instrument will at the same time be
pulled downward by gravity. But we have already
shown how the greatest part of that force is disposed
of, and, as for the rest, we will satisfy ourselves for the
present with the fact that it is disposed of in some way,
and wait till the problem is solved.

Since these forces, x and y, (fig. 15), are renewed at
each reversal, and no force opposes them, the horizontal
movement will be a uniformly accelerated one, unless

1 “ Reversals of momentum,” not that the direction of the momentum is reversed, but
only its effect. It is as when a weight is shifted from one pan ina pair of balances to the
other. The direction of the downward pull is unchanged, but its effect is reversed.

AL(O}7¢

124 AN EMPIRICAL STUDY OF GYRATING BODIES.

prevented in some way of which we, as yet, have had no
inkling. For the only counteracting influences thus far
considered are friction and the resistance of the air,
These we have seen eliminated, and yet all the phe-
nomena were the same as before—except a little change
in rate, that is all. It would seem that there ought soon
to result a very considerable horizontal velocity.

But it is found on trial that the horizontal motion is
very moderate, and, so long as the rotation is sensibly
uniform, there is apparently no acceleration.

This is a very curious and important fact, that the
horizontal movement ought to be an accelerated one, and
yet it is not.

Why not? What becomes of the energy that ought to
be expended in sending the gyroscope with ever-in-
creasing rapidity around the supporting point? How is
it expended ?

Tanswer: Accelerating the horizontal movement tends
to make the gyroscope rise ; it acts against, and, to that
extent, neutralizes gravity, and gravity, being thus
counteracted, there is less and less fall to produce the
acceleration ; and therefore that, too, grows less, till it
practically ceases, i. e., becomes exceedingly small if not
absolutely nothing.

That accelerating the horizontal movement makes the
gyroscope rise, is proved by an experiment already
shown. I refer to that in which a string attached to the
free end of a gyroscope is pulled in various directions.
You all saw that when the string was pulled so as to
make the horizontal motion more rapid, the free end of
the instrument rose towards a vertical. This proof of
the law is absolute ; but we are now seeking to find the
reasons for all these things. Fig. 16 will help us in our
search.

The observer is supposed to stand squarely facing the

wheel, and the weight on the arm (both arm and weight
108

C. B. WARRING. 125

are invisible) to be so placed that it just balances the
wheel. However rapidly the wheel is made to revolve,
there will be no gyration. But now I pull the string
horizontally to the right. The right hand side, a, moves
(a little) from the observer, and the other side, d, to-
wards him. (The same movements that are shown in
fig. 15 by the arrows x and y, only there they happen to
be reversed). But the wheel is revolving on its axis ;
when, therefore, a comes to the top, its motion from the
observer (which has not in any way been reduced) tends
to push the upper edge in that direction, or, in other
words, tends to tilt the instrument upwards. What is
true of a is also true of d, only it goes down instead of up.

If ¢ is pulled downward, b will tilt towards the ob-
server, and when the wheel has gone 90° of a revolution,
it will still tend to move towards him, and consequently
tend to send the instruments to the right, i. e., in the
direction of the lower arrow.

In the same way we can determine the result when c
is pulled upwards ; or when it is pulled to the left."

Now I move the weight towards the gyroscope so that
the end towards the observer is the heavier, and again
set the wheel to revolving in the same direction as before.
At once, C begins to go to the right. Then pull the
string in the same direction as before.

The results are embodied in these four laws:

1. Accelerating the gyration causes an upward tend-
ency, greater, equal to, or less than the effect of gravity
according to the extent of acceleration.

2. Decreasing the gyration causes more rapid fall.

3. Pulling the free end upward causes a retardation,
or even a reversal, of the gyration.

4. Pulling the free end downward quickens the
gyration.

1Clearness of conception will be greatly promoted by going through these movements
with a tee-square. It is easier for the mind and eye to follow it than to follow the gyroscope.

109

126 AN EMPIRICAL STUDY OF GYRATING BODIES.

The effect of accelerating the gyration, or horizontal
movement, is beautifully shown by the following easy
experiment :

Suspend from the ceiling by a stout cord, a balanced
gyroscope, its axle being horizontal when at rest. At-
tach crosswise to the cord, a few inches above the in-
strument, a small stick, so as to be able easily and
quickly to twist the cord to the right or left. Now set
the wheel to revolving. The instrument will stand per-
fectly still. Twist the cord so that its torsion tends to
make the gyroscope move in the same direction as the
bottom of the wheel. It will begin to rise. Stop the
torsion, and the rising ceases. Twist the cord the other
way, the instrument tilts down. Then move the weight
on the arm so that the wheel side becomes the heavier,
one or two pounds, or more, if you please. Again, set the
wheel to revolving. The gyroscope will at once start
off horizontally, and also begin to tilt downward.
Twist the cord as before, it will tilt down less rapidly.
Twist the cord a little more, the gyroscope will cease
falling. Twist it yet more, and the gyroscope will be-
gin to tilt upwards.

We are now, I think, in a position to answer intelli-
gently the question which we passed over: Why does
the gyroscope in actual operation fall so much less than
is indicated by the formula, z..a? Why, e. g., does
it, in fact, fall only one one-hundredth of an inch, when,
apparently, it should fall four or five inches? The
reason is found in that acceleration of the horizontal
movement.

If the acceleration continued at the rate at which it
commences, it would cause the gyroscope to rise to a
vertical. But when it begins to resist gravity, gravity
produces less and less downward movement, and the
less there is of this the less is the acceleration. Hence,

a bale)

Bei)»
"7 Ay fi

-

C. B. WARRING. 7

there is an approximation to equality of upward and
downward tendencies.’

Now we can see what becomes of the energy which
ordinarily would be expended in acceleration. It is em-
ployed in resisting the action of gravitation.

We can also understand why the horizontal movement
becomes (sensibly) uniform, provided the rate of rotation
undergoes no change, and so long as the axis remains
nearly horizontal.

One question remains—a question of a good deal of
importance. I have said the upward and downward
tendencies experience an approximation to equality.
Why not say, reach equality, and consequently that a
frictionless gyroscope would never fall, and so agree
with General Barnard and Sir William Thomson ?

I cannot say so, because it has been shown that such a
statement implies the monstrous absurdity of attributing
infinite power of resistance to an instrument that I can
turn with my finger ; and I have shown experimentally,
that a frictionless gyroscope does fall. If it falls there
must be a reason why, and what that is I shall now at-
tempt to show:

The formula, h varies as“, h being the time of hori-
zontality, shows, as has been said, that h would be in-
finite if v were infinite, i. e., if the reversal took abso-
lutely no time at all. The interval required in that case
for A and B, fig. 6, to reverse being zero, the downward
velocity acquired, d, would also be zero. Hence our
formula, d X £%3,,, would give zero, or, in other
words, there would be, in case of infinite velocity of ro-
tation, no downward movement at all, and the horizon-

11 wrote first ‘“‘the upward and downward movements ;*” but this conveys a wrong
meaning, or at least, a meaning not intended.

Ido not think that there is an oscillatory or vibrating movement, but there are two
tendencies, or stresses, by virtue of which the path described by the free end of the gyro-
scope is a very slightly descending spiral, the action of gravity being a Jittle more than suf-
ficient to overcome the upward tendency due to the acceleration.

elalal

128 AN EMPIRICAL STUDY OF GYRATING BODIES.

tality would be forever. Thus, by two roads, we arrive
at the same result.

But we have to do with velocities far below infinite.
It takes some time—very small indeed—for our tee-
square, or section, to reverse, and there is one position
(that in which the arms are vertical) in which the lateral
acceleration adds nothing to the lifting power, and an-
other (when the arms are horizontal)' in which the action
of gravity adds nothing to the acceleration ; yet gravity
acts all the time, and during these exceedingly short
moments, each a mere infinitessimal of a revolution, it
acts unimpeded. It is to these intervals of no influence
that the fall is due.

Since the length of these periods depends upon the
time it takes the tee (or section) to pass through what,
for lack of a better name, J may style the zero regions
it is not difficult to see why the gyroscope falls faster
the slower the wheel revolves, for the greater the time of
a revolution, the greater the fraction of it spent in those
regions, and consequently gravity has more time to pro-
duce downward motion.

HEAVY AND LIGHT GYROSCOPES.

If it were possible to make a gyroscope whose ring
and axle were without weight or mass, we should find,
all other things being the same, that a heavy and a light
gyroscope would have equal horizontal movements and
equally slow descent. The reason is this: A heavy and
a light body fall with the same velocity, and the motion
acquired in falling is the source of all the other move-
ments.

WHEN A LOAD IS PUT ON THE TWO GYROSOOPES,
There is then no longer identity of results. In the

1If a tee-square be held so that its arms are horizontal (the leg also being horizontal) and
the standard at the left and, as in fig. 5, and it be let fall a little, both arms will move
equally to the left ; hence neither will tend to produce horizontal rotation about the point
of support. The same reasoning applies when the arms are vertical and we are considering
a lateral force.
aba l-2.

Cc. B. WARRING. 126

previous case, each particle in both the instruments went
down, but on reversal all helped to make the upward
force which tended to keep the instrument up. Suppose
we attach a load of say eight ounces to a heavy gyro-
scope, and an equal amount to a light one, the former
will show greater. power of resistance. The resistance
comes from the momentum of the wheels, section by
section, as has been shown. The momentum of the light
wheel is less than that of the heavy wheel, yet it has, in
proportion to its weight, more work to do. The momen-
tum of the ight wheel divided by its mass and load, or,
ata iS less than 275, where m equals mass of small
wheel, and nm the mass of the large one, and v, the
falling velocity of each.

Tt follows that a load of two ounces will make the
gyration and descent more rapid than would a load of
one ounce, and so on; but, of course, not twice as rapid.

We may also conclude that a heavy wheel has greater
stability, i. e., power of resisting a push, or a pull, or
other outside force, than a light one. Yet, of them-
selves, the one will stay up as long and gyrate as fast as
the other.

This is another outcropping of the inertia-character
(if I may use so awkward an expression) of this instru-
ment. ‘Two stones, however different in mass, will fall
equally fast, but if we attempt to slide them, even on a
frictionless plane, we will find a resistance proportionate
to the masses.

THE TRANSFER OF WEIGHT FROM CENTRE OF GRAVITY
TOP LEH POUNT OWS Sli2P ORD.

I showed with the balances that, in some way, the
weight while the Gyroscope stood out horizontally (as
in fig. 1), was transferred from the centre of gravity to
the point of support.

The explanation becomes very simple by examination
118

1380 AN EMPIRICAL STUDY OF GYRATING BODIES.

of fig. 17, representing the composition of the two forces,
BP and PA, at the instant of reversal of the section or
tee. Their resultant passes through P.

Perhaps, however, the ability of two opposite equal

forces.acting on the ends of the arms of a tee-square to
transfer the weight to the end of the axis, will be more
clearly seen by the non-mathematician by the help of fig.
18. <A and B are two projecting pins made, we will sup-
pose, by means of friction rollers, or otherwise, so that
the arms of the tee can move against them without sen-
sible friction.

Place the tee-square as in the diagram. Nothing
keeps it from falling except the pressure of the two pins.
The spring-balance will show the weight of the whole
tee-square just as if it hung suspended on it alone.

Fig. 17 explains also why one feels so much resist-
ance when pressing down the free end of the gyroscope.
By the curious transfer of force, he really presses against
a fixed point. This, of course, is on condition that there
is freedom to move laterally. For I showed by experi-
ment that if the horizontal or lateral motion is pre-
vented, or if it is stopped after commencing, the gyro-
cope will no longer sustain itself. Why ?

The staying up depends upon the right and left
motion of the end of the tee (fig. 6) being in full opera-
tion at the instant of complete reversal. This is im-
possible unless they continue to move while they are
passing through the horizontal position ; and it is the
right and left moving of the arms while horizontal that
makes the horizontal revolution. Consequently, if this
is stopped, the right and left movement stops, and no
force remains when the reversal is completed to counter-
act gravity.

It goes without saying, that if there is no downward
movement there will be no gyration. Also that there

alt:

Cc. B. WARRING. 131

is no gyration when the instrument is supported at both
ends, or when balanced.

A reversal of all the motions occurs when the arm of
the gyroscope, fig. 2, is made to overbalance the wheel.
It is the same as if gravity pulled up instead of down;
consequently the gyration is in the opposite direction.

The tendency of the gyroscope to go in a direction
perpendicular to the force applied—as has been formu-
lated in the four laws—accounts for the squirming feel-
ing produced when one takes the instrument in his hands
and tries to twist it, or turn it, in various directions.
The rationale is easily seen.

ANOTHER NEW PARADOX.

I refer to the experiment in which I showed my
balanced gyroscope (fig. 2) rapidly moving around the
supporting-point, under the influence of a weight at-
tached by a thread to the free end ; and then I cut the
thread by bringing a blaze against it. The gyration in-
- stantly ceased, as if the machine had run against an ob-
stacle. The momentum of such an instrument weigh-
ing, as mine does, several pounds, moving with very
considerable rapidity, is quite an amount, yet it disap-
peared in an instant. There was a tremor, a circling up
and down, and then rest, but no advance.

ITasked what had become of the momentum. Now
we can see.

When the weight was flashed off it left the instru-
ment balanced. Neither side being the heavier, there
was, therefore, no fall of the gyroscope, hence no im-
pelling power. The instrument would have remained
perfectly stationary but for the momentum previously
gained. That acts in the same sense as the string (fig.
16) which we used for accelerating the horizontal move-
ment; i. e., it makes the gyroscope go faster than the

velocity due, at that instant, to the fall Gn this case zero,
fs

132 AN EMPIRICAL STUDY OF GYRATING BODIES.

because the weight being removed there is no longer any
downward movement).

Hence, by our first law, the gyroscope rises; but
making it rise is the same in effect as pulling it upward
by the string; and that, in accordance with our third
law, sends it backwards and so stops the gyration.

But this is not all. Sending the gyroscope backward
makes it fall (by our second law); and falling makes it
go forward (fourth law); and going forward makes
it rise (first law); and rising makes it go backward
(third law). Thus we get a complete circle with no
loss of energy except from friction. If that and the air
were removed, this motion, so far as I now see, would
go on forever.

We have here the curious case of a body whose centre
of gravity revolves around a fixed immaterial line, at a
sensible distance from it, under the influences of forces
wholly within itself. This more nearly resembles the lat-
ter case where the actual axis revolves around one of the
two stable principal axes. It does not, however, seem to
be identical, for in this case both axes pass through the
centre of gravity, which, itself remains at rest, while the
center of gravity of the wheel revolves around a fixed
point. There is apparently no tendency to approach
that point, or to leave it. Circular motion without cen-
tripetal or centrifugal force !

I have called this ContcaL Roratron, for the axis of
the Gyroscope describes the surface of a horizontal cone,
whose vertex is at the point of support.

THE UNDULATORY MOTION.

When a gyroscope first starts there is often in un-
skilled hands, a brief undulatory movement of the free
end. This has attracted considerable attention. General
Barnard has devoted to it a large part of his articles in

the Amer. Jour. Education.
116

Cc. B. WARRING. 133

On trial it will be found that the gyroscope will start
in its horizontal journey without these up-and-down
movements, if a little pains are taken to prevent its fall-
ing too rapidly at the start. Thisiseasily accomplished,
after a little practice, by supporting the free end by a
string, and keeping the hand vertically over it.

It will be found also that when the gyroscope is moving
with entire steadiness, these undulations can be pro-
duced at pleasure by pushing, or pulling, or striking the
free end.

The following experiments show this very easily and
prettily: I set No. 2 (fig. 2) so that the wheel-end is
the heavier ; I made it twelve ounces heavier. Then I
attached to the hook, by a fine thread, a weight of six-
teen ounces—any other weight or proportion would do—
and set the wheel in motion and started it off. As I held
the end from falling too fast there was little or no undu-
lation. When it was gyrating with entire steadiness, I
flashed off with a match-blaze the attached weight. In-
_stantly the gyration became very much slower and beau-
tiful undulations began.

At another time with the weight, w, set as before, I
started the instrument, having first attached to the hook
a string ten or twelve inches long. As soonas the move-
ment was perfectly steady I pulled downward on the
string. Undulations at once set in proportional to the
degree of pull. By renewing the pull, I kept them up
indefinitely. If, however, the pull was steady and con-
tinuous, there were no undulations.

These experiments prove that the undulations serve
no purpose in keeping the gyroscope up; that they are
an accident not easily avoided save in skillful hands,
like the oscillations of a pair of balances; and that
they are due to peculiar conditions of short continuance,
such as a blow, a momentary pull, or a sudden fall.

ally /

134 AN EMPIRICAL STUDY OF GYRATING BODIES.

The following laws in reference to these undulations
are easily experimentally demonstrated :

1. The less the downward pull, the less the undula-
tions.

2. The greater the rotational velocity, the less the un-
dulations. In each case the converse also is true.

3. In all cases undulations follow a somewhat ab-
rupt disturbance of previous conditions. ;

THEIR RATIONALE.

This is best seen by taking the case in which the un-
dulations are produced in an instrument which had been
egvrating with steadiness—such as is described in the last
experiment but one.

We here have the gyroscope moving ‘‘ horizontally ”’
under the joint influence of the weight of the wheel and
the additional weight attached to the hook at the free
end. This horizontal movement, being proportional to
the load, is more rapid than it would be if either part of
the load acted alone. If, now, the weight is flashed off,
the velocity for the instant will be in excess, and the
condition is what it would be if, while the instrument
was moving under the weight of the wheel alone, the
motion was accelerated. But, by our first law, accelera-
tion makes the gyroscope rise, and rising tends to make
it go backward ; and going backward tends to make it
fall; and making it fall tends to send it forward. At
the same time, the remaining weight—that of the wheel
—tends to drive it steadily forward. There results from
the two motions a series of up-and-down, fast and slow
(relatively) movements, which are the undulations. To
apply this to the case of a starting gyroscope, we need
only to remember that the forward motion—the gyra-
tion—is the result of the falling motion ; and that there
is an instant, after the fall begins, before the lateral mo-

tion comes into play, while the fall continues unchecked.
11s

Cc. B. WARRING. 135

This gives what, for lack of a better name, I may call an
abnormai downward impulse, whose action and effect
are such as were seen when we flashed off the weight.

It would be easy to multiply experiments, and to pro-
duce some curious results, but if I have succeeded in
making clear the principles involved in those already
considered, the others will offer no great difficulty.

For myself, I have found nothing so helpful as to
follow the movements of a tee-square falling freely, and
to note what it does when rotated quickly—instantly,
would be better—from a vertical to a horizontal position,
then to a reversal, and again back to its first position.
This mode of treatment I have applied from beginning
to end of these papers.

Of course, in a gyroscope there is no break in the con-
tinuity of movement. Every section goes gradually
from one position to another ; but we may, without detri-
ment, consider all the effect as concentrated into certain
portions of the time so occupied.

THE RISING OF THE GYROSCOPE.

Two familiar principles have sufficed to explain all the
phenomena of this instrument thus far. But now we
come to another paradoxical movement, and for that
shall require a third principle—the law of reaction.
Every action is accompanied by an equal and opposite
reaction. I push the table, the table pushes me. A
man standing on the deck of a boat propels it along by
pushing against the immovable bottom of the stream.
It is reaction of the fixed rail against the yielding wheel
that sends the locomotive along the iron road.

The gyroscope, under certain conditions, pushes itself
up. How it does so, I now shall try to show.

In all our operations thus far there has been no actual
rise of the centre of gravity. But sometimes such a rise

119

186 AN EMPIRICAL STUDY OF GYRATING BODIES.

occurs, and the centre of gravity actually ascends till it
is vertically over the point of support.

There are two cases of this kind varying in some im-
portant respects. Itake that first whose explanation is
least difficult.

I place before me any unbalanced gyroscope, fig. 16,
with axis horizontal and wheel inrapid motion. The ar-
rows bb, show the direction of the rotation of the wheel,
and § that of the gyration. I take a book, or something
similar, and I bear down with some force on the upper
side of the wheel. The reaction from the friction will
send the gyroscope to the right; that is, it accelerates
the horizontal movement ; and this, by the first of our
four laws, makes the instrument rise. With judicious
management, it is easy to start from any position, even
from one much below the horizontal, and make it rise to
a vertical.

In place of a book, I find it much better to use a circle
of book-board ten or twelve inches in diameter. A loop
of tape tacked to the back enables me to hold it firmly.
When used, its centre should be approximately over
the supporting point. The experiment is novel and
pretty, and, with reasonable skill, never fails. The same
result may be produced by pressing the finger on the
upper side of the axle. If touched on the under side,
the friction acts against the horizontal movement, and
the instrument drops, as it ought, according to the
second of the four laws.

The experiment is an interesting one. The axle seems
to be attached to and to follow the finger.*

In all these instances we have a fixed point of resist-
ance outside of the gyroscope and its standard; and
consequently the problems presented are of no great
difficulty. It is no more than the case of the man in the

1 For this last experiment, the balanced gyroscope is much the best, as it is easy to regu-
late its movements. With the other the gyration is so rapid that the experiment is very
difficult.

L2@

Da

C. B. WARRING. 137

boat pushing against the solid bottom. The bottom
won’t give, and therefore the boat moves. The rim of
the wheel, or the surface of the axle, pushes against the
book-cover or the fingers. If this is on the upper side
the reaction sends the gyroscope forward ; if on the
lower, it sends it backward, and it rises and falls ac-
cordingly.

But sometimes the gyroscope rises to a_ vertical,
apparently without any outside assistance—certainly
nothing is applied toit. You set the wheel (fig. 1) going
as usual. The instrument begins at once its horizontal
movements ; generally it falls a little first, but sometimes
it appears to go around without rising or falling for a
considerable time. Then very slowly it rises, but with
an increasing gyration, until at last the axis becomes
vertical. There it spins for a time, until its energy is
pretty well exhausted, and then it descends. It is very
interesting to watch its movements. They apparently

contradict not only the law of gravitation but its own
previous behavior.

I have been able to find very little in reference to these
extraordinary performances.

Professor Snell, in a note, page 706, vol. ii., Amer.
Jour. Hd., alludes to this upward movement, and at-
tempts to explain it. He says: ‘‘If the wheel is spun
very rapidly, and elevated several degrees above the
horizontal position, the friction of the indentation on the
standard, instead of depressing the disk, will cause it to
rise towards a vertical.’”’ How entirely he failed to find
the true reason is manifest by the fact that the less the
friction the better the instrument rises! The same
gyroscope, as I have often seen, will refuse to rise, be-
cause the friction of the indentation is too great, and,
then, when transferred to a glass plate (fig. 20), where the
friction is less, will rise, although in the meantime the

velocity of the wheel has diminished !
om

138 - AN EMPIRICAL STUDY OF GYRATING BODIES.

General Barnard, in his second article on the gyro-
scope, offers an explanation’ which does not explain.
He merely says that these upward movements are due to
a component which, when the axis is above the hori-
zontal, sends the instrument up, and when the axis is
below the horizontal, sends it down. This is undoubt-
edly true, but not very satisfactory, for he does not ex-
plain how, or whence, the component comes.

For lack, then, of other explanation, I offer one of my
own:

As already stated in the list of things done by the
gyroscope, two conditions are necessary for the success
of this experiment. (1.) The point of support when the
axis is horizontal must be a little above the axis pro-
duced. (2.) When set in operation, the axis must be
very much inclined. I find an angle of 60° or 70° gives
good results,” and that nothing is better to rest it upon
than a pane of glass.

Fig. 21 will help us to trace out the curious combina-
tions that lead to this result ; a bisa bar of light wood
eight inches long, two and one-half inches wide, and
one-half inch thick; pisa cone of tin passing through
the bar, and ending in a small steel cap. The standard
ends ina steel wire four inches long, on the polished top
of which the steel cap rests; e is a movable weight to
balance the gyroscope; d is a cap of tin that slides
snugly over the bar; 1, 2, 3 and 4 are small tubes
soldered to d into which the lug cf the gyroscope fits
firmly. By means of these the gyroscope can be placed
at different angles to the bar,a b. The cap d can be
moved towards or from the center.

If the wheel be set in rapid motion, and placed as in

1Am. Jour. Ed., vol. iv., page 532.

2 Probably with careful adjustment of the point, and with a very small load in propor-
tion to the mass of the rim of the wheel, and with higher speed than I can give, the gyro-
scope would rise from a much lower angle. I cannot say what the limit is, except that the

axis must be above the horizontal.
122

Cc. B. WARRING. 139

the diagram, a b will revolve around the supporting
point, and in the same direction as the wheel itself.

The explanation is this: The friction of the axle of
the gyroscope on the side toward b tends to make the
bar move in the direction of the arrow, m, while the
friction on the opposite side tends to send it back-
ward. These are equal, but their influence is not equal
because the moment of the first, 1. e., its product by
its distance from the fixed point, p, is greater than that
of the second. Hence, since the stronger prevails, the
bar goes in the first direction, that of the arrow m. The
difference in the effect of these moments increases as
the distance from the centre grows less; therefore the
rotation around p grows more rapid as d is moved to
points nearer to the centre.

If, instead of being vertical, the gyroscope is put in
tube No. 2, the same result follows, but with less speed
of revolution of the horizontal bar. The effect continues
to diminish if the inclination is increased, until the axis
is horizontal, and then it becomes nothing.

In every case the result is the same as would be pro-
duced by a force varying according to the position of the
axis, applied perpendicularly to the bar, in the plane of
its motion, and pushing it around the supporting point
in the same direction as that in which the wheel revolves.

It makes no difference whether we have an upright,
separate support, as in fig. 21, or whether the bar is bent
down so that the tip rests on the table (on a plate of
glass), as in fig. 22. In this case, too, the difference in
the moments of the frictional forces on the two sides of
the axle will act as a gentle pressure applied at d, caus-
ing the gyroscope to accelerate its gyration :—remember
that this last is always in the direction in which the
lower side of the wheel goes.

But, by our first gyroscopic law, accelerating the gyra-

123

140 AN EMPIRICAL STUDY OF GYRATING BODIES.

tion causes the gyroscope to rise. Hence it goes up to
a vertical, Q. E. D.

Tf the wire hook is bent so that p is in the prolonga-
tion of the axis, the ring as well as the wheel of the
gyroscope will revolve around the axis, and the whole
will become simply a top subject to the laws of that in-
strument.

I will anticipate so far as to say that in this case—c,
d and p being in a straight line—the gyroscope will not
rise if p isa fine, sharp point. Why not? Simply for
the reason that the ring revolves in the same sense as the
wheel, and nearly or quite as fast. If it revolves quite
as fast there will be absolutely no friction at d; and if
nearly as fast, there will be almost none. In the first
case there will be no acceleration, and in the second, too
little to be of any service.

To discuss the effect of friction at p, it would be nec-
essary to anticipate what will be said when speaking of
the top. I may, however, say now that if p is confined
to one point on the glass plate, the friction, so far as it
would have any influence, would tend not to accelerate
the gyration but to retard it, and hence to make the
gyroscope fall instead of rising. The friction at p, in
its effect, is a force pushing backward against the rotat-
ing body.

A curious experiment described by General Barnard
comes properly here :

Let a gyroscope be placed as in fig. 23, taking care
that the pulley in the ceiling is exactly over the centre
of the standard. Set the wheel in motion, first lower-
ing c till the axis is horizontal. There will be no gyra-
tion, since c cannot fall at all, and since the friction on
the end of the axle has, in this position, no tendency to
cause it.

Now raise c till the axis makes a sensible angle with

the horizon. The end ¢ being supported by the cord,
124

Cc. B. WARRING. 141

there can be no fall, and, hence, no gyration from that
source ; but the axis being oblique, the difference in the
moments of the friction (just as in fig. 21) causes the in-
strument to gyrate in the same sense with the side
which is farthermost from the support, 1. e., with b, and
as is indicated by the directional ellipse B.

If the angle the axle makes with the horizon is quite
large—50° or 60°—and the hook is bent so that the point
is a little above the line of the axis, the instrument will
gyrate more and more rapidly, and soon begin to rise,
continuing till it reaches the vertical.

Again: place the gyroscope as in fig. 24, inclining 50°
or 60° below the horizon. The side of the axle towards
a, being farther from the standard, the moment of the
friction on that side is the greater, consequently gyra-
tion commences in the direction of the arrow next to
a, or as indicated by the arrows in the ellipse A. If
now the cord is slackened so that ¢ is free to fall, the
part a will (as in case of our tee-square) move with a
certain velocity to the right, and, when in its rotational
movement it has gone 90°, it will still have its motion to
the right, and that will push c away from us, and so
cause a gyration in the direction of the ellipse arrows
D. And so the gyration will continue in the direction
of arrows of A when the string is taut, and of D when
it is slackened.

If, however, you pull the cord so that all, or almost all,
the weight is taken from the standard, p will now be
the end that can fall, and the instrument will gyrate in
such a sense that p moves from you and ¢ towards you;
in other words, the effects of gravity and of friction now
codperate. The friction now accelerates the gyration,
and the effect of that, by our first law, is to make the
free end of the gyroscope rise.

General Barnard says the free end will of itself leave

125

142 AN EMPIRICAL STUDY OF GYRATING BODIES.

the standard and rise. I have not been able to make
mine do so.

THE GYROSCOPE NOT A MODIFIED PENDULUM.

General Barnard says that the gyroscope belongs to
the class of instruments of which it stands at one end
and the pendulum at the other.

It seems to me that they are radically different. In
the pendulum everything depends upon the length of the
rod (distance from centre of oscillation to point of sup-
port), and nothing upon the weight of the bob. In the
gyroscope, the rate of the gyratory motion, and also
that of the descending motion, changes as the weight
changes, other things being constant, while the distance
from the point of support to the load may be made longer
or shorter without effect, provided the angle a (fig. 8) is
unchanged.

In Thomson and Taits Natural Philosophy we are
told that the motion of the gyroscope, top, etc., may be
represented by the rolling of a cone fixed in the body,
on another cone fixed in space.

This statement to represent actual conditions must be
supplemented by the words ‘‘ whose vertical angle is not
fixed, but which, in the most general exemplification of
such bodies, passes from infinitely near 0° to 180°, and
from that to 0°.”

This is a corollory of the principle that a gyrating
body, in general, yields to the force which tends to make
it revolve around an axis perpendicular to its first axis.

PEE VEO:

The theory of the top is regarded as very difficult. J.
C. Maxwell says the problem of the top surpasses that
of the precession of the equinoxes.!

In my study of this instrument I have used the disk

1 Transactions of Roy. Soc. Ed. Vol. —, page —.
126

Cc. B. WARRING. 143

and axle of my medium-size gyroscope. ‘The form is
peculiarly favorable to a clear exhibition of its peculiari-
ties. To adapt it to my purpose, I had several points
made of hardened steel, which screwed into a movable
socket, d, fig. 25. These ‘‘ points’? were centered, pol-
ished, and fitted with the utmost care, so that they are
as nearly ‘‘ true”’ as possible.

They are of various forms, as shown in the diagram.
Of truncated cones I have several, measuring across the
face from one-eighth to one-fiftieth of an inch. In all
cases, unless otherwise stated, the top was spun upon
a large pane of glass, laid as flat as possible on an ordi-
nary table. From the point to the center of the wheel
measures one and three-quarters inches. The wheel is
three and three-quarters inches in diameter. The weight
is almost allin the rim. The whole weighs eight and
one-quarter ounces avoirdupois.

A theoretical top revolves on a mathematical point
situated in its axis of figure and mass. ‘The nearest
approach possible is my top with one of its very sharp
points. So soon as the point becomes so far blunted
that when turned towards the light any disk, however
small, can be seen, it is unfit for my purpose—the ex-
hibition of the theoretical top—and is laid away in the
box of truncated points.

Until the contrary is stated, I shall use only the fine
points.

If such a top be set going, it does not move about, nor
will it rise from an oblique to a vertical position. At
whatever angle of inclination the axis happens to be
when it starts off, at that it apparently remains, but
after a little time, one can see that the inclination is be-
coming larger ; the rim getting nearer and nearer to the
glass, while at the same time the gyration is growing
more and more rapid.

It is interesting to watch such a top as it whirls
LAT

144 AN EMPIRICAL STUDY OF GYRATING BODIES.

around with the edge of the wheel in close proximity to
the glass, till at last—perhaps after six or seven minutes
—it strikes, and then it rushes backward till its remain-
ing energy is expended.

We naturally ask, first, why does it not fall at once?

The top is, in reality, only a ringless gyroscope, with
the end of its axis resting directly on the supporting
body. Ishall, therefore, attack these problems in the
same way that I did those of the gyroscope.

I take a tee-square, and hold it so that the arms are
in a vertical plane, and the other end of the leg rests on
the glass plate as in fig. 26, the instrument being inclined
at any convenient angle. If it be let fall from the posi-
tion indicated by the heavy lines to that indicated by
dotted ones the ends A and B will acquire motions each
of which can be decomposed into two, a vertical and a
horizontal, the former not represented in the diagram,
the latter indicated by the arrow m for the mass A, and
n for the mass B.

If at this moment, and before the arms stop, they are
instantly reversed—a process which will not affect mand
n, since it is at right angles to them—n, coming now on
the upper side, will push its end towards the left, while
m, for a similar reason, will push its end towards the
right. Together they tend to push the top back to its
first position. It is our gyroscope over again, and it is
unnecessary to go any farther. The same reasoning ap-
plies and we get the same result—the instrument seems
to defy gravity ; for although it really descends, it is
with so slow a movement that it requires several minutes
to reach the plane on which it is revolving.

The total velocity which gravity can produce is indi-
cated by the formula obtained for the gyroscope, viz.,
cosacos>_, where b equals the inclination of the axis to the
horizon, and a, the angle between the axis and a line

drawn from the ‘‘point’’ to the circle, which, in a top
128

ne a
) Cee

Nady

Cc. B. WARRING. 145

like mine, is the axis of the rim. Since cos b grows
smaller as b grows larger, it follows that the nearer up-
right a top is, the slower its descent and consequent gy-
ration. And, vice versa as it comes down, the more
‘apid the gyration.

By striking the axle of the top, in manner which I
shall explain hereafter, the inclination can be varied as
often as we please. In every case the result conforms to
our formula, the descent and consequent rate of hori-
zontal movement varying as does cos b.’

Hence those err, who attribute this increase to the
gradual loss of axial velocity from friction. The same
results, but in a somewhat less degree, would follow if
in some way the rotation of the top on its axis were
kept absolutely uniform.

The cause of the top’s horizontal motion is the same
that makes the gyroscope move in a similar manner.
There is the same process of reversing, and the same
pushing to the right and left when the arms are hori-
zontal. It is the same story throughout.

Why, when the top reaches the table, does it always
2o backward ¢

The lower side of the top goes in the same direction
that it gyrates. If b and b (fig. 27) represent the direc-
tion of the rotation of the disk, d will indicate the
direction of the gyration. Now, it is evident that ifa
wheel revolving rapidly on its axis, and at the same time
moving slowly in the direction of d, be set down on the
floor or on the table, the lower side will be stopped by
the friction, while the upper half will continue its
motion, and consequently send the wheel backward.
So with the top. The rim goes very fast, the centre
moves in the same direction that the under side does, and
when the latter strikes the table, the upper side sends
the top backward.

{It must be borne in mind that the top for these experiments must have a yery fine and
well-centred point.
129

146 AN EMPIRICAL STUDY OF GYRATING BODIES.

TOPS WHOSE ‘POINTS’? ARE NOT POINTS.

Few tops have fine and true points, accurately centered.
The great majority end either in truncated cones, or in
forms more or less nearly hemispherical. For the pur-
pose of studying the laws of such tops, a truncated cone
is to be preferred since in that case the size of the ‘‘ point”
does not vary, whilein spherical forms the ‘‘ point,’ 1. e.,
the amount of surface that comes in contact with the
supporting plane, varies with the inclination of the axis.

If we set one of the former going, we shall find, in ad-
dition to most of the peculiarities which have been dis-
cussed, certain others which stand in need of explanation.
For example, we shall see it start off im a circle of larger
or smaller radius, and after a series of movements in
gradually narrowing spirals, shall see it by degrees be-
coming more and more nearly perpendicular to the floor,
till the axis becomes vertical. Then it will stand for a
long time ‘‘sleeping,’’ as the children call it, until at
last it begins to incline to one side, and, in a moment
more, falls to the floor.

Before attempting to answer the questions that arise,
it is best to study experimentally the movements of the
top.

It is commonly believed that the top revolves in a
circle, more or less perfect, around the projection of its
centre of gravity. Fig. 28 is drawn to show this. It
represents the top as leaning towards the circle des-
cribed by its point, and whose centre is directly under
the centre of gravity. This is General Barnard’s idea,
as set forth both by a diagram and in the text on page
536, Am. Jour. Hd. vol. iv. He says also that the center
of gravity will have no horizontal motion.’ To deter-

1 General Barnard says that the centre of gravity will have an up-and‘down motion. To
this he attributes great importance, and regards it as the cause of the top’s staying up.
This appears to me to be an error, as was shown when treating the gyroscope. The top,

save from accidental disturbance, has no such vibrating movement, This will be shown
when we come to nutation.

130

Cc. B. WARRING. 147

mine whether this is in accordance with the facts, I
placed a fine point on my top, and set it spinning on a
plate of glass well blackened with smoke. The point
traced a clear line through the lampblack, and I was
thus able to see its path, the position of the axis, and of
the center of gravity. The result is shown in fig. 29.
In no case, save when the axis was vertical, did the
center of the top’s gyration correspond with the projec-
tion of the center of gravity. The radius of the small
circle was often twenty or thirty, or even fifty times less
than the distance from its center to the foot of the per-
pendicular let fall from the center of gravity. In all
cases, except when the axis was vertical, it leaned as in
fig. 29; that is, the point of support and the projection
of the center of gravity were always on opposite sides of
the center of the circle described by the former.

If the rotation of the top were absolutely without
friction, it would, as General Barnard says, revolve
around a perpendicular passing through its center of
gravity. But, in fact, there is resistance at both ends,—
that of the air, which is very small’, and that of the fric-
tion of the point on the glass, which is relatively large.
If the friction is such that the point cannot move at all, as
sometimes, when the point bores a little into the
glass, the gyrating center is at that point. When the
friction allows a little movement then this center is near
the point of the top, and so situated that the distance
from the point to the projection of the center of gravity
is divided by it into two parts, which are to each other
inversely as the friction at the point, and the resistance
of the air.

The important thing just now, for our purpose, is that
the top and its point are on opposite sides of the center
of that circle, and consequently move in opposite

1 The resistance here spoken of is not the friction of the air on the surface of the top,
but that which opposes the gy.ation. and as this is very slow, the resistance is very small,

131

148 AN EMPIRICAL STUDY OF GYRATING BODIES.

directions, while the rotation of the axle is necessarily
the same in every part.

With these facts in view we are prepared to attack the
problems which its movements offer.

Why does a top rise? Itis a real rise, for the center
of gravity becomes actually higher. It may start from
a great degree of obliquity, and rise to a vertical.

I have already noted the fact that a top with a suffi-

ciently fine and well-centered point never rises. We -

must, therefore, take one of a different form.

We shall quickly see why. The most convenient
‘‘point’’ that I have found is a truncated cone, that
marked c, fig. 25. The smaller diameter should not ex-
ceed one eighth of an inch ; one-twentiethis better. Iplace
this on my top, and set it going, the axis being inclined,
as Shown in fig. 80. Since in all cases—save the impos-
sible one of no friction—the top gyrates around a point
between d, the point of support, and g, the foot of the
perpendicular let fall from the center of gravity, it fol-
lows that if, at any moment, c is coming towards you, d
is going from you. In other words, c and d, like the op-
posite sides of a wheel, move in opposite directions.

It has been shown that the top gyrates in the same
direction that the under side moves, and being all one
piece, the cone, or ‘‘point,’’ revolves on its own axis
(which is also the top’s) in the same direction. Hence,
d, by its friction, pushes its end away from the observer,
and, of course, makes the other end, c, approach him
more rapidly than it otherwise would. Fig. 31 will
make this clearer. Here we have a wheel on the end of
a shaft, free to move horizontally around the support a,
the rim resting on the surface of the table. Now, if the
wheel is made to revolve in the direction of the small
arrows—the lower side coming towards us—the end, b,
on which the wheel is, will be made, by the friction on

the table, to recede from us, and the other end to ap-
182

Cc. B. WARRING. 149

proach us. It isin this way that the vis viva of the top
is expended in accelerating its gyration, and this accel-
eration makes it rise.

To see the reason why, let us suppose our top (fig. 30)
is turning on its axis in the direction of the arrows, and
is gyrating with all the speed gravity can give it. In
some way, push c towards you, i. e., accelerate the gyra-
tion ; b will, in consequence, get an extra (if we may use
the term) motion to the right, and a to the left. Ina
fraction of a second, a will beata’, and bat b’, each push-
ing in the same direction as before. But pushing a’ to
the left and b’ to the right means tilting the top towards
a vertical. It is as if a string tied ata’ had been pulled
horizontally to the left, and one at b’, horizontally to the
right. Such pulling, it is easy to see, would tend to
make the axis vertical. In fact this is only another in-
stance of the working of our ‘‘first law’’ of gyrating

bodies.
THE SLEEPING OF THE TOP.

If a top, having for a ‘‘point’’ either a truncated
cone, or some form resembling a hemisphere, is set go-
ing with its axis inclined, it will rise to a vertical, and
remain so quiet that, in common parlance, it is said ‘‘ to
sleep.”’ If disturbed, it quickly returns to its upright
position, and resumes its sleep. Every one has seen
this, and wondered why the top should do so.

Disturbing an upright top, means tilting it, and that
causes it to rest on one edge of its ‘‘ point ;’? and when
this happens, it strives, as was shown when answering
the last question, to rise to a vertical. Every disturb-
ance, therefore, results in a force sending it back to an
upright position ;—and there is no counteracting force ;
therefore, it stays there, or ‘‘ sleeps.”’

A hemispherical ‘‘ point”’ is best for this purpose,
because, when erect, it meets, if running upon a glass

plate, or other hard and smooth surface, almost as little
188

150 AN EMPIRICAL STUDY OF GYRATING BODIES.

friction as does a point, while, if inclined, the friction is
only the same as for a truncated cone.

A sharp point on a hard and smooth surface will
gyrate, but will not really “sleep.’’ The least disturb-
ance will throw it out of the vertical, and once out it
will not go back.

From all that we have done, we may draw these gen-
eralizations :

(1.) Fora top to become upright it is necessary that
the point of contact with the supporting plane should
not be in the axis of rotation.

(2.) The tendency to become upright is proportional
to the distance this point is from the axis.

We have all noticed how some tops run about the floor
when spinning, and, doubtless, have wondered why they
behave in this manner.

To show the reason, we take a top ending in a truncated
cone measuring, for example, one-eighth of an inch
across the lower surface. It revolves on its axis—any
good top does—some thirty or more times a second. If
the axis is inclined, the weight comes on the edge of
this small surface, but as that revolves, say, thirty times
in a second, it tends to roll along twelve or thirteen
inches in that time. If the ‘‘ point’’ is larger, of course
the top will roll along faster, and vice versa.

Sometimes it is desirable to change the obliquity with-
out much disturbing the top. Suppose fig. 29 is such
atop, and that it is revolving as indicated by the small
arrows. The gyrational, or precessional, movement
will be from the observer. Now with a small light stick
—a lead pencil is excellent—strike the axle near its up-
per end a smart, horizontal blow, taking care to strike
squarely and firmly. If the blow isstruck from behind,
the top will rise towards a vertical, and a succession of
blows will put it in that position. But, if the blow is
delivered in front, the obliquity will increase.

1384

C. B. WARRING. 151

Why is this? Fix the mind on two points in fig. 29,
which, at the instant of striking, are at the ends of a
horizontal diameter, calling the one nearest the observer
x and the other y. The blow in the rear tends to tilt
the instrument in such a manner that x moves away
from the ‘‘ point’’ of the top. More exactly speaking,
it moves for the initial instant parallel to the axis.
Motion once imparted continues forever, or till some
work is done by the moving body. Therefore x, when
in the course of its very rapid rotation,'it comes on the
under side of the axis, will push that side in the same
direction, which means raising the top towards a vertical.
The mass, v, at the initial instant goes downward, but
being brought on the upper side of the axis by a semi-
revolution, its influence aids that of x.

If this is understood, it will be easy to see why strik-
ing the axle in front makes it more oblique, and causes
it to gyrate more rapidly, while striking it behind makes
it gyrate less rapidly.

Both cases are merely illustrations of our first and
second laws.

Instead of striking the axle of the top with a stick,
it is, in some respects, a better plan to insert a small

1 Two important remarks occur to me here, which are equally applicable to all gyrating
bodies.

1. ‘Rapid rotation.’ All gyrating effects may be produced with slow rotation, provided
the action of gravity be neutralized (as in fig. 2), and the tilting force due to gravity be
replaced by a more moderate force, the pull of a string, for example. The necessity of very
rapid rotation is a mere accident, dependent upon the degree of strength and constancy of
the pull.

2. If when x comes on the upper side it tends to pull the top towards a vertical, why, when
it returns to the lower side, does it not pull the top back again ? Simply because it expanded
all its energy in lifting. To do anything more there must be a new influx of energy, and
this can only come from a renewal of the fall. There is, therefore, a constant gain of energy
by the top from the fall, and an expenditure in lifting. As the lateral motion requires no
expenditure of energy, it would seem as if those were right who say that, but for friction,
the top would stay up forever.

The explanation given for the gyroscope applies here. The fall during the instant a
section is horizontal imparts equal momentum to each end of it, and in the same direction,
viz., downward. Consequently, when the plane of the section becomes vertical, there is
from this source no upward tendency. Hence a top will fall even ina yacuum and with-
out friction,

135

152 AN EMPIRICAL STUDY OF GYRATING BODIES.

wire an inch long or so in the small hole at the end of
the axle, and then to place over it a small loose ring
with eight or ten inches of string attached. By pulling
backward or forward, the same paradoxical movements
will be produced that were produced with the stick.

ANOTHER PARADOX.

If we wish to make our top gyrate more slowly we
must strike the axle from behind; in other words, at-
tempt to push it along faster. It will show its contrari-
ness by going slower. To make it go faster we strike it
in front, as if we meant to stop it.

The philosophy of this is equally simple. The gyra-
tion, as has been shown, increases with the load. The
nearer the top is to a vertical, the less is that part of the
load which tends to tilt it. This part, for distinction,
may be called the effective load.' I have shown that
striking the top from behind causes it to rise, and the
nearer the axis is to the vertical the less effective the
load becomes ; and, in consequence of that, the gyration
or precessional movement grows less rapid.

TRACINGS MADE BY THE TOP.

The paths described by the ‘‘ points” are very curious
and beautiful. They may be preserved by using a large
pane of smoked glass for the points to rest on, and after-
wards, flowing the traces with demar varnish.

No description can do justice to the exquisite beauty
of these paths. They are spiral, large or small, accord-
ing to the size of the ‘*‘ points’’ and the obliquity of the
axis.

The path is a remarkably regular spiral, generally
largest at the beginning, but very gradually diminishing
to the end. Ina few cases, the spirals remained of uni-
form size. These were very small—possibly one-eighth

1 It varies as the cosine of the obliquity.

136

Cc. B. WARRING. 153

of an inch in diameter. In one case, the curves began,
say, three-eighths of an inch in diameter, gradually grew
a little smaller, and then as gradually grew larger. In
another case the spiral was decidedly smaller at the
beginning than at the end.

When the point is not properly centered, each line will
seem strung with dew-drops placed with the utmost
regularity, each corresponding toa revolution of the top
on its axis.

It may help us to see the reason for the varying size
of these spirals, if we reflect that the less the friction of
the ‘‘point’’ the greater the distance from 0, fig. 30, the
center of the gyrations, to d, the point of contact, and
consequently the greater the radius of the curve de-
scribed. The rolling of the *‘ point’’ always tends to in-
crease the rate of gyration; but its influence varies
directly as its size (diameter), and inversely as its dis-
tance from the center of the spiral, and also directly as
the rotation of the top.

As the top rises, g, the projection of the center of
gravity (fig. 80), moves nearer to d, and consequently
the distance from o, the centre of gyration, to d, grows
less, and therefore the spirals also grow smaller, at last
becoming only a point.

The abnormal forms which sometimes occur are due to
changes of condition which it isnot always easy to trace,
but which are reducible to the same principles.

THE GYROSTAT.

This instrument was invented by Sir Wiliam Thom-
son. It is described in Thomson & Tait’s Watural Phi-
losophy, page 397, also in Wature, Vol. xv., page 297.
In both of these there is a drawing ofit. As there repre-
sented, it is rather an expensive and formidable instru-
ment; but, at a very trifling expense, any gyroscope
san be turned into an excellent gyrostat.

is 7

154 AN EMPIRICAL STUDY OF GYRATING BODIES.

The specific difference between the two is that the
gyroscope is supported on a point at one end of the axis,
while the gyrostat rests on a point in or near the plane
of the wheel’s equator. By changing the position of
this point the same instrument assumes the character-
istics of either gyroscope or gyrostat.

Fig. 32 represents my gyrostat with itsadjuncts. The
latter consist of two semi-circular troughs of tin, so
made that nearly half of the ring of the gyroscope fits
snugly into them—so snugly that they will not easily
come off.’

Now place the ring of the gyroscope in either of the
troughs. Put the ring in the vise, turning it upside
down so as not to injure the tin. Set the wheel in rapid
motion. Take the instrument out of the vise and set it
down on a glass plate some ten or twelve inches square.

Instead of tilting over, it will stand with remarkable
steadiness. You may use it roughly—may strike with
sufficient force to send it across the glass—without per-
ceptibly disturbing its upright position. You may strike
on either end (at S or T) as severe a vertical blow with
a hammer as you dare, lest you injure the instrument,
and vou will make but little disturbance.

There, as in the gyroscope, the resistance is propor-
tioned to the force applied. A gentle, continuous push,
or pull, will upset it more easily than willa severe blow.

If the wheel revolves very fast, and is nearly or quite
vertical, the instrument will, for a considerable time,
show no indication of falling. After a while, however,
it will be seen to be leaning over more and more, and at

1 To make these troughs, lay the ring of the gyroscope flat on a sheet of tin, and mark an
almost semi-circle on each side, twice as many, of course, as you want troughs. Cut out
half as many straight strips somewhat wider than the thickness of the ring, and solder so as
to make a bottom to each trough.

Cut out of heavy tin the pieces A and B. It will be convenient for certain purposes here-
after to make one strip, e. g., A, five or six inches long, with loops at twocorners. Cut B of
the same length, and slightly curve the under side, like the diagram. Solder each to the
middle of a trough and at right angles to it. Across A, and about two inches apart, solder
two stout sharp pins.

138s

ee

co. B. WARRING. 155

the same time revolving around a vertical axis in a
direction dependent upon the way the wheel revolves
and the direction in which it leans. If either of these
be changed the instrument goes the other way. If both
are changed it is unaffected.

The rationale of these movements is no more difficult
than of those already considered. In fact it is the same
thing slightly modified. Let fig. 33 represent our in-
strument with wheel in rapid rotation. Suppose it falls
a little towards the observer. Any molecule on the
upper side, e. g., m., will, by that fall, acquire a motion
in the same direction. Suppose it to be carried in an
instant to the position p ; it will tend to push that side
of the instrument towards the observer, and since the
friction at the point where the curved edge rests on the
glass plate is almost zero, q, will, at the same instant,
recede from him. In another exceedingly small fraction
of a second, q will be at the top while still receding,
and consequently it will tend to push the top back toa
vertical.

If m had tilted from the observer at the start, the ro-
tation of B A, which in the first case was with the hands
of a watch, would have been in the opposite direction.

It will be seen that horizontal rotation of B A is neces-
sary in order that the instrument should stay up. The
rotation, or angular motion may be exceedingly small,
but there must be freedom for it to exist, or the gyrostat
will fall.

Experimental proof: Set the knife edge B A ina
groove so that it can move neither to the right nor left,
and it will fall as quickly when the wheel is rotating as
when it is not.

Or, use the piece with pins, fig. 32, H A. Set the
wheel in motion, and place the instrument on wood. It
will fall at once ; place it on glass, it will stay up. In

the first case, the points entering the wood prevent hori-
1389

156 AN EMPIRICAL STUDY OF GYRATING BODIES.

zontal rotation, and the instrument falls. In the second
case, they slide on the glass, thus permitting horizontal
rotation, and the instrument stands.

Instead of tilting the gyrostat, we may attach a weight
to one side, say, at T, fig. 832. The effect is the same.

A very pretty and instructive experiment is as follows :

Set the instrument, fig. 83, going, and place it on a plate
of glass. After a time it will begin to lean, say to the
right, and to gyrate more and more rapidly as the incli-
nation increases. Now apply with the finger, or in any
other way, to the side of the foot-piece, a very slight
pressure, in the direction in which it is moving (i. e.,
hurry it)—the instrument will at once straighten up.
Retard the foot-piece by gently pressing the other way,
and the fall will be increased. It requires some effort
to do this aright, for when a thing appears to be about
to fall we instinctively put our hand in front of it to
stop it; but in this case, to put our hand in front of
the instrument, would accelerate its fall, while pushing
from behind is the way to stop its falling; and more
than that, if it is almost down, pushing from behind
will make it become upright. From this contradiction
of our experience, we are very apt to put the pressure
on the wrong side.

Rationale: The mass q will be pushed from the ob-
server, and hence, when it arrives at top—remember it
loses no energy in this motion—it pushes the top from
the observer. On the other hand, p expends its energy
in trying to make the supporting edge slide towards the
observer. The friction almost wholly prevents this.

Experiment: Remove B A, and substitute for it a
similar knife blade considerably longer than B A, with,
however, the lower side concave, so that the instrument
rests on the two extremities. Set the wheel to rotating
as before, and place it on the glass plate. It will fall at

once, if the foot is long enough.
140

Cc. B. WARRING. 157

Rationale: Friction prevents the foot-piece from re-
volving horizontally. Hence when the top molecule, m,
tilts towards the observer, and moves towards p, it can-
not push the opposite molecule, q, away from him, and
consequently q will, when it arrives at the top, be desti-
tute of any tendency to push that portion away from
him, or, in other words, it will have no power to push
the instrument back to its place.

THE GYROSTAT ON STILTS AND ON WHEELS.

Fig. 334, plate II, shows another form of gyrostat. It
explains itself, except, perhaps, that I should say that
the little wheel is placed so that its axis is approximate-
ly in the plane of the large wheel, and that its frame is
connected at a, rigidly with the frame of the gyroscope.
The point d may either rest in a loose socket, or may
be free upon the surface of the glass plate x y.

Set the wheel in motion, and let it slightly lean to-
wards the observer; the whole system will begin to re-
volve around d in the direction of the arrow m. Let it
lean the other way; at once the little wheel will begin
to go backward. In either case, the leaning will slowly
increase (velocity m also increasing at the same time), un-
til at last the instrument falls. That the fall is not in-
duced by the loss of velocity on the part of the gyroscope
wheel from friction, is evident, because the machine may
be set up and made to go through the process several
times with one winding of the wheel; and, furthermore,
the fall will be very greatly accelerated by friction at the
axle of the little wheel, or by obstructions in its way.

If, in any case, when the instrument is falling, e. ¢.,
towards the observer, pressure be applied at o, in the
same direction, it will become vertical again.

Rationale: That of the horizontal motion is the same
as in the previous experiments. The rationale of the

rise to a vertical is in principle the same, but somewhat
141

158 AN EMPIRICAL STUDY OF GYRATING BODIES.

different in its application. ifa particle on the wheel at q
be pushed horizontally towards the observer it will retain
its momentum when it arrives ats. At the same time h
will, relatively to the centre of the wheel, move from the
observer and, retaining its motion when it gets tor, the
joint effect of the two particles will be to tilt the wheel
from the observer, or in other words, towards a vertical.

Another and very curious experiment is described by
Sir William Thomson, page 389, Thomson & Tait’s Wat.
Phil., where is an excellent drawing of his form of the
instrument. He calls it a gyrostat on stilts, but says
very little by way of explanation.

Fig. 34 will give a correct idea of my machine. Atba
stout wire is soldered, ending in an acute point, which
rests loosely in the socket a. At d and e are similar
sockets, in which a double-pointed wire rests with great
freedom to move in any direction.

Set the wheel in rapid motion. In a moment or two
it will begin to sway towards and away from the ob-
server (who is supposed to stand here as in all the ex-
periments with right hand opposite b, and left opposite
d). These swayings slowly increase in extent till the
instrument falls. The fall is not due to loss of rotary
velocity, for the process can be gone through several
times with once setting the wheel going.

If, by sliding a sleeve from the wire to the frame
(or by any other means), the joint d becomes rigid, the
swaying will not occur. On the contrary, the instru-
ment will fall at once. This last is merely an illustra-
tion of the principle before pointed out, viz., that the
knife-edge must have freedom to move laterally.

Take off the sleeve so that d is free again, then re-
move the socket e. If the supporting surface is so smooth
and hard that the point e moves over it almost without
friction the instrument will at once fall. If e cannot

slide, the instrument will stand.
142

Cc. B. WARRING. 159

Again: Remove the wire, de, support the end of the
frame, d, by a cord from the ceiling, and set the wheel
in rapid motion.

The instrument will begin slowly to revolve around
ab, but will fall before making a revolution, probably
before going 90°, the distance depending upon the
length of the string and its position.

This experiment proves that the cause of the swaying
is in some way connected with the rod d e.

The rationale, I think, is dependent upon that law of
which we have had so many illustrations, viz., accel-
erating the horizontal movement causes the instrument
to rise. IfI push it towards me, g gets a horizontal
momentum, which, when at the bottom, tends to throw
that part towards the observer, i. e., to cause it to re-
volve around an axis passing through d a, and hence
to throw h away from him.

If, therefore, h was leaning forward, the effect of my
pushing would be to throw it, h, back to the vertical, or
even beyond. If it went beyond, then the tilting would
be the other way, and the push should be applied so as
to cause d to recede from the observer, and this would
send h back to the vertical.

The question remaining is, Where does the accelera-
tion come from #

Of course, it is impossible to place the instrument in
stable equilibrium. The moment d e ceases to be ver-
tical, d falls with a velocity depending upon the short-
ness of the wire, while h would fall at a slower rate, be-
cause of its greater distance from the supporting points,
on the well-known principle of the pendulum, the
longer the rod the slower the motion (inversely as the
square root of the length). Therefore, as d_ inclines
toward the observer, the rod d e pushes d more rapidly
than it would go under the influence of h alone ; in other

words, it accelerates d, and consequently the instru-
148

160 - AN EMPIRICAL STUDY OF GYRATING BODIES.

ment is thrown back to the vertical, and by the peculiar
and indescribable twist or rolling motion, which is pro-
duced by rotation about the axis d a (the twist must be
seen to be understood), the instrument tilts the other
way, and the whole process is gone through again,
causing quite a number of vibrations, each of greater
amplitude than its predecessors, till at last the instru-
ment falls.

Experiment: Replace the wire p d (fig. 334), by a
wheel, the same as is attached to the other end of the
frame at o. The instrument is then mounted upon two
wheels (see fig. 343, plate Il), whose axes are approxi-
mately in the plane of the large wheel ; (there is no need
of exactness here). Set the wheel in motion, and place
the instrument on asmooth, hard surface ; (glass is best).
It will stand up with great firmness, and execute a re-
markable series of pirouettes.

Rationale: There is nothing new here, and no further
explanation is needed.

If we call the point at which there is freedom of motion
a joint, there is only one joint in a gyroscope, and one
in atop; there is only one in the common gyrostat.
About these joints there is also horizontal rotation.
With the gyrostrat on wheels there are two joints ; but
at least one must have liberty to revolve around the
other. They both may move; but if both are unable to
move, the instrument falls. With the gyroscope on
stilts, there must be three joints; and the two points of
support must not change their position. If neither leg
has a free socket at top the instrument will fall, or if
both legs have it; or, if with one free socket at top,
either or both bottom joints are free to change their
positions, the same result follows.

GYROSTATIC TRAPESE AND TIGHT ROPE PERFORMANCES.

By means of the loops n and m, fig. 32, attach the
144

Cc. B. WARRING. 161

eyrostat to a wire yoke, and then suspend from the ceil-
ing, as fig. 365.

Set the wheel in rapid motion, and leave the machine
to itself. It will keep its vertical position, although
swung back and forth and roughty handled.

The explanation is the same as when the gyrostat
stands on a plate of glass. There is the same rapid re-
versal of positions and consequent play of forces as was
seen in fig. 33. .

STABILITY.

By stability I understand that condition or property
by which a body, if disturbed from its position, returns
to it unless forcibly prevented. The body is said to be
stable. A weight hanging below the point of support is
stable. A rod balanced on its lower end is unstable.
A body, therefore, in a stable position, will never leave it.

If these definitions are correct, and if Thomson &
Tait use the word in that sense, their statements on pp.
397 and 398 appear not to bear the test of experiment.

Out of their seven ‘‘stabilities,’’ only one (viz., No. 1,
p. 399), is stable in the above sense.

If we define stability to be nothing more than resist-
ance to acceleration of motion, then their seven ‘‘sta-
bilities ’’ are justified by experiment ; i. e., if you push
the gyrostats out of position faster than they are going
of themselves, you will feel a resistance.

There will not, however, be a going back to their posi-
tion, except in case of the stilted gyrostat, where ap-
parently there is an exception. It does go back to its
first position, but does not stop there, as a stable body
would. It goes beyond and then back, each time in-
creasing the amplitude of the are, till it falls. This can
hardly be called stability.

GYROSTATIC TIGHT ROPE PERFORMANCE,

There is a form of the gyroscope, fig. 36, which is often
145

162 AN EMPIRICAL STUDY OF GYRATING BODIES.

seen in the hands of the street toy venders on Broadway,
New York. Almost any pleasant day they may be found
exhibiting before an interested little crowd. All that is
needed for such exhibitions is a piece of smooth hard
cord eight or ten feet long, and a somewhat peculiar
gyroscope. Onthe ring in line with the axis are soldered
two small round projections, one at each end. One of
these is solid ; the other has a slot in it about the size
and shape of the slot in the head of a common wood-
screw. The solid end acts as the point of a gyroscope,
or top, and presents nothing peculiar. It is with the
other end that we have to do. The wheel is set in rapid
motion, and then the instrument is placed on the string
which has been fastened securely to an object sufficiently
distant to draw it taut, (fig. 36). The slot straddles the
string. The exhibitor raises the end next to him, and
the gyroscope moves securely down the incline. Then
he lowers the same end, and the instrument slides back.

Why does it not fail off ?

Let fig. 37 represent a section of the wheel and its axle,
omitting the ring and the upper half of the shaft (we
thus get our tee-square again). The slit for the string is
seen at a, and just above, at d, is the pivot on which the
axle revolves with little friction. Suppose the tee to be
vertical. In a moment it begins to tilt, b, for example,
going up and ¢ going down. As soon as this is done—
say in one-fiftieth of a second —suppose the tee to be in-
stantly reversed ; b will continue going up and e will
continue going down, and this means pushing the tee -
back towards its first position. There will bea little loss
each time, but the principle is the same that we have
considered in case of the gyroscope and top. In reality,
a gyroscope thus placed is only a top in a frame, and is
subject to all the laws of a top, the frame merely keeps
it from slipping off the string. No farther explanation
is needed.

146

Cc. B. WARRING. 163

THE GYROCYCLE.

If a broad band (or hoop) be put snugly around the
gyroscope, an instrument (fig. 38) will be formed, differ-
ing from either thus far described in the fact that the
centre of form, of gravity, and of motion, coincide.

A tinsmith will make such a band (about two inches
is a good width) for a trifle. The most remarkable thing
about this is its repugnance to rolling down hill,’ and its
fondness for turning a rectilinear movement into a
spiral one.

If the reader understands the previous instrument he
will find no difficulty with this.

BOHNENBERGHER’S MACHINE.

This instrument, as usually constructed, consists of a
sphere concentric with three rings, so arranged as to
give freedom of movement in all directions, while the
centre of gravity and form is a fixed point.

In my experiments I have used a form of my own
devising, which affords greater facilities for the study of
the horizontal and vertical movements than do any of
the instruments which I have seen figured in encyclope-
dias, or elsewhere. Itis represented in fig. 39, and con-
sists of a common gyroscope suitably mounted. In the
plane of the wheel are two pins, y y, screwed into the
ring, as nearly as possible in a horizontal line, passing
through the centre of gravity.

They rest in slots in the semi-circular brass piece,
y A y, and permit the ring to revolve on them with very
little friction. The ring in the diagram is represented
as horizontal, so that only its side is seen. Attached to
this, and in line-with the axis, isa pin, B, to whicha
weight can be attached.

T used the wheel instead of a sphere, simply because I
a The only limit to the steepness of the inclined plane is lack of friction, If smooth and

too high, the gyrocycle will slide down it—not roll.

ILeayy

164 AN EMPIRICAL STUDY OF GYRATING BODIES.

happened to have it. But in fact the wheel, in pro-
portion to its mass, is more efficient. The results are the
same with either.

A is a conical steel point, very fine and hard, resting
in a polished cup of hardened steel. Two stout wires
are firmly screwed into the brass semi-circle, and by the
two weights attached, lower the centre of gravity, and
give stability to the instrument when balanced on the
point A. Two small hooks, h h, are used when it is
desired to suspend the machine from the ceiling. The
arrows denote the direction of rotation.

Now set the wheel to revolving in the direction of the
arrows o o. It will run perhaps ten minutes, but no
other motion will be produced. Attach a weight to the
pin, B. The instrument will at once start off in a hori-
zontal movement in the direction indicated by the di-
rectional ellipse around the standard. As the instru-
ment is carefully balanced in every way, and moves with
very little friction, a fiftieth part of the same weight on
the pin before the wheel was set revolving would at once
have tilted it till the axis was vertical, but now, ap-
parently, it does not tilt at all. This, however, is an
illusion. It is slowly tilting so that the weight is de-
scending all the time-—a fact that in a minute or two be-
comes very evident. Here, as elsewhere, we have the
law. No fall, no gyration.

We have in the Bohnenbergher some of the problems
that met us in the gyroscope. The rationale is equally
simple. The weight on B causes the axle to tilt down a
little ; that makes the lower 0 move from you; as it
rises in its rotation to the horizontal line, having lost no
energy, it pushes that end (the right hand of the figure)
from you. This causes the gyration ; and, as it rises to
the top, it pushes that side from you. And, pushing
the upper side from you, means pushing against the

weight that seeks to pull B down. The upper o goes
148

©. B. WARRING. 165

through a similar round, and aids in producing the same
result.

In fig. 40 we have the same thing. A B represents a
section of the wheel with its axle M N, and standing so
that the eye is supposed to be in the plane of the wheel.
The centre, c, is immovable, while permitting freedom of
all other parts. The dark lines represent a section
while the axle is horizontal. The dotted lines repre-
sent the same after reversal. The arrows denote the di-
rection of the different motions.

The momentum which B gets from the pulling of w,
would, when B is on the upper side (at B’), push it back
to the vertical, but it has to meet the continued action
of gravity on w as well as its (w’s) momentum. It can
overcome only one; consequently, the other carries it
down.

There is the same struggle between the action of
gravity and the momentum of the previous instant, as
in case of the gyroscope, resulting for the same reasons
in a uniform and very slow rate of fall ; and this, in its
turn, is reduced to almost zero by the acceleration of the
lateral or gyrating motion.

It is found also, that the ‘‘ time of staying up’’ varies
directly as the angular velocity of the wheel, and, in-
versely, as the load. Conseqently, whatever the velocity,
short of infinite, the weight descends. Any other con-
clusion would bring the same absurd result that we
found in case of the gyroscope ; to wit, infinite power
of resistance so long as the rotation continued uniform.

If, while the Bohnenbergher is in operation, the finger
be pressed with some force upon the upper side of the
axle, the side which is pressed down will rise even
though a considerable load is attached. It is another
paradox ; pressing down either side makes it rise. It
does apparently just what it ought not to do.

The explanation is this. In the first case the reaction
149

166 AN EMPIRICAL STUDY OF GYRATING BODIES.

against the finger accelerates the gyration and by our
first law, causes the weight to rise; while the reaction on
the other side retards the gyration, and, therefore,
causes the weight to fall.

All through it is the same story as was told about the
gyroscope. In fact, the Bohnenbergher is really a gy-
roscope, whose point of support is at the centre of
gravity. It presents no difficulties not easily solved by
one who has mastered that instrument.

The ‘‘four laws’’ apply to both, and are as easily
verified for the one as for the other.

THE EARTH AS A GYROSCOPIC BODY.

Whatever be the value of the explanation which I
have offered of the curious phenomena which we have
been studying ; whether it will or will not bear the test
of analysis, it at least has great advantages as a working
hypothesis. It seems to account for all the paradoxical
behavior of gyroscopic bodies; and it certainly enables
us to predict what they will do in new and untried con-
ditions.

But, should this explanation prove to be incorrect or
insufficient, and be brushed aside as worthless, yet there
will still remain a body of curious results resting upon
no theory, but upon the solid ground of experience.
Among these is the following law:

If a body revolving upon an axis passing through its
centre of gravity, be acted upon by a force tending to
make it revolve around another axis perpendicular to the
first, it will, if perfectly free, take two movements or
rotations ; one in the direction of the applied force, and
the other at right angles to it. There will be no
change in what may be called the geographical position
of the first axis, and the body will continue to revolve

about it with its angular velocity unaffected.
150

Cc. B. WARRING. 167

There will therefore be three rotations:

1. That around the original axis.

2. A lateral rotation or gyration.

3. A tilting in the direction of the applied force.

Frisi’s celebrated law differs from this. He says:
‘‘ When a body revolves on an axis passing through its
centre of gravity, and a force is impressed upon it tend-
ing to make the body revolve about another axis also
passing through its centre of gravity, the body will re-
volve about neither, but a third axis, which lies in the
same plane with the other two,”’ etc., etc.’

This law includes in itself three distinct propositions :

1. ‘*The body will not continue to revolve around the
original axis.”’ But we have seen that it does.

2. ‘*The body will not revolve around the second
axis.’’ But we have seen that it describes at least a part
of a revolution around the second axis.*

3. ‘The body will revolve around a third axis, which
lies in the same plane of the first and second axis.’’ As
it stands, this also is not true. If by the ‘‘ third axis”
is meant the first axis in a new position, still it is not
true unless we also suppose the plane passing through
the first and second axis to revolve on the latter.

The most important discrepancy is found in the asser-
tion that there will be no movement of rotation around
the second axis, i. e., no tilting under the operation, and
in the direction of the second force.

I propose to apply these principles to our earth in its
actual astronomical conditions.

In all laboratory experiments upon gyrating bodies—

11 add the rest of this famous law: ‘‘ And so situated as to divide the angle which they
contain into two part, such that the series of the parts are to each other in the inyerse ratio
of the angular velocities with which the body would have reyolyed about the said axes
respectively.”

2‘ A part of a revolution.’ This ‘‘ part’? may be almost 180° ; but cannot be more than
that unless the direction of the applied force is changed. By judiciously changing that, the
body can be caused to make as many revolutions as you please around the second axis.
The force in the case spoken of above ceases to cause any tilting when the line of its direc-
tion passes through the fixed point of the gyrating body.

abeyal

168 AN EMPIRICAL STUDY OF GYRATING BODIES.

the weight which causes them to tilt—and which, for
convenience, may be called the tilting force, acts upon a
point in the axis, or axis produced, and it may be thought
by some who have not reflected upon the matter, that a
force applied elsewhere might not produce the same ef-
fect. To make the case as different as possible, we will
suppose the second force to be parallel to the axis, and
applied at the equator, but in such a way as to allow per-
fect freedom of rotation—a thing easily imagined but not
easily attained with laboratory appliances. Furthermore,
because it suits my purpose better, we will suppose the
gyrating body to be asphere. If we imagine this force
to pull upon an inextensible cord running to the pole,
and moving without friction over the surface as the body
revolves, we shall have the same amount of force tangent
at the pole, acting in the same plane, and tilting the body
in the same sense. Hence, so far as tilting is concerned,
we may indifferently speak of a force perpendicular to
the equator, or to the axis at the pole, provided the
plane in which it lies is the same.

It is hardly necessary to remark that the size of the
gyrating body is a matter of indifference; whether, for
example, it be one inch in diameter, or eight thousand
miles, since all bodies are equally obedient to the laws
of motion. We may, therefore, apply gyroscopic laws
to the movements of our earth as if it were no larger
than our gyroscopes and Bohnenberghers.

If our earth were a perfect sphere, it would revolve
upon its axis and travel on its journey around the sun,
as now. ‘lhe moon would accompany it, and would wax
and wane as now, and to all, save to astronomers, there
would be no difference between what would then appear,
and what we now see. In such a case, the attraction of
other bodies would have no tendency to change the
direction of the earth’s axis, since the influence upon one

152

SS

GC. B. WARRING. 169

part would always be counterbalanced by that upon
another symmetrically placed.

But the earth is not a sphere. Encircling its equator
is an immense protuberant ring inclined 233° to the
ecliptic. The part of this protuberance towards the
moon, or the sun, being four thousand miles nearer to
them than is the centre of the earth, is attracted by them
more strongly than the spherical part, which may be
regarded as if its mass were a point at the centre. The
opposite part of the ring being four thousand miles more
distant is attracted less strongly.

The effect of this difference is easily seen in fig. 41.
If S (the sun or the moon) pulls A more strongly than it
pulls c, A will tend to tilt in the direction of the small
arrow, m.. And if cis pulled more strongly than B, it
will tend to go towards 5S faster than B, or what is the
same thing, B will pull back, and, as a consequence,
take the direction of the other small arrow, n. Notice
that m and n act together, and tend to lessen the inelina-
tion of the equator to the ecliptic. In six months the
earth will have moved to the opposite side of the sun, and
a similar tilting tendency will be produced, and here, as
before, the effect is to lessen the obliquity of the equator.
In either case, and consequently, in all cases, the tenden-
ey of the solar and lunar attraction is to make the
earth’s axis more and more nearly perpendicular to the
plane of its orbit.

This tilting force varies greatly, reaching its maxi-
mum when the ring experiences the combined ef-
fect of the sun and moon, when at time of conjunction
or opposition, both happen to be in perigee, and the moon
and the equator to be on opposite sides of the ecliptic
and the sun at one of the solstitial points. For then
they are nearest to the earth, and have, if I may so

1 The small arrows spoken of above have been omitted by the engraver. They are seen,
however, although not lettered, on the right hand part of the diagram.

153

170 AN EMPIRICAL STUDY OF GYRATING BODIES.

speak, each its greatest possible leverage ; moreover, in
this position, the tilting forces of the two bodies act so
as to aid each other ; or, in other words, the total effect
is the sum of the individual effects.

From this maximum the tilting force runs down to
nothing, when the declination of sun and moon is zero.

As already said, two movements are produced, one at
right angles to a plane, through P, c, and 8, and the
other in the direction of the pulling force, or towards S.

Of course these’ combine into one, but it is more con-
venient to consider them separately.

We will study the lateral motion first. This move-
ment being affected by the earth’s orbital revolution, re-
sults in that peculiar change in the position of the
nodes, or equinoxes, which astronomers call

PRECESSION.

While studying this phenomenon we must constantly
remember that we have here only a particular case of the
effects of changing momentum from one side of a fixed
point to the opposite, as we have seen them developed
in our reversing tee-square, and illustrated in our Bohn-
enbergher and top.

Let fig. 42 represent the earth at time of winter solstice,
as seen from some remote point in the direction of the
pole of the ecliptic, and let the paper represent the
plane of this circle. Let the large arrow denote the di-
rection of the earth in its orbit.

The solar attraction causes the protuberance, A, to
move towards the ecliptic with a certain small but real
velocity, as indicated by the small arrows, m and n, fig.
41. The effective component of the downward pull is
not the tangents, m and n, but perpendiculars from A
and B to the ecliptic.

1In case of the earth, the lateral movement is much the larger, and this is generally so
in laboratory work also ; but, sometimes, it is the smaller, e. g.. when the velocity of rota-
tion is small and the downward, or tilting force, great.

L542

‘ Dek

Cc. B. WARRING. Tl

The earth’s diurnal rotation, being at right angles to
this tilting movement, neither increases nor diminishes it ;
consequently, therefore, when A (fig. 42) comes to X, or,
more accurately speaking, to X’—for the lateral move-
ment of P isina plane at right angles to C S—it pulls
the pole westward, i. e., backward in reference to the
orbital motion.’ At the same time that part of the
equator is depressed, and consequently, crosses the
ecliptic sooner than it otherwise would. In other words,
the node X moves in a direction opposite to that of the
earth. It goes from east to west.

We have thus far taken no account of the sun’s ap-
parent annual motion (the earth’s real motion), and for
a moment longer will continue to regard their centres as
at rest.

Of course, there would be no orbit, but we may sup-
pose the orbital plane—the ecliptic—to remain. There
would be nodes, of course, and the points between them,
90° from each, may still be called, as a matter of con-
venience, solstitial points.

The continuous pull of the sun on A, as in each daily
revolution it comes around into the plane P A 8, would
cause P to continue to descend towards X’, and X (the
node) to move westward. ‘The final effect would be that
P would pass below the ecliptic and up the other side,
and so around and around. Inthe meanwhile, P C would
be slowly but constantly yielding to the pulling force,
and thus become more and more nearly perpendicular to
the line C8, until, at last, having attained that condition,
the movement of the node, which had all along been
growing slower, would cease. It will be readily seen
that this is the history of a Bohnenbergher, as experi-
mentally developed. Ifa weight be applied at B, fig. 39,
precession and tilting will at once begin, and continue

1 Of course A pulls the earth towards the ecliptic not only at X but allalong. We are,

however, considering the total effect as concentrated at the moment A crosses the ecliptic,

155

172 AN EMPIRICAL STUDY OF GYRATING BODIES.

till the weight, the point of attachment, and the centre
of the body, are all in a straight line and then both
movements will cease.

Weare now brought to the question, Why do not these
results really occur? Why does P describe a circle (or
ellipse) which, instead of crossing the ecliptic, is parallel
to it? What has the motion of the earth around the sun
to do with it?

To answer this question we will, for the present, con-
sider only that part of the action which occurs at the
time of the solstices. These being 90° from the equi-
noxes, must move with them to the westward 50" a year ;
consequently the direction of their pull is constantly
changing to the same extent, and in the same sense.
What is true of the direction of the sun’s influence at
the solstices, is true of it at any distance therefrom, and
consequently everywhere. It is constantly moving west-
ward.

Fig. 424 may make this movement more easily under-
stood. Suppose the sun at winter solstice to be at 4,
and the pole (P) to be at a. P will move towards b,
and the solstitial point will in a year move to 38, when
the sun will meet it as it comes around from the east.
The next year a similar movement will bring P to ec, and
the solstitial point will meet the sun at 2,andsoon. The
movement is always perpendicular to the line from P to
sun, and hence, in a circle, having for its axis the axis
of the ecliptic.’

N. B. Evidently P may move either way in the line
of force ; i. e., it may approach or recede from Z without
interfering with this process.

To verify these results experimentally, take the gyro-
scope (fig. 2), and adjust the weight till the axle is in-
clined about 234° beiow the horizon. Attach a cord at

1 Any line perpendicular to an infinite plane, may be called its axis. In this case the

‘axis’? passes through the centre of the earth.

156

Cc. B. WARRING. Ali;

c, and pass it over a fixed pulley in the ceiling, vertically
above the point of the screw 8. Set the wheel revolving,
and hook to the free end of the cord a weight—for my
instrument two or three pounds,—and then leave the ap-
paratus to itself. The pole, c, wili slowly yield to the
pull of the cord, and, at the same time, revolve with great
comparative rapidity around the fixed point. The axis
will soon rise to a horizontal—i. e., it becomes perpen-
dicular to the line reaching to the pulley, or, if we trans-
fer this all to the solar system, perpendicular to a line
from the rotating body to the sun.

This illustrates the first and simplest kind of precession,
to wit, when the earth and sun do not change their rela-
tive positions. Incase of ourearth, however, the pulling
force becomes zero so soon as the axis becomes perpen-
dicular to the line from centre to the sun, and therefore
the process stops ; but in our experiment, the pull does
not become zero, and consequently the tilting process
would continue till ¢ comes into the line between the
pulley overhead and the point of the screw, 8.

To show what occurs when the direction of the sun is
constantly changing—as if it really revolved around the
earth,—use the same instrument, adjusted as before—
axis inclined 234° below the horizon. As it would be in-
convenient to have the cord as long as in the previous
experiment, and, as its length is immaterial, since it is
direction and not distance that produces the result, I
use a cord only ten or twelve inches long. I first pull ¢
with a moderate force vertically upward ; it goes hori-
zontally from me. I then pull the cord horizontally
from me; c¢ drops vertically downward. I pull ¢ ver-
tically downward ; it moves horizontally towards me. I
then pull c horizontally towards me; and it rises. It
has made a circuit of 360° around a horizontal line
passing through the fixed point at bottom of s. This

line corresponds to the line from centre of the earth to
157

174 AN EMPIRICAL STUDY OF GYRATING BODIES.

that point which we call the pole uf the ecliptic, and the
change of direction in the pull of the sun corresponds to
the different directions in which I pulled the string.

Since the revolving body always tilts in the direction
of the applied force,—which, in this case, is our string—
c, steadily, although very slowly, moves towards the
axis about which it is revolving. In case of our earth
the same thing occurs, and the obliquity of the axis
tends to grow less—in fact, does grow less for nine years
out of eighteen. What happens in the other nine years
I shall consider hereafter.

What I have said of the sun applies, mutatis mu-
tandis, to the moon.

The precessional movement is exceedingly like the
gyration of a top, the only difference being that the
latter gvrates in the direction in which it is revolving on
its axis, while the former gyrates the opposite way.
The reason for this is as follows :

The ‘* tilting force,’ i. e., gravity, tends to make the
upper end of the top recede from the vertical axis about
which it is gyrating; while in case of the earth the
‘*tilting force’’ tends to make its pole approach the
vertical axis (i. e., a perpendicular to the ecliptic) about
which it gyrates. Hence the resulting lateral move-
ments are in opposite directions.

The causes which affect the rate of precession, and

consequently the form of the path described by the

terrestrial pole, are numerous, but all may be reduced
to one principle, already demonstrated, to wit, ‘‘ An in-
crease in the tilting force causes a more rapid gyration,”’
and the converse.

Ist. There is the variation in the distance of the sun.
This, with present eccentricity, makes a difference of
about one-tenth between summer and winter effects.’ The
eccentricity itself varies in the course of ages even to

1 The tilting force varies inversely as the cube of the distance.

158

CO. B. WARRING. 1%)

three or four times its present amount. Hence, at such
times, the difference between summer and winter rate of
precession would be far greater than it now is.

9d. As the earth moves from the solstices to the
nodes, the tilting influence of the sun grows smaller,
and, hence, the precessional rate less, until, at the node,
it becomes zero.

3d. The moon constantly changes its distance from
the earth as well as its declination, and these movements
result in increasing or decreasing the tilting force, and,
therefore, in variation in the rate of precession.

As the result of all the forces with their varying in-
tensities, the path of the pole is an ellipse of ever-chang-
ing eccentricity.

NUTATION.

As has been said, the sun and moon tend to tilt the earth
always in one direction—towardsa vertical. The planets
exert their influence in the same sense. It would seem,
therefore, that the axis of the earth must have been
more oblique in the past than at present, and that,
eventually, it will become perpendicular to the ecliptic.

Unwilling to accept such a conclusion, I enquired
whether the motion of the earth in its orbit around the
sun, did not in some way, introduce a compensation by
which the tilting influences were prevented from pro-
ducing their legitimate results. Buta very little thought
sufficed to show that the effect of the annual revolution
is to reduce by one day in the year, the relative
motion of the earth on its axis. It is asif the velocity
of axial rotation was diminished, or the length of the
day increased. Experiment, as well as theory, proves
that a decrease of axial velocity increases the rate of
tilting ; consequently the effect, and so far as I could
then see, the only effect of the earth’s orbital motion,
was an increase of the movement for which I was seeking

a compensation.
159

176 AN EMPIRICAL STUDY OF GYRATING BODIES.

For a time the argument for a gradual decrease of the
inclination of the earth’s axis seemed unanswerable.
Two facts, however, stood inthe way. It seemed impos-
sible, with the refined methods of the present day, that
such a movement should escape notice.

This, however, presented no insurmountable obstacle,
for, until the contrary was shown, it could be answered
by the obvious fact that the movement might be so small
as not to have accumulated sufficiently to show itself in
the very brief period—cosmically speaking—of which we
have any record.

The other fact presented far greater difficulties, and
could not be turned by any such answer. This fact was
the existence of that up-and-down movement of the pole
which astronomers style nutation.

The earth’s axis has been proved by careful measure-
ments to describe in its precessional revolution not a
regular curve, but one scolloped, as it were (fig. 43), the
pole actually rising and falling, now nearer to, now far-
ther from, the pole of the ecliptic, and consequently the
equator making corresponding changes in reference to
that circle." The movement towards the ecliptic was all
right enough. It was just exactly what ought to happen
as the result of the tilting force ; but the movement from
the ecliptic, that was directly in the face of our experi-
ence thus far. HKvidently, no further progress was possi-
ble till this movement was accounted for.

Whatever the explanation, the existence of such a
back-and-forth movement proved that there was a force
somewhere which, at least to a certain extent, counter-
acted the tilting effect of sun and moon. <As a complete
nutation requires about nineteen years, the same time

1 R, fig. 48, is the pole of the ecliptic. The ellipse is the path which the pole of the earth,
P, ought to describe, if, as General Barnard says, a gyroscopic body without friction would
keep up forever. A line not quite returning into itself, but forming a slowly lessening spi-
ral, would seem to represent the actual path, since the attraction of the sun and moon and
planets draws the equatorial belt towards the ecliptic. But observation proves that the real
path is approximately represented by the little curves.

160

Cc. B. WARRING. EG

that the moon requires to go through all possible posi-
tions, it seemed most probable that it depended on the
moon’s movements, as indeed we have all read in our
astronomies. But how could the moon produce such an
effect? How could it make the equator move from the
ecliptic when its pull is always towards it? As the moon
is sometimes on the upper side of the equator, and
sometimes on the lower side, and consequently, pulls
the equatorial protuberance alternately north and south,
it may be thought that in this alternation les the true
explanation of nutation. In fact, this appears to many
to be the true cause of this phenomenon, and it is inter-
esting that this conclusion is apparently confirmed by
the fact just mentioned, that a complete nutation is
identical in duration with that period which the moon
occupies in going through its various changes, till it has
given equal portions of its time and influence to each
side of the equator.

It is true that the moon is sometimes north and some-
times south of the equator; but it is not true that it
sometimes makes the equator go towards the ecliptic,
and sometimes from it. Wherever it is, and however it
acts, it always pulls toward the ecliptic, as can easily be
shown.

Fig. 413 shows the moon’s orbit, at different epochs,
say nine years apart. When the moon is at either A or
B, it is north of the equator, and when it is at either A’
or B’, it is south of the equator. Whether at A or B,
or at A’ or B’, the attraction on the equatorial protuber-
ance tends to move it toward the ecliptic, E EK’. Wemay
put the moon in all possible positions with the same
result.

It follows, therefore, in the actual arrangement of our
system, that when the equator is drawn north it goes to-
wards the ecliptic, and when it is drawn south, it still

goes towards the ecliptic.
161

178 AN EMPIRICAL STUDY OF GYRATING BODIES.

Evidently, we have here no force that accounts for the
tilting of the protuberance from the ecliptic. Yet such
a movement certainly occurs.

Reflecting upon this in the light of the laws of gyra-
ting bodies, I recollected that any force tending to send
the gyroscope forward in its horizontal movement more
rapidly than it would go under the influence of gravity
alone, made it rise against gravity, or, in other words,
made it go ina direction opposite to the force that was
pulling it down.

Could this law — it is our ‘‘ first law’’—-apply to the
earth? Does it ever gyrate more rapidly than is due to
the pull, at that very instant, of the sun and moon? As
these act in the same sense, we may, for convenience,
speak only of one, say the moon ; remembering that what
is true of that is true, although in a less degree, of the
sun.

When the moon is nearest to us, and at the same time
the angle between it and the equator is greatest, then,
evidently, its tilting power is at its maximum. But
soon the moon’s distance from the earth begins to in-
crease, and the angle between it and the earth’s equator
to grow less, and hence its tilting power also diminishes ;
but as this does not affect the precessional velocity of
the previous instant it follows that the earth, in this sec-
ond instant, gyrates more rapidly than it would if it
were acted upon only by the pull of the moon ; and-
therefore the equator ought to rise. In other words, it
ought to recede from the plane of the eciiptic, and it
should continue to recede as long as the tilting force con-
tinues to grow less. When the tilting force ceases to
grow smaller, the receding should stop. If the tilting
force becomes zero, both precession and nutation should
cease.

When the tilting force begins to grow larger, preces-
sion recommences, and the equator commences to tilt to-

162

a

Cc. B. WARRING. L79

wards the ecliptic till the maximum is reached, and then
this force begins to die away, the pole once more recedes,
and so on forever.

But apparently correct reasoning, especially when
dealing with such illusive movements as those of rotating
bodies, sometimes fails, either from error in our logic,
or from the unobserved omission of some important fact
from our calculation.

I therefore asked myself, Will this bear the test of
experiment /

After thinking over several plans for solving the
problem, I adopted the following :

I attached to my large balanced gyroscope, at ¢, fig. 2,
and approximately in line with the axis, a small tin pail
(one-half pint or thereabouts), having an opening in the
bottom. I then adjusted the movable weight till the
axis of the wheel was horizontal. The opening was
closed with an outside valve, so supported that setting
fire to a thread would cause it to fall. I then putin the
pail two or three pounds of fine shot, and set the wheel
in motion. The instrument began immediately to move
laterally—quite rapidly, and also to tilt downward.
When this had gone on a few moments, I opened the
valve, while the instrument was in motion, by bringing
a blaze against the thread. The shot at once began to
pour out; the lateral motion continued in the same
direction, but the loaded end, which had been going
down, began to rise. The precessional motion grew
slower and slower, as the loaded end went up, until, at
the moment the pail became empty, both precession and
tilting ceased.

At another time, I closed the valve when perhaps one-
half of the shot had escaped ; the gyroscope at once in-

1 To succeed best with this, the bottom of the pail should be conical, and the opening
three-eighths of an inch, or so, in diameter. The point of support should be only a very
little above the centre of gravity of the whole system, so that the instrument will oscillate

with very little force.
163

180 AN EMPIRICAL STUDY OF GYRATING BODIES.

creased its precessional movement, and began to descend.
I opened the valve again ; the precessional motion began
to grow less, and the gyroscope to ascend.

At another time I reversed the experiment. I closed
the valve of the empty pail, and set the wheel going as
before. There was no horizontal or vertical movement.
The wheel revolved, and the instrument stood still. I
then poured into the pail a little shot, and then more
and more. The gyroscope started off in both horizontal
and downward movements, increasing, as I poured in the
shot, until the rapidity of the motion compelled me to
desist.

The precessional movement went on in the same direc-
tion, whether the shot were dropping out, or were being
poured in, but the tilting was first up and then down,
and the precession varied its rate.

It may perhaps be questioned whether we can con-
fidently reason from this experiment to the movements
of our earth, because in the gyroscope, the fixed point
of support is at one end of the axis, and in our earth it
is at the centre. I therefore tried the same experiment
on my Bohnenbergher (fig. 39), in which the fixed point
is at the centre, and found the results the same.

We may, therefore, formulate the following most ex-
traordinary law which, so far as I know, is new:

THE LAW OF NUTATION.

If a body revolving on its axis be acted upon by a
force tending to make it revolve about another axis per-
pendicular to the first, it will tilt in the direction of. the
applied force, if this is constant or increasing; and it
will tilt in the opposite direction, if it—the applied
force—is decreasing.

In other words, pulling down will, in one case, send
the body down, and in the other will send it up, as the

pull is an increasing or diminishing one.
164

Cc. B. WARRING. 181

In any given case, therefore, we need only to deter-
mine whether the pull is an increasing or diminishing
one, to decide whether the tilting of the equator is to, or
from the ecliptic.

If to this we add: The lateral or precessional move-
ment increases, or diminishes, as the applied force
varies, but does not change its direction, we have an
explanation of nutation in longitude also.

Now we can see why the average obliquity of the
earth’s axis is a constant quantity, notwithstanding the
fact that the pull of the sun, moon and planets is always
towards the ecliptic. When their pull decreases the obliq-
uity increases, and when the pull increases the obliquity
decreases, and as the time of the variations are equal, no
real change is produced.

Now, too, we can see why it is that Frisi’s law was
not long ago disproved by the accumulated effect of that
tilting whose existence it denies. For by this curious
law of nutation, although the tilting takes place, its
effects do not accumulate. Like Saturn’s offspring,
they are destroyed as soon as they are born.

Sir John Herschel, in his ‘‘Outlines of Astronomy,”
sect. 649, says: ‘‘The solar influence alone would pro-
duce no effect upon the excursions of the earth’s axis to
and from the pole of the ecliptic. It would increase the
length of the wave, but not its depth.”

But we have seen that nutation, in its depth as wellas
its length, is the effect of an alternate increase and de-
crease of the pull of the attracting body. The pull of
the sun varies from solstice to equinox, and from equi-
nox to solstice. Hence, solar influence alone would pro-
duce an effect in the excursions of the earth’s axis to
and from the pole of the ecliptic.

As, however, the changes in the tilting force of the
sun are very much slower and less in their extent than

165

182 AN EMPIRICAL STUDY OF GYRATING BODIES.

those of the moon, the nutational effect of the former are
less than those of the latter.

Prof. Nichol, in his Physical Sciences, says: ‘‘ If the
moon’s orbit had been coincident with the ecliptic we
should simply have had a luni-solar precession.”’

It is true that the inclination of the moon’s orbit to
the ecliptic gives it, for half of the time, a greater tilting
power thanif it were always inclined 234° to the earth’s
equator (in the ratio of the sine of 29° to the sine of 233°),
and hence the nutational movement would be less than
at present if the moon’s orbit were in the ecliptic. But
so long as the lunar pull varied, nutation would go on.

It is easy to imagine a system in which the moon, ai-
though in the ecliptic, would cause a more rapid and
deeper nutation than at present. If the eccentricity of
the moon’s orbit were so increased that it was much
nearer at perigee than at present, or if, with present ec-
centricity, its mass were greatly increased, such an ef-
fect would follow.

CONCLUSION.

All the phenomena of precession and nutation are cor-
related by this new law, as the effect of that principle
with which we started in the beginning of the study of
the gyroscope; to wit, a body in motion will continue
to move in the same direction and without decrease of
momentum till some force directly opposes it. If to

this we add: Action and reaction always coexist and are

equal, we have the key to all the phenomena presented
by gyroscopic bodies.

NOTE ON NUTATION.

It may be thought that the experiment in which the
gyrating body rises as the tilting force (the weight ap-
plied) grows less, contradicts that which I have else-
where spoken of as the foundation principle of gyra-
tional action, to wit: no descent, no gyration.

166

_

Cc. B. WARRING. 183

The case of an over-balanced instrument is no ex-
ception, because there the fall changes its sign, and so
does the gyration. But, in the case considered under
nutation, the sign of the applied force is not changed, yet
the instrument rises, and the precession continues in
the same direction as before.

There is, however, no real contradiction. Descent
here precedes the gyration, and the ascent is due to the
momentum acquired ; for, although gyroscopic bodies
in one of our experiments, appeared to have no mo-
mentum; yet it really was there, and showed itself in
what I styled conical rotation, causing the instrument
to rise from the point at which the weight was dropped
off, to a height approximately as great as that from
which it had descended. Inthe present case, the weight
being removed gradually, the instrument rises gradually,
and, at the same time, is sent forward by the remaining
weight.

To see how this is, suppose we have our instrument
(fig. 2.), well balanced with the wheel in rapid motion.
There will be no descent and no lateral movement. Now
attach a weight, say one ounce. The instrument will at
once start off with a lateral velocity, a; then attach an-
other ounce, the increase of velocity, we will call b; then
for another ounce, c; and for a fourth, d, etc., ete.
The velocity will be, after say four ounces have been -at-
tached, at+b+c+d. If now, the last ounce be dropped off,
the instrument will at the instant following, have a ve-
locity in inches per second greater than would be pro-
duced by the three remaining ounces alone. ‘The effect
is exactly the same as if the free end was accelerated d
inches by pulling a string ; hence, as shown when dem-
onstrating the ‘‘first law,’? the instrument will rise in
proportion to that acceleration. The same is true for
the next ounce and so on.

at Sh7

184 AN EMPIRICAL STUDY OF GYRATING BODIES.

THE ‘‘GYROSTATIC BALANCE.”’

At the meeting of the British Association at Montreal,
Sir William Thomson, in a paper entitled, ‘‘ Steps To-
ward a Kinetic Theory of Matter,’’ read a description of
a new instrument which he called a gyrostatic balance.
His paper, together with a wood cut representing the in-
strument, has been widely published in scientific jour-
nals. That in Wature, for Aug. 1884, page 419, is now
before me.

The balance consists of four ‘‘ gyrostats,’’* connected
by joints, which allow no lateral motion. ‘‘It might
have been constructed of two members, but four are
shown in the diagram for symmetry.’ Together they
form a kind of square enclosed in a spherical shell—the
latter being ‘‘of no use except to prevent the interior
being seen.”’ At the upper corner of the square is a
hook by which to suspend it, and at the lower, another
hook to which a weight may be attached.

The four *‘ gyrostats’’ are wound up all in one direc-
tion, and then set going at once. Of course they all re-
volve in one direction,i. e., if their axes were in a line all
the wheels would be rotating in the same sense. This
Sir William indicates very plainly by his directional el-
lipses.

Now hang them up by the upper hook, and attach a
moderate weight to the lower hook.

Sir William affirms the following four propositions, al-
though not in the same order :

1. There will be no rotation about the vertical axis—
and of course no horizontal rotation.

2. A weight attached to the lower hook will vibrate

up and down, as if attached to the hook of a spring bal-
ance.

1Gyrostats only in name andform. In reality they are gyroscopes, since they are sup-

ported at one end of the axis, while in the gyrostat the point of support is in the plane of
the wheel.

168

Cc. B. WARRING. 185

3. If this vibration be stopped, the weight will hang
down at rest, and the lower hook will be drawn out to a
distance proportional to the weight.

4. In an absolutely frictionless instrument the vibra-
tion would continue forever.

All these are stated explicitly except the first. As to
that, I infer it from his saying, ‘‘The gyrostatic model
spring-balance is arranged to have zero moment of mo-
mentum as a whole.”’

By the instrument being ‘‘so arranged that it has zero
moment of momentum,”’ I understand that the moment
of momentum of the upper two gyrostats neutralizes
that of the lower two. Iam confirmed in this belief by
his saying in the next sentence: ‘‘ But now let there be
a different’ rotational velocity imparted to the jointed
square round the axis of the two hooks, such as to give
a resultant moment of momentum around any given
line through the centre of inertia of the system.”’

It seems to me that Sir William meant that when the
gyrostats revolve all in the same direction there will be
no rotation of the whole instrument, but if the wheels
revolve in different directions, there will be rotation of
the whole.

This statement of Sir William’s is to me exceedingly
obscure,” and grows more so as I reflect upon it. I
wrote, therefore, to him while he was at Baltimore,
stating my difficulty, and asking whether I had cor-
rectly made out his meaning.

Not having received a reply I am obliged to rely upon

1 By “‘ different rotational velocity’ he may mean that the upper pair of wheels rotate to
the right, and the lower pair to the left, or he may mean that the upper wheels rotate faster
than the lower ones. I take the first to be what was intended.

2 This obscurity is increased by a note at foot of page 419, of Natwre, written, apparently,
after the body of the paper, and certainly after the diagrams had been made, in which he
says: ‘* Each of the hooks is connected to the framework through a swivel joint **— the di-
agram is made without such joints —‘‘so that the whole gyrostatic framework may be ro-
tated about the axis of the hooks in order to annul the moment of momentum of the frame-
work about this axis, due to the rotation of the fly-wheels in the gyrostat.’’ Yet, as quoted

above, he says the balance is so arranged as to have no moment of momentum.

169

186 AN EMPIRICAL STUDY OF GYRATING BODIES.

my own deduction, and to proceed upon the assumption
that he intended to say that an instrument made as he
describes and suspended in that manner will not rotate
horizontally.

It has been shown that a gyroscope (his four * gyro-
stats’? are really gyroscopes) will not stay up at all if not
permitted to rotate horizontally. If, therefore, there is
no such rotation, the instrument will drop till the axes
are vertical, or as nearly so as the interference of the
wheels will permit. There will be no up and down vibra-
tion,’ consequently there can be no continuing forever,
even in case of a frictionless machine, and there will be
no ‘* drawing out of the rod to a distance proportional to
the weight.”’ Lack of horizontal rotation puts an end
to the other propositions.

But suppose that I have misunderstood the dis-
tinguished gentleman, and that the instrument being
‘“so arranged that there is no moment of momentum”’
means that it does revolve on a vertical axis. It is
necessary to take this view of the matter, because, in
fact, it does so revolve.

It has been shown in every case of horizontal rotation
—friction or no friction—that the weight descends, not
to a ‘‘distance proportioned to the weight,’’ but to the
lowest possible point that the form of the instrument
permits, and that this occurs whatever the weight, the
only difference being not in the distance it descends but
in its rate of downward movement. In no case—save
when the axes have become as nearly vertical as the form
of the instrument will permit—will the weight hang down
at rest ; and in no case, whatever, will ‘‘the hook be
drawn out to a distance proportional to the weight.”’

There may, or there may not, be an up and down

1If a gyroscope be suspended from a point in the line of the axis in such a way as to give
freedom to vibrate in one plane like a pendulum, but with no liberty of lateral motion, it
will swing back and forth just the same in all respects, whether it is rotating or not. This,
however, is a very different kind of vibration from that of which Sir William speaks.

al 7)

> oe

Cc. B. WARRING. 187

vibration when the instrument starts off—this depends
much upon the operator—but it soon ceases.

All these statements seem to me to have been amply
verified. But thinking that perhaps it would be more
satisfactory to apply to this also the test of experiment,
I determined to make a gyrostatic balance, and see what
it would do.

I found it no easy matter to wind up and set going
at once four ‘‘gyrostats,’’ until, after several more or
less unsatisfactory attempts, I adopted the arrangement
shown in figs. 44and 45. The standard, aa, isa polished
steel rod, three-sixteenths of an inch in diameter, stand-
ing firmly in a solid base, and having at its upper end a
highly polisked and hardened cup,’ or depression, to re-
ceive the conical point (fine and hard) shown in the dia-
gram. At top and bottom are two strips of brass, b b,
b b, through the lower one of which is a hole permitting
it to play freely up and down on the steel rod. At each
angle, and also at cc, is a small brass hinge, allowing
free motion in a vertical plane, but none laterally. Be-
tween the brass pieces are four gyroscopes. Their axles
are hidden in the diagram by their supporting rings.

To wind it up, i laid the whole thing on a flat frame,
having openings for the wheels and for the cords that
were to set itin motion. The four were then wound up,
and four equal weights hooked on, which, by a very
simple arrangement, were all started at once, and the
cords set loose from the axles as the weights reached the
floor.

By winding the cords so that the two on the right
hand descend on the inside of the axis, and the two
others on the outside, rotation was imparted to all the
wheels in the direction of the arrow ellipses on the gyro-
scope, in fig. 44, and shown in the diagram in Wature
and in Science. ;

1 The cup is broad and shallow, so that only the point of the cone touches it.
BY (aa

188 AN EMPIRICAL STUDY OF GYRATING BODIES.

It will be seen that this arrangement is in principle
exactly the same as the ‘‘ gyrostatic balance’’ of Sir
William, but far more easily manipulated. Weights
can be attached to the hooks in the lower brass piece if
desired.

In his paper, he says the ‘‘gyrostats’’ are all set
going at once in one direction, and then hung up by the
hook in the upper corner. Ido the same with mine, save
that I place it with its point in the steel cup a, and lift
up the under piece, as in fig. 45. If there were no mo-
ment of momentum, the instrument should have no rota-
tion around a vertical axis. I take my hand from the
lower cross piece, and leave the instrument to itself.
Immediately it begins to rotate in the direction of the
arrow ellipse A (fig. 45). When the hand was taken
away abruptly, the lower end exhibited a slight oscilla-
tion for an instant or so, and then descended with no great
velocity, but quite uniformly as to rate, until the axes
were vertical, as in fig. 44. There was no pulling down
‘*to a distance proportional to the weight ;”’ in fact, the
only stoppage was at the end of its greatest possible fall.
With moderate skill in loosing hold of the lower piece
there was no oscillation whatever, at least none that
was large enough to be visible.

The descent of the gyroscopes is not due to loss of
velocity from friction, for, by raising the lower cross-
piece, the process may be gone through several times
with once winding the wheels. The descent, even if
the rotational velocity were uniform, would still occur,
for the reasons pointed out when discussing the same
question for the simple gyroscope.

Sir William appears to think that the effect of one
‘‘ovrostat’’ neutralizes that of the other, or would do
so if all things were equal; hence, he might say, per-
haps, that the rotation around the vertical axis was due

to the fact that, for some cause, some one of the ‘‘gyro-
172

b)

Cc. B. WARRING. 189

stats’? was more efficient than its opponent, and hence
carried it with if.

But apart from all theory, it is not difficult to show
that such is not the case. We have only to set one, two,
three, or four wheels going, and vary them in every pos-
sible manner, taking care only that the wheels shall re-
volve in the direction of the arrow ellipses, and in every
case the whole system will revolve in the direction indi-
cated by the arrow ellipse A.

It may, however, be thought that the horizontal rota-
tion is due to the friction of so many axles, and conse-
quently that if these were frictionless, there would be
no such rotation, and that Sir William Thomson is right
after all.

But, in fact, this motion is in direct opposition to the
friction. A very pretty proof is the following. Set the
instrument in operation, placing the bottom so that the
four axes make a kind of square, as in fig. 45, and leave
it to itself. The bottom wiil descend, and soon the axes
become vertical, as in fig. 44, while the wheels are yet in
rapid motion. The machine which had, up to this time,
been rotating in the direction indicated by the arrow el-
lipse A, fig. 45, will now gradually come to a stop, and
then begin to revolve in the opposite direction ; in other
words, go backwards, increasing in speed to a very con-
siderable velocity. Therefore, the friction of the bear-
ings tends to prevent the gyroscopic motion, and to pro-
duce the opposite.

Attach a cord to the bottom piece, and pass it up
through a little eyelet attached to the upper piece near
the conical point. By means of this it is easy to raise or
lower the bottom without otherwise disturbing the instru-
ment. Hold the cord when the wheels are in operation
and the instrument gyrating as shown by fig. 45, so that
the bottom cannot fall at all ; the horizontal rotation will

cease. Slacken the cord, it will commence again.
173

190 AN EMPIRICAL STUDY OF GYRATING BODIES. .

Put the instrument in the position of fig. 45, and let it
rotate horizontally. The bottom will stay up and the
square keep its form for some time. Now stop the ro-
tation by applying the fingers to the upper brass piece,
b b, which is easily done without disturbing the ‘‘bal-
ance ;’ it will instantly become limp, and take the form
shown in fig. 44. Leave it a few moments and it will be-
gin to go backwards, but there will be no vibration
whatever.

As to whether, in a frictionless instrument, the ‘*‘ oscil-
lation would continue forever,’ I can here add nothing
to what was said under the gyroscope ; and if that es-
tablishes the descent in case of a frictionless instrument,
it follows, of course, that the vibration also would cease.

Experiment shows that the ‘‘gyrostats” arranged
as in the gyrostatic balance, do not act against each
other. It remains to show why they do not.

Since only one pair of gyrostats is of any use in
the balance. I will use only one pair. Those shown in
fig. 46 weigh about two pounds. They are suspended
from the ceiling by a hook and cord. At h they are
connected by a broad, strong hinge, permitting great
freedom of vertical motion, but none of lateral. Tf,
now, both gyroscopes are set going at once, and in the
same direction as indicated by the arrows, we shall see
the whole system rotate around an axis passing through
the upper and lower hooks, instead of acting against
each other, and so preventing ‘‘any moment of mo-
mentum as a whole.”’

The reason is easily seen if we remember that the
gyration of the end—the end that falls—is always in the
same direction as the under side of the wheel. There-
fore, h, in connection with the upper gyroscope, will
tend to move away from the observer. And p, the fall-
ing, or free end of the lower gyroscope, will tend to

move towards him. But a tendency for p to rotate in
174

of

©. B. WARRING. 191

any direction means a tendency for the other end of the
axis to go directly opposite. Hence, if p tends to come
towards the observer, the other end, h, tends to go from
him, or in the same direction that it was made to go by
the upper gyroscope.

Ina ‘‘balance’’ made of two theoretical gyroscopes,
i. e., frictionless gyroscopes with massless rings and
axles, the result is curious. The upper gyroscope will
slowly drop towards a vertical, while the lower one will
rise as far as the form of the balance will permit. If
pulled down a little (not to. the vertical) it will rise
again, and so for several times. If sufficient load is
attached to the lower hook it will go down of itself.
There will not, however, be an oscillation nor a drawing
out in proportion to the weight. If the rotation is kept
uniform in both, the conclusion will be as follows: The
upper gyrostat will become vertical, and then the lower
one, and at last the two axes will be in one vertical line.

IT get nearly such an instrument by counterbalancing
the weight of the rings and axles (a partial approxima-
tion is sufficient for a qualitative experiment). I attach
movable weights w’ and w to projecting rods, as shown
in the diagram, fig. 46. They le in line with the axes.
I move w till it counterbalances the ring and axle, and
then adjust the upper one in like manner. The instru-
ment, when adjusted and at rest, will stand nearly verti-
eal. Now set the wheels both going at once and in the
same direction. Lift up the lower gyroscope by its free
end so that the instrument takes near about the position
it has in the diagram.

We shall have the horizonta! rotation again, but in-
stead of the hook, p, gradually falling till the axes are
vertical, it will rise — not vibrate — till the wheel of the
one strikes the axle of the other. Therebound produces
a momentary fall, but the wheel rises again as before.

The rationale is this. The load on the upper gyroscope
175

192 AN EMPIRICAL STUDY OF GYRATING BODIES.

is greater than that on the lower, hence, as the horizontal
movement is proportional to the load —the velocity of
the wheels being, we will suppose, the same — the upper
instrument gyrates more rapidly than the lower one
would if left to itself; consequently it pushes that ahead.
The effect of this is, by the ‘‘ first law,’ to make the
lower gyroscope rise.

We can trace out the movements in this case. Suppose
the gyroscopes to be rotating and the whole system such
that for the moment it may be considered to be in equi-
librium. The point p will be almost at rest, and h will
be moving from the observer at what may be called the
normal rate, i. e., the rate due to the rotation of the
wheels and the load. Now, by some means, make it go
faster’, p still being stationary. There will result asmall
upward motion of the mass which happens to be at 0, in
a direction parallel to the small arrow, m, which I have
drawn in the margin. In a very small fraction of a sec-
ond the rotation carries this mass too’, 90° from o. By
its inertia it retains its motion, unchanged either in
amount or direction ; consequently there is at o’ an up-
ward push, and this tends to tilt up theend, p. Aso
represents each portion of the rim as it passes around,
the effect is a continuous one.

Mr. George Forbes, in WVature for April, 1885, p. 602,
in an article on ‘‘ Molecular Physics,”’ a sort of commen-
tary on Sir William Thomson’s paper, describes a ‘‘ gy-
rostatic molecule.’’ It consists of two gyrostats inside
of a massless shell, suspended in the ether.. He says:
‘Tf the shell be frictionless the ether can only give
translational movement to it, and the double gyrostat
produces a gyrostatic effect when the molecule—the
massless shell with its two gyrostats—is accelerated in
any direction except along the axis.”’

1 This is easily done by pulling a st.ing- which may be attached near the joint h, only

taking care that the pull be in the direction of a tangent to the horizontal movement,

a bras

Cc. B. WARRING. 193

If I understand Mr. Forbes aright, he means that no
possible movement in the ether can cause the shell to
revolve on its axis. It may blow east or west, north or
south, up or down, or in any intermediate direction,
and will carry the shell with it, but there will be no ten-
dency to rotation ; and this doubtless is true. And, fur-
thermore, that a gyrostatic effect will be produced in
every case, except when the molecule is accelerated
along its axis.

This last statement shows a strange ignorance of the
cause of gyrostatic effects. It has been shown that there
can be no such effects without (1) the rotation of the
gyroscopic body on its axis, and (2) another force tend-
ing to make the body revolve around a second axis inter-
secting the first at right angles. Futhermore, it has
been shown that in every case of gyrostatic effect the
first axis changes its direction. So long, therefore, as
the axis remains parallel to itself, which will be forever,
unless some force other than the ether acts upon it, the
ether may drift the molecule not only along its axis,
but in any other conceivable direction, and in no case
will any gyrostatic effects be produced.

Experimental proof: set a gyroscope in action ; move
it in any direction, keeping the axis parallel to itself,
there is no resistance and no gyration. Again: set a
Bohnenbergher in rotation ; place it so that its axis is
parallel to that of the earth. It is moving in space with
enormous velocity, and not ‘‘along its axis,’’ yet no
gyrostatic effect is produced.

For there can be no gyrative effect without the simul-
taneous existence of rotation on one axis, and of a force
tending to produce rotation on a second axis, perpen-
dicular to the first. If there is, as in case of Mr.
Forbes’s molecule, only the rotation on an axis, and a
motion of translation, the second indispensable element

is wanting.
pli ay 4

194 AN EMPIRICAL STUDY OF GYRATING BODIES.

SIR WILLIAM THOMSON’S ‘‘GYROSTATIC’’?’ MODEL OF THE
DIPPING NEEDLE.

In the ‘‘ Report of British Association,’’ Vatwre, Sept.
95, 1885, page 524, is an account of an instrument named
as above, and of certain experiments which Sir William
Thomson ‘‘believes will be very easily performed,
although he has not yet found time to try them.’? The
following describes the instrument with sufficient accu-
racy. Suppose a horizontal line to pass through the
centre of gravity of the wheel of a gyrostat, perpen-
dicular to the axis, and so out through the frame, or
ring (if a gyroscope is used), till it projects both ways
an inch or so. Suppose, from the ring out, this line to
become an infinitely fine and perfectly rigid rod. (These
projecting pieces correspond to Sir William’s knife
edges. See WVatwre).

If, now, the instrument be placed so that the plane
passing through this line and the axis of the wheel, is
horizontal, the two supports being in an east and west
line, and, of course, the axle in the meridian; and if
the wheel be made to revolve in the same direction as
the earth, the north end will rise till it is parallel to the
earth’s axis, i. e., it shows the latitude. If carried
south, the axis will be level at the equator, and, below
that, the other end will rise, till, at the pole, it points
vertically upward.

This, with an absolutely perfect instrument—which
means one without friction,—would take place; but
such an instrument is unattainable, and I doubt whether
one sufficiently near perfection can ever be made to do
it, because the earth’s angular motion is so exceed-
ingly slow. The principle, however, can easily be illus-
trated, the movements all being greatly exaggerated.
All we have to do is to place the instrument, a gyrostatic
dipping-needle, or compass, or whatever it may be

called, on a turn-table (fig. 47).
178

—_

CG. B. WARRING. 195

On causing the latter to rotate with very moderate
speed about the axis X, the end A will rise to a vertical.
There is neither mystery nor paradox about it. But,
first, I will explain my diagram. It represents two
‘‘ovrostats’’ (or rather the same one in two positions).
M and n are standards, five or six inches high, to sup-
port the instruments. They rest on the turn-table.
The ring is the ring of my gyroscope. The dotted lines
are merely to show the case which, to make a gyrostat,
is placed, instead of the ring, around the wheel.

The rationale is easily made out. Suppose our tee-
square to be held horizontally, the leg coinciding with
the part of the axis extending towards A, and the two
arms to be a section through the centre of the wheel. As
the table turns in the direction of the large arrow, the
wheel turning in the direction of the little elliptical ar-
rows, the arm towards m will move to the left of its
present position (the direction is indicated by the small
straight arrows). While this arm of our tee (or section)
is going down to a vertical it retains that motion, and
therefore still moves towards the left. For a like
reason the other arm of our tee (now comes to the top)
moves to the right ; hence, the end, A, of the axle is
moved upwards, and, as this process continues, the axle
soon becomes vertical. If the centre of our turn-table
could be placed at the north pole the axle would become
parallel to the axis of the earth.

If the gyroscope were carried from the pole (supposing
that we now have for our purpose that impossible thing,
a perfect instrument) its axis will remain parallel to the
earth’s. Hence, as it goes south, it will show less and
less elevation, until, at the equator, the axle will be
horizontal. Still going south, the other end will begin
to go down, until, at the south pole, the axle will again
be vertical.

Place the gyroscope so that the axle points east and
179

196 AN EMPIRICAL STUDY OF GYRATING BODIES.

west, as in the left hand side of fig. 47. It will, with
equal readiness, rise to a vertical, and so far the results
are the same whether the axis pointed, when horizontal,
east and west or north and south. This, however, would
be in high latitudes, in fact, quite near the pole. But
as our instrument—we are supposing it to be absolutely
perfect—is carried from the pole, the tendency to rise
becomes less and less, until, at the equator, it becomes
null, and the axis may be placed at any angle, and there
it will remain. Turn the instrument around 90°, and
the axis will pass from any position to a horizontal one.
Turn the instrument back 90°, and it again becomes in-
different.

The same rationale, mutatis mutandis, applies here.

Sir William Thomson says, that with the axis of the
perfect “ gyrostat’’ pointing north, it will oscillate like
a dipping-needle if it be drawn out of its position. This
is true only when the centre of gravity is below the
line of the supporting edges.’ In this case the vibration
or oscillation, is that of a pendulum, the rotation of the
earth being so slow as practically to produce no effect.
But if the turn-table is in motion, the axis of the gyro-
stat will become parallel to the axis of the former ; but
will not oscillate in the least.

With a perfect instrument, without friction and with
the centre of gravity in the line of the support, the axle
will become, as has been said, parallel to the earth’s
axis ; but there will be no oscillation. It will move into
position and then stop.

Some interesting experiments can be performed with
this instrument.

Block the turn-table so as to prevent rotation or un-
steadiness. Set the wheel to revolving rapidly on its
axis. Then set it to revolving on the axis whose line is

1It is important to remember that in the ‘compass ” there is a absolutely no freedom of
motion in azimuth.

180

Cc. B. WARRING. 197

in the plane of the wheel. It will show no tendency to
stop, and will offer no resistance, although the plane of
original rotation is rapidly changing its direction. Stop
the wheel; you will find no change, the instrument re-
volves around the cross axis equally well whether the
wheel is rotating on its own axis or not.

It was to this experiment that I referred in the first of
my papers when refuting the belief that there is a pecu-
liar and inherent power of resistance in rotating bodies.

By way of contrast, loosen the turn-table and again at-
tempt to go through the above experiments.

THE GYROSCOPIC PENDULUM.

The gyroscopic pendulum (fig. 48), consists of a rigid
rod supporting, in place of the usual bob, a rigidly con-
nected gyroscope. |

If the wheel is set to revolving, and then the pendu-
lum set to beating, it will not move back and forth in
one plane, but will describe a curious series of curves.
What is their rationale ?

Our tee-square will prove helpful here. Suppose fig.
49 to represent one of these squares supported at A, and
in different positions. The arms are placed in the plane
of the vibrations. Imagine a horizontal line, shown by
the dots, to pass through the point p, and to remain
horizontal in ali positions of the tee. If the instrument
is placed at some distance from the centre of the arc, as
represented on the right hand side of the diagram, a
will be some distance above the horizontal line. As the
tee goes towards the middle of the are, a falls towards
that line, and, as it passes on to the left, a falls farther
and farther below it, till the instrument ceases to rise.
What is true of a is true of b, only in the opposite sense.
When a goes down b goes up, and vice versa. The

result is that a and b make a partial revolution about
1s1

198 AN EMPIRICAL STUDY OF GYRATING BODIES.

the point p with each vibration of the pendulum. In
this we have a key to the movements of the instrument
under consideration.

Suppose, then, the wheel in fig. 48 being in motion
around its axis, that it be drawn to the right. To avoid
unconscious direction, I use a fine cord, attach one end
to m, and the other to some fixed point, and when all
is steady, I cut the string with the blaze of a match.
If the wheel were at rest, the vibration would be in a
fixed plane—at least till the rotation of the earth, or
some imperfection in the support at A, had time to
manifest itself. Leaving these out of consideration—
for we shall be through with our experiment before
they have time to show themselves—we fix our atten-
tion upon a molecule, d. As the pendulum moves
from its high position at the right towards the centre,
d tilts downward a very little, but enough to impart
to it a certain momentum. When, therefore, it comes
to d’ (90° from its first position) it pushes vertically
downward. ‘The effect of such a force is to push the
gvroscope away from the spectator. Turning to the
molecule, b, opposite to d, we find that it goes up-
ward while d was going downward, and, consequently,
when it gets around to b’, it pushes up. Hence, a
and b work together, and tend to send the instrument
from the observer (i. e., behind the plane of the paper),
What is true of d and b is true of every other opposite
pair of molecules, and so is true of the whole. As the
amount of the push depends upon the veiocity of b’s
and d’s motions, the lateral movement will be zero when
the vibration commences, will reach its maximum at
bottom of arc, and decrease to zero as the bob ascends to
the limit of the are.

When the bob begins to return from the left to right,
d will move up from the horizontal, and b down from it,

consequently d’ and b’ will reverse their previous action,
182

C. B. WARRING. 199

and thereby, cause the gyroscope to move towards the
observer. The result is that the plane of vibration is
constantly changing. To show the projection of the
ares, I attached at m, fig. 48, a conical pail with a small
opening at the bottom, and partially filled it with fine
sand, thoroughly dried to make it flow more readily.
The sand coming out as the gyroscope swung back and
forth left a line on a sheet of paper placed as closely as
possible beneath it. This is approximately copied in
fig. 50. To see the effect, one must follow the lines in
the order of the letters. Starting at A, it swings around
in an are of a circle, passing through the centre and on
to B. At B there is a slight fullness in the curve, which
then becomes convex the other way, and passes on to C.
Here is a similar change in the sign of the convexity,
and, again going through the centre, the line reaches D.

When a string is used instead of a rod the curves as-
sume a greater variety of forms, but as no new condi-
tions are involved it seems needless to pursue the matter
further.

By way of contrast, as well as to exhibit the lack of
‘‘inherent power ”’ on the part of a rotating body to re-
sist change of direction of the plane of rotation, I sus-
pended my pendulum (fig. 48) by two cords attached at
o, and fastened at their upper ends to two staples, some
two feet apart. I released the end A, and drew a cord
from one staple to the other, passing it securely around
the upper end of the rod, so as to prevent its slipping
either to right or. left, my gyroscope thus being at the
vertex of an isosceles triangle, while the rod represented
the perpendicular to the base. I then pulled the ‘* bob”’
one side and noted the beats. Then I set the wheel in
motion and again pulled it one side and letit go. I
could see no difference ; the rotation neither accelerated,
nor retarded, the movement of the pendulum.

183

900 AN EMPIRICAL STUDY OF GYRATING BODIES.

Note on Frist?'s Law.

The first part of Frisi’s Law is demonstrated! as follows: WNES is
a section of a sphere revolving on the axis, NS, N ow
in such a manner that E rises from the paper.

Let a force be applied at N tending to depress it

below the paper. There will be a line between

the two axes that will neither go down with N y |~ E
nor up with EK, and that will be the new axis

about which E and N will revolve. N’ will be

the new pole and N’ A will be the polar distance

of some point, as A. a)

The movement of the pole is found to be about 50” in a year, or 5000"
in a century ; therefore if Frisi’s law is true, the latitude of A and of
other places should change constantly. But there is no such change,
ergo, there is something wrong about the demonstration. The error is
this : No account is taken of the earth’s being a solid, subject to the
laws of momentum. The earth may be considered as composed of an
infinite number of material diameters (more accurately, small cones
whose vertices are at the centre) each rigidly in place. Fix the mind
upon the one which at the instant the force is applied at N, is perpen-
dicular to NWSE, and call itm. When the force depresses N, m will
acquire an equal motion towards the north, and, as there is no force to
stop it, it will, when it gets to W, still move northward, and tend to
tilt the axis NS into the position N’S’. What is true of m is true of all
these diameters. As A is rigidly connected with m, it will move in the
same sense. Its latitude, therefore, will not change, but the old axis
will take a new position in space ; but not a new position relatively to
points on the surface of the earth.

1 See Airy’s Astronomical Tracts.
Also, Encycl. Brit. 8th ed., Vol. xix., p. 440.

tS

Co. B. WARRING. 201

INDEX.
Definition, and Literature of Gyrating Bodies, ; : ; 3) HOR
THE GYROSCOPE, : 2 : . . : : : 99
What the Gyroscope ee : ; : é : : . 100
Theories of the Gyroscope, ; : : : : , ; 104
No Inherent Power of Resistance, : F : ; ‘ OK
Appleton’s Cyciopedia, Theory in, . : : ‘ - 3 105
General Barnard’s, Theory of G., : : : ; : 2 105
Frictionless G. will fall, . 3 ; : ; : : ; 107
Electro-Magnetic G., . : j 5 3 : . : 5 NY
Law of tilting of G. “agile : ° A : : ; 111
College Text Books, Their sodligaaysone, ; p ; ; ae ete
The Rationale of the G., . : F ; : F : ; 113
When a equals any Susie : j : 4 j LAG
Why stability is less for smaller emerers . é c F 118
Effect of heavy and of light rims, : é ; : F slits:
If axis is not horizontal, . : : : é : : ; 121
Application of results to actual G., . : . : ; Sapa
Residual Velocity, What Becomes of It ? ; : ; : 122
The Four Gyroscopic Laws, : ; : 3 ¢ awleD
Why the Gyroscope falls so very little, 5 : : . 126
Why the up-and-down stresses do not become nL : 5 BR
Heavy, light and loaded G., j ; ; : P F ‘ 128
Transfer of weight to point of support, . d é : leg
When, no Gyration, : . : ; 3 : : : 130
Overbalancing the G., : é ; : : : ‘ 5 dS
A New Paradox—No Momentum, . : ; ; : : 131
Conical Rotation, : ‘ : : ; 5 ‘ : alae
The Undulatory Motion, . - ‘ ‘ : ; ; P 132
Laws of the same, : 5 é : . : : : . 184
Their rationale, : ; : : : ‘ : : - 134
The rising of theG., . 2 ’ ‘ ; ; 3 A lS
First case, : : : : : ; : : : : 136
Second case, - ‘ : : : ; - : ele
Prof. Snell’s Agility ; : ; ‘ : : ‘ 137
Gen. Barnard’s explanation, : : : . i : . 1388
Present writer's, : : : : : 138
Curious experiment by on Eee : : : : . 140
The G. not a modified pendulum. . . L 142
Thomson & Tait’s Rolling of a cone needs to ie modified: . 142

L185

902 AN EMPIRICAL STUDY OF GYRATING BODIES.

THE Top,
Why it does not fall,
Its backward motion after falas ,
Tops whose ‘‘ points” are not points,
Gen. Barnard’s idea about Tops,
Why does the Top rise,
The sleeping of the Top,
Why Tops run about the floor, :
How to change the obliquity of the Top,
‘“ Rapid Rotation.” (Note) .
Another Paradox, ‘
Tracings made by the Top, .
THE GYROSTAT,
The rationale of,
Effect of pushing the foot- Eee.
The Gyrostat on Wheels,
The Gyrostat on Stilts,
Gyrostatic Trapeze,
Thomson & Tait’s ‘ Stabilities,”
Gyrostat on a tight-rope,
THE GYROCYCLE,
BOHNENBERGHER’S MACHINE,
Effect of pressure on the axle,
THE EARTH AS A GYROSCOPIC Bopy,
Frisi’s Law,
Note on the same,
Precession, . ;
If no orbital motion,
With orbital motion, .
Difference between Precession of Earth dnd of Top,
Causes affecting rate of Precession.
Nutation,
The pull is always onan ihe ecliptic)
Experimental verification of Nutation,
New Law of Nutation,
What Sir John Herschel says,
What Professor Nichol says,
Note on Nutation, .
THE GYROSTATIC BALANCE,
The horizontal rotation not due to Heo:
Why the Gyrostats do not act against each other,
Mr. George Forbes’s idea,
Gyrostatic Dipping-Needle,
THE GYROSCOPIC PENDULUM,
Note on Frisi’s Law, . ;
L186

* 161

142
144
145
146
146
148
149
150
150
151
152
152
153
155
156
157
158
160

161
168
163
165
166
167
200
170
171
178
174
174
175
177
179
180
181
182
182
184
189
190
192
194
195

RECENT CELESTIAL PHENOMENA. 203

MARCH 11, 1885—THIRTY-FIFTH STATED MEETING,

Prof. W. B. Dwight, chairman, presiding; many
members and guests present.

In the absence of its author, a paper by Prof. Maria
Mitchell, entitled ‘‘ Recent Celestial Phenomena,’’ was
read by Miss Mary Whitney. In consequence of its
having been published elsewhere, a brief abstract only
will be given here.

Prof. Mitchell spoke of the failure on the part of as-
tronomers interested in the search for a supposed planet
within the orbit of Mercury, to establish a belief in such
a body. She called attention to the fact that red protu-
berances around the sun were not observed prior to
1842. Where were they previously? Since 1869 all
observers have noted the vivid color of these prominences.

Comets have been very frequent of late years. That
of 1843 threw a train from horizon to zenith ; it passed
nearer to the sun than any other comet, and is supposed
to have penetrated its outer envelope. The most strik-
ing comet since 1843 has been that of 1858, which lighted
up the autumn skies all night. For scenic effects no
other comet has equalled that of 1858 for the last
seventy years. Within fifteen months, in the years
1881 and 1882, four large comets appeared—an occur-
rence never before reported.

The ‘‘red glows”’ of the evening skies in late years
were discussed, and the unsatisfactory character of all
explanations hitherto given was shown.

The height of the atmosphere of the earth was spoken
of as a question of great uncertainty. We know more
of the extent of the atmosphere of some other planets,
as of Jupiter, for instance, than of our own.

A collision between some comet and the earth, at some
future time, was alluded to as quite possible ; but we
may anticipate beneficial or baneful resuits as equally
likely.

Ags) 7/

904 THE SUN-SPOTS OF THE PAST FEW YEARS.

The following paper was also read :

THE SUN-SPOTS OF THE PAST FEW YEARS.

BY MISS MARY WHITNEY.

Since 1874 photographs of the sun have been taken at
the observatory of Vassar College, on pleasant noons
during college session, with considerable regularity.
For the past two years a daily record has also been kept
of the number of spots on the sun’s surface. This
record was introduced to supplement the sun photo-
eraphs, since the photographs are not large enough to
give the smallest spots or the finer details ; also, because
the past three years have been of unusual interest as
containing the epoch of maximum spot development.
Occasionally, also, when a striking group has presented
itself, drawings have been made of certain portions of
especial prominence.

The most remarkable single display which I have
noted since March, 1888, occurred in July, 1888. I have
seen larger spots and more remarkable groups, but never
such a striking combination. Eight groups, containing
sixty-two spots, stretched across the sun’s dise from one
limb to the other. This number was counted with a
three-inch object-glass and power of thirty diameters.
The arrangement was a striking one, as they lay nearly
in the same parallel of heliocentric latitude, giving the
appearance of a belt, and quite near to the equator.
This belt arrangement I have noticed once since (April
93, 1884).

I have represented one of the eight groups as seen on
three successive days, and I will give, in connection,
some of the physical features of spots in general.

Firstly, I may mention that spots do not appear instan-
taneously, although the process is sometimes very rapid.

In a telescope of sufficient power the phenomenon is
188

MARY WHITNEY. 205

generally announced sometime in advance by an agita-
tion of the photosphere, which manifests itself as faculee.
Sometimes a group of small dark points will appear,
change rapidly and disappear, without developing into
a typical sun-spot group.

The nucleus or umbra of spots exhibits rapid changes.

Er Se ;
de seeks
SA al haces A ga
eoeteee aR:
JULY 2%,
4 by |
fre
FI 8 4 i a 3
2 bh is) =) 3 = po
3 = =| i} a
E S 4 5 3 q =
A c i) 4 4 2 =
— ————— —— : = > ee
Pe Ap | Fabs ] iy “~ | rin}
fea) | Bal ol a a oe L ke aN (a)
ha! Fa \ rian vtemali lyk | er Sean (epee | mal hits ' [- an ait
\ . ¢
} \ ; \ “ls \
— aN t LENE SEEN if wi =
j \ i a aa teas x |
/ i H \ ' i \ | |
ream iit = 1 Sy P ea ae Nn = >
Heeallbe Hilla
ai
epee ee ree ee NNEC ee ee = i 1 eels aut
Teo ‘la eae | A]
i ; Ff :
i i : t Lt Nara | | wt /
: a beret be fe i = — ees eel te 4 . \e el
i ’ oman Smal : ,
: 1] ja ile Ni ‘ U
+ PiSes 4 4 =. 1-4. rca { = yy! = —— eI
Nee 1| i H { \
‘ 4 4) Hi | ¥ | ‘ t
ai 1A j T | i DRA
Wahi ri
Nt Wee | | | |
ct) co } = ath u + 4 1 + —
¥ | | |
4 i Sh ac LS a [ee au | :

Sun-spots, three views of one group, July, 1883.
Diagram of monthly variation in number of sun-spots, 1883-1885, p. 211.

The above group, selected from the belt of July, 1883,
illustrates this. The changes in form, number and ar-
rangements are very striking. Umbras multiply either
by the formation of new pores in the same penumbra, or
by subdivision of the primary umbra into two or more
parts. The method of this division I do not detect with
the glass I use, but I can plainly see that in many cases
itis division and not new formation.

Larger telescopes, however, show that when this sub-
division takes place a mass of the brilliant matter of the
photosphere projects itself across the umbra. Some-
times it is thrown across very rapidly. Halley has

watched the full process of such a bridging of the nu-
189

206 THE SUN-SPOTS OF THE PAST FEW YEARS. A

cleus. Careful measurement shows that when a spot
divides or undergoes a marked change in form a sudden
movement occurs, and it is always a forward movement,
i. e., in the direction of increasing longitude.

Another interesting fact is, that when the nuclei are
round, the filaments of the penumbra are directed to-
ward the centre. In irregular spots, they le at various
angles ; sometimes (as seen by Secchi) apparently over-
lying one another and implying a difference of level.
The luminous masses of the penumbra project more or
less into the dark nucleus, forming a ragged interior
edge ; and high power will often show the rapid dissolv-
ing away of those projecting extremities. As the umbra
of a spot approaches the circular form its career becomes
more stable ; and it is from round nuclei that the move-
ments of rotation are preferably obtained. <A large spot
rarely disappears during a single rotation of the sun.
Secchi says that when a large spot disappears, another
often appears a short distance from the first and always
in advance of it. The group of July, 1883, shows the
train of smaller spots which usually attends the main
body of a group. These smaller spots are, in general,
a later development. They change much in form, size,
and arrangement, and lag more and more behind the
larger and earlier portion. It is a marked fact of obser-
vation that these trains follow, almost never precede, the
main body of the group.

Another almost universal accompaniment of a spot are
the facule. Faculee are lines of light brighter than the
photosphere, running more or less regularly about the
spot. They are more noticeable near the sun’s limb ;
than toward its centre. It is not supposed that they ex- (
ist in larger number near the edge, but that they are
seen more plainly there because of the darkening of the
photosphere toward the sun’s borders. If they are (as

they are supposed to be) elevations of the photosphere
190

MARY WHITNEY. 207

produced by eruptions from the interior, these elevated
ridges are seen under Jess absorption from the solar at-
mosphere than the surrounding photosphere. Near the
border the photosphere is observed through a deeper
layer of atmosphere than at the centre, and there is a
perceptible darkening. The facule show by contrast.
Near the centre the contrast between elevated ridge and
average surface being less apparent the faculee are not
generally seen.

Facule are pretty surely Known to be prominences in
the atmosphere, because, viewed on the sun’s edge with
a sufficiently high power, they have been seen to project
like teeth.

In spots of regular form the facule incline to radiate
with considerable regularity from the spot umbra. In
irregular spots their distribution is likewise irregular.
I have observed that faculee are much more frequently
seen behind the spot than in advance of it. In eleven
hundred thirty-seven observations made at the Kew
observatory, five hundred eighty-four spots pre-
sented facule following, five hundred eight gave a
comparatively regular arrangement, and only forty-five
gave facule preceding. Secchi notices that they are
smaller and more brilliant when preceding, more numer-
ous and extended when following.

Faculee often exist independently of spots, and their
distribution is more extended. Spots are rarely seen be-
yond 30° of heliocentric latitude. One spot as near the
pole as 50° has been reported by Peters (when in Naples),
but this is exceptional. Facule, however, are not un-
commonly seen as near the pole as 60°. Still, they
abound where spots abound.

Besides the belt of July, 1883, several other remarka-
ble spot phenomena of the past three years have been
noted in our records. The most striking single group
appeared in November, 1882. At first the nucleus

191

208 THE SUN-SPOTS OF THE PAST FEW YEARS.

was very large and irregular. On November 20th,
when next photographed, it was still remarkable.
The umbra had subdivided into four prominent sections.
While this group was crossing the visible disc, there oc-
curred an unusual magnetic storm accompanied with ex-
tensive auroral displays. During this time I was ob-
serving the transit of the large comet of 1882, which
crossed the meridian quite low in the south, and during
its passage I noticed flashings of the aurora around and
below the comet.

Another striking single group, attended by a brilliant
auroral display, was observed in April, 1882. This group
was not so remarkable as the preceding, however, either
in size or form of umbral positions. The most re-
markable single nucleus appeared in October, 1882.
This nucleus approached the round and stable form,
and made a return with but slight change in shape.
On October 2d, it presented a pear-shaped outline. It
was also followed by a group of small spots near
enough to be called in its train. On October 30th,
when it had made a complete revolution, its form was
still pear-shaped and somewhat larger. The train of
October 2d had disappeared. The intermediate pho-
tographs of October 25th and 28th show the foreshorten-
ing of the nucleus as seen on the other limb of the sun."

It will be noticed that the groups and spots I have
mentioned (and they comprise the most striking of the
past three years) appeared in 1882 and early in 1883.
This has interested me, from the fact. that, as deduced
from my counting of spot number, the maximum epoch
did not occur till later.

In 1883 I have noted beside the belt of July some
three or four groups of especial interest; and in 1884
four or five drawings were made. On May 14th there

1 The several photographs referred to, showing the character and changes of the Novem-
ber, April and October groups, were exhibited.

192

a

MARY WHITNEY. 209

was a large round nucleus, a photograph of which I
have brought with me. But I should say from my ob-
servation that the striking groups appeared before the
period of maximum activity.

As I have before said, the sun-spots of the past two or
three years have been of interest to astronomers because
the period of sun-spot activity has culminated during
this time. So far, however, have the phenomena varied
from those predicted that astronomers differ as to their
bearing upon theory.

The sun-spots were first systematically observed by
Schwabe, of Dessau. During the years from 1826 to
1868 he counted the spots and made drawings. In 1851
he published the results of twenty-five years of obser-
vation.

Carrington’s observations began later and covered
several years. These were made with more exactness
than Schwabe’s, and gave also change in latitude and
longitude of spots. Beside these valuable series, there
are the observations of Spoerer, at Potsdam, and those
of Secchi. The solar photographs taken at the Kew
Observatory have also been made use of in determining
the period of variability. In the earlier observations
the spots were counted only. Later investigators have
measured the areas, on the ground that the number of
spots is not so true a measure of solar activity as the
amount of surface disturbed.

De la Rue gave great labor to the measurement of
areas in the Schwabe and Carrington series, and the
Kew photographs were also measured in this way. The
areas of umbra and penumbra are measured separately,
and correction is made for the foreshortening of spots
seen obliquely. Although these careful modern obser-
vations cover a considerable number of years, the time
is yet too short for a confident determination of the

period of variability.
198

210 THE SUN-SPOTS OF THE PAST FEW YEARS.

Prof. Wolf, of Zurich, who is well versed in the history
of astronomy, has made a study of ancient records,
going back as far as 1615. He regards the ancient, and,
therefore, comparatively unreliable, series as extending
from 1615 to 1760. In this series he supposes the dates
of maximum to be known within a limit of two years.
In the modern series they are known within a limit of
half a year. From his investigations Wolf has arrived
ata mean period of 11.1 years. Other astronomers agree
nearly with him in dates of maximum. Thus Wolf
makes maximum epochs of 1837.2, 1848.6, 1860.2, and
De la Rue of 1836.97, 1847.89, and 1859.67. Spoerer
makes the period 11.3 years.

The maximum follows minimum by a less time than
it preceeds the succeeding minimum. The ordinate of
the curve of variability increases through (Wolf) 3.07
years, and decreases through 7.04 years. Rue makes
the figures 3.52 and 7.55 years. This isa close approach,
as Wolf reckoned by number and Rue by area.
Spoerer differs considerably from both, giving the num-
bers 4.78 and 6.55.

In the diagram constructed by Prof. Wolf to represent
the periodic changes since 1615, there is evident, beside
the well-recognized period of eleven years, another less-
marked rise and fall along the whole length of the curve.
Wolf has himself deduced a second long period of about
fifty-five years. That such a semi secular period exists
most astronomers are inclined to admit, but they do not
yet possess material enough to judge with any accuracy
of its length. The superposition of this period on the
shorter one would account for many of the irregularities
of the latter.

The present maximum was looked for as early as
1882. The last minimum occurred about 1878.8. In
the last two periods the intervals between minimum and

maximum were 4.4 years and 3.6 years. Applying the
194

MARY WHITNEY. OE

mean of those to 1878.8 we have 1882.8. Wolf's theoret-
ical mean would place it earlier, and Spoerer’s later, at
1883.5.

The display of 1882 was so remarkable that some ob-
servers considered that the period was then completed.
This was the opinion of Faye as late as April, 1884. He
regarded the great outburst of April, 1882, as indicative
of maximum, and held that the display of April and
July, 1883, were secondary maxima, which often occur
in the progress of periodic phenomena. Wolf considered
in the spring of 1884 that the question was still open.

Consulting our record, I find that in 1883 there were
four days without visible spot. In 1884 I find but one
day—November 8th. I notice that Prof. Todd, of Am-
herst, gives also the date November 7th, but I have
recorded one small spot for that day. On January 12th,
i885, there was no spot seen by my assistant who was
then making the count.

During the two years the highest monthly number
occurred in July, 1883, the month of the belt of which I
have spoken. Directly following, however, there is a
rapid fall. There is a rise again in October, with a fall
succeeding ; but not so low a number is reached as in the
preceding fall. In January, 1884, a rise again occurs,
and the number keeps high through February, March
and April. May and June give diminishing numbers ;
and the monthly numbers have continued compara-
tively small up to this time.

I give on page 205 the diagram I have constructed from
my values. Judging from this, I incline to place the
maximum epoch early in 1884, since the longest sus-
tained activity occurs at that time.

Spoerer, in his last publication in the Astronomische
Nachrichten, places it provisionally at 1884.0. Appar-
ently, then, the maximum is late, even if we regard the

latest theoretical epoch 1883.5 as the most correct one.
195

212 THE SUN-SPOTS OF THE PAST FEW YEARS.

Furthermore, comparing the number of spots which
has appeared during this spot-period with those of the
two preceding periods, we find that the number of this
period has been smaller. |

Still another difference presents itself, which I will
give from the records of the Potsdam Observatory.

Dr. Spoerer, of the Potsdam Observatory, is an assid-
uous observer of sun phenomena, and he has recently
published in the Astronomische Nachrichten interesting
results deduced from his researches of the past few
_ years, combined with investigations based upon a series
of observations covering thirty years. He directs his at-
tention especially to the distribution of the spots rela-
tively to heliocentric latitude. It has for some years
been noticed that during minimum the altitude attained
by the spots is lower than during maximum. In 1883
Spoerer published in the Wachrichten a table which
gives the distribution of spots in zones of 5° of latitude,
during a period of thirty years. The appearance of the
table is at once striking to the eye, since its arrangement
shows the regular run of values. This regularity was
so marked that Spoerer ventured to predict the behavior
of the spots in this regard during 1884; that is, that the
greatest spot-number would occur in the zone between
10° and 15°, and that the zone beyond this, 15°—20°,
would be less abundantly supplied than the one below,
i. e., 5°—10°. The observations of 1884 verified his sup-
position. The largest number of spots has appeared in
zone 10°—15°, while in the zone 5°—10° the number is
more than twice that of 15°—20°. This prediction, how-
ever follows from the portions of the table immediately
preceding 1884, and not upon the conditions of previous
maximum. Here enters an important difference. Al-
though the maximum epoch has been delayed or pro-
longed, the mean latitude of largest frequency has been

lowered. The mean latitude during previous maxi-
196

MARY WHITNEY. 913

mum was about 17°. This was higher than the average,
which Spoerer thinks is about 15°. Calling 1884.0 the
time of maximum, the mean latitude was about 12°.

Spoerer holds that the last two maxima were too early.
This has been too late. He argues further, from his ta-
bles, that instead of this maximum being followed by a
correspondingly belated minimum, the next minimum
will follow in a period of time less than his mean, 6.5
years.

Of the spot-period, whose maximum has recently
passed, we can, therefore, say: 1st, that it has produced
a smaller number of spots than the preceding ; 2d, that
the maximum has been later than the mean period
would place it ; and 3d, that the mean latitude attained
by the spots has been lower.

MARCH 25, 1885—THIRTY-SIXTH STATED MEETING.

Prof. W. B. Dwight, chairman, presiding.

The following donations were made to the museum:
An Indian bow, with quiver and arrows, and an egg of
the emu, by W. G. Stevenson, M. D.; an herbarium of
North American ferns, containing one hundred and ten
species, all mounted and labeled, by C. N. Arnold.

APRIL 8, 1885—THIRTY-SEVENTH STATED MEETING.

Prof. W. Bb. Dwight, chairman, presiding; seven
members and ten guests present.

The evening was occupied in the informal study of a
large variety of specimens under the microscope.

Lucy M. Hall, M. D. was elected a member.

APRIL 22, 1885—THIRTY-EIGHTH STATED MEETING.

There being no quorum present the meeting was ad-

journed to the evening of May 5.
197

214. TRANSACTIONS OF SCIENTIFIC SECTION.

MAY 5, 1885—ADJOURNED SESSION OF THE THIRTY-EIGHTH
STATED MEETING.
Prof. W. B. Dwight, chairman, presiding ; nine mem-
bers present.
The chairman presented the following Annwal Report:

Members of the Scientific Section, Vassar Brothers
Institute: During the session of 1884-85, now at its
close, nothing has occurred to interrupt the course of
our regular meetings. The evenings of November 5 and
19, and of December 3, 1884, were occupied by Dr. C. B.
Warring in presenting before the society the results of
much original study of the gyroscope and kindred
instruments, under the titles, ‘‘ The Gyroscope: what it
does, and the reason for its peculiarities,’’ and ‘‘The
Top, Gyrostat, Gyrocycle, and Bohnenbergher Machine:
their rationale.’’ These papers were fully illustrated by
various forms of apparatus, ingeniously devised, and
were listened to with much interest.

On December 17, Dr. J. M. DeGarmo read a paper
entitled ‘‘Scraps from a Worker’s Note-book,”’ setting
forth, in a way both interesting and instructive, various
methods, incidents, and experiences of zodlogical re-
search.

The session of January 14, 1885, was devoted to micro-
scopic work. Dr. H. F. Parker explained some of the
most approved methods of the section-cutting of tissues,
and illustrated the subject by preparing such sections in
the presence of the members. Various objects of in-
terest were brought forward by different members and
examined in the microscope.

On January 28, in place of the paper expected from
Prof. Maria Mitchell, who was unable to attend, the
evening was filled profitably by miscellaneous contribu-
tions and discussions of items of scientific intelligence.
Among these was a description, by Prof. L. C. Cooley,

of the ‘‘ Jolly Specific Gravity Balance,’’ and the values
198

am

GHAIRMAN’S ANNUAL REPORT. 215

of the results possible from its use. Professor Cooley
also called attention to the most serious difficulty in
manipulating this instrument—the optical difficulty in
the reading of the scale in the cross-lights of an or-
dinary room. He described a simple contrivance, by
means of which he had succeeded in entirely over-
coming this disadvantage.

On February 11 a paper was read by the chairman on
“The Peculiar Structure of Clark’s Clay-beds, near
Newburgh, N. Y.”’

February 25 was filled by the closing paper, by Dr.
Warring, on gyroscopic movements, entitled, ‘‘ Various
Results and Final Studies: Precession of the Equinoxes ;
Frisi’s Law, and Other Topics.’ This paper, like the
preceding ones, was ingeniously illustrated, and fur-
nished much material for thought on the mysteries of
gyroscopic motions.

March 11 a paper was presented, by Prof. Maria
Mitchell, on ‘‘ Recent Celestial Phenomena.’’ On ac-
count of the illness of Professor Mitchell, the paper was
read by her assistant, Miss Mary Whitney.

On the same evening, Miss Mary Whitney presented
a paper on ‘‘ Sun Spots,’’ founded to a considerable ex-
tent on her personal observations.

On March 25 Dr. De Garmo, having been prevented by
illness from reading an expected paper, the evening was
occupied pleasantly by the consideration of various
miscellaneous items. Mr. C. N. Arnold took this oc-
casion to exhibit to the section, accompanied by ex-
planations, a fine set of ferns of this vicinity and other
parts of the country, mostly collected and carefully
mounted by himself, which collection he also presented
to the Museum of the Institute.

The last meeting for scientific work on April 8 was de-
voted to the microscope and to miscellaneous communi-

cations. Several microscopes were brought to the hall
199

216 TRANSACTIONS OF SCIENTIFIC SECTION.

by members, and objects in considerable variety were
described and examined.

Many of the papers above mentioned were followed by
questions and discussion on the part of members present,
which added much to the interest of these occasions.

The attendance has for the most part been about equal
to that of last year.

Respectfully submitted,
WILLIAM B. Dwieut,
Chairman.

The following gentlemen were elected officers of the
Section for 1885-86 :

Chairman, : : : . C. B. WARRING: Phas
Secretary, f ; . C. N. Arnoxp, Esq.
CORRIGENDA.

In my paper on ‘‘ An Interesting Geological Locality at Cornwall, N.
Y.,” in the Transactions of Vassar Brothers Institute for 1883-4, there
stated to be only the preliminary observations of a single brief visit,
the ‘‘ Van Duzer” mine is assumed to be identical with the *‘ Town-
send” mine, mentioned formerly by Horton and Mather. This was
the impression made on my mind by the scanty information gained
on the ground. But I have received, since, more reliable informa-
tion from Mr. Nelson H. Darton, who is making a thorough strati-
graphic exploration of that region. It appears that the Townsend mine
is distinct from the Van Duzer, though similar in its features, and that
it lies a little farther to the south. Statements quoted in the paper of
Horton and Mather, with reference to the Townsend mine, had a mis-
application, therefore, in some minor respects, as referred to the Van
Duzer mine. :

Also, in the list of waterlime fossils, in place of ‘‘ Atrypa plicata,”

read ‘‘Spirifer vanuxemi.”
W. B. Dwiaeur.

200

PLATE I.

PLATE II.

af. Hi beh f

ASS

} 5
Ag Lah

c
Car
, Va

fee

y ‘

hs ae
hoe nt

nt RL
ae a)

ine
Vie

rey
2h fs

PLATE Itt.

a TT CEES SEES ET ae
aa os y

PLATE IV

TRACINGS MADE BY A SPINNING TOP.

The largest of the above spirals was made with a“ point’ about one-fortieth of an inch in diam-
eter, with axis much inclined, ‘The second in size was made with the same point, but with axis less
Inclined. The third was made with a needle point. It is noticeable for its freedom from waviness
—due to more perfect ring, and for its abrupt change of direction,

ae

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