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Full text of "Transactions of the Royal Society of Edinburgh"

TRANSACTIONS 



OF THE 



ROYAL SOCIETY 



OK 



EDINBURGH. 



VOL. XXVI. 



EDINBURGH: 

PUBLISHED BY ROBERT GRANT & SON, 54 PRINCES STREET. 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. 



MDCGCLXXII. 



ROYAL SOCIETY OF EDINBURGH. 



THE KEITH, BRISBANE, AND NEILL PBIZES. 



The above Prizes will be awarded by the Council in the following manner : — 

I. KEITH PRIZE. 

The Keith Prize, consisting of a Gold Medal and from £40 to £50 in 
Money, will be awarded in the Session 1873-74, for the " best communication 
on a scientific subject, communicated, in the first instance, to the Royal Society 
during the Sessions 1871-72 and 1872-73." Preference will be given to a 
paper containing a discovery. 

II. MAKDOUGALL BRISBANE PRIZE. 

This Prize is to be awarded biennially by the Council of the Royal Society 
of Edinburgh to such person, for such purposes, for such objects, and in such 
manner as shall appear to them the most conducive to the promotion of the 
interests of science ; with the proviso that the Council shall not be compelled 
to award the Prize unless there shall be some individual engaged in scientific 
pursuit, or some paper written on a scientific subject, or some discovery in 
science made during the biennial period, of sufficient merit or importance in 
the opinion of the Council to be entitled to the Prize. 

1. The Prize, consisting of a Gold Medal and a sum of Money, will be 
awarded at the commencement of the Session 1874-75, for an Essay or Paper 
having reference to any branch of scientific inquiry, whether Material or 
Mental. 

2. Competing Essays to be addressed to the Secretary of the Society, and 
transmitted not later than 1st June 1874. 

VOL. XXVI. PAET IV. b 



VI 



3. The Competition is open to all men of science. 

4. The Essays may be either anonymous or otherwise. In the former case, 
they must be distinguished by mottoes, with corresponding sealed billets super- 
scribed with the same motto, and containing the name of the Author. 

5. The Council impose no restriction as to the length of the Essays, which 
may be, at the discretion of the Council, read at the Ordinary Meetings of the 
Society. They wish also to leave the property and free disposal of the manu- 
scripts to the Authors ; a copy, however, being deposited in the Archives of 
the Society, unless the Paper shall be published in the Transactions. 

6. In awarding the Prize, the Council will also take into consideration any 
scientific papers presented to the Society during the Sessions 1872-73 and 
1873-74, whether they may have been given in with a view to the Prize or not. 

III. NEILL PRIZE. 

The Council of the Royal Society of Edinburgh having received the bequest 
of the late Dr Patrick Neill of the sum of £500, for the purpose of " the 
interest thereof being applied in furnishing a Medal or other reward every 
second or third year to any distinguished Scottish Naturalist, according as such 
Medal or reward shall be voted by the Council of the said Society," hereby 
intimate, 

1. The Neill Prize, consisting of a Gold Medal and a sum of Money, will 
be awarded during the Session 1874-75. 



i & 



2. The Prize will be given for a Paper of distinguished merit, on a subject 
of Natural History, by a Scottish Naturalist, which shall have been presented 
to the Society during the three years preceding the 1st May 1874, — or failing 
presentation of a paper sufficiently meritorious, it will be awarded for a work 
or publication by some distinguished Scottish Naturalist, on some branch of 
Natural History, bearing date within five years of the time of award. 



Vll 



AWARDS OF THE KEITH, MAKDOUGALL BRISBANE, AND NEILL PRIZES, 

FROM 1827 TO 1872. 



I. KEITH PRIZE. 



1st Biennial Period, 1827-29. — Dr Brewster, for his papers "on his Discovery of Two New Immis- 
cible Fluids in the Cavities of certain Minerals," published in 
the Transactions of the Society. 

2d Biennial Period, 1829-31. — Dr Brewster, for his paper "on a New Analysis of Solar 

Light," published in the Transactions of the Society. 

3d Biennial Period, 1831-33. — Thomas Graham, Esq., for his paper "on the Law of the Diffusion 

of Gases," published in the Transactions of the Society. 

4th Biennial Period, 1833-35. — Professor Forbes, for his paper "on the Eefraction and Polarization 

of Heat," published in the Transactions of the Society. 

5th Biennial Period, 1835-37. — John Scott Eussell, Esq., for his Eesearches " on Hydrodynamics," 

published in the Transactions of the Society. 

6th Biennial Period, 1837-39. — Mr John Shaw, for his Experiments "on the Development and 

Growth of the Salmon," published in the Transactions of the 
Society. 

7th Biennial Period, 1839-41. — Not awarded. 

8th Biennial Period, 1841-43. — Professor Forbes, for his Papers " on Glaciers," published in the 

Proceedings of the Society. 

9th Biennial Period, 1843-45. — Not awarded. 

10th Biennial Period, 1845-47. — General Sir Thomas Brisbane, Bart., for the Makerstoun Observa- 
tions on Magnetic Phenomena, made at his expense, and 
published in the Transactions of the Society, 

11th Biennial Period, 1847-49. — Not awarded. 

12th Biennial Period, 1849-51. — Professor Kelland, for his papers "on General Differentiation, 

including his more recent communication on a process of the 
Differential Calculus, and its application to the solution of 
certain Differential Equations," published in the Transactions 
of the Society. 

13th Biennial Period, 1851-53. — W. J. Macquorn Eankine, Esq., for his series of papers " on the 

Mechanical Action of Heat," published in the Transactions of 
the Society. 

14th Biennial Period, 1853-55. — Dr Thomas Anderson, for his papers "on the Crystalline Con- 
stituents of Opium, and on the Products of the Destructive 
Distillation of Animal Substances," published in the Trans- 
actions of the Society. 



viii THE KEITH, MAKDOUGALL BRISBANE, AND NEILL PRIZES. 

15th Biennial Period, 1855-57. — Professor Boole, for his Memoir "on the Application of the Theory 

of Probabilities to Question of the Combination of Testimonies 
and Judgments," published in the Transactions of the Society. 

16th Biennial Period, 1857-59. — Not awarded. 

17th Biennial Period, 1859-61. — John Allan Broun, Esq., F.R.S., Director of the Trevandrum 

Observatory, for his papers "on the Horizontal Eorce of the 
Earth's Magnetism, on the Correction of the Bifilar Magnet- 
ometer, and on Terrestrial Magnetism generally," published in 
the Transactions of the Society. 

18th Biennial Period, 1861-63. — Professor William Thomson, of the University of Glasgow, for his 

Communication " on some Kinematical and Dynamical 
Theorems," published in the Transactions of the Society. 

19th Biennial Period, 1863-65. — Principal Eorbes, St Andrews, for bis " Experimental Inquiry into 

the Laws of Conduction of Heat in Iron Bars," published in 
the Transactions of the Societj-. 

20th Biennial Period, 1865-67. — Professor C. Piazzi Smyth, for his paper "on Eecent Measures at 

the Great Pyramid," published in the Transactions of the 
Society. 

21st Biennial Period, 1867 -69. — Professor P. G. Tait, for his paper "on the Rotation of a Rigid 

Body about a Eixed Point," published in the Transactions of 
the Society. 

22d Biennial Period, 1869-71. — Professor Clerk Maxwell, for his paper "on Figures, Frames, 

and Diagrams of Forces," published in the Transactions of the 
Society. 



II. MAKDOUGALL BRISBANE PRIZE. 

1st Biennial Period, 1859. — Sir Roderick Impey Murchison, on account of his Contributions to the 

Geology of Scotland. 

2d Biennial Period, 1860-62.— William Seller, M.D., F.R.C.P.E., for his "Memoir of the Life 

and Writings of Dr Robert Whytt," published in the Trans- 
actions of the Society. 

3d Biennial Period, 1862-64. — John Denis Macdonald, Esq., R.N., F.R.S., Surgeon of H.M.S. 

" Icarus," for his paper "on the Representative Relationships 
of the Fixed and Free Tunicata, regarded as two Sub-classes 
of equivalent value; with some General Remarks on their 
Morphology," published in the Transactions of the Society. 

4th Biennial Period, 1864-66. — Not awarded. 

5th Biennial Period, 1866-68. — Dr Alexander Crum Brown, and Dr Thomas Richard Fraser, for 

their conjoint paper " on the Connection between Chemical 
Constitution and Physiological Action," published in the 
Transactions of the Society. 

6th Biennial Period, 1868-70. — Not awarded. 

7th Biennial Period, 1870-72. — George James Allman, M.D., F.R.S., Emeritus Professor of Natural 

History, for his paper 'on the Homological Relations of 
the Ccelenterata,' published in the Transactions, which forms 
a leading chapter of his Monograph of Gymnoblastic or Tubu- 
larian Hydroids — since published. 



IX 



III. NEILL PRIZE. 

1st Triennial Period, 1856-59. — Dr W. Lauder Lindsay, for his paper "on the Spermogones and 

Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens," 
published in the Transactions of the Society. 

2d Triennial Period, 1859-62. — Eobert Kaye Greville, LL.D., for his Contributions to Scottish 

Natural History, more especially in the department of Cryp- 
togamic Botany, including his recent papers on Diatomaceae. 

3d Triennial Period, 1862-65. — Andrew Crombie Kamsay, F.R.S., Professor of Geology in the 

Government School of Mines, and Local Director of the 
Geological Survey of Great Britain, for his various "Works and 
Memoirs published during the last five years, in which he has 
applied the large experience acquired by him in the Direction 
of the arduous work of the Geological Survey of Great Britain 
to the elucidation of important questions bearing on Geological 
Science. 

4th Triennial Period, 1865-68. — Dr William Carmichael M'Intosh, for his paper " on the Structure 

of the British Nemerteans, and on some New British Annelids,'' 
published in the Transactions of the Society. 

5th Triennial Period, 1868-71. — Professor Turner, for his papers " on the great Firmer Whale; and 

on the Gravid Uterus, and the Arrangement of the Foetal 
Membranes in the Cetacea," published in the Transactions of 
the Society. 



VOL. XXVI. PART IV. 



LAWS 



OF THE 



ROYAL SOCIETY OF EDINBURGH, 



AS REVISED JANUARY 1873. 



LAWS. 



[By the Charter of the Society (printed in the Transactions, Vol. VI. p. 5.), the Laws cannot 
be altered, except at a Meeting held one month after that at which the Motion for 
alteration shall have been proposed.] 

I. 
THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Title. 
Honorary Fellows. 

II. 

Every Ordinary Fellow, within three months after his election, shall pay Two The fees of Ordi- 
Guineas as the fee of admission, and Three Guineas as his contribution for the ing in Scotland. 
Session in which he has been elected ; and annually at the commencement of every 
Session, Three Guineas into the hands of the Treasurer. This annual contribution 
shall continue for ten years after his admission, and it shall be limited to Two 
Guineas for fifteen years thereafter.* 



III. 

I 

be exempted from farther payment 



All Fellows who shall have paid Twenty-five years' annual contribution shall Payment to cease 

•> J after 25 years. 



The fees of admission of an Ordinary Non-Resident Fellow shall be £26, 5s., Fees of Non-Resi- 

. J > > dent Ordinary 

payable on his admission ; and in case of any Non-Resident Fellow coming to Fellows. 

reside at any time in Scotland, he shall, during each year of his residence, pay 

the usual annual contribution of £3, 3s., payable by each Resident Fellow ; but 

after payment of such annual contribution for eight years, he shall be exempt 

from any farther payment. In the case of any Resident Fellow ceasing to reside Case of Fe !i ow * 

J L J J & becoming Non-Re- 

sident. 

* At the Meeting of the Society, on the 5th January 1857, when the reduction of the Contribu- 
tions from £3, 3s., to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was 
resolved that the existing Members shall share in this reduction, so far as regards their future annual 
Contributions. 

A modification of this rule, in certain cases, was agreed to 3d January 1831. 

VOL. XXVI. PART IV. d 



XIV 



Defaulters. 



in Scotland, and wishing to continue a Fellow of the Society, it shall be in the 
power of the Council to determine on what terms, in the circumstances of each 
case, the privilege of remaining a Fellow of the Society shall be continued to 
such Fellow while out of Scotland. 

V. 

Members failing to pay their contributions for three successive years (due 
application having been made to them by the Treasurer) shall be reported to 
the Council, and, if they see fit, shall be declared from that period to be no 
longer Fellows, and the legal means for recovering such arrears shall be 
employed. 



VI. 

Privileges of None but Ordinary Fellows shall bear any office in the Society, or vote in 

the choice of Fellows or Office-Bearers, or interfere in the patrimonial interests 
of the Society. 



Numbers Un- 
limited. 



Fellows entitled 
to Transactions. 



VII. 

The number of Ordinary Fellows shall be unlimited. 

VIII. 

The Ordinary Fellows, upon producing an order from the Treasurer, shall 
be entitled to receive from the Publisher, gratis, the Parts of the Society's 
Transactions which shall be published subsequent to their admission. 



Mode V»f Recom- 
mending Ordinary 
Fellows. 



Honorary Fellows, 
British and 
Foreign. 



IX. 

Candidates for admission as Ordinary Fellows shall make an application in 
writing, and shall produce along with it a certificate of recommendation to the 
purport below,""" signed by at least four Ordinary Fellows, two of whom shall 
certify their recommendation from personal knowledge. This recommendation 
shall be delivered to the Secretary, and by him laid before the Council, and 
shall afterwards be printed in the circulars for three Ordinary Meetings of 
the Society, previous to the day of election, and shall lie upon the table during 
that time. 

X. 

Honorary Fellows shall not be subject to any contribution. This class shall 

* "A. B., a gentleman well versed in Science (or Polite Literature, as the case may be), being 
" to our knowledge desirous of becoming a Fellow of the Royal Society of Edinburgh, we hereby 
" recommend him as deserving of that honour, and as likely to prove a useful and valuable Member." 



XV 

consist of persons eminently distinguished for science or literature. Its number 
shall not exceed Fifty-six, of whom Twenty may be British subjects, and Thirty- 
six may be subjects of foreign states. 

XI. 

Personages of Royal Blood may be elected Honorary Fellows, without regard Royal Personages. 
to the limitation of numbers specified in Law X. 

XII. 

Honorary Fellows may be proposed by the Council, or by a recommenda- Recommendation 
tion (in the form given below*) subscribed by three Ordinary Fellows ; and in lows. 
case the Council shall decline to bring this recommendation before the Society, 
it shall be competent for the proposers to bring the same before a General 
Meeting. The election shall be by ballot, after the proposal has been commu- Mode of Election. 
nicated viva voce from the Chair at one meeting, and printed in the circulars 
for two ordinary meetings of the Society, previous to the day of election. 

XIII. 

The election of Ordinary Fellows shall only take place at the first Ordinary Election of ordi- 

n.£irv Fellows. 

Meeting of each month during the Session. The election shall be by ballot, 
and shall be determined by a majority of at least two-thirds of the votes, pro- 
vided Twenty-four Fellows be present and vote. 

XIV. 

The Ordinary Meetings shall be held on the first and third Mondays of Ordinary Meet- 
every month from November to June inclusively. Regular Minutes shall be 
kept of the proceedings, and the Secretaries shall do the duty alternately, or 
according to such agreement as they may find it convenient to make. 

XV. 

The Society shall from time to time publish its Transactions and Proceed- T]ie Transactions. 
ings. For this purpose the Council shall select and arrange the papers which 

We hereby recommends 



for the distinction of being made an Honorary Fellow of this Society, declaring that each of us from 
our own knowledge of his services to [Literature or Science, as the case may be) believe him to be 
worthy of that honour. 

(To be signed by three Ordinary Fellows.) 



To the President and Council of the Royal Society 
of Edinburgh. 



XVI 



How Published. 



The Council. 



Retiring Council- 
lors. 



Election of Offico 
Bearcrs. 



Special Meetings ; 
how called. 



Treasurer's Duties. 



Auditor. 



they shall deem it expedient to publish in the Transactions of the Society, and 
shall superintend the printing of the same. 

XVI. 

The Transactions shall be published in parts or Fasciculi at the close of 
each Session, and the expense shall be defrayed by the Society. 

XVII. 

There shall be elected annually, for conducting the publications and regu- 
lating the private business of the Society, a Council, consisting of a President ; 
Six Vice-Presidents, two at least of whom shall be resident ; Twelve Council- 
lors, a General Secretary, Two Secretaries to the Ordinary Meetings, a Trea- 
surer, and a Curator of the Museum and Library. 

XVIII. 

Four Councillors shall go out annually, to be taken according to the order 
in which they stand on the list of the Council. 

XIX. 

An Extraordinary Meeting for the Election of Office-Bearers shall be held 
on the fourth Monday of November annually. 

XX. 

Special Meetings of the- Society may be called by the Secretary, by direction 
of the Council ; or on a requisition signed by six or more Ordinary Fellows. 
Notice of not less than two days must be given of such Meetings. 

XXI. 

The Treasurer shall receive and disburse the money belonging to the Society, 
granting the necessary receipts, and collecting the money when due. 

He shall keep regular accounts of all the cash received and expended, which 
shall be made up and balanced annually ; and at the Extraordinary Meeting in 
November, he shall present the accounts for the preceding year, duly audited. 
At this Meeting, the Treasurer shall also lay before the Council a list of all 
arrears due above two years, and the Council shall thereupon give such direc- 
tions as they may deem necessary for recovery thereof. 

XXII. 

At the Extraordinary Meeting in November, a professional accountant shall 
be chosen to audit the Treasurer's accounts for that year, and to give the neces- 
sary discharge of his intromissions. 



XV11 

XXIII. 

The General Secretary shall keep Minutes of the Extraordinary Meetings of General Secretary** 

. . - TT Duties. 

the Society, and of the Meetings of the Council, in two distinct books. He 
shall, under the direction of the Council, conduct the correspondence of the 
Society, and superintend its publications. For these purposes he shall, when 
necessary, employ a clerk, to be paid by the Society. 

XXIV. 

The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, Secretaries to 
in which a full account of the procedings of these Meetings shall be entered; 
they shall specify all the Donations received, and furnish a list of them, and of 
the Donors' names, to the Curator of the Library and Museum ; they shall like- 
wise furnish the Treasurer with notes of all admissions of Ordinary Fellows. 
They shall assist the General Secretary in superintending the publications, and 
in his absence shall take his duty. 

XXV. 

The Curator of the Museum and Library shall have the custody and charge Curator of Museum 
of all the Books, Manuscripts, objects of Natural History, Scientific Produc- 
tions, and other articles of a similar description belonging to the Society ; he 
shall take an account of these when received, and keep a regular catalogue of 
the whole, which shall lie in the Hall, for the inspection of the Fellows. 

XXVI. 

All Articles of the above description shall be open to the inspection of the Use of Museum 
Fellows at the Hall of the Society, at such times and under such regulations, a "' ' rary ' 
as the Council from time to time shall appoint. 

XXVII. 

A Register shall be kept, in which the names of the Fellows shall be Register Book. 
enrolled at their admission, with the date. 



VOL. XXVI. PART IV. 



DIRECTIONS TO THE BINDER FOR PLACING THE PLATES IN THIS VOLUME. 



Plate 



TT ' I Illustrating Mr J. Clerk Maxwell's Paper on Reciprocal Figures, Frames, and 
TT y j Diagrams of Forces, To face page 1 

( Illustrating the Eev. Thomas Brown's Paper on the Old River Terraces of the 
IV. < Earn and Teith, viewed in connection with certain Proofs of the Antiquity 

( of Man, 149 

V i 

VI. (Illustrating Professor Turner's Paper, Account of the Great Finner Whale 

VII. f (Balainoptera Sibbaldii) stranded at Longniddry. Part I. — The Soft Parts, 197 

VIII. ) 

IX. ^ Illustrating Dr W. C. M'Intosh's Paper on some Points in the Structure of 
X. j TuUfex, 253 

XI. \ 

XII I 
Yttt' Illustrating Dr James Bell Pettigrew's Paper on the Physiology of Wings, 

Yyv ) being an Analysis of the Movements by which Flight is produced in the 

Y^t Insect, Bat, and Bird, . . . . . . . . .321 

XVI. J 

XVII. 1 Illustrating Professor Turner's Paper on the Gravid Uterus, and on the Arrange- 
XVIII. J ment of the Foetal Membranes in the Cetacea, . . . . .467 

XIX. "j 

XX. (illustrating Professor Alexander Dickson's Paper on Some Abnormal Cones of 
XXI. C Pinus Pinaster, . . . . . . . . . .505 

XXII. ) 

XXIII. ^ 

vvtv' I Illustrating Dr Thomas R. Fraser's Paper on an Experimental Research on the 

VVT7- f Antagonism between the Actions of Physostigma and Atropia, . .529 

"X"X"VT ( Illustrating Mr J. A. Broun's Paper on the Lunar Diurnal Variation of Magnetic 
XYVTT< Declination at Trevandrum, near the Magnetic Equator, deduced from 
YYVTTT I Observations made in the Observatory of His Highness the Maharajah of 
AJLViii. ^ Travancore, G.C.S.I 735 



XXIX 



C Illustrating Professor Turner's Paper on the Occurrence of ZipMus cavirostris in 



-^-^-^-'-j the Shetland Seas, and a Comparison of its Skull with that of Sowerby's 

\ Whale (Mesoplodon Sowerbyi), . . . . . . . .759 

XXXI. \ Illustrating Professor Balfour's Paper, Remarks on the Ipecacuan Plant (Cephaelis 
XXXII. _j Ipecacuanha, Rich ), as cultivated in the Royal Botanic Garden, Edinburgh, 779 



CONTENTS. 



PART I. (1869-70.) 



TAGE 



I. — On Reciprocal Figures, Frames, and Diagrams of Forces. 
By J. Clerk Maxwell, F.R.SS. L. & E. (Plates I., 
II., and III.), ...... 1 

II. — On Scientific Method in the Interpretation of Popular Myths, 
with special reference to Greek Mythology. By Professor 
Blackie, ...... 41 

III. On the Extension of Brouncker's Method to the Comparison of 

Several Magnitudes. By Edward Sang, Esq., . . 59 

IV. — On Green's and other Allied Theorems. By Professor Tait, . 69 

V. — On the Heat Developed in the Combination of Acids and Bases. 
Second Memoir. By Thomas Andrews, M.D., F.R.S., 
Hon. F.R.S.E., Vice-President of Queen's College, 
Belfast, . . . . . . .85 

VI. — The Genetic Succession of Zooids in the Hydroida. By 

Professor Allman, . . . . .97 

VII. — Influence of the Vagus upon the Vascular System. By 
William Rutherford, M.D., F.R.S.E., Professor of 
Physiology, King's College, London, . . .107 

VIII. — On the Old River Terraces of the Earn and Teith, viewed in 
connection with certain Proofs of the Antiquity of Man. 
By the Rev. Thomas Brown, F.R.S.E. (Plate IV.), . 149 

VOL. XXVI. PART IV. f 



xxn CONTENTS. 



PAGE 



IX. — On Spectra formed by the Passage of Polarized Light through 
Refracting Crystals. By Francis Deas, M.A., LL.B., 
F.R.S.E., 177 

Addition to the above Paper. By J. Clerk Maxwell, LL.D., 

F.R.SS., L. & E., 185 

X. On the Oxidation of Products of Picoline. By James Dewar, 
F.R.S.E., Chemical Demonstrator in the University of 
Edinburgh, and Lecturer on Chemistry at the Edinburgh 
Veterinary College, . . . . .189 

XI. An Account of the Great Finner Whale (Bakenoptera Sib- 
baldii) stranded at Longniddry . Part I. — The Soft Parts. 
By William Turner, M.B., (Loncl.), Professor of Anat- 
omy in the University of Edinburgh. (Plates V.-VIIL), 197 



PAKT II. (1870-71.) 

XII. On Some Points in the Structure of Tubifex. By W. C. 

M'Intosh, M.D., F.R.S.E. (Plates IX. and X.), . 253 

XIII. — On the Place and Power of Accent in Language. By Pro- 
fessor Blackie, ....... 269 

XIV. — On the Average Quantity of Rain in Carlisle and the Neigh- 
bourhood. By Thomas Barnes, M.D., F.E.S.E., . 313 

XV. — On the Physiology of Wings, being an Analysis of the Move- 
ments by ivhich Flight is produced in the Insect, Bat, and 
Bird. By James Bell Pettigrew, M.D., F.RS., Path- 
ologist to the Royal Infirmary of Edinburgh, and Curator 
of the Museum of the Royal College of Surgeons of 
Edinburgh. Communicated by Professor Turner. 
(Plates XI. to XVI.), . . . .321 



CONTENTS. XXlll 



PAGE 



XVI. — Additional Note on the Motion of a Heavy Body along the 
Circumference of a Circle. By Edward Sang, Esq., 
F.R.S.E., . . . . . . .449 

XVII. — On the Homological Relations of the Cwlenterata. By Pro- 
fessor Allman, ...... 459 

XVIII. On the Gravid Uterus and on the Arrangement of the Foetal 
Membranes in the Cetacea. By Professor Turner. 
(Plates XVII. and XVIII.), . . . .467 

XIX. — On some Abnormal Cones of Pinus Pinaster. By Alexander 
Dickson, M.D., Regius Professor of Botany in the 
University of Glasgow. (Plates XIX. to XXII.), . 505 



PART III. (1870-71.) 

XX. — Account of the New Table of Logarithms to 200000. By 

Edward Sang, Esq., F.R.S.E., .... 521 

XXI. — An Experimental Research on the Antagonism between the 
Actions of Physostigma and Atropia. By Thomas R. 
Fraser, M.D., Lecturer on Materia Medica and 
Therapeutics at Surgeon's Hall, Edinburgh. (Plates 
XXIII.-XXV.), 592 



PART IV. (1871- 2) 

XXII. — On the Decomposition of Forces externally applied to an Elastic 
Solid. By W. J. Macquorn Rankine, C.E., LL.D., 
F.R.SS. L. & E., 715 

XXIII. — On the Geometrical Mean Distance of Two Figures on a Plane. 

By Professor J. Clerk Maxwell, F.R.S., . . 729 



XX1V CONTENTS. 



PAGE 



735 



XXIV.-On the Lunar Diurnal Variation of Magnetic Declination at 
Irevandrum, near the Magnetic Equator, deduced from 
Observations made in the Observatory of His Highness the 
Maharajah of Travancore, G.C.S.L By J A Broun 
F.RS. (Plates XXVI.-XXVIII), 

¥ 

XXV. -On the Occurrence tf/Ziphiuscavirostris in the Shetland Seas, 
and a Comparison of its Skull with that of Sowerby's 
Whale (Mesoploden Sowerbyi). By Professor Turner 
(Plates XXIX., XXX.), 

XXVl-Xemarks on the Ipecacuan Plant (Cephaelis Ipecacuanha 
Rich), as cultivated in the Royal Botanic Garden, Edin- 
burgh. By John Hutton Balfour, M.D., F.R.S., Sec. 
R.S.E., F.L.S., Hon. Mem. Pharm. Soc, and Professor 
of Medicine and Botany in the University of Edinburgh 
(Plates XXXI. and XXXII), . 781 



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TRANSACTIONS. 



I. — On Reciprocal Figures, Frames, and Diagrams of Forces. By J. Clerk 
Maxwell, F.R.SS. L. & E. (Plates I. II. III.) 

(Received 17th Dec. 1869 ; read 7th Feb. 1870.) 

Two figures are reciprocal when the properties of the first relative to the 
second are the same as those of the second relative to the first. Several kinds 
of reciprocity are known to mathematicians, and the theories of Inverse Figures 
and of Polar Reciprocals have been developed at great length, and have led to 
remarkable results. I propose to investigate a different kind of geometrical 
reciprocity, which is also capable of considerable development, and can be 
applied to the solution of mechanical problems. 

A Frame may be defined geometrically as a system of straight lines connect- 
ing a number of points. In actual structures these lines are material pieces, 
beams, rods, or wires, and may be straight or curved ; but the force by which 
each piece resists any alteration of the distance between the points which it joins 
acts in the straight line joining those points. Hence, in studying the equilibrium 
of a frame, we may consider its different points as mutually acting on each 
other with forces whose directions are those of the lines joining each pair of points. 
When the forces acting between the two points tend to draw them together, or 
to prevent them from separating, the action along the joining line is called a 
Tension. When the forces tend to separate the points, or to keep them apart, 
the action along the joining line is called a Pressure. 

If we divide the piece joining the points by any imaginary section, the 
resultant of the whole internal force acting between the parts thus divided will 
be mechanically equivalent to the tension or pressure of the piece. Hence, in 
order to exhibit the mechanical action of the frame in the most elementary 
manner, we may draw it as a skeleton, in which the different points are joined 
by straight lines, and we may indicate by numbers attached to these lines the 
tensions or pressures in the corresponding pieces of the frame. 

The diagram thus formed indicates the state of the frame in a way which is 

VOL. XXVI. PART I. A 



2 MR CLERK MAXWELL ON 

geometrical as regards the position and direction of the forces, but arithmetical 
as regards then magnitude. 

But, by assuming that a line of a certain length shall represent a force of a 
certain magnitude, we may represent every force completely by a line. This 
is done in Elementary Statics, where we are told to draw a line from the point 
of application of the force in the direction in which the force acts, and to cut off' 
as many units of length from the line as there are units of force in the force, and 
finally to mark the end of the line with an arrow-head, to show that it is a force and 
not a piece of the frame, and that it acts in that direction and not the opposite. 

By proceeding in this way, we should get a system of arrow-headed forces 
superposed on the skeleton of the frame, two equal and opposite arrows for 
every piece of the frame. 

To test the equilibrium of these forces at any point of concourse, we should 
proceed by the construction of the parallelogram of forces, beginning -with two 
of the forces acting at the point, completing the parallelogram, and drawing the 
diagonal, and combining this with the third force in the same way, till, when all 
the forces had been combined, the resultant disappeared. We should thus have 
to draw three new lines, one of which is an arrow, in taking in each force after 
the first, leaving at last not only a great number of useless lines, but a number 
of new arrows, not belonging to the system of forces, and only confusing to 
any one wishing to verify the process. 

To simplify this process, we are told to construct the Polygon of Forces, by 
drawing in succession lines parallel and proportional to the different forces, each 
line beginning at the extremity of the last. If the forces acting at the point 
are in equilibrium, the polygon formed in this way will be a closed one. 

Here we have for the first time a true Diagram of Forces, in which every 
force is not only represented in magnitude and direction by a straight line, but 
the equilibrium of the forces is manifest by inspection, for we have only to 
examine whether the polygon is closed or not. To secure this advantage, how- 
ever, we have given up the attempt to indicate the position of the force, for the 
sides of the polygon do not pass through one point as the forces do. We must, 
therefore, give up the plan of representing the frame and its forces in one 
diagram, and draw one diagram of the frame and a separate diagram of the 
forces. By this method we shall not only avoid confusion, but we shall greatly 
simplify mechanical calculations, by reducing them to operations with the 
parallel ruler, in which no useless lines are drawn, but every line represents an 
actual force. 

A Diagram of Forces is a figure, every line of which represents in magnitude 
and direction the force acting along a piece of the frame. 

To express the relation between the diagram of the frame and the diagram 
of forces, the lines of the frame should each be indicated by a symbol, and the 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 3 

corresponding lines of the diagram of forces should be indicated by the same 
symbol, accented if necessary. 

We have supposed the corresponding lines to be parallel, and it is necessary 
that they should be parallel when the frame is not in one plane ; but if all the 
pieces of the frame are parallel to one plane, we may turn one of the diagrams 
round a right angle, and then every line will be perpendicular to the corres- 
ponding line. 

If any number of lines meet at the same point in the frame, the correspond- 
ing lines in the diagram of forces form a closed polygon. 

It is possible, in certain cases, to draw the diagram of forces so that if any 
number of lines meet in a point in the diagram of forces, the corresponding lines 
in the frame form a closed polygon. 

In such cases, the two diagrams are said to be reciprocal in the sense in 
which we use it in this paper. If either diagram be taken as representing 
the frame, the lines of the other diagram will represent a system of forces 
which, if applied along the corresponding pieces of the frame, will keep it in 
equilibrium. 

The properties of the " triangle " and " polygon " of forces have been long 
known, and a " diagram " of forces has been used in the case of the " funicular 
polygon," but I am not aware of any more general statement of the method of 
drawing diagrams of forces before Professor Rankine applied it to frames, roofs, 
&c, in his "Applied Mechanics," p. 137, &c. The " polyhedron of forces," or 
the proposition that forces acting on a point perpendicular and proportional to 
the areas of the faces of a polyhedron are in equilibrium, has, I believe, been 
enunciated independently at various times, but the application of this principle 
to the construction of a diagram of forces in three dimensions was first made 
by Professor Eankine in the "Philosophical Magazine," Feb. 1864. In the 
"Philosophical Magazine" for April 1864, I stated some of the properties of 
reciprocal figures, and the conditions of their existence, and showed that any 
plane rectilinear figure which is a perspective representation of a closed poly- 
hedron with plane faces has a reciprocal figure. In Sept. 1867, I communi- 
cated to the British Association a method of drawing the reciprocal figure, 
founded on the theory of reciprocal polars. 

I have since found that the construction of diagrams of forces in which each 
force is represented by one line, had been independently discovered by Mr W. 
P. Taylor, and had been used by him as a practical method of determining 
the forces acting in frames for several years before I had taught it in King's 
College, or even studied it myself. I understand that he is preparing a state- 
ment of the application of the method to various kinds of structures in detail, 
so that it can be made use of by any one who is able to draw one fine parallel 
to another. 



4 MR CLERK MAXWELL ON 

Professor Fleeming Jenkin, in a paper recently published by the Society, 
has fully explained the application of the method to the most important cases 
occurring in practice. 

In the present paper I propose, first, to consider plane diagrams of frames 
and of forces in an elementary way, as a practical method of solving questions 
about the stresses in actual frameworks, without the use of long calculations. 

I shall then discuss the subject in a theoretical point of view, and give a 
method of denning reciprocal diagrams analytically, which is applicable to 
figures either of two or of three dimensions. 

Lastly, I shall extend the method to the investigation of the state of stress 
in a continuous body, and shall point out the nature of the function of stress 
first discovered by the Astronomer Royal for stresses in two dimensions, extend- 
ing the use of such functions to stresses in three dimensions. 

On Reciprocal Plane Rectilinear Figures. 

Definition. — Two plane rectilinear figures are reciprocal when they consist 
of an equal number of straight lines, so that corresponding lines in the two 
figures are at right angles, and corresponding lines which meet in a point in 
the one figure form a closed polygon in the other. 

Note. — It is often convenient to turn one of the figures round in its own 
plane 90°. Corresponding lines are then parallel to each other, and this is 
sometimes more convenient in comparing the diagrams by the eye. 

Since every polygon in the one figure has three or more sides, every point in 
the other figure must have three or more lines meeting in it. Since every line 
in the one figure has two, and only two, extremities, every fine in the other figure 
must be a side of two, and only two, polygons. If either of these figures be taken 
to represent the pieces of a frame, the other will represent a system of forces 
such that, these forces being applied as tensions or pressures along the correspond- 
ing pieces of the frame, every point of the frame will be in equilibrium. 

The simplest example is that of a triangular frame without weight, ABC, 
jointed at the angles, and acted on by three forces, P, Q, R, applied at the 
angles. The directions of these three forces must meet in a point, if the frame 
is in equilibrium. We shall denote the fines of the figure by capital letters, 
and those of the reciprocal figure by the corresponding small letters ; we shall 
denote points by the lines which meet in them, and polygons by the lines which 
bound them. 

Here, then, are three lines, A, B, C, forming a triangle, and three other 
lines, P, Q, R, drawn from the angles and meeting in a point. Of these forces 
let that along P be given. Draw the first line p of the reciprocal diagram 
parallel to P, and of a length representing, on any convenient scale, the force 
along P. The forces along P, Q, R are in equilibrium, therefore, if from one 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 5 

extremity of p we draw q parallel to Q, and from the other extremity r parallel 
to R, so as to form a triangle pqr, then q and r will represent on the same scale 
the forces along Q and R. 





To determine whether these forces are tensions or pressures, make a point 
travel along p in the direction in which the force in P acts on the point of con- 
course of PQR, and let the point travel in the same direction round the 
polygon pqr. Then, the direction in which the point travels along any side 
of the polygon will be the direction in which the force acts along the corres- 
ponding piece of the frame on the point of concourse. If it acts from the 
point of concourse, the force is a tension ; if towards it, it is a pressure. 

The other extremity of P meets B and C, and the forces along these three 
pieces are in equilibrium. Hence, if we draw a triangle, having p for one side 
and lines parallel to B and C for the others, the sides of this triangle will 
represent the three forces. 

Such a triangle may be described on either side of p, the two together would 
form a parallelogram of forces; but the theory of reciprocal figures indicates 
that only one of these triangles forms part of the diagram of forces. 

The rule for such cases is as follows : — Of the two extremities of p, one cor- 
responds to the closed figure PRB, and the other to the closed figure PQC, 
these being the polygons of which P is a side in the first figure. 

We must, therefore, draw b parallel to B from the intersection of p and r, 
and not from the other extremity, and we must draw c parallel to C from the 
intersection of p and q. 

We have now a second triangle, pbc, corresponding to the forces acting 
at the point of concourse of P, B, C. To determine whether these forces are 
tensions or pressures, we must make a point travel round pbc, so that its 
course along p is in the opposite direction to its course round pqr, because the 
piece P acts on the points PBC and PQR with equal and opposite forces. 

If we now consider the equilibrium of the point of concourse of QC and A, 
we shall find that we have determined two of these forces by the lines q and c, 
and that the third force must be represented by the line a which completes the 
triangle qca. 

We have now constructed a complete diagram of forces, in which each force 

VOL. XXVI. PART I. B 



6 MR CLERK MAXWELL ON 

is represented by a single line, and in which the equilibrium of the forces meet- 
ing at any point is expressed visibly by the corresponding lines in the other 
figure forming a closed polygon. 

There are in this figure six lines, having four points of concourse, and form- 
ing four triangles. To determine the direction of the force along a given line 
at any point of concourse, we must make a point travel round the corresponding 
polygon in the other figure in a direction which is positive with respect to that 
polygon. For this purpose it is desirable to name the polygons in a determi- 
nate order of their sides, so arranged that, when we arrive at the same side in 
naming the two polygons which it divides, we travel along it in opposite direc- 
tions. For instance, if pqr be one of the polygons, the others are pbc, qca, rab. 

Note. — It may be observed, that after drawing the lines p, q, r, b, c with the 
parallel ruler, the line a was drawn by joining the points of concourse of q, r 
and b, c; but, since it represents the force in A, a is parallel to A. Hence the 
following geometrical theorem : — 

If the lines PQR, drawn from the angles of the triangle ABC, meet in a point, 
then if pqr be a triangle with its corresponding sides parallel to P, Q, R, and if 
a, b, c be drawn from its corresponding angles parallel to A, B, C, the lines 
a, b, c will meet in a point. 

A geometrical proof of this is easily obtained by finding the centres of the 
four circles circumscribing the triangles ABC, AQR, BRP, CPQ, and joining 
the four centres thus found by six lines. 

These lines meet in the four centres, and are perpendicular to the six lines, 
A, B, C ; P, Q, R ; but by turning them round 90° they become parallel to the 
corresponding lines in the original figure. 

The diagram formed in this way is definite in size and position, but any 
figure similar to it is a reciprocal diagram to the original figure. I have 
explained the construction of this, the simplest diagram of forces, more at 
length, as I wish to show how, after the first line is drawn and its extremities 
fixed on, every other line is drawn in a perfectly definite position by means of 
the parallel ruler. 

In any complete diagram of forces, those forces which act at a given point 
in the frame form a closed polygon. Hence, there will be as many closed 
polygons in the diagram as there are points in the frame. Also, since each 
piece of the frame acts with equal and opposite forces on the two points which 
form its extremities, the force in the diagram will be a side of two different 
polygons. These polygons might be drawn in any positions relatively to each 
other ; but, in the diagrams here considered, they are placed so that each force 
is represented by one line, which forms the boundary between the two polygons 
to which it belongs. 

If we regard the polygons as surfaces, rather than as mere outlines, every 



RECIPEOCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 7 

polygon will be bounded at every point of its outline by other polygons, so 
that the whole assemblage of polygons will form a continuous surface, which 
must either be an infinite surface or a closed surface. 

The diagram cannot be infinite, because it is made up of a finite number of 
finite lines representing finite forces. It must, therefore, be a closed surface 
returning on itself, in such a way that every point in the plane of the diagram 
either does not belong to the diagram at all, or belongs to an even number of 
sheets of the diagram. 

Any system of polygons, which are in contact with each other externally, 
may be regarded as a sheet of the diagram. When two polygons are on the 
same side of the line, which is common to them, that line forms part of the 
common boundary of two sheets of the diagram. If we reckon those areas 
positive, the boundary of which is traced in the direction of positive rotation 
round the area, then all the polygons in each sheet will be of the same sign as 
the sheet, but those sheets which have a common boundary will be of opposite 
sign. At every point in the diagram there will be the same number of positive 
as of negative sheets, and the whole area of the positive sheets will be equal to 
that of the negative sheets. 

The diagram, therefore, may be considered as a plane projection of a closed 
polyhedron, the faces of the polyhedron being surfaces bounded by rectilinear 
polygons, which may or may not, as far as we yet know, lie each in one plane. 

Let us next consider the plane projection of a given closed polyhedron. 
If any of the faces of this polyhedron are not plane, we may, by drawing 
additional lines, substitute for that face a system of triangles, each of which is 
necessarily in a plane. We may, therefore, consider the polyhedron as bounded 
by plane faces. Every angular point of this polyhedron will be defined by its 
projection on the plane and its height above it. 

Let us now take a fixed point, which we shall call the origin, and draw from 
it a perpendicular to the plane. We shall call this line the axis. If we then 
draw from the origin a line perpendicular to one of the faces of the polyhedron, 
it will cut the plane at a point which may be said to correspond to the projec- 
tion of that face. From this point draw a line perpendicular to the plane, and 
take on this line a point whose distance from the plane is equal to that of the 
intersection of the axis with the face of the polyhedron produced, but on the 
other side of the plane. This point in space will correspond to the face of the 
polyhedron. By repeating this process for every face of the polyhedron, we 
shall find for every face a corresponding point with its projection on the plane. 

To every edge of the polyhedron will correspond the line which joins the 
points corresponding to the two faces which meet in that edge. Each of these 
lines is perpendicular to the projection of the other ; for the perpendiculars 
from the origin to the two faces, lie in a plane perpendicular to the edge in 



8 MR CLERK MAXWELL ON 

which they meet, and the projection of the line corresponding to the edge is the 
intersection of this plane with the plane of projection. Hence, the edge is 
perpendicular to the projection of the corresponding line. The projection of 
the edge is therefore perpendicular to the projection of the corresponding line, 
and therefore to the corresponding line itself. In this way we may draw a 
diagram on the plane of projection, every line of which is perpendicular to the 
corresponding line in the original figure, and so that lines which meet in a point 
in the one figure form a closed polygon in the other. 

If, in a system of rectangular co-ordinates, we make z=0 the plane of pro- 
jection, and x = y = z = —c the fixed point, then if the equation of a plane be 

z = Ax + By + C , 
the co-ordinates of the corresponding point will be 

£ = cA v = cB f = - c , 

and we may write the equation 

<*+£) = a£ + yr, . 

If we suppose £, ??, £ given as the co-ordinates of a point, then this equation, 
considering x, y, z as variable, is the equation of a plane corresponding to the 
point. 

If we suppose x, y, z the co-ordinates of a point, and £, -q, £ as variable, the 
equation will be that of a plane corresponding to that point, 

Hence, if a plane passes through the point xyz, the point corresponding to 
this plane lies in the plane corresponding to the point xyz. 

These points and planes are reciprocally polar in the ordinary sense with 
respect to the paraboloid of revolution 

2cz = o? + y 2 . 

We have thus arrived at a construction for reciprocal diagrams by consider- 
ing each as a plane projection of a plane-sided polyhedron, these polyhedra 
being reciprocal to one another, in the geometrical sense, with respect to a cer- 
tain paraboloid of revolution. 

Each of the diagrams must fulfil the conditions of being a plane projection 
of a plane-sided polyhedron, for if any of the sides of the polyhedron of which 
it is the projection are not plane, there will be as many points corresponding to 
that side as there are different planes passing through three points of the side, 
and the other diagram will be indefinite. 

Belation between the Number of Edges, Summits, and Faces of Polyhedra. 

It is manifest that after a closed surface has been divided into separate faces 
by lines drawn upon it, every new line drawn from a point in the system, either 
introduces one new point into the system, or divides a face into two parts, 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 9 

according as it is drawn to an isolated point, or to a point already connected 
with the system. Hence the sum of points and faces is increased by one for 
every new line. If the closed surface is acyclic, or simply connected/" like that 
of a solid body without any passage through it, then, if from any point we draw 
a closed curve on the surface, we divide the surface into two faces. We have 
here one line, one point, and two faces. Hence, if e be the number of lines, 
s the number of points, and /the number of faces, then in general 

e — s — f = m 

when m remains constant, however many lines be drawn. But in the case of a 
simple closed surface 

m = — 2 . 

If the closed surface is doubly connected, like that of a solid body with a 
hole through it, then if we draw one closed curve round the hole, and another 
closed curve through the hole, and round one side of the body, we shall have 
e — 2, s = 1,/— 1, so that n = 0. If the surface is n-lj connected, like that 
of a solid with n — 1 holes through it, then we may draw n closed curves 
round the n — 1 holes and the outside of the body, and n — 1 other closed curves 
each through a hole and round the outside of the body. 

We shall then have 4(^ — 1) segments of curves terminating in 2(n — 1) 
points and dividing the surface into two faces, so that e = 4(w — 1), 
s = 2 (n — 1), and/= 2, and 

e — s — f —In — 4 , 

and this is the general relation between the edges, summits, and faces of a 
polyhedron whose surface is ra-ly connected. 

The plane reciprocal diagrams, considered as plane projections of such 

* See Riemann, Crelle's Journal, 1857, Lehrsatze aus der analysis sitits, for space of two dimen- 
sions ; also Catley on the Partitions of a Close, Phil. Mag. 1861 ; Helmholtz, Crelle's Journal, 1858, 
Wirbelbewegung, for the application of the idea of multiple continuity to space of three dimensions ; J. 
B. Listing, Gottingen Trans., 1861, Der Census Raumlicher Complexe, a complete treatise on the 
subject of Cyclosis and Periphraxy. 

On the importance of this subject see Gauss, "Werke, v. 605, " Von der Geometria Situs die Leibnitz 
ahnte unci in die nur einem Paar Geometern (Euler unci Vandermonde) einen schwachen Blick zu thun 
vergb'nnt war, wissen und haben wir nach anderthalbhundert Jahren noch nicht viel mehr wie nichts." 

Note added March 14, 1870. — Since this was written, I have seen Listing's Census. In his 
notation, the surface of an rc-ly connected body (a body with n — 1 holes through it) is (2k — 2) 
cyclic. If 2n — 2 = K 2 expresses the degree of cyclosis, then Listing's general equation is — 

s- ( e - K x ) + (/- K 2 + *r 2 ) - - K 3 + «r a - to) = , 

where s is the number of points, e the number of lines, K a the number of endless curves, /the number 
of faces, K 2 the number of degrees of cyclosis of the faces, sr 2 the number of periphractic or closed 
faces, v the number of regions of space, K 3 their number of degrees of cyclosis, sr 3 their number of 
degrees of periphraxy or the number of regions which they completely surround, and to is to be put 
= 1 or = 0, according as the system does or does not extend to infinity. 

VOL. XXVI. PART I. C 



10 MR CLERK MAXWELL ON 

polyhedra, have the same relation between the numbers of their lines, points, 
and polygons. It is manifest that since 

h = e 2 , s 1 =f 1 , and f x = s 2 , 

where the suffixes refer to the first and second diagrams respectively 

or the two diagrams are connected to the same degree. 

On the Degrees of Freedom and Constraint of Frames. 

To determine the positions of s points in space, with reference to a given 
origin and given axes, 3s data are required; but since the position of the origin 
and axes involve 6 data, the number of data required to determine the relative 
position of s points is 3s — 6. 

If, therefore, the lengths of Ss — 6 lines joining selected pairs of a system of 
s points be given, and if these lengths are all independent of each other, then 
the distances between any other pair of points will be determinate, and the 
system will be rigidly connected. 

If, however, the lines are so chosen that those which join pairs of points of 
a system of s' of the points are more than 3s' — 6 in number, the lengths of 
these lines will not be independent of each other, and the lines of this partial 
system will only give 3s' — 6 independent data to determine the complete system. 

In a system of s points joined by e lines, there will in general be 3s — 6 — e 
= p degrees of freedom, provided that in every partial system of s' points joined 
by e' lines, and having in itself p' degrees of freedom, p' is not negative. If in 
any such system p is negative, we may put q = — p, and call q the number of 
degrees of constraint, and there will be q equations connecting the lengths of 
the lines ; and if the system is a material one, the stress along each piece will 
be a function of q independent variables. Such a system may be said to have 
q degrees of constraint. If p' is negative in any partial system, then the 
degrees of freedom of the complete system are p — p', where p and p' are got 
from the number of points and lines in the complete and partial systems. If s 
points are connected by e lines, so as to form a polyhedron of / faces, enclosing 
a space n times connected, and if each of the faces has m sides, then 



We have also 


mf = 2e . 
e — s - f = 2n — 4, 


and 




whence 


3s — e = p + 6 , 




P = 6(1 - n) + (2 - £) 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 11 

If all the faces of the polyhedron are triangles, m = 3, and we have 

p = 6(1 — n) . 

If n = 1, or in the case of a simply connected polyhedron with triangular 
faces, p = o, that is to say, such a figure is a rigid system, which would be no 
longer rigid if any one of its lines were wanting. In such a figure, if made of 
material rods forming a closed web of triangles, the tensions and pressures in the 
rods would be completely determined by the external forces applied to the figure, 
and if there were no external force, there would be no stress in the rods. 

In a closed surface of any kind, if we cover the surface""" with a system of 
curves which do not intersect each other, and if we draw another system inter- 
secting these, and a third system passing diagonally through the intersections of 
the other two, the whole surface will be covered with small curvilinear triangles, 
and if we now substitute for the surface a system of rectilinear triangles having 
the same angular points, we shall have a polyhedron with triangular faces 
differing infinitely little from the surface, and such that the length of any line 
on the surface differs infinitely little from that of the corresponding line on the 
polyhedron. We may, therefore, in all questions about the transformation of 
surfaces by bending, substitute for them such polyhedra with triangular faces. 

We thus find with respect to a simply connected closed inextensible surface 
— 1st, That it is of invariable form ;t 2d, That the stresses in the surface depend 
entirely on the external applied forces ;J %d, That if there is no external force, 
there is no stress in the surface. 

In the limiting case of the curved surface, however, a kind of deformation is 
possible, which is not possible in the case of the polyhedron. Let us suppose 
that in some way a dimple has been formed on a convexo-convex part of the 
surface, so that the edge of the dimple is a plane closed curve, and the dimpled 
part is the reflexion in this plane of the original form of the surface. Then the 
length of any line drawn on the surface will remain unchanged. 

Now let the dimple be gradually enlarged, so that its edge continually 
changes its position. Every line on the surface will still remain of the same 
length during the whole process, so that the process is possible in the case of 
an inextensible surface. In this way such a surface may be gradually turned 
outside in, and since the dimple may be formed from a mere point, a pressure 
applied at a single point on the outside of an inextensible surface will not be 
resisted, but will form a dimple which will increase till one part of the surface 
comes in contact with another. 

In the case of closed surfaces doubly connected, p = — 6, that is, such sur- 

* On the Bending of Surfaces, by J. Clerk Maxwell. Cambridge Transactions, 1856. 
(" This has been shown by Professor Jellett, Trans. R.I.A., vol. xxii. p. 377. 
\ On the Equilibrium of a Spherical Envelope, by J. C. Maxwell. Quarterly Journal of 
Mathematics, 1867. 



12 MR CLERK MAXWELL ON 

faces are not only rigid, but are capable of internal stress, independent of 
external forces, and the expression of this stress depends on six independent 
variables. 

In a polyhedron with triangular faces, if a number of the edges be taken 
away so as to form a hole with e 1 sides, the number of degrees of freedom is 

p == gj — Qn + 3 . 

Hence, in order to make an n-\j connected polyhedron simply rigid without 
stress, we may cut out the edges till we have formed a hole having 6 n — 3 edges. 
The system will then be free from stress, but if any more edges be removed, the 
system will no longer be rigid. 

Since in the limiting case of the inextensible surface, the smallest hole may 
be regarded as having an infinite number of sides, the smallest hole made in a 
closed inextensible surface connected to any degree will destroy its rigidity. 
Its flexibility, however, may be confined within very narrow limits. 

In the case of a plane frame of s points, we have 2s data required to deter- 
mine the points with reference to a given origin and axes ; but since 3 arbitrary 
data are involved in the choice of origin and axis, the number of data required 
to determine the relative position of s points in a plane is 2s — 3. 

If we know the lengths of e lines joining certain pairs of these points, then 
in general the number of degrees of freedom of the frame will be 

p = 2s - e - 3 . 

If, however, in any partial system of s 7 points connected by e' hues, the quantity 
p' = 2s' — e' — 3 be negative, or in other words, if a part of the frame be self- 
strained, this partial system will contribute only 2s' — 3 equations independent 
of each other to the complete system, and the whole frame will have p — p' 
degrees of freedom. 

In a plane frame, consisting of a single sheet, every element of which is 
triangular, and in which the pieces form three systems of continuous lines, as at 
p. 11, if the frame contains e pieces connecting s points, s' of which are on the 
circumference of the frame and s 1 in the interior, then 

3s — s = c + 3 . 

Hence 

p=-(s-s') = -s l , 

a negative quantity, or such a frame is necessarily stiff ; and if any of the points 
are in the interior of the frame, the frame has as many degrees of constraint as 
there are interior points — that is, the stresses in each piece will be functions of 
Sj variables, and s 1 pieces may be removed from the frame without rendering it 
loose. 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 13 

If there are n holes in the frame, so that s' points lie on the circumference of 
the frame or on those of the holes, and s x points lie in the interior, the degree 
of stiffness will be 

— p = Sj + 3n . 

If a plane frame be a projection of a polyhedron of /faces, each of m sides, and 
enclosing a space n times connected, then 

to/ = 2e 
e — s — f=2n — 4 
2s — e =p + 3 , 

whence 



P — 5 — 4:71 + ( 1 ) 

1 \ TO/ 



If all the faces are quadrilaterals m = 4 and p = 5 — 4w, or a plane frame which 
is the projection of a closed polyhedron with quadrilateral faces, has one degree 
of freedom if the polyhedron is simply connected, as in the case of the projec- 
tion of the solid bounded by six quadrilaterals, but if the polyhedron be doubly 
connected, the frame formed by its plane projection will have three degrees of 
stiffness. (See Diagram II.) 

Theorem.— It every one of a system of points in a plane is in equilibrium 
under the action of tensions and pressures acting along the lines joining the 
points, then if we substitute for each point a small smooth ring through 
which smooth thin rods of indefinite length corresponding to the lines are 
compelled to pass, then, if to each rod be applied a couple in the plane, whose 
moment is equal to the product of the length of the rod between the points 
multiplied by the tension or pressure in the former case, and tends to turn the 
rod in the positive or the negative direction, according as the force was a tension 
or a pressure, then every one of the system of rings will be in equilibrium. For 
each ring is acted on by a system of forces equal to the tensions and pressures 
in the former case, each to each, the whole system being turned round a right 
angle, and therefore the equilibrium of each point is undisturbed. 

Theorem. — In any system of points in equilibrium in a plane under the 
action of repulsions and attractions, the sum of the products of each attraction 
multiplied by the distance of the points between which it acts, is equal to the 
sum of the products of the repulsions multiplied each by the distance of the 
points between which it acts. 

For since each point is in equilibrium under the action of a system of attrac- 
tions and repulsions in one plane, it will remain in equilibrium if the system 
of forces is turned through a right angle in the positive direction. If this opera- 
tion is performed on the systems of forces acting on all the points, then at the 
extremities of each line joining two points we have two equal forces at right 

VOL. XXVI. PART I. D 



14 MR CLERK MAXWELL ON 

angles to that line and acting in opposite directions, forming a couple whose 
magnitude is the product of the force between the points and their distance, and 
whose direction is positive if the force be repulsive, and negative if it be attractive. 
Now since every point is in equilibrium these two systems of couples are in 
equilibrium, or the sum of the positive couples is equal to that of the negative 
couples, which proves the theorem. 

In a plane frame, loaded with weights in any manner, and supported by 
vertical thrusts, each weight must be regarded as attracted towards a horizontal 
base line, and each support of the frame as repelled from that line. Hence the 
following rule : — 

Multiply each load by the height of the point at which it acts, and each 
tension by the length of the piece on which it acts, and add all these products 
together. 

Then multiply the vertical pressures on the supports of the frame each by 
the height at which it acts, and each pressure by the length of the piece on 
which it acts, and acid the products together. This sum will be equal to the 
former sum. 

If the thrusts which support the frame are not vertical, their horizontal 
components must be treated as tensions or pressures borne by the foundations 
of the structure, or by the earth itself. 

The importance of this theorem to the engineer arises from the circum- 
stance that the strength of a piece is in general proportional to its section, so 
that if the strength of each piece is proportional to the stress which it has 
to bear, its weight will be proportional to the product of the stress multiplied 
by the length of the piece. Hence these sums of products give an estimate 
of the total quantity of material which must be used in sustaining tension and 
pressure respectively. 

The following method of demonstrating this theorem does not require the 
consideration of couples, and is applicable to frames in three dimensions. 

Let the system of points be caused to contract, always remaining similar 
to its original form, and with its pieces similarly situated, and let the same forces 
continue to act upon it during this operation, so that every point is always in 
equilibrium under the same system of forces, and therefore no work is done by 
the system of forces as a whole. 

Let the contraction proceed till the system is reduced to a point. Then the 
work done by each tension is equal to the product of that tension by the distance 
through which it has acted, namely, the original distance between the points. 
Also the work spent in overcoming each pressure is the product of that pressure 
by the original distance of the points between which it acts ; and since no work 
is gained or lost on the whole, the sum of the first set of products must be 
equal to the sum of the second set. In this demonstration it is not necessary 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 15 

to suppose the points all in one plane. This demonstration is mathematically 
equivalent to the following algebraical proof : — 

Let the co-ordinates of the n different points of the system be x 1 y 1 z x , 
x 2 y 2 z 2 , x p y p z p , &c, and let the force between any two points p, q, be ~P pq , 
and their distance r pq , and let it be reckoned positive when it is a pressure, and 
negative when it is a tension, then the equation of equilibrium of any point p 
with respect to forces parallel to x is 

(x p - asj)^ + (ocp - x 2 )^ + &c. + (xp - x g )^ + &c. = , 
t Pi r P2 r pq 

or generally, giving t all values from 1 to n, 

P 



x\{(x p -x t )^} = 0. 



Multiply this equation by x p . There are n such equations, so that if each is 
multiplied by its proper co-ordinate and the sum taken, we get 

2? 2? { (x P - ^) 2 — 1 = , 
1 l (. r pt ) 

and adding the corresponding equations in y and z, we get 

which is the algebraic expression of the theorem. 

General Theory of Diagrams of Stress in Three Dimensions. 
First Method of Representing Stress in a Body. 

Definition. — A diagram of stress is a figure having such a relation to a 
body under the action of internal forces, that if a surface A, limited by a closed 
curve, is drawn in the body, and if the corresponding limited surface a be drawn 
in the diagram of stress, then the resultant of the actual internal forces on the 
positive side of the surface A in the body is equal and parallel to the resultant 
of a uniform normal pressure p acting on the positive side of the surface a in 
the diagram of stress. 

Let x, y, z be the co-ordinates of any point in the body, £ ??, I those of the 
corresponding point in the diagram of stress, then £ -q, £ are functions of x, y, z, 
the nature of which we have to ascertain, so that the internal forces in the body 
may be in equilibrium. For the present we suppose no external forces, such 
as gravity, to act on the particles of the body. We shall consider such forces 
afterwards. 

Theorem 1. — If any closed surface is described in the body, and if the stress 
on any element of that surface is equal and parallel to the pressure on the cor- 



16 MR CLERK MAXWELL ON 

responding element of surface in the diagram of stress, then the resultant stress 
on the whole closed surface will vanish ; for the corresponding surface in the 
diagram of stress is a closed surface, and the resultant of a uniform normal 
pressure p on every element of a closed surface is zero by hydrostatics. 

It does not, however, follow that the portion of the body within the closed sur- 
face is in equilibrium, for the stress on its surface may have a resultant moment. 

Theorem 2. — To ensure equilibrium of every part of the body, it is necessary 
and sufficient that 

*~ dx V dy ^~ dz' 

where F is any function of x y and z. 

Let us consider the elementary area in the body dy dz. The stress acting 
on this area will be a force equal and parallel to the resultant of a pressure p 
acting on the corresponding element of area in the diagram of stress. Resolving 
this pressure in the directions of the co-ordinate axes, we find the three com- 
ponents of stress on dy dz, which we may call p xx dy dz, p^ dy dz, and p xz dy dz, 
each equal to p multiplied by the area of the projection of the corresponding 
element of the diagram of stress on the three co-ordinate planes. Now, the 
projection on the plane yz, is 

/dr,c]X _ dr L dZ\ ( l h 
\dy dz dz dy) ^ 

Hence we find for the component of stress in the direction of x 

lxx ~ 2 \dy dz dz dyj' 
which we may write for brevity at present 

Similarly, 

Pxy = pJ(£, Ziy,z) Pxz = pJ(£, 77 ; y , z) . 

In the same way, we may find the components of stress on the areas dz dx 
and dx dy — 

Pyx = PJ(V > £; * > x ) Pyy = p2(£> £ > z > x ) Py; = pJ (£ > V, * , %) 

Pxz =pJ(v>%\ x >y) Pzy =^J(?;^; ®,y) Pzz =p3{%,y, x >y) ■ 

Now, consider the equilibrium of the parallelopiped dx dy dz, with respect to 
the moment of the tangential stresses about its axes. 

The moments of the forces tending to turn this elementary parallelopiped 

about the axis of x are 

dz dx p yz . dy — dx dy p zy . dz . 

To ensure equilibrium as respects rotation about the axis of x, we must have 

Pyz = Pzy • 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 17 

Similarly, for the moments about the axes of y and z, we obtain the equa- 
tions 

Pzx = Vx* and P*v — iV • 

Now, let us assume for the present 

§ = B,-C„|=A,, § = B 1 + C„ 

| = B ! + C ! ,| = B 1 -C J , § = A S . 

Then the equation ^ = p zy becomes 

/d^&n d^_^n\ _ (WML _ dXdJL\ 

P \dz dx dx dz) ~ P \dx dy dy dx) 
or 

(B 2 - C 2 ) (B, - C 3 ) - A, (B, + C x ) = (B 2 + C 2 ) (B 3 + 0.) - A, (B x - C,) 

= A X G X + B 3 C 2 + B 2 C 3 . 

Similarly, from the two other equations of equilibrium we should find 

= A 2 C 2 + B 1 C 3 + B 3 C 1 
= A 3 C 3 + B 2 C X + B^ . 

From these three equations it follows that 



Hence 



and £dx + rjdy + £dz is a complete differential of some function, F, of x, y and z, 
whence it follows that 

dx dy dz 

F may be called the function of stress, because when it is known, the diagram 
of stress may be formed, and the components of stress calculated. The form 
of the function F is limited only by the conditions to be fulfilled at the bound- 
ing surface of the body. 

The six components of stress expressed in terms of F are 

/cPFd?F /d 2 F\ 2 \ _ /d?F<£F (d 2 F\ 2 \ _ /d 2 F dF 2 ( d 2 F\ 2 \ 

p xx -Py dy2 dz 2 \dydz) ) ' Pyy ~ P \dz 2 dx 2 \dzdx) } Pzz ~ p \ dx 2 dy 2 \dxdy) ) ' 

/ d 2 F d 2 F ^ 2 F^ 2 F\ _ / d 2 F d 2 F d 2 F d 2 F \ _ /d 2 F d 2 F d 2 F d 2 F\ 
yi ^\dzdxdxdy dx 2 dydz)' '^ zx ~ P \dxdydydz dy 2 dzdx)' Pxy ~^\dydzdzdx dz 2 dxdy) ' 
VOL. XXVI. PART I. E 



c x = o 


c 2 = o 


c 3 = o. 


dr) _ dt, 

dz dy ' 


d£ _ d% 

dx ~ dz 


d% _ dr) 

dy ~ dx 



18 MR CLERK MAXWELL ON 

If -T- = z, F becomes Airy's function of stress in two dimensions, and we have 

d 2 Y d 2 F d 2 F 

Pxx ~ P dy 2 ' Pvv - 13 cW ' P *» - P d^dy • 

The system of stress in three dimensions deduced in this way from any 
function, F, satisfies the equations of equilibrium of internal stress. It is not, 
however, a general solution of these equations, as may be easily seen by taking 
the case in which p xz and p yz are both zero at all points. In this case, since 
there is no tangential action in planes parallel to xy, the stresses p xx , p xy and p yy 
in each stratum must separately fulfil the conditions of equilibrium, 

d ^ _ n ^ ^ _ n 

dx Pxx + ty Pxv ~ ' dl,? xy + ~df }y] > ~ ' 

The complete solution of these equations is, as we have seen, 

cPf d*f d 2 f 

Vxx ~ dy 2 ' *" - dxdy ' lhjy ~ da? ' 

where / is any function of x and y, the form of which may be different for every 
different value of z, so that we may regard /as a perfectly general function of 
x y and z. 

Again, if we consider a cylindrical portion of the body with its generating 
lines parallel to z, we shall see that there is no tangential action parallel to z 
between this cylinder and the rest of the body. Hence the longitudinal stress 
in this cylinder must be constant throughout its length, and is independent of 
the stress in any other part of the body. 

Hence 

p„ = <l>(psy), 

where <f> is a function of x and y only, but may be any such function. But 
expressing the stresses in terms of F under the conditions p xz = , p yz = , we 
find that if F is a perfectly general function of x and y 

d 2 ¥ n , d 2 Y 

= and , , = , 



dx dz dy dz 

whence it follows that -j- and -j- are functions of x and y only, and that -^- is a 

function of z only. Hence 

F = G + Z, 

when G is a function of x and y only, and Z a function of z only, and the com- 
ponents of stress are 

d*G d 2 Z cPG d 2 Z (<m cPG ~WG\ 2 

Vxx-f-g^ dz2 > Pyy-P -^2 dz 2 > Pm ~ P ^2 dy * dxdy ) 

d 2 G d 2 Z 

p yz = o, P , x = o, Pxy = -p d - lyl? . 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 19 

Here the function /which determines the stress in the strata parallel to xy is 

Now, this function is not sufficiently general, for instead of being any function of 
x, y and z, it is the product of a function of x and y multiplied by a function of z. 
Besides this, though the value of p zz is, as it ought to be, a function of x and 
y only, it is not of the most general form, for it depends on G, the function which 
determines the stresses^, p xy , andp^, whereas the value oip zz may be entirely 
independent of the values of these stresses. In fact, the equations give 

„ „ PxxPvy — Pxy 

Pzz ~ P fd 2 Z\* 

This method, therefore, of representing stress in a body of three dimensions 
is a restricted solution of the equations of equilibrium. 

On Reciprocal Diagrams in Three Dimensions. 

Let us consider figures in two portions of space, which we shall call respec- 
tively the first and the second diagrams. Let the co-ordinates of any point in 
the first diagram be denoted by x, y, z, and those of the corresponding point in 
the second by £, 17, £, measured in directions parallel to x, y, z respectively. 
Let F be a quantity varying from point to point of the first figure in any con- 
tinuous manner ; that is to say, if A, B are two points, and F 1 , F 2 the values 
of F at those points ; then, if B approaches A without limit, the value of F 2 
approaches that of F x without limit. Let the co-ordinates (£, 77, £) of a point in 
the second diagram be determined from x, y, z, those of the corresponding point 
in the first by the equations 

£F _ dF dF 

? ~~ dx ' dy ' ' ~ dz ' ^ '' 

This is equivalent to the statement, that the vector (p) of any point in the 
second diagram represents in direction and magnitude the rate of variation of F 
at the corresponding point of the first diagram. 

Next, let us determine another function, <f>, from the equation 

xZ + i JV + zZ=F+ <j> (2), 

<£, as thus determined, will be a function of x, y, and z, since £, tj, £ are known 
in terms of these quantities. But, for the same reason, </> is a function of £ 17, £. 
Differentiate <f> with respect to £, considering x, y and z functions of £ 77, £, 

deb „ dx dy . dz dF 

-Z-x + Z-^+V-JL + t;-^-- 



20 MR CLERK MAXWELL ON 

Substituting the values of £, 77, £ from (1) 

dd> dF dx dF dy dF dz dF 

dg dx dg dy d^ dz d% d% 

dF dF 

= x 
Differentiating <f> with respect to -q and £, we get the three equations 

x - d% y - d V z - d$ • (°>> 

or the vector (r) of any point in the first diagram represents in direction and 
magnitude the rate of increase of </> at the corresponding point of the second 
diagram. 

Hence the first diagram may be determined from the second by the same 
process that the second was determined from the first, and the two diagrams, 
each with its own function, are reciprocal to each other. 

The relation (2) between the functions expresses that the sum of the func- 
tions for two corresponding points is equal to the product of the distances of 
these points from the origin multiplied by the cosine of the angle between the 
directions of these distances. 

Both these functions must be of two dimensions in space. Let F' be a 
linear function of xyz, which has the same value and rate of variation as F 
has at the point x y Q z 

f = f. + c_o fo + (y _ yo) <| + ( ,_ 2o) a, (4) 

The value of F 7 at the origin is found by putting x t y and z — 

F = F - x£ - y oV - z£ = - tf> . . . . (5), 

or the value of F' at the origin is equal and opposite to the value of 4> at the 
point £ 7), I 

If the rate of variation of F is nowhere infinite, the co-ordinates $ 77 £ of the 
second diagram must be everywhere finite, and vice versa. Beyond the limits 
of the second diagram the values of x, y, z, in terms of £ 77, £, must be impossible, 
and therefore the value of <j) is also impossible. Within the limits of the second 
diagram, the function <f> has an even number of values at every point, corre- 
sponding to an even number of points in the first diagram, which correspond 
to a single point in the second. 

To find these points in the first diagram, let p be the vector of a given point 
in the second diagram, and let surfaces be drawn in the first diagram for which 
F is constant, and let points be found in each of these surfaces at which the 
tangent plane is perpendicular to p, these points will form one or more curves, 
which must be either closed or infinite, and the points on these curves corres- 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 21 

pond to the points in the second diagram which lie in the direction of the 
vector p. If p be the perpendicular from a point in the first diagram on a 
plane through the origin perpendicular to p, then all those points on these curves 

at which -r- = p correspond to the given point in the second diagram. Now, 

since this point is within the second diagram, there are values of p both greater 

and less than the given one; and therefore -y- is neither an absolute maximum 

nor an absolute minimum value. Hence there are in general an even number 
of points on the curve or curves which correspond to the given point. Some of 
these points may coincide, but at least two of them must be different, unless 
the given point is at the limit of the second diagram. 

Let us now consider the two reciprocal diagrams with their functions, and 
ascertain in what the geometrical nature of their reciprocity consists. 

(1.) Let the first diagram be simply the point P a , {x 1 ,y v zj, at which F = F 1 , 
then in the other diagram 

<j) = x^ + y lV +e l C-F 1 (6), 

or a point in one diagram is reciprocal to a space in the other, in which the 
function </> is a linear function of the co-ordinates. 

(2.) Let the first diagram contain a second point P 2 , {x v y v z 2 ) at which F = F 2 , 
then we must combine equation (6) with 

= ^ + 1/ 2 V + *<£- F 2 • • • ■ (7), 

whence eliminating <f>, 

(«i-a^)£+ fa-yjv + (%-z 2 )f = F : -F 2 . 

If r 12 is the length of the line drawn from the first point P x to the second P 2 ; 
and if l 12 m 12 n 12 are its direction cosines, this equation becomes 

F — F 

*ia£ + m i2*? + n uZ = -*z — > 

'12 

or the reciprocal of the two points P x and P 2 is a plane, perpendicular to the line 
joining them, and such that the perpendicular from the origin on the plane 
multiplied by the length of the line P X P 2 is equal to the excess of F 2 over F^ 

(3.) Let there be a third point P 3 in the first diagram, whose co-ordinates are 
# 3 y z z 3 and for which F = F 3 ; then we must combine with equations (6) and (7) 

</> = a' 8 £ + VaV + z*K- F 3 .... (8). 

The reciprocal of the three points P a P 2 P 3 is a straight line perpendicular to 
the plane of the three points, and such that the perpendicular on this fine from 
the origin represents, in direction and magnitude, the rate of most rapid increase 
of F in the plane I t 1 P 2 P 3 , F being a linear function of the co-ordinates whose 
values at the three points are those given. 

VOL. XXVI. PART I. F 



22 MR CLERK MAXWELL ON 

(4.) Let there be a fourth point P 4 for which F = F 4 . 

The reciprocal of the four points is a single point, and the line drawn from 
the origin to this point represents, in direction and magnitude, the rate of 
greatest increase of F, supposing F such a linear function of xyz that its values 
at the four points are those given. The value of <f> at this point is that of F at 
the origin. 

Let us next suppose that the value of F is continuous, that is, that F does 
not vary by a finite quantity when the co-ordinates vary by infinitesimal 
quantities, but that the form of the function F is discontinuous, being a 
different linear function of xyz in different parts of space, bounded by definite 
surfaces. 

The bounding surfaces of these parts of space must be composed of planes. 
For let the linear functions of xyz in contiguous portions of space be 

Fj = a x x + fay + 7l s - fa 

F 2 = a r >- + j3 2 y + y 2 z - fa, 

then at the bounding surface, where F x = F 2 

{a x -a 2 )x + (P x -fa)*f + (7i-7-2)- = 01— 4>i ■ ( 9 )> 

and this is the equation of a plane. 

Hence the portion of space in which any particular form of the value of F 
holds good must be a polyhedron or cell bounded by plane faces, and therefore 
having straight edges meeting in a number of points or summits. 

Every face is the boundary of two cells, every edge belongs to three or more 
cells, and to two faces of each cell. 

Every summit belongs to at least four cells, to at least three faces of each 
cell, and to two edges of each face. 

The whole space occupied by the diagram is divided into cells in two different 
ways, so that every point in it belongs to two different cells, and has two values 
of F and its derivatives. 

The reciprocal diagram is made up of cells in the same way, and the 
reciprocity of the two diagrams may be thus stated : — 

1. Every summit in one diagram corresj3onds to a cell in the other. 

The radius vector of the summit represents the rate of increase of the func- 
tion within the cell, both in direction and magnitude. 

The value of the function at the summit is equal and ojDposite to the value 
which the function in the cell would have if it were continued under the same 
algebraical form to the origin. 

2. Every edge in the one diagram corresponds to a plane face in the other, 
which is the face of contact of the two cells corresponding to the two extremities 
of the edge. 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 23 

The edge in the one diagram is perpendicular to the face in the other. 
The distance of the plane from the origin represents the rate of increase of 
the function along the edge. 

3. Every face in the one diagram corresponds to an edge in which as many 
cells meet as there are angles in the face, that is, at least three. Every face 
must belong to two, and only two cells, because the edge to which it corresponds 
has two, and only two extremities. 

4. Every cell in the one diagram corresponds to a summit in the other. 
Every face of the cell corresponds and is perpendicular to an edge having an 
extremity in the summit. Since every cell must have four or more faces, every 
summit must have four or more edges meeting there. 

Every edge of the cell corresponds to a face having an angle in the summit. 
Since every cell has at least six edges, every summit must be the point of 
concourse of at least six faces, which are the boundaries of cells. 

Every summit of the cell corresponds to a cell having a solid angle at the 
summit. Since every cell has at least four summits, every summit must be the 
meeting place of at least four cells. 

Mechanical Reciprocity of the Diagrams. 

If along each of the edges meeting in a summit forces are applied propor- 
tional to the areas of the corresponding faces of the cell in the reciprocal 
diagram, and in a direction which is always inward with respect to the cell, 
then these forces will be in equilibrium at the summit. 

This is the "Polyhedron of Forces," and may be proved by hydrostatics. 

If the faces of the cell form a single closed surface which does not intersect 
itself, it is easy to understand what is meant by the inside and outside of the 
cell; but if the surface intersects itself, it is better to speak of the positive and 
negative sides of the surface. A cell, or portion of a cell, bounded by a closed 
surface, of which the positive side is inward, may be called a positive cell. If 
the surface intersects itself, and encloses another portion of space with its 
negative side inward, that portion of space forms a negative cell. If any portion 
of space is surrounded by n sheets of the surface of the same cell with their 
positive side inward, and by m sheets with their negative side inward, the space 
enclosed in this way must be reckoned n — m times. 

In passing to a contiguous cell, we must suppose that its face in contact 
with the first cell has its positive surface on the opposite side from that of the 
first cell. In this way, by making the positive side of the surface continuous 
throughout each cell, and by changing it when we pass to the next cell, we may 
settle the positive and negative side of every face of every cell, the sign of 
every face depending on which of the two cells it is considered for the moment 
to belong to. 



24 MR CLERK MAXWELL ON 

If we now suppose forces of tension or pressure applied along every edge of 
the first diagram, so that the force on each extremity of the edge is in the 
direction of the positive normal to the corresponding face of the cell corres- 
ponding to that extremity, and proportional to the area of the face, then 
these pressures and tensions along the edges will keep every point of the 
diagram in equilibrium. 

Another way of determining the nature of the force along any edge of the 
first diagram, is as follows: — 

Round any edge of the first diagram draw a closed curve, embracing it and 
no other edge. However small the curve is, it will enter each of the cells which 
meet in the edge. Hence the reciprocal of this closed curve will be a plane 
polygon whose angles are the points reciprocal to these cells taken in order. 
The area of this polygon represents, both in direction and magnitude, the whole 
force acting through the closed curve, that is, in this case the stress along the 
edge. If, therefore, in going round the angles of the polygon, we travel in the 
same direction of rotation in space as in going round the closed curve, the stress 
along the edge will be a pressure ; but if the direction is opposite, the stress will 
be a tension. 

This method of exjDressing stresses in three dimensions comprehends all cases 
in which Rankine's reciprocal figures are possible, and is applicable to certain 
cases of continuous stress. That it is not applicable to all such cases is easily 
seen by the example of p (18). 

On Reciprocal Diagrams in Two Dimensions. 

If we make F a function of x and y only, all the properties already deduced 
for figures in three dimensions will be true in two ; but we may form a more 
distinct geometrical conception of the theory by substituting cz for F and c£ for 
<f>. We have then for the equations of relation between the two diagrams 

_ dz dz 

? ~" dx dy 

X ~ C d£ ]J ~ % 

x % + yv = cz + c K ■ 

These equations are equivalent to the following definitions : — 
Let z in the first diagram be given as a function of x and y, z will lie on a 
surface of some kind. Let x Q , y be particular values of x and y, and let z be the 
corresponding value of z. Draw a tangent plane to the surface at the point 
x , y , z , and from the point £ = 0, -q = 0, £ — — c ; in the second diagram draw 
a normal to this tangent plane. It will cut the plane £ = at the point £ r) cor- 
responding to xy, and the value of £ is equal and opposite to the segment of the 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 25 

axis of z cut off by the tangent plane. The two surfaces may be denned as recip- 
rocally polar (in the ordinary sense) with respect to the paraboloid of revolution 

x 2 + y 2 = 2cz (11), 

and the diagrams are the projections on the planes of my and £77 of points and 
lines on these surfaces. 

If one of the surfaces is a plane-faced polyhedron, the other will also be a 
plane-faced polyhedron, every face in the one corresponding to a point in the 
other, and every edge in the one corresponding to the line joining the points 
corresponding to the faces bounded by the edge. In the projected diagrams 
every line is perpendicular to the corresponding line, and lines which meet in a 
point in one figure form a closed polygon in the other. 

These are the conditions of reciprocity mentioned at p. 8, and it now 
appears that if either of the diagrams is a projection of a plane-faced poly- 
hedron, the other diagram can be drawn. If the first diagram cannot be a pro- 
jection of a plane-faced polyhedron, let it be a projection of a polyhedron whose 
faces are polygons not in one plane. These faces must be conceived to be filled 
up by surfaces, which are either curved or made up of different plane portions. 
In the first case the polygon will correspond not to a point, but to a finite por- 
tion of a surface ; in the second, it will correspond to several points, so that the 
lines, which correspond to the edges of such a polygon, will terminate in several 
points, and not in one, as is necessary for reciprocity. 

Second Method of representing Stress in a Body. 
Let a, b be any two consecutive points in the first diagram, distant s, and a, /3 
the corresponding points in the second, distant cr, then if the direction cosines 
of the line a b are /, m, n and those of a (3, X, fi, v 



(12). 



o-X = sl-^r- + sm-^- + sn-f- 
dx dy dz 

Art drt drt 

oiJb = si-— + sm-r + sn-^r- 

dx dy dz 

At dt dt 

av = sl-^r- + sm-^r- + sn^- 

dx dy dz ' 

Hence 

j(a + ^ +)! ,)=^| +m f +K f + ^ + |) +K <| + f) + ,<| + |)(iB). 

If we put IX + m\L + nv — cos e, where e is the angle between s and cr, and 
if we take three sets of values of linn, corresponding to three directions at right 
angles to each other, we find 

<r, 0-0 a. dP dr, d£ d 2 ~F d 2 ~F d 2 ¥ nu 

- 1 - cos e, + — ?- cos e 9 + — *■ cos e 3 = -f- + -~- + ^- = j-s + j-s + -7^2 ( 14 )- 

Sj s 2 s 3 dx dy dz dx/ dy* dz 1 

VOL. XXVI. PART I. G 



26 



MR CLERK MAXWELL ON 



Hence this quantity depends only on the position of the point, and not on the 
directions of s 1 s 2 s 3 or of x y z, let us call it A 2 F. 

Now, let us take an element of area perpendicular to s, and let us suppose 
that the stress on this element is compounded of a normal pressure = pA 2 F, 

and a tension parallel to o- and equal to p - . 



By the rules for the composition of stress, we have for the components of the 
force on this element, in terms of the six components of stress, 



X = lp xx + mp xy + tvpua — pi ZA 2 F — \- j 

Y = Ip X y + Vipyy + «£>„« = pltll/^F ~ f^ ) 

Z = lp xz + mp,, z + wp a = p>( «A 2 F — v- J 



(15). 



Hence, 



p xx = P ( A 2 F - £) = p ( A'F - ^ = P (^ + ^ 

/ f / 2 F d 2 F\ /^ 2 F d 2 F\ /d 2 F d-Y\ 



(16). 



P* = -P 



d 2 F 



p !X = -p 



d 2 F 



P*rP : 



d 2 F 



dxdy ' rzx r dzdx ' rxyr dxdy 

By substituting these values in the equations of equilibrium 



dp, 



XX + dpxy + dpxZ_ _ Q &(;i 

dx dy dz 



(17), 



it is manifest that they are fulfilled for any value of F. 

The most general solution of these equations of equilibrium is contained in 
the values 



P* 



d 2 B d?C 

dz 2 dy 2 



Pyy = 



d 2 G d?A 
dx 2 dz 2 



Pvz=~ 



d 2 A 

dydz 



Pzx — 



d 2 B 

dzdx 



Pzz = 



Pa 



d 2 A d 2 B 
dy 2 dx 2 

d 2 G 
dxdy 



(18). 



By making A = B = C = pF we get a case which, though restricted in its 
generality, has remarkable properties with respect to diagrams of stress. 
"We have seen that a distribution of stress according to the definition above 
(16), is consistent with itself, and will keep a body in equilibrium. Since the 
stresses are linear functions of F, any two systems of stress can be compounded 
by adding their respective functions, a process not applicable to the first method 
of representation by areas. 

Let us ascertain what kind of stress is represented in this way in the case 
of the system of cells already considered. 

Since F in each cell is a linear function of x, y, z, there can be no stress at any 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 27 

point within it. Let us take a and b two contiguous points in different cells, 
then a and /3 will be the points at a finite distance to which these cells are 

a 

reciprocal, and A 2 F ="-r > which becomes infinite when ab vanishes. 

If a and b are in the surface bounding the cells, a and /3 coincide. Hence 
there is a stress in this surface, uniform in all directions in the plane of the 
surface, and such that the stress across unit of length drawn on the surface is 
proportional to the distance between the points which are reciprocal to the two 
cells bounded by the surface, and this stress is a tension or a pressure according 
as the two points are similarly or oppositely situated to the two cells. 

The kind of equilibrium corresponding to this case is therefore that of a 
system of liquid films, each having a tension like that of a soap bubble, depend- 
ing on the nature of the fluid of which it is composed. If all the films are 
composed of the same fluid, their tensions must be equal, and all the edges of 
the reciprocal diagram must be equal. 

On Airy's Function of Stress. 

Mr Airy, in a paper " On the Strains in the Interior of Beams,"* was, I 
believe, the first to point out that, in any body in equilibrium under the action 
of internal stress in two dimensions, the three components of the stress in any 
two rectangular directions are the three second derivatives, with respect to these 
directions, of a certain function of the position of a point in the body. 

This important simplification of the theory of the equilibrium of stress in 
two dimensions does not depend on any theory of elasticity, or on the mode in 
which stress arises in the body, but solely on the two conditions of equilibrium 
of an element of a body acted on only by internal stress 

S*- + ajf** = o and &r« + -%p» = ° • ■ < 19 )> 

whence it follows that 

*-=W Pxv== ~^dy *» = <& • ■ • (20) > 

where F is a function of x and y, the form of which is (as far as these equations 
are concerned) perfectly arbitrary, and the value of which at any point is in- 
dependent of the choice of axes of co-ordinates. Since the stresses depend on 
the second derivatives of F, any linear function of x and y may be added to F 
without affecting the value of the stresses deduced from F. Also, since the 
stresses are linear functions of F, any two systems of stress may be mechanically 
compounded by adding the corresponding values of F. 

The importance of Airy's function in the theory of stress becomes even more 

* Phil. Trans. 1863. 



28 



ME CLERK MAXWELL ON 



manifest when we deduce from it the diagram of stress, the co-ordinates of whose 
points are 



t = -j- and « = 



dx 



(21). 



For if s be the length of any curve in the original figure, and o- that of the cor- 
responding curve in the diagram of stress, and if Xds, Yds are the components 
of the whole stress acting on the element ds towards the right hand of the 
curve s 



Xds _ „ ( Jy f F cJ i fh -. d Z c !i (h _ <*£ ll(T 

j\xlo — J/xx ~tT Llo — ~~ 7 9 ^^ Clo — -5— ^^ (to — —j— U (J 



and 



dy 2 ds 



,, , dx , c/ 2 F cfo 7 

Y* = - Ar 3T-& =~ si t. ds = ffi 5 & = J & 



<7y da; 1 _dy 



(22). 



VZs 



rfa; 2 cZs 



Hence the stress on the right hand side of the element ds of the original curve 
is represented, both in direction and magnitude, by the corresponding element 
da of the curve in the diagram of stress, and, by composition, the resultant 
stress on any finite arc of the first curve s is represented in direction and 
magnitude by the straight line drawn from the beginning to the end of the 
corresponding curve o\ 

If Pj, P 2 are the principal stresses at any point, and if P x is inclined a to the 
axis of x, then the component stresses are 

p xx = Pj cos 2 a + P 2 sin 2 a ) 

p xy = (P x — P 2 ) sin a cos a I . . (23). 

p yy = T 1 sin 2 a + P 2 cos 2 a J 



Hence 



tan 2a = 



P 1 + P 2 



P*> — 



Pxx Pyy 



Pxx "T ]?yy '■ 



d 2 F 
dxdy 



d*F 



-T i-E 2 — Pxx Pyy Pxy — 



d 2 F d 2 F 
dx 3 dy 2 

cPFd?F 
dx 2 dy 2 



cPF 
df 



dxdy 



(24). 



) 



Consider the area bounded by a closed curve s, and let us determine the sur- 
face integral of the sum of the principal stresses over the area within the curve. 
The integral is 

By a well-known theorem, corresponding in two dimensions to that of Green in 
three dimensions, the latter expression becomes, when once integrated, 



f(dF dx dF dy\ 
J \dy ds dx ds) 



(26), 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 29 

/(*! + *D* <27) ' 

These line integrals are to be taken round the closed curve s. If we take a 
point in the curve s as origin in the original body, and the corresponding point 
in cr as origin in the diagram of stress, then £ and 77 are the components of the 
whole stress on the right hand of the curve from the origin to a given point. 
If p denote the line joining the origin with the point £77, then p will represent in 
direction and magnitude the whole stress on the arc <x. 

The line integral may now be interpreted as the work done on a point which 
travels once round the closed curve s, and is everywhere acted on by a force 
represented in direction and magnitude by p. We may express this quantity 
in terms of the stress at every point of the curve, instead of the resultant stress 
on the whole arc, as follows : — 

For integrating (27) by parts it becomes, 



"/ (' S + ,J t) ds = - /< x * + Y ?<) * ^ 



or if Hds is the actual stress on ds, and r is the radius vector of ds, and if R 
makes with r an angle e, we obtain the result 

ff '(Pj + T 2 )dxdy = -J 'Br cos eds (29). 

This line integral, therefore, which depends only on the stress acting on the 
closed curve s, is equal to the surface integral of the sum of the principal 
stresses taken over the whole area within the curve. 

If there is no stress on the curve s acting from without, then the surface 
integral vanishes. This is the extension to the case of continuous stress of the 
theorem, given at p. 13, that the algebraic sum of all the tensions multiplied 
each by the length of the piece in which it acts is zero for a system in equili- 
brium. In the case of a frame, the stress in each piece is longitudinal, and the 
whole pressure or tension of the piece is equal to the longitudinal stress multi- 
plied by the section, so that the integral Jf(Pi + P 2 ) dxdy for each piece is its 
tension multiplied by its length. 

If the closed curve s is a small circle, the corresponding curve cr will be an 
ellipse, and the stress on any diameter of the circle will be represented in direc- 
tion and magnitude by the corresponding diameter of the ellipse. Hence, the 
principal axes of the ellipse represent in direction and magnitude the principal 
stresses at the centre of the circle. 

Let us next consider the surface integral of the product of the principal 
stresses at every point taken over the area within the closed curve s. 

J J \dx dy dy dxj J ' 
VOL. XXVI. PART I. H 



30 me clerk maxwell on 

or by transformation of variables 



-ff, m 



Hence the surface integral of the product of the principal stresses within 
the curve is equal to the area of the corresponding curve o- in the diagram of 
stress, and therefore depends entirely on the external stress on the curve .«. 
This is seen from the construction of the curve <r in the diagram of stress, since 
each element da represents the stress on the corresponding element ds of the 
original curve. 

If p represents in direction and magnitude the resultant of the stress on the 
curve s from the origin to a point which moves round the curve, then the area 
traced out by p is equal to the surface-integral required. If Xds and Yds 
are the components of the stress on the element ds, and / the whole length of 
the closed curve s, then the surface integral is equal to either of the quantities. 



/ T fXds . ds , or - f X fxds . ds . 



In a frame the stress in each piece is entirely longitudinal, so that the pro- 
duct of the principal stresses is zero, and therefore nothing is contributed to 
the surface integral except at the points where the pieces meet or cross each 
other. To find the value of the integral for any one of these points, draw a 
closed curve surrounding it and no other point, and therefore cutting all the 
pieces which meet in that point in order. The corresponding figure in the 
diagram of stress will be a polygon, whose sides represent in magnitude and 
direction the tensions in the several pieces taken in order. The area of this 
polygon, therefore, represents the value of 'f/V \P 2 dxdy for the point of concourse, 
and is to be considered positive or negative, according as the tracing point 
travels round it in the positive or the negative cyclical direction. 

Hence the following theorem, which is applicable to all plane frames, whether 
a diagram of forces can be drawn or not. 

For each point of concourse or of intersection construct a polygon, by draw- 
ing in succession lines parallel and proportional to the forces acting on the 
point in the several pieces which meet in that point, taking the pieces in cyclical 
order round the point. The area of this polygon is to be taken positive or 
negative, according as it lies on the left or the right of the tracing point. 

If, then, a closed curve be drawn surrounding the entire frame, and a poly- 
gon be drawn by drawing in succession lines parallel and proportional to all the 
external forces which act on the frame in the order in which their lines of 
direction meet the closed curve, then the area of this polygon is equal to the 
algebraic sum of the areas of the polygons corresponding to the various points 
of the frame. 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 



31 



In this theorem a polygon is to be drawn for every point, whether the lines 
of the frame meet or intersect, whether they are really jointed together, or 
whether two pieces simply cross each other without mechanical connection. In 
the latter case the polygon is a parallelogram, whose sides are parallel and pro- 
portional to the stresses in the two pieces, and it is positive or negative accord- 
ing as these stresses are of the same or of opposite signs. 

If three or more pieces intersect, it is manifestly the same whether they 
intersect at one point or not, so that we have the following theorem : — 

The area of a polygon of an even number of sides, whose opposite sides are 
equal and parallel, is equal to the sum of the areas of all the different parallelo- 
grams which can be formed with their sides parallel and equal to those of the 
polygon. 

This is easily shown by dividing the polygon into the different parallelograms. 



On the Equilibrium of Stress in a Solid Body. 

Let PQE be the longitudinal, and STU the tangential components of stress, 
as indicated in the following table of stresses and strains, taken from Thomson 
and Tait's "Natural Philosophy," p. 511, § 669 :— 



Components of the 


Planes, of which 

Relative Motion, or 

across which Force, 

is reckoned. 


Direction of 

Relative Motion 

or of Force. 


Strain. 


Stress. 


e 
f 
9 

a 
b 
c 


P 

Q 
R 

S 
T 
U 


yz 
zx 
xy 

(yx 

\ zx 

\xy 
f xz 


X 

y 

2' 

y 

z 
z 

X 
X 

y 



Then the equations of equilibrium of an element of the body are, by § 697 
of that work, 



dP cW dT _ 

dx dy dz 



dU <iJQ 

dx dy 



f- + Y = 

dz 



dT dS dU „ A 
dx dy dz 



(1)> 



32 MR CLERK MAXWELL ON 

If we assume three functions ABC, such that 
and put 



d 2 A 
dydz 


T == - — 

dzdx 


u - d2C 

dxdy 


X == — 
dx 


dy 


z== — 

dz 



(2), 



then a sufficiently general solution of the equations of equilibrium is given by 
putting 

p = (PB d*C _ y 

dz 2 dy 2 



(IH) 

d-r 2 



q = v; - v: - v 



d*A 
dz 2 



> ■ 



(3), 



rf?/ 2 da a 



I am not aware of any method of finding other relations between the com- 
ponents of stress without making further assumptions. The most natural 
assumption to make is that the stress arises from elasticity in the body. I 
shall confine myself to the case of an isotropic body, such that it can be deprived 
of all stress and strain by a removal of the applied forces. In this case, if 
a (3 y are the components of displacement, and n the co-efficient of rigidity, the 
equations of tangential elasticity are, by equation (6) §§ 670 and 694 of Thoms< >n 
and Tait, 



dz dy n n dydz 



(4), 



with similar equations for b and c. A sufficiently general solution of these equa- 
tions is given by putting 

a = ± 4-(a-b^g) ^ 

In d:c \ / 

^ = ^|( B - C - A ) I • • • W 

2n dz \ J J 

The equations of longitudinal elasticity are of the form given in § 693, 

*-(»*J-)£+(»-S-)(f*3) • • • «, 

where k is the co-efficient of cubical elasticity, with similar equations for Q and 
R. Substituting for P, a, /3 and y in equation (6) their values from (3) and (5), 

3\ / 2 \/d 2 B_dK>_d 2 A dK_dPA_d^B\ 
?) + \ 3 n J\dy 2 dy 2 dy 2 +dz 2 dz 2 dz 2 ) ' 



. /d 2 B d 2 G „\ /, ,4 \(d 2 A 



d 2 A d?B_d 2 C 
dx 2 dx 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 33 

If we put 

d 2 A d 2 B d 2 C , d 2 d 2 cl 2 A2 

~M + If + 37 =p ' and fa 2 + 7hf dJ 2 ~ A ' 

this equation becomes 

(k + ^n\fA 2 A + A 2 B + A 2 C S \-fk + 1 ^oA2p-2nY=2nA 2 A > . (7). 

We have also two other equations differing from this only in having B and 

C instead of A on the right hand side. Hence equating the three expressions 

on the right hand side we find 

A 2 A = A 2 B = A 2 C = D 2 , say, .... (8), 

(3k + n)2p = (3k + 2?i)3T> 2 -2nV, .... (9), 
and 

_ - ^ 9&D 2 -2V 07 p-SV 

These equations are useful when we wish to determine the stress rather than 
the strain in a body. For instance, if the co-efficients of elasticity, k and n, are 
increased in the same ratio to any extent, the displacements of the body are 
proportionally diminished, but the stresses remain the same, and, though their 
distribution depends essentially on the elasticity of the various parts of the 
body, the values of the internal forces do not contain the co-efficients of elasti- 
city as factors. 

There are two cases in which the functions may be treated as functions of 
two variables. 

The first is when there is no stress, or a constant pressure in the direction 
of z, as in the case of a stratum originally of uniform thickness, in the direction 
of z, the thickness being small compared with the other dimensions of the body, 
and with the rate of variation of strain. 

The second is when there is no strain, or a uniform longitudinal strain in the 
direction of z, as in the case of a prismatic body whose length in the direction 
of z is very great, the forces on the sides being functions of x and y only. 

In both of these cases S = and T = 0, so that we may write 

p-^-v u---^- o-^'-v rm 

df U ~ dxdy y ~ dx 2 V • (11} - 

This method of expressing the stresses in two dimensions was first given by 
the Astronomer Royal, in the " Philosophical Transactions" for 1863. We shall 
write F instead of C, and call it Airy's Function of Stress in Two Dimensions. 

Let us assume two functions, G and H, such that 

F= _ d 2 G and y _ dm 

dxdy ' ' dxdy ' ^ " J '' 

VOL. XXVI. PART I. I 



34 MR CLERK MAXWELL ON 

then by Thomson and Tait, § 694, if a is the displacement in the direction of a 

2»<<r + i)-J£ = P-»(Q + B) .... (13). 

Case I. — If R = this becomes 

o ( -\\^ a - d 2 j d 2 G cl 2 G . i\xj) 

^ ' clx dxdy \ dy' 1 dx 2 ) 

Integrating with respect to x we find the following equation for a— 

fc<r + l).= £{^-4g + (.-l)H} + Y • (14), 

where Y is a function of y only. Similarly for the displacement /8 in the 
direction oiy, 

c* +1 >< 3 =s{!?-<'i£ + (*- 1 > H } + x ■ • < 15 >- 



2n 



where X is a function of x only. Now the shearing stress U depends on the 
shearing strain and the rigidity, or 



u =»(t+f) < 16 >- 



Multiplying both sides of this equation by 2 (a + 1) and substituting from (11), 
(14), and (15), 



Hence 



„, 1N d*G d*G . d*G d*G , 1N /^ 2 H d 2 K\ dX dY .,_. 
2(<r + ^dxW 2 = W~ dxW + dx* + {a ~ VyM + If) + Kx~ + dy~ (l7) ' 

(d 2 d 2 \ 2 „ dX dY „ .( d 2 d 2 \ Tr 

{d^ 2 + dY 2 ) G+ d^ + ^ = ^-^{dx- 2 + df) K - ^> 



an equation which must be fulfilled by G when the body is originally without 
strain. 

Case II. — In the second case, in which there is no strain in the direction of 
z, we have 

g = K-<r(P + Q) = (19). 

Substituting for R in (13), and dividing by cr + 1, 

2n^=(l-a)J>-aQ 

d 2 j„ .d 2 G d 2 G „) 
= dxTyV 1 -^df-°lW +(7K \ ■ • < 2 °)' 

with a similar equation for /3. Proceeding as in the former case, we find 

/d 2 j^Yg dX dY _ a /d 2 ^_\ H 

\dx 2 dy 2 ) dx dy ~~ 1 — a \dx 2 dy 2 ) ^ '' 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 35 

This equation is identical with that of the first case, with the exception of the 
coefficient of the part due to H, which depends on the density of the body, and 
the value of a-, the ratio of lateral expansion to longitudinal compression. 

Hence, if the external forces are given in the two cases of no stress and no 
strain in the direction of z, and if the density of the body or the intensity of the 
force acting on its substance is in the ratio of a to (1 — o-) 2 in the two cases, the 
internal forces will be the same in every part, and will be independent of the 
actual values of the coefficients of elasticity, provided the strains are small. 
The solutions of the cases treated by Mr Airy, as given in his paper, do not 
exactly fulfil the conditions deduced from the theory of elasticity. In fact, the 
consideration of elastic strain is not explicitly introduced into the investigation. 
Nevertheless, his results are statically possible, and exceedingly near to the 
truth in the cases of ordinary beams. 

As an illustration of the theory of Airy's Function, let us take the case of 

j- _ 1 r 2 P cos 2 p0 (22). 

In this case we have for the co-ordinates of the point in the diagram corres- 
ponding to {xy) 

£ = ^ = r^cos^-l)^ v = -r' i P- l $m(2p-l)d . . (23), 

and for the components of stress 

*■ = % = ~ (2i>-l)r 2 *- 2 cos (2p-2)0 = - g = - Pvv ] 

*F y (24) - 

If we make 

G = - 1* cosp0 and H = - r* sinpd . . . (25), 
p p 

then 

"|2 



/0 ,.{dGf dGc\ 2 \ 



(26). 



Hence the curves for which G- and H respectively are constant will be lines of 
principal stress, and the stress at any point will be inversely as the square of 
the distance between the consecutive curves G or H. 

If we make 

£ = p cos (f> and v = p sin <£ ~] 

then we must have y ■ (27). 

p = r 2p-l an( j 0=s(2p-l)0 J 

If we put 

?for 2^T then p + l = 2 and (2P-1)(2 2 -1)=-1, 



36 MR CLERK MAXWELL ON 

so that if/, g, h in the diagram of stress correspond to F, G, H in the original 
figure, we have 

f = 2-p 2q cos2q<f> g = -p?cosq<p h = - pi sin q<f> . (28). 

Case of a Uniform Horizontal Beam. 

As an example of the application of the condition that the stresses must be 
such as are consistent with an initial condition of no strain, let us take the case 
of a uniform rectangular beam of indefinite length placed horizontally with a 
load = h per unit of length placed on its upper surface, the weight of the beam 
being k per unit of length. Let us suppose the beam to be supported by vertical 
forces and couples in a vertical plane applied at the ends; but let us consider 
only the middle portion of the beam, where the conditions applicable to the ends 
have no sensible effect. Let the horizontal distance x be reckoned from the 
vertical plane where there is no shearing force, and let the planes where there 
is no moment of bending be at distances ± a from the origin. Let y be 
reckoned from the lower edge of the beam, and let b be the depth of the beam. 

Then, if IT - — j—r is the shearing stress, the total vertical shearing force 

through a vertical section at distance x is 

and this must be equal and opposite to the lveight of the beam and load from 
to x, which is evidently (// + k)x. 

Hence 

dF 

— =-(h + k)xcj>(jj) where 0(6) - </>(0) = 1 . . (29). 

From this we find the vertical stress 

Q = 5? + J* = -(* + *)*<*) + 5 If. 

The vertical stress is therefore a function of y only. It must vanish at the 
lower side of the beam, where y — 0, and it must be — h on the upper side of 
the beam, where y = b. The shearing stress U must vanish at both sides of the 
beam, or <f>'(y) = 0, when y = 0, and when y = b. 

The simplest form of <p (y) which will satisfy these conditions is 

<Ky) = p (3% 2 - 2^) . 

Hence we find the following expression for the function of stress by integrating 
(29) with respect to x, 

F = ^ ^ ~ ^ VW ~ 2 ^ + Y • • • • ( 3 °)> 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 37 

where a is a constant introduced in integration, and depends on the manner in 
which the beam is supported. From this we obtain the values of the vertical, 
horizontal, and shearing stresses, 

<J = g + ir=!»-^<W-V)- • ■ • Pi). 



d*¥ _„h + k 

dxcly ~~ b 3 



u = - izi:. = 6 -w x v ( h ~y) ( 33 )- 



The values of Q and of U, the vertical and the shearing stresses, as given by 
these equations, are perfectly definite in terms of h and k, the load and the 
weight of the beam per unit of length. The value of P, the horizontal stress, 
however, contains an arbitrary function Y, which we propose to find from the 
condition that the beam was originally unstrained. We therefore determine 
a and /3, the horizontal and vertical displacement of any point (x, y), by the 
method indicated by equations (13), (14), (15) 

2n{* + l)a = * + * { (3a 2 * - «•) (b - 2y)-*x(3by* - 2tf) } - a \vy + »^+ T (34), 
2n(a + l)/3=- ] ^{^f-ly^ + 3a(a^-^Xby-f)}+llf-a d ^ + X' (35), 

where X' is a function of x only, and Y' of y only. Deducing from these dis- 
placements the shearing strain, and comparing it with the value of the shearing 
stress, U, we find the equation 

* + *{6aV»-2 B P+l&(By r .^)}+«rJ« = flj p+g+^ . (36). 
Hence 

**-12 ^(fiy-f) (37), 

f-!»Ji(IA-^ + ^ 1 f = . . (33). 

If the total longitudinal stress across any vertical section of the beam is zero, 

d¥ 
the value of -j- must be the same when y = and when y = b. From this con- 
dition we find the value of P by equation (32) 



-p _ h + Jc 



| 3(« 2 - x 2 ) + 2y 2 - 2by - b 2 } (b - 2y) . . . (39). 



The moment of bending at any vertical section of the beam is 



f\ydy={K + k)Q 2 {x' i -a 2 ) + \vy . . . (40). 



VOL. XXVI. PART I. K 



38 



MR CLERK MAXWELL ON 



This becomes zero when x = ± a where 



2 

a 2 - E b 2 
5 



(41). 



If we wish to compare this case with that of a beam of finite length supported 
at both ends and loaded uniformly, we must make the moment of bending zero 
at the supports, and the length of the beam between the supports must therefore 
be 2a Q . Substituting a for a in the value of P, we find 



P = 



h + k 



t 3 



-(s«:- 



3/; 2 + 2y 2 -2% + 



\b^{b-2y) 



(42). 



If we suppose the beam to be cut off just beyond the supports, and supported 
by an intense pressure over a small area, we introduce conditions into the 
problem which are not fulfilled by this solution, and the investigation of which 
requires the use of Fourier's series. In order that our result may be true, we 
must suppose the beam to extend to a considerable distance beyond the sup- 
ports on either side, and the vertical forces to be applied by means of frames 
clamped to the ends of the beam, as in Diagram Va, so that the stresses arising 
from the discontinuity at the extremities are insensible in the part of the beam 
between the supports. 

This expression differs from that given by Mr Airy only in the terms in the 
longitudinal stress P depending on the function Y, which was introduced in 
order to fulfil the condition that, when no force is applied, the beam is un- 
strained. The effect of these terms is a maximum when y = -12788 b, and is 
then equal to (h + &)314, or less than a third of the pressure of the beam and 
its load on a flat horizontal surface when laid upon it so as to produce a uniform 
vertical pressure h + k. 



RECIPROCAL FIGURES, FRAMES, AND DIAGRAMS OF FORCES. 39 



EXPLANATION OF THE DIAGRAMS (Plates I. II. III.). 

Diagrams I.a and 1.6 illustrate the necessity of the condition of the possibility of reciprocal 
diagrams, that each line must be a side of two, and only two, polygons. Diagram I.a is a skeleton of 
a frame such, that if the force along any one piece be given, the force along any other piece may be 
determined. But the piece N forms a side of four triangles, NFH, NGI, NJL, and MM, so that if 
there could be a reciprocal diagram, the line corresponding to N would have four extremities, which is 
impossible. In this case we can draw a diagram of forces in which the forces H, I, J, and K are each 
represented by two parallel lines. 

Diagrams II. a and II. 6 illustrate the case of a frame consisting of thirty-two pieces, meeting four 
and four in sixteen points, and forming sixteen quadrilaterals. Diagram Il.a may be considered as a 
plane projection of a polyhedron of double continuity, which we may describe as a quadrilateral frame 
consisting of four quadrilateral rods, of which the ends are bevelled so as to fit exactly. The pro- 
jection of this frame, considered as a plane frame, has three degrees of stiffness, so that three of the 
forces may be arbitrarily assumed. 

In the reciprocal diagram II. 6 the lines are drawn by the method given at p. 7, so that each 
line is perpendicular to the corresponding line in the other figure. To make the corresponding lines 
parallel we have only to turn one of the figures round a right angle. 

Diagrams IILa and III. 6 illustrate the principle as applied to a bridge designed by Professor F. 
Jenkin. The loads Qj Q 2 , &c, are placed on the upper series of joints, and R x R 2 , &c, on the lower 
series. The diagram III. 6 gives the stresses due to both sets of loads, the vertical lines of loads being 
different for the two series. 

Diagrams IV. a and IV.6 illustrate the application of Airy's Function to the construction of 
diagrams of continuous stress. 

TV.a represents a cylinder exposed to pressure in a vertical and horizontal direction, and to 
tension in directions inclined 45° to these. The lines marked a, b, c, &c, are lines of pressure, and 
those marked o, p, q, are lines of tension. In this case the lines of pressure and tension are rectangular 
hyperbolas, the pressure is always equal to the tension, and varies inversely as the square of the 
distance between consecutive curves, or, what is the same thing, directly as the square of the distance 
from the centre. 

IV.6 represents the reciprocal diagram corresponding to the upper quadrant of the former one. 
The stress on any line in the first diagram is represented in magnitude and direction by the corres- 
ponding line in the second diagram, the correspondence being ascertained by that of the corresponding 
systems of lines a, 6, c, &c, and o, p, q, &c. 

"We may also consider IV.6 as a sector of a cylinder of 270°, exposed to pressure along the lines 

_ 2 

a, 6, c, and to tension along o, p, q, the magnitude of the stress being in this case r 3 . The upper 

quadrant of IV. a is in this case the reciprocal figure. This figure illustrates the tendency of any 
strained body to be ruptured at a re-entering angle, for it is plain that at the angle the stress becomes 
indefinitely great. 

In diagram IV. a — 

F = - r* cos 40 G = - r % cos 20 H = - r 2 sin 20 . 

4 2 2 

In diagram IV.6 — 

/=-/>^cos-<£ g = -p 5 cos -cj> h= -p* sin -<}>. 

Diagrams Y.a and V.6 illustrate Airy's theory of stress in beams. 

V.a is the beam supported at C and D by means of bent pieces clamped to the ends of the beam 
at A and B, at such a distance from C and D, that the part of the beam between C and D is free from 
the local effects of the pressures of the clamps at A and B. The beam is divided into six strata by 



40 MP, CLERK MAXWELL ON RECIPROCAL FIGURES, FRAMES, ETC. 

horizontal dotted lines, marked 1, 2, 3, 4, 5, 6, and into sixteen vertical slices by vertical lines marked 

a, b, c, &c. 

The corresponding lines in the diagram Y.h are marked with corresponding figures and letters. 
The stress across any line joining any two points in Y.a is represented in magnitude by the line in Y.b, 
joining corresponding points, and is perpendicular to it in direction. 

These illustrations of the application of the graphic method to cases of continuous stress, are 
intended rather to show the mathematical meaning of the method, than as practical aids to the engineer. 
In calculating the stresses in frames, the graphic method is really useful, and is less liable to accidental 
errors than the method of trigonometrical calculation. In cases of continuous stress, however, the 
symbolical method of calculation is still the best, although, as I have endeavoured to show in 'this 
paper, analytical methods may be explained, illustrated, and extended by considerations derived from 
tlio graphic method. 



( 41 ) 



II. — On Scientific Method in the Interpretation of Popular Myths, with special 
reference to Greek Mythology. By Professor Blackie. 

(Read 17th January 1870.) 

Of all the branches of interesting and curious learning, there is none 
which has been so systematically neglected in this country as mythology — 
a subject closely connected both with theology and philosophy, and on 
which those grand intellectual pioneers and architects, the Germans, have 
expended such a vast amount of profitable and unprofitable labour. The 
consequence of this neglect has been, that of the few British books we have 
on the subject, the most noticeable are not free from the dear seduction of 
favourite ideas, which possess the minds of the writers as by a juggling witch- 
craft, and prevent them from looking on a rich and various subject with that 
many-sided sympathy and catholic receptiveness which it requires. In fact, 
some of our most recent writers on this subject have not advanced a single 
step, in respect of scientific method, beyond Jacob Bryant, unquestionably the 
most learned and original speculator on mythology of the last century ; but 
whose great work, nevertheless, can only be compared to a grand chase in the 
dark, with a few bright flashes of discovery, and happy gleams of suggestion by 
the way. For these reasons, and to make a necessary protest against some 
ingenious aberrations of Max Muller, Gladstone, Inman, and Cox in the 
method of mythological interpretation, I have undertaken to read the present 
paper ; which, if it possess only the negative virtue of warning people to be 
sober-minded and cautious when entering on a path of so slippery inquiry, 
cannot be deemed impertinent at the present moment. 

For the sake of distinctness and compactness, I will state what I have to 
say in a series of articulate propositions. 

I. By the mythology of a people, I understand the general body of their 
traditions, handing down from the earliest times the favourite national ideas and 
memories, in a narrative form, calculated to delight the imagination and stimu- 
late the affections of love and reverence. 

II. The dress of all mythology, as appealing to the imagination, is neces- 
sarily poetical ; the contents of it are generally four fold — (1.) Theological ; 
(2.) Physical ; (3.) Historical ; and (4.) Philosophical and Moral. 

VOL. XXVI. PART I. L 



42 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

III. In the theological and moral myth, the idea is the principal thing, the 
narrative only the medium ; in the historical and physical myth, the fact is the 
principal thing ; what goes beyond the fact is mere scenic decoration or imagi- 
native exaggeration.* 

IV. A myth intended to convey an idea is distinguished from an allegory or 
parable by the consciousness of purpose with which allegories and parables 
strictly so called are put forth and received. 

V. As it has been well said of popular proverbs, that they are the wisdom 
of many and the wit of one, so theological and moral myths grew up in the 
popular imagination, and were nursed there till in happy season they received a 
definite shape from some one representative man, whose inspiration led him to 
express in a striking form what all felt to be true and all were willing to 
believe. 

VI. The first framers of myths were, no doubt, perfectly aware of the real 
significance of these myths ; but they were aware as poets, not as analysts. 
It is not, therefore, necessary to suppose that in framing these legends they 
proceeded with the full consciousness which belongs to the framers of fables, 
allegories, and parables. A myth is always a gradual, half-conscious, half- 
unconscious growth ; a parable is the conscious creation of the moment. 

VII. During a certain early stage of national life, which cannot be accurately 
defined, but which always precedes the creation of a regular written literature, 
the popular myth — like a tree or a plant — becomes subject to a process of growth 
and expansion, in the course of which it not only receives a rich embellishment, 
but may be so transformed by the vivid action of a fertile imagination, and by 
the ingrafting of new elements, that its original intention may be altogether 
obscured and forgotten. How far this first significance may in after times be 
rightly apprehended, depends partly on the degree of its original obviousness 
partly on the amount of kindred culture possessed by the persons to whom it is 
addressed. 

VIII. As of essentially popular origin and growth the myth cannot, in the 
proper sense, be said to have been the creation of any poet, however distin- 
guished. Much less could a popular minstrel, like Homer, using a highly 
polished language, and who manifestly had many predecessors, be said to have 

* Sometimes, however, a historical person, like Faust, may be seized on by the people, merely as 
a convenient vehicle for embodying a floating mass of mythological notions. In this case tbe person 
is really a secondary consideration : a real person he remains, no doubt ; but, for a legendary nucleus, 
any other person would have done as well. 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 43 

either created the characters or invented the legends about the Greek gods, 
which form what the critics of the last century used to call the machinery of 
his poems. In regard to theological myths, which are most deeply rooted in the 
popular faith, such a poet as Homer could only turn to the best account the 
materials already existing, with here and there a little embellishment or expan- 
sion, where there was no danger of contradicting any article of the received 
imaginative creed. 

IX. The two most powerful forces which act on the popular mind, when 
engaged in the process of forming myths, are the physical forces of external 
nature, and the more hidden, though fundamentally more awful powers of the 
human will, intellect, and passions. It is to be presumed, therefore, that all 
popular myths will contain imaginative representations of both these powers ; 
and, in their original shape, they are in fact nothing more than the assertion of 
the existence of these two great classes of forces in a form which speaks to the 
imagination — that is, in the form of personality ; and there will be a natural pre- 
sumption against the adopting of any system of mythological interpretation 
which ignores entirely either the one or the other of these elements. If this 
proposition be correct, the objections of Max Muller (Chips, ii. 156) to the 
Greek derivation of 'E/hvu?, from the old Arcadian epiwveiv (Pausan. viii. 25, 6), 
are unfounded. 

X. The most fertile soil for purely theological myths is polytheism ; and the 
most obvious as well as the largest field for a religion of multiform person- 
alities, is external nature. In the interpretation of such myths, therefore, we 
shall be justified in searching primarily for the great forces and phenomena of 
the physical world, as underlying the imaginative narrative and imparting to it 
its true significance ; and in proportion to the prominence of these phenomena, 
and the potency of these forces, will the probability be that we shall find them 
fully represented in any body of polytheistic theology. 

XL As the essence of polytheism thus consists in the habitual elevation 
of what we call physical facts and forces into divine personalities, the line 
betwixt a purely physical myth and a theological myth will naturally be 
extremely difficult to draw. Zeus, for instance, as the Thunderer, represents 
a physical fact as well as a theological doctrine ; nevertheless, it would be 
wrong to assume that there is no such element in tradition as a strictly physical 
myth. Certain striking facts of volcanic action or geological change, strange 
and grotesque shapes of rocks and other natural objects, unusual conforma- 
tions of landscape, not to mention the occasional discovery of gigantic fossil 
bones, and even entire skeletons of animals no longer existing, might well 



44 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

form the basis of what is properly termed a physical or a geological, rather than a 
theological myth; and, as Hartung well remarks (Gr. Myth. i. p. 168), notable 
recurrent events in nature, such as the heavy rains at the end of summer, are 
peculiarly calculated to impress the popular imagination, and to produce 
myths. 

XII. But as to man there is, after all, nothing more interesting and more 
important than man, it is in the highest degree unreasonable, in the interpreta- 
tion of myths, to proceed on the assumption that all myth is idea, and that no 
myth contains any historical element. It may be true, no doubt, that in the case 
of some particular nation, all action of the popular imagination on human per- 
sonalities has been excluded ; but such a one-sided action is not to be presumed ; 
it must be proved ; and that in such a rich and various mythology as the Greek 
all reference to human characters and human exploits should be systematically 
excluded is in the highest degree improbable. In a country where the gods 
descended so easily into humanity, it were strange if men had not occasionally 
ascended into godhood. 

XIII. In a theology so thoroughly anthropomorphic as the Greek, the 
distinction between the divine and human element will sometimes be difficult 
to trace ; for the same feelings, situations, and actions will necessarily belong to 
human gods and to godlike men. But this state of the case, in the interpretation 
of any particular myth, is a ground for doubt, not for dogmatism. It includes 
the possibility or the probability of one or two explanations, but the certainty 
of neither. 

XIV. The incredible exaggerations or embellishments with which the name 
of any national hero may have been handed down in a popular myth afford no 
presumption against the genuine historical character of its nucleus. On the 
contrary, it is just because extraordinary characters have existed, that extraor- 
dinary and incredible, miraculous and even impossible stories are invented about 
them. A plain, sober, critical, matter-of-fact account of its early popular heroes 
is not to be expected from any people. 

XV. The error of certain ancient rationalising interpreters of the Greek 
myths did not consist in presuming historical fact as the nucleus of some 
myths, but in the indiscriminate application of the historical interpretation to 
all myths, and that often in a very prosaic and altogether tasteless way. 

XVI. The error of certain modern idealising interpreters of the Greek 
mythology does not consist in endeavouring to recover the ideas which 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 45 

originally lay at the root of some myths, the full significance of which had been 
lost so early as Homer, but in the partial and one-sided application of a few 
favourite ideas to all physical facts, and in the broad denial of any historical 
elements underlying any personality of early tradition. 

XVII. Among the ancients, the extreme of the rationalising interpretation 
of the Greek theological myths is what may be called the irreligious, godless, 
and altogether prosaic system of Euhemerus (b.c. 300), who wrote a book to 
prove that all the Greek gods, not even excepting Jove, had been originally 
dead men deified. The error of this system consisted, not in the assertion that 
the elevation of extraordinary human characters to a divine rank with religious 
honour after death, is an element traceable in the Hellenic, as in some other 
popular theologies, but in the wholesale declaration that religious worship had 
no other origin, and that this element, which is always secondary and derivative 
in the popular creed, is primitive and exclusive. 

XVIII. In order to ascertain how far the principle of Euhemerus may apply 
to any particular case, the general religious tendencies and habits of the nation 
or people must be considered in the first place, and then the whole circum- 
stances and features of the mythical narrative must be accurately surveyed and 
carefully weighed, and a separation of the canonised man from the deified nature 
element with which he may have been mixed up, made accordingly. 

XIX. Euhemerus, however, was altogether wrong in supposing that this 
system of interpretation could be applied on any extensive scale to the mythical 
theology of the Greeks ; and the few French and English writers who, in the 
flatness of the last century, gave a limited currency to this idea, have found no 
followers in the present. 

XX. An opposite theory to that of Euhemerus, much in fashion with the 
Germans, is that, whereas he said the gods were elevated men, we ought rather 
to say that many men, perhaps all the heroes of legendary story, are degraded 
gods. That in the course of religious development, especially when mixed up 
with great changes in the political relations of different races, such a degrada- 
tion may have taken place is certain ; that it has taken place in certain special 
cases will be a just conclusion from an analysis of the character and worship of 
certain heroes, when a cumulative view of the myths connected with them 
suggests the theory of a divine rather than a human significance ; but there is 
no scientific warrant for the assertion which it is now the fashion to make 
(Baring Gould, Rel. bel. vol. i. p. 167), that the old heroic names of a country, 
as King Arthur, for instance, are in the mass to be treated as degraded gods. 

VOL. XXVI. PART I. M 



46 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

XXI. The best authorities for the facts of a myth are not always the poets, 
nor even the most ancient poets, as Homer, who in the exercise of their art 
often took large liberties with sacred tradition; but the reliable witnesses are 
rather such as Pausanias, who record the old temple lore in its fixed local 
forms. This distinction, often forgotten, has given rise to not a little con- 
fusion, and created some needless difficulty in mythological interpretation ; 
and Hartung (i. 184) has done important service to comparative mythology by 
drawing attention emphatically to the difference between sacred legends as 
believed by the people, and religious myths freely handled by the poets. 

XXII. In the interpretation of any popular myth, the first thing to be done 
is to ascertain carefully what the thing to be interpreted actually is ; and this 
can only be done by collecting all the facts relating to it, working them up 
into a complete, and if possible consistent picture, and not till then attempting 
an explanation. Now, as the facts relating to any single god, let us say in the 
Greek Pantheon, are scattered over a wide space, and come from various sources, 
to attempt the explanation of these facts without the previous labour of critical 
and well-digested scholarship, may be an ingenious amusement, but never can 
be a scientific procedure. All the facts must be collected, and all the criticisms 
weighed, before a verdict can be pronounced. 

XXIII. But the mere collection of facts will never help a prosaic or an 
irreverent man to the interpretation of what is essentially j)oetic and devout. 
A book supplies what must be read ; but the eye that reads it can see only 
what by natural faculty and training it is fitted to see. As the loving and rever- 
ential contemplation of nature was the original source of the polytheistic myths, 
so the key to them will often be recovered by a kindred mind acting under influ- 
ences similar to those which impressed the original framers of the myth ; and if 
this may be done with a considerable amount of success by a poetical mind, 
acted on by nature in any country, much more will such success be achieved by 
such a mind in the country where the myths were originally formed. But as 
the aspects of nature are various, and the fancies of poetic minds no less so, it 
will always be necessary to verify any modern notion of an ancient deity, thus 
acquired, by confronting it accurately and continuously with the traditional 
materials contained in books and works of art. Highly poetical minds, such as 
Shelley, Keats, and Buskin, when dealing with Greek mythology, without the 
constant correction of accurate scholarship, are not seldom found using Greek 
myths to represent modern ideas, rather than human ideas to interpret Greek 
myths. And the example of the Germans proves, that in minds naturally fertile 
and ingenious, no amount of erudition affords a safeguard against the besetting 
sin of mythological interpreters, to find in all myths a select field and enclosed 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 47 

hunting ground for the pleasant disport of an unfettered imagination. Dis- 
coveries are easy to make in a region where plausibility so readily gains currency 
for proof. 

XXIV. An important aid in the interpretation of myths will often be 
supplied by the etymology of the names of the mythological personages ; and 
in this way new deities will sometimes be found to have arisen from the mere 
epithets of old ones, as Jacob Bryant saw clearly nearly 100 years ago ; nay, 
even magnificent myths may at times be traced to no more sublime origin than 
a false etymology which had taken possession of the popular ear. The signi- 
ficance of divine names must, of course, be sought in the first place in the 
language to which the mythology belongs ; but in applying this test, with 
the view of obtaining any scientific result, great care must be taken to avoid 
treating doubtful etymologies in the same way that certain ones may be treated. 
For where the etymology is uncertain, that is, does not shine out plainly from 
the face of the word (as in the case of the Harpies in Hesiod), then the elements 
of doubt are often so many, that it is wiser to abstain altogether from this 
aid, than to attempt founding any serious conclusions upon it. For, in the 
first place, we may not have the word in its original form ; and, in the second 
place, two or three etymologies may be equally probable. The best etymologies, 
whatever Bryant, and Inman, and Max Muller may say to the contrary, 
are only accessories of scientific mythological interpretation. 

XXV. If the mythological names have no significance in the language 
to which they belong, then reference may be made to cognate languages ; 
and in the case of European tongues, with propriety to the Eastern sources 
from which they are demonstrably derived. But here a double caution is 
necessary ; for accidental resemblances may be found in all languages, and 
extensive learning, coupled with a vivid imagination, may readily supply the 
most plausible foreign derivations, which are merely fanciful. 

XXVI. By referring to another, and it may be a more jDrimitive and ancient 
language, for the etymological key to a religious myth of any people, we are 
treading on historical ground extrinsic to the people with whose myths we may 
be dealing. For comparative philology, like archaeology, recovers the earliest 
history of a people before writing was known ; and this raises the inquiry, 
whether a mythology which bears a foreign nomenclature on its face may not 
convey foreign ideas in its soul — that is, to take an example, whether the 
Greek mythology, if the names of its personages are more readily explained in 
Hebrew or Sanscrit than in Greek, may not in respect of its ideas and legends 
be more properly interpreted from original Hebrew or Sanscrit, than from native 



48 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

Greek sources ? And may we not hope, in this way, in the Hebrew Scriptures, 
or the Sanscrit Vedas perhaps, to put our fingers on the ancient germs of 
those anthropomorphic myths which Homer and Hesiod present to us in adult 
completeness and full panoply ? and thus the highest end of scientific research 
will be obtained, not only to dissect the flower, but to trace it to the seed, and 
follow it through every stage of its rich and beautiful metamorphosis. 

XXVII. The prospect this holds out of tracing famous European religious 
myths to their far home in the East is extremely inviting.* It satisfies at once 
scientific minds by the promise of going to the root of a matter which has 
hitherto been treated superficially, and that not inconsiderable class of literary 
men and scholars who have a keener eye for an ingenious novelty, than for 
a stable truth. When we bear in mind also the significance of the homely 
proverb, that " far birds have fair feathers," and the well-known fact, that 
every mother is apt to prefer her own bairn to others which may be more healthy 
and beautiful, we shall see reason to proceed, not without hope indeed, but with 
more than Scottish caution, in this Oriental adventure. There is a class of 
persons in the world who have a strange pleasure in travelling a thousand leagues 
to quarry out a truth, which they might have picked up from beneath their nose. 
Against these seductions therefore, in the first place, while prosecuting this 
foreign chase, we must be on our guard. We ought to know that we are hunting 
on very deceitful ground ; that we are dealing with a class of phenomena, that, 
like clouds and kaleidoscopic figures, are very apt to change their shape, not 
only by their own nature, but specially also according to the position of the 
observer ; and that the same nebulous conglomerate may at one moment 
look very like a whale, at another moment very like Lord Beougham, and at a 
third moment very like Olympian Jupiter. And in the prospect of such a 
possible ridiculous conclusion to the sublime adventure on which he is starting, 
every inquirer into the remote origin of European myths ought to take with 
him these cautions — 

(1.) That there is no necessity and no scientific warrant for seeking a foreign 
explanation of deities, which already sufficiently explain themselves by the 
character which they bear, or the symbols which they exhibit in their own 
country. 

(2.) That the formative power by which myths were created, viz., the imagina- 
tion, possesses a wonderful magic, in virtue of which the materials on which it 
acts, especially with a quick and vivid people unfettered by formal creeds, are 
subjected to a perpetual process of transmutation, which renders the recogni- 
tion of the original identity of two diverging myths an extremely difficult and 

* " The whole theology of Greece was derived from the East." — Bryant, vol. i. p. 1 84. 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 49 

not seldom an altogether hopeless task. In this respect the recognition of the 
original identity of different words in cognate languages by comparative 
philology is a much more safe and scientific process than a similar recognition 
of the identity of different persons of two Pantheons through the shifting masks 
< >f comparative mythology. 

(3.) That the principal relations under which the great objects of nature, 
such as the sky, the sun, the sea, &c, may appear, when subjected to the process 
of imaginative impersonation, are in many cases so obvious that two different 
polytheistic peoples may easily hit upon them without any historical connection. 
Even in the free exercise of poetical talent in the case of individual poets of 
highly potentiated imagination, we constantly stumble on comparisons which 
have been made independently by other poets at other times or in distant 
countries, and which superficial critics are sometimes eager to fasten on as 
plagiarisms ; much more, in the vulgar exercise of the imagination, by the mass 
of the people on certain given natural objects may we expect frequent instances 
of coincidence without connection. This consideration will restrain a prudent 
investigator in this department from building any theory of foreign origin of 
myths on a few points of natural similarity. 

Taking these cautions along with us, we now observe, in reference to the 
probable Eastern origin of certain Greek myths — 

XXVIII. That the borrowing of one nation from another in the province of 
mythological ideas, as in the case of philological materials, may take place in a 
twofold fashion, either in the way of original descent from a common stock, far 
back in the cradle of the race, or by importation through the medium of com- 
merce or great religious revolutions and invasions. Of these two methods of 
borrowing, it is impossible to say, a priori, which promises the greater amount 
of gain to the adventurous inquirer ; for, while the advantage of greater close- 
ness belonging to the original identity of stock may be in a great measure 
neutralised by the distance of time and place, and the changes which they 
induce, the disadvantage of a more loose connection which belongs to the foreign 
importer may be amply compensated by the firm hold which the commerce, and 
polity, and intelligence of a superior people may take of an inferior people. 

XXIX. It must be borne in mind, also, that the recognition of a supposed 
identity between the gods of any two polytheistic peoples may easily take place 
without any real borrowing. For the desire of harmonising and classifying dis- 
cordant phenomena, which belongs to the very nature of intellectual action, is 
particularly displayed in the field of popular religion — to such an extent, indeed, 
that it became a fixed habit of the Greek and Roman mind to identify the 
deities of foreign countries with their own native deities by certain signs more 

VOL. XXVI. PART I. N 



50 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

or less superficial. The testimony of the Greeks, therefore, with regard to the 
supposed identity of certain personages in their Pantheon with certain gods or 
goddesses in the Egyptian or Phoenician, and their consequent foreign extrac- 
tion, will require to be examined with the severest scrutiny. 

XXX. In deriving any god from a foreign source, even though his foreign 
origin should appear in some respects perfectly certain, we must not conclude 
that all the phenomena which his person and character present are to be 
explained from abroad. Nothing is more natural than that he should be 
a compound god, one half native and one half foreign, or even a monstrous 
conglomerate of many gods. 

XXXI. Of all the foreign sources to which the Hellenic mythology has at 
different times been referred by the learned, Egypt is at once the most reputable 
and the least likely. For here we have neither original connection by identity 
of stock, nor any such commercial or political action of the more ancient over 
the more modern people, as would lead to the importation of religious ideas. 
The ancient Greeks had a great respect, and a sort of awful reverence for the 
wisdom and the antiquity of the Egyptians ; but this respect and reverence was 
more likely to lead them, as in fact it often did, to the recognition of super- 
ficial resemblances (as in the case of Io and Isis), than to the trace of original 
identity. Modern researches have added nothing to the probability of the 
favourite notion of Bryant and Blackwell, that the principal persons and 
legends of Hellenic mythology came directly from the land of Ham. 

XXXII. For the Hebrew origin of some of the Greek theological ideas — the 
darling notion of Church Fathers and Protestant theologians, and which has 
been recently revived by a statesman of distinguished character, talent, and 
erudition — there is even less to be said. For, in the first place, here we 
are comparing a polytheistic system with a monotheistic, where antagonism 
rather than similarity is to be looked for ; the elements of original or super- 
induced connection between the two peoples are altogether wanting ; and the 
original unity of the human family, which is the only link that binds the Greek 
to the Jew, is so remote that it requires no inconsiderable amount of hardihood 
to drag them into the arena of the present comparison. This hardihood, how- 
ever, has never been wanting ; and besides its own virtue, has always found 
great favour with the religious public, which is pleased with nothing so much 
as the idea that everything good, beautiful, or excellent in any way that 
heathen religions may be allowed to possess must have come either from the 
Hebrew Scriptures directly, or from some more ancient source of primeval 
revelation. And no doubt there may be a certain truth in this view ; but it is 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 51 

a truth which affects the monotheistic element, that in the person of Zeus lies 
the background of the Hellenic polytheism, rather than the polytheistic per- 
sonages to whom it has been applied. A consciousness of this, no doubt, led the 
early mythological interpreters of this school to apply the principle of Euhemerus 
largely to the Old Testament, in such a way only as to recognise the venerable 
Hebrew patriarchs under various masks of old Pelasgic gods or demigods. 

XXXIII. For the Phoenician influence on the formation of the early Greek 
theology there is much more to be said. We can, indeed, scarcely imagine a 
race of such distinguished merchants and navigators, commanding the Greek 
seas in the early ages of EurojDean civilisation, without supposing some such 
contagion and ingrafting of religious ideas, as the genius of polytheism was on 
all occasions prone to invite. We shall, therefore, be disposed to receive 
favourably any distinct proof, or even probable indication, of the derivation of 
Greek gods from a Phoenician source ; but we must bear in mind at the same 
time, that the Phoenicians were known to the Greeks as mere traders, with 
temporary settlements on the coast of the Mediterranean, and that their 
character, as exhibited in the Odyssey, was by no means possessed of such 
attractions as might aid to allure the Greeks to the adoption of any of their 
peculiar objects of worship. 

XXXIV. The last source of Greek myths, for which a strong claim has 
recently been put forth by a German of distinguished talent, taste, and 
learning in this country, is Sanscrit. And here at last some people seem to 
think, that with all certainty we have got at the true source of the many- winding 
mythological Nile. But after looking into this matter with all possible care, 
and with no prejudice whatever (for nothing would please me so much as to 
catch the infant Mercury in the bosom of a cloud, floating over the shining 
peak of the Hindoo Koosh, or to hook Proteus in one of his many forms at the 
mouth of the Ganges), I must -honestly confess, that hitherto the interpreters 
of Hellenic myths from Sanscrit roots and Vedic similes have inspired me 
rather with distrust than with confidence. The principal characters of the 
Hellenic Pantheon tell their own story, to a poetical eye, more obviously and 
effectively than with the help of a Sanscrit root ; and those few of them which 
are more doubtful, such as Hermes and Athena, seem to be precisely those in 
which the Sanscritizing mythologers have most egregiously failed. I consider, 
therefore, that, while the Vedic mythology, preferably to any other polytheistic 
system, presents an ample field from which some of the Hellenic legends may 
be aptly illustrated, and a few, perhaps, correctly interpreted, the attempt to 
explain the great and prominent phenomena of the Greek Pantheon, by an 
ingenious application of a few favourite physical ideas variously impersonated 



52 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

by the fancy of the Vedic poets, must be regarded in the meantime, at least, as 
a failure." 

XXXV. Without, therefore, in the slightest degree wishing to throw- 
discouragement on the delightful and interesting study of comparative mytho- 
logy, — a study that promises the most fruitful results in the domain of theology 
and moral philosophy, — the procedure of exact science seems to demand that, 
before venturing on extensive excursions into foreign regions, we should, in 
the first place, carefully survey and exhaust our home domain — that is to say, 
that the Greek traditions with respect to their gods, interpreted by themselves, 
and the general principles of mythical interpretation laid down in the above 
propositions, afford a surer basis for this branch of mythological science than 
hints suggested by Oriental etymologies, or analogies from the Vedic hymns. 
And in order to make this more clear, I will select a few examples of person 
ages from the motley theatre of Hellenic legend, which may be best adapted 
for testing the value of the different methods of interpretation. 

XXXVI. As examples of how the elemental significance of the Hellenic 
gods reveals itself to a sympathetic eye, from the mere presentation, epithets, 
attitudes, and badges of the mythologic personages, we need do no more than 
mention Zeus, Poseidon, and Apollo, in whom all the ancients, who exercised 
reflection at all on the matter, recognised, with one voice and by an unerring- 
instinct, the great elemental powers of the sky, the sea, and the sun. And 
these are precisely the powers which, from their prominence, might a priori have 
been predicated as certain to obtain a conspicuous place in an anthropomorphic 
Pantheon of elemental origin. Of these three great gods also, be it noted, that 
the first is the only one of which we can trace the etymology with any certainty ; 
but neither does this one etymology, when recognised in the Sanscrit word 
Diva, to shine, add anything to the already recognised idea of the Hellenic 
Zeus, nor does the lack of an etymon in the other two cases render our percep- 
tion of the character of the two gods less clear, or our knowledge of their 
significance more certain. With regard to Poseidon, Mr Gladstone's recent 
attempt to fix on him a Phoenician pedigree must be regarded as unsuccessful. 
The people who at an early period sailed to Colchis and to Troy, did not 
require to borrow a lord of the flood from the merchants of Tyre and Sidon. 

XXXVII. In Hera who, to the people and the people's poet, was simply 
the spouse of Zeus, a large class of ancient speculators, as is well known, were 

* It may be proper to state, that the interpretation of certain personages in the Greek Pantheon 
from sources of Sanscrit etymology, to which Max Muller has given currency, is not at all con- 
firmed by the judicious sobriety of our countryman Dr Mum. See his paper in our Transactions, 
vol. xxiii. p. 578. 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 53 

inclined to recognise the lower region of the atmosphere, of which Zeus repre- 
sented the aldrjp, or upper region. But a little consideration has convinced most 
modern interpreters that this idea was a mistake. When by the completion of 
the anthropomorphic process, the original ovpavos had become " Father Jove," 
it was most natural that his elemental counterpart Trj, Mother Earth, should 
become the matron Hera ; and with this supposition, the well-known description 
of the sacred marriage of Zeus and Hera (II. xiv. 345), together with the 
cow-symbolism belonging to the Bo<£m?, and her Argive priestess Io, notably 
harmonise. It is no objection to this view, that Ceres or Demeter is also the 
anthropomorphised earth ; for " the many names of one shape " (ttoWwv 
ovofMOLTcov fxop(f>7) fjiia), characteristic of the oldest elemental theology, could easily, 
and did often crystallise into two or more shapes of one power. We shall, 
therefore, say with no rash confidence, that the Hellenic Hera means the earth ; 
and we readily allow the etymological conjectures connected with her name 
to remain conjectures. 

XXXVIII. On Athena, Max Muller says, " The Sanscrit root Ah, which 
in Greek would regularly appear as Ach, might likewise then have assumed 
the form of Ath ; and the termination Ene, is Sanscrit Ana " (" Science of 
Language," vol. ii. p. 503) ; and again, " How Athena being the Dawn, should 
have become the goddess of wisdom, we can best learn from the Vedas. In 
Sanscrit, Budh means to wake and to know " (Do. p. 504). 

But this is manifestly following out a favourite idea upon theories of the 
most flimsy texture. If any etymology is to be sought for the syllable A0, the 
native root al6 which signifies to glow, corresponding as it does with the familiar 
epithet of yXauKwis, or " flashing-eyed " (which I think Welcker suggests), is 
preferable to that suggested by the distinguished Sanscrit scholar. But here, 
as in other slippery cases, the principles laid down in the preceding propositions 
lead me to set etymology aside, and to look at the finished figure of the goddess, 
with her badges, relations, and actions, as the natural and sure index to her 
significance. Now if Zeus, according to the Greek conception, was the strong, 
stormy, and thunderous element of the sky — as his epithets K€huve<fyqs, and 
ipifipepeTT)?, and TepiriKepavvos, sufficiently declare — his flashing-eyed daughter, 
who alone is privileged to wield his thunderbolt (^Eschyl. Eumen., 814), must be 
some action or function of the sky. Let her, therefore, be the flashing lightning, 
or the bright rifted azure sky between the dark rolling thunder clouds, or both 
if you please, and you have at once an elemental theory which explains 
adequately her anthropomorphic parentage and presentation. As to her moral 
and mental significance, that follows necessarily from her Jovian fatherhood. 
When the all-powerful was recognised as at the same time the all- wise, and the 
great counsellor (^rc'era Zeus), his daughter, as a matter of course, became the 

VOL. XXVI. PART I. 



54 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

goddess of practical wisdom, that is, of the great arts of peace and labour (as 
the vases largely show), and the patron and protector of all men of valour 
like Achilles, and of sagacity like Ulysses. 

XXXIX. The Hellenic Hermes is one of those mythological personages 
who from an originally simple root, has grown up into such a rich display of 
graceful ramification, that, when we approach him from his most familiar side 
we are the least likely to interpret his true significance. But if we attend to 
the earliest indication of his functions as found in Homer, and as displayed in 
the familiar phallic symbol (Herod, ii. 51), we can have no difficulty in evolving, 
by a series of graduated expansions, his final avatar as a god of eloquence, from 
his original germ as a pastoral god of generation and increase (Hom. II. xiv. 
491). As the god of shepherds and mountaineers, he was necessarily the 
guide of all wanderers through the many winding glens, and across the many- 
folded hills of the Arcadian Highlands. This early function accordingly appears 
in Homer : he is the friendly guide of all persons who have lost their way or 
who wander in the dark (Od. x. 277 ; II. xxiv. 334). His connection with 
music and with wrestling, the natural recreations of a pastoral people, of course 
belong to this his earliest Hellenic character. Afterwards, when in the 
necessary progress of society, the patriarchal shepherd of the hills resigned 
his social position into the hands of the rich merchant of the great towns, 
Hermes became the god of gain generally ; and, with gain, of all those arts of 
adroitness and sharpness which belong to the career of a successful trader. 
The kindly guide of night-wandering shepherds has now become the expert 
negotiator, and the trusty messenger ; he is the winged servant of the gods 
above ; and among men his oaten pipe is exchanged for the charm of winged 
words, which sway the counsels of the wise, and soothe the clamours of the 
turbulent. With this natural and obvious interpretation of a purely Hellenic 
deity, as given within the bounds of Greece itself, we shall raise only a brilliant 
confusion, if we follow Max Muller across the Hindoo Coosh, and ingeniously 
attempt to find the germ of the Pelasgic shepherd god in the breeze of the 
early dawn, which ushers in the inarch of the busy day. Such remote 
conjectures may be both beautiful and ingenious, but they are a mere play of 
fancy, and travel obviously far out of the way of a sober, a scientific, and 
a stable interpretation. 

XL. Dionysus was a god of comparatively recent introduction into Greece 
(Herod, ii. 49), confessedly of Asiatic origin, and in whom the union of fervid 
wine with the phallic symbol and violent orgies, can leave no doubt as 
to his true character. He is the male god of generation, according to the 
Asiatic conception, as the Syrian goddess of Lucian (De Dea Syria, 16) was 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 55 

the female one ; and the old Heraclitan principle that fire is the origin of all 
things, rudely conceived by the popular imagination, is manifestly that which 
in this god identifies the fervour of the vine juice, the brewst of the sun, with 
the fervour of the generative process. The fact that the worship of Dionysus 
was not native in Greece, but travelled from the East, naturally led to the 
representation of this god as a wonderful conqueror, in the fashion of Sesostris 
and Alexander the Great ; from which analogy, coupled with his preaching 
the gospel of wine, Bryant and other speculators have been eager to find in 
him a perverted Noah ; but the application of the principle of Euhemerus in 
this case evidently rests on too slender a foundation to afford any grounds for a 
scientific interpretation. 

XLI. Aphrodite is that goddess in whose case Mr Gladstone's favourite 
idea of Phoenician influence on the Greek Pantheon has long been recognised 
as the most certain (Herod, i. 105 ; Pausan. i. 14, 6). The recognition of this 
Phoenician element, however, does by no means imply that the existence of an 
original Hellenic impersonation of the passion of love, and the seductions of 
personal beauty, should be denied. On the contrary, the female deity whom 
the Phoenicians were seen worshipping in their factories on the coasts of the 
Mediterranean, would most probably be accepted by the ancient Pelasgic tribes 
chiefly because they found in her attributes a striking identity with their own 
native Aphrodite. 

XLII. Phoenician influence is also undoubtedly to be acknowledged in the 
very complex and composite mythology connected with the name of Heracles. 
But the person of Heracles, as we find him in Homer, exhibits nothing beyond 
the exaggerated traits of a stout and muscular humanity in combat with late 
and circumstance, and the wild beasts of the forest — a plain ITellenic counter- 
part, in fact, to the Hebrew Samson, of whose historical reality, to a mind not 
violently possessed by German theories, there cannot be the slightest reason 
to doubt. The exaggerations connected with his story are the natural and 
necessary effects of the excited popular imagination brought to bear on such 
a character; but these exaggerations, taken at their highest, are exhibited 
on a very small platform in Homer, and present a very modest array of achieve- 
ments compared with, the multiform mass of myth that afterwards accumulated 
round this representative Greek hero. The principle of growth, of such 
luxuriant vitality in popular myths, has been obviously at work here ; and the 
sort of omnipresence latterly attributed to this wandering queller of monsters 
is most readily explained from the influence of the Phoenician factories in the 
Mediterranean, in whose Melcarth the Greeks delighted to recognise their 
own stout son of Jove and Semele. And if this Tyrian Hercules, as Phoenician 



56 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS, 

scholars incline to believe (Moevers, vol. i. p. 385), really was a sun god, the 
twelve labours of Hercules will, of course, only be the symbolical expression 
for the progress of the Titan sun through the twelve months of the solar year. 
This the ancients themselves, in the Orphic theology, at least distinctly recognised. 

XLIV. In Bellerophon the Germans find a favourite example of their 
theory, that all the heroes of the so-called heroic age are the degraded gods of 
an early elemental worship. How this theory is worked out in the present case 
it may be instructive to consider. The winged steed, of course, brings you at 
once into the region of the sun. Then you turn up Eustathius' commentary on 
the well-known episode of the Corinthian hero in the sixth book of the Iliad 
(v. 181), and you find there that there was an old Greek word eXXepos, used by 
Callimachus, which is equivalent to kcikos or bad; but bad things are black 
things ; therefore, with the help of the digamma, transmuting eXXepos into 
/3eXXepo?, we arrive at the conclusion that fie\\epo(f>6vTr)<s means the slayer of 
darkness, and, of course, can be nothing but the light, or the sun. Bellerophon 
is thus, by a dexterous etymological feat, already a solar god in full panoply ; 
and when, in addition to this, we find that the worship of the sun was much 
practised at Corinth, the native place of the hero, and that he died in Lycia, a 
country famous for its devotion to the same deity, the case for a degraded 
"HXto? seems to be satisfactorily made out. But, on the other hand, the oldest 
version of the story in Homer has no hint of the winged horse ; and for the 
rest, looks in every trait as much like a purely human history of those early 
Greek times as the story of St Columba shows like a real legend of a real 
Catholic apostle in early Christian times. "We shall, therefore, in my opinion, 
more wisely say that the airy flight of the grandson of Corinthian Sisyphus on 
his winged Pegasus, is only the imaginative painting out of a real human journey 
made from such real and natural causes as those which Homer details ; and, if 
the winged horse has anything to do with the worship of the sun at Corinth, it 
is more reasonable to suppose that such a blazon should have been added for 
the glorification of a real great man, than that all the great men of early Corinth 
should have been clean swept from the popular memory to make way for an 
unmeaning Pantheon of degraded and forgotten gods. 

XLV. Descending lower down into the region of what has the aspect, not 
of metamorphic theology, but of plain human fact, we may take the names of 
Achilles and Theseus as examples of how far the German school is inclined 
to carry its peculiar tactics of finding nothing in all early tradition but theolo- 
gical ideas and symbols. As to Achilles, the favourite notion with most German 
writers is that this hero is a water god, — a notion founded on nothing that I can 
see, save on the etymological analogy of Achelous, the happy coincidence of 



WITH SPECIAL REFERENCE TO GREEK MYTHOLOGY. 57 

Peleus with the Greek name for mud (7777X05), and the fact that the mother of 
the hero was a sea-goddess ; and on this notion Forchhammer, I believe, or some 
one of the erudite fancymongers beyond the Rhine, constructed a theory that 
the Iliad is really a great geological poem, in which water power is represented 
by Achilles, and land power by Hector (from fya), to hold, restrain, keep back) ! 
This is really too bad. If a man in Thurso, to take a modern example, named 
Waters — and it is a characteristic name in that quarter, were to marry a woman 
called Loch — a well-known name in Sutherland — and a daughter, the offspring 
of this marriage, should join herself in wedlock to an English gentleman named 
Rivers, no sane person could see in this conjunction of congruous etymologies 
anything but one of those curious coincidences which amuse a newspaper reader 
for a minute, and then are forgotten. Why, then, we ask, should the occurrence 
of water, and mud, and a sea-nymph, among the family names of an old Thessa- 
lian throne, be supposed to possess any more profound significance, even on the 
supposition that the etymologies are certain, which they certainly are not % 
And accordingly, we find this favourite water theory discarded by the Germans 
themselves, the moment it does not suit the theory of the interpreter. To Max 
Muller Achilles can be nothing but a solar god ; for his imagination, fired 
with sunlight from the flaming east, can see nothing in the stout battles of 
Greeks and Trojans in the Iliad but the grand struggle between the powers of 
light and darkness. Of the probability of this theory I have sought in vain for 
the shadow of a proof. If Helen of Troy, whose name can obviously be identi- 
fied with brightness (cre'Xas aehjvr)), must on this account take her place with 
her brothers, as a sidereal phenomenon (sic Fratres Helenas, lucid a sldera), this 
does seem to me an exceeding weak foundation for the transformation of the 
whole topographical and traditional heroes of the Iliad into a meteoric 
spectacle. 

If, according to the views set forth in this paper, there is no scientific 
ground for raising Achilles into the category of gods, whether aquarian or 
solar, much stronger are the reasons which induce us, with unsophisticated 
old Plutarch, to see in Theseus no myth, but a great historical reality. If the 
principle be once accepted, that a single miraculous fact or incredible story con- 
nected in the popular imagination with a great popular name, shall deprive him 
simpliciter of all claim to a historical existence, we shall make strange havoc, I 
fear, with some of the most brilliant and the most instructive pages of national 
record. There is no need of believing all the wonderful stories that Athenian 
reverence and wonder accumulated round the name of Theseus, as little as there 
is of believing all the silly miracles that the Lausiac history narrates of the 
Egyptian ascetics ; but there is certainly as little wisdom in roundly denying 
the historical germ to which, in all such cases, these accretions were attached. 

I have thus pointed out, in a rapid and succinct way, what seem to be the 
vol. xxvi. part 1. p 



58 PROFESSOR BLACKIE ON INTERPRETATION OF POPULAR MYTHS. 

leading principles on which a sound and safe interpretation of early popular 
myths must proceed. I have kept myself purposely within the bounds of what 
appears to me sober statement, not being eager for the glory of adventure in 
this nebulous field; and if I shall seem to have achieved a very small thing when 
I keep myself within these bounds, I have at least kept myself clear of non- 
sense, which in mythological science is as common as sunk rocks in the Shetland 
seas. To Max Muller, and other Sanscrit scholars, I hope I shall always be 
grateful for any happy illustrations which they may supply of the general 
character of Aryan myths, and of occasional coincidences of the Hellenic mode 
of imagining with the Indian ; and I think the somewhat cold and unimaginative 
race of English scholars are under no small obligations to him for having taught 
them to recognise poetical significance and religious value in some legends, 
which passed in their nomenclature for silly fables or worthless facts ; but I 
profess to have been unable to derive any sure clue from the far East to the 
most difficult questions of Greek mythology ; nor do I expect that, when every 
obsolete word in the Rigveda shall have been thoroughly sifted and shaken, 
a single ray of intelligible light will thence flow on the Athena of the Parthenon, 
or the Hermes of the Cyllenian slopes. I believe that in the region of mytho- 
logy they will ultimately be found to be the wisest, who are at present content 
to know the least; that while some mythological fables are too trifling to 
deserve interpretation, others are too tangled to admit of it ; and that the man 
who, at the present day, shall attempt to interpret the Greek gods from the 
transliteration of Sanscrit or Hebrew words, will be found, like Ixion, to have 
embraced a cloud for a goddess, and to have fathered a magnificent lie from 
the fruitful womb of his own conceit. There is no more dangerous passion than 
that which an ingenious mind conceives for the fine fancies which it begets. 



( 59 ) 



III. — On the Extension of Brouncker's Method to the Comparison of Several 

Magnitudes. By Edward Sang, Esq. 

(Read 7th February 1870.) 

The discovery of those numbers which shall, either truly or approximately, 
represent the ratio of two magnitudes, necessarily attracted the attention of the 
earliest cultivators of exact science. The definition of the equality of ratios 
given in Euclid's compilation clearly exposes the nature of the process used in 
his time. This process consisted in repeating each of the two magnitudes until 
some multiple of the one agreed perfectly or nearly with a multiple of the 
other ; the numbers of the repetitions, taken in inverse order, represented the 
ratio. Thus, if the proposed magnitudes were two straight lines, Euclid would 
have opened two pairs of compasses, one to each distance, and, beginning at 
some point in an indefinite straight line, he would step the two distances along, 
bringing up that which lagged behind, until he obtained an exact or a close 
coincidence. 

He seems to have assumed that, in the case of incommensurable magnitudes, 
the further continuation of the process must give still closer approximations ; 
but we do not find any indication of a knowledge of the fact that, in the course 
of that continuation, we shall certainly come upon coincidences still more close 
than any which we have already obtained. 

This process for finding the numerical expression for a ratio is inconvenient 
from its bulkiness ; it is also unnatural, for the mind, in comparing two unequal 
magnitudes, is rather inclined to regard them as made up each of so many 
measures, than to consider how many times the one must be augmented in order 
that the result may be a multiple of the other ; it prefers the direct to the 
inverse comparison. 

Lord Brouncker's method of continued fractions enables us with great 
rapidity and within the compass of the magnitudes themselves, to determine 
directly their ratio. It is one of the great landmarks in the progress of the 
science of numbers. 

By one or two slight improvements in the mode of calculation, the chain or 
continued fraction became a ready tool in the hands of arithmeticians. It placed 
in a clear light the whole doctrine of indeterminate equations of the first degree, 
leaving scarcely anything further to be desired in this branch of the Diophantine 
analysis. 

VOL. XXVI. PART I. Q 



60 MR EDWARD SANG ON THE EXTENSION OF BROUNCKER'S METHOD 

On applying Brouncker's method to two incommensurable quantities of the 
second degree, it was found that the denominators eventually came to be 
repeated or circulated indefinitely; and Lagrange showed that while every cir- 
culating chain-fraction was known to represent the root of a quadratic equation, 
the roots of all such equations were developable in such a fraction. Hence the 
conclusion was drawn that the root of no equation of a higher order can possibly 
be represented by a circulating chain-fraction. 

Although, to the mind of Brouncker, the continued fraction presented the 
readiest way of expounding his idea, it is not essential thereto ; a much clearer 
view of the true nature of the process may be obtained without it. The opera- 
tion consists, essentially, in deducting, as often as possible, the less from the 
greater ; the remainder again from the preceding subtrahend, and so on ; in 
keeping note of the numbers of the subtractions ; and in computing from these 
numbers the value of the magnitudes in terms of the ultimate subtrahend. The 
chain-fraction is merely one way of representing the final computation. By 
stopping at the first denominator, then at the second, afterwards at the third, 
and so on, we obtain a series of fractions alternately too great and too small, 
but approaching rapidly to each other and to the true expression for the ratio. 
Now this series may be deduced directly from the equations representing the 
various subtractions ; wherefore, in our subsequent investigations, we may put 
the idea of the chain-fraction entirely aside, without thereby changing the in- 
trinsic character of the Brounckerian process. 

On examining the two series converging to the two roots of a quadratic 
equation, I observed that the circulating quotients are the same for both, but that 
their order is inverted. This observation led me to a singular law, which some 
years ago I submitted to the Society. It is this, that if we continue the forma- 
tion of the series for one root beyond the non-circulating quotients, obliterate 
these and the fractions adjoining them, and then, using only the circulators, 
compute the series backwards, we shall obtain the other root of the equation; 
so that both roots are given by a, so to speak, two-headed progression. 

The periodical recurrence of the quotients enables us to approximate as 
closely as may be desired to the roots of equations of the second order, with 
very little labour ; and a kind of regret accompanied the conviction that the 
same facilities cannot be obtained for equations of higher degrees. On con- 
sidering the arguments on which this conviction rested, it appeared to me that 
the whole circumstances of the case had not been taken into account ; one, and 
a most influential one, had been concealed under the notation employed, that is, 
under the scheme of continued fractions. If we assume any two fractions to 
take the place of two contiguous terms in a Brounckerian progression, and 
operate upon these in the usual way, that is, by adding to a multiple of each 
member of the second fraction the corresponding member of the preceding ; and 



TO THE COMPARISON OF SEVERAL MAGNITUDES. 61 

if we continue this operation, using always the same multiplier, or a circulating 
set of multipliers, the fractions so resulting converge to the root of a quadratic 
equation. If we should assume three fractions, and combine fixed multiples of 
their members, so as to form a progression of the third order, as we may call it, 
to what value do the terms of this progression converge ? 

In a paper read by me some time ago to the Society, it was shown that the 
convergence in this case is toward the root of a cubic equation; and that the 
same arrangement may be extended to the still higher orders ; as examples of 
the application of this method, two cases may be cited. 

If we begin with the two fractions q > ^ and form a progression by adding 

to the double of each member of the last, the corresponding member of the 
preceding, we form the well-known progression 

1 1 3 7 17 41 99 o 
' 1 ' 2 ' 5 ' f2 ' 29 ' 70 ' ' 

which converges toward the ratio of the diagonal to the side of a square. 

If, beginning with the same pair, we form a progression by taking the sums 
of the members of the last and of the penult, we obtain 

1 1 2 3 5 8 13 21 34 o 
6' I* 1' 2' 3' 5' "8 ' 13' 21' ' 

which converges toward the ratio of the diagonal of a regular pentagon to its 
side. In this case, the numerator of one fraction becomes the denominator of 
the succeeding, so that it is unnecessary to write both progressions. These 
are familiar examples of quadratic roots. 

Let us now assume three terms, 0, 0, 1, and continue a progression by 
adding to the double of the last term the difference between the two previous 
ones, thus — 

0, 0, 1, 2, 5, 11, 25, 56, 126, 283, 636, 1429, 3211, 7215, 16212, 36428, 

81853, 183922, &c, 

and we obtain an approximation to the ratio of the long diagonal to the side of 
a regular heptagon. Thus, if the side of the heptagon be 283, its longest 
diagonal is almost exactly 636. 

Or again if, assuming the same three terms 0, 0, 1, we form a series by 
deducting the antepenult from the triple of the last term, thus — 

0, 0, 1, 3, 9, 26, 75, 216, 622, 1791, 5157, 14849, 42756, 123111, 354484, &c, 

we obtain an approximation to the ratio of the long diagonal of an enneagon to 
its side. 

I have shown that, in progressions of this kind, that is, where the numerator 



62 MR EDWARD SANG ON THE EXTENSION OF BROUNCKER'S METHOD 

of the one fraction becomes the denominator of the other, the approximation is 
toward that root of the equation which is farthest from zero ; and that if the 
progression be carried backwards, the approximation is then toward the root 
nearest to zero. 

These remarks may suffice to show that this branch of the theory of numbers 
promises to yield important results. Now, the whole doctrine of quadratic 
recurrence sprung from the comparison of two magnitudes ; and so the com- 
parison of three magnitudes must be the true foundation on which to build 
the doctrine of cubic recurrence. I propose, therefore, in the present paper, to 
discuss the elementary operation by which the ratios of three incommensurable 
magnitudes may be approximately ascertained. 

Let there be three homogeneous quantities, A, B, C, arranged in the order 
of their magnitudes, and let it be proposed, if possible, to find their common 
measure. 

By repeatedly subtracting the second B from the greatest A, we obtain a 
remainder less than B ; this remainder may or may not be greater than C ; if it 
be greater, we may take C from it until we obtain a remainder D less than the 
least of the three proposed quantities. In this way we have an equation of 
the form 

A=p 1 B + q 1 C +D, 

in which p cannot be zero, while q may. 

Treating now the three quantities B, C, D, in the same way we have a new 
equation 

B=p 2 C+q 2 B + E } 

and we may proceed in this way until there be no remainder, or until the 
remainder be so small as to pass the limits of exactitude demanded by the 
nature of the case in hand. 

We are now able, by means of successive substitutions, to obtain values of 
A, B, C, in terms of the ultimate remainders ; and our first business is to devise 
some convenient arrangement for this purpose. 

For the sake of giving greater generality to our investigations, let us put 
the successive equations in the form 

A = p 1 B + q x C + r x D , 

B = p 2 C + q 2 D ■ + r 2 E , 
C = P s D + q a E + r s F , 

Q = p n E + q n S + r a T , 

in which r lt r s , . . . . have been written for the unit of the usual process. 



TO THE COMPARISON OF SEVERAL MAGNITUDES. 63 

By successive substitutions we arrive at a value of A, in terms of R, S, T, 
which may be conveniently represented by the equation, 

A = yn . R + On . S + ^n . T , 

and our business becomes to discover the law of formation of the functions fn, 
On, \fm. 

Continuing the operation one step further, we have 

B, = P„ + 1 .S + g B + 1 .T + r n + , . U , 

and substituting this value for E in the preceding equation, 

A = {p„ + i- <pn + On] S + {q n + x . <pn + xjjn} T + r n + l . <pnU , 

wherefore the law of successive formation is contained in the three equations — 

<p(n + 1) = p n + 1 . <pn + On , . . . (1), 
0(n + 1) = q n + 1 .Qn + xjtn, . . . (2), 
xjj(n + 1) = r n + 1 . <pn, .... (3). 

Now these forms hold good for every value of n, wherefore 

xjjn = r n . <p(n - 1) , 
and consequently 

0(n + 1) = <p n+1 . <pn + r n . <?(n - 1) , 
whence 

On = qn . q(n — 1) + ;•„ _ x . <p(n — 2) , 

so that the equations (1), (2), (3) become 

<p(n + 1) = p n+1 . pi + q n . <?{n - 1) + r n _ x . <p(n - 2) , (1), 

0{n + 1) = q n + 1 . <pn + r n . <p(n - 1) , . . . (2), 
xjj(n+ 1) =r n + 1 .pi, (3). 

By means of these formulae we can construct the series of functions tpn 
independently of the others, and thence we can readily deduce the progression 
On ; as for the third progression \pn it is, in the usual case of r = 1, a mere 
transcript of the progression <pn moved one step back. The arrangement of the 
work is very simple, and may be best studied from a numerical example. 

The arrangement of the intervals in music has to follow the natural sub- 
division of a vibrating column, and so must be made, primarily, to suit the 
ratios 1 : 2, 1 : 3, 1 : 5, and their compounds. If, then, it be proposed to tune a 
musical instrument so as to permit of transposition from one key to another, the 
ratio represented by the smallest interval on it must be contained exactly, or 
very nearly, in each of these three ratios. Therefore the arrangement of the 
gamut on an instrument of equable temperament must be obtained by a com- 

VOL. XXVI. PART I. K 



64 MR EDWARD SANG ON THE EXTENSION OF BROUNCKER'S METHOD 

parison of the logarithms of the three prime numbers 5, 3, and 2. These 
logarithms are incommensurable, and so it is impossible to tune a keyed instru- 
ment perfectly. The comparison of these three logarithms furnishes a con- 
venient instance of the application of our method. 

Putting, for shortness' sake, A = log 5, B = log 3, C = log 2, we obtain the 
following equations : — 



■69897 


00043 


= 


A = 


l.B + 0.C + D 


•47712 


12547 


= 


B = 


l.C + 0.D + E 


•30102 


99956 


= 


C = 


l.D + 0.E + F 


•22184 


87496 


= 


D = 


l.E + 0.F + G 


17609 


12590 


= 


E = 


2.F + 0.G + H 


7918 


12460 


= 


F = 


1.G + l.H + J 


4575 


74905 


= 


G = 


2.H + 0.J + K 


1772 


87669 


= 


H = 


l.J + 0.K + L 


1569 


49885 


= 


J = 


l.K + 2.L + M 


1029 


99566 


= 


K = 


5.L + 0.M+ N 


203 


37784 


= 


L = 


1.M + 5.N + P 


132 


74750 


=z 


M = 


10.N + 0.P + Q 


13 


10644 


= 


N = 


2.P + l.Q + R 


5 


09810 


= 


P 




1 


68303 


= 


Q 




1 


22720 


— 


R j 





and, in order to compute from these the successive approximations, we may 
write the three sets of coefficients, p, q, r, in three horizontal lines, as in the 
subjoined scheme: — 



r 


1 1 1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


9 











1 








2 





5 





1 


P 


111 


1 


2 


1 


2 


1 


1 


5 


1 


10 


2 



A 1 1 1 2 3 7 9 28 35 44 318 353 5164 10638 
B 1 1 1 2 5 6 19 24 30 217 241 3525 7267 

C 1 1 1 3 4 12 15 19 137 152 2224 4585 

Having written unit beneath the first p, to serve as the beginning of the 
series A, we multiply that unit by p x to get 1, the second value of A 2 , which 
value we write beneath p r We now take the products A 2 p 2> A x q 1} the sum of 
which gives us A 3 = 1. Thereafter we take the sum of A 3 ^? 3 , A 2 q 2 , A 1 r t , to 
obtain A 4 = 2. In this example the first five q's happen to be zeroes, and so 
the middle terms of the expressions are awanting ; the middle term is first 
found in the expression for A 8 , which is A 7 .p 7 + A e . q 6 + A 5 . r 5 = 18 + 7 + 3; 



TO THE COMPARISON OF SEVERAL MAGNITUDES. 65 

and again we have it in the value of A n , which is A 10 .p xo + A 9 . q Q + A 8 . r 8 = 
220 + 70 + 28. 

The series for B is formed exactly in the same way, only that its commence- 
ment is delayed one step ; in other words, B x is held as zero, and B 2 is made unit. 

Similarly for C, C 1? C 2 are held as zeroes, and C s is made unit. We may 
in the same way find series for D, E, F, and so on. 

The eighth set of values give 28, 19, 12 as nearly proportional to the 

logarithms of 5, 3, and 2. Assuming these as sufficiently near for the purposes 

of musicians, we must divide the interval corresponding to the ratio 1 : 2, called 

by them an octave, into 12 parts, to which the name semitone is given. In this 

way, counting in semitones, we have log 2 = 12, log 3 = 19, log 5 = 28 ; 

3 5 

whence log 9 = 7, log ^ = 4 , and so on ; whence the arrangement of the 

gamut is at once obtained. According to these values, we should have 

9 10 

log g = 2, and log Q = 2 , wherefore the degree of precision obtained by these 

numbers is not sufficient to discriminate between the tone major and the tone 

minor. 

In order to obtain a closer approximation, we must proceed further along 

the series. Now it is important to keep to the nomenclature and arrangement 

of semitones ; wherefore we search among the series C for some member 

divisible by 12 ; no one of those above given is so divisible, and therefore we 

look for some compound of two of them which may be a multiple of 12. Thus 

362 
C 10 + C n = 156, so that, still counting in semitones, we have log 5 = -r^ = 

11 247 156 

27 j3 , log 3 = jcr = 19 , log 2 = -J3 =12. From these values the logarithm 

9 
of the tone major represented by the ratio g is still 2, but that of the tone minor 

represented by q- is 1 jo ; in the same way the corrected values of the other 

musical intervals may be obtained. 

By putting A, B, C to represent the periodic times of three astronomical 
phenomena, we may ascertain the intervals between their simultaneous recur- 
rence. Thus, if we put A for the time of revolution of the moon's node, B and 
C for the earth's and moon's periodic times, we shall obtain directly the law of 
recurrence of eclipses. 

If we take three contiguous sets of values, and thence compute the succeed- 
ing set, we obtain 

A n _|_ 3 = p „ + 2 . Aj + 2 + 9\ n + 1 • A n +1 + r n A» 

B„ + 3 = p n + 2 • B„ _|_ 2 + q n + 1 . B„ _|_ i + T n B n 

^n + 3 = P n + 2 • ^n + 2 + ?» + l • Ui+1 + *'n ^n I 



K 


A„ + i 


Ai + 2 


B„ 


B„ + i 


B„ + 2 


c„ 


C„ + i 


^n+2 



tfti 



MR EDWARD SANG ON THE EXTENSION OF BROUNCKER S METHOD 



eliminating^ and q from these three equations, we obtain, omitting the sub- 
scribed „ for shortness, 

r n { A B 2 C, - A B, C 2 + B A 3 C 2 - B A 2 C x + C A 2 B 1 - C A x B 2 } = 
{A 3 B 2 C x - A 3 B x C 2 + B 3 A, C 2 - B 3 A 2 C, + C 3 A 2 B x - C 3 A t B 2 }. 

Now the first of these quantities within the ties is the determinant obtained 
from the coefficients 



A 
B 

a 



A, 
B, 



A c 




A, 


A 2 


B 


B x B 2 


C 


Cx c 2 


mi 


nant from the 




A 2 




A, 




B 2 


= 


Bx 




C 2 




Cx 



while the second is the determinant from the next three sets of values ; or, 
using Cayley's notation 



B 2 
C 



A 3 
B, 



Now, in the usual operation, and when the three magnitudes are incommensur- 
able, r is unit all along ; wherefore the determinant from nine contiguous values 
never changes. But at the beginning this determinant is obviously unit, and 
thus we have the ordinary well-known theorem for the usual progression in 
reference to two magnitudes extended to the case of three ; that is to say, the 
value of the determinant is -I- 1 all along. In the case of two magnitudes, the 
value is alternately + 1 and — 1 ; whereas, in the case of three magnitudes, 
the sign is preserved. 

The above statement holds good in the case of incommensurable quantities ; 
but when there is a common measure the quotient r may disappear toward the 
end of the operation, and then all the subsequent determinants become zero. 

If, in the case of three commensurables, we complete the calculation, as in 
the following example in which the three primes 99137, 30763, and 3229 are 
compared, a remarkable yet obvious law is seen. 



1 


1 


1 


1 


1 


1 


1 








r 


2 


4 














2 









Q 


3 


9 


8 


2 


1 


1 


3 


11 


3 




P 
A 


1 


3 


29 


245 


493 


522 


767 


2794 


32790 


99137 




1 


9 


76 


153 


162 


238 


867 


10175 


30763 


B 






1 


8 


16 


17 


25 


91 


1068 


3229 


C 








1 


2 


2 


3 


11 


129 


390 


D 










1 


1 


1 


4 


47 


142 


E 


i 










1 


1 
1 


3 
3 
1 


36 

35 

11 

1 


109 

106 

33 

3 

1 


F 

G 

H 

I 

K 



TO THE COMPARISON OF SEVERAL MAGNITUDES. 



67 



If we compare the last three values of A, which are in this case 
A 10 , A 9 , A 8 ; we observe that the order of the quotients must necessarily be, 
A 10 = p 9 A 9 + q & A 8 + r 1 A 7 ; that is to say, the computation must take the 
form 



1 


1 


1 


1 


1 


1 


1 













2 














4 


2 








3 
1 


11 


3 


1 


1 


2 


8 


9 


3 • 






3 


33 


106 


109 


142 


390 


3229 


30763 


99137 


a 




1 


11 


35 


36 


47 


129 


1068 


10175 


32790 


b 






1 


3 


3 


4 


11 


91 


867 


2794 


c 








1 


1 


1 


3 


25 


238 


767 


a 










1 


1 


2 


17 


162 


522 


e 












1 


2 
1 


16 
8 
1 


153 

76 
9 
1 


493 

245 

29 

3 

1 


f 
(J 
h 
i 
k 



Hence, if the values of q were written above and between the contigu- 
ous values of p, and similarly with those of r, as in the subjoined scheme, 
the computation carried from left to right leads to the ultimate values of 
A, B, C ; when carried from right to left it leads to those of A*, A^ , 
and so on ; but in each case it gives the same aggregate group of numbers ; 
with a difference merely in position ; and hence, whenever the numbers 







1 




1 




1 




1 




1 




1 




1 








2 




4 
























2 









3 




9 




8 




2 




1 




1 




3 




11 




3 



Po>Pi>Ps > Qo > 5i ' #2 , • • • , &c., are arranged symmetrically, the series 

of values A , A x , A 2 . . . .is identic with A x B x d read inversely. 

The continuation of the same process to the case of a greater number of 
magnitudes is so obvious as to stand in no need of farther illustration. The 
application of this process to problems involving the higher powers of numbers 
may be expected, as the Brounckerian process has already done for squares, to 
throw considerable light upon that difficult branch of the Theory of Numbers. 



VOL. XXVI. PART I. 



( 69 ) 



IV. — On Green's and other Allied Theorems. By Professor Tait. 

(Received April 29th, read May 16th, 1870.) 

I was originally attracted to the study of Quaternions by Sir W. R. 
Hamilton's ingeniously devised and most valuable operator 

^j . d . d . d 

dx •' dy dz ' 

to which he called special attention (Lectures on Quaternions, § 620) on account 
of its promise of usefulness in physical applications. But I soon found that 
in order that its full power may be applied, in general investigations, it is 
necessary that we should have processes of definite integration, of the kinds 
required in physics, applicable to quaternion symbols and not merely to scalar 
variables. I often consulted Hamilton about this want, and he promised to 
endeavour to supply it at some future time. I fancy that shortly before his 
death he must have in some way supplied it, though he certainly did not print, 
nor does he appear even to have written, anything on the subject. In one of 
the last letters I received from him, he said that he intended to conclude the 
final chapter of his Elements, which is devoted to physical applications, by 
some sections on the use of the operator mentioned above. That chapter 
remains unfinished, and as Hamilton rarely wrote down the steps of even a 
complex train of mathematical reasoning until he had mentally completed it, it 
is to be feared that this portion of his investigations is entirely lost. So far as 
the analytical aspect of Quaternions is concerned, this loss is very serious 
indeed, for there can be little doubt that Hamilton's solution would have been 
of immense value from the purely mathematical point of view. 

I have recently succeeded to a certain extent, by a simple, though not very 
direct, process, in supplying the want — so far at least as to enable me to use 
quaternions in inquiries connected with potentials — and have thus arrived at 
very simple proofs of Green's celebrated theorem and various allied results, 
some of which appear to be new and valuable. The quaternion calculus can, 
in consequence, be applied without loss of its enormous special advantages to 
various general theories, such as Attractions, Spherical Harmonics, Fluid 
Motion, &c, &c. Curiously enough, I find that I had almost arrived at one of 
the general theorems given in the present paper so long ago as 1860 (Quaternion 
Investigation of the Potential of a Closed Circuit, Quarterly Math. Journal), but 

VOL. XXVI. PART I. T 



70 PROFESSOR TAIT ON GREEN'S AND OTHEE ALLIED THEOREMS. 

though I then gave a special case I did not see that a very slight modification 
of my work would have enabled me to generalise it. I was then seeking to 
derive from my formulae the well-known physical result, and not thinking of 
extending the calculus itself. 

Even the little advance that I have made in the present paper has enabled 
me to see, with a thoroughness of comprehension which I had despaired of 
attaining (at least by Cartesian processes), the mutual relationship of the many 
singular properties of the great class of analytical and physical magnitudes 
which satisfy what is usually known as Laplace's equation. This is, of course, 
solely due to the simplicity and exjDressiveness of quaternions in general. 

1. In what follows we have constantly to deal with integrals extended 
over a closed surface, compared with others taken through the space enclosed by 
such a surface ; or with integrals over a limited surface, compared with others 
taken round its bounding curve. The notation employed is as follows. If Q 
per unit of length, of surface, or of volume, at the point x y z, Q being any 
quaternion, be the quantity to be summed, these sums will be denoted by 

f/Qds and ffffyh, 

when comparing integrals over a closed surface with others through the 
enclosed space ; and by 

f/Qds and fQTJp, 

when comparing integrals over an unclosed surface with others round its 
boundary. No ambiguity is likely to arise from the double use of 

JfQds , 

for its meaning in any case will be obvious from the integral with which it is 
compared. 

2. I have already shown (Proc, R.S.E., April 28th 1862,) that, if o- be the 
vector displacement of a point originally situated at 

p = ix + jy + kz , 
then 



S.V 



<x 



expresses the increase of density of aggregation of the points of the system 
caused by the displacement. (See Appendix to this paper.) 

3. Suppose, now, space to be uniformly filled with points, and a closed 
surface 2 to be drawn, through which the points can freely move when 
displaced. 

Then it is clear that the increase of number of points within the space 2, 
caused by a displacement, may be obtained by either of two processes — by 
taking account of the increase of density at all points within 2, or by estimating 



PROFESSOE TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 71 

the excess of those which pass inwards through the surface over those which 
pass outwards. These are the principles usually employed (for a mere element 
of volume) in forming the so-called " Equation of Continuity." 

Let v be the normal to 2 at the point p, drawn outwards, then we have at 
once (by equating the two different expressions of the same quantity above 
explained) the equation 

ff/S.Vack =ff S.aTJv els, 

which is our fundamental equation so long as we deal with triple integrals. 

4. As a first and very simple example of its use, suppose o- to represent 
the vector force exerted upon a unit particle at p (of ordinary matter, electricity, 
or magnetism) by any distribution of attracting matter, electricity, or magnetism 
partly outside, partly inside 2. Then, if P be the potential at p, 

o- = VP, 

and if r be the density of the attracting matter, &c, at p, 

Vo- = V 2 P = 4nr 

by Poisson's extension of Laplace's equation. 

Substituting in the fundamental equation, we have 

krrfffrds = 4ttM = f/S . VPUv ds , 

where M denotes the whole quantity of matter, &c, inside 2. This is a well- 
known theorem. 

5. Let P and ~P 1 be any scalar functions of p, we can of course find the 
distribution of matter, &c, requisite to make either of them the potential at p ; 
for, if the necessary densities be r and ?\ respectively, we have as before 

V 2 P = 47JT , V 2 P X = 477TJ . 

Now 

V.PP 1 = PVP 1 + PxVP, 

and 

V 2 .PPj = PV 2 P X + P X V 2 P + 2S .VPVP X . 
But, by the fundamental theorem, 

fffV\V?sk =ffS.(V.¥? l )JJvds =^S.(PVP X + ¥y¥)\Jvds. 
Substituting the above value of V 2 . PP X , this becomes 

f/S.(pV¥ x + P^LWs =fff(PV 2 P 1 + P^P)^ + 2/# r S.VPVP 1 $ ? . 
But, obviously, we have also by the fundamental theorem 

#S.(PVP X - PiVPJUvtfe =^(PV 2 P 1 - P^P)^, 



72 PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS, 

and the two latter equations give 

^/•S.VPVP^s = -fff^Wch +ff? 1 S.VYVvd8 , 
= -fffPV 2 ~Pid<s +f/PS.VPJJvds , 

which are the common forms of Green's Theorem. Sir W. Thomson's extension 
of it follows at once from the same proof. 

6. If P x be a many-valued function, but VPi single-valued, and if 2 be a 
multiply-connected* space, the above expressions require a modification which 
was first shown to be necessary by Helmholtz, and first supplied by Thomson. 
For simplicity, suppose 2 to be doubly-connected (as a ring or endless rod, 
whether knotted or not). Then if it be cut through by a surface s, it will be- 
come simply-connected, but the surface-integrals have to be increased by terms 
depending upon the portions thus added to the whole surface. In the first form 
of Green's Theorem, just given, the only term altered is the last : and it is 
obvious that if jh be the increase of P x after a complete circuit of the ring, the 
portion to be added to the right hand side of the equation is 

p 1 ffS.VPTJvd8 

taken over the cutting surface only. Similar modifications are easily seen to be 
produced by each additional complexity in the space 2. 

7. The immediate consequences of Green's theorem are well known, so that 
I take only one instance. 

Let P and P x be the potentials of one and the same distribution of matter, 
and let none of it be within 2. Then we have 

///{VVfck =ff¥S.VY\Jvds, 

so that if VP is zero all over the surface of 2, it is zero all through the interior, 
i.e., the potential is constant inside 2. If P be the velocity-potential in the 
irrotational motion of an incompressible fluid, this equation shows that there 
can be no such motion of the fluid unless there is a normal motion at some part 
of the bounding surface, so long at least as 2 is simply-connected. 
Again, if 2 is an equipotential surface, 

JffiVPyds = FffS.VFTJvds = F/ffV 2 Fd? 

by the fundamental theorem. But there is by hypothesis no matter inside 2, 
so this shows that the potential is constant throughout the interior. Thus there 
can be no equipotential surface, not including some of the attracting matter, 
within which the potential can change. Thus it cannot have a maximum or 
minimum value at points unoccupied by matter. 

* Called by Helmholtz, after Ribmann, mehrfach zusammenhangend. In translating Helm- 
holtz' s paper (Phil. Mag. 1867) I used the above as an English equivalent. Sir W. Thomson in his 
great paper on Vortex Motion (Trans. R.S.E. 1868) uses the expression "multiply-continuous." 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 73 

8. If, in the fundamental theorem, we suppose 

o- = Vt , 
which imposes the condition that 

S.Vo- = 0, 

i.e., that the a displacement is effected without condensation, it becomes 

ff&.VrVvdp =fff&.V\ch = 0. 

Suppose any closed curve to be traced on the surface 2, dividing it into two 
parts. This equation shows that the surface-integral is the same for both parts, 
the difference of sign being due to the fact that the normal is drawn in opposite 
directions on the two parts. Hence we see that, with the above limitation of 
the value of a, the double integral is the same for all surfaces bounded by a 
given closed curve. It must therefore be expressible by a single integral taken 
round the curve. The value of this integral will presently be determined. 

9. The theorem of § (4) may be written 

fffV 2 ¥ds =ffS.TJvV¥ds = J r S(UvV)P<fe. 
From this we conclude at once that if 

o- = iP + /P, + kV 2 , 
(which may, of course, represent any vector whatever) we have 

ff/V^ck =ff&{UvV)<Tds t 
or, if 

W = T, 

fffrd,=ff^(VvV-')rds. 

This gives us the means of representing, by a surface-integral, a vector-integral 
taken through a definite space. We have already seen how to do the same for 
a scalar-integral — so that we can now express in this way, subject, however, to 
an ambiguity presently to be mentioned, the general integral 

where q is any quaternion whatever. It is evident that it is only in certain 
classes of cases that we can expect a perfectly definite expression of such a 
volume-integral in terms of a surface-integral. 

10. In the above formula for a vector-integral there may present itself an 
ambiguity introduced by the inverse operation 

v- 1 

to which we must devote a few words. The assumption 

VV = T 

VOL. XXVI. PART I. U 



74 PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 

is tantamount to saying that, as the constituents of cr are the potentials of 
certain distributions of matter, &c, those of t are the corresponding densities 
each multiplied by 4:n. 

If, therefore, r be given throughout the space enclosed by 2, cr is given by 
this equation so far only as it depends upon the distribution within 2, and must 
be completed by an arbitrary vector depending on three potentials of mutually 
independent distributions exterior to 2. 

But, if cr be given, t is perfectly definite ; and as 

Vo- = v-v , 

the value of V -1 is also completely defined. These remarks must be carefully 
attended to in using the theorem above : since they involve as particular cases 
of their ajoplication many curious theorems in Fluid Motion, &c. To these, 
however, I shall not further allude here, as I propose to make them the subject 
of a separate communication to the Society. 

11. We now come to relations between the results of integration extended 
over a non-closed surface and round its boundary. 

Let cr be any vector function of the position of a point. The line-integral 
whose value we seek as a fundamental theorem is 

f S . a(h, 

where r is the vector of any point in a small closed curve, drawn from a point 
within it, and in its plane. 

Let cr be the value of o- at the origin of r, then 

Cr = cr - S(tV)ct 

(Proc. R.S.E., 28th April 1862 ; see also Appendix to this paper), so that 

fS.a-dr =/S.((t — S (tV) cr Q )dr . 
But 

fdr = , 

because the curve is closed; and (Tait on Electro- Dynamics, § 13, Quarterly 
Math. Journal, Jan. 1860) we have generally 

/S.rVS.cr/Zr = 1S.V(tSo- t - aJY.rdr) . 

Here the integrated part vanishes for a closed circuit, and 

^/Y.rdr = dsJJv , 

where ds is the area of the small closed curve, and U*> is a unit-vector perpen- 
dicular to its plane. Hence 

/S.o-//r = S.Vo- Vv.ds. 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 75 

Now, any finite portion of a surface may be broken up into small elements such 
as we have just treated, and the sign only of the integral along each portion of 
a bounding curve is changed when we go round it in the opposite direction. 
Hence, just as Ampeee did with electric currents, substituting for a finite closed 
circuit a network of an infinite number of infinitely small ones, in each con- 
tiguous pair of which the common boundary is described by equal currents in 
opposite directions, we have for a finite unclosed surface 

fS.adp =jrS.V<rUv.ds. 

There is no difficulty in extending this result to cases in which the bounding 
curve consists of detached ovals, or possesses multiple points. This theorem 
seems to have been first given by Thomson (Thomson & Tait's " Natural 
Philosophy," § 190 (j) ; Thomson on Vortex Motion, Trans. R.S.E., 1868-9, 
§ 60 (?) )> where it has the form 

/(«* + ** + ■& =Jr* ('(I -f ) + -(£-£) + Ki-t)) • 

It solves the problem suggested by the result of § 8 above. 

12. If o- represent the vector force acting on a particle of matter at 

p, — S.crdp represents the work done while the particle is displaced along dp, 

so that the single integral 

J* S.crdp 

of last section, taken with a negative sign, represents the work clone during a 
complete cycle. When this integral vanishes it is evident that, if the path be 
divided into any two parts, the work spent during the particle's motion through 
one part is equal to that gained in the other. Hence the system of forces must 
be conservative, i.e., must do the same amount of work for all paths having the 
same extremities. 

But the equivalent double integral must also vanish. Hence a conservative 
system is such that 

ffds&.VcrUv= 0, 

whatever be the form of the finite portion of surface of which ds is an element. 

Hence, as Vcr has a fixed value at each point of space, while Uv may be altered 

at will, we must have 

VVo- = 0, 
or 

Vo- = scalar. 

If we call X, Y, Z the component forces parallel to rectangular axes, this 
extremely simple equation is equivalent to the well-known conditions 

^X_^Y_ dY __dZ_Q ^_^ = o 
dy dx ' dz dy ' dx dz 



76 PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 

Keturning to the quaternion form, as far less complex, we see that 

Vo- = scalar = 477T, suppose, 
implies that 

cr = VP, 

where P is a scalar such that 

V 2 P = 4tt>- ; 

that is, P is the potential of a distribution of matter, magnetism, or statical 
electricity, of volume-density r. 

Hence, for a non-closed path, under conservative forces 

-fS.<rd P = -fS.VPdp 
= ~/&(dpV)? 

= fd dp P =y>/P (see Appendix) 
- P — P 

depending solely on the values of P at the extremities of the path. 

13. A Vector theorem, which is of great use, and which corresponds to the 
Scalar theorem of § 11, may easily be obtained. Thus, with the notation already 
employed, 

/V.adr =/V(o- - S{rV)a )dr, 

= -/S(rV)V.ov/T. 
Now 

V(V.VV. rdr)a = - S(rV)V.oy/T - S(tfrV)Vro- , 
and 

d(S (tV) Vo- O r) = S (rV) V. oy/r + S {d T V)Va r . 

Subtracting, and omitting the term which is the same at both limits, we have 

/V. a-dr = V. ( V."LW)a-o ds . 

Extended as above to any closed curve, this takes at once the form 

/V. o-dp =ffdsY. (V.U^V)o- . 

Of course, in many cases of the attempted representation of a quaternion 
surface-integral by another taken round its bounding curve, we are met by 
ambiguities as in the case of the space-integral (§ 9) : but their origin, both 
analytically and physically, is in general obvious. 

14. If P be any scalar function of p, we have (by the process of § 11, above) 

/Vdr =/(P - S(rV)P )r/r 
= -/S.rVP .f/T. 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 77 

But 

Y.VV.tcIt = ^/tS.tV - rS.drV , 

and 

d(rSrV) = (ItS.tV + rS.^rV . 

These give 

fPdr = - i(rSrV - V.VrrfrV)P = dsY.JJvVP . 

Hence, for a closed curve of any form, we have 

fPdp =ffdsY.TJvVY, 

from which the theorems of §§ 11, 13 may easily be deduced. 

15. The above are but a few of the simpler of an immense host of theorems 
which any one with some knowledge of quaternions may easily work out for 
himself, by developing a little farther, or applying to other combinations, the 
processes just explained. I shall, therefore, give no more of them until I have 
an opportunity of, at the same time, showing their ready applicability and great 
value in physical investigations. 

Appendix, added June 3d 1870. 

16. At the instance of Prof. Kelland, to whom this paper was referred, 
I append a slight sketch of some of the properties of the operator V, of which 
so much use has been made in the foregoing paragraphs. Most of the results 
now to be given have been already published by myself, but the mode in which 
they were formerly deduced has been abandoned for one more purely quaternionic. 

17. It may perhaps be useful to commence with a different form of definition 
of the operator V, as we shall thus, if we desire it, entirely avoid the use of 
ordinary Cartesian co-ordinates. For this purpose we write 

S . aV = — d a , 

where a is any unit-vector, the meaning of the right hand operator (neglecting 
its sign) being the rate of change of the function to ivhich it is applied per unit 
of length in the direction of the unit-vector a. If a be not a unit-vector we 
may treat it as a vector-velocity, and then the right hand operator means the 
rate of change per unit of time due to the change of position. 

Let a, /3, y be any rectangular system of unit-vectors, then by a fundamental 
quaternion transformation 

V = - aSaV — /3S/3V - ySyV = ad a + fidp + yd y 

which is identical with Hamilton's form given above. (Lectures, § 620.) 

18. This mode of viewing the subject enables us to see at once that the effect 

VOL. XXVI. PART I. X 



78 PROFESSOR TAJT ON GREEN'S AND OTHER ALLIED THEOREMS. 

of applying V to any scalar function of the position of a point is to give its vector 
of most rapid increase. Hence, when it is applied to a potential u, we have 

Vz« = vector-force at p. 

If u be a velocity-potential, we obtain the velocity of the fluid element at p ; 
and if u be the temperature of a conducting solid we obtain the flux of heat. 
Finally, whatever series of surfaces is represented by 

u = C, 

the vector Vw is the normal at the point p, and its length is inversely as the 
normal distance at that point between two consecutive surfaces of the series. 
Hence it is evident that 

S.dpVu = — du , 
or, as it may be written, 

— S . dp V = d ; 

the left hand member therefore expresses total differentiation in virtue of any 
arbitrary, but small, displacement dp. 

19. To interpret the operator V.aV let us apply it to a potential function u. 

Then we easily see that a may be taken under the vector sign, and the 

expression 

V(aV)u = V.aVtt 

denotes the vector-couple due to the force at p about a point whose relative 

vector is a. 

Again, if o- be any vector function of p, we have by ordinary quaternion 

operations 

V(aV).cr = S.aVVa- + aSVa - VSacr . 

The meaning of the third term (in which it is of course understood that V 
operates on o- alone) is obvious from what precedes. It remains that we 
explain the other terms. 

20. These involve the very important quantities (not operators such as the 
expressions we have been hitherto considering), 

S.Vo- and V.Vo- , 

which occur very frequently in the preceding paper. There we looked upon cr 
as the displacement, or as the velocity, of a point situated at p. Let us now 
consider the group of points situated near to that at p, as the quantities to be 
interpreted have reference to the deformation of the group. 

21. Let r be the vector of one of the group relative to that situated at p. 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 79 

Then after a small interval of time t, the actual co-ordinates become 

p + to- 
and 

p + t + t(a- — S(tV)o-) 

by the definition of V in § 17. Hence, if <p be the linear and vector function 
representing the deformation of the group, we have 

The farther solution is rendered very simple by the fact that we may assume t 
to be so small that its square and higher powers may be neglected. 
If <p' be the function conjugate to <p, we have 

<p'r = t — ^VSrcr . 
Hence 

<p T = £(<? + <p> + i(<P -<P')t 



[S (tV)o- + VSro-1 - ^V.tVVo- 



The first three terms form a self-conjugate linear and vector function of t, which 
we may denote for a moment by tot. Hence 

$T — T7TT — p V.tVVcT , 

or, omitting f as above, 

<pT = err -„V. rarVVtr . 

Hence the deformation may be decomposed into — 1st, the pure strain zs, 2d, the 
rotation 

Jyv„. 



Thus the vector-axis of rotation of the group is 



iVV 



2" 



O" 



If we were content to avail ourselves of the ordinary results of Cartesian 
investigations, we might at once have reached this conclusion by noticing that 



Wcr = i & 



dzj J \dz dxj \dx dyj ' 



and remembering the formuke of Stokes and Helmholtz. 
22. In the same way, as 

m _ _d% _chj __d% 

' dx dy dz ' 

we recognise the cubical compression of the group of points considered. It 
would be easy to give this a more strictly quaternionic form by employing the 
definition of § 17. But, working with quaternions, we ought to obtain all our 
results by their help alone ; so that we proceed to prove the above result by 



80 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 



finding the volume of the ellipsoid into which an originally spherical group of 
points has been distorted in time t. 

For this purpose, we refer again to the equation of deformation 

$T = T-*S(tV)o", 

and form the cubic in <p according to Hamilton's exquisite process. We easily 
obtain, remembering that f is to be neglected, 4 - 



or 



= <p 3 - (3 - tSVa) <p + (3 - 2*SV<r) <p - (1 - tSVa) , 

= (<p-l) 2 (<p-l + ASVo-). 



The roots of this equation are the ratios of the diameters of the ellipsoid whose 
directions are unchanged to that of the sphere. Hence the volume is increased 
by the factor 

1 - ^SVo- , 

from which the truth of the preceding statement is manifest, 

23. As the process in last section depends essentially on the use of a non- 
conjugate vector function, with which the reader is less likely to be acquainted 
than with the more usually employed forms, I add another investigation. 
Let 

JJT = <pr = r — tS (tV) a . 



Then 



t = <p~V = ot + *S(arV)<r . 



Hence since if, before distortion, the group formed a sphere of radius 1, we 
have 

Tt = 1, 

Thus, in Hamilton's notation, X, /x, v being any three non-coplanar vectors, and m, m„ w, the 
coefficients of the cubic, 

— mS.'Kfiv = S.<p'X<p'/xp'v 

= S.(\ - tVSko)(ji - tVSfia)(p - tVSva) 
= S.(\ - tVS\a)(Yfiv - tVfxVSva + tVvVSfio) 
= S.Xfiv - t[S./ivVS\a + S.vXVS/xa + S.fytVSw] 
= S.Xfiv - tS.[XS.fxvV + fxS.vXV + j/S.\/iV]o- 
= S . X/xv — tS . X/xvS Ver . 
m ft. X/xv = S.X<p'/x<p'v + S./x<p'v<p'X + S.vf'X<p'/x 

= S.X(Y/xv - tY/xVSva + tYvVS/xa) + &c. 
= S.X/xv — tS.X/xVSva — tS.vXVS/xa + &c. 
= 3S.\/iv - 2t8Va-S.Xfiv. 
— m^.X/xv = S.X/xcp'v + S./xv<p'X + S.vXcp'/x 
= S.X/xv — tS.X/xVSvcr + &c. 
= 3S. Xpv — tSVaB.X/xv. 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 81 

the equation of the ellipsoid is 

T(ttt + *S(raV)<r) = 1, 
or 

OT 2 -i- 2*SotVSwo- = - 1 . 
This may be written 

S.OT^ra- = S.^(trr + ^VSoto" + #S(otV)o-) = — 1 , 

where x is now self-conjugate. 

Hamilton has shown that the reciprocal of the product of the squares of 
the semiaxes is 

whatever rectangular system of unit-vectors is denoted by i, j, k. 
Substituting the value of x, we have 

-S.(i + tVSia + *S(iV)o-)(j + &c.)(* + &c.) 

= _ S. (t + tWSia- + *S(zV)<r)(« + 2tiSVa - *S(«V)o- - tVSi<r) 

= 1 + 2*SV<r . 

The ratio of volumes of the ellipsoid and sphere is therefore, as before, 

1 



s/l + 2t$Va 



= 1 - *SV<x 



24. Before concluding I may append a generalised form of Green's Theorem, 
which is obviously fitted to be of use in quaternion investigations. If we put 

T = iP + jY + kV", 

we easily see by the equations at the end of § 5 that 

fffSFV,. V)*fe = -fffV^rd, + J 0rp i S(U*.V)«fe , 

= -fffrVV^ck +ffrS.VV 1 Vv.ds . 
As a particular case, let 

P a = Sap 
so that 

VPj = iSia + yS/a + k$ka = — a , 

V^ = , 

we have 

jQfjrSiaVjrds =fffSapV*rds -//Sap${TJvS7)Tds , 

=ffT$.a\Jvds . 

VOL. XXVI. PART I. Y 



82 PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 

Any constant may be added to the value of P x . The additional terms thus 
introduced must vanish. This gives, as in § 9, 

fffV 2 Tch=ffS(UvV)rds. 
As another verification, suppose r constant, and we have 

ffS.aTJvds = 0, 

which is obviously true. Interesting results are obtained by treating this by 
the processes of §§ 8, 11. 

25. From one of the theorems above — viz., 

fffS(aV)rds =f/TS.aUvds, 
we have by the formula of § 17 

ff/Vrd,=ffVv.rds, 

a considerable extension of the fundamental theorem of § 3, which is, in fact, 
only its scalar part, It might have been obtained, however, as the reader will 
easily see, by a much more direct process. The vector part 

ff/YVrds =/PfUv.rds , 

as we see by the meaning of VVt in § 21, is of great importance in physical 
applications, especially in connection with Electricity and with Fluid Motion. 
When 

T = VP, 

where P is is a scalar, the left hand member vanishes, and the value of the right 
hand member limited to a non-closed surface is then found as in § 14. 

26. Again, let 

?x = P 2 , 
which gives 

VP, = - 2p , 

V 2 P X = 6 . 
We have 

- 2fffS(pV)rds = -fffp^rd, +ffp*${VvV)Tds 

= ~ Sfffrds - 2/frS.pUvds . 

Now if the constituents of t be homogeneous functions of p of the n ih degree, we 
have for any one of them 

S.pV£ = -«£, 

so that under these circumstances 

(n + 3)fffrd, = -ffrS.pUvds . 



PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 83 

Of this a particular case is 

(it + S)fff&k = -ff&.pUvds, 

which suggests many curious theorems. 

27. As a verification of it, let the closed surface 2 which determines the 

limits of the integrations be itself 

f=C, 

which, of course, subjects the form of £ to further limitations. 
The right hand member is obviously equal to 

3C x vol. of 2, 

because — S.pUv is the perpendicular from the origin to the tangent plane at p 
to the element ds. The left hand side may be broken up into a set of shells 
bounded by surfaces whose equations are 

where e varies from to 1. [This follows from the assumption that £ is homo- 
geneous.] The volume of the surface corresponding to any value of e is obviously 

e 3 x vol. of 2 . 
Hence 

d<; — 3e 2 de x vol. of 2 , 

so that the left-hand member of the equation above becomes 

(ft + 3) /* dCeT+'de x vol. of 2 = 3C x vol. of 2 , 

• J 

and the proposition is proved. 

28. A very interesting case is when 

g Tp 3 ' 
in which case n = — 3, and our equation appears to become 

(3 - SW^p = = - CTS.^TJvds. 

It is obvious, however, that there is an infinite element on the left hand, 
when Tp = 0, i.e., when the origin lies inside 2 ; and it is easy to see that the 
correct result is a simple case of the well-known equation of § 4. In fact, the 
expression on the right denotes, as is evident, the whole spherical opening sub- 
tended at the origin by 2. Its value is therefore if the origin be without 2, 
and 477 if within — 2 being supposed to be simply-connected. 

29. As a final example let us suppose in § 26 that f is a Spherical Harmonic. 



84 PROFESSOR TAIT ON GREEN'S AND OTHER ALLIED THEOREMS. 

Then, in addition to the condition of homogeneity there given, we have the 
condition 

V 2 £=0, 

and the general equation of the section referred to gives 

2nfff^U=ffp^.VvV^ds, 

so that, with the help of the final equation of § 26 we have for any closed sur- 
face whatever 



ff&.Uv{2np£ + n + 3 P 2 Vg)ds = . 

This integral, whose value is obviously the same for all surfaces bounded by 
a given closed curve, can be reduced to the form 

#(T P ) 4 ^s.u,v(V S^-W 

(Tp)" + 3/ 

where q is any quaternion which satisfies the condition 

Vq = (). 

This is susceptible of various remarkable transformations, both as a double and 
as a single integral. But this digression might be indefinitely extended, and 
perhaps has already gone too far. 

30. The essential basis of the whole of this theory is the great invention of 
Hamilton, by which it is made possible to represent as a vector-operator the 
square root of Laplace's operator 

d? d*_ d^ 

dx 2 dy % dz 2 ' 

which has not yet been done by any but quaternion symbols, at least in a sym- 
metrical, easily intelligible, and practically useful form. 

It is rash to make any definite assertions on such matters, especially when 
a writer of such extraordinary fertility, knowledge, and power as Sir W. R. 
Hamilton is concerned, but to the best of my knowledge the greater part of 
the results given above is my own. Hamilton's treatment of V, so far as I am 
aware of its having been published, will be found in Proc. R.I. A., 1846 and 
1854, (in the latter of which there is a very curious and interesting proof of 
Dupin's Theorem,) and in his Lectures on Quaternions, § 620. My own is to 
be found in Quarterly Math. Journal, October 1860; Proc. R.S.E., 1861-2, 
1862-3 ; and Elementary Treatise on Quaternions, §§ 317, 319, 364, &c, 418, 
421-8, Ex. 24 to Chap. IX. and 10 to Chap. XL 



( 85 ) 



V. — On the Heat Developed in the Combination of Acids and Bases. Second 
Memoir. By Thomas Andrews, M.D., F.R.S., Hon. F.RS.E., Vice- 
President of Queen's College, Belfast. 

(Read 6th June 1870.) 

In a paper communicated to the Eoyal Irish Academy in 1841, I gave an 
account of a large number of experiments on the heat disengaged when acids and 
bases, taken in the state of dilute solution, enter into combination, and when 
bases, insoluble in water, are dissolved in dilute acids. The following general 
conclusions or laws were deduced from those experiments : — 

Law 1. — The heat developed in the union of acids and bases is determined 
by the base and not by the acid, the same base producing, when combined with 
an equivalent of different acids, nearly the same quantity of heat ; but different 
bases, different quantities. 

Laiv 2.- — When a neutral is converted into an acid salt, by combining with 
one or more atoms of acid, no change of temperature occurs. 

Law 3. — When a neutral is converted into a basic salt, by combining with 
an additional proportion of base, the combination is accompanied with the 
evolution of heat. * 

Three years later I laid before the Royal Society of London the results of 
an experimental investigation of the heat developed when one base is substi- 
tuted for another in chemical compounds. The law deduced from this inquiry 
is implicitly involved in the foregoing, of which it may indeed be regarded as a 
necessary consequence. It was enunciated in the following terms : — 

Laiv 4. — When one base displaces another from any of its neutral combina- 
tions, the heat evolved or abstracted is always the same, whatever the acid 
element may be, provided the bases are the same.t 

Finally, the law of metallic substitutions, first announced in the " Philo- 
sophical Magazine" for August 1844, was thus stated in a paper published in 
the "Philosophical Transactions" for 1848. 

Law 5. — When an equivalent of one and the same metal replaces another 
in a solution of any of its salts of the same order, the heat developed is always 
the same ; but a change in either of the metals produces a different development 
of heat. 

In 1845 a paper appeared by Graham on the heat disengaged in combina- 
tions, the second part of which refers to the heat produced when hydrate of 

* Transactions of the Eoyal Irish Academy, vol. xix. p. 228. 
f Philosophical Transactions for 1844, p. 21. 

VOL. XXVI. PART I. Z 



86 DR ANDREWS ON THE HEAT DEVELOPED IN THE 

potash is neutralised by different acids. 4 ' The results arrived at by this distin- 
guished chemist exhibit a close agreement with those contained in my first 
communication to the Royal Irish Academy. 

The concluding part of the elaborate memoir of MM. Favre and Silber- 
mann on the heat disengaged in chemical actions is chiefly devoted to the same 
subject. A large number of experiments are described, which are nearly a 
repetition of those I had previously published. Their results bear a general 
resemblance to those given by myself in 184i ; but they widely differ in the 
details. The authors of this able memoir fully recognise the accuracy of my 
fourth law, which asserts the equality of thermal effect when one base is sub- 
stituted for another. " M. Andrews," they observe, " avait en effet etabli que, 
quelque soit l'acide d'un sel, la quantity de chaleur degagee par la substitution 
d'une base a une autre pour former un nouveau sel est la meme, lorsque Ton 
considere les deux memes bases, "t 

In a preceding paragraph of the same memoir, the authors object to what 
they conceive to be my first law, and state that it is not in accordance with the 
results of their investigations. As the question is one of some importance, I 
may perhaps be permitted to quote the passage in the original language. " Ses 
conclusions, savoir : que la chaleur degagee par l'equivalent d'une meme base 
combinee aux divers acides est la meme, ne s'accordent pas avec les resultats 
de nos recherches, et ne nous paraissent pas pouvoiretre admises." No doubt, 
through inadvertence, MM. Favre and Silbermann have here given an inaccurate 
statement of my first law. It did not declare that precisely the same amount 
of heat is disengaged by all the acids in combining with the same base, but 
that the heat is determined by the base, "the same base producing, when 
combined with an equivalent of different acids, nearly the same quantity of 
heat." A comparison of the results of MM. Favre and Silbermann with those 
in my original memoir will show that I had fully recognised and described the 
deviations from the other acids, exhibited, on the one hand, in excess, by 
the sulphuric acid, and on the other, in deficiency, by the tartaric, citric, 
and succinic acids. " If we refer," I remarked, in the original memoir of 
1841, "to the first, second, and fourth tables, as being the most exten- 
sive, from the large number of soluble compounds formed by potash, soda, 
and ammonia, it will be observed that the sulphuric acid developes from o- 8 to 
nearly 1° more than the mean heat given by the other acids; while the tartaric, 
citric, and succinic acids fall from 0°4 to o, 55 short of the same. A minute 
investigation of the influence of the disturbing sources of heat will no doubt 
discover the causes of these discrepancies. The high numbers for sulphuric 

* Memoirs of the Chemical Society, vol. ii. p. 51. 

f Annales de Chimie et de Physique 3 feme serie xxxvii. p. 497 (1853). 



COMBINATION OF ACIDS AND BASES. 87 

acid are probably connected with that acid's well known property of developing 
much heat when combining with successive atoms of water. All the other acids 
develope nearly the same amount of heat in combining with the same base, the 
greatest divergences from the mean quantity being, in the case of potash, 
+ 0°-24, and - 0°13 ; in that of soda, + 0°-26, and - 0°14 ; and in that of 
ammonia, 4- o, 17 and — 0°05. These differences are almost within the limits 
of the errors of experiment."* 

But although there is a superficial agreement between my original results 
and those of MM. Favre and Silbermann, they will be found, when examined 
closely, to differ widely in detail, and on points of great importance. I had 
found that the oxalic acid disengages almost exactly the same amount of heat 
in combining with the soluble bases as the hydrochloric, nitric, and many other 
mineral acids, and this observation I have always regarded as one of the main 
foundations of Law 1. MM. Favre and Silbermann, on the contrary, 
have inferred from their experiments that " the following organic acids — the 
oxalic, formic, valeric, and citric — disengage sensibly the same quantity of heat, 
but it is less (plus faible) than that given by the foregoing mineral acids "■ — 
among which they enumerate the nitric and hydrochloric. According to my 
experiments, no distinction of this kind can be admitted between acids derived 
from the mineral and organic kingdom, inasmuch as the oxalic acid developes 
at least as much heat in combining with the bases as the hydrochloric, nitric, 
and several other strong mineral acids. 

The experiments to be described in this paper were made some years ago, 
but their publication has been deferred from accidental circumstances. I have, 
however, recently repeated a few of the more important of them, with a 
slightly modified form of apparatus. The solutions were taken in so dilute a 
state that the heat disengaged never exceeded 3 0, 5 C. A standard solution of 
sulphuric acid was prepared and carefully analysed, by precipitating a given 
weight with a soluble salt of barium, and weighing the sulphate of barium. The 
strength of the alkaline solutions was adjusted with great care by means of this 
standard acid. The same solution of each alkali was employed in all the experi- 
ments, and the quantity used in each experiment was determined by careful 
weighing. The acid solution was of such a strength that, after being mixed with 
the alkali, an excess of two or three per cent, of acid was present. The alkaline 
solution was contained in a light glass vessel, in which a large platinum crucible 
holding the acid was carefully floated. By giving a rapid rotation, by means of 
a light stirrer, to the acid solution in the platinum crucible, a perfect equilibrium 
of temperature was soon established between the two liquids. The initial tem- 
perature of the solutions was usually about 1°5 below that of the air, and the 
final temperature of the mixture about 1°5 above it. The corrections for the 

* Transactions of the Royal Irish Academy, vol. xix. p. 240. 



88 DR ANDREWS ON THE HEAT DEVELOPED IN THE 

heating and cooling action of the surrounding medium were determined with 
great care. The mechanical process of adding the acid to the alkaline solution 
produced no change of temperature, and as the heat disengaged in the com- 
bination raised the liquid almost instantly to the maximum temperature, the 
whole correction required was for cooling. The first temperature was read one 
minute after the addition of the acid to the alkaline solution, the mixture being 
stirred during the whole of that time. If 8 represents the correction, and e the 
excess of temperature above the air in centigrade degrees, the value of 8 will be 
given by the following expression : — 

8 = e x 0°012 . 

As a proof of the accuracy of the method of mixture adopted in this inquiry, 
I may mention that, being desirous to know whether the dilute acids em- 
ployed in these experiments produced any change of temperature when mixed 
with water, I made the experiment with nitric acid by the method just described, 
substituting water for the alkaline solution, with the unexpected result of a fall 
of 0°01. On varying the conditions of the observation, so as to obtain a larger 
effect, it was ascertained not only that a diminution of temperature had actually 
occurred, but that the observed fall represented approximately its true amount. 
When hydrochloric acid of equivalent strength was diluted to the same extent, 
an elevation of temperature of 0°05 was produced. 

The accuracy of experiments of this kind, where the whole thermal effect 
observed amounts only to 2° or 3°, depends greatly on the thermometer employed. 
Unless its indications are perfectly trustworthy in every part of the scale, the 
labour of the inquirer will only end in disappointment. I have therefore taken 
every precaution to secure this important object. The tube of the thermometer 
was calibrated and divided with care, according to an arbitrary scale, by means 
of a dividing instrument contrived for the purpose, and provided with a short 
screw of great accuracy made by Troughton & Simms. The divisions, etched 
finely on the glass, corresponded to about o, 05 C, and the readings could be 
made with certainty to less than 0°01. The division of the scale, corresponding 
to 0°, was determined from time to time in the usual way ; and another point, 
about 30° C, was fixed by comparison with four other thermometers similarly 
constructed, whose scales extended from the freezing to the boiling point of water. 
The readings of these four instruments, when reduced to degrees, rarely differed 
from each other within the limits to which they could be read, or o, 02. The 
reservoir of the thermometer used in these experiments was 75 millimetres 
long, and, when immersed in the liquid, occupied nearly its entire depth. 

As some uncertainty always exists with regard to the thermal equivalent of 
glass vessels, I made two sets of comparative experiments — one with a thickly 
varnished copper vessel, and the other with a vessel of platinum. The mean 



COMBINATION OF ACIDS AND BASES. 89 

result of these experiments coincided almost exactly with the result obtained 
when the glass vessel was employed. 

The weight of the glass vessel which contained the alkaline solution was 58 
grammes, and corresponded thermally to 1 1 4 grammes of the solutions formed. 
The thermal equivalent of the reservoir of the thermometer and of the stirrer 
was 9 grammes. The alkaline solution weighed 160 grammes, and contained 
the equivalent of 1738 grammes of S0 3 . The acid solution weighed 42*5 
grammes. Hence the entire thermal value of the apparatus, in terms of the 
solution, formed, was — 

Solution, . . . . . . 202-5 

Glass vessel, . . . . . 11 4 

Thermometer and stirrer, . . . . 0'9 



214 - 8 grammes. 

A correction (additive) of ^y was made to the direct readings for the 
mercury in the stem of thermometer. The results are given to thousandths of 
a degree, but this apparent minuteness is due to the reduction of the indica- 
tions of the arbitrary scale to degrees. 

In the following detailed statement of the experimental results, Inc. is the 
increment of temperature observed, corrected for the mercury in stem, and 8 is 
the correction for cooling. 

Potash and Sulphuric Acid. 

Inc. 3°-358 3°-356 3°366 

6 -010 -024 -021 



Inc 



3°368 


3°380 3°-387 


Mean increment 


corrected, 3°-378 


Potash and Nitric Acid. 


2°-971 


2°-976 2°-977 


■018 


■019 -017 


2°-989 


2°-995 2°-994 


Mean increment corrected, 2° # 993 



Potash and Hydrochloric Acid. 

Inc. 3°-004 3°-002 3°-005 

8 -017 -019 -017 



Inc 



3°021 3°-021 


3°022 


lean increment corrected, 3° 


•021 


Potash and Oxalic Acid. 




3°'036 3°-048 


3°'040 


■017 -017 


■016 


3°053 3°-065 


3°-056 


\Iean increment corrected, 3' 


'•058 



VOL. XXVI. PART I. 2 A 



& ( > DR ANDREWS ON THE HEAT DEVELOPED IN THE 



Potash and Acetic Acid. 

Inc. 2°-835 2°-846 

& -016 -007 



2°-851 2°-853 

Mean increment corrected, 2 0- 852 

Potash and Tartaric Acid. 

Inc. 2°-707 

h -014 



2°-717 
•014 


2 


2°-730 
013 


2°-731 

ected, 


2 D 743 
'•732 



2°-721 
Mean increment corrected, 



Soda and Sulphuric Add. 

Inc. 3°-322 3°'335 

h -025 -024 



3°-347 3°-359 

Mean increment corrected, 3 C, 353 

Soda and Nitric Acid. 

Inc. 2°-914 2°-919 

d -012 -012 



2°-926 2°-931 

Mean increment corrected, 2 0, 929 

Soda and Hydrochloric Acid. 

Inc. 2°-963 

a -019 



2°-982 
Increment corrected, 2 0, 982 

Soda and Oxalic Acid. 

Inc. 3°-029 3°-013 

h -019 -020 



3°-048 3°-033 

Mean increment corrected, 3 o, 040 

Soda and Acetic Acid. 

Inc. 2°-816 2°-812 

3 -017 -018 



2°-833 2°-830 

Mean increment corrected, 2 0- 831 



COMBINATION OF ACIDS AND BASES. 91 



Soda and Tartaric Acid. 

Inc. 2°-693 2°'693 

h -019 '015 



2°-712 2°-708 

Mean increment corrected, 2 o, 710 

Ammonia and Sulphuric Acid. 

Inc. 2°-967 2°-959 

d -017 -010 



2°-984 2°-969 

Mean increment corrected, 2°'976 

Ammonia and Nitric Acid. 

Inc. 2°-556 2°-551 

d -010 -015 



2°-566 2°-566 

Mean increment corrected, 2°'566 

Ammonia and Hydrochloric Acid. 

Inc. 2°-609 2°-607 

5 -015 -015 



2°-624 2°-622 

Mean increment corrected, 2 0, 623 

Ammonia and Oxalic Acid. 

Inc. 2°-635 2°-630 

d -015 -016 



2 Ol 650 2°-646 

Mean increment corrected, 2°"648 

Ammonia and Acetic Acid. 

Inc. 2°'469 2°-482 

h -017 -016 



2°-486 2°-498 

Mean increment corrected, 2°'492 

Ammonia and Tartaric Acid. 

Inc. 2°-365 2 0> 354 

d -017 -016 



2°-382 2°-370 

Mean increment corrected, 2 C, 376 



Soda. 


Ammonia 


3°-353 


2°-976 


3°-040 


?°-648 


2°-982 


2°-623 


2°-929 


2°-566 


2°-832 


2°-492 


2°710 


2°-376 



92 DR ANDEEWS ON THE HEAT DEVELOPED IN THE 

In the following table I have collected the foregoing results, arranging the 
acids in the order of their thermal action. 

Acid. Potash. 

Sulphuric Acid, . . 3° - 378 

Oxalic Acid, . . . 3°-058 

Hydrochloric Acid, . . 3°-021 

Nitric Acid, . . . 2°-993 

Acetic Acid, . . . 2°-852 

Tartaric Acid, . . . 2°'732 

It is interesting to observe how closely the results in the three vertical 
columns agree relatively with one another. The acids follow in the same order 
under each base, and even the differences in the amount of heat disengaged by 
the several acids in combining with the different bases approximate in many 
cases closely to one another. Thus the heat given out when the sulphuric acid 
combines with potash exceeds that given out when the oxalic acid combines 
with the same base by o- 320, the corresponding differences in the case of 
soda and ammonia being 0°313 and o, 328. If, in like manner, we compare the 
differences between the heat disengaged by the acetic and tartaric acids, we fall 
upon the numbers o, 120, 0°122, and o, 116. Even in the case of the oxalic, 
hydrochloric, and nitric acids, which disengage so nearly the same amount of 
heat, the same order is observed with the three bases. It must be particularly 
remarked that the oxalic acid disengages from 0°022 to o, 058 more heat in 
combining with these bases than the hydrochloric acid, and from o, 065 to 
0°111 more than the nitric acid. The conclusion of MM. Favee and Silbee- 
mann, that the organic acids (oxalic, formic, acetic, &c.) disengage sensibly less 
heat than the mineral acids, is thus entirely disproved ; and the original results 
recorded in my work of 1841, according to which the oxalic acid disengages at 
least as much heat as the nitric, phosphoric, arsenic, hydrochloric, hydriodic, 
boracic, and other mineral acids (with the exception of the sulphuric acid) are 
fully confirmed. The tartaric, citric, and succinic acids, it is true (as was also 
shown in the same work), give out about j^th less heat than the average of the 
other acids ; but the acetic and formic acids fall scarcely ^th below the mean, 
and the oxalic acid is always above it. These results, in all their main features, 
are fully corroborated by the experiments recorded in this paper, which were 
performed with a more perfect apparatus and a more exact thermometer 
than I had at my command in my earlier investigations. A reference to the 
same paper will show that, while acids, differing so widely from one another as 
the oxalic, phosphoric, arsenic, nitric, hydrochloric, and boracic acids, scarcely 
present any sensible difference in the quantities of heat which they disengage in 
combining with the bases ; and while of the other acids examined the sulphuric 
acid (and probably also the sulphurous acid) presents an extreme deviation of 



COMBINATION OF ACIDS AND BASES. 93 

about -|th above the mean, and the tartaric acid group a deviation of about -g^th 
below it ; the bases, on the contrary (and the subsequent researches of Favre and 
Silbermann have confirmed this result), differ altogether in thermal power from 
one another. Thus equivalents of the oxides of magnesium and of silver give out 
4 0, 1 and 1 0, 8 of heat respectively in combining with nitric acid, the former oxide 
having therefore 23 times the thermal power of the latter. Yet, as is well 
known, both these bases fully saturate the acid, and the resulting solutions are 
even neutral to test paper. For these reasons, I have no doubt whatever that 
the first law, as enunciated in 1841, is the expression of a true physical law, 
and that in the combination of acids and bases in presence of water the heat 
disengaged is determined by the base and not by the acid. It is true that in 
this, as in similar physical inquiries, experimental results cannot immediately 
be obtained free from complication or disturbing influences. The same remark 
applies to the experimental proof of the great law discovered by Dulong and 
Petit, which connects the specific heats and atomic weights of the elementary 
bodies, and also to that of the remarkable relations discovered by Kopp between 
the composition and boiling points of many organic liquids. We have already 
seen an illustration of one of these disturbing influences, in the fact that dilute 
nitric acid, when mixed with water, gives a slight fall of temperature, hydro- 
chloric acid, a rise ; and the differences of specific heat in the solutions formed 
will to a small extent modify the results. But the cause of the higher thermal 
power of sulphuric acid I have not been able to discover, and future researches 
must decide whether it depends upon some disturbing cause, or (which is less 
probable) upon its possessing an exceptionally high thermal power. One 
condition is, however, essential, or Law 1 will not apply. The acid and base 
must be capable of combining when brought into contact, and of forming a 
stable compound. In the paper so often referred to, I showed that hydro- 
cyanic acid and potash, which fail to fulfil this condition, do not disengage the 
normal amount of heat when mixed ; and the same observation will doubtless 
be found to apply to a large number of metallic oxides, which form unstable 
compounds with, and imperfectly neutralise, the bases. 

As regards the experimental proofs of the other laws, even those of the 
fourth law, the truth of which is admitted by MM. Favre and Silbermann, 
they are only approximative ; and here also we meet occasionally with peculiar 
and unexpected results. Thus a slight fall of temperature occurs, as Hess 
showed long ago, in the conversion of the neutral sulphate of potash into the 
acid salt ; and I found, as indeed might have been expected from their alkaline 
reaction, that in the conversion of the ordinary phosphates and arseniates into 
super salts, a disengagement of heat occurs, amounting to about one-seventh of 
that disengaged in the formation of the salts themselves. In other cases results, 
at first view startling and apparently anomalous, will be found to be strictly in 

VOL. XXVI. PART I. 2B 



94 DR ANDREWS ON THE HEAT DEVELOPED IN THE 

accordance with the general principles already laid down. In the formation of 
double salts there is no disengagement of heat — a principle announced in 
1841, and which ought perhaps to be enunciated as a distinct law, although it 
is implicitly involved in Law 2. Again, if tribasic phosphoric acid or arsenic 
acid is added in fractional portions to a solution of potash till the subsalts are 
formed, the heat disengaged on each addition of acid corresponds to the amount 
of acid added ; but after this point has been reached, the disengagement of heat 
follows a different law. The pyrophosphoric acid, on the other hand, behaves 
in the same way as the nitric and most other acids, when added in successive 
portions to solutions of potash or soda; equal increments of heat being evolved 
for equal additions of acid, till the pyrophosphate of potash or soda is formed.'- 

APPENDIX. 

In the following tables I have given the results described in this communi- 
cation and those of 1841 in a form which admits of comparison with one 
another, and with those of MM. Favre and Silbermann. I have also added a 
few determinations recently made by M. Thomsen of Copenhagen, t It will be 
seen that the original experiments of 1841 exhibit, on the whole, a fair agree- 
ment with those now communicated to the Society. From the small scale on 
which they were performed (the whole weight of the solutions after mixture 
being less than 30 grammes), the imperfect form of the apparatus, and the 
uncertainty of the thermometric indications, I have indeed been surprised to 
find them so near the truth. The results of MM. Favre and Silbermann do 
not exhibit the precision which might have been expected from the high char- 
acter of those experimentalists, and from the accuracy of other parts of their 
great work. The mercurial calorimeter employed by them appears to have 
been little adapted to its purpose ; but after making due allowance for its im- 
perfections, I am at a loss to account for the serious errors into which they have 
fallen. M. Thomsen's experiments have evidently been made with care, and 
his results agree comparatively with my own ; but the absolute amount of heat 
obtained by him falls far short of what I have found. It is indeed much easier 
to obtain results relatively than absolutely correct. The numbers given in this 
paper will, I believe, be found rarely to differ relatively more than ^oth from 
the truth, but they may hereafter require a small correction in respect to their 
absolute value. That correction can, however, be scarcely more than -^th of 
the whole amount ; and I have little doubt that the number, for example, 

* Transactions of the Royal Irish Academy, vol. xix. pp. 245-248. The observations of Graham 
confirm the statement that no heat is evolved in the formation of any double salt. Memoirs of the 
Chemical Society, vol. i. p. 83. 

t Poggendorff's Annalen, cxxxviii. p. 78. 



COMBINATION OF ACIDS AND BASES. 



95 



given by Thomsen to express the heat disengaged in the combination of soda 
with nitric acid will prove to be as far below the true number as that given by 
MM. Favre and Silbermann is above it. 



Table I. — Potash. 



Acid. 


Andrews, 


Favee and 


Andrews, 


1841. 


Silbermann. 


1870. 


Sulphuric, . 


16330 


16083 


16701 


Nitric, 


15076 


15510 


14800 


Hydrochloric, 


14634 


15656 


14940 


Oxalic, 


14771 


14156 


15124 


Acetic, 


14257 


13973 


13805 


Tartaric, 


13612 


13425 


13508 



Table II. — Soda. 



Acid. 


Andrews, 
1841. 


Favee and 
Silbermann. 


Andrews, 
1870. 


Thomsen. 


Sulphuric, 


16483 


15810 


16580 


15689 


Nitric, 


14288 


15283 


14480 


13617 


Hydrochloric, 


14926 


15128 


14744 


13740 


Oxalic, 


14796 


13752 


15032 




Acetic, 


14046 


13600 


14000 




Tartaric, 


13135 


13651 


13400 





Table III. — Ammonia. 



Acid. 


Andrews, 


Favre and 


Andrews, 


1841. 


Silbermann. 


1870. 


Sulphuric, . 


14135 


14690 


14710 


Nitric, 


12440 


13676 


12683 


Hydrochloric, 


12440 


13536 


12964 


Oxalic, 


12684 




13088 


Acetic, 


12195 


12649 


12316 


Tartaric, . ... 


11400 




11744 



( 97 ) 



VI. — The Genetic Succession of Zooids in the Hydroida. By Professor 

Allman. 

(Read 16th May 1870.) 

Though most of the terms employed in the following paper have already 
become part of the language of science, some definitions may be here given with 
the view of rendering the subject more intelligible. 

The Zooids are the more or less individualised members of which the hydroid 
colony is composed. 

The Hydranth is the proper nutritive zooid. 

The Blastostyle is a columnar zooid destined not for nutrition, but for the 
origination of sexual buds. 

The Blastocheme is a medusiform zooid which gives origin to generative 
elements, not immediately, but through the intervention of special sexual 
buds. 

The Gonophore is the ultimate generative zooid, that which immediately 
produces the generative elements. It may be either medusiform or sacciform. 

The Trophosome is the entire assemblage of nutritive zooids in a colony. 

The Gonosome is the entire assemblage of generative zooids in a colony. 

From all the facts which the study of the Hydroida has made apparent, we 
may regard it as certain that however long zooidal multiplication may continue, 
this is not sufficient for the perpetuation of the species, but that a period must 
at last come in the life of the hydroid when by an act of true sexual reproduc- 
tion, new individuals are produced for the indefinite extension of the species 
through time. 

This truth finds its expression in Steenstrup's famous law of " Alternation 
of Generations," — a law which, though not very correctly enunciated by its 
framer, may be regarded when properly expounded as a statement of the fact, 
that in certain animals every act of embryonal development is followed by 
one or more acts of zooidal development, which invariably conduct us to an 
ovum in which embryonal development followed by zooidal development again 
occurs, and the entire series becomes thus repeated. . 

Now the various series expressing this alternation of sexual with non- 
sexual development, exhibit among the Hydroida different degrees of complica- 
tion, which will be more easily understood if we attempt to present them in 
the somewhat technical shape of formulas. 

VOL. XXVI. PART I. 2C 



98 PROFESSOR ALLMAN ON THE GENETIC SUCCESSION 

Let t be the trophosome, and g the gonosome, then 

I. t +g x t + y x t + g x &c, 



will be the general expression for the genetic succession in the life of the 
hyclroid, the sign + indicating succession by zooidal development, and x by 
embryonal. 

It is very seldom, however, that the trophosome consists of only a single 
zooid. Such rare instances are presented by corymorpha (fig. 1), and by cer- 
tain allied forms, whose trophosomes never become developed into a colony of 
mutually dependent hydranths, and I believe it better to regard the hydrorhizal 
fibres here as elsewhere in the light of mere extensions of the hydrorhizal or 
fixed end of the colony, rather than in that of proper zooids — a view supported 
by their mode of development in the primordial hydranth. In almost every 
other case, the hydranths composing the trophosome become greatly multiplied 
by budding. 

Still less tendency is there in the gonosome to present an absolutely simple 
condition. Indeed, the gonosome is perhaps never limited in its normal state 
to a single zooid, and we frequently find hundreds and even thousands of zooids 
entering into the composition of this portion of the hyclroid colony. 

But the zooids of which the colony is thus composed may not only be 
numerous, but may also vary in form. Those indeed which constitute the 
trophosome are always of a different form from those of the gonosome. In the 
trophosome it is rare to find any other form of zooid than that of the proper 
hydranth. In Hydractinia, however, there is associated with the ordinary 
hydranths the peculiarly modified ones, whose spiral form confers upon the 
trophosome of this genus one of its most striking features, while the nemato- 
phores of the Plumalaridce can scarcely be regarded otherwise than as special 
zooids whose morphological differentiation from the other zooids of the colony 
is carried to a maximum. 

In the gonosome, on the other hand, the usual condition is that of variety 
of form among its component zooids ; and it is quite common to find in one 
and the same gonosome, three different kinds of zooids, each with its special 
form among the associated zooids, and its special duty in the generative 
functions of the hydroid. 

While the type of heteromoiphism, or variety of form, among the zooids is 
fixed for every species, the pdlymerism, or simple multiplication of the com- 
ponent zooids, is indefinite, and varies with the age, perfection of nutrition, &c, 
of the individual. 

If we specialise the general expression already given (I.), so as to make it 



OF ZOOIDS IN THE HYDKOIDA. 



99 



directly applicable to particular cases of heteromorphic succession in the life of 
the hydroid, we shall obtain the following formulae, where h is used for the 
hydranth, Us for blastostyle, bkh for blastocheme, and gph for gonophore — 



ii. 1 1 



h + gph x h + gph x &c, Corymorpha. (fig. 1.) 



III. | >h + bis + gph x h + bis + gph x &c, Dicoryne. (fig. 2.) 



a i 

IV. I >h + bis + blch +gph x h + bis + bkh + gph x ...&c, Campanularia.(fig. 3.) 






These formulae present three types of heteromorphism. In II. the hetero- 
morphism is binary, in III. ternary, in IV. quaternary. 




Fig. 1. — Diagram of Corymorpha. 

A, the entire colony composed of 
trophosome and gonosome ; aaa, 
the trophosome, consisting of a 
solitary zooid ; b, the gonosome, 
consisting of numerous zooids. 
B, a single zooid (gonophore) of 
the trophosome become free and 
mature. 




Fig. 2. — Diagram of Dicoryne. 
a aaa, the trophosome, consisting 
of numerous zooids ; b c, the 
gonosome, consisting of blasto- 
style, b, and gonophores, c. 




Fig. 3. — Diagram of Campanularia. 
A, portion of the entire colony ; a«. 
the trophosome ; b c, the gonosome ; 
b, blastostyle ; cc, blastochemes. E, 
a blastocheme become free and 
mature, and carrying within its bell 
special zooids, which are the ulti- 
mate sexual buds or gonophores. 



But the hydranth may and does in almost every instance — either directly 
or through the medium of the common basis or hydrophyton — repeat itself 



100 PROFESSOR ALLMAN ON THE GENETIC SUCCESSION 

indefinitely by budding (fig. 2) before the time arrives when an element of the 
gonosome is to be budded off ; and a series of homomorphic zooids may thus 
introduce themselves into the heteromorphic succession, as expressed in the 
following formulae — 

V. h + h + /i + &c. + Ms +gph x h + h + h+ &c. + Ms +gph x &c. 

where the hydranth becomes indefinitely repeated in the formula of ternary 
heteromorphism (III.) given above; and the same will apply to each of the other 
two types of heteromorphism. 

Now, in all these cases, the succession from the primordial nutritive zooid to 
the ultimate generative zooid, or gonophore, admits of being expressed in a 
continuous line ; but one or more of the zooids of the trophosome may emit 
buds which will diverge from the direct line of succession, and which may 
then either form the starting-point for another similar fine of succession, or 
may be destitute of all power of continuing the succession of the zooids. Thus, 
(figs. 4 and 7) the primordial hydranth, or any of those derived from it, may 
repeat itself by a bud which will diverge from the direct fine, produce other 
zooids by gemmation, and thus start off a new series, as expressed in the 
following formula : — 



*s 



VI. It 



( + It +h + It + &c. + bis + gph \ , ( ) o 

\ + k + h + It + &c. + Ms + gph ) ( '" J 



And this state of things may also repeat itself indefinitely, giving rise to an 
indefinite number of collateral series diverging from one another, and from the 
primary axis of succession. 

As already said, however, the diverging zooid may have no power of con- 
tinuing the succession. Thus, the spiral hydranth of Hydractinia is not inter- 
calated in the direct succession of zooids. It is a diverging zooid, like that 
which starts off the collateral series in formula VI., but one which here never 
gives rise to buds, and is therefore incapable of either continuing or originating 
a new succession."" 

The following formula, where h' is the spiral hydranth, will express the 
place and power of this zooid in Hydractinia : — 

/ 7 7 7 7 ( + Ms + gph x &c. 

VII. h \ + f + «P* x M + V 

The case expressed in the formulae given above is the simple one, where only 
the last hydranth in the succession of buds composing a j3eriod is supposed to 

* The bifurcation occasionally observed in the spiral hydranth of Hydractinia is evidently 
abnormal, and cannot be regarded as invalidating the above statement. 



OF ZOOIDS IN THE HYDKOIDA. 101 

give origin to a bud of the gonosome. But any other hydranth in the succes- 
sion may just as well bud off a member of the gonosome, which may thus 
form a collateral gonosomal axis. This, indeed, is by far the most usual case, 
and is what is actually represented in the diagrams (see figs. 2, 4, 7). The 
axis, however, thus produced will be necessarily definite, and will contrast 
in this respect with the indefinitely extended axis of the trophosome, while it 
will differ from the diverging bud, h' in formula VII., by the fact of its having 
the power of repeating the colony by sexual reproduction, while h' has no 
power of reproduction, either sexual or non-sexual. 

This condition may be expressed by the following formula, in which not 
only the last hydranth of the period gives off a bud of the gonosome, but the 
primordial hydranth emits a collateral gonosomal axis : — 

viii. h | + k + + *<£»* + &c - + Us + ,Jph } x h | } x &c. 

Besides the particular cases now given, certain other modifications of the 
plan of gemmation will at once occur to any one who has made the Hydroida 
a subject of study. Those here adduced, however, will serve to convey an 
adequate idea of the essential features in hydroid gemmation. 

It is thus, by the combination of heteromorphic and homomorphic multipli- 
cation, and of direct and diverging series indefinitely repeated, that the animal 
attains to the condition of those wonderful complex colonies which impress 
themselves so strongly on the mind of the observer. 

So also the gonosome may present not only a heteromorphic but a homo- 
morphic multiplication of zooids. In no case, however, so far as I am aware, 
does any zooid of the gonosome repeat itself by homomorphic gemmation, except 
in some comparatively rare instances of budding in the medusa ; for though 
the homomorphic repetition of zooids may be in the gonosome as in the tropho- 
some, carried to a great extent, it is almost always the result of budding from 
a zooid of a different form. Thus the blastostyle never emits buds destined to 
repeat its own form, and this form, however frequently repeated in the gono- 
some, is always budded off from the hyclranthal element in the trophosome, 
its own buds, however numerous, being always heteromorphic with itself. 

In the formulae now given, one fact is obvious, namely, that the groups 
included between every two acts of embryonal development are exactly similar 
to one another in the nature and succession of their heteromorphic elements ; in 
other words, that the life series of the hydroid may be represented by definite 
groups of zooids exactly repeated after each generative act.""' We are indebted 
to Huxley for having assigned to our conception of the biological individual its 

* The mere number of zooids in two or more of these groups may of course vary, depending an 
this does on the accident of abundant or deficient nutrition and the like. 

VOL. XXVI. PART I. 2 D 



102 



PROFESSOR ALLMAN ON THE GENETIC SUCCESSION 



proper limits, when he denned it as " the total result of the development of a 
single ovum," and compared the definite groups of zooids which constitute the 
life series of animals presenting the phenomenon of " alternation of genera- 
tions " to the single organisms known as the individuals, which make up the 
species in other animals. These groups form the periods of the series ; the 
period repeats itself by true generation, and this repetition continues itself 
indefinitely, like a circulating decimal, so as to represent the indefinitely 
extended life of the species, while the life of the individual — in its technical 
sense as the component of the species — is expressed by each period singly. 




Fig. 4. — Diagram of Laomedea. 
a ii a a, hydranths belonging to the primary or direct line of succession ; a'a'a'a', hydranths belonging 
to a secondary or diverging line of succession ; b, blastostyle of the primary line of succession, bearing 
gonophores, and surrounded by a gonangium ; V, blastostyle with gonophores and gonangium of the 
diverging line. 

It is a universal law in the succession of zooids, that no retrogression ever 
takes place in the series. In other words, no bud ever becomes developed into 
a zooid which is of a different form from the budder, and has at the same time 
preceded it in the line of succesion. Thus, true hydranths are never emitted 
either by blastostyle, blastocheme, or gonophore ; and to this law the peculiar 
gemminate hydriform bodies which are found on the summit of the female 
blastostyle in certain species of Halecium form no exception ; for though closely 
resembling true hydranths, they appear to have a different signification, con- 



OF ZOOIDS IN THE HYDROIDA. 103 

tributing probably in some way as yet unknown to the generative functions of 
the hydroid, while they have no power of continuing the succession in a direct 
or collateral line like the proper hydranths of the trophosome. 

The hydranth normally continues the axis in the hydroid colony, just as the 
leaf-bud in the plant continues the vegetable axis ; the gonophore, on the other 
hand, has no power of continuing the axis, and constitutes the terminal zooid 
in each period of the series, just as the flower-bud stops the elongation of the 
axis in the plant. This analogy, however, must not be pushed too far, for while 
the hydranths and gonophores are simple zooids, the leaf-buds and flower-buds 
are complex associations of the corresponding element of individuality in the 
plant. 

The normal order of succession of the buds in the trophosome is from the 
proximal or fixed to the distal or free end of the hyclrosoma, so that the older 
buds are met with towards the base or hydrorhizal end of the main stem and 
branches, the younger ones towards the summit. In the gonosome, on the 
other hand, the order of succession is sometimes towards the distal, sometimes 
towards the proximal end of the axis. In the calyptoblastic genera, represented 
by campanularian, sertularian, and allied forms, the order of succession of the 
sporosacs or blastochemes is invariably from the distal towards the proximal 
extremity of the blastostyle on which in these genera they are always borne. 
When a blastostyle is present in the gymnoblastic or tubularian genera, the 
gonophores succeed one another, sometimes from the proximal towards the 
distal end (Hydractinia echinata), sometimes from the distal towards the 
proximal (Dicoryne conferta). In Tubularia their succession is from the distal 
towards the proximal end of the common peduncle, which is more or less 
developed in the various species of this genus ; and the same order of succession 
occurs in Corymorpha. 

Where no special gonosomal axis is developed, the succession is usually 
from the proximal to the distal extremity of the branch {Bougainmllia, Perigoni- 
mus), thus corresponding to that of the zooids of the trophosome. Sometimes, 
however (Syncoryne, Gemmaria), it is from the distal to the proximal. 

We have thus, then, in the gonosome of the Hydroida, as in the inflorescence 
of plants, both a centripetal and a centrifugal order of development. It is 
possible, however, that irregularities may occur, and that a new bud may be 
abnormally emitted at the distal side of a centrifugal series, or at the proxi- 
mal side of a centripetal one, so as to disturb in individual cases the normal 
sequence of the zooids. 

Some further points admitting of comparison with the inflorescence of plants 
may be noticed in the gonosome of such hyclroids as possess a special gonosomal 
axis. In Tubularia indivisa (fig. 5), and in the male colonies of Tubularia 
larynx, the gonophores are — like the flowers of a raceme — carried on short 



104 



PROFESSOR ALLMAN ON THE GENETIC SUCCESSION 



pedicels along the sides of a long common peduncle, which springs from the 
body of the hydranth. Their order of development, however, is centrifugal, or 





Fig. 5. — Diagram of Tubularia indivisa. 
a a, hydranth on its stalk ; b, shortly stalked gono- 
phores borne on a common peduncle, and increasing 
in maturity from the proximal to the distal extremity 
of the peduncle. 



Fig. 6. — Diagram of Tubularia larynx (Female). 
a a, a hydranth on its stalk ; b, gonophores at- 
tached by short stalks to a common branched 
peduncle, and increasing in maturity from the 
proximal to the distal extremities of the 
branches. 



from the distal to the proximal extremity of the peduncle, so that the whole 
group may be compared to a reversed raceme. In the female colonies of Tubu- 
laria larynx (fig. 6), and in Corymorpha nutans, the pedicels become branched 




Fig. 7. — Diagram of Eudendrium. 

aaaaa, hydranthal zooids of the direct line of succession ; a'a'a', hydranthal zooids of a diverging line ; 

b b, suppressed hydranthal zooid, bearing gonophores, which are disposed in an unbelliform group. 

with a similar order of development, which thus gives us the compound re- 
versed raceme or cyme. 

In certain proliferous medusae, the buds are borne on the manubrum with 






OF ZOOIDS IN THE HYDROIDA. 



105 



a centripetal order of development, thus giving us, according as the buds are 
sessile or pedunculated, the true spike, or the true raceme. 

The reversed spike, or spike with a centrifugal development, shows itself in 
such forms as Dicoryne conferta (fig. 2, be); while in Campanularia (fig. 3), 
Laomedea (fig. 4, b b'), Obelia, and other calyptoblastic forms, we have a reversed 
spike surrounded by the gonangial sheath ; and were it not for the centrifugal 
development of the generative buds upon the blastostyle, and the complete 
closure of the gonangium, strongly recalling the spadix with its spathe in the 
inflorescence of an araceous plant. 

In Eudendrium the male gonophores are disposed in an umbel (fig. 7, b) with 
the axis, in some cases prolonged beyond it, while in others there is little or 
no extension of the axis beyond the depressed portion which carries the gono- 
phores. Though we cannot here recognise any difference in the order of 
development among the gonophores composing the umbel, we are justified 
in assuming this order to be as in the true umbel — a centripetal one ; for in the 
female colonies of most species of this genus, such as Eudendrium ramosum, 





Fig. 8. Fig. 9. 

A blastostyle of Sydractmia, carrying its gono- A hydranth of Clava with its gonophores surround- 

phores, which increase in maturity toward s lie ing it in globular clusters. 
proximal or attached end. 



the gonophores are separated from distance to distance upon the stem imme- 
diately below the hydranth ; and here their order of development is plainly seen 
to be centripetal. 

In Hydractinia echinata (fig. 8) we have the closely approximated gonophores 
sessile on a blastostyle, and the development centripetal, as in the true spike, 
while the axis extends beyond it as a naked prolongation, reminding us of the 
naked prolongation of the spadix in certain Aracece. 

In Clava sqicamata, and in Clava multicornis, the gonophores form dense 

VOL. XXVI. PART I. 2 E 



106 PROFESSOR ALLMAN ON THE GENETIC SUCCESSION. 

clusters, surrounding the hydranth in a sort of verticil (fig. 9). Each cluster 
consists of sessile gonophores, borne on a greatly depressed common peduncle, 
and thus recalling the form of inflorescence known as a capitulum. The order 
of development, however, appears to be centrifugal, instead of being, as in the 
true capitulum, centripetal, and would therefore, perhaps, more truly suggest 
a comparison with the depressed cyme which constitutes the axillary inflores- 
ence in many Ldbiatce. 

In the comparison just instituted between the gonsome of the Hydrohla 
and the inflorescence of plants, it will be noticed, that whenever' in the 
Hydroida the generative buds are borne upon a special gonsomal axis, like 
the flowers in an inflorescence, the order of succession is far more frequently a 
centrifugal than a centripetal one. In the calyptoblastic forms, indeed, it is 
always centrifugal. This is exactly the opposite of what prevails in plants ; 
for here the centripetal forms of inflorescence greatly exceed the centrifugal 



ones. 



We must be careful, however, not to assign to the resemblances which may 
be noticed more importance than they are justly entitled to. But yet, after 
setting aside such as are merely superficial and accidental, many still remain 
which have their origin in certain deep-seated properties, and may be referred 
to the common phenomenon of gemmation, which by agamic multiplication in 
the animal as weU as in the plant, gives rise to colonies whose members in each 
case, mutually dependent on one another, continue to be organically associated 
into definitely arranged and determinate groups. 



( 107 ) 



VII. — Influence of the Vagus upon the Vascular System. By William Ruther- 
ford, M.D., F.R.S.E., Professor of Physiology, King's College, London. 

(Received, April 1869. Read, 3d May 1869.)* 

The innervation of the vascular system is a subject which has engrossed the 
attention of physiologists ever since the days of Galen. Yet, notwithstanding 
the number of distinguished observers who have contributed to our knowledge 
of this difficult topic, there are still many points of the greatest importance 
which are enveloped in the deepest obscurity, and not a few regarding which 
opinions are much at variance. 

During the past three years I have been more or less engaged in prosecuting 
an inquiry, the chief object of which, at the outset, was to ascertain as pre- 
cisely as possible the influence which the pneumogastric nerve exerts over the 
heart. But, as the investigation proceeded, various ideas started forth which 
led me to inquire into the influence which the vagus exerts over certain 
vascular territories, more especially the blood-vessels of the stomach. This 
line of research, although intricate and difficult to pursue, has nevertheless led 
to important results, and has enabled me to throw some light upon the manner 
in which the tissues rule over the blood-vessels which minister to their nutrition. 

I need not, however, further anticipate here what is fully expounded in the 
following pages ; but, before proceeding further, I desire to express my deep 
obligations to many of my pupils for the valuable assistance which they afforded 
me in the performance of the experiments. My thanks are especially due to 
Mr Haining, Mr Adam, Mr Alleyne, Mr Hamilton, and Mr Spence, without 
whose skilful co-operation my kymographic experiments must have lacked 
much of the precision which they happily possess. 

Innervation of the Heart. 

That the heart possesses within itself the conditions necessary for its 
rhythmical movement is a theory which was advanced by Galen, and is now 
believed by all physiologists. 

The peculiar nervous arrangements essential for the rhythmical movement 
are — as Remak points out — ganglia situated in various parts of the organ. 

* An Abstract of this paper was printed in the Proceedings of the above date. Urgent duties 
prevented me from preparing the paper in an extended form for the Transactions of 1869. By the 
permission of the Council its publication has therefore been delayed for a year. 

VOL. XXVI. PART I. 2 F 



108 DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 

It has long been known that the movements of the heart may be influenced 
by nerves connecting it with the cerebro-spinal axis. It is unnecessary, however, 
that I should enter into a full historical account of this subject, inasmuch as this 
has already been given at great length by Von Bezold. - I need, therefore, only 
say that it is now perfectly ascertained that the nerves which convey influences 
between the cerebro-spinal axis and heart are branches of the sympathetic and 
vagus. The sympathetic filaments take origin in the brain and medulla 
oblongata, pass through the cervical portion of the spinal cord, the last cervical 
and first dorsal sympathetic ganglia, and from thence to the heart (M. and E. 
Cyon).! These nerves convey to the cardiac organ influences which accelerate 
its action. Von Bezold| thought he had proved that they are continually 
prompting the heart to move ; he having observed that on dividing the cervical 
portion of the spinal cord — wherein these nerves are contained — that the heart 
beats more slowly than it does previous to the injury. He, however, omitted 
to take into account the fact, that on dividing the cervical portion of the spinal 
cord nearly all the blood-vessels of the body are paralysed, and that the lowered 
bloocl-pressure which results therefrom may be the cause of the slower action 
of the heart which follows the lesion. The brothers Cyon found, that although 
retardation of the pulse follows division of the spinal cord, no such change is 
usually observed if the cardiac motor nerves coming from the last cervical and 
first dorsal ganglia are divided, although these same nerves are cut across when 
the cervical portion of the spinal cord is divided. We have, therefore, no 
reason whatever for supposing that these nerves are continually in action, but, 
on the contrary, the evidence advanced by the brothers Cyon is entirely 
opposed to such an idea. 

It has also been maintained by Von Bezold § and others, that cardiac motor 
nerves are to be found in the trunk of the cervical sympathetic nerve. With 
regard to this matter, I have performed many experiments on rabbits, and have 
invariably failed to observe any excitement of the heart follow stimulation 
of this nerve unless the irritant (electricity) was transmitted through the nerve 
close to the inferior cervical ganglion. In that case accelerated cardiac action 
often followed the irritation ; but such result is no proof that the trunk of the 
cervical sympathetic contains motor nerves for the heart, seeing that the irritant 
was applied to the nerve near enough to the inferior cervical ganglion to throw 
into action the cardiac motor nerves derived from the spinal cord. I therefore 
agree with Ludwig and Weinmann,|| in considering the cervical sympathetic as 
not at all a cardiac nerve. 

* Von Bezold, Untersuchungen liber die Innervation des Herzens, l* 6 und 2 te Abtheilung. 
Leipsic, 1863. 

t M. and E. Cyon, Rbichert and Du Bois Reymond's Arcliivs, 1867, p. 389. 

X Lib. tit. 2 te Abtheilung, pp. 230 and 257. § Lib. tit. 1 te Abtheilung, p. 147. 

|| L,udwig's Lehrbuch der Physiologie, ii ter Band, p. 178. 



UPON THE VASCULAR SYSTEM. 109 

The heart is connected with the vagus by a superior and an inferior branch. 
The former, in the rabbit, leaves the vagus with the superior laryngeal nerve, 
or it may be somewhat below the origin of the latter ; it courses down the back 
in close proximity to the sympathetic, joins one or two branches of the inferior 
cervical ganglion with which it proceeds to the heart. In dogs this nerve is 
bound up with the trunk of the vagus and cervical sympathetic in one common 
trunk ; in cats it is joined to the sympathetic. The function of this nerve 
was discovered by Ludwig and Cyon.* It is a vaso-inhibitory and also an 
excitocardio-inhibitory nerve ; that is to say, when it acts it dilates vessels, 
and it also excites the filaments of the vagus (inferior cardiac branch) which 
inhibit the heart's movements. The influences which travel through the nerve 
start from the heart and pass to the medulla oblongata, there to inhibit the 
nerve-cells in the medulla connected with the motor nerves for the abdominal 
blood-vessels, and also to excite the nerve-cells in the medulla connected 
with the cardio-inhibitory fibres of the vagus. This nerve was named by 
the discoverers of its function " Nervus Depressor," because it lowers the 
blood-pressure ; this it does by diminishing the work done by two great portions 
of the vascular system — the heart — and abdominal blood-vessels. The in- 
fluences which travel through the nerve pass towards the medulla, probably 
their only starting-point is in the heart ; but with the cause which determines 
the action of the nerve we are totally unacquainted. Its discoverers always 
failed to find it in action ; that is to say, they never saw the blood-pressure 
rise when the nerve was divided. This of course was a very unsatisfactory 
circumstance, not a little calculated to cast grave doubts as to the real function 
of the nerve having been discovered at all. I am glad to say, however, that in 
the course of experiments hereafter to be detailed, I succeeded in finding this 
nerve in action on several occasions (see Experiments XLL, XLIV., XL VI., 
LI.) The nerve certainly acts in the manner indicated by Ludwig and Cyon ; 
but my experiments do not enable me to state what are the causes of its being 
thrown into action. 

The inferior cardiac branch of the vagus usually arises with the inferior 
laryngeal nerve, and from this origin it proceeds to the heart, where, according 
to BEALE,t it joins the cells of the cardiac ganglia.;): 

* Sachs. Acad. Bericht, 1866, p. 307. 

f Philosoph. Trans. 1863, p. 562, and fig. 41. 

X From physiological evidence it is generally believed that the cardio-motor nerves (sympathetic) 
are also connected with the ganglia in the heart. The termination of the depressor nerves ■within the 
heart is quite unknown. 



110 DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



Function of the Inferior Cardiac Branch of the Vagus. Is it motor as 

well as inhibitory ? 

Effect of Stimulating the Nerve. 

In 1845, the brothers Weber* made the well-known observation that, on 
irritating the vagi, or those portions of the central nervous system from which 
they spring, that the heart beats more slowly, and may even come to a stand- 
still in a state of relaxation. From this observation they concluded that the 
vagus exercises an inhibitory power over the heart's action. The accuracy of 
the experiment has ever been beyond dispute, but the explanation, though now 
accepted by nearly all — if not by all — physiologists, has nevertheless been 
opposed by such distinguished investigators as ScHiFF,t Moleschott,;}; and 
Lister. §. These authorities, while admitting that powerful stimulation of the 
vagus arrests cardiac action, maintained that gentle stimulation quickens it. 
They, therefore, concluded that the vagus is really a motor nerve of the heart, 
and that the arrest of cardiac action which follows powerful irritation of the 
nerve, is due to exhaustion of the latter. 

As it is unnecessary to slay the slain, I need not adduce the arguments 
necessary to show how fallacious is the method of reasoning upon which these 
authors have hinged their conclusion, — that has already been ably done by 
Pfluger,|| Von Bezold,H and others. I will only make a single remark, 
namely this, — were it true that while powerful stimulation slows the heart, 
weak stimulation quickens it, the conclusion that both effects must necessarily 
be due to the influence of the stimulant upon the same fibres of the vagus is by 
no means warranted. It seems to me that the only legitimate explanation 
which Schiff and others could have given of their facts, is that the excitement 
of the heart due to stimulation of the lower end of the vagus — after its section 
in the neck — results either from general excitement of the animal, or from the 
presence of cardiac motor nerves in the vagus-^z^ addition to those which 
inhibit the heart's movements ; a weaker stimulus being necessary for the 
former than is required for the latter. 

It is settled beyond all dispute that the inferior cardiac branch of the vagus 
contains fibres which inhibit the heart. The experiments hitherto performed 

* Omodei Annali Universali di Medicina, vol. cxvi. p. 225, November 1845. 
"J* Experimentelle Untersucbungen uber die Nerven des Herzens. Arcbiv. fiir Pbysiolog. Heil- 
kunde 8 ter Jabrgang. 

% Wiener Med. Wocb.enscb.rift, 25ter Mai 1861. 
§ Proc. Roy. Soc. vol. ix. p. 367. 

|| Reichert's and Du Bois Retmond's Arcbivs, 1859, p. 13. 
IT Lib. cit. Erste Abtbeilung. 



UPON THE VASCULAR SYSTEM. Ill 

do not, however, seem to me to conclusively show that cardiac motor fibres 
are absent from this nerve. Schiff's statement is that when the vagi are 
divided in the necks of rabbits, and the lower end of one or both nerves 
very gently stimulated, the heart's action is quickened. He has further said 
that it is difficult to hit upon the precise amount of stimulation which will effect 
this. Although other observers of undoubted reputation for skilful experi- 
mentation have failed to obtain this result, the above statement is nevertheless 
positive evidence which cannot be discarded unless the negative evidence be 
very strong. It seemed to me that it was possible to investigate this matter in 
a manner more exact and reliable than that adopted by previous experimenters ; 
accordingly, I performed a number of experiments in 1866-67, in the following- 
manner : — In frogs and rabbits I exposed the vagi in the neck, and then opened 
the trachea and larynx anteriorly, — in order that asphyxia and consequent ex- 
citement might be prevented, and also to enable me to see movements of the 
arytenoid cartilages. I then divided the vagi on a level with the thyroid 
cartilage. I always stimulated the nerve by induced currents obtained from 
Du Bois Reymond's induction machine. The electrodes consisted of clean 
copper wire ; the battery of one of Daniell's cells. On stimulating the lower 
end of the vagus, I always watched the corresponding arytenoid cartilage as 
well as the heart. The movement of the former served as a strict test for the 
proper application of the electrodes, in short — for the proper stimulation of the 
nerve. The observations were begun by ascertaining the strength of current 
necessary to affect the recurrent laryngeal filaments in the vagus — so that 
movement of the arytenoid cartilage ensued. Having ascertained this, I made 
the current still weaker, and then began the observations on the heart. As is 
well known, the strength of the induced currents obtained from Du Bois Rey- 
mond's machine depends on the distance between the primary and secondary 
coils. The strength is inversely as the distance. Seeing that I began with 
very weak currents — that is, with the secondary far removed from the primary 
coil — and, being anxious to test the effect of all currents intermediate between 
the very weak ones at the commencement and those strong enough to retard 
the pulse, I always increased the strength of the current while the nerve was 
being stimulated, and the effect upon the heart observed. As long as the 
stimulus was not strong enough to slow the heart, the nerve was usually 
stimulated for about half a minute. Whenever the animal struggled, the obser- 
vation was at once abandoned, and repeated when all excitement had subsided, 
— the effect of struggling being to increase the cardiac movement. In the case 
of rabbits, the cardiac pulsations were counted with the aid of a stethoscope, 
the number being taken previous to and during the stimulation of the nerve. 



VOL. XXVI. PART I. 2 G 



112 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



EXPERIMENTS ON RABBITS. 

EXPERIMENT I. — 8th August 1866. — Strong Rabbit. Trachea and Larynx opened. 
Both Vagi divided in the Neck. Du Bois Reymond's Induction Machine with one 
Daniell's element employed as the stimulating agent. 







Distance in Millimetres of 

Primary from Secondary Coil 

of Induction Machine. 


Pulse 


in 10". 


State of Laryngeal 
Muscles. 


Time. 


Before Irritation of 
Vagus. 


During Irritation of 
Vagus. 








Cardiac end of 










left Vagus. 




4 


•22' 


740 






Contraction. 




•23' 


800 


51 


50 


Rest. 




■24' 


800—750 


52 


52 






25' 


750—730 


52, 52 


52, 52 


Contraction. 




•26' 


730—700 


51, 52 


52 






27' 


700—670 


51 


51 






28' 


670—640 


52, 52 


52, 52 


» 




30' 


640—620 


51, 52 


52, 51 






31' 


620—630 


51, 50, 51 


51, 50, 50 


» 




33' 


630—640 


50, 51 


51, 50 


» 




38' 


640—600 


52, 51 


50, 51 


» 




•40' 


600—550 


51, 50 


51, 51 


)> 




41' 


550—500 


50, 50 


51, 50 






44' 


500—450 


50 


50 


» 




45' 


450—400 


50 


49 


» 




48' 


400—350 


52, 50 


50 


>> 




52' 


350—300 


50, 50 


50, 48, 49 


!> 




54' 


300—250 


48, 49, 50 


49, 50 


>> 




59' 


250 


50, 49 


49, 49 


» 


5 


r 


250—230 


48, 50 


33, 29 


» 




5' 


250 


48, 48 


48, 48 


)J 


•8' 


240 


48, 49 


19, 19 


3i 



EXPERIMENT II. — Strong Young Rabbit. Trachea and Larynx opened. 

divided in the Neck. 1 Daniell. 



Both Vagi 



Time. 


Distance in Millimetres of 

Primary from Secondary 

Coil 


Pulse 


in 10". 


State of Laryngeal 
Muscles. 


Before Irritation of 


During Irritation of 






Vagus. 


Vagus. 










Cardiac end of 
right Vagus. 




10-15' 


550 






Contraction. 


•17' 


700 


45 


45 


Rest. 


•19' 


700—650 


44 


45 


>) 


•21' 


650—600 


46, 45 


46, 46 


» 


•23' 


600—550 


45 


45 


Contraction. 


•28' 


550—450 


46 


46, 46 


V 


•30' 


450—400 


46 


47 


>> 


•32' 


450—400 


46,46 


46, 46 


it 


•34' 


400—350 


46 


46, 45, 46 


» 


•36' 


350—300 


45 


45, 44 


>1 


•38' 


300—250 


44 


45, 44 


>) 



UPON THE VASCULAR SYSTEM. 



113 



EXPERIMENT II.— continued. 



Time. 


Distance in Millimetres of 

Primary from Secondary 

Coil. 


Pulse 


in 10". 


State of Laryngeal 

Muscles. 


Before Irritation of 
Vagus. 


During Irritation of 
Vagus. 


10-44' 


250—220 


42 


42 


Contraction. 


•46' 


220—200 


43,44 


44, 44 


» 


•50' 


200—180 


42 


42 


>> 


•52' 


180—170 


43 


43 


>> 


•54' 


170—160 


42 


42 


y> 


11 o'clock. 


160—150 


43 


43 


>> 


• 5' 


150—140 


42 


42 


>> 


• 8' 


140—130 


42 


38 


» 


•10' 


130—100 


42 


Stoppage. 


>! 



EXPERIMENT III. — Strong Old Rabbit. Trachea and Larynx opened. 

DIVIDED IN THE NECK. 1 DANIELL. 



Both Vagi 



Time. 


Distance in Millimetres of 

Primary from Secondary 

Coil. 


Pulse ) 


n 10". 


State of Laryngeal 
Muscles. 


Before Irritation of 


During Irritation of 






Vagus. 


Right Vagus. 




3-38' 


700 


48 


48 


Rest. 


•40' 


700—650 


48 


48 


j) 


•48' 


630 


48 


48 


Contraction. 


•51' 


630—600 


48, 49 


49, 48 


>■> 


•55' 


600—560 


49, 48 


47, 48 


>> 


4-2' 


560—460 


48 


48, 49, 47 


?) 


•5' 


460—400 


48 


48 


J? 


•6' 


400—350 


48 


48 


jj 


•8' 


350—300 


48 


48 


j? 


•10' 


300—250 


48 


47 


>> 


•11' 


250—220 


47 


48, 47 


j? 


•14' 


220—200 


48 


40 

Cardiac end of 

left vagus. 


>> 


4-18' 


700 


47 


47 


Rest. 


•21' 


700—650 


47 


48, 47 


)> 


•23' 


650—600 


48, 49 


49, 49 


J? 


•25' 


600—580 


47 


48 


Contraction. 


•28' 


580—500 


48 


48, 47 


i> 


•30' 


500—450 


46, 45 


45, 45 


j, 


•35' 


450—400 


45 


45, 44 


j> 


•38' 


400—350 


43, 44 


44, 43 


jj 


•42' 


350—300 


43 


42, 43 


J? 


•46' 


300—250 


44 


44, 44 


>? 


•49' 


250—200 


43 


43 


,} 


•54' 


200—185 


42 


36, 34 


,; 


•58' 


150 


44 


26 


,j 


5 o'clock. 


100 


44 


Stoppage. 


j? 



114 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



I might give the results of nine other experiments similar to the foregoing, 
but these so thoroughly agree with the above that I think it unnecessary to 
detail them. I shall, however, have occasion to refer to some of their results in 
the sequel. 



EXPERIMENTS ON FROGS. 

EXPERIMENT XIII. — Strong Frog. Both Vagi Divided. Larynx laid open anteriorly. 
Heart Exposed. Pericardium Unopened. 1 Daniell. 







Pulse in Half a Minute. 




Time. 


Distance in Millimetres of 

Primary from Secondary 

Coil. 




State of Laryngeal 

Muscles. 


Before Irritation of 


During Irritation of 






Vagus. 


Vagus . 










Eight vagus. 




9-ir 


800 


16 


16 


Rest. 


•14' 


800—750 


16 


16, 16 


>i 


•17' 


750—700 


16 


16 


J! 


•19' 


700—650 


16 


16 


>3 


•22' 


650—600 


16 


16 


J) 


•26' 


600—550 


16 


19 


Contraction. 


•30' 


560 


16 


16, 16 


Rest. 


•34' 


550 


16 


15, 16 


Contraction. 


•37' 


550—500 


16, 16 


16,16 




•43' 


500—450 


16 


16, 16 


j» 


•48' 


450—400 


16 


16, 16 


>■> 


•53' 


400—350 


15 


15, 15 


>9 


•56' 


350—300 


15 


16, 15 


>i 


•59' 


300—250 


15 


15, 15 


)) 


10-4' 


250—200 


14 


14, 13 


» 


•9' 


200 


14 


14, 12, 12 


» 


•14' 


200—170 


14 


12, 12, 10 


>> 


•20' 


170—140 


15, 14 


14, 12, 11 


» 


■25' 


140—100 


15 


8, Arrest. 


>> 



The left vagus was then irritated, but only with a view to ascertain what was 
the feeblest current necessary to produce movement in the larynx, and also the 
weakest current which could arrest the heart's movements. A current at 530 
mm. was the weakest which threw the left recurrent laryngeal nerve fibres 
into action, while the weakest which sufficed to arrest the heart was one at 
170 mm. Further observations on the left vagus were not undertaken, seeing 
that the heart's action had become irregular. 



UPON THE VASCULAR SYSTEM. 



115 



EXPERIMENT XIV.— Strong Frog. Both Vagi Divided. Larnyx Opened. Heart 

Exposed. Pericardium Intact. 1 Daniell. 







Pulse in Half a Minute. 




Time. 


Distance in Millimetres of 

Primary from Secondary 

Coil. 




State of Laryngeal 
Muscles. 


Before Irritation of 


During Irritation of 






Vagus. 


the Vagus. 










Left vagus. 




414' 


700 


17 


17 


Rest. 


■16' 


700—650 


17 


16 


j) 


■19' 


650—600 


16 


16 


35 


•22' 


600—580 


16 


16 


Contraction. 


•25' 


580—550 


16 


16, 16 


5> 


•30' 


550—500 


16 


16, 16 


33 


•34' 


500—480 


16, 16 


16, 16 


>! 


•39' 


480—450 


16, 16 


16 


33 


•44' 


450—440 


16, 17 


17, 17 


33 


•48' 


440—420 


17, 18 


17, 16 


>3 


•52' 


420—400 


17, 17 


17, 17 


33 


•57' 


400—380 


17 


16 


33 


•59' 


380—360 


16 


16 


33 


54' 


360—340 


16 


16, 16 


S3 


•8' 


340—320 


16, 16 


16, 16 


33 


•13' 


320—300 


16 


16, 16 


I! 


•17' 


300—280 


16, 16 


16, 16 


3 3 


•21' 


280—260 


16 


16 


3; 


•26' 


260—250 


16 


16 


33 


•30' 


240 


16 


15 


33 


•32' 


220 


16 


15 


33 


•35' 


200 


16 


16 


33 


•37' 


180 


15 


16 


33 


•42' 


160 


17 


13 


33 


•44' 


140 


17 


13 


33 


•48' 


120 


18 


12 


33 


•51' 


100 


21 


Arrest. 


33 



It is unnecessary for me to give the results of other two experiments upon 
frogs, seeing that they are precisely similar to the above. The experiments al- 
ready detailed amply suffice to show the method of experimentation adopted in 
the inquiry. I am at a loss to conceive a mode of research better calculated to 
yield accurate results. The stimulation of the recurrent laryngeal fibres of the 
vagus served as an index of the effect of the irritant upon the very nerve sup- 
posed to contain motor fibres for the heart, and enabled me to judge whether 
or not the vagus was being properly stimulated. Hence the fact that I never 
observed quickening of the heart's action follow stimulation of the nerve although 
negative in its nature, is, nevertheless, I venture to think, exceedingly reliable 
on account of the method of procedure adopted. It may be well, however, for 
me to repeat, that I never registered the heart's pulsations while the animal was 
restless ; had I done so, I might have shown that accelerated cardiac action 

VOL. XXVI. PART I. 2 H 



116 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



often follows stimulation of the vagus, but such observations must obviously 
have been utterly fallacious, seeing that violent movements invariably excite the 
heart's action. With a view to explain how Schiff and his supporters obtained 
their results, Eckhard* has hinted that possibly the irritating current may have 
been sent through the vagus so low in the neck that it affected other nerves in 
addition to the vagus. Certainly Eckhard's conjecture is sufficient to serve as 
an explanation of the above, but whether or not it be the true explanation, I 
cannot say, inasmuch as I did not see Schiff and his supporters perform their 
experiments. 

A striking fact is very clearly brought out by the above mode of experi- 
menting — viz., that a very much stronger irritant is necessary so to stimulate 
the cardio-inhibitory fibres of the vagus, that the heart's action may be re- 
tarded, than is required to stimulate the recurrent laryngeal fibres, so that the 
laryngeal muscles may be thrown into action. The following table demonstrates 
this fact : — 

TABLE I. — Showing Comparative Strength of the Stimuli necessary to throw the 
Inferior Laryngeal and the Inferior Cardiac Nerves into Action. 



No. of Experiment. 


Nature of Animal. 


Vagus Divided in Neck, Lower End Stimulated. 

Distance in Millimetres of Primary from Secondary Coil indicating 

the Weakest Current necessary. 


(A.) To throw the Laryngeal 
Muscles into Action. 


(B.) To Inhibit the Heart's 
Action. 


I. 


Rabbit. 


740 


240 


II. 


J5 


550 


130 


III. 


)) 


630 Right Vagus. 


210 


Do. 


;j 


590 Left 


190 


IV. 


J5 


600 


240 


V. 


)* 


575 


220 


VI. 


?J 


650 


250 


VII. 


?) 


520 


170 


VIII. 


7> 


610 


260 


IX. 


)} 


660 


200 


X. 


)> 


630 


210 


XI. 


JJ 


580 


185 


XII. 


?> 


620 


200 


XIII. 


Frog. 


550 


200 


XIV. 




580 


160 


XV. 


)9 


620 


200 


XVI. 


» 


550 


200 



It may be seen, from the above table, that the strength of current necessary 
to stimulate the inferior laryngeal and inferior cardiac filaments in the trunk of 
the vagus, differed in different cases. The cause of this is probably threefold : 
1st, The strength of the electrical current was not absolutely constant ; 2d, The 



Experimental Physiologie des Nervensystems, 1867, p. 201. 



UPON THE VASCULAR SYSTEM. 117 

degree of sensibility varies in different animals ; M, The preparation of the 
nerve cannot, of course, be conducted so that precisely the same amount of 
injury is inflicted upon it in different cases. When I first elicited the difference 
between the results given in column A. and those in column B., it occurred to 
me that possibly the inferior laryngeal nerve fibres are more excitable than 
those of other motor nerves. But a few experiments on rabbits and frogs satis- 
fied me that such is not the case. It is to the last degree unlikely that the 
inferior laryngeal nerve is more excitable than the inferior cardiac nerve, and, 
therefore, I think, we must look to the peripheral terminations of the two 
nerves for the explanation of the facts above given. An ordinary motor nerve 
may be supposed to encounter little — if any — opposition when it acts upon the 
muscular plasm, but the inhibitory nerve has to act on a nervous apparatus 
in which there are counter-influences constantly at work. Only a powerful inhi- 
bitory influence can hold these in check, and indeed so powerful are these 
promptings to motion within the heart, that stimulation, however strong, of the 
inhibitory nerve, cannot keep the heart quite still for more than a few seconds. 

Having, in the above manner,"" entirely failed to find any acceleration of the 
heart follow stimulation of the vagus, another method of experimentation 
suggested itself to my mind. It has been shown by Botkin that atropia 
paralyses the cardio-inhibitory fibres of the vagus, that is to say, it so affects 
them or their terminations in the heart, that when they are stimulated the 
frequency of the pulse is no longer diminished.t I determined to produce this 
paralysis, and then see whether or not acceleration of the heart's action followed 
irritation of the lower end of the vagus. 

Experiment XVII. — In a rabbit I divided both vagi in the neck, and stimu- 
lated the lower end of the right vagus by a powerful current (Secondary 40 mm. 
distant from primary coil of induction machine. One Daniell). The heart's 
action was arrested. I then injected ten milligrammes of atropia sulphate into 
the jugular vein. When two minutes had elapsed, I stimulated the same nerve 
with a current of the same strength. The heart's action, instead of being 
arrested as before, was slightly accelerated. Before stimulation of the nerve, 
the pulse in 20" numbered 90 — during stimulation it numbered 96. After an 
interval of four minutes, I stimulated the nerve again with the same current. 
Before stimulation the pulse was 104 in 20" — during stimulation it rose to 
112. After a further lapse of time, I excited the lower end of the left vagus in 
the same manner, but no acceleration of the pulse ensued. The acceleration of 

* Should the reader at any time have occasion to repeat the above experiments, he will require to 
observe the arytenoid cartilages very narrowly, in order to detect the finest movements which may re- 
sult from irritation of the vagus. The animal should be arranged so that the light may be reflected 
from the inner surface of the arytenoid cartdage. The slightest movement of the glittering mucous 
surface can then be readily detected. 

t Vihchow's Archivs, Band xxiv., 1862, p. 89. 



118 DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 

the pulse in this case took place when no signs of excitement were exhibited 
by the animal, it therefore seemed to indicate that the right vagus, at any rate, 
contains efferent cardio-motor nerves""" which are not paralysed by atropia 
sulphate. The following experiment led me to abandon this idea : — 

Experiment XVIII. — In a rabbit I divided the trunk of the left vagus in 
the neck, dissected down upon the subclavian artery, and divided the inferior 
cardiac branch of the right vagus. I then severed the trunk of the vagus on 
the right side of the neck and irritated its lower end with an induced current 
(secondary coil 80 mm. from primary coil. One Daniell). The heart's action 
was accelerated. Before stimulation the heart gives 92 beats in 20" — during 
stimulation the number rose to 100. On repetition of the above a similar result 
was obtained. The acceleration in this case could not possibly be due to the 
action of any motor nerves contained in the inferior cardiac branch of the vagus, 
for that branch had been divided on the same side as that on which the trunk 
of the vagus was irritated. I, therefore, concluded that in this and in the pre- 
ceding experiment, the acceleration of the heart's action was probably due to a 
reflex excitement of the heart resulting from spasm of the laryngeal and 
oesophageal muscles, as well as the greatly increased movement of the stomach 
and intestines which follows powerful stimulation of the lower end of the vagus. 

I have, therefore, entirely failed to find any evidence to the effect that the 
inferior cardiac branch of the vagus contains any cardio-motor fibres in addition 
to those which are cardio-inhibitory in their action. 

Effect upon the Vascular System of Section of the Vagi in the Neck. 

It is well known that division of both vagi in the cervical region is — in the 
case of mammals at any rate — usually followed by accelerated cardiac action 
and increase of the arterial blood-pressure. 

(a.) Cause of the accelerated Cardiac Action. 

REiDt ascribed it to "the struggles and terror of the animal produced by 
division of the nerves." Undoubtedly this is to some extent true, but accelera- 
tion of the heart may be observed after division of the vagi during complete 
narcotism produced by opium. Brown- Sequard} thought that the excitement 
of the heart is due to accumulation of carbonic acid in the blood • — it being well 
known that division of the vagi is usually followed by a slower rate of respira- 

* Since the above was read I have experimented still further with regard to this point. The 
experiments which I have performed on rabbits and cats have convinced me thoroughly that the vagus 
does not contain " accelerator" fibres for the heart, and that any acceleration of the heart which may 
be observed when the lower end of the vagus is stimulated after atropia-poisoning is not due to a direct 
action of the vagus upon the heart. 

f Physiological Researches, 1848, p. 132. 

| Jl. de la Physiologie, v. p. 656. 



UPON THE VASCULAR SYSTEM. 119 

tion. Considering that this distinguished physiologist long ago pointed out the 
irritating effects upon certain nervous centres, which result from accumulation 
of this substance in the blood, it is not surprising that he should have advanced 
the above theory. The following experiment shows, however, that acceleration 
of the pulse may follow section of the vagi although a hyperoxygenated con- 
dition of the blood be maintained before and after the section. 

Experiment XIX. — In a strong rabbit I exposed the vagi, introduced a 
canula into the trachea, and then by means of a special apparatus maintained 
artificial respiration with such rapidity, that the respiration could be completely 
stopped for twenty seconds without slowing of the heart ensuing. It was, 
therefore, certain that a hyperoxygenated state of the blood had been fairly 
produced.*" While care was taken to maintain the artificial respiration at the 
same rate, I divided the vagi and watched the results for some time after. 
They arethe following : — 



Time. 




Pulse in 15". 


5-12' 


Previous to Hyperoxygenation 


60 61 59 


„16' 


„ division of Vagi 


59 60 58 


„ 17' 14" 


Vagi divided 




22' 




65 64 64 


„2& 




66 64 65 



The above facts show that a quickened action of the pulse may follow section 
of the vagi although the slightest approach to asphyxia is prevented. Further, 
recent researches by Voit and RAUBERt prove, that until the pulmonary textures 
undergo inflammation the increased depth of the respirations after division of 
the vagi entirely compensates for their diminished frequency, so that the amount 
of oxygen and carbonic acid in the blood undergoes no change. 

It is now generally believed that the acceleration of the pulse after division 
of the vagi is due to escape of the heart from the restraining influence of these 
nerves, and seeing that the acceleration very frequently follows the above- 
mentioned lesion, it is inferred therefrom that the cardio-inhibitory fibres of the 
vagi are in almost constant action. It occurred to me that if this explanation be 
the true one, and the only one, we should expect to find no acceleration of the heart 
follow division of the vagi after their cardio-inhibitory fibres have been paralysed 
by such a substance as atropia. Accordingly, I performed a number of experi- 
ments with a view to test this point ; but as these bear equally upon the 
following question, I shall briefly allude to it before proceeding further. 

* Usually within three seconds after the respiration of a rabbit is arrested the heart comes almost 
to a stand-still. This is due to irritation of cardio-inhibitory nerves by the asphyxiated condition of 
the blood. 

f Centralblatt. 1868. No. 47. 

VOL. XXVI. PART I. 2 I 



120 



DE, RUTHERFORD ON THE INFLUENGE OF THE VAGUS 



(b.) Cause of the Increased Blood-Pressure. 

During the operation of the cardio-inhibitory nerves, the work done by the 
heart is diminished (see fig. 2). The rise in the blood pressure, which com- 
monly follows section of the vagi, is therefore ascribed by all to increased force 
and frequency of the heart's contractions. If this be the only cause of the rise 
in the blood-pressure, then we ought to find that it undergoes no exaltation on 
division of the vagi during a paralysed state of their cardio- inhibitory fibres. 

The following experiments were undertaken with a view to furnish an 
answer to this question. Do accelerated cardiac action and increased blood- 
pressure follow division of the vagi — during paralysis of their cardio-inhibitory 
fibres — produced by such a substance as atropia sulphate ? — 



Experiments showing the Effect upon the Blood-Pressure and Frequency 
of the Pulse which sometimes follows Section of the Vagi in Animals 
where the cardio-inhibitory nerves are paralysed by sulphate of 
Atropia. 



EXPERIMENT XX. 



-A Small Terrier Dog. 
Trachea orEN. 



Caxula in Carotid Artery. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
of Hg.* 


General Notes. 


11-44' 


16 


4-5 




47' 


16 


4-5 




30" 






- 67 milligramme atropia sulphate 
injected into vein. 


48' 30" 


40 


4-65 




50' 30" 


29 


4-2 




52' 


22 


4-4 




30" 






0'4 milligramme atropia sulphate 
injected into vein. 


53' 


35 


4-2 




54' 


29 


4 




55' 30" 


25 


3-9 




56' 






Eight vagus divided in the neck. 


57' 30" 


23 


4 




58' 30" 






Left vagus divided in the neck. 


59' 


56 


5-9 




45" 


50 


5-9 




12 - 2' 


42 


6-4 




8' 


43 


8-45 




30" 






Distal end of left vagus irritated 
by a strong induced current, but 






9 


no effect was produced on the 
heart's action, clearly showing 
that the cardio-inhibitory nerves 
were completely paralysed. 



* In all these experiments Ludwig's Mercurial Kymograph was used. 



UPON THE VASCULAR SYSTEM. 



121 



In the above, notwithstanding the paralysis of the inhibitory nerves of the 
heart, section of the vagi was followed by a most distinct increase in the fre- 
quency of the heart's contractions, and a rise in the blood-pressure. 

EXPERIMENT XXI. — A Middle-sized Collie Dog. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


12- 3' 


29 


5-9 




9' 






0'67 milligramme atropia sulphate 
injected into vein. 


10' 


35 


5'6 




30" 


35 


5-3 




11' 






0'4 milligramme atrophia sulphate 
injected into vein. 


12' 


36 


5-2 




13' 


33 


5'6 




15' 


32 


5-3 




30" 






Left vagus divided. 


17' 


35 


5-8 




20' 30" 






Right vagus divided. 


22' 


39 


6-6 




23' 


39 


6-8 




28' 


40 


6-8 




29' 






Cardio-inhibitory nerves proved to 
he paralysed. 



EXPERIMENT XXII. — A Spaniel Dog, five months old. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 15*. 


Mean Pressure in inches 
ofHg. 


General Notes. 


11-19' 


27 


36 




20' 30" 


26 


4-6 




23' 


26 


4-05 




30" 






0'67 milligramme atropia sulphate 
injected into vein. 


24' 


30 


4-05 




27' 


38 


4-05 




30" 






0'4 milligramme atropia sulphate 
injected into vein. 


28' 30" 


66 


4-3 




30' 


60 


41 




31' 30" 


60 


3-9 




35' 


50 


3-9 




40' 


53 


4-1 




41' 






Left vagus divided. 


42' 


60 


4-3 




30" 






Right vagus divided. 


45' 


68 


5-1 




47' 






The cardio-inhibitory nerves were 
found to be completely paralysed. 



122 



DE RUTHERFORD ON THE INFLUENCE OF THE VAGUS. 



EXPERIMENT XXIII. — Old Spaniel Dog. Canula in Carotid Artery. Trachea open. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


4.28' 


25 


51 




30" 






2 milligrammes atropiae sulph. in- 
jected into vein. 


29' 


46 


71 




34' 






Clot in canula. Apparatus cleaned. 


42' 


42 


4-9 




43' 


38 


43 


Hitherto the respiration has heen 
rapid and irregular. 


48' 


40 


4-7 


Animal sobhing. 


49' 






20 minims Tincture Opii given. 


30" 


40 


61 




52' 






Clot in canrda. Apparatus cleaned. 


54' 


33 


4-6 




55' 






0*13 milligramme atropine sulph. 
given. 


56' 30" 


34 


4-6 




59' 






Left vagus divided. 


5 o'clock. 






Clot. Apparatus cleaned. 


3' 30" 


— 1 


4-9 




4' 






Eight vagus divided. 


5' 30" 


41 


51 




6' 30" 


40 


5-61 




9' 


43 


52 




12' 


44 


5-4 




13' 






Cardio-inhibitory nerves found to | 
be completely paralysed. 



These experiments show that in dogs division of the vagi in the neck may 
be followed by accelerated cardiac action and increased blood-pressure, although 
the cardio-inhibitory nerves be paralysed. It is clear, therefore, that physiolo- 
gists generally are mistaken in supposing that the acceleration of the pulse 
which commonly follows division of the vagi, is entirely due to the heart's being 
liberated from its controlling nerves. A portion — perhaps, in some cases, the 
whole — of that acceleration may be due to division of other filaments than those 
which retard the heart's action. I shall not, at present, enter into a discussion 
of the causes of the increased blood-pressure observed in these experiments. 
The reason for this will be readily perceived when my remarks upon other 
experiments performed on dogs have been perused. (See page 137.) 

The consideration of these changes which follow division of the vagi will be 
resumed after we have inquired into the present state of our knowledge regard- 
ing the 

Innervation of Blood-Vessels. 
By the investigations of Bernard and Brown-Sequard, it has been estab- 



UPON THE VASCULAR SYSTEM. 123 

lished that the contractile elements of the blood-vessels are supplied by motor 
nerve filaments derived from the sympathetic. Diminution in the calibre of the 
blood-vessels is produced by these nerves. According to Ludwig and Thiry, 
the general centre for the vasomotor nerves is situated in the medulla oblongata. 
This cerebro-spinal centre is more or less constantly in action, whereby vessels 
are usually kept in a semi-contracted state. The amount of contraction in the 
vessels — in other words, the degree of activity of the cells in the vasomotor centre 
— may be increased or diminished by certain nerves which convey influences to 
the medulla. Bernard""" was the first to show, by experiment, that vessels may 
be dilated by the irritation of certain nerves. He found that when he divided 
the auricular nerves in rabbits, and excited their central ends, the vessels of the 
ear of the same side became turgid. Slight contraction preceded the dilatation. 
LovENt has confirmed Bernard's observation, and has shown that dilatation of 
vessels in the rabbit's leg follows irritation of its afferent nerves ; in short, that 
dilatation of the vessels of a part may be produced by influences transmitted 
through the afferent nerves of that part to the cerebro-spinal vasomotor centre. 
Like Bernard, he found that transient contraction generally precedes the dila- 
tation of the vessels so induced. The most remarkable instance of a nerve 
capable of dilating vessels is to be found in the superior cardiac branch of the 
vagus already alluded to. When this nerve is divided and its cranial end 
stimulated, dilatation of abdominal blood-vessels takes place without any previous 
contraction, such as commonly results when a mixed nerve such as the sciatic 
or the trunk of the vagus is stimulated. In all the above cases the vascular 
dilatation succeeds stimulation of the central ends of the divided nerves ; that is 
to say, the peripheral end of the cranial portion of the divided nerve. Two 
facts, however, have been discovered which are opposed to the idea that the 
motor centre for all the blood-vessels of the body lies in the medulla oblongata ; 
one concerns the submaxillary ganglion, the other, the ganglia upon the nervi 
erigentes of the penis. It is well known that if the chorda tympani nerve be 
divided, and its peripheral end stimulated, dilatation of the blood-vessels in the 
submaxillary gland is the result. In like manner, as recently shown by 
Eckhard| and Loven§, when the nervi erigentes are divided in the dog and the 
peripheral portions stimulated, erection of the penis results, principally from the 
dilatation of vessels induced by the irritation. On these nerves there are many 
ganglionic corpuscles ; and the most feasible explanation of this vascular dilata- 
tion in the case of the submaxillary gland and penis is, that the ganglionic cells 
existing in connection with these structures, are in part, at any rate, vasomotor 
cells, and correspond to the ganglia in the heart, These three groups of ganglia 

* Jl. cle la Physiologie, 1862, p. 416. \ Beitrage. Giessen, 1863. 

+ Lov£n, Ludwig's Arbciten, 1866, p. 1. § Lib. tit. p. 18. 

VOL. XXVI. PART I. 2 K 



124 DR RUTHERFORD ON THE INFLUENCE OF THE YAGUS 

forming three peripheric motor centres connected with the vascular system, the 
only ones as yet known. But it is interesting to observe that the submaxillary 
and cardiac ganglia are obviously very directly connected with the medulla 
oblongata by motor and inhibitory nerves, and although nothing can be stated 
with precision regarding the central connections of the ganglia presiding over 
the vessels of the penis, they have, nevertheless, probably an intimate con- 
nection, like the others, with the medulla. The dilatation of vessels which 
results from the action of these vaso-inhibitory nerves is, as regards the vessel, 
passive ; it is due to the elasticity and blood-pressure being no longer opposed 
by the action of the contractile elements of the vascular wall, these having been 
brought to rest by a cessation of action in the vasomotor nerve apparatus. 

The vasomotor nerves may have their action increased as well as diminished 
by the action of other nerves. The contraction of vessels in distant parts by 
the sudden application of cold to it may be a small extent of skin. The remark- 
able increase in the blood-pressure which follows stimulation of the central end 
of the superior laryngeal nerve (Aubert and Soever),'" the contraction of 
vessels and increase of blood-pressure which usually follows the gentle stimula- 
tion of the central ends of mixed nerves, are some of the facts which support 
this idea; such nerves may be very appropriately termed excito-vasomotor 
nerves. These nerves appear all to pass inwards to the vasomotor centre in 
the medulla oblongata. 

Other facts might be mentioned, but I may briefly say that every advance in 
our knowledge of this question only tends more and more convincingly to show 
that the innervation of the contractile elements of the blood-vessels is similar to 
that of the cardiac muscular fibres. These contractile elements are directly 
supplied by motor nerve fibres ; and the evolution of energy in the cells con- 
nected with the latter may be diminished by one set of nerve fibres — cardio and 
vaso-inhibitory — and increased by another — excito-cardio and excito-vaso- 
motor. 

The idea commonly prevails that when a part becomes the seat of active 
nutritive change, its blood-vessels undergo dilatation by reason of the increased 
attraction for blood manifested by the tissues. The vis a f route, is supposed to 
become so powerful that it can overcome the contraction of the arterial walls, 
and thereby produce dilatation. It struck me that the vascular dilatation in 
such a case is possibly the result of an influence transmitted by the tissue 
through its vaso-inhibitory nerves. The only author who has come near to this 
idea is Loven. A considerable time after the above had presented itself to my 
mind, he published the excellent memoirt to which reference has already been 
made. He showed that the blood-vessels of a part may be dilated by artificial 

* Centralblatt, 1868, p. 578. f Llh - cit - 



UPON THE VASCULAR SYSTEM. 



125 



Fig. 1. — Diagram showing innerva- 
tion of Gastric Blood-vessels. 



stimulation of the afferent nerves of that part. There, however, he stopped. 
He has advanced no theory regarding the bearings of this fact upon our con- 
ceptions of the mode in which vascular dilatation in a part commonly takes 
place, nor has he thrown out any suggestion as to the agent by which these 
nerves are normally brought into play. I believe that the experiments which 
I have yet to detail will be found to very decidedly advance our knowledge 
regarding this matter. 

The vasomotor nerves for the blood-vessels of the stomach are contained in 
the splanchnic nerves. The vaso-inhibitory and excito-vasomotor nerves of 
that organ appear to me to be for the most part, if not entirely, contained in 
the pneumogastric nerves. If it be true — as I imagine — that when the gastric 
blood-vessels undergo dilatation, vaso-inhibitory nerves are brought into play, 
we should — if these nerves be contained in the vagi — expect to find that if the 
vagi be divided during dilatation of gastric blood-vessels, the vessels will undergo 
contraction, and we should desire to see that stimu- 
lation of the upper end of the divided nerve is able 
to produce dilatation of vessels. In order that the 
sequel may be better understood, I would refer the 
reader to the following diagram representing the 
stomach, s ; the vagus, v ; the splanchnic nerve, sp ; 
the medulla oblongata, m. o.; and the spinal chord, 
s. c. The arrow near the vagus indicates the direc- 
tion in which vaso-inhibitory and vaso-excito motor 
influences travel through the vagus to affect the vaso- 
motor centre in the medulla oblongata — while the 
arrow near the splanchnicus indicates the direction 
in which vasomotor influences travel through that 
nerve to the gastric blood-vessels. 

The following experiments were undertaken to 
ascertain whether or not one can obtain evidence 
of the passage of vaso-inhibitory influences through 
the vagus during the dilatation of the blood-vessels of the stomach which takes 
place during digestion, and also to ascertain the effect of irritating the vagus 
upon the gastric blood-vessels : — 



m.o. 




Stomach, s. Spinal Cord, s.c. Me- 
dulla Oblongata, m.o. Vagus, v. 
Splanchnicus, sp. 



126 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



Influence of the Vagi upon the Blood-vessels of the Stomach. 

Effect of Division and Irritation of the Nerves, 
(a.) During Digestion. 

Experiment XXIV. — Eabbit two months old. Three hours after food was 
given the vagi were exposed, and the trachea opened in order to prevent 
asphyxia and consequent struggling. The abdomen was opened, and the 
stomach found to be largely distended with food, and its outer surface very 
vascular. Intestines were moderately vascular. The stomach was then opened 
by an incision extending from right to left along its anterior surface, and its 
contents partially everted. The lining membrane was of a dusky red hue. The 
vagi were divided in the neck four minutes after the exposure of the gastric 
mucous membrane. Pallor of the membrane followed immediately upon the divi- 
sion of the nerves, and remained during the time occupied by the rest of the 
experiment — forty-five minutes. The superior cardiac branches of the vagi 
(depressor nerves) were then divided ; the result was a slight increase in the 
pallor of the mucous membrane. 

The effects of irritating the vagi were now attended to. The irritant used 
was Faradic Electricity from Du Bois Keymond's machine, with 1 Smee's cell. 



Time after Division 
of Vagi. 


Distance of Primary from 

Secondary Coil of Machine 

in Millimetres. 


Nerve Stimulated. 


Result as regards redness of 
Gastric Mucous Membrane. 


10' 


230 


Upper end left vagus. 


No evident change. 


12' 


180 


Upper end left vagus. 


Became redder. 


13' 


10 milligrammes atr 


opiae sulph.* given to paralyse cardio-inhibitory fibres 






of vagus. 




15' 


180 


Lower end left vagus. 


No evident change. 


21' 


120 


Upper end right vagus. 


Pallor followed by slight 
redness. 


25' 


80 


Upper end right vagus. 


Pallor. 


34' 


70 


Lower end right vagus. 


No evident change. 


44' 


70 


Lower end left vagus. 


No evident change. 



Experiment XXV. — Full-grown strong rabbit fed two and a half hours 
before the experiment was begun. Abdomen opened ; stomach and intestines 
very vascular. Division of the vagi was followed by decidedly diminished 
vascularity of the outer surface of the stomach which was in this case unopened. 
Owing to an interruption the experiment was not carried beyond this point. 



Although this substance paralyses the eanfoo-inhibitory, it does not paralyse the waso-inhibitory 



nerves. 



UPON THE VASCULAR SYSTEM. 127 

Experiment XXVI. — Strong full-grown rabbit. Fed two hours before the 
experiment. The cavity of the stomach was not opened. When the superior 
cardiac branches'* of the vagi were divided, no evident change resulted in the 
vascularity of the stomach or intestines. On dividing the vagi the ivhole outer 
surface of the stomach became paler ; but no such change was observed in the 
mesentery or intestines. The vascular change in the stomach was permanent. 

The upper ends of both vagi were then repeatedly stimulated, with variable 
results. Sometimes the surface of the stomach became paler, at other times 
redder. Irritation of the lower ends of the nerves produced no effect. 

Experiment XXVII. — Rabbit ; fed an hour before the vagi were divided. 
The outer surface of the stomach was not apparently so vascular as in the three 
former cases. Division of the vagi produced no evident change on the gastric 
vessels. 

Experiment XXVIII. — A cat fed on milk an hour previous to division of 
the vagi. On section of these nerves the vascularity of the outer surface of the 
stomach instantly became greatly diminished, and remained so. 

(b.) Section of the Vagi during Fasting. 

Experiment XXIX. — Full-grown rabbit which had fasted for twelve hours. 
Outer surface of stomach pale. Division of depressor nerves produced no 
evident change in gastric or intestinal vessels. Division of both vagi likewise 
produced no evident change in gastric or intestinal vessels. Irritation of upper 
end of right vagus (1 Smee, secondary 200 mm. distant from primary coil) 
caused slight reddening of outer surface of stomach, no change on intestinal 
vascularity. This observation was repeated with a stronger current (secondary 
coil at 150). A slight increase in the pallor of the stomach was the immediate 
result, but this yielded during the continuance of the irritation to distinct red- 
dening of the gastric wall. The irritation was continued for twenty seconds. 
Anaesthesia was then produced by means of chloroform in order to get rid of 
the effects of the irritant upon the sensory nerve centres. The upper end of 
the right vagus was then stimulated (secondary coil at 100). Slight but distinct 
increase in the gastric vascularity at once ensued. Irritation of the upper end 
of the left nerve yielded the same result. Irritation of the lower ends of the 
nerves caused no change. 

Experiment XXX. — Full-grown rabbit which had fasted for fourteen hours. 
Division of the nervi depressores and vagi produced no evident change on the 
vascularity of the outer wall of the stomach or of the intestines, which both 
before and after the division were but slightly vascular. 

* These nerves produce dilatation of abdominal blood-vessels. 
VOL. XXVI. PART I. 2 L 



128 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



Time after Division 
of Vagi. 


Distance of Primary from 

Secondary Coil of Induction 

Machine. 


Nerve Stimulated. 


Result as regards Gastric 
Vascularity. 




mm. 






7' 


200 


Upper end of right vagus 
irritated for 30". 


Slight reddening. 


12' 


150 


Upper end of right vagus 


Pallor succeeded by well- 






irritated for 30". 


marked redness. 


15' 


120 


Upper end of right vagus 
irritated for 15". 


The same result. 




Chloroform was now given until complete anaesthesia resulted. 


20' 


120 


Upper end of right vagus 


Slight increase of pallor suc- 






irritated for 30". 


ceeded by well-marked 
redness. 


24' 


80 


Upper end of right vagus 


The same result. 






irritated for 30". 





Experiment XXXI. — Cat which had fasted for sixteen hours. The blood- 
vessels of the outer surface of the stomach were small and contracted. Division 
of the nervi depressores and vagi produced no apparent change in the vascu- 
larity of the stomach or intestines. Irritation of the upper end of the vagus 
caused tolerably distinct blushing of the gastric wall. 

The general result of the experiments just given is, that section of the vagi 
produces no change in the gastric blood-vessels if these be not in a dilated con- 
dition, such, e.g., as obtains during digestion, while division of these nerves 
during dilatation of the gastric vessels is generally followed by marked and 
permanent contraction of these vessels. It is true that this result did not occur 
in one (experiment xxvii) of the five experiments in which the nerves were 
divided during digestion. In that case, however, it was quite evident that the 
gastric vessels were not so dilated as they usually are ; but, of course, such a 
statement is not without fallacy, seeing that every case cannot be identical as 
regards the vascular dilatation that obtains during digestion. I am not, there- 
fore, prepared to give any decided opinion regarding the results of experiment 
xxvii ; but it seems clear that the general result of the effects of division of the 
vagi supports the idea that, during digestion, vaso-inhibitory influences pass in 
a centripetal direction through the vagi. The effects of irritating the cut ends 
of the nerves were various. It is certain that no evident change in the vascu- 
larity was ever produced by stimulating the lower ends of the nerves, so we 
may safely say that the influences which pass through the nerves to control the 
gastric vessels certainly do not pass in a centrifugal direction. When the upper 
ends of the nerves were subjected to sufficiently powerful stimulation, pallor of 
the gastric wall sometimes followed, at other times blushing ; frequently the 
blushing succeeded the pallor, and sometimes no perceptible effect resulted. 



UPON THE VASCULAR SYSTEM. 129 

These results receive a feasible explanation by the supposition that the vagus, 
like other mixed nerves, contain fibres which excite, and those which inhibit 
contraction of the vessels. Because the vagus is a mixed nerve, the results 
of its division must obviously be more trustworthy than the results of its 
stimulation. We cannot suppose that while during digestion influences pass 
from the stomach through the vagi to inhibit the gastric vessels, there are 
also influences travelling from the same source which produce an opposite 
effect ; and, therefore, we may expect that when we divide these nerves 
during the dilatation of vessels which obtains during digestion, we shall simply 
stop the transit of those vaso-inhibitory influences from the stomach, hence 
the division of such nerves is a much simpler case than artificial stimulation, 
seeing that during such stimulation we must throw into play fibres whose 
functions are antagonistic. 

Seeing that the experiments just given show what are the evident changes 
in the gastric vessels that follow stimulation of the vagi, it is convenient to give 
here results of experiments which show the effect of this stimulation upon the 
arterial blood-pressure. 

Effect upon the Arterial Blood-Pressure which follows Stimulation of 
the Vagus after its section in the Cervical Region. 

(a.) Stimulation of the Lower End of the Nerve. 

If the lower end of the vagus be stimulated by a sufficiently powerful cur- 
rent, the heart's action is retarded, the work done by that organ is diminished, 
and in consequence the arterial blood- 
pressure falls. The following tracing by 
Ludwig's Kymograph from the carotid 
artery of a rabbit affords a good illustra- 
tion of the above fact. The tracing must 
be read from right to left. The vertical 
lines have been added to show when the 
vagus was at rest and when it was stimu- A %^niatJtf^ Bef ° re ~ 

lated. The portion of the tracing between 

the two lines shows the influence of the cardio-inhibitory fibres of the vagus 
upon the heart. 

The above trace shows the influence of the vagus upon the heart, but it con- 
tains no indication as to whether or not the vagus contains vasomotor fibres. 
This fact can only be ascertained by stimulating the nerve after its influence 
over the heart has been got rid of. I accordingly paralysed the cardio-inhibi- 
tory fibres by sulphate of atropia, and then stimulated the lower end of the 
nerve as before. The results were various. If the animal were not paralysed 




130 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



by curara, a slight rise in the blood-pressure frequently resulted from the 
stimulation. Such a result is shown in the following tracing from a rabbit. 



Fig. 3. 



During — Before— 

Stimulation of the Vagus * 

A change similar to the above is, however, by no means the rule even in the 
same animal. The following tracing shows no change in the blood-pressure 
during stimulation of the vagus, although it was taken shortly after the fore- 
going from the same animal, and although the lower end of the same vagus was 
stimulated by a current of the same strength. 

Fig. 4. 



During — 



Before- 



Stimulation of the Vagus. 



This tracing represents what I always found when the atropised vagus was 
stimulated in cases where the influence of extraneous movements upon the 
blood-pressure had been got rid of by means of curara paralysis. We may, 
therefore, say, that the vagus certainly contains no vasomotor-nerve fibres 
which act in a centrifugal direction, for if it did, stimulation of the nerve 
after palsy of its cardio-inhibitory fibres would always raise the blood-pressure 
whether curara be given or not. 

(b.) Stimulation of the Upper End of the Nerve. 

Already much has been written with regard to the changes in the blood- 
pressure which result from stimulating the upper end of the vagus after it has 
been cut across in the cervical region. According to DRESCHFELDt such stimu- 

* In reading tracings taken by such an instrument as Ludwig's Kymograph, it is necessary to 
remember that the vertical variations in the mercurial column are always the double of what the tracing 
indicates, because the tracing shows the movements of a column of mercury in a U-shaped tube. 

t Von Bbzold's Untersuchungen, 1867, p. 326. 



UPON THE VASCULAR SYSTEM. 131 

lation always raises the blood-pressure, but if the cerebrum be removed, 
or if it be paralysed by morphia, vagus stimulation always lowers the 
pressure. 

This is simply untrue. Stimulation of the nerve may increase or lower the 
pressure whether morphia narcotism be induced or not. Since I performed 
my experiments on this subject, Kowalewsky and Adamuk,* Aujbert and 
RoEVERt have published the results of their researches regarding this question, 
and I am glad to say that these exactly agree with what I had previously found. 
Seeing that these authors have already published results similar to mine, I 
need not do more than briefly say, that when the upper end of the vagus is 
stimulated, the respiration is very apt, more especially in rabbits, to come to a 
stand-still. As a result of this, carbonic acid accumulates and oxygen diminishes 
in the blood, thereby bringing about a condition of that fluid which acts as an 
irritant to the vasomotor centre in the medulla, and increases the tonicity of 
the blood-vessels so that the blood-pressure is raised. This source of fallacy 
must be guarded against by using artificial respiration. Struggling, too, is apt 
to result from stimulation of the upper end of the vagus, to guard against which 
we may narcotise the animal by means of opium, or may produce paralysis by 
curara. When we give opium or curara and then stimulate the nerve, a rise in 
the blood-pressure is not so frequently observed as when the nerve is stimulated 
before these poisons are administered; obviously because extraneous convulsive 
movements have been got rid of. However, whether we give these toxic agents 
or not, stimulation of the upper end of the vagus in rabbits and cats (where the 
depressor nerve is a separate branch) may be followed by increase or by 
diminution of the blood-pressure, most frequently the latter. I have often ob- 
served that in the same animal a rise or fall of the blood-pressure may be 
obtained by using for the production of the latter a more powerful stimulus than 
that which may have been found sufficient to produce the former. The explana- 
tion of this seems to be, that in the case of the vessels, as in that of the heart, 
a weaker stimulus suffices to throw the excito-motor nerves into action than is 
necessary to cause the inhibitory nerves to produce their effect. The following 
tracings illustrate the results of stimulating the upper end of the vagus. They 
must be read from left to right. 

The fibres in the vagus, then, which influence blood-vessels, all convey in- 
fluences towards the medulla oblongata, and these fibres appear to be both 
vaso-inhibitory and excito-vasomotor, the former causing dilatation of blood- 
vessels and consequent lowering of the blood-pressure (fig. 5), the latter caus- 
ing contraction of blood-vessels and consequent increase of the blood-pressure 
(fig. 6). Doubtless the influences which travel through these two kinds of 

* Centralblatt, 1868, p. 546. + Ibid. p. 578. 

VOL. XXVI. PART I. 2 M 



132 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



nerve-fibres start from the parts to which the vagus is distributed, principally 
therefore, from the stomach and lungs. 

Fig ' iS;7 Fa11 in . bl , ood :P res ! u f e on irritating upper end of vagus in a rabbit (both vagi divided) to which 10 milli 
grammes of atiopia sulphate had been given. (Secondary 30 mm. distant from^prinSry coil One Danlell) 




Before — 



Stimulation of the Vagus. 



During- 



FIg ' !^ R i Se ^ blood -P r 1 essure / On irritating upper end of vagus in the same rabbit as that from which the fore- 
going tracing was taken. (Secondary 120 mm. distant from primary coil. One Daniel].) 




Befbre- 



Stimulation of the Va^us. 



During- 



Having seen what are the effects upon gastric blood-vessels of division and 
stimulation of the vagi, and also the changes which the latter gives rise to as 
regards the blood-pressure, we shall now consider the effect of division of the 
nerves as regards the blood-pressure. The experiments on each class of animals 
are divided into two groups : 1st, those showing the effect of dividing the nerves 
during digestion, and those showing the effect of this during fasting. The 
main object of the whole being to ascertain whether or not during the former, 
vaso-inhibitory influences are transmitted from the stomach through the vagi to 
dimmish the action of the vasomotor nerves ruling over the gastric blood- 
vessels, and thereby to bring about dilatation of these. While this is the main 
point of the experiments, they at the same time furnish data which serve to 
explain the acceleration of the pulse which sometimes follows division of the 
vagi after paralysis of their cardio-inhibitory fibres (see page 122). 



UPON THE VASCULAR SYSTEM. 



133 



Experiments showing the Effect of Division of the Vagi upon the Blood- 
Pressure and Frequency of the Pulse in Animals during Digestion, 
and during fasting. 

A. EXPERIMENTS ON DOGS. 

(a.) During Digestion. 

Cardio-inhibitory Nerves paralysed by Atropia. 

EXPERIMENT XXXII. — Reteiever Puppy about Three Months old, fed Three hours 

BEFORE THE EXPERIMENT. CANULA IN CAROTID ARTERY. TRACHEA OPEN. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


4-51' 


34 


4-5 


- 


59' 30" 






3 milligrammes atrop. sulph. in- 
jected into vein. 


5-0' 15" 


46 


47 




5' 


46 


4-7 




12' 






Both vagi divided. 


16' 


52 


5-9 




21' 


50 


6-1 




27' 


50 


5-9 




33' 


54 


63 




34' 






Cardio-inhibitory nerves found to 
be completely paralysed. 



Result. — Increase of pressure and acceleration of pulse after division of vagi. 

EXPERIMENT XXXIII.— A Terrier Dog, fed at 1.30 p.m. Canula in Carotid 

Artery. Trachea open. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


332' 20" 


30 


5.7 




50" 


30 


5-7 




37' 






1 milligramme atrop. sulph. injected 
into vein. 


38' 15" 


56 


6-6 




40' 


62 


6-7 




45' 


56 


6-7 


Vagi not paralysed. 


55" 


56 


6-2 




50' 






1 milligramme atrop. sulphate given. 


20" 


56 


6-2 




53' 50" 






Both vagi divided. 


55' 


62 


74 




35" 


60 


7-6 




58' 55" 


54 


7 




59' 15" 






Cardio-inhibitory nerves found to 








be quite paralysed. 



Result. — Permanent increase of pressure, and temporary acceleration of 
pulse after division of vagi. 



134 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



EXPERIMENT XXXIV. — A Strong Retriever Dog, fed Two hours before the 

EXPERIMENT. CANULA IN CAROTID. TRACHEA OPEN. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


12-14' 


32 


6 




17' 


32 


6 




23' 






2 milligrammes atrop. sulph. in- 
jected into vein. 


25' 


28 


4-8 




27' 


30 


5 




31' 30" 


30 


5-4 


Vagi not quite paralysed. 


32' 






1 milligramme atrop. sulph. given. 


30" 


42 


4-1 




35' 


36 


4-8 




36' 


32 


4-8 




38' 30" 


35 


5 




43' 






Both vagi divided. 


50' 


38 


6-4 




52' 


35 


6-8 




1- 3' 


34 


6-7 




4' 






Cardio-inhibitory nerves still para- 
lysed. 



Result. — Permanent increase of pressure, and temporary acceleration of 
pulse after division of vagi. 

EXPERIMENT XXXV— Small Dog Fed at One o'Clock. Canula in Carotid. 

Trachea open. 



Time. 


Pulse in 15" 


Mean Pressure in inches 
ofHg. 


General Notes. 


5-49' 


30 


5 




50' 






2 milligrammes atropia sulphate 
injected into vein. 


40" 


70 


5-8 




53" 


66 


5-4 




54' 10" 


66 


5 


Both vagi divided. 


40" 








56' 


64 


9-1 




59' 


60 


7-9 




6- 2' 


56 


6-4 




5' 


56 


6-5 




10' 


53 


6-6 





Result. — Increase of pressure after division of vagi. The frequency of the 
pulse was diminished ; but it is doubtful whether or not a similar decrease 
would not have taken place had the vagi remained intact. When the pulse un- 
dergoes a great increase in frequency on the administration of atropia, as in the 
present instance, a steady decrease almost always sets in shortly afterwards. 



UPON THE VASCULAR SYSTEM. 



135 



(b.) During Fasting. 

1. Cardio-inliibitory Nerves Paralysed by Atropia. 

EXPERIMENT XXXVI. — A Strong Retriever Dog which had Fasted for Seventeen 
Hours. Canula in Femoral Artery. Trachea open. 3 Milligrammes Atropia 
Sulphate Injected into Vein at 10-10 a.m. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


10-15' 


33 


6 




16' 


33 


6 




18' 


33 


6-4 




20' 






Both vagi divided. 


23' 30" 


34 


6-4 




45" 


33 


6-6 




24' 10" 


33 


6-3 




40" 


34 


6 




26' 


33 


6-4 




27' 


32 


63 




28' 


34 


6 




30" 






Cardio-inliibitory nerves found to 
be completely paralysed. 



Result. — Division of vagi, followed by no change in blood-pressure, or fre- 
quency of pulse. 



EXPERIMENT XXXVII. — Terrier which had Fasted for Eighteen Hours. Canula in 

Carotid Artery. Trachea open. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


11-46' 


30 


5 




51' 


31 


5-3 




52' 






2 milligrammes atropia sulphate 
injected into vein. 


57' 


50 


5-5 


Both vagi divided. 


58' 








59' 39" 


49 


5-4 




12- 2' 


48 


5-5 




8' 


46 


5-2 


Cardio-inhibitory nerves ascer- 


8' 30" 






tained to be paralysed. 



Result. — Division of vagi, followed by no change in blood-pressure or fre- 
quency of pulse. 

VOL. XXVI. PART I. 2 N 



136 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



EXPERIMENT XXXVIIL— Strong Retriever Dog which had Fasted for Seventeen 
Hours. Trachea open. Canula in Femoral Artery. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


1223' 


28 


53 


Animal sobbing. 


25' 20" 


24 


5-4 


Animal sobbing. 


40" 






3 milligrammes atropia sulpbate 
injected into vein. 


26' 50" 


28 


5-4 


The animal is now quiet. 


49' 20" 


27 


5-2 




51' 45" 






Botb vagi divided. 


56' 10" 


22 


5-9 




58' 


22 


6 




1- 1'40" 


20 


5-6 




6' 


22 


6 




16' 


22 


5-9 




17' 






Cardio-inhibitory nerves still para- 
lysed. 



Result. — Division of vagi, followed by increased blood-pressure and dimin- 
ished frequency of the pulse. 

TABLE II. — General Results of the Foregoing Experiments on Dogs. 



No. of Experiment. 


Vagi divided during 


Blood-Pressure. 


Pulse. 


XXXII. 


Digestion. 


Increased. 


Accelerated. 


XXXIII. 


n 


>> 


Unaltered. 


XXXIV. 


» 


n 


ii 


XXXV. 


» 


>) 


» 


XXXVI. 


Fasting. 


Unaltered. 


>> 


XXXVII. 


>> 


» 


ii 


XXXVIII. 


>) 


Slightly increased. 


Retarded. 


In all tbese experiments tbe cardio-inhibitory nerves were paralysed previous to the division 


of tbe 


vagi. 





When these experiments were performed, I was too much influenced by the 
fact that Ludwig and Cyon * had always failed to find the depressor nerve 
in action ; I therefore fancied that although it is impossible to divide the vagi 
in dogs without at the same time dividing the nervi-depressores, such experi- 
ments might nevertheless serve to show whether or not the gastric and vaso- 
inhibitory fibres of the vagi are thrown into action during digestion. But, on 
several occasions in experimenting on rabbits and cats, I have, as before stated 
(see page 109), had the good fortune to find the nervi-depressores in action — as 
shown by the rise in the blood-pressure which followed their section. I am 
therefore convinced that the depressor branches of the vagus are by no 

* Lib. cit. 



UPON THE VASCULAR SYSTEM. 



137 



means so inactive as their discoverers have concluded, from the small number 
of experiments performed by them. Seeing, therefore, that these nerves are 
not unfrequently in action, and seeing that in the dog, as above stated, the 
trunks of the vagi cannot be divided without at the same time cutting across 
the depressor nerves, I am compelled to admit that, in the group of experiments 
on dogs just given, the increased blood-pressure which followed section of the 
vagi may have resulted from section of the depressor nerves, and from these 
only. The question at issue must therefore be decided by experiments on cats 
and rabbits, seeing that in these animals the superior cardiac branch (depressor 
nerve) leaves the vagus high in the neck, and can therefore be divided sepa- 
rately from the trunk of the latter.* If, however, the results of the foregoing 
experiments on dogs were due to the action of the depressor nerves, then we 
should require to adopt the conclusion that these nerves act during digestion, 
and are inactive during fasting. Such a conclusion is opposed by the results of 
experiments on rabbits and cats, which are yet to be detailed. There is no 
evidence whatever that the depressor nerve acts more during digestion than 
during fasting ; and therefore, after all, these experiments on dogs really do 
support the idea that during digestion vaso-inhibitory fibres, distinct from the 
" depressor " nerve fibres, in the vagus are thrown in action. 

The following experiments on rabbits and cats are, however, entirely free 
from the source of fallacy that obtains in the case of dogs, because in the 
former animals the nervi-depressores can be divided without the vagi being at 
the same time implicated. 



B. EXPERIMENTS ON EABBITS AND CATS, 
(a.) During Digestion. 

Carclio-inhibitory Nerves paralysed by Atropia. 

EXPEBIMENT XXXIX. — Strong Babbit fed at 2 p.m. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


3-57' 


44 


4 




59' 






10 milligrammes atropiae sulph. 
injected into vein. 


30" 


44 


4-5 




4" 1' 






Both depressors divided. 


30" 


40 


4-4 




2' 






Both vagi divided. 


3' 


39 


5-5 




4' 15" 


38 


5-3 




6' 20" 


38 


5-2 




10' 


39 


53 





* The reader -will now understand why remarks on the blood-pressure were omitted from the 
commentary on the first group of experiments on dogs (see page 122). 



138 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



Result. — Division of vagi followed by increased pressure, but no change in 
frequency of pulse. 



EXPERIMENT XL. — A Strong Eabbit, which had Fasted foe Twelve Hours, was Fed 
at 1-30 p.m. Canula in Carotid. Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


3- 5' 


38 


35 




6' 


38 


3-4 




8' 


39 


3-55 


Both depressors divided. 


9' 






10 milligrammes atropia sulphate 
injected into vein. 


10' 20" 


42 


35 




11' 40" 






Right vagus divided. 


12' 20" 


41 


37 




14' 






Left vagus divided. 


16' 


46 


4-2 




19' 10" 


45 


4-4 




21' 15" 


44 


43 




22' 






Cardio-inhibitory nerves still para- 
lysed. 



Result. — Division of vagi followed by increased pressure and acceleration of 
pulse. 



EXPERIMENT XLI. — A Strong Rabbit fed at 1 p.m. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


3-19' 


42 


33 




20' 


43 


34 




24' 






10 milligrammes atropia sulphate 
injected into vein. 


3-25' 


52 


35 




26' 10" 






Both depressors divided. 


27' 40" 


47 


4-1 




28' 30" 


45 


4 




29' 25" 






Right vagus divided. 


31' 


46 


4-2 




32' 5" 






Left vagus divided. 


34' 


50 


4-8 




35' 


52 


4-7 




38' 15" 


51 


4-8 




40' 35" 


50 


4-9 





Result. — Increase of pressure and acceleration of pulse following division of 



vagi. 



UPON THE VASCULAR SYSTEM. 



139 



EXPERIMENT XLII. — Strong Rabbit, fed at 10 a.m. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


12- 2' 


36 


3-6 




4' 5" 


37 


3-6 




5' 






9 milligrammes atropise sulph. in- 
jected into vein. 


30" 


50 


3-8 




6' 15" 


46 


3'8 




7' 35" 


44 


36 




8' 15" 


43 


3-7 




9' 






Both depressors divided. 


10' 25" 


42 


36 




11' 40" 


41 


37 




13' 






Right vagus divided. 


14' 10" 


40 


36 




15' 20" 






Left vagus divided. 


17' 30" 


50 


4-9 




18' 15" 


51 


5 




40" 






Cardio-inhibitory nerves proved to 
be paralysed. 


20' 10" 


49 


4-8 




22' 


47 


4-7 




24' 5" 


47 


4-8 





Result. — Division of vagi, followed by increased pressure and accelerated 
pulse. 

EXPERIMENT XLIII. — Strong Rabbit, eed at 10.30 a.m. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


1-15' 


41 


4-1 




16' 10" 


42 


3-9 




17' 15" 


41 


3-9 




18' 5" 






10 milligrammes atropia sulphate 
injected into vein. 


55" 


58 


4-2 




20' 


54 


4 




22' 8" 


52 


4-1 




23' 15" 


53 


4 




24' 5" 






Both depressors divided. 


25' 30" 


52 


4-1 




26' 5" 


50 


3-9 




27' 






Both vagi divided. 


28' 30" 


54 


5-2 




30' 


55 


5 




34' 


54 


4-9 




37' 1" 


55 


4-9 





VOL. XXVI. PART I. 



2 



140 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



Result. — Division of vagi, followed by decided rise in pressure and slight 
acceleration of pulse. 



EXPERIMENT XLIV. — Strong Rabbit fed at 1.5 p.m. Canula in Carotid. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


2-56' 


34 


32 




57' 5" 


34 


31 




58' 






10 milligrammes atropia sulphate 
given. 


59' 30" 


58 


34 




3- 2' 


56 


34 




4' 5" 


54 


3 3 




5' 10" 






Both vagi divided. 


6' 20'/ 


52 


45 




7' 40" 


50 


4-4 




10' 


45 


46 




12' 


44 


4-5 




13' 10" 






Both depressors divided. 


50" 


45 


4-9 




15' 


44 


4-8 




19' 45" 


42 


4' 8 





Result. — Division of vagi, followed by increase of pressure and retardation of 
pulse. Division of nervi-depressores, followed by increased pressure, but by 
no change in pulse. 

The rise in the pressure observed in this group of experiments was certainly 
not due to any voluntary muscular movements on the part of the animal. In 
all cases, none of the recorded observations were made during struggling or 
other violent movements, unless it is so stated in the General Notes. In order, 
however, to satisfy all that this increase of blood-pressure is really due to a 
change in the state of the vascular system not dependent upon extraneous 
muscles, I performed the following experiment, in which, in addition to the 
atropine, I gave curara, in order to paralyse all voluntary movement. 



UPON THE VASCULAR SYSTEM. 



141 



EXPEEIMENT XLV. — Strong Eabbit Fed at 11 a.m. Canula in Carotid Artery. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


1-28' 






8 milligrammes atropia sulphate 
injected into vein. 


35' 


46 


3 




37' 


44 


2-75 




44' 






2 milligrammes curara injected into 
vein. 


47' 


44 


2-8 




48' 30" 


41 


2-7 




49' 






Both depressors divided. 


51' 


42 


2-8 




52' 10" 






Eight vagus divided. 


53' 


43 


3 




30" 






Left vagus divided. 


54' 20" 


42 


4-2 




55' 40" 


41 


4-1 




57' 


40 


4-2 




59' 10" 


43 


4-3 




2- 2' 


40 


4-1 


Cardio-inhibitory nerves still para- 
lysed. 



Result. — Division of vagi followed by rise in bloocl-pressure, but by no change 
in frequency of pulse. The animal having been paralysed by curara as well as 
by atropine, this rise in pressure cannot be ascribed to anything but a change 
within the vascular system independent of extraneous muscular movements. 

EXPEEIMENT XLVL— A Full-Sized Cat Fed at 2.20 p.m. Canula in Cakotid. 

Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


4-40' 


30 


4-5 




45' 






5 milligrammes atrop. sulph. injected 
into vein. 


30" 


38 


4 




47' 






Both depressors and cervical sym- 
pathetica divided.* 


48' 


36 


5-1 




49' 30" 


36 


5-1 




52' 






Both vagi divided. 


53' 


39 


6-4 




58' 


39 


6-3 




5- no" 


38 


6-2 




4' 


39 


6-4 




5' 30" 






Cardio-inhibitory nerves still para- 
lysed. 



* In the cat the depressor nerve usually joins the trunk of the sympathetic soon after leaving 
the vagus in the upper part of the neck. It is, therefore, most convenient to divide both sympathetic 
and depressor. 



142 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS. 



Result. — Division of vagi and depressors followed by increased blood- 
pressure ; but no change in the frequency of the pulse. 

(b.) During Fasting. 

EXPERIMENT XLVII. — Strong Rabbit which had Fasted foe Eighteen Hours. Canula 

in Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean Pressure in inches 
ofHg. 


General Notes. 


12-28' 


38 


4 




30' 


38 


4 




32' 






8 milligrammes atropia sulphate 
injected into vein. 


35' 


57 


36 




36' 


55 


4-2 




37' 






Both nervi-depressores divided. 


30" 


54 


4-3 




38' 






Right vagus divided. 


45" 


53 


4-2 




40' 


51 


41 




41' 






Left vagus divided. 


42' 


50 


4 




44' 


49 


3-9 




45' 


50 


3-9 





Result. — Division of vagi followed by no change in pressure or pulse. 



EXPERIMENT XLVIIL— Rabbit which had Fasted for Eight Hours and a Half. 
Canula in Carotid Artery. Tra.chea open. 



Time. 


Pulse in 15". 


Mean Pressure in inches 
ofHg. 


General Notes. 


4-54' 


48 


3-8 




56' 


50 


4 




5-10' 






9 milligrammes atropia sulphate 
injected into vein. 


13' 


74 


3-8 




15' 


76 


3-6 




18' 


74 


3-5 




30" 






Both depressors divided. 


20' 


75 


3-5 




21' 






Both vagi divided. 


27' 


77 


34 




30' 


74 


3-5 




32' 


70 


3-6 




34' 10" 


68 


3-4 





Result— Division of vagi followed by no change in pressure or pulse. 



UPON THE VASCULAR SYSTEM. 



143 



EXPERIMENT XLIX. — Strong Rabbit which had fasted foe nine hours. Canula in 

Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean pressure in inches 
ofHg. 


General Notes. 


3-58' 


40 


3-9 




4- 4' 


41 


4-2 




5' 






10 milligrammes atropia sulphate 
injected into vein. 


r is" 


54 


37 




8' 20" 


52 


3-9 




9' 30" 






Both depressors divided. 


11' 15" 


51 


38 




13' 






Both vagi divided. 


14' 45" 


58 


3-7 




16' 20" 


49 


3-8 




19' 


48 


3-8 





Result. — No change in pressure or pulse followed division of vagi. 



EXPERIMENT L. — Strong Old Rabbit which had fasted for sixteen hours. Canula in 

Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean pressure in inches 
ofHg. 


General Notes. 


11-30' 25" 


48 


4-5 




32' 


47 


4-4 




33' 




- 


10 milligrammes atropia sulphate 
given. 


34' 


49 


4-5 




36' 18" 


48 


4-6 




37' 






Both depressors divided. 


39' 15" 


47 


4-8 




41' 






Right vagus divided. 


42' 35" 


48 


4-7 




45' 






Left vagus divided. 


48' 20" 


47 


4-8 




50' 


48 


4-7 




54' 5" 


48 


45 




57' 


46 


4-6 





Result. — Division of vagi followed by no change in pressure or pulse. 



VOL. XXVI. PART I. 



2 p 



144 



DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 



EXPERIMENT LI. — Strong Rabbit which had fasted for eighteen hours. Canula in 

Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean pressure in inches 
ofHg. 


General Notes. 


4- 6' 


44 


4-5 




8' 






8 milligrammes atropia sulphate 
given. 


9' 30" 


46 


4-6 




11' 45" 


47 


4-5 




12' 






Both depressors divided. 


13' 15" 


50 


5-8 




14' 5" 


49 


5-6 




16' 






Blood coagulated. Canula cleaned. 


20' 


45 


52 




21' 20" 






Both vagi divided. 


24' 


46 


5'2 




28' 


45 


5-2 




30' 


46 


53 





Result. — Section of vagi followed by no change in pulse or pressure. Sec- 
tion of superior cardiac branches of vagi followed by increased pressure and 
temporary acceleration of pulse. 



EXPERIMENT LII. — Strong Rabbit which had fasted for twelve hours. Canula in 

Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean pressure in inches 
ofHg. 


General Notes. 


3-35' 


40 


3-8 




36' 






8 milligrammes atropia sulphate 
given. 


30" 


50 


3-5 




38' 


50 


37 




40' 






Both depressors divided. 


45" 


49 


36 




43' 


50 


37 




44' 






Both vagi divided. 


45' 


54 


4d 




46' 20" 


52 


39 




49' 10" 


50 


3-7 




53' 


48 


3-8 





fi esu lt. — Division of vagi followed by a transient rise in pressure and pulse. 
This was probably due to excitement, seeing that it soon disappeared. 



UPON THE VASCULAR SYSTEM. 



145 



EXPERIMENT LTII. — A Large Strong Cat which had fasted for thirteen houbs. 
Canula in Carotid Artery. Trachea open. 



Time. 


Pulse in 10". 


Mean pressure in inches 
ofHg. 


General Notes. 


9-20' 


32 


36 




22' 


33 


35 




23' 






5 milligrammes atropia sulphate 
given. 


30" 


40 


3-7 




25' 


41 


3-8 




28' 






Both depressors and cervical sym- 
pathetics divided.* 


29' 30" 


40 


3-7 




32' 






Both vagi divided. 


33' 25" 


38 


3-8 




35' 15" 


39 


3-9 




38' 


37 


3-8 




40' 5" 


38 


39 





Result— Division of vagi followed by no noteworthy change in pulse or 
pressure. 

The general result of the foregoing experiments on rabbits and cats may be 
learned from the following table. 



TABLE III. — General Results of the Foregoing Experiments on Rabbits and Cats. 



No. of Experiment. 


Nature of Animal. 


Vagi divided during 


Blood-Pressure. 


Pulse. 


XL. 


Rabbit. 


Digestion. 


Increased. 


Accelerated. 


XLI. 


» 


3) 


i' 


5) 


XLII. 


» 


» 


)> 


J! 


XLIII. 


)> 


1> 


»! 


)> 


XLIV. 


)> 


» 


)) 


Retarded. 


XXXIX. 


>> 


)) 


!> 


Unchanged. 


XLV. 


)> 


)) 


»J 


5) 


XLVI. 


Cat. 


!> 


>} 


5) 


XLVII. 


Rabbit. 


Fasting. 


Unchanged. 


!> 


XLVIII. 


>) 


>) 


)> 


J> 


XLIX. 


)! 


j) 


)5 


)) 


L 












)> 


>> 


)) 


J) 


LI. 


J) 


!) 


>! 


5> 


LII. 


)) 


>> 


)> 


)> 


LIU. 


Cat. 


" 


55 


»> 


In all these experiments the cardio-in" 


libitory nerves were 
of the vagi. 


paralysed previous 


to the division 



See note to Experiment XLVI. 



146 DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS 

These experiments (XXXIX.-LIII. inclusive) show, — 

1st. That in rabbits division of the vagi may be followed by increased blood- 
pressure and accelerated pulse, although the cardio- inhibitory nerves are 
paralysed, and therefore totally inactive before the division of the nerves. 

2d. In experiments XXXIX., XLV., XLVL, the pulse was unaffected by 
the section : in experiment XLIV. it was retarded, and, notwithstanding, the 
blood-pressure was increased in all these cases. A rise in the blood-pressure 
following division of vagi may therefore be quite independent of the heart. 

3d. The blood-pressure was unaffected when the vagi were divided during 
fasting, while it rose after their section during digestion. When we remember 
that when the vagi are divided during digestion a permanent blanching of the 
stomach takes place (see p. 126), it is evident that the rise in pressure in the 
experiments under consideration must be ascribed to contraction of gastric 
vessels chiefly if not entirely. It therefore appears that the increased blood- 
tension which frequently follows division of the vagi cannot — as has hitherto 
been supposed — be wholly ascribed to increased action of the heart liberated 
from its inhibitory nerves (see p. 120). Instead of depending only on one 
factor it really depends on two. Cessation in the action, 1st, of cardio-inhibi- 
tory ; and 2d, of vaso-inhibitory fibres of the vagi. 

4th. The evidence afforded by these experiments and those previously given 
(see page 126), shows that during digestion inhibitory influences pass from the 
stomach through the vagi to paralyse those vasomotor cells in the medulla 
which preside over the gastric blood-vessels. But during fasting, when the 
gastric blood-vessels are in a contracted state, both the vaso-inhibitory and 
excito-vasomotor fibres of the vagi are at rest. (Were the latter in an active 
state, a fall in the blood-pressure would follow division of the vagi during 
fasting). It appears, therefore, that although the vaso-inhibitory fibres of the 
vagus play an important part in dilating the gastric blood-vessels, the role 
assigned to the gastric excito-vasomotor fibres of the vagi is as yet unknown. 
Vasomotor nerve-cells appear, like their homologues the cells of the cardiac 
ganglia, to be continually evolving energy. By reason of this, they would 
constantly keep the blood-vessels in at least a semi-contracted state, were it not 
that their power of generating energy may be controlled by inhibitory nerves. 
These nerves appear to be brought into play by the tissues of a part when it 
demands a greater influx of blood, but when it has no such demand, it does not 
appear that the excito-vasomotor nerves are brought into action to increase the 
evolution of f jrce in the vasomotor nerve-cells, but it seems that in this case the 
tissues simply cease to excite vaso-inhibitory nerves. I am, therefore, inclined 
to think that these excito-vasomotor nerves discharge their functions on occasions 
much more extraordinary than those on which the vaso-inhibitory fibres operate ; 
but what those are must be left for future research to determine. 



UPON THE VASCULAR SYSTEM. 147 

5th. Although in all the experiments the pulse remained unchanged when 
the pressure underwent no alteration after division of the vagi, it was variously 
affected when the pressure was increased. In four cases (see Table III.) it was 
accelerated, in three it remained unchanged, while in one it was retarded. 
Seeing that the acceleration in these cases and in those previously given (see 
page 120) took place when the cardio-inhibitory nerves had been paralysed 
previous to the section of the vagi, it is certain that it could not be due to 
escape of the heart from control. To what cause, then, shall we ascribe it ? I 
can think of none other than a direct influence of the increased blood-pressure 
upon the lining membrane of the heart. It is now generally agreed that — as 
Ludwig and Trtry* pointed out — if the vagi have been previously divided, — 
that is, if the cardio-inhibitory nerves are not in operation, increased blood- 
pressure usually accelerates and very rarely retards the pulse.t The retardation 
is commonly the result of an extraordinary increase of the pressure. My expe- 
riments on this question have convinced me of the truth of the above, but I have, 
moreover, frequently noticed that a considerable rise in the blood-pressure may 
take place without causing any change in the rapidity of the heart's action. As 
these results are all illustrated in Table III., I therefore think that in the first 
five experiments there recorded, the acceleration and retardation of the pulse 
were due to the increased blood-pressure. Whether this be or be not the true 
explanation, it is certain that the acceleration of the pulse which so frequently 
follows section of the vagi, is not, as is generally supposed, dependent merely on 
escape of the heart from the influence of its controlling nerves, but depends on at 
least another cause — and that probably is — a rise in the blood-pressure. Seeing 
that such is the case, the amount of acceleration of the pulse which may follow 
division of the vagi, cannot any longer serve as an accurate index to show the 
extent to which the cardio-inhibitory fibres of the vagi may be in action previous 
to their section, indeed we have as yet no accurate test by means of which this 
may be ascertained. It has, indeed, been stated by Von Bezold, that a trust- 
worthy test is to be found in the action of atropia. Most of my experiments 
show that when sulphate of atropia is administered previous to division of the 
vagi, a varying degree of acceleration of the pulse almost always ensues. It 
has been said by the above-named author^ that this acceleration is entirely due 
to palsy of the cardio-inhibitory nerves — the heart simply attaining the speed 
which it would maintain but for the inhibitory action of these nerves. Von 
Bezold came to this conclusion from observing that atropia never accelerates 

* Wiener, Sitz. Berichte, 1864, Band 49. 

t Much, confusion has been produced by certain authors discussing the influence of the blood- 
pressure upon the cardiac movements without distinguishing between the influence of the pressure before 
and after section of the cardio-inhibitory nerves. 

% Von Bezold. Untersuchungen aus dem physiologischen Laboratorium. Wiirzburg, 1867, 
Erstes Heft. 

VOL. XXVI. PART I. 2 Q 



148 DR RUTHERFORD ON THE INFLUENCE OF THE VAGUS, ETC. 

the pulse if it be given after division of the vagi. Unhappily this is untrue. I 
have more than once noticed that if atropia sulphate be administered to rabbits 
and dogs after division of the vagi, a decided acceleration of the pulse was the 
result. For example — 

Experiment LIV. — I clivided the vagi of a rabbit, and after waiting five 
minutes, I counted the pulse and found it 228 in the minute. I then very 
slowly injected 50 milligrammes of atropia sulphate dissolved in one cubic centi- 
metre of water into the jugular vein. The speed of the pulse at once rose to 
258 in a minute. Ten minutes afterwards the pulse was 240 in the minute. I 
then gave another dose of 25 milligrammes atropia sulphate dissolved in half a 
cubic centimetre of water. The pulse very rapidly rose to 270. The blood- 
pressure was slightly diminished by these doses. It therefore appears that 
atropia may stimulate the cardio-motor nerve apparatus as well as paralyse the 
cardio-inhibitory nerves, and so we cannot trust this substance to indicate the 
times of action and inaction of the cardio-inhibitory nerves. 

Much that is obscure yet remains in connection with the innervation of 
vascular system, but I venture to think that the researches detailed in the 
foregoing communication clear away not a little fallacious dross from this 
matter, while they likewise fill up some important blanks, and thereby render 
more complete our knowledge of this complicated and recondite subject. 



Tr.ne.Koy Sue Idm' Vol XXVI 



Ui'Il Hani 









( 149 ) 



VIII. — On the Old River Terraces of the Earn and Teith, viewed in connection with 
certain Proofs of the Antiquity of Man. By the Rev. Thomas Brown, 
F.R.S.E. (Plate IV.) 

(Read 3d January 1870.) 

Introductory. 

No subject of modern scientific inquiry is more important than the series of 
deposits in which geology comes in contact with the period of human history. 
This must be my apology for some of the seemingly trivial details contained in 
the following paper. When these observations were begun, nothing could be 
further from my thoughts than any reference to the antiquity of man. But I 
shall perhaps best introduce the subject by simply narrating the way in which 

I was led forward step by step, till the whole inquiry assumed the form in which 
it is here presented. 

In the autumn of 1863, I spent some weeks at Bridge of Earn, on the estuary 
of the Tay, and noticed, as every one must, the carse lands lying along the river 
Earn, from which they rise by a steep escarpment, running on a dead level back 
to the base of the hills. They were deposited, our recent geological authorities* 
say, at a time when the land stood lower and the sea higher than now, and 
are the estuarine mud of that former period. I had no idea of questioning this 
opinion, or of examining the deposit, but in my walks I was struck by the 
marked absence of marine fossils. Long ranges of sections were beautifully 
laid open, and the absence of marine organisms seemed so remarkable that I 
was led to make a closer examination. In the deposit I found there were two 
divisions, a lower and a higher, separated by a bed of peat about a foot in 

* It may be enough to refer to a series of papers from 1860 to 1866 in the Journal of the Geological 
Society of London, by Mr Jamieson, of Ellon, forming one of the most valuable contributions made of 
late years to Scottish geology, and one frequently quoted and relied on by Sir C. Ltell. I give two 

I I notations : — 

" The land sank again until the sea in most places reached a height of from 30 to 40 feet above 

the present tide-mark The clays and beds of silt forming the carses of the Forth, Tay, and 

other rivers were accumulated." — 1860. Vol. xvi. p. 371. 

" A depression now took place In the valley of the Tay and Forth this old coast-line 

was 25 or 30 feet above the present, but on the coast of Aberdeenshire, not more than 8 or 10. The 
old estuarine beds or carses of the Forth, Tay, and other rivers were formed, together with correspond- 
ing shingle beaches and caves along the coast." — 1865. Vol. xx. p. 195. In this paper the deposits 
of the Earn are specially described. 

VOL. XXVI. PART I. 2 R 



150 REV. THOMAS BROWN ON THE OLD RIVER TERRACES 

thickness, which ran for miles through the sections. Taking the order of 
succession as it usually occurs, we find the following series : — Immediately 
beneath the surface soil (sometimes 3 to 4 feet), there is the carse clay from 
9 to 10^ feet in thickness, grey-coloured, tenacious, unlaminated, intermingled 
with sand towards the base. Underlying this is a stratum of peat, the materials 
of which seem to have been drifted from some distance, and one remarkable 
thing is that the leaves, &c, which form this peat are found passing up into the 
clay, plentifully intermixed with it at first, but getting less abundant as you 
ascend. The clay and peat are in this way so associated that one might 
almost view them as forming a single deposit. The portion of the series which 
underlies the peat consists of laminated clay with partings of sand, and 
laminated sands with partings of clay, going down under the surface of the 
river. This lower series is unconformable to the overlying peat and clay, and 
occasionally the former surface is seen to have been denuded, and the peat 
and clay are found filling up the hollows. Some miles further up, near the 
railway station at Forgandenny, the sandy layers are found to predominate, 
with small gravel intermixed, and the whole has been consolidated into a 
tolerably compact sandstone conglomerate, two yards of which are exj)osecl at 
the base of the cliff underlying the peat. In regard to the peat itself and the 
immediately overlying clay, it is found everywhere to contain wood, marsh 
plants, such as the Arundo phragmites, hazel-nuts, mosses, &c. At one point 
I found a series of leaves — willow, plane, &c. — in a singular state of pre- 
servation, spread out between laminae of clay, displayed as in a herbarium, 
and this continued layer after layer for a yard above the peat. The hazel- 
nuts which occur in the peat are of a large size, and still show something of 
the shining brown colour which belongs to them. There are occasional speci- 
mens of beetles also, the elytra of which retain much of their brilliancy. My 
examination of these deposits was by no means complete, but their general 
character seemed sufficiently obvious. What was to be said in favour of 
their marine or estuarine origin I really could not tell. No single trace of any 
marine organism would turn up. For miles and miles the deposit was 
laid open, but examine it where you might, all the remains were fresh- 
water or land. The evidence was indeed to a great extent negative, and I 
was not willing to come to any definite conclusion, but everything seemed 
to indicate that these beds were merely a river formation. They rise about 
27 feet above the present level of the stream. If only we could suppose a 
time when the river floods had, like those of the Nile, the power of rising 
27 feet, how natural and how easy the explanation of the whole phenomena 
would be. 

Next autumn (1864) I went to Crieff, further up the Earn. Even on approach- 
ing the town, looking through the windows of the railway carriage, I was struck 



OF THE EARN AND TEITH. 



151 



by the resemblance of the high banks lying along the river to those already 
observed at Bridge of Earn. The general aspect of these terraces is well shown 
in the sketch here given, where a represents the level of the present banks of 
the river, b an intermediate terrace on the opposite side, and c the high level 
terrace. This last was obviously a formation similar to what I had seen the 
previous year. It lay more than 100 feet higher above the sea than that at 
Bridge of Earn. The only agent holding the same relation to it in both 
localities was the river, along which lay the steep escarpment and level surface, 
telling in each case the same story. And again the question presented itself, 
was not this simply a river formation in both cases % might not the sea have as 




Sketch 1.— Near Crieff. 



little to do with that deposit at the Bridge of Earn as in the neighbourhood of 
Crieff? I had long felt, however, that much time and attention would be 
required for the satisfactory examination of these river deposits. Men had too 
often been content to take a bit here and a bit there from different river-courses, 
without the continuous examination of any one in particular. If reliable results 
were to be reached, it seemed that some one of our rivers must be fixed on, 
followed from the hills to the sea, and made to tell its story from end to end. 
This was the more apparent on comparing the deposit at Crieff with that at 
Bridge of Earn. But such an examination demanded more time than was then 
at my disposal. 

The succeeding season I spent some weeks at Comrie, still higher up the 
Earn, and there the same deposits again presented themselves in a form which 
seemed still more to deserve investigation in connection with the carse lands 
at the mouth of the river. 

I had gone one day to the foot of Glenartney, near Cultibregan, where the 
Ruchil flows from the hills down on the plain of Dalginross. Looking up the 



152 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



valley there appeared three terraces, as represented in sketch 2.* Along the 
river side is the lowest terrace, a, about six feet above the water, being the 
height of the present banks. Further back, and rising above it, is the second 
terrace, b, about sixteen feet higher than the first, or twenty-two feet above 
the water ; and still further back is the third, running along the sides of 
the valley, its level being, at the point where I measured it, about 57 feet above 
the bed of the stream. In this last the line of escarpment has been somewhat 
broken by denudation, but the continuity of the terrace itself is obvious at a 
glance. The whole of these levels consist of gravels and sands with clay in 




Sketch 2. — Near the Foot of Glenartaey. 



different proportions. Near the point c, the highest terrace was well laid open, 
and showed the following structure, beginning at the surface : — 



1. Gravel with clay, the pebbles lying on their flat sides, 

2. Pan, . 

3. Gravel, sandy above, coarser beneath, 

4. Fine brown sand, in layers, . 

5. Fine gravel with sand, 



Feet. 
2 


Inches. 




2 



1 
3 

8 


depth 


unknown. 



This was evidently the work of running water, and the question again arose 
whether it had not been deposited by the river at some period when its floods 
ran much higher than at present, and whether that threefold system of 
terraces might not be found to throw light on the whole of these old river 
deposits. On going across to the Turrit, where it comes out from the hills 

* For this series of sketches I am indebted to a young friend, Mr W. B. Murray, an art-student 
of our Edinburgh School, who has been very successful in his rendering of the scenes. Along the 
Earn it has, in three or four cases, been necessary to suppose the woods thinned, in order to show 
the real form of the ground, but this has been done as sparingly as possible. On the Teith there was 
less need for this except in Sketch 12, and even on the Earn all the finest examples of the terraces, 
such as those in Sketches 6 and 7, are given exactly as they appear in nature. 



OF THE EARN AND TEITH. 153 

below Ochtertyre, I found the same three levels in still more striking propor- 
tions, and it at once became a question how far they could be continuously 
traced along these river valleys. 

Beginning at the foot of Glenartney there could be no doubt as to the lowest 
level forming the present banks of the river. It passes downwards and spreads 
out into extensive meadows. And equally marked was the extension of the 
second terrace, the steep escarpment of which goes sweeping for miles, forming 
a great irregular triangle from Cultibregan to Lennoch, the level flatness of the 
surface being not less remarkable than that of the Carse lands at Bridge of Earn. 
The highest terrace, however, is often discontinued, especially along the right 
bank of the river ; but away to the north, beginning at Coneyhill, portions of it 
may be seen at Tomperran, Lawers, and especially at Monzievaird. It soon 
became apparent that these terraces were a good deal interrupted, appearing 
and disappearing by turns, while at intervals the threefold system is in full 
preservation. But these interruptions are not to be wondered at, when we 
think of the denuding agencies to which the deposits were exposed. The 
loose sands and gravels, of which they were composed, were just the materials 
most liable to be washed away, and their position on the sloping sides of the 
valleys was precisely that on which the denuding agencies would most power- 
fully act. It is plain also, that the rains and floods of the old time were much 
more powerful than now, and, if we picture them to ourselves, rising to a height 
and acting with a force to which nothing at the present day can be compared, 
it is little wonder that the terraces have in many places been removed, and in 
others greatly worn down and obscured. 

Making fair allowance for all this, it became a question, whether anything 
like a continuous chain of these deposits could be traced along the course of 
the valley. During the autumn of 1865, and again in 1866, I had some weeks 
of leisure on my hands, and I thought something might be done to ascertain 
the point. Taking the Ordnance Survey map in my hand, I filled in as I went 
along the results of my observations, using a separate colour to mark each of 
the three levels. At all points of importance I endeavoured to ascertain, from 
actual sections, the internal structure of the terraces, for there is always a risk 
of mistaking for a terrace what is really due to the rocky structure of the 
country. I took also a series of measurements showing the height of the 
deposits above the river course ; but being alone I had to content myself with 
only approximate results. Thus, I followed the Earn, from where it leaves the 
loch to where it meets the tide, through many pleasant days, amidst scenes of 
quiet river-side beauty, which I shall not soon forget. The results are given 
in the accompanying map (Plate IV.) That I have succeeded in all cases 
in reading the deposits aright, or in tracing their boundaries, is, I am afraid, 
more than I can hope for. I offer it merely as an approximative eye-sketch, 

VOL. XXVI. PART I. 2S 



154 REV. THOMAS BROWN ON THE OLD RIVER TERRACES 

sufficient, I believe, to show the general course of these deposits. Their outline 
on the side furthest from the river is not attempted. 

Having thus examined the Earn, it seemed desirable to test these views in 
some different district ; and next summer (1867), accordingly, I went to 
Callander, on the banks of the Teith, the chief stream in the basin of the Forth. 
From the details about to be given it will be seen that the same terrace system 
is developed along the Teith, if possible, more strikingly than I had seen it 
on the Earn. Other occupations made it impossible for me at once to follow 
up the subject, but, having during last autumn verified the leading points, I 
shall now endeavour to state the results. 

Origin of the Terraces. 

The great point of interest is the question as to how these terraces were 
formed, and I go into the discussion of this the more willingly, because it will 
lead me to describe the way in which these deposits occur, and will show their 
continuity along the different valleys. 

One explanation ascribes their formation to the sea at a time when the 
land was to a great extent submerged, and when our river courses were fiords. 
These terraces, it is said, are the old shores, against which the tides rose and 
fell. Great prominence has been given to this view by various writers, and 
especially by Dr Robert Chambers in his work on " Ancient Sea Margins," 
part of which refers to the Tay and its tributaries."" There is one difficulty, 
however, in the way of this opinion, from the utter absence of marine fossils. 
Even where the most delicate leaves of land plants are beautifully preserved we 
can find no trace of the sea. Another difficulty lies in the impossibility of con- 
ceiving how the threefold terrace system could have been formed by marine 
action. The sea can lay down only one line of beach at a time. Take the 
valley, sloping upwards for 240 feet from Bridge of Earn to the foot of Glen- 
artney, — suppose it once filled by the waters of the sea, and that they gradually 
retired, leaving, as they went, the highest terrace, how is the second terrace 
to be formed ? Will you let down the land, reintroduce the sea, and bring it 
again to the foot of Glenartney ? But what would become of the highest 
terrace, in the meantime, all down the valley, at Kinkell for example? Exposed 
to tides and waves, must it not have been swept away ? There is yet another 
difficulty, not less fatal, to which we shall immediately refer. 

Some of our leading geologists, rejecting this view, have held these terraces 
to be the margins of ancient lakes. The flow of the waters, it is said, had been 
barred, and our valleys had become the beds of old lakes. From time to 

* Nowhere, perhaps, is this opinion more ingeniously stated and defended than in a series of 
papers by the late Mr Charles Maclaeen. See his Select Writings recently published, vol. ii. 
pp. 186-201. It is from the valley of the Tay that he takes his examples. 



OF THE EARN AND TEITH. 155 

time the barriers had been lowered, and as the waters fell these terraces are 
the old lake margins showing the different heights at which the waters once 
stood* 

One fatal objection which applies equally to this view and to the theory 
of their marine origin, is that these terraces lie up and down the valley not 
horizontally, but according as the bed of the stream rises and falls. The 
parallel roads of Glenroy are an example of how it would have been if they had 
been formed either by the sea or by the standing waters of a lake. In Glen 
Roy they lie on a horizontal level, keeping their own height without regard to 
the bottom of the valley. On the Earn, however, the case is reversed ; the 
terraces follow the inclination of the river bed ascending as it ascends towards 
the hills, descending as it descends towards the sea. Take the intermediate 
terrace, for example, on which lies the Roman Camp south of Comrie. Beginning 
at a point above Cultibregan we can trace it as it spreads out and goes down 
to Lennoch three and a half miles below. To the eye it seems to lie on a dead 
level ; and yet, as shown by the Ordnance Survey, it has a decided incline, 
being 71 feet higher at Cultibregan than it is at Lennoch, while its height 
above the river bed is nearly the same. The river course appears to have 
descended about 68 feet, so that the two have nearly kept pace with each other, 
and the same thing is found all along the valley. The terraces descend as the 
river descends from where they leave the hills to where they meet the tide. 

This is of course decisive, but the true nature of these deposits can only be 
fully understood when one follows them continuously from point to point along 
the whole river valley. There are localities, it must be confessed, where to an 
ordinary spectator the theory of lake margins would suggest itself as exceed- 
ingly probable. Near Strowan, for example, under the hill on which stands 
the monument to Sir David Baied, the river passes through a gorge, and looking 
up along its course you see the terrace-like deposits lining the wide open valley 
on either side, one of them bearing on its surface the church of Monzievaird. 
Would not one naturally say that the gorge had once been barred and a lake 
formed, of which these are the old margins ? But the fallacy of this is seen 

* As this paper deals only with, a question of local geology, I do not refer to any writers except 
those who have treated of the two rivers to which these researches are confined. 

Mr Milne-Home applies this explanation of Lake Margins to the Terraces of the Teith, Trans. 
Roy. Soc. of Edin., vol. xvi. p. 416, 

Dr Fleming supposes a lake to have occupied these river valleys, Lithol. of Edin. p. 76, 1859. 

I may refer also to a discussion before the Geol. Society of Edin., 19th March 1867, the report 
of which appeared at the time. Only two theories, the Lacustrine and Marine, found support. 

Mr Charles Nicolson, M.A., B.Sc, read a paper on the Surface Formations of the Tay at Perth, 
describing the Terraces, and advocating the view that they are of Lacustrine origin. 

The President Dr Page, Mr Coyne, C.E., and others, gave " their opinion on these Terraces in 
opposition to Mr Nicolson's Lacustrine Theory maintaining their marine origin, Dr Page instancing 
the minute examination by Dr R. Chambers of the old sea margins, and Mr Coyne giving his 
opinion from minute measurements and personal observations." 



156 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



when you pass through the gorge to the lower side of the supposed barrier, and 
find portions of the same terraces on the farm of Trowan, thus holding on their 
course utterly disregarding the supposed limits of the lake. Another instance, 
to which, as will be seen, some importance attaches, occurs on the Turrit, and 
especially on the side valley that goes up towards Monzie. In the angle 







Sketch 3. — On the Shaggie above its junction with the Turrit. 

between the two we have the three terraces strikingly developed as represented 
in sketch 3, where, however, a row of bushes and trees are supposed to be 
removed, in order that the form of the ground may be seen. 










Sketch 4. — On the Shaggie above its junction with the Turrit. 



Supposing the spectator to cross the bridge shown in sketch 3, and ascend 
the second terrace b, then turn and look down the stream, he would have 
before him the view given in sketch 4. 



OF THE EARN AND TEITH. 



157 



Here we have in front the narrow ravine between the spectator and the 
point R through which the stream passes ; and we might have argued that the 
glen had once been closed, a lake formed, and that these terraces are the 
former margins. But following the course of the deposits we find the terrace 
c passing into the ravine and continuing especially along the right bank. And 




Sketch 5. — Dalvreck Bridge on the Turrit. 

what is more decisive, if you go to the other end and look across and up the 
glen where the water comes out from under the Bridge of Dalvreck, the three 
terraces come out distinctly as here given in sketch 5. On the one bank the 




Sketch 6. — Dalpatrick. 

second level b holds its course at a similar height above the river bed, while 
in the other bank the highest level c passes'" out into the open going round 

* There is a beautiful section showing that it consists of finely laminated sands with a little 
gravel and clay. 

VOL. XXVI. PART T. 2 T 



158 



REV. THOMAS BROWN" ON THE OLD RIVER TERRACES 



over the grounds of Ochtertyre ; and when one finds these deposits in the 
same position above the ravine and below it, it seems vain to ascribe them to 
some lake formed by the barrage of the river. 

Tracing the course of the Earn from Crieff to Dalpatrick, we again reach a 
point above the old castle of Innerpeffray where the channel is narrowed between 
high grounds. Standing near Easter Dalpatrick and looking upwards, we have the 
scene as represented in sketch 6. The present banks and meadows, a, are sur- 
mounted by the second terrace b, and that by the higher level c, all in full 
preservation.* Again, the idea might be suggested of a bar above Innerpefiray 
forming a lake, but again the explanation is forbidden by the continuous course 
of the deposits, and more especially by their appearance when the narrow 
portion of the river has been passed, and the banks again spread out into a 
wide open valley. This takes place immediately below Kinkell, where the 
threefold terrace system is very remarkable, as shown in sketch 7. 




wf?c 







Sketch 7. — Kinkell Bridge, looking up. 

A section of terrace c, on the eastern side of the Machany, is laid open by 
the cutting of the road, and is given in PL IV., fig. 1. The details are — 

a, Humus. 

b, Carse clay, grey, unlaminated tenacious. 

c, Laminated clay with partings of sand. Laminse a half inch in thickness. 

The series of deposits at this point are specially important, because there is no 
position further down the valley where it is possible to suppose that a barrier 
could have ever been thrown across. These are not lake margins. 

The lower portions of the river, as it passes Dunning, Forteviot, &c, were 
examined somewhat more rapidly. The threefold system of terraces seems to 
have been less distinctly preserved. A point, however, is given in sketch 8, 



* Immediately beyond the farm-house the railway gains the summit of terrace c, and the view 
shown in sketch 1 is seen looking up the valley. 



OF THE EARN AND TEITH. 



159 



some distance below the bridge of Dalreoch, where the three levels are present, 
the second especially being well exposed.* They may be seen also distinctly at 
Forgandenny, from the railway crossing, looking across towards Boatmill. 
But all through these lower portions of the river course the higher and middle 
terraces show a tendency to coalesce, forming, with the present meadows, only 




Sketch 8. — Near Dunning. 



two levels. It was the higher of these which first attracted my attention at 
Bridge of Earn. By comparing the map with the series of views, the reader 
will have some idea of how continuously these terraces pervade the whole course 
of the river valley of Strathearn from the mountains to the sea. 




Sketch 9. — Loch Lubnaig, looking up. 

Turning now to the river Teith, we have first to notice the shore deposits of 
Loch Lubnaig, along the western side of which they may be seen running 



The highest terrace c is made too prominent in the sketch. 



ItiO 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



under the shadow of Ben Ledi. First, there is the present shore of the lake, 
above which rises the second terrace to the height of nearly fourteen feet, and 
this in its turn is surmounted by the third, about thirty-seven feet over the 
water. Their position is well given in sketch 9. The point seen in the 
distance is perhaps the spot where the highest terrace is best displayed, and. 
is given more fully from the upper side in sketch 10. When I first saw it in 
1867 its form was that of the dotted line, a shelf projecting and running at its 
own level along the mountain side. Now it has been cut up by the railway, 
which has been carried for a considerable distance through these terraces, 
showing many remarkable examples of drifted gravels and stratified .sands, 
with, in some instances, underlying boulder-clay. 




Sketch 10. — Loch Lubnaig, looking down. 



These deposits on Loch Lubnaig would seem to point to a time when the 
waters of the lake stood permanently higher than now. One of our best geo- 
logists, Mr Milne Home, has advocated this view, placing the barrier which 
held back the waters, at the pass of Leny ; and it would have been difficult 
to resist this opinion, but for the circumstance that when we get below the pass 
we find the same terraces quietly falling into their 'places, and resuming their 
course as before. Sketch 11 shows their form when they leave the narrow por- 
tion of the valley, going off towards Callander on the left bank — a similar appear- 
ance being presented as they sweep round towards Loch Vennachar on the right. 
The height of the terrace levels is almost identically the same with those on 
the shores of Loch Lubnaig, and there is the closest resemblance in their inter- 



OF THE EARN AND TEITH. 



161 



nal structure. If it be said that these in sketch 11 are the margins of a lower 
lake, there is, first, the difficulty of accounting for their being so exactly the 
same height above the water, and then there is the fact of their continuity 
down past all supposed barriers at Gart or elsewhere. Leaving the pass of 
Leny, and going on towards Callander, we find it is for the most part on these 
terrace levels that the new west end villas are built ; and when the railway was 
being cut in 1867, it was striking to observe the close resemblance which the 
fine grey sands, with their false beddings, and the coarse gravels, bore, 
both in their structure and relative positions, to those seen in the sections on 
Loch Lubnaig.* 




r^y^K _ 



i 




Sketch 11. — Looking from below the Pass of Leny towards Callander. 



Further to the east it would be easy to give from different points of the 
river course examples of the threefold levels ; but it may be interesting to take 
one from its great feeder, the Keltie, so well known as forming the Falls of 
Bracklin. It is seen (sketch 12) a little above its junction with the Teith, 
and the view will serve to show that the same system found on the main stream 
pervades also the tributaries. The upper level presents itself in two stages, 
and to this fact we shall afterwards refer. 

The succeeding portion of the Teith, down as far as Doune, shows a con- 
tinual succession of the same deposits. The village of Dalvaich especially lies 
in the midst of a series of these terraces, deserving a far more careful examina- 
tion than it was in my power to give them. They may be followed down 
through the grounds of Lanrick Castle, and come out well at the fine old 
churchyard of Kilmadock. But one of the most striking examples either on 
the Earn or Teith is that given in sketch 13, above Deanston, on the opposite 

* To illustrate this, two sections are given in Plate IV. Pig. 2 is from the terrace on the 
shores of Loch Lubnaig ; fig. 3 is from the railway cutting at Callander. In both the fine grey lami- 
nated sands, with their false beddings, are seen to have been denuded in a remarkable way, and are 
overlaid by coarse gravels. 

VOL. XXVI. PART I. 2 U 



162 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



side of the river, near the farm-house of Clarkton. The highest terrace there 
shown passes on to the railway station, and has a great part of the town of 
Doune built on it. It is the same also which may be traced across the river 
into the grounds of Blair-Drummond, where, in the view immediately opposite 




Sketch 12. — On the Keltie, near Gambusmore. 



Doune Castle, the three levels are distinctly seen ; and here a point is reached 
of great importance in regard to these terraces. The Carse of Stirling, lying 




Sketch 13. — On the Teith above Deanston. 

between the Forth and Teith, begins to spread out its flat level, and the highest 
terrace gradually descends and coalesces with the second, just what we saw 
take place on the Earn, when approaching the Carse lands in the neighbour- 
hood of the sea ; and yet all the way some traces of the threefold system may 
here and there be found. Even at Kildean, near Stirling, and well within tide 



OF THE EARN AND TEITH. 



163 



mark, this is shown. The highest bank c is only twenty -four feet above the river, 
while the lowest a is six ; but the opposite side shows an intermediate level b 
of some twelve or fourteen feet. The whole are thus on a very inferior scale. 
Perhaps it may be thought that this diminution is due to the greater width of the 
valley. But a still stronger reason, I believe, is the comparative weakness of 
the current arising from the lower gradient of the incline along these portions 
of the river course. To this I shall again refer. 

The details thus given make it plain that we cannot have recourse to the 
lake theory, for the terraces are not horizontal, but slope with the valley, and 
in the case of both rivers we reach a point below which any barrage is incon- 
ceivable, and yet these deposits hold on their course. 

But there are certain additional circumstances to which I ask attention, and 
which I was led to notice only as the result of having continuously examined 
the whole course of these rivers. 




Sketch 14. — Kildean on the Forth. 



First, there is the difference between the upper Earn and its feeder, the 
Ruchil. There are three streams which meet at Comrie, where the Earn, 
coming straight from its loch, is joined by the Lednoch from the north, and the 
Ruchil from Glenartney in the south. Both these feeders show the terraces, 
those on the Ruchil being, as we have seen, specially remarkable. On search- 
ing for them along the upper Earn I was struck by the difference. The present 
banks of the stream are unusually low, and above these there is a second 
terrace, some 12 or 14 feet over the river ; and this was all I could make out. 
Some banks which I took for the highest terrace I found were due to the rock 
structure of the country, and some gravel deposits near Aberuchil belonged 
evidently not to the Earn, but to a mountain stream which comes from the 
south. The general appearance of these low terraces along this part of the 
river will be seen from sketch 15, which the reader is requested to compare 
with sketch 2, when the difference of scale will be obvious. The threefold 



164 



EEV. THOMAS BEOWN ON THE OLD EIVEE TEEEACES 



terrace system of the Ruchil is feebly represented by the 12 or 14 feet 
banks which are continued along the Earn, past Dunira, and on to the loch. 
In seeking the explanation of this difference a remarkable circumstance was 
brought out. The floods which come down the Earn at the present day are 
quite feeble compared with those of its tributaries. The Ruchil is remarkable 
for the suddenness and strength of its floods, while the flow of the Earn is 
quiet and equable. Now, the height of the old terraces on the two streams 
exactly corresponds with this. The coincidence is striking, and can have only 
one meaning. Along the stream, where the floods are still powerful, the 
old terraces are powerfully developed. Along the stream, where the floods are 
feeble, the old terraces are feebly developed. The only possible conclusion is, 




Sketch 15. — On the Upper Earn. 

that it was by the floods of these rivers that the old terraces were really built 
up in a former age, and that their flooding power was then in proportion to 
what it is at present. 

A second circumstance of the same kind is seen when we compare Loch Earn 
with Loch Lubnaig. Along the shores of the latter, as we have already shown, 
there are well marked terraces, and on Loch Earn also a similar deposit is 
present, but in far less proportions, spreading out especially towards the bottom 
of the lake, where in September 1869 I found it 12 to 14 feet above the water. 
This is a weak representative of the 37 feet terrace of Loch Lubnaig. But 
the remarkable thing is that it almost exactly corresponds to the proportionate 
rise and fall of the water in the two lochs at present, as caused by a flood on 
the one hand, and a drought on the other. Both lakes, I was told, were at the 
lowest ebb at which they had been seen for years. In the case of Loch Earn, 



OF THE EARN AND TEITH. 165 

the water was between 3 and 4 feet below the highest water-mark that could 
be found ; while on Loch Lubnaig the difference was about 8 feet. How much 
of this was due to the absolute depth of the water, and how much to the action 
of the wind, I could not, of course, say. It was the western shore of the loch 
in both cases where I took the measurements. But the striking thing is to 
observe the closeness with which the results correspond with the proportions of 
the old terraces. In the loch, where the floods and winds of the present day 
raise the waters 3 to 4 feet, you have the old terrace about 14 feet high. In the 
loch, where the waters at present are raised some 8 feet, you have the old 
terrace lying 37 feet high. It is hardly possible to resist the inference that 
these old terraces are due simply to the greater flooding power of some former 
epoch. 

A third fact which came out was, that these old terraces vary in height just 
as the present banks of the stream vary at different parts of the river course, and 
in something like the same proportions. Usually the present banks and haughs 
of the Earn are 5 to 6 feet above the stream, but in some places we find them only 
3, and in other cases they rise to about 10, as near the Bridge of Strowan. 
The difference is due to the form of the valley, and still more, I believe, 
to the force of the current. Now, there is precisely the same kind of 
variation in the levels of the old terraces. As the present banks and haughs 
may be anything from 3 to 10 feet, so the second terrace varies from 16 
to 24, and the highest from 35 to 60. The cases where extremes occur 
are rare ; but this general truth must be recognised, that as the present banks 
vary in height with the locality, so do the ancient terraces. 

Connected with this, however, there is one further circumstance which 
deserves to be noted ; the height of the old terraces varies with the incline of the 
river bed. Where the incline is greatest, there, of course, the current ran 
strongest, and there the terraces are highest. When the gradient is low, the 
terraces get low. It is difficult, indeed, to bring out the exact truth on this 
point, for it is necessary to make allowance for the varying width of the valley ; 
but in comparing the different parts of the river, there is seen to be a distinct 
proportion between the steepness of the incline and the height of the deposits. 
Thus, from the foot of Glenartney to Kinkell, the distance in a straight line is 
about ten miles, and there the descent of the river is nearly 200 feet. From 
Kinkell to Bridge of Earn is more than eleven miles, and there the descent is 
about fifty feet. Now, it is along all the upper section, where the current ran 
strong, that the terraces rise high ; and along all the lower portion, where the 
current ran slow, the terraces subside. Precisely the same thing is seen on the 
Teith. Above Doune the descent is rapid, and the current strong. Below 
Doune all is flat, and the current gets slow, and it is in the upper portion that 
the terraces are raised high, while below Doune their height markedly diminishes. 

VOL. XXVI. PART I. 2 X 



166 REV. THOMAS BROWN ON THE OLD RIVER TERRACES 

Here, again, the facts point to these river currents as the agent which built 
up the terraces. In estimating the facts, however, care must be taken to 
include some considerable length of the river course. A short reach, where 
the water runs level and slow in the midst of rapids, may be the very place 
where the deposits most accumulate. But take any considerable distance, and 
it will be found that in proportion as the gradient is steep'"" these old terraces 
rise in height, and as the gradient gets low the terraces diminish. 

If we could only suppose a time when the river had the power of rising in 
flood to the requisite height, the whole phenomena would admit of the most 
easy and natural explanation. The simple key to the whole would be the 
principle, that just as the river deals now with its present channel and present 
banks, so it dealt in the old time ivith those high lying ter races. \ 

Putting together then the whole of these facts, we can now see what this 
threefold system of terraces means. It is simply a record of the different levels 
at which the most powerful river floods stood at different periods of the past. 
The highest of these lines of deposit is evidently the oldest, a gravelly and 
sandy terrace which runs along our valleys at a height of from 35 to 60 feet. 
Then we find a descending scale as the floods grew less and less powerful, 
subsiding towards the present state of things. Bather more than half way 
down the scale there is an intermediate terrace about 16 to 24 feet above the 
river, and forming an outstanding feature of these deposits. It seems to 
indicate that when the descending waters reached that stage a pause of con- 
siderable duration took place, during which the action of the highest floods 
went on at that level. Subsequently there was a descent from the middle 
terrace to the present banks. Between each of the stages indeed, there are 
intermediate lines of deposit occurring here and there in different localities, 
and putting them all together it would be possible to construct a whole series 
of graduations by which the highest terrace would be found to descend to the 
second, and the second to the lowest. Still there can be no doubt that the 
three terraces form the prominent feature of these deposits. 

The general result thus seems to be, that along the sides of these river 
valleys, we read the history of various ages during which the floods gradually 
ran at a lower and lower level, and in that record there are three great lines 
which stand out from the rest as indicating each some considerable period 
during which the waters remained stationary, till at last the intervals were all 
passed over and the present state of things was reached. 

* This does not apply when one follows the stream up among the mountains, where for the most 
part the terraces are absent. Is it that denudation has swept them wholly away? or is it that during 
the epoch of these old floods there were glaciers still lingering in the upper portions of the river- valleys ? 

t More than twenty years ago, Mr Milne-Home described the terraces above Perth as haughs 
or river flats, but he seems to connect their formation with the bursting of lakes. See " Trans. Boy 
Soc. Ed.," vol. xvi. p. 418. I do not refer to other districts. 



OF THE EARN AND TEITH. 167 

Their Geological Position and Age. 

In regard to the time when these terraces were formed it is difficult to 
pronounce with confidence, but there are certain indications which deserve 
attention. 

Near Comrie we find some antiquarian remains which go a good way back 
into the past. The site of the Roman Camp is close to the village, and a little 
further to the east there is what the Government Surveyors have laid down as 
a small roundel or Druidical structure, a circle raised above the surrounding 
ground, in the middle of which there once stood a rude and apparently 
unsculptured monolith, now prostrate. These Roman and Druidical remains 
are all on the expanse of the second terrace formerly referred to. So far back 
then as they carry us the intermediate terrace had been already formed. 

Leaving archaeology and appealing to the methods of the geologist, it is 
clear that these deposits have been laid down subsequently to the glacial epoch 
in Scotland, for no glacier can have touched the valleys since the terraces were 
deposited. We have traced them on Loch Lubnaig up to a height of 400 feet 
above the sea, and their state of preservation makes it plain that up to that 
level at least no glacier nor icecake has since their formation grazed hill or 
valley. 

It is equally plain, and for the same reason, that the sea had finally retreated 
from the land. Some minor change of level there may have been about the 
Carse of Stirling, but already the sea must have finally left the valleys free for 
the action of the river floods. 

There seems indeed to be good ground for believing that a series of peculiar 
deposits is interposed between the oldest of these terraces and the glacial 
epoch. In working back, and trying to make out stratigraphically the place of 
the highest terrace, we are in contact with a set of gravels, &c, which in the 
present state of our knowledge are particularly obscure. I refer to a series of 
mounds or hillocks sometimes round or sinuous, sometimes drawn out as long 
lines in the form of escars or kames, but invariably when laid open showing 
that they have been deposited by water in a state of disturbance. Occasionally 
they come down into the valleys, but for the most part they stretch away out 
over the higher grounds. Examples are to be seen along the course of the 
Earn, but they are still more striking on the Teith, and especially near the 
village of Dalvaich. In sketch 12 it will be observed that the highest terrace c 
is shown in two stages. Following the oldest and highest of these stages it 
appears to connect itself with the deposits in question, which, a little to the 
west of Dalvaich and north of the turnpike road, begin to spread out and go far 
up over the face of the country. One of these lines of kames is given in sketch 
16 showing another and higher ridge of the same kind behind it. The end 



168 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



view of the first of these lines is seen in sketch 17, showing the form which 
these deposits assume. The question as to how they were formed is one of the 




Sketch 16. — Karnes west of Dalvaich. 



most difficult in geology. That they are not due properly to the action of 
flooded rivers is plain, for they may be traced up and out over the level face 
of the coimtry, and are nowhere more fully developed than towards the water- 





Sketch 17. — Karnes west of DalvaicL 



shed between the basins of the Forth and Tay, where the action of streams 
must have been feeblest. It would be natural to suppose that they were 



OF THE EARN AND TEITH. 169 

submarine banks belonging to the time when Scotland was submerged, but 
this seems disproved by the fact, that wherever such submarine banks occur, 
they swarm with all kinds of marine life, while in regard to any trace of such 
life, these kames are invariably an utter blank. But, indeed, similar difficulties 
attend all the theories hitherto suggested. Nor ought this to surprise us. 
We do not know what it is for a country once incased in ice as Greenland 
now is, to have the ice-sheet lifted off or melted from the face of hill and plain. 
Into what forms the subjacent materials of gravel and sand would be thrown — 
what would be the modes of operation of the forces let loose, it is difficult to 
conjecture. No example of such a process has been witnessed, and yet it is 
certain that Scotland passed through it. It is little wonder if among its results 
there should be some residual phenomena for which it is difficult to account. 
Among these it would seem we must place the kames or escars, and the gravel 
mounds associated with them. At all events, their position appears to lie 
between the period of arctic climate and the time of that series of terraces 
which this paper describes, and which were, it is probable, built up out of the 
materials furnished by these pre-existing gravel deposits. 

In deciding the geological position of the terraces, however, we must not 
forget the fossils of the peat and the associated carse clays referred to at the 
beginning of this paper. For several miles above Bridge of Earn these remains 
occur in abundance, but evidently they have been drifted from some distance, 
brought down by the current, and they show what the flora of Stathearn had 
been at the time when the peat and carse clay were deposited. In regard to 
the extension of the carse clay itself, it can be traced up as far as Kinkell, 
where its grey colour and fine unlaminated structure were quite distinct/"" form- 
ing part of terrace c, as shown in sketch 7. Above Kinkell, the same terrace runs 
on, but the place of the clay is taken to a great extent by sands and gravels, 
and these materials get on the whole coarser the further you go up the stream. 
All this is easily explained. The coarser the material, the less easily is it 
moved forward by the current, while clay in the form of mud is floated to the 
furthest distance. The highest terrace, therefore, which consists at first of 
gravel and sand, with a little clay, presents through all the lower reaches of the 
river little else than large sections of the finest carse clay. These carse clays, 
and the underlying peat near Bridge of Earn, form, as we have seen, properly 
only one deposit, and the result would seem to be that these fossil leaves and 
hazel nuts, &c, give us the flora which grew along the valley at the time when 
the oldest of these terraces were formed.t 

* See Fig 1, PL iv. 

' There seems good ground for holding that the peat heds of the Earn belong to the time when 
the land stood comparatively high. But when Mr Jamieson makes the land again sink, and brings 
in the sea in order to deposit the estuarine mud of the carse, not only does the fossil evidence go 
against this, but there is the decisive fact already pointed out, that the peat and the carse clay are so 

VOL. XXVI. PART I. 2 Y 



170 REV. THOMAS BROWN ON THE OLD RIVER TERRACES 

If this be so, it would appear that the glacial epoch must, to a great extent 
at least, have passed away. Its close had been marked by the formation of 
the kames, those ridges of gravel whose strange forms meet us on our 
uplands and over the face of the country. Then there came a more genial 
time, shown by the large size of the hazel nuts, when the present Flora was 
established. And then it was that those vast floods seem to have flowed forth, 
which filled our valleys, and left their record in these highest terraces. What 
was done during the Moray floods may have been clone of old on a still greater 
scale, and these high-lying deposits may be the proof of it. 

Antiquity of Man. 

The views thus far stated must be judged of on their own merits, apart from 
any question as to the antiquity of man. The advocates of extreme opinions 
on this subject have relied to a great extent on geological evidence, and some 
of their strongest arguments have been derived from the flint implements of the 
Somme in France, and the Brixham Cave in Devonshire. It is held that 
wrought weapons, the work of man, are found along with the remains of extinct 
mammalia, and occur in such a way as to show that man had been their co- 
temporary. If this were all, however, the argument would have little force, for 
the inference would be perfectly open, either that the human period must be 
carried further back, or that the time of these extinct mammalia must be 
brought further down. Were we mistaken as to the duration of man — must 
it be carried much further back among these extinct animals ? or were we 
mistaken about these extinct animals — do they come down into the human 
period ? Men would lean to one or other alternative according to their pre- 
possessions. Other circumstances had therefore to be appealed to, and, in fact, 
the stress of the argument has come to rest on the position of the deposits in 
which these remains occur. Those on the Somme were examined by one of 
our best observers, Mr Prestwich, who reports that the oldest beds containing 
these fossils lie along the valley, at the height of about 80 feet above the river 
course. The time when these were deposited was the time when man and 
the mammoth lived together. Since then the river has worn down the valley, 
cutting through rock, &c. some 80 feet, and the human period must be carried 
back through the ages which can rationally be supposed needful for this opera- 
tion. He refuses to admit " hundreds of thousands of years," but if his view 
be taken, the period must be very long. The argument in the case of the 
Brixham cave is similar. The remains of human art and of these extinct 
animals are found together in a deposit which must have been carried by 
running water into its present position. But the entrance to the cave is in the 

associated as to form properly one deposit. At whatever time the one was formed, the other was also. 
The conclusion to which all the evidence seems to point is, that the whole system of these river 
terraces was formed at the time when the land was elevated above its present level. 



OF THE EARN AND TEITH. 



171 



side of a valley 60 feet above the present bed of the stream, and we are told 
that the human period must be carried back through the long ages needful for 
wearing down the rocky floor of the valley. These are, I believe, among the 
strongest arguments from geology. 

But now, if the analogy of our Scottish rivers may be trusted, there seems 
fair ground for asking whether such arguments have not been carried too far. 

1. First, it is plain that previously to the time when these high-level terraces 
were deposited along our river courses, the rocky structure of our Scottish 
valleys had been hollowed out as deep as they are now. In proof of this, it is 
enough to refer to the fact that the boulder-clay which belongs to an ante- 
cedent period is found occasionally forming the floor of the valley over which 
the streams flow."" If, then, the formation of the valleys of France and Devon- 
shire were analogous to ours in Scotland, their rocky structure was excavated 
not after, but before, the dej)osition of the high-level gravels. 

2. Secondly, The floods which piled up these old high-level deposits seem to 
have had the power of doing so at a time when the river-bed was cleared of 
all other materials, and stood at as low a level as the present streams. 

This might be shown by various examples along the Earn ; but we take a 




Sketch 18.— Below the Castle of Monzie, 1866. 



single case from the valley of Monzie. Sketch 18 shows a spot where the 
stream has cut into the highest terrace,t laying it open from the base up to a 
height of 50 feet, and showing that it is composed of stratified gravels, sands, 

* Seen in the valley of the Turrit, for example, above Crieff, and also in that of Monzie, in both of 
which it underlies the high-level gravels. My attention has been called to the fact that this view had 
been brought forward in the Memoirs of the Government Survey on Berwickshire, p. 50. 1863. 

I" This forms a continuation of terrace c shown in Sketch 4 on the left bank of the stream. It 
lies a short way further up the valley. 



172 



REV. THOMAS BROWN ON THE OLD RIVER TERRACES 



&c, the work of running water flowing down the valley. Eighty yards further 
up, the same bank (sketch 19) is laid open up to its whole height of 120 feet, 
where, in one of the gullies, innumerable alterations of the same strata are 
shown. The last 20 feet* at the top are particularly well seen, as also are the 
50 feet at the base in Sketch 18. 

Now that this terrace was formed by river floods is shown by its connection 
with similar deposits further down the stream. Those seen in Sketch 1 must 




Sketch 19. — Below the Castle of Monzie. 

have been a river formation from the slope of their surface down the stream, 
and not only is their structure identical with that at Monzie, but — allowing for 
the effects of partial denudation — they may be traced running on till the one 
series actually meets and passes into the other, forming two stages of terrace c, 
as in Sketch 12. 

But if these deposits were formed by river floods, a single glance at such a 
section as that in Sketch 18 will satisfy every geologist that the running water 
began its work at the bottom, down on the level of the present river bed. 
When the first stratum was laid down, the running water had found the valley 
cleared out down as low as it is now. Explain that matter how we may, these 
old floods must have had the power of doing this ; beginning at the level where 
the stream runs now, they could form a terrace, piling stratum above stratum, 
up to the height of 120 feet, as far, indeed as the water was able to rise. 

It is plain, therefore, that if the analogy of our Scottish rivers will apply to 

* See Plate iv. fig. 4, showing the arrangement of the gravels and sands forming the upper portion 
of the terrace. 



OF THE EARN AND TEITH. 173 

those of France and England, the long period required for the supposed lower- 
ing of the river-bed is got rid of. If the stream which flows through the valley 
at Brixham could do what has been done by the burn in the valley of Monzie ; 
or if the Somme could do what the Teith has done along its course, any amount 
of high-level gravels might have been piled up, or carried into caves after the 
valleys had been hollowed out, and the bed of the stream brought down to 
where it now is. 

But are we right in supposing that the analogy of our Scottish rivers will 
apply to those of England and France ? The presumption certainly is that 
their formation was analogous.""" But we have more than mere presumption. 
Mr Tyler, an English geologist, has been investigating the case of the Somme, 
and finds evidence of a pluvial period — a time of high floods sufficient to 
account for the high-level gravels. The body of facts which he has brought 
together deserve careful consideration, and it will certainly be matter of deep 
interest if the deposits of the Somme are found to record the same story whicli 
we have been reading along the Earn and Teith.t 

I have no wish to push this argument beyond what is perfectly fair. These 
terrace-like deposits form a subject which has been too little investigated. It 
may turn out that they reveal to us a period of river floods much greater in 
volume than men are generally prepared as yet to admit. And it may also be 
that those inferences which have been drawn as to the duration of the human 
period may be very seriously affected. It would surely be safe to have more 
complete examination before judgment is given. These deposits belong to what 
in geology is a very recent period indeed, and all I would ask is that the facts 
be more fully investigated, lest in arguing for extreme views as to the antiquity 
of the race men be found importing fallacious elements into the calculation. 

But how shall we account for the volume of water necessary to produce 
such floods f Looking to the width of some of our valleys, and to the height 
of these deposits, is it not difficult to believe in the existence of such torrents \ 
In dealing with this question care must be taken not to exaggerate the diffi- 

* An attempt has been made to deny this on the ground that Scotland was submerged during the 
glacial epoch, while Picardy and Devonshire were not — the object being to show that the French 
valleys were excavated at a later period than the Scottish. But this argument can hardly be urged by 
those who hold that the formation of valleys is due mainly to subaerial forces and hardly at all to 
marine action. If the difference between the two countries be that Erance not having been submerged 
was continuously acted on by these eroding agencies, while Scotland was withdrawn from them by 
being buried beneath the sea, how will that prove the French valleys to be of later formation than the 
Scottish 1 So far as that difference goes it should surely prove the reverse. 

t " On the Amiens Gravel," by Alford Tyler, Esq., F.G.S., " Journal Geol. Soc. Lond." vol. xxiv. 
p. 103. In one respect Mr Tyler's reading is different. He regards the lower terrace, the loess, as 
the bank of the ancient river when in its ordinary state, and the higher terrace as its bank when in 
flood — referring both to the same period. This differs materially from the view which I have been led 
to take, namely, that each terrace is the highest flood-mark of its own time, just as the present banks 
aud haughs are related to the floods of the present time. 

VOL. XXVI. PART I. 2 Z 



174 REV. THOMAS BROWN ON THE OLD RIVER TERRACES 

culty. Our rivers, as we see them at present, flow along a comparatively 
narrow channel, the greater part of the river valley being usually occupied by 
level meadows. When a flood comes, it is only the narrow channel that needs 
to be filled ; and then, should the water rise but a very little over the brim, it 
will spread out like a sea on either hand. But, after all, it is the banks and 
meadows which fill the space of the valley. Except in the central channel the 
sheet of water may be comparatively shallow. And so in that old time the 
river would have only its central channel lined by banks proportionally higher. 
The flood would be needed to fill the river bed, flowing perhaps over the brim 
and out over the surface. In this way these old terraces would be formed just 
as the present meadows are. The volume of water needed was by no means 
what would have been required to fill the valley if it had been empty. It would 
be enough if the confined river bed were filled to overflow. 

But, if things were on such a scale that the river channel was lined with 
banks 50 or 60 feet in height, where was the water to come from which could 
rise to such a height ? One explanation has been sought for in the melting of 
the ice and snow as the glacial epoch passed away. At present, when the ice 
and snow melt in northern latitudes, the arctic rivers rise annually from 40 to 
50 feet. This of itself would go a long way to solve the problem. Besides, 
there was more than the annual melting which takes place at present under 
ordinary conditions. The fact that the glacial epoch was passing away, must be 
taken into account. If these terraces may be taken as a record of the time when 
the great icy covering was melting off the face of the land, and Scotland was 
passing from the rigour of an arctic climate to its present condition, the currents 
which filled our valleys may have been increased to an extent which it is diffi- 
cult to estimate. Swollen lake and flooded river may have risen to a height 
sufficient to meet all the conditions of the problem we are considering. 

Another explanation which has been suggested, is the existence of a period 
of great rain-fall — a " pluvial epoch," as it has been named by Mr Tyler. 
This may have arisen either from the quantity of rain having been increased, or 
from the rain-fall having been concentrated — a greater amount falling in a 
given time. Some idea of these floods of the old time may be got from the 
account of the Moray floods, as given so admirably by Sir Thomas Dick Lauder. 
They occurred in 1829, and were owing to a fall of rain to the amount of 
3 1 inches having taken place in twenty-four hours. In regard to the height 
to which, on that occasion the water rose, the writer mentions having himself 
seen a man wade into the water and capture a salmon on the haughs 50 feet 
above the usual level of the Findhorn, pursuing the fish with his umbrella and 
driving it ashore. The violence and velocity of the currents he describes 
in striking terms. " It was scarcely possible to follow with the eye the trees 
and wreck which floated on its surface. The force was as much more than 



OF THE EARN AND TEITH. 175 

that of a raging ocean as gunpowder ignited within the confined tube of a 
cannon is more terribly powerful than the same material when suffered to 
explode on the open ground."* It is no wonder if, with such force at work, 
there should be strange tales to tell of the results of denudation. Instances 
of farms, where six, eight, or ten acres were eroded and swept away, are so 
common as hardly to deserve notice. At Mains of Orton, on the Spey, when 
the proprietor, Mr Wharton Duff, came, after the flood, to examine his farm, 
he found he must make a new bargain with the tenant, and deduct some 50 
or 60 acres which were gone. At Braemoray, the whole low land was 
annihilated, and the green slopes of the hill converted into naked precipices. 
At Relugas, the pleasure-ground and lawn were swallowed up, and in their 
place that river might be seen raging for 300 yards along the brink of a red 
alluvial precipice 50 feet high. At Dalrachney, the river Aven attacked a 
wooded bank from which it carried off a mass of not less than 90,000 cubic 
yards, leaving a sandy precipice 90 feet high. At Tillyglens, on the Dorbach 
part of the farm, an acre in extent was carried off bodily before the eyes of the 
farmer ; and, as he looked at it sailing away, he observed another half acre 
detach itself from the hillside and descend some 60 feet into the valley, carrying 
a grove of trees on its surface. 

But if the flood could thus tear down, in the same proportion it could build 
up, often leaving its deposits where they were little welcome. On one of the 
farms of Captain Macdonald of Coulnakyle, consisting of 200 acres, 150 were 
ruined by a deposit of sand and gravel to the depth of 3 feet. At the mansion 
house of Ballindalloch, the garden was covered by sand to such an extent that 
only the tops of the apple trees were seen rising through it, presenting a strange 
appearance still laden with fruit. Yet more remarkable was the height of the 
deposits at the Mill of Logie, near Relugas. The flood completely filled with 
sand the lower story of the mill rising 28-| feet above the ordinary level of the 
river. These examples are instructive ; but, in order to appreciate the subject, 
the whole volume should be studied, showing the marvellous power of such 
torrents, both in denuding and in building up. If we suppose, that from what- 
ever cause,t there had occurred in the old times a series of torrents, surpassing 
the Moray floods as these latter surpassed the ordinary summer floods of 

* Page 101. 

t It has been suggested by Mr Buchan of the Scottish Meteorological Society, that if the bed of 
the sea round our coast were elevated, and especially in the direction of Greenland the effect on 
the climate would be greatly to increase the river floods. Now already, on stratigraphical grounds, we 
have been led to the conclusion that it was precisely at that period of elevation that our high river 
terraces were formed. (See note, page 169.) The coincidence is remarkable. The whole strati- 
graphical evidence makes it probable that these high gravels were deposited just at the time when 
meteorology teaches us to expect that the river floods would be much beyond the present ; and if even 
in the present state of things there could be such results as the Moray floods have to show, we may be 
prepared for the still more striking effects of that former age. 



176 REV. THOMAS BROWN ON THE OLD RIVER TERRACES. 

our rivers, nothing could be easier than to explain the whole phenomena of 
these terraces with their high-level gravels. 

There need be little difficulty as to where the materials would be found 
which were to form the great masses of these sandy and gravelly deposits. The 
escars and the associated mounds sufficiently show what immense accumu- 
lations of such materials had been provided under the action of ice, and perhaps 
of the under-ice rivers of the glacial period. If exposed to the action of torrents 
on a somewhat greater scale than those of the Moray floods, such materials 
would soon be disposed of. No great lapse of time need to be supposed. If 
the whole of the above results in Morayshire were produced in about twenty- 
four hours, it would be difficult to say what might not be done by a single 
century of such inundations. 

Note. — In this paper attention has been called to the absence of marine fossils from the terraces 
at Bridge of Earn and elsewhere. If such fossils should occur, it would be important to inquire 
whether they belonged to the time when the terraces were formed. Sometimes portions of antecedent 
deposits are overlaid or enclosed by the materials of the terraces — portions of rock in situ, for example, 
or of boidder clay. In the same way there might be found portions of those marine shell clays which 
belong to a previous period. 



( 177 ) 



IX. — -On Spectra formed by the passage of Polarised Light through Double 
Refracting Crystals. By Francis Deas, M.A., LL.B., F.K.S.E. 

(Read, 6th. June 1870.) 

It is familiarly known as one of the commonest experiments in optics that 
when a beam of polarised light is passed through a thin film of mica or selenite, 
and subsequently analysed either by reflection or by double refraction, two 
colours are seen complementary to one another, and alternating with one another 
at each 90° of a revolution of the analysing plate or prism. 

It might be expected that the coloured light thus obtained would, if thrown 
into the form of a spectrum by means of dispersion prisms, exhibit some 
peculiarities, and such is the case as will be seen from the following experi- 
ments : — 

To make the experiments intelligible, it may be well in the first place to say 
a few words about the instrument employed, and the method of using it. 

Any spectrum microscope ought to answer the purpose provided that in 
addition to the spectroscopic arrangement a pair of Nicol's prisms can be 
attached, one below the stage and the other over the eye piece. Both should 
be capable of being rotated, and it tends much to facility of working as well as 
to exactness of result that both the polarising and the analysing prism should 
carry graduated heads, so that their axes may readily be turned to any re- 
quired degree of inclination to one another. 

The instrument I employed was a large Smith and Beck. The spectro- 
scopic arrangement consists of an adjustable slit attached to the under part of 
the substage below the achromatic condenser, and a set of direct vision prisms 
which are inserted in the body of the instrument immediately above the object 
glass. 

By proper focusing, an image of the slit is thus formed by the achromatic 
condenser in the focus of the object glass, and a fine spectrum obtained filling 
the whole field. 

This arrangement, it will be seen, differs considerably from the spectrum 
microscope in common use in which the dispersion prisms are placed close to 
the observer's eye, the slit being in the focus of the eye lens. The former 
arrangement has this manifest advantage, that owing to the distance of the 
prisms from the eye, the spectrum fills the whole field ; also, that the apparent 
breadth of the spectrum can be varied at pleasure by a change of the magnify - 

VOL. XXVI. PART I. 3A 



178 FRANCIS DEAS ON SPECTRA FORMED BY THE PASSAGE OF 

ing power employed. Each form of arrangement has, however, its advantages 
as well as disadvantages, which it would be out of place to discuss here. 4 '" 

The polarising part of my apparatus consists of two Nicol's prisms, for one 
of which, when desired, a double image prism can be substituted. 

The polarising prism is carried on the substage. It is inserted just above 
the slit in a short tube in which it can be freely turned by a graduated head. 
The analysing prism is placed in the usual way — in a cap over the eye piece. 

The film of selenite to be examined having first been mounted in balsam 
between two thin glasses is placed on the stage of the microscope like an 
ordinary object. 

It is a great convenience in this class of experiments to have the stage of the 
microscope not only capable of rotation in the optical axis of the instrument, 
but graduated. 

By this means we can at any time, without displacing the film under exami- 
nation, adjust its neutral axes at any required angle to the plane of polarisation. 

With regard to the mounting of the selenite films for examination the 
following method will be found convenient : — Make in the turning lathe several 
wooden disks about two inches diameter and one-eighth of an inch thick. 
Through the centre of each a hole must then be bored of about half an inch 
diameter. A small portion round the hole is then scooped out so as to form a 
cup, and in this the selenite is placed and secured with sealing-wax. 

The axes of the selenites are then determined and marked on the rims of 
the clisks.t In this way any two or more selenites can be used in combination 
with their axes set at any required angle to one another. 

It remains only to trace the course of a beam of light in passing through the 
foregoing combination. First the ray, having been reflected from the mirror, 
passes through the slit. It is then polarised by the first Nicol's prism, after 
which it passes through the lenses of the achromatic condenser, and appears as 
an image of the slit in the focus of the object glass. Having passed through 
the selenite and the object glass, the ray enters the dispersion prisms and is 
drawn out into a spectrum. This is magnified by the eye piece through which 
the ray, having passed, is lastly analysed by the second Nicol's prism. 

The loss of light from the number of the above media is not so great as 
might be supposed, still an intense source of light is desirable for satisfactory 
results. A good artificial light placed close to the mirror will be found the best. 
In diffused day-light rays are apt to enter the object glass by reflection from 
the brass work without first passing through the polariser, by which the beauty 
of the spectrum is impaired. 

* A similar form of instrument will be found described in tlie "Quarterly Journal of Science" 
for October 1869. 

t Tbe graduated rotatoiy stage above mentioned, and wbicb is supplied by Smith and Beck, 
affords a ready means of doing this. 



POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 179 

To understand the bearing of the experiments, it is necessary to keep in 
view the different effects of a doubly refracting film upon polarised light, accord- 
ing to the position of its axes, with respect to the planes of polarisation. 

Suppose we take a film of selenite, such as those commonly sold as an 
adjunct to the polarising microscope, giving, as its two colours, a pinkish red 
and its complementary green. Such a film will, if examined between two 
Nicol's prisms, act on the light according to the following laws : — 

1st. When a neutral axis of the film is in the plane of primitive polarisation, 
the film will exercise no influence on the light ; if, therefore, the prisms are set 
with their axes perpendicular the field will remain dark, if the prisms have 
their axes parallel the field will contain only white light. 

2d. If the prisms are placed with their axes perpendicular, and the film 
is made to rotate, there will be four points of darkness at each quarter of a 
revolution, viz., when an axis of the film is in the plane of polarisation, and 
between these four points, the same colour (say green) will occur. 

3d. If the prisms are set with their axes parallel, and the selenite is rotated, 
the field will be white at the four points where it was previously dark, and of 
the complementary colour (red) between each of these four points. 

Mh. If the selenite is fixed with its neutral axis inclined 45° to the plane of 
primitive polarisation, and the analyser made to rotate, the field will be alter- 
nately red and green in the four quadrants. 

5th. The colours are always of maximum brightness when the axes of the 
prisms are perpendicular or parallel, and the axes of the selenite inclined 45° to 
the plane of polarisation. 

Suppose, now, we repeat the above experiments, using the polarising spectrum 
microscope above described, and let us call the point in the revolution of the 
selenite at which either of its axes is in the plane of primitive polarisation, the 
zero point, from which the number of degrees through which it is turned are 
measured. 

Let the prisms be set with their axes perpendicular to one another, and the 
selenite rotated on the stage. The spectrum will, of course, vanish at the four 
zero points. Between these points, however, remarkable phenomena occur. A 
person unacquainted with the true nature of the colours of polarisation, and 
proceeding on the analogy of homogeneous light, might expect to get a spectrum 
consisting only of green rays, seeing that that is the colour of the field when the 
spectrum arrangement is removed. This, however, is not the case, and the 
result very beautifully illustrates to the eye what is well known theoretically to 
be the true nature of these colours. What we obtain is a continuous spectrum 
consisting of all the prismatic colours, in greater or less intensity, with the 
striking peculiarity that there is a well-marked dark band in the red, similar in 
appearance to the well known absorption bands which many substances pro- 



180 FRANCIS DEAS ON SPECTRA FORMED BY THE PASSAGE OF 

duce in the spectrum, only blacker and better denned than these are ever 
seen. 

The following is the mode in which the band makes its appearance. As the 
zero point is passed, the light first makes its appearance in the green of the 
spectrum, from which point, as the selenite is rotated, the light opens out in 
both directions. When the light reaches the red, the black band makes its 
appearance, and attains a maximum blackness when the selenite is at 45°, viz., 
when, without the use of the dispersion prisms, the field would contain green 
light of maximum brightness. When this point of revolution is passed, the 
band again fades, the spectrum becomes obscured at each end, the darkness 
creeping in towards the green, till at 90° the spectrum has again vanished. The 
same phenomena recur at each quarter of a revolution. 

Let the Nicol's prisms now be set with their axes parallel, and the same 
selenite rotated on the stage as before. The result is what we should be led to 
expect from the last experiment. At the zero points the selenite exercises no 
influence, and we have a continuous ordinary spectrum. As a zero point is 
passed, however, a dark band makes its appearance, but this time in the green 
rays. The band is at first faint and nebulous, but becomes blacker and sharper 
as the stage is rotated, till at 45° it attains its maximum. The spectrum in this 
experiment never vanishes, but is apparently quite continuous throughout, save 
for the appearance of the black band. 

Lastly, let the selenite be fixed at 45° from the zero point, and the analyser 
rotated. We have now a combination of the two previous experiments. The 
band in the red appears alternately with the band in the green at each quarter 
revolution, the former being at its maximum when the axes of the prisms are 
perpendicular, the letter when these axes are parallel.* 

The above are the appearances which present themselves in the case of most 
films of selenite of a medium thickness. In some cases, however, two, or even 
three, black bands occur simultaneously, these being always followed by as 
many complementary bands, when the analyser is turned through 90°. The 
number of bands can generally be multiplied by using two or more films in 
combination, and the appearances can be still further varied by changing the 
degree of inclination of the axes of the two films to one another. If the two 
films are placed with their similar axes coincident, we obtain, of course, the 
spectrum appropriate to a film equal to the sum of the thicknesses of the two 
films, while, if dissimilar axes are superposed, the spectrum is that due to the 
difference of the same. I have two films which, when properly combined, give 
no less than six well-marked bands simultaneously. 

* If the axis of the selenite makes a greater or less angle than 45° with the plane of polarisation, 
the result is that while the same band still recurs after 180° of a revolution of the analyser, the com- 
plementary band is no longer separated from it by 90°, but by a greater or less angle. 



POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 181 

But the most striking of the phenomena presented by films which give more 
than a single band, remains still to be noticed, viz., the motion of the bands along 
the length of the spectrum. This can generally be easily seen by using two films 
in combination, and properly adjusting their axes. 

The following may be taken as an illustration of this experiment, of which 
many varieties may be made. Suppose the two films are so adjusted as to give 
two black bands, one in the orange and one in the blue, which we may call a 
and b respectively. On rotating the analyser, each band is seen to divide into 
two halves. The right hand half of band a runs along the spectrum, and unites 
with the left hand half of band b, which advances to meet it, the two coalescing 
into a single band in the green. At the same time that this has been going on, 
two entirely new bands have made their appearance. These seem to originate 
respectively beyond the visible rays at each end of the spectrum, and to advance 
in opposite directions till they are met respectively by the left hand half of the 
original band a and the right hand half of the original band b. The result is, 
that when the analyser has been turned through 90°, we have a spectrum with 
three black bands, one in the extreme red, one in the green, and one in the 
indigo. 

Continuing still further to turn the analyser the above phenomena are re- 
versed. Each of the three bands splits into two, moving in the reverse of their 
former directions, until when 180° is reached the original spectrum with its two 
bands recurs. 

A curious variety of this experiment occurs when a circularly polarising film 
is interposed between the analyser and the film producing the bands. The 
nature of the movements of the bands is now entirely changed, the order of 
motion being all in the same direction, and the bands appearing to chase one 
another along the length of the spectrum, making their appearance at one end 
and disappearing at the other. To produce this effect, the " band-producing" 
film should be set with its neutral axis at 45°, and the circularly polarising film 
superposed with its neutral axis in the plane of primitive polarisation. If the 
axis of either film is turned through 90°, the motion of the bands is reversed ; 
i.e., if the bands formerly moved from left to right, they now move from right 
to left. If the two films are both placed with their axes at 45° to the plane of 
polarisation, the only effect of the circularly polarising film is to alter the posi- 
tion of all the bands by a corresponding amount [i.e., to increase or diminish 
their refrangibility) without affecting the nature of their motions.* 

A very pleasing and beautiful variety of the foregoing experiments may be 
obtained by using a double image prism as the analyser instead of the Nicol's 

* The effect of circularly polarising the light before it passes through the selenite, is simply that 
the occurrence of the hands is irrespective of the inclination of the axis of the selenite to the plane 
of primitive polarisation, and depends solely on the position of the analyser. 

VOL. XXVI. PART I. 3 B 



182 FRANCIS DEAS ON THE SPECTRA FORMED BY THE PASSAGE OF 

prism. Two spectra formed respectively by the ordinary and extraordinary 
ray are thus obtained, which by rotating the double image prism may be made 
to lie parallel to one another, or be partially superposed at pleasure, while by 
turning the polarising prism the spectra can be made of any desired relative 
intensity. Suppose that we adjust the two prisms with their axes at right 
angles, and interpose the selenite used in the first experiment, which gave a 
band alternately in the red and in the green, we get now two spectra parallel 
to one another, the band in the red of the one occurring simultaneously with 
the band in the green of the other. The two bands are thus seen to be strictly 
complementary, for the band in the red of the one spectrum appears, attains its 
maximum, and vanishes simultaneously with the similar changes of the band in 
the green of the other spectrum. This coincident appearance of the bands, 
moreover, is independent of the inclination of the axis of the selenite to the 
plane of polarisation, the only effect of a change in which is to increase or 
diminish the maximum intensity of both bands alike, a result which, as has 
been noticed, does not hold with regard to the alternation of the two bands in 
the same spectrum.* 

When the two prisms are placed with their axes parallel, so that the two 
images of the slit are seen alongside one another, and consequently the two 
spectra partially superposed and different colours mixed, the appearance of the 
bands is very striking. A band occurring in either spectrum is no longer black, 
but of the colour of that part of the other spectrum which coincides with it. 
The appearance is, in fact, as if a stripe had been cut out of the one spectrum 
through which the colour of the other spectrum is seen, while on either side of 
the band we have in striking contrast the colours due to the compounding of the 
different parts of the two sjDectra. 

The beauty of the effect depends of course greatly on the extent to which 
the double image prism separates the two images. It should be so cut that the 
compound colours caused by the overlapping of the spectra shall be as different 
as possible from either of their constituent colours. The selenite should then 
be set at 45°, so as to make the spectra of equal and the bands of maximum 
intensity. 

With films which give numerous bands the effect is very beautiful, and may 
be still further enhanced by rotating the polariser, when the bands will shift 
their position, at the same time changing their colours. 

Experiments with Sections of Double Refracting Crystals giving Coloured Rings. 

The coloured rings produced when polarised light is transmitted through a 
double refracting crystal cut perpendicularly to its axis, have always been 

* See Note on p. 180. 



POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 183 

admitted to be among the most beautiful of the phenomena which the science 
of optics can produce. 

When homogenous light is used it is well-known that the rings assume 
entirely the colour of the light used, the spaces between the coloured rings 
being black. 

The splendour of the phenomena, however, obtained by the use either of 
ordinary or of homogenous light, is incomparably inferior to that displayed by 
projecting the rings against the spectrum. The spectrum microscope is admir- 
ably suited for this exhibition. 

The method I adopted was simply to place the section of the crystal imme- 
diately over the eye lens of the microscope, and between it and the analysing 
prism. 

The rings are thus seen of every colour in the spectrum, alternating with 
jet black rings between each, those in the red being the broadest ; and the 
breadth of the rings gradually diminishing to the most refrangible end of the 
spectrum. 

It is impossible to give any satisfactory idea of the appearances by mere 
description, and no little skill or labour would be required to paint any 
adequate representation of the effects seen in some of the following combinations. 

Take, as an example, a section of a crystal of sugar which gives a very fine 
system of rings. I have counted easily as many as forty-five when projected 
against the spectrum. This crystal is one of those which gives in polarised 
light two black brushes, not a black cross like Iceland spar. When the Nicol's 
prisms are at right angles the brushes are at their maximum intensity, and the 
spectrum with its series of rings is seen to be cut in two by the jet black 
brushes. When the analyser is turned through 90° the brushes which would 
now, if seen by ordinary polarised light, be white, are of every colour in the 
spectrum acording to the part of it they fall upon, and shaded off at their sides 
by a nebulous haze of colour through which the black rings are visible. 

In intermediate positions of the analyser the brushes become entirely nebu- 
lous, so that the rings can be seen through their whole extent. In this position 
of matters the circle appears divided into four quadrants, and the rings are 
distinctly seen to be dislocated so to speak, i.e., the rings in the alternate 
quadrants are pushed out so that each coloured ring in the one quadrant is con- 
tinuous with a black ring in the next. 

This effect is still better seen by circularly polarising the light before its 
passage through the crystal. The effect of this is a curious one. Instead of 
the circle being divided into four alternate quadrants, it is now divided into 
two semicircles, the rings in the one being alternate with those in the other. 
The semicircles are separated by two narrow coloured brushes which revolve 
with the analyser, and seem as if they swept out the black rings in the one 



184 FRANCIS DEAS ON THE SPECTRA FORMED BY THE PASSAGE OF 

segment to be replaced by the coloured rings of the next. If we again circu- 
larly polarise the light by interposing a second circularly polarising plate between 
the crystal and the analyser, the brushes entirely disappear, and both the black 
and the coloured rings are continuous throughout, forming perfect circles. 

When the analyser is rotated through 90°, the centre of the system which 
was formerly black is now coloured, and, at the same time, all the black rings 
have exchanged places with the coloured rings, the change being effected by a 
lateral displacement in opposite directions of the two halves of the circle. 

If, for the second circularly polarising film, we substitute a film of a different 
thickness, the rings assume curiously distorted forms. With one film which I 
used the rings became ellipses, with another they all united so as to form a 
circular helix, which appeared to unwind like a screw as the analyser was 
turned. 

The appearances produced by using different crystals are, of course, similar 
mutatis mutandis. 

By circularly polarising the light before and after its passage through a 
crystal of nitre, the brushes are wiped out, and the lemniscates are beautifully 
seen, unbroken throughout. 

When a crystal of Iceland spar is used, and the Nicol's prisms set with their 
axes inclined 45° we get eight segments, of which the four light segments look 
as if they stood out in relief against the dark segments, while the sections of 
the black rings, especially near the centre of the system, look more like straight 
lines than circular arcs, and form a system of octagons. 

The effect upon the rings, produced by placing on the stage a film of selenite 
in the position in which it should give the black bands previously described, 
is a strange one. Instead of a black band occurring, the coloured ring 
belonging to that part of the spectrum is seen to split into two. It sends off 
a branch as it were from its lower part, which shoots across the adjoining 
black ring, and joins itself with the lower part of the next coloured ring. 
This last ring then in turn sends off a branch from its middle part, which in 
like manner unites with a third ring, which in turn does the same to its neigh- 
bour. All this takes place within the space which should be occupied by the 
black band. 

The beauty of these last experiments, wonderful as it is, may be still further 
enhanced by the use of a double image prism as the analyser. The result is 
analogous to that obtained with the same arrangement in the case of the selenite 
previously described. We now get not only two spectra but two systems of rings 
which, by superposing the spectra, may be made to interlace with one another. 
Wherever a black ring of the one spectrum crosses a black ring of the other, 
the intersection is of course still black. Where a coloured ring of the one 
system crosses a black ring of the other, it retains its original colour ; but if a 



POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 185 

coloured ring crosses a coloured ring, the intersection is of the resultant colour 
of the two combined. 

Still more complex figures are got by employing two or more crystals in 
combination. 

Indeed, there is no end to the variety of exquisite beauty, both in colour and 
in pattern, which a little ingenuity may produce. Pigments would be almost 
as helpless as words in representing many of these. The appearance produced 
by a single crystal with a double image prism as analyser, may be not inaptly 
compared to a tesselated pavement of every colour made for a fairy palace, 
while that produced by combining two crystals may be said to resemble a suit 
of chain armour wrought for a fairy king in jewels of which no two are of the 
same hue. 



Addition to the above Paper. By J. Clerk Maxwell, LL.D., F.R.SS. L. & E. 

In Mr Deas' paper a number of interesting experiments are described, in 
which, by means of a spectroscopic microscope fitted with polarising and analys- 
ing prisms, the true nature of the phenomena observed by Brewster, Biot, 
and others, in plates of selenite, &c, is made exceedingly intelligible to the 
understanding, while, at the same time, the eye is satiated with new forms of 
splendour. 

The subject is one to which the attention of experimenters is not so strongly 
directed as it was fifty years ago ; and therefore it is desirable that the remark- 
ably simple methods of observation here described, and the perfection with which 
the phenomena may be seen by means of modern instruments, should be more 
generally known. 

In the text, the paper appears purely descriptive, without any theoretical 
application, and the aesthetic beauty of the phenomena might be assumed to be 
the object of the experiments. But the carefulness of the selection of the 
experiments and the faithfulness of the description make me think that the 
author himself looked at what he saw in the light of the theory of double 
refraction and the interference of light. I, therefore, think that a simple state- 
ment of the relation of the visible things here described to the results of theory 
would greatly increase the value of the paper ; for in scientific education the 
identification of what is observed with what is deduced from theory is of more 
value than either the process of observation or the process of deduction. 

This might be done as follows : — 

Begin with the plane polarised light, the equations of motion of which are 

x = c cos nt y — 0. 
Now let it pass through a plate of crystal of which the axis is inclined a to 

VOL. XXVI. PART I. 3C 



186 



FRANCIS DEAS ON THE SPECTRA FORMED BY THE PASSAGE OF 



the axis of x ; and let this crystal produce a retardation whose phase is p in 
the light polarised in the plane of the axis 

parallel to axis x' — c cos a cos {nt + p) 

perpendicular to axis y' — c sin a cos nt . 

Next, let the light fall on an analyser in a plane inclined yS to the axis of 
the crystal. The analysed light will be 

x" = c cos a cos /3 cos (nt + p) + c sin a sin /3 cos nt . 

The intensity of this light will be 

c 2 {cos 2 a cos 2 /3 + sin 2 a sin 2 /3 — 2 sin a cos a sin /3 cos /3 cos p\ 

or g c 2 1 1 + cos 2a cos 2/3 — sin 2a sin 2/3 cosj? j . 

We may represent this whole process geometrically as follows : — 

Let OCO' represent the original polarised 
light, OCA the angle between the plane of 
polarisation and the axis of the crystal. 
The light is resolved into ACA' and DCD'. 
Now, let a semicircle be drawn with radius 
OA, and let OAp — p be the phase of retar- 
dation ; draw pT perpendicular to AO, and 
draw an ellipse with centre C and touching 
AO in T and also the other sides of the 
parallelogram. This ellipse is the path of the 
light emergent from the crystal. Now let BCB' be the plane of the analyser. 
Draw Tb T'b' tangents to the ellipse perpendicular to BB 7 , then bCb' represents 
the amplitude of the emergent light. 

The result of the process may be made still simpler thus : 

Draw CO = c, in the plane of polarisation, CA parallel to 
the axis of the crystal, and CB parallel to the analyser. 
Draw OA perpendicular to CA, AB to CB, and OD to CB, 
then CB = c cos a cos /3, and BD = c sin a sin (3 ; make DBP =p, 
the phase of retardation, and BP = BD. Then CP represents 
the amplitude of the emergent light. 

The emergent light will be either a maximum or a 
minimum when p = 0° or nir. 

The minimum will be zero, or blackness, only in the following cases, 

1. When a + /3 = \ and p = or 2mr. 





2. When a — /3 = \ and p = (2ra + l)n. 



POLARISED LIGHT THROUGH DOUBLE REFRACTING CRYSTALS. 187 



3. When a = and £= \. 

4. When a = J and /3 = 0. 

To compare our results with the experiments, we observe that for a given 
thickness of the crystal p is a function of the kind of light, so that in passing 
from one end of the spectrum to the other the value of p increases (or dimi- 
nishes) in a continuous manner. When the film is thick, p will make several 
entire revolutions within the spectrum. When it is thin, there will be only one 
or two, or a fraction of a revolution. Take the case of a thick film, then there 

will be a certain set of black bands when /3 = ^ — a. We may call these No. 1. 

For these p = 2mr. 

When ft — ? + a there will be another set of black bands, No. 2, inter- 
mediate in position to No. 1. For these _p = (2 n + 1) n. 

When /3 = or „ the system of bands vanishes. 

When (3 = — a the black bands of No. 1 become bright and of maximum 
intensity. 

When /3 = a the black bands of No. 2 become bright and of maximum 
intensity. 

When a = I" all these phenomena are at their greatest distinctness. 

In turning the analyser there is simply a dissolution of one system into the 
other, without motion of the system of bands in the case of a single plate of 
crystal. But if we place the crystal with its ■axis inclined 45° to the plane of 

primitive polarisation, and place above this a film of retardation ~ with its axis 

parallel to the original polarisation, then we have as before for the light emerg- 
ing from the first crystal, 

of = c — r= cos (nt + p) y' = c— y= cos nt . 

Resolving these rays in the direction of the axis of the second film, we have 

x" = o c (cos (nt + p) + cos nt\ 

y" = g c (cos (nt + p) — cos nt) , 
and since x" is retarded |" it becomes 

x" = s c (sin (nt + p) — sin nt j , 



188 ON THE SPECTEA FORMED BY THE PASSAGE OF POLARISED LIGHT, ETC. 
y" remaining the same. We may put these values into the form 



x" — c cos ( nt + f j cos| 



y" — c cos ( nt + ~ j sin p 



2 



This shows that after emerging from the circular polarising film the ray is 

plane-polarised, that the plane of polarisation inclined „ p to that of primitive 

polarisation. 

If the emergent light is analysed by a dispersion prism, and a Nicol's prism 
inclined (B to the plane of primitive polarisation, there will be black bands 
(perfectly black) for all colours for which 

p = 2/3 or 2/3 + 2nv , 

and as the prism is turned these bands will march forwards in a regular manner 
across the spectrum. 

This very beautiful experiment, in which the phenomena of rotatory polarisa- 
tion are imitated, is not so well known as it deserves to be. One form of it is 
due, I believe, to Biot, and another to Wheatstone, but the arrangement here 
described is by far the most convenient. 

When the second plate is thick, then for some points of the spectrum its 
retardation is (2 n + £) it. At these points the bands will move forwards when 
the analyser is turned. At an intermediate set of points the retardation is 
(2n— ^)ir. At these points the bands will appear to move backwards. At 
intermediate points the retardation is nw. At these points the bands will not 
move, but will become deeper or fainter. I suppose this to be the explana- 
tion of the experiment described at p. 181, but the arrangement of the films 
is not very precisely described. 

The experiments with the rings in crystals are very well described, and 
must be beautiful, but are not so instructive to a beginner as those with the 
selenite plates. Those, however, who have made out the meaning of the expe- 
riments first described have a good right to regale themselves with gorgeous 
entanglements of colour. 



( 189 ) 



X. — On the Oxidation Products of Picoline. By James Dewar, F.R.S.E., 
Chemical Demonstrator in the University of Edinburgh, and Lecturer 
on Chemistry at the Edinburgh Veterinary College. 

(Read 6th June 1870. ) 

The combined researches of Anderson and Williams on the basic compounds 
contained in coal tar have led to the discovery of two well-defined series of 
organic bases, called respectively the Pyridine and Chinoline series, the mem- 
bers of both of which possess the properties of nitrile bases. The isomerism 
between the pyridine and the aniline series of bases excited considerable 
interest at the time of its discovery. The subsequent researches of Williams 
on the products of the distillation of chinchonine led to the discovery of bases 
having the same composition as the members of the pyridine and chinoline 
series of coal tar. When first discovered they were supposed to be identical. 
Since that time, however, a careful examination and comparison of the tar 
series of bases with the chinchonine series has led Mr Williams to the interest- 
ing discovery that the two lutidines, as also the two chinolines, are in reality 
not identical, but isomeric. This introduces a greater complexity into the 
study of the constitution of these compounds. 

I began this investigation in the summer of 1867 under the able direction 
of Professor Aug. Kekul£, in the University of Ghent. At that time the 
whole of the then known facts regarding the properties of these bases had been 
accumulated by Anderson and Williams, and by Perkin, who had obtained 
pyridine from a naphthaline derivative. Save by this latter method the only 
process of preparation known was destructive distillation. All the attempts 
that had been made to elucidate the internal constitution and relationship of 
these bases had failed to yield positive results, their extreme stability in 
presence of the most powerful reagents presenting a barrier to investigation. 
In 1869 Professor Adolphe Baeyer made the brilliant syntheses of picoline 
through the action of tri-brom-allyl and of acryl aldehyd, respectively, on 
ammonia; and through the action of higher aldehyd homologues has shown the 
reaction to be general. Thus, by the synthetical labours of Baeyer, we have 
acquired for the first time a definite knowledge regarding the mode of forma- 
tion and constitution of this class of organic compounds. 

Having formerly employed permanganate of potassium in the oxidation of 
phenol (see Proc. Roy. Soc. Edin. Session 1866-67, p. 82), I naturally attempted 
the oxidation of these bases by the same agent ; and I have since found that 
vol. xxvi. part i. 3d 



190 MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 

A. W. Hofmann had successfully employed it to oxidise chinoline into ammonia 
and oxalic acid. Finding the members of the pyridine series to be easily 
attacked by this reagent, I commenced a careful examination of the products 
of the oxidation of picoline, with the object of learning something regarding its 
internal structure. A preliminary note on the results obtained was communi- 
cated to the British Association at its Norwich meeting, 1868 (see Report Brit. 
Assoc. 1868). 

I am indebted to my friend Dr Ronalds of Bonnington for a liberal supply 
of a quantity of bases that he had carefully prepared, with the object of insti- 
tuting an investigation into these compounds himself. The crude bases placed 
in my hands had been repeatedly fractionated on a large scale, and the indi- 
vidual fractions were thus tolerably pure to begin with. Finding they contained 
traces of pyrrol and hydrocarbons, I redissolved in acid the fraction boiling 
from 130° to 160° C, and subsequently treated it in the way recommended by 
Anderson and Williams to purify these bodies. The mixture of bases thus 
obtained was subjected to a series of careful fractional distillations. With the 
object of effecting the best possible separation, T employed the method recom- 
mended by Warren, and found it admirably suited to effect a comparatively 
easy separation, so far as fractional distillation can be made to yield a pure 
product. The bases were transferred to a retort connected with an ascending 
spiral of copper tube enclosed in a paraffine bath of large dimension, the tem- 
perature of which was continuously equalised by constant stirring. Five suc- 
cessive fractionations by this method gave a separation as complete as was 
necessary for the object I had in view. From the laborious researches of 
Anderson and Williams, we know that these bases for a large range of tem- 
perature have the same composition, and that perfectly pure products can be 
obtained only through the fractional precipitation of the platinum salts. 
Although I did not make an exhaustive separation by Warren's method, the 
fractionation was so effective that, by comparing the temperature of the boiling 
vapour in the retort with the temperature of the paraffine bath throughout the 
whole course of a distillation, a difference of 10° C. at starting gradually 
increased to 20°. No fraction that I obtained, separated in this process by a 
difference of 2° C in the intermediate condenser, had a perfectly constant 
boiling point. On different occasions fractions separated in this way, boiling 
between 130° and 140° C, have been employed in the following experiments. 
Analyses of the platinum salts of portions boiling between those temperatures 
showed the fractions to be substantially picoline, with a possible trace of 
lutidine. 

Picoline, as is well known, resists oxidation by the most powerful agents 
adapted for this purpose, nitric and chromic acids being without visible action, 
even at high temperatures. Of all oxidising agents, permanganic acid, or its 



MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 191 

potassium salt, seems to be the most powerful. Having on a former occasion 
employed this reagent to effect the oxidation of phenol alcohol, I naturally 
investigated the action effected on these nitrile bases. I found that the whole 
of the members of this series of compounds could be readily oxidised by the 
use of this substance. The higher members of the series were oxidised more 
readily than the lower, but in all cases it was effected with ease and rapidity. 
The following is a description of the apparatus used in the experiments on the 
oxidation products of these substances and of the mode of conducting the 
operation. A flask, about three litres in capacity, was connected by a wide 
tube with a large reversed Liebig's condenser, so as to effect a rapid condensa- 
tion of volatile products and their immediate return to the field of chemical 
action. The flask having been placed on a sand bath, 150 grms. potassium 
permanganate, 1^ litres water, and 25 grms. picoline were introduced, and the 
whole heated to near the boiling point. The reaction began suddenly, with 
great evolution of heat, necessitating the removal of the source of external heat. 
The reduction of the permanganate was completed in half an hour. After the 
contents of the flask had cooled, the oxide of manganese was separated by 
filtration from the strongly alkaline liquid, and washed repeatedly with boiling 
water. The alkaline liquid was then transferred to a flask, and the basic sub- 
stances distilled off*. The residual alkaline liquid was then concentrated by 
evaporation to 200 c.c. and 300 c.c. and dilute sulphuric acid (containing 70 per 
cent. H 2 S0 4 ) added to it. After standing for some time this acid liquid became 
thick from a deposit of long white crystalline needles of a complex of new 
acids. In different experiments the relative proportions of the reacting sub- 
stances were considerably varied, but the yield of the new acids in every case 
was small, a large portion of the picoline having been completely oxidised, while 
some of it had remained unacted upon. This must always be the case, as a 
large quantity of the original base, from the violence of the reaction, was driven 
away from the flask, and, when condensed, it fell back into a boiling liquid of 
increasing alkalinity, in which the base was comparatively insoluble. After 
separating, by filtration, the new crystalline acid referred to, the filtrate was 
transferred to a retort, and the volatile acids distilled off. 

General Eesults of Oxidation. — When the dilute alkaline fluid was taken 
immediately after the permanganate was exhausted, it was found to contain 
carbonate of potassium. When neutralized with hydrochloric acid and chloride 
of calcium added, a white precipitate of oxalate of calcium was obtained. The 
oxalate was mixed with a small quantity of some higher acid, probably malonic, 
as the per-centage of lime found was 36 3, oxalate containing 38 -3 per cent. 
The quantity of volatile acid produced by the reaction was small. The 
presence of nitric and acetic acids, however, was readily proved. The surplus 
base remaining after the oxidation operation was transformed into the double 



192 MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 

platinum salt, and a fractional crystallisation made. The platinum was deter- 
mined in these different salts as follows : — 

1st Crystallisation— 0' 177 grm. pt-salt gave 0'077 grm. pt=43'7 per cent. 
2d „ -0-6910 „ „ 0-2102 „ =33-95 per cent. 

The first sample agreed in composition with the double chloride of platinum 
and ammonium ; the second, with that of a mixture of the double platinum salts 
of pyridine and picoline. There was produced by the reaction, therefore, 
carbonic, nitric, oxalic, acetic, and a complex of new acids, ammonia, and pro- 
bably a small quantity of pyridine. The relative proportion of the products 
obtained depended on the quantity of the oxidising agent used, the volume of 
the solution, rapidity of the action, and the quantity of bases present in the field 

of action. 

( CO IT 

Di-carbo-pyridenic Acid C 5 H 3 N < nr) tj- — The crystalline acid substance 

separated by adding excess of sulphuric acid to the concentrated alkaline fluid, 
after standing overnight was collected on a filter, and repeatedly crystallised 
from hot water (in which it was easily soluble) until free from oxalic acid and 
potassium salts. When first separated from the acid solution it appeared in 
long needles ; but after several recrystallisations from water it was obtained in 
the form of perfectly colourless plates, resembling naphthaline. (The crystallo- 
graphic constants of this acid have not yet been determined.) The crystals 
did not contain any water of hydration. The following are the results of the 
analyses of the acid and its silver salt : — 

Acid. 

Weight of acid taken, ......... - 2195 grm. 

Carbonic anhydride produced, ....... 00685 „ 

Water produced, ......... 0'4040 „ 

Nitrogen found by Gottlieb's method to bear to the C0 2 produced, the 

proportionate vol. of, . . . . . . . 1 to 14'2 

Calculated centesimally these figures give — 

Sample. C 7 H 5 NO.. 

Carbon, ... 50d9 50"29 

Hydrogen, 347 2'99 

Nitrogen, .......... — — 

Silver Salt." 

As with the acid, the salt was dried at 100° C. 

Weight of salt taken, ...... 

Carbonic anhydride produced, .... 

Water produced, ...... 

Weight of salt taken, ...... 

Silver obtained, ....... 

* I. and II. were samples of silver salts obtained from different experiments. I. was got by double 
decomposition of the sodium salt ; II. from the ammonium salt. 



I. 

0-8766 grm. 
0-6985 „ 
0-0554 „ 


II. 
0*5456 grm. 
0-4518 „ 
0-0602 „ 


0-6980 grm. 
1-5111 „ 


0-3951 grm. 
0-6525 „ 



I. 


II. 


C 7 H 3 NAg 2 4 . 


21-73 


22-58 


22-04 


0-70 


1-22 


0-78 


56-60 


56-78 


56-69 



MR JAMES DEWAE ON THE OXIDATION PRODUCTS OP PICOLINE. 193 

Calculated centessimally these results give — 

Carbon, ........ 

Hydrogen, ........ 

Silver, ......... 

In order to determine the equivalent of the acid, I took 0*5392 grm. of acid 
dried at 100° C. and titrated with pure caustic soda solution, every 1-813 c.c. 
containing 23 mgrm. of sodium ; 1 1 *7 c. c. of soda neutralised the acid taken. The 
point of saturation was well marked. The equivalent of the acid, from this de- 
termination, was, therefore, 83*55; as determined by analysis of the silver salt it 
was 83*5. The atomic weight of the acid taken as C^H.NO^ was exactly double the 
equivalent found, which, if true, would necessarily involve the acid being bibasic. 
In order to determine the basicity of the acid, the ammonium salts were the 
only combinations that I specially examined. 0*4739 grm. of the acid carefully 
treated with excess of ammonia, and dried at 100° C, increased in weight by 
0*0481 grm., gain = 10*13 per cent. ; gain on the acid ammonium salt of fore- 
going formula = 10*17 per cent. The neutral ammonium salt was extremely 
soluble in water, whereas the acid salt was much less soluble, and could readily 
be obtained in the form of fine silky needles when the solution was evaporated. 
From the above data there can be little doubt that the acid was bibasic, bearing 
the same relation to pyridine that phthalic acid does to benzol. The acid melted 
at a temperature of about 210° C, frothed, evolved a small quantity of carbonic 
anhydride, and emitted the readily recognisable smell of these bases. It was 
easily decomposed when heated with soda-lime, evolving a basic substance, no 
doubt pyridine. The mercury, copper, cadmium, and zinc salts were all readily 
soluble in water. The barium and calcium salts were also soluble, and were 
obtained by adding the respective chlorides to the neutral sodium or ammonium 
salt ; they crystallised in minute prismatic needles. The silver salt of this acid 
was specially characteristic. On the addition of nitrate of silver to a solution of 
the acid or its neutral ammonium salt, a white gelatinous precipitate immediately 
separated out — it was insoluble in boiling water, and was not visibly affected by 
exposure to light. The insolubility of this salt would enable us more readily to 
separate the acid from the other products of the oxidation reaction than the 
process first quoted in this paper. 

Along with the acid just described, as separated by the process detailed, 
there was found associated with it another acid substance having a very much 
higher atomic weight. The crystalline mass, obtained by the addition of sul- 
phuric acid to the alkaline liquid from the oxidation operation, purified by solu- 
tion in and recrystallisation from alcohol, and dried over sulphuric acid by means 
of an air-pump, had an equivalent weight of 121. The crystals were hydrated, 
and lost 4*9 per cent, of their weight when dried at 100° C. The sodium 

VOL. XXVI. PART I. 3 E 



194 MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 

salt of this mixture gave, on the addition of nitrate of silver, a gelatinous preci- 
pitate agreeing in appearance and composition with that got from dicarbopyri- 
denic acid ; it contained 56 6 per cent, of silver. The equivalent of this mix- 
ture, as determined by the composition of the ammonium salt dried at 100° C, 
was 336 ; 0*8335 grm. of acid mixture dried at 100° C, and treated with 
ammonia, increased in weight by 0*0422 grm. This acid substance, therefore, 
was clearly a mixture of dicarbopyridenic acid with some acid of a very much 
higher atomic weight. It remained solid when heated to 220° C, at which 
temperature dicarbopyridenic acid readily melted, and was much less soluble 
in water than the latter. 

The difficulty and expense of obtaining these oxidation products in any 
quantity, prevented me from making the exhaustive investigation I would have 
liked. 

The formation of dicarbopyridenic acid by the oxidation of a mixture of 
picoline and lutidine, whether obtained from lutidine alone or by the complete 
destruction of picoline, is quite analogous to the formation of phthalic or teraph- 
thalic acid, by the oxidation of the homologues of benzol, or by the complete 
destruction of benzol itself, as shown by Carius ; the only difference being that 
Carius employed the lowest member of the benzol series, whereas picoline is the 
second known member of the basic series. The production of the same acid from 
pyridine itself would in no wise influence speculation regarding the constitution 
of the higher members of the series. For the present, we may consider pyridine 
as the nucleus from which all the other members of the series are derived. 
Although such a supposition must be considered purely hypothetical, in reality 
it is a great advantage to classify by analogy, relatively to other series, disjointed 
groups of organic compounds. The two series of bases, viz., the coal-tar and 
the chinchonine, bear the same empirical relation to pyridine that benzol does 
to its homologues and to naphthaline. 



Benzol. 


Toluol. 


Naphthaline. 


C 6 H 6 


C 6 H 6 

CH 2 


C 6 H 6 

C 4 H 2 


Pyridine. 


Picoline. 


Chinoline. 


C 5 H 5 N 


C 5 H 5 N 


C 5 H 5 N 




C H 2 


C 4 H 2 



Now, although it has not yet been proven that lutidine and chinoline have a 
similar formative relation to pyridine that tolnol and naphthaline have to 
benzol, still it is by no means an improbable analogy. The isomerism in the 
pyridine series, so far as is known, commences with the third member, lutidine, 
as found by Williams on comparing the chinchonine lutidine with the coal-tar 
lutidine ; whereas the chinoline obtained from either source differs essentially 
in chemical characters. If we consider picoline as in all likelihood methyl- 



H H 


H 


C = c x 


^C = N ^ 


CH 


HC CH 


C -C* 


xX c-c^ 


H H 


H H 



MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 195 

pyridine, then the a and /3 lutidines may, in all probability, be represented as 
dimethyl-and ethyl-pyridine respectively, and we would expect the dimethyl- 
pyridine to give directly dicarbopyridenic acid, or an isomer, on oxidation. 
Pyridine may be written graphically as benzol in which nitrogen functions in 
place of the triatomic residue CH'", and thus may be represented as a closed 
chain, — 



HC 



And, considering the stability and mode of formation of these bases it is not at 
all improbable that they may not be produced by the simultaneous action of 
acetylene and its derivatives on hydrocyanic acid ; thus as three molecules of 
acetylene condense and form benzol, so may two molecules of acetylene, and 
one of hydrocyanic acid, condense and produce pyridine. 

There is a large class of substances that bear the same relation to the mona- 
mines that dicarbopyridenic acid does to pyridine, with this difference, that the 
best known are all monobasic instead of being bibasic acids. Thus glycocol, 
alamine, leucine, and their homologues, may be looked upon as the monocarbo- 
acids of the ethylamines, in which the carboxyl radicle is united directly to the 
carbon, the isomeric carbamic acids (or urethanes, as they are called) being the 
derivatives in which the carboxyl is united directly to the nitrogen, — 



Ammonia. 


Methylamine. 


Glycocol. 


Methyl-carbamic Acid 


H 


CH 3 


CH 2 C0 2 H 


CH 3 


N H 


N'H 


N H 


N H 


H 


H 


H 


C0 2 H 



Analogous derivatives are obtained from the aromatic ammonias. A class of 
derivatives similar to the above, must necessarily be derivable from the diamines. 
In the case of the nitrile bases or triamines, only derivatives could be obtained 
analogous to glycocol and its homologues. Bodies of a like constitution to 
glyCocol readily break up into carbonic anhydride, and the corresponding 
ammonia ; the reverse transformation has not yet been effected. The amido- 
bibasic acids bear the same relation to the monamines that dicarbopyridenic 
acid does to pyridine, with the exception of the difference in the constitution of 
the closed nitrile nucleus. No bibasic acid, other than pyridenic, has been 
discovered. A strictly analogous compound, in the monobasic series, is the 
acid carbo-pyrrolic, C 5 H 5 N0 2 , which bears a similar relation to pyrrol that the 
amido-mono-carbon acids do to the ammonias, only that the pyrrol, although a 
nitrogenous body, is not, strictly speaking, a nitrile base. But the close analogy 



196 MR JAMES DEWAR ON THE OXIDATION PRODUCTS OF PICOLINE. 

between pyrrol and true nitrile bases, they being simultaneously produced in 
the majority of reactions, would lead us to expect a like class of derivatives 
being obtainable from pyridine. 

Hubner (Ann. Chem. u. Pharm., vol. 141) has described the oxidation 
products of nicotine, got by the action of sulphuric acid and bichromate of 
potassium. In that memoir he describes an acid so obtained, having the 
formula C 5 H 5 N0 2 . This acid is identical in composition with mono-carbopyri- 
denic acid. The base nicotine itself differs from dipyridine by only four hydro- 
Nicotine. Dipyridine. 
C 5 H 7 N C 5 H 5 N 
C 5 H 7 N C 5 H 5 N 

gens ; and as the nucleus of nicotine is a nitrile nucleus, it is not at all impro- 
bable that this acid may be a member of the series to which dicarbopyridenic 
belongs, so that nicotine may be similarly constituted to Anderson's poly- 
merised bases. 

The stability of these bases to the majority of reagents (especially the 
primary member of the group, pyridine) would predispose us to look upon it as 
analogous to benzol, and to suppose that the atoms are symmetrically grouped. 
The syntheses of Baeyer support this view, and there is not any reason why 
we may not have as many stable derivatives from this nucleus as from benzol. I 
have already pointed out the analogy between the chinoline series and the 
pyridine series ; and in a short time I hope to be able to publish details support- 
ing the theoretical relations above given. 

In the meantime, the following analogies may be pointed out between 
benzol- and nitrile-clerivatives ; thus — 



Benzol. 


Naphthaline. 


Anthracine. 


Pyridine. 


Chinoline. 


C 2 H 2 


C 6 H 4 


C 6 H 4 


C 2 H 2 


C 5 H 3 N 


C 2 H 2 


C 2 H 2 


C 2 H 2 


NCH 


C 2 H 2 


C 2 H 2 


C 2 H 2 


C 6 H 4 


C 2 H 2 


C 2 H 2 



Indol, from its general characteristics, evidently belongs to the pyrrol series, 
the following showing, in all probability, the relative structure of indol and 
pyrrol : — 



Indol. 


Pyrrol. 


C 6 H 4 


C 2 H 2 


NH 


NH 


C 2 H 2 


C 2 H 2 



According to this hypothesis indol is simply benzol-pyrrol. 



vfvf.K'y-- ■■ 



Sfh.l fe * d 






■>*»?«& 



( 197 ) 



XI. — An Account of the Great Finner Whale (Balsenoptera Sibbaldii) stranded 
at Longniddry. Part I. The Soft Parts. By Wm. Turner, M.B. (Lond.), 
Professor of Anatomy in the University of Edinburgh. (Plates V., VI., 



VII., VIII.) 



(Received November, 1870.)*' 



CONTENTS. 



Introduction, 

External Form and Dimensions, 

Colour, 

Foetus and Membranes, . 
Skin and Blubber, 
Mammary Gland, . 



PAGE 

197 
199 
202 
203 
209 
211 



Baleen, . 

Organs of Alimentation, 
Organs of Circulation, . 
Organs of Respiration, . 
Genito-urinary Organs, . 
Comparison with other Finners, 



PAGE 

212 
222 
227 
235 
240 
242 



On the 3d November 1869, a huge Finner whale was stranded on the beach 
at Gosford Bay, Longniddry, Firth of Forth. 

Most of the large Fin whales which have been examined by British and 
Continental anatomists have been found floating dead on the surface of the sea, 
and have then been towed ashore by their captors. But, from the account 
which was given in the Edinburgh daily newspapers, it would appear that, for 
some days previously, this animal had been recognised by the fishermen, swim- 
ming to and fro in the Firth. On the morning of the 3d it was seen from the shore, 
blowing with great violence from its nostrils, flapping its huge tail, and obviously 
struggling to disengage itself from the rocks and shoals, amidst which an un- 
usually high tide had permitted it to wander. Shots were fired at it, and, from 
the wounds produced, blood poured forth which tinged the surrounding waves. 
As the tide receded, the animal was fairly stranded ; and, after some vigorous 
but ineffectual attempts to disengage itself from its position, it slowly died. 
The animal lay some yards above low- water mark, so that for several hours each 
day it could be examined, and photographs taken from various points of view. 

Under the powers conferred by Act of Parliament, the carcase was taken 
possession of by the receiver of wrecks for the Board of Trade and sold by public 
auction. It was purchased by Mr John Tait, Oil Merchant, Kirkcaldy, for 
L.120. After lying for a fortnight on the beach at Longniddry, a strong rope 

* A preliminary account of this animal, illustrated by a number of specimens, photographs, and 
drawings, was read to the Society on the 20th December 1869, and an abstract of this communication 
was printed in the Proceedings of that date. By permission of the Council I have been allowed to 
supplement the preliminary notice with additional observations, and to extend it in a form for the 
Transactions of the Society. 

VOL. XXVI. PART I. 3 F 



198 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

was secured around the root of the tail, and, when afloat at high water, it was 
towed by a powerful steamer to Kirkcaldy, a town on the opposite shore of the 
Firth, distant about ten miles. 

It was flensed on the beach, immediately to the east of Kirkcaldy harbour ; 
and, as this could only be done at low water, the process of removing the 
blubber, taking out the fat within the abdomen, cutting off" the baleen and flesh, 
disarticulating and removing the bones, occupied several men for nearly a 
month. 

As one of the largest sized whalebone whales comes so very seldom within 
comparatively easy access of a great city, the opportunity was taken by crowds 
of persons to inspect the huge creature, not only as it lay on the beach at 
Longniddry, but whilst the process of cutting up was going on at Kirkcaldy. 

As the classification and structure of the larger Cetacea possess many in- 
teresting points for investigation, I gladly availed myself of the presence of this 
rare visitor to devote such time as I could spare, in the midst of the work of 
the University session, to its examination. 

The colour, general form, and dimensions of the animal were observed when 
the whale was lying on the shore at Longniddry. The observations on the in- 
ternal structure were made as it was being cut up at Kirkcaldy, or on speci- 
mens which were brought over to the Anatomical Museum of the University, 
and submitted there to a more careful examination than could have been con- 
ducted on the sea beach. 

The distance from Edinburgh at which the whale was lying, during the 
flensing, rendering a journey by rail and steamer necessary at each visit, the 
exposed position of the animal on the sea beach below high- water mark making 
access to it practicable only at low water, the great bulk of the creature, the 
difficulty of getting at the internal parts owing to the size of the cavities, the 
greasy, slippery condition of all the surroundings, and the impediments offered 
to handling or removing the viscera on account of their magnitude and weight, 
have made the examination of this whale a very laborious task. For these 
reasons, as well as from the putrid state into which the carcase passed, the 
extremely offensive gases generated by so huge a mass of putrifying flesh, and 
the great heat evolved by its decomposition, it was impossible to study many of 
the structures to which I should have wished to have devoted my attention. 
In many respects, therefore, I regret to say that my description will necessarily 
be incomplete and fragmentary. 

In conducting the examination, I was most ably assisted by the thoroughly 
cordial and, I may say, enthusiastic, co-operation of my assistant, Mr Stirling, 
and my pupils, Mr Millen Coughtrey and Mr James Foulis, to whom I take 
this opportunity of expressing my thanks for the important aid which they ren- 
dered. To Mr John Tait of Kirkcaldy I and my assistants are indebted for 



STRANDED AT LONGNIDDRY. 1 99 

permission to examine the parts as they were exposed during the flensing, and 
to remove such specimens as could conveniently be taken away. 

External form and dimensions. — The whale was a female. When I first 
saw the animal on Gosford beach, it was lying with its head pointing inland, 
and it rested on the right side of the belly, chest, and right lower jaw. The 
middle line of the belly was in contact with the ground, and the under surface 
of its horizontal tail lay on the shingle. The head, owing to its great weight, 
had fallen over to the right, so that it overhung the right lower jaw, and per- 
mitted the whole length of the inner surface of the left half of the lower jaw, 
and a large part of the dorsum of the tongue to be seen, together with the outer 
edges of the baleen plates on the left side (Plate V. fig. 1). 

The length of the animal, measured with a graduated tape-line along the 
curve of the middle line of the back from the tip of the lower jaw to the end of 
the tail, was 78 feet 9 inches. The girth of the body immediately behind the 
flipper was estimated at 45 feet, dimensions which it preserved almost as far 
back as the extent of the abdominal plicae, behind which it tapered off rapidly 
to the tail. Its girth in line with the anal orifice was 28 feet, whilst around the 
root of the tail it was only 7 feet 9 inches. In front of the flipper the girth 
was considerable, as far forward as the swell or greatest projection of the lower 
jaw, but in front of this it tapered off to the symphysis. The lower jaw arched 
outwards and forwards with a wide sweep from the angles of the mouth ; then the 
two halves converging met at the symphysis and formed there a keel-like ridge. 
The tip of the lower jaw projected 1\ foot beyond the tip of the upper jaw. 
The inner surface of the lower jaw was bevelled off close to its upper border, 
so as to admit the edge of the upper jaw within it. The length from the angle 
to the tip of the mouth, along the upper curved border of the lower jaw, was 
21 feet 8 inches, and 17 feet 4 inches in a straight line. 

The dorsum of the upper jaw was not arched in the antero-posterior direc- 
tion as in the Balama mysticetus. It sloped gently upwards and backwards to 
the blow-holes, from which a low but readily recognised median ridge passed 
forwards on the beak, gradually subsiding some distance behind its tip. On 
each side of this ridge was a shallow concavity. Immediately in front of the 
blow-hole the ridge bifurcated, and the forks passed backwards for several 
inches enclosing the nostrils, and then subsided. The outer borders of the 
upper jaw were not straight, but extended forward almost parallel to each other 
from the angle of the mouth for some distance in a gentle curve, and then con- 
verging in front formed a somewhat pointed tip. Their rounded palatal edges 
fitted within the arch of the lower jaw. The transverse diameter of the upper 
jaw over its dorsum between the angles of the mouth, was 13 feet 3 inches. 

From the blow-holes the outline of the back curved upwards and backwards, 
it was uniformly smooth and rounded, and for a considerable distance presented 



200 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

no dorsal mesial ridge. But somewhat in front of the posterior fourth of the 
back a ridge appeared, which culminated in the dorsal fin. Unfortunately the 
height of this fin could not be taken, as the summit had been cut away before I 
saw the animal. It was triangular in form, its anterior border convex, its 
posterior border falcate, whilst its apex had obviously projected upwards and 
backwards. A line drawn from its posterior border vertically down the side of 
the whale reached the ventral mesial line some distance behind the anus. From 
the tip of the lower jaw to the anterior border of the dorsal fin was 59 feet 3 
inches. Behind the dorsal fin the sides of the animal sloped rapidly down- 
wards to the ventral surface, so that both the dorsal and ventral mesial lines 
were clearly marked, and the sides tapered off" backwards to the tail. 

The lobes of the tail curved outwards and backwards from the terminal 
part of the sides of the animal ; a rounded interlobular median notch marked 
the termination of the caudal spine, and separated the two lobes from each 
other. The anterior border of each lobe was rounded, and convex from root to 
tip, the posterior was sharp, and concave from root to tip ; the tip was pointed 
and the surfaces flattened. The greatest girth of one of the tail lobes was 5 
feet 8 inches, whilst the distance between the tips of the two lobes was some- 
what more than 16 feet.* 

The ventral surface of the throat, and the sides and ventral surface of the 
chest and belly, were marked by numerous longitudinal ridges and furrows. 
Some extended as far forward as the symphysis of the lower jaw, others to the 
angle of the mouth ; some mounted as high as the root of the flipper, and even 
above its posterior border. These folds terminated at their hinder ends with 
great regularity .along a line, which commencing some distance behind the root 
of the flipper sloped obliquely downwards and backwards to the ventral sur- 
face. The ventral folds were consequently the longest, one about the middle of 
the belly measured 45 feet. The number of these folds on each side of the 
ventral mesial line it was difficult exactly to determine, on account of the posi- 
tion in which the whale was lying, but at least thirty appeared to be present, 
though as a ridge occasionally bifurcated or gave off a branch, and as, after some 
time, its forks blended with adjacent ridges, the number necessarily varied in 
different localities. When I first saw the animal the furrows separating the 
ridges were not more than from J to f an inch broad, whilst the ridges them- 
selves were in many places 4 inches in breadth, but as the body began to swell 
by the formation of gas from decomposition, the furrows were opened up, be- 
came wider and shallower, and the ridges underwent a corresponding diminu- 
tion in breadth. At the same time a considerable change took place in the 
contour of the body in the thoracic and abdominal regions, which presented 

* The extreme ends, probably one foot from each lobe, bad unfortunately been cut away before 
the measurement was taken. 



STRANDED AT LONGNIDDRY. 201 

a huge lateral bulging, giving a greater girth than when it first came 
ashore. Close to the posterior ends of the mesial abdominal plicae was a deeply 
puckered scar, the umbilicus. 

The nipper projected from the side of the body 31 feet 4 inches behind the 
tip of the lower jaw, measured in a straight line, and 14 feet behind the angle 
of the mouth. It curved outwards and backwards, terminating in a free pointed 
end. Its surfaces were flattened ; its anterior border rounded and convex from 
root to tip, measured 12 feet 3 inches ; its posterior border concave from root 
to tip 10 feet, whilst its girth at the root was 9 feet 6 inches. The distance 
between the two flippers, measured over the back, between the anterior borders 
of their roots, was 18 feet 6 inches. 

The slit-like entrance to the female passage was situated 22 feet in front of 
the fork of the tail. Its antero-posterior diameter was 16 inches. It was 
bounded laterally by elongated prominent folds of the integument, which 
represented the labia majora, and were indented by longitudinal furrows. 
In front of the aperture was a rounded elevation representing the mons, 
which was placed 10 feet behind the longitudinal plicae on the middle of the 
belly. Behind the mons was a deeply depressed part of the integument, 
immediately posterior to which was a thick clitoris, triangular in its outline. 
Its length was 6 inches, the breadth at the root 4 inches (Plate VI. fig. 6). The 
clitoris curved backwards, and overlapped the external orifice of the urethra, 
which orifice was surrounded by a well-marked fold of mucous membrane. 
Both on its superficial and deep aspects it presented a rugose appearance. 
On each side of the root of the clitoris a projecting fold lying between the 
labia majora passed backwards, external to the urinary meatus. These two 
folds formed the labia minora ; they bounded the vestibule, and their inner 
surfaces, as well as the floor of the vestibule, possessed a number of complex 
ridge-like elevations of the mucous membrane. When this membrane was cut 
through, a quantity of erectile tissue, in which were many large veins, was 
seen. Eight inches on each side of the female passage was a funnel-shaped 
elevation of the integument, at the summit of which a circular aperture, which 
readily admitted the tips of the fingers into a fossa about 4 inches deep, was 
seen. Projecting from the bottom of this fossa, but not through the circular 
aperture at its summit, was a large nipple about 3 inches long, which possessed 
an orifice at its free end — the termination of the great lacteal duct — into which 
the forefinger could be passed. A number of pedunculated papillae were situated 
at the summit of the nipple around this orifice (fig. 7). 

Thirteen inches behind the female passage was the orifice of the anus, 
which was small and contracted, but could easily be dilated so as to admit 
the hand. The integument immediately around the orifice was rugose, and in 
the neighbourhood both of the intestinal and genital openings the skin was 

VOL. XXVI. PART I. 3 G 



202 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

indented by several longitudinal furrows (fig. 8). A well-marked sphincter was 
observed beneath the integument around the anus. The mucous membrane at 
the anal end of the rectum had a blackish tint. 

The eye was situated immediately above the angle of the mouth, from which 
it was 1 foot 6 inches distant. The fissure between the lids lay antero-pos- 
teriorly. The ear orifice was a narrow slit situated in a line behind the eye, 
from which it was distant 3 feet 10 inches. The transverse distance over the 
dorsum between the two eyes was 11 feet 5 inches, the corresponding distance 
between the two ears was 13 feet 7 inches. 

The blow-holes were placed in the fossa between the two subdivisions of 
the dorsi-mesial ridge of the beak. Two longitudinal slits or nostrils, each 
large enough to admit the extended hand, were separated by an intermediate 
septum. Anteriorly the slits were only 4 inches asunder, but owing to their 
divergence the posterior ends were 15 inches apart, and the transverse diameter 
of the septum was correspondingly increased. The upper surface of the septum 
was marked by a longitudinal mesial groove. The antero-posterior diameter 
of the blow-holes was 1 foot 6 inches. From the tip of the lower jaw to the 
anterior end of the blow-holes, 14 feet 9 inches. From the anterior end of 
the blow-holes to the mesial notch of the tail 64 feet. 

Colour. — On the dorsum of the beak and of the cranium, on the back of the 
body, and for some distance down its sides, the colour was dark steel grey, 
amounting in some lights almost to black. On a line with the pectoral flipper 
the sides were mottled with white, and on the ventral surface irregular, and in 
some cases, large patches of a silvery grey or milk whitish tint were seen. An 
experienced whaling seaman, Mr Walter Roddam, who had charge of the car- 
case, told me that he had repeatedly seen this kind of whale in the northern seas, 
and stated that, owing to the silvery hue of the belly, it was known to the whalers 
by the name of "silver bottom.""" The surfaces of the clitoris and of the labia 
minora were mottled with black and silvery grey tints like the skin of the belly. 

The dorsal fin was steel-grey or black, except near its posterior border, 
where it was a shade lighter and streaked with black lines. The anterior 
margin of the lobes of the tail, its upper surface near the root and for the ante- 
rior two-thirds, were black, whilst the posterior third of the same surface and 
the interlobular notch were lighter in tint. The ventral folds had a light sepia 
colour, and the furrows were not so dark as the ridges. The upper surface of 
the flipper was steel-grey, mottled with white at the root, at the tip, along its 

* In the 2d vol. of Dr Scoeesbt's Account of the Arctic Eegions, p. 531, it is stated, on the 
authority of Captain Day, that amongst the whales pursued by the southern whale-fishers is one called 
" sulphur bottom," a species of Fin whale of great length and swiftness. Can it be that sulphur 
bottom is a corruption of silver bottom 1 and that this whale frequents both the northern and southern 
oceans ? 



STRANDED AT LONGNIDDKY. 203 

posterior or internal border, and on the under surface ; white patches were also 
seen on the upper surface near the tip, and here they were streaked with black 
lines running in the long axis of the nipper. White patches also extended from 
the root of the flipper to the adjacent parts of the sides of the animal. The 
outside of the lower jaw was black, whilst the inside was streaked with grey 
and brown. 

A few days after the death of the whale, the scarf skin had become loose, 
and large portions of it had separated, leaving the pinkish-white cutis exposed, 
and giving therefore a different colour to these parts of the integument than 
they had originally possessed. This circumstance is worthy of note, and may 
serve to explain appearances which have been described by some authors in 
connection with the colour of the skin in specimens of fin whales which they 
have examined. The surface of the skin was smooth and shining. No parasites 
were found attached to it, and no hairs or bristles were observed to project 
from any part of its surface. 

Although the animal had reached the enormous length of nearly 80 feet, 
yet it had not attained its perfect adult state. For, as the subsequent exami- 
nation of the skeleton showed, the disk-like epiphyses of the thoracic and 
lumbar vertebrae were not yet united to the bodies of those bones. The whale, 
therefore, was at the period of growth which, as Professor Flower has pointed 
out,""" may very appropriately be termed " adolescent." 

Foetus and Membranes. — When the whale was lying on the beach at Long- 
nidclry, the seaman in charge told me that he believed the animal to be in calf. 
On the fourth day after the operation of flensing on the beach at Kirkcaldy had 
commenced, as I was watching a man taking away the blubber and muscles from 
the posterior part of the side of the abdominal wall, I observed an elongated, 
dark-coloured mass lying loose amidst the coils of intestine, almost opposite 
the umbilical scar. I requested the man to hand it to me, and at once re- 
cognised it to be a wreath of young baleen about 4 feet long, which had 
obviously become detached from the roof of the mouth of a young animal, 
and had by some means or other escaped into the abdominal cavity of the 
parent. The discovery of this baleen clearly proved that the whale was in the 
gravid state. We at once commenced to remove a larger portion of the abdo- 
minal wall in order to obtain a view of the uterus, but before this could be accom- 
plished, the rising tide compelled us to cease our operations. As this happened 
on a Saturday, work could not be resumed until the Monday following, and as 
my University duties prevented me from being present, the search was conducted 
by Messrs Coughtrey and Foulis, who after several hours of hard work ex- 
posed the head of the calf by the removal of a mass of blubber from the right 

* Proc. Zoological Society, Nov. 8, 1864. 



204 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

side of the neck of the parent animal. The head of the calf indeed was so far 
forward that the tip of its beak was only 2 feet 9 inches behind the condyle of 
the mother's right mandible. An additional mass of blubber was then taken away 
from the exterior of the ribs on the right side, when more of the calf was ex- 
posed. It was lying obliquely between the blubber and the muscles which 
covered the outer surfaces of these ribs, and the space in which it was contained 
had obviously been formed by a forcible separation of the blubber from the sub- 
jacent muscles ; for when the blubber was cut through, the pressure on the 
calf, owing to its position between a weighty mass of blubber and the elastic 
ribs, was so great that its head protruded through the incision, and even 
partially tore through the superficial textures. 

The lower jaw of the calf was directed towards the ventral surface of the 
mother, and the left side of its body was in relation to the outer surface of her 
right ribs, and its tail was directed to her abdominal cavity. After the removal 
of an additional portion of blubber, the calf was extracted by my assistants, and 
in the process of removal it was observed that about 5 feet from the tail the body 
of the calf was so twisted on itself, that the position of the two lobes of the tail was 
reversed. A large quantity of the foetal membranes lay alongside of the calf, 
more especially near its caudal end ; but they were torn, and had lost their bag- 
like form. Some coils of the intestine were also situated beside the tail. It 
is much to be regretted that the uterus could not be preserved in the course of 
this examination. The huge size of the coils of the intestine, and the desire 
which the men employed had to get rid, on account of the smell, of the con- 
tents of the abdominal cavity, rendered it impossible to make such an exami- 
nation of these viscera as was desired. 

From a consideration of the position of the calf there can be no doubt that 
either immediately before or after the death of the mother, the foetus had been 
disconnected from its proper attachments and extruded into an artificial space 
external to the abdominal cavity. The torn state of the foetal membranes and 
umbilical cord, the presence of coils of the intestine in the space in which the 
foetus was lying, and the loose mass of baleen in the abdominal cavity of the 
mother, all point to a rupture not only of the uterus, but of the wall of her 
abdomen, which had permitted the passage out of the cavity both of the foetus 
and of portions of the gut. 

To what cause, then, are we to ascribe the rupture and consequent displace- 
ment % Some of those who examined the whale were of opinion that they had 
been occasioned by a severe injury sustained by the mother prior to, or at the 
time she came ashore. But I am rather inclined to think they must have 
occurred whilst she was being towed by the tail across the Firth from Long- 
niddry to Kirkcaldy. For, during the two weeks she lay on the beach at the 
former place, decomposition had advanced to a considerable extent, putrid 



STRANDED AT LONGNIDDRY. 205 

gases were disengaged, and consequent softening of the soft parts had occurred. 
As the sternum is short, and only articulates with the first pair of ribs, and 
as the inner ends of the remaining ribs diverge considerably from each other, 
and have no strong attachments in the ventral mesial line, the great pressure of 
the sea on the wall of the abdomen, as she was towed by the tail, would tend 
to rupture the uterus and abdominal wall, to drive the contents of the abdomen 
forwards towards the head, and to force the foetus into the position in which it 
was found. 

Owing to the displacement of the foetus, the dissection of this animal does 
not enable me to state with certainty the normal position of the foetus in 
utero in this cetacean. Very little indeed is known of the uterine position of the 
foetus in this group of mammals. In a communication made to the Royal 
Belgian Academy,* M. van Beneden figures the position in utero of the foetus 
in Globiceps. Its head is directed to the maternal genital orifice, its body is bent, 
and the tail is folded backward under the thorax, so as to lie close to its flipper. 
He believes that the foetus of Balwnoptera rostrata has the same position in 
utero, and doubts the statement made by M. Boeck, that the young of rostrata 
is born first by the tail. In the Longniddry Balwnoptera, on the other hand, 
the head of the foetus was directed towards the head of the mother ; and unless 
we suppose that during the displacement a complete revolution in the relative 
position of its caudal and cephalic ends had taken place — an occurence which, 
owing to the great length of the foetus, scarcely seems possible — the uterine 
direction of the young one would have been with its tail towards the maternal 
genital passage. 

The gravid state of the whale necessarily exercised an influence on its shape, 
more especially by increasing its girth in the abdominal region — a circumstance 
which should be kept in mind in comparing the drawing of this animal (fig. 1) 
with those which have been given by other naturalists of the Finners which have 
come under their observation. 

The form of the foetus differed in several particulars from that of the mother. 
Its greatest girth was around the head, from which it tapered forwards along 
the beak, and backwards to the root of the tail. From the unexpanded con- 
dition of the lungs, and the flaccid state of the hollow viscera of the abdomen, 
the thoracic and abdominal cavities had not attained their proper girth, and the 
body and caudal end of the foetus presented a peculiar, elongated, worm-like 
appearance. The dorsal fin did not rise so abruptly in the foetus as in the adult, 
so that it was difficult to determine its exact antero-posterior length. Its post- 
erior border had a well-marked falcate curve (Plate V. fig. 2). 

The foetus was a male. The penis, 11 inches long, hung pendulous, from the 
ventral surface, and at each side of its root a crescentic fold of skin arched out- 

* Bulletins, vol. xx. 2d series, No. 12. 
VOL. XXVI. PAKT I. 3 H 



206 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

wards (Plate VI. fig. 9). Behind each of these folds was the mouth of the 
shallow nipple fossa ; the nipple was rudimentary, and concealed by the promi- 
nent anterior border of the fossa. The posterior border was feeble, and here the 
fossa blended with the general surface of the abdominal wall. Passing back- 
wards, midway between these fossse, was a well-defined raphe reaching to the 
anus. The abdominal wall was much torn in front and at the root of the 
penis, and the exact attachment of the umbilical cord could scarcely be recog- 
nised, but it was estimated to be connected about 18 inches in front of the 
root of the penis ; for the cord, though carefully divided at the time when the 
foetus was removed from the mother, had been used, along with the penis, as 
a convenient object to lift with by the men employed to carry the calf, and con- 
sequently both they, and the part of the wall to which they were connected, had 
sustained injury. The tail was subdivided into two elegantly curved horizontal 
lobes (fig. 3). The sides and ventral surface showed the characteristic plicated 
appearance (fig. 4). On the top of the head, 1 foot 5 inches behind the blow- 
hole, was an oval patch 1 inch long by f ths broad. It was raised somewhat above 
the level of the integument. The shape of the flipper is represented in fig 5. 

The colour of the integument was a warm grey, mottled here and there with 
yellow. Patches of dark steel-grey pigment were observed on the back ; but 
none of the light silver-grey tints, seen in the large whale, were observed on the 
belly. I believe that desquamation of the cuticle had taken place very exten- 
sively before the calf came into my possession. 

I had anticipated that the comparatively small size of the foetus would, 
by giving me greater command over the dissection, have enabled me to have 
worked out all those points in the anatomy of this whale, which I could not 
overtake in the older animal. But in many respects I was disappointed, for 
the weight of the foetus, which amounted to about half a ton, and its length of 
almost twenty feet, rendered it a most unwieldy object to transport to the 
Anatomical Museum. Moreover, putrefaction had to some extent advanced 
before I had the opportunity to examine it ; the abdominal wall was torn, and 
the viscera in that cavity were so much injured, that but little definite informa- 
tion respecting the stomach and intestines could be obtained. The muscles also 
had undergone a remarkable kind of decomposition ; the odour exhaled from 
them was peculiarly acrid and offensive, which, together with their softened 
condition, rendered it impossible to make a proper study of those important 
parts of the locomotory system. The bones of the skull and spine were also to 
some extent displaced. 

A number of measurements were taken, a table of which I subjoin ; but in 
consequence of the displacement just referred to, some of the dimensions are 
probably not absolutely exact, but are to be regarded as the closest approxima- 
tion which could be obtained : — 



STRANDED AT LONGNIDDRY. 



207 



Length of male fcetus, ..... 

From tip of lower jaw to posterior end of blow holes, 

From posterior end of blow-holes to posterior border of dorsal fin, 

From posterior border of dorsal fin to interlobular median notch of tail, 

Antero-posterior diameter of blow-holes, . 

Transverse diameter of blow-holes, 

From tip of lower jaw to angle of mouth in a straight line, 

From tip of lower jaw along curve to angle of mouth, 

From angle of mouth to anterior border of root of flipper, 

From tip of lower jaw in a straight line to anterior border of root of flipper 

Length of flipper along anterior border, . 

Greatest diameter of flipper from anterior to posterior border, 

Girth of flipper at root, ..... 

Girth of body just behind dorsal fin, 

Girth round root of tail, .... 

Between extreme points of tail-lobes in a straight line, 

Between extreme points of tail-lobes along posterior concave border, 

Greatest girth of tail-lobe, .... 

From median notch of tail to anal orifice, 

Transverse distance between nipple fossae, 

From anal orifice to midway between nipple fossse, 

From nipple fossa to fold of skin at root of penis, 

Length of penis, ..... 

Vertical diameter of dorsal fin, . 

Greatest transverse diameter of cavity of mouth, . 



Feet. 


Inches 


19 


6 


3 


9 


10 


8 


5 


1 





6 





31 


3 


11 


4 


6 


1 


10 


5 


9 


3 


7 





9 


1 


10J 


3 


6 


1 


6 


4 


7 


5 


6 


2 


7 


6 


2 





3 





H 





n 





ii 





°2 


1 


9 



A vertical line, drawn from the root of the posterior border of the dorsal fin 
to the ventral mesial line, was 16^ inches behind the anal orifice. 

The displacement of the foetus and the torn state of the membranes did not 
give me the opportunity of observing the exact relations of the latter to the fcetus 
and to the mucous surface of the uterus. Although several square yards 
passed through my hands, yet I did not succeed in recovering the whole extent 
of these important structures. Notwithstanding these deficiencies many points 
of interest bearing on the placentation of the cetacea were observed. 

The outer surface of the chorion had the general villous appearance which 
is characteristic of the diffused form of placenta. In my first, and somewhat 
hurried inspection of this membrane, I did not notice any portion which did 
not possess villi. But on a second examination, made at more leisure on the 
membrane preserved in spirit, I observed that a portion of the chorion was 
bare. Unfortunately this had been torn across and a portion lost, so that the 
proper form of the non-villous part could not be ascertained. It had appa« 
rently, however, been of some extent, for the portion preserved was oblong in 
form, and measured 11 inches by 3. In all probability it had formed a part of 
one of the prolonged poles of the membrane. 

The villi began at the edge of this bare part by a well-defined line ; immediately 
beyond and parallel to which the chorion was doubled on itself, so as to form a 



208 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

strong marginal fold, which projected for about one inch, and was thickly studded 
with villi on its surface and free edge. (Plate VII. fig. 17.) A second fold, 
also covered with villi, lay close and parallel to the marginal fold. Similar 
villous covered folds of the chorion, many of which were one foot and upwards 
in length, traversed the chorion in various parts of its extent ; frequently they 
ran parallel to each other, and two or more were sometimes close together, but 
at other times they were separated by intervals of 3, 4, or 5 inches. Usually 
the greatest projection of one of these folds was about 2 inches, though some- 
times it reached 3, or even 4, but towards their extremities they gradually sub- 
sided to the general plane of the chorion. 

Besides these elongated folds, villous covered folds of another form, but not 
so numerous, projected from the surface of the chorion. They were triangular 
in shape, flattened on their surfaces, and with the apex and lateral borders 
free. A very characteristic specimen is represented in Plate VII. fig. 18. Its 
margin of attachment was 4 inches, whilst its diameter from this margin to the 
free apex was 5^ inches. On the elongated and triangular folds, but more 
especially the former, the villi were thickly studded, but on the intermediate 
surface of the chorion they were more sparingly distributed, and were for the 
most part collected on minute and ridge-like elevations, which intersected each 
other, and presented an irregularly reticulated appearance. The membrane 
between these slight ridges was comparatively smooth and transparent. 

The mucous surface of the uterus in the mother must have possessed 
numerous depressions of considerable length and depth, into which the elongated 
and triangular folds of the chorion would have fitted. In the special aggregation 
of the villi on these folds an approach to the cotyledonary type of the placenta 
found in the Ruminantia may be traced. 

The opposite surface of the chorion was in relation to the placental blood- 
vessels, some of which were of considerable size ; one, which was measured, had 
a circumference of 2f inches. Where the folds on the villous surface were well 
marked an artery coursed along and gave off many collateral branches, which 
entered into the fold to end in the villi. The chorionic vessels were surrounded 
by a delicate connective tissue, which was loosely connected with the attached 
surface of the amnion. Lying in this connective tissue were numerous opaque, 
white, slender threads, which differed from the small arteries in not being tor- 
tuous, and in giving off their branches at very acute angles. These threads 
had to the naked eye the appearance of fine nerves. When examined with the 
microscope, they were found to possess an external investment of well-marked 
connective tissue, which surrounded lines of an irregular granular or semi- 
globular substance which looked like the disintegrated medullary sheaths of 
nerve fibres. The free surface of the amnion was smooth and glistening. 

Although nothing definite seems to be known of the period of gestation of 



STRANDED AT LONGNIDDRY. 209 

the Finners, yet from the length of the calf, and the well-developed state of its 
parts, it is probable that the whale was at or about her full time. Dr Scoresby 
considered that February and March were the months in which the Balcena 
mysticetus gave birth to her young,* but Eschricht and Relnhardt, from obser- 
vation made at the Danish whaling factories, think that it is between the end of 
March and the beginning of May.t If my supposition be correct that the whale 
was at her full time, then this Balamoptera gives birth to its young in the later 
autumn months, and not, like the Greenland Right whale, in the spring of the year. 

This view of the period of parturition of the great Finner is strengthened 
by evidence which I have received from another source. In the month of 
October 1869, a large female Finner, which, from information that I have ob- 
tained,;}; I believe to be of the same species as the Longniddry whale, was 
found in a creek about a quarter of a mile to the south of Hamna Voe, North- 
maven, Shetland. It was dead, and floating by its side was a dead calf, which 
was well developed, and bore to the mother about the same proportion as the 
Longniddry animals did to each other. Alongside the calf was a quantity of 
membranes, which, from the statements of the fishermen, were evidently the 
foetal membranes. The calf had obviously been born about the time of the 
death of the mother, and had apparently reached the full period. The maternal 
mammary glands were so charged with milk that a quantity was observed to 
flow out through the teats. 

The capture of two of these whales in the pregnant condition within so 
short a period in arms of the sea, lends support to the statement which has 
more than once been made, that the Finners resort to bays and creeks for the 
purpose of bringing forth their young. 

Skin and Blubber. — The colour of the skin has already been described ; a 
few words may, however, be said on its structure. The epidermis readily 
peeled off the cutis when decomposition had begun. It was distinctly laminated 
and thicker than the human cuticle. On the belly, for example, it measured 
|th of an inch, and on no part indeed of the surface of the trunk was it 
seen to possess a greater thickness. In this respect it contrasts strongly with 
the skin of the Balcena mysticetus, which in some places has the cuticle one 
inch thick.§ The superficial layer could be peeled off as a thin horny stratum, 

* Account of the Arctic Regions. I., 470. 

+ Memoir translated for the Ray Society, p. 10. 

\ I am indebted for information regarding this whale in part to Mr J. Walker of Maryfleld 
House, Eressay, and in part to Mr Coughtret. The latter gentleman has just returned from a visit to 
the Shetland Isles, and when there not only collected at my request various interesting facts about this 
animal, but also procured for me a number of its bones. 

§ Dr Knox (Catalogue of Anatomical Preparations of the "Whale, Edinburgh, 1838) points out 
the thinness of the cuticle in the species of the great northern Rorqual which he dissected ; nowhere, 
he says, did it exceed f^tbs of an inch. He compares it with the B. mysticetus, and shows how 
in the one there are conjoined thin cuticle and short baleen, in the other thick cuticle and long baleen. 

VOL. XXVI. PART I. 3 I 



210 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

which, when dried, had the appearance of gold-beater's skin. The deeper 
layers contained more pigment than the superficial, and in those parts of the 
skin where the colour was most marked the deep surface of the cuticle had a 
rich black hue. When the epidermis was removed, rows of distinct elongated 
papillae were seen ; and in vertical sections through the entire skin the rela- 
tions of these papillae to the cuticle* could be studied (Plate VIII. fig. 29). 
The papillae were filiform, and as a rule simple, but in some cases two or 
even three papillae arose by a common stem, which then subdivided. They 
were comparatively long, and their apices reached therefore much nearer 
to the surface of the skin than might have been supposed. In some of the 
sections I observed distinctly the small arteries of the cutis giving off branches 
which entered the bases of the papillae and extended for some distance within 
them. 

The blubber or subcutaneous tissue was composed of adipose tissue, for the 
oil was contained in well-defined fat cells. These cells were supported by 
bands of connective tissue, many of which possessed considerable breadth and 
strength. Blood-vessels passed in some numbers through the blubber, partly 
for its nutrition, and partly for the nutrition of the integuments on its 
surface. The blubber varied considerably in thickness in different parts of 
the subcutaneous tissue of the adolescent animal. On the sides and upper 
edge of the lower jaw, it was from 10 to 16 inches. Beneath the ear-slit 8 
inches ; along the ventral surface about 4 inches. On the top of the beak 
and cranium 8, 12, and even 15 inches. In front of the dorsal fin from 12 to 
16 inches, and behind this projection from 14 to 21 inches, which seemed to be 
the maximum thickness. The thickness of the blubber at the tip of the caudal 
spine was 3 inches, and at the symphysis of the lower jaw 4^ inches, so that 
the length of the skeleton was within 1\ inches that of the entire animal. In 
the foetus the blubber was very imperfectly formed ; and the thickness of the 
subcutaneous tissue was almost uniform, on the belly not exceeding one inch ; 
and on the back scarcely reaching two inches. 

In the older animal, an enormous mass of soft fat was situated within, and 
formed a sort of fatty lining for the abdominal cavity. From the heat which 
was disengaged by the putrefaction of the carcase, this fat was liquefied, and 
ran in streams on to the shingle, where it again solidified, and was collected 
into barrels. 

Mr Tait estimated that he had obtained from the blubber ten tons of oil, 
and from the inside fat six tons, so that the pecuniary value of the whale from 

* In the Anatomical Museum of the University of Edinburgh are several specimens (161 to 164) 
prepared upwards of twenty years ago by the late Professor Goodsir, one from the B. mysticetus, three 
from a " Rorqual," probably the Balcenoptera mitsculus, which give most illustrative views of the fili- 
form papillae of those animals. 



STRANDED AT LONGNIDDEY. 21 1 

these sources alone was very considerable. He has also furnished me with an 
estimate of the weight of the other portions of the carcase; from which we 
may make an approximation to the weight of the entire animal. The flesh 
and viscera 36 tons, the baleen and " gum" 10 cwt., the skeleton 9 tons 10 
cwt, the blood and refuse 12 tons, which, with the oil and fat, make in all 
74 tons as an estimate of the weight of the entire animal. 

Mammary Gland. — The position of the nipple has already been described in 
the section on the external form of the animal. The gland itself was exposed 
by the removal of the blubber on one side of, and for several feet anterior to, 
the genital fissure. It formed an elongated body, and measured between 7 and 8 
feet in its antero-posterior diameter, and of this extensive mass only 8 inches lay 
behind the nipple. Its greatest transverse diameter was 20 inches, and the thick- 
ness of the gland substance, which surrounded any part of the great central 
duct, was more than 6 inches. Its broadest part was in the region of the nipple, 
gradually tapering off to its anterior end. Its colour was a rich red ; and its 
subdivision into lobules by bands of connective tissue could be readily recog- 
nised by the naked eye. When cut into, it was seen to be traversed along its 
entire length by a central duct, which increased in size as it passed from before 
backwards, and at the base of the nipple formed an enormous sinus, the trans- 
verse diameter of which was about 8 inches. Numerous large ducts, into many 
of which the closed hand could be passed for some distance, opened out of this 
central duct, and extended into the various parts of the gland. The transverse 
diameter of one of these ducts was 5^ inches. The orifices of the primary ducts 
opening into the great central canal, and those of the smaller ducts which opened 
into the primary, were mostly oblique in their direction, and a well-marked 
fold of the mucous membrane bounded one-third, and sometimes more, of the 
aperture. As a general rule, the direction of these ducts was towards the 
nipple, but some ran in the opposite direction. The mucous membrane which 
lined the ducts and central canal was firm, and marked on its free surface by a 
characteristic ridge and furrow-like appearance (Plate VI. fig. 11). These ridges 
were parallel to the long axis of the duct. At the base of the nipple the great 
sinus-like dilatation of the central canal suddenly narrowed to the duct within 
the nipple, which was not larger than would admit the middle finger or thumb. 
The lobules of the gland were polygonal in shape and variable in size; some of 
the larger ones had a diameter of ^th inch. Sections through the lobules 
examined microscopically gave very illustrative views of the structure of a com- 
pound racemose gland. The clusters of acini or gland vesicles, with their con- 
tained secreting cells, could be seen with great distinctness, and the arrange- 
ment of the interlobular connective tissue could be traced. 

In the subcutaneous tissue around the nipple and at its base, numerous 
plexiform vessels were seen, so that it is probable that erectile tissue exists 



212 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

in this locality. Lying outside the mammary gland was a muscle which, by its 
contraction, would aid in expelling the milk along the ducts, and through the 
orifice of the nipple. 

The size of the secondary ducts of this gland, and the dilatation of the single 
central duct into a great reservoir for the collection of the milk, have obviously 
special reference to the aquatic mode of life of an animal which suckles its 
young. For, as John Hunter long ago pointed out,* the mode in which these 
animals give suck is very inconvenient for respiration, as if the mother were to 
turn round so as to elevate the nipple to the surface then her nares would be 
under water ; whilst, if the mother remains in her normal position, then the 
nose of the calf must be under water, and the time of sucking can only be 
between each respiration. It is necessary, therefore, that the gland should be 
so constructed as to allow of a considerable accumulation of milk in the ducts, 
which may be readily drawn off by the calf in the intervals between the respi- 
ratory acts. 

Baleen. — When the lower jaw was removed by cutting through the massive 
fibrous columns, which connected the condyles of this bone to the base of the 
skull, and when the occipito-atloid joint was disarticulated, the skull was turned 
over on its dorsum, and a complete view of the roof of the mouth, and of the 
baleen in situ was obtained. Extending from behind forward in the mesial 
plane of the palate was the great central crest or keel, which was much broader 
and more prominent posteriorly than anteriorly, and was covered on its 
free surface by a black mucous membrane. Immediately on each side of the 
base of the keel the palate was covered by a smooth and almost flat, black 
mucous membrane, and external to this again was the lateral series, or wreath, 
of deep black baleen plates with their inferior free edges fringed with black 
setse. 

The wreaths of baleen plates on the two sides converged as they passed for- 
wards, and at the anterior part of the mouth they became continuous with each 
other, as is the rule indeed in the Finner whales.t Posteriorly, where they lay 
close to the entrance into the gullet, they were separated by a considerable 
interval ; though here also they inclined inwards to the base of the great mesial 
palatal keel. The inner edge of each wreath had a curved outline with the 
concavity towards the mesial keel. The outer edge was convex, and in its 
curvature closely corresponded to that of the margin of the beak itself. This 
border was bounded by a raised fold, the coronary or wreath-band (Horn- 
Kranzband of Rosenthal), and was situated one foot within the outer edge of 
the beak. Where the two wreaths became continuous in front, the junction 
took place seven inches within the tip of the beak. 

* Structure and Economy of Whales. Phil. Trans. 1787. 

t Eschricht and Reinhardt. I. have also seen this in two specimens of Balcunoptera rostrata. 



STRANDED AT LONGNIDDRY. 213 

Each wreath was estimated to contain about 370 rows of plates,* and each 
row consisted of several plates or blades or bristles. The rows lay transversely 
and parallel, though not in straight lines, for they were somewhat curved, the 
convexity forwards, the concavity backwards, and the smaller inner subsidiary 
plates were arranged in an oblique manner. Intervals varying from one 
half to three-eighths of an inch existed between the rows in different parts 
of the series. The transverse and vertical diameters of the plates varied 
considerably, not only in different parts of the wreath, but also in each row, 
for the plates diminished in size from the outer to the inner edge of the row. 
At the anterior part of the mouth they were little more than coarse black 
bristles, and the free part of these projected in some only half an inch, in 
others one inch and a half, into the cavity of the mouth. Extending backwards 
along the outer or labial part of the wreath the baleen increased in size, at first 
being somewhat elongated narrow plates, and then increasing in their trans- 
verse diameter at their base of attachment, until they assumed the unequally 
four-sided form, with its surfaces directed forwards and backwards, of the blade 
represented in Plate VI. fig. 12, which may be regarded as a very character- 
istic specimen of one of the large plates of this Balamoptera. The dimen- 
sions of this plate were as follows. The transverse diameter along its base of 
attachment 1 foot 6 inches ; vertical diameter, inclusive of the part imbedded in 
the intermediate substance, along outer free border, 2 feet 9^ inches, along- 
inner free border 8 inches. Length along the border fringed with setae 3 feet 
3 inches. The setae varied in their length, some measuring as much as 17 
inches. On the surface of the plate numerous longitudinal parallel lines, which 
at its inferior edge became continuous with the setae, were observed. Transverse 
rings, which sometimes were close together, at others were separated by wider 
intervals, passed from one surface to the other around the outer and inner free 
edges of the plate. A plate of this form and of somewhat similar dimensions 
formed the external or labial blade of each transverse row in by far the greater 
portion of the wreath. 

Internal to this large plate the baleen, though of the same black 
colour, was elongated and narrow ; the blades possessed the form represented 
in Plate VI. fig. 13, their transverse diameter was not more than ^ths of an 
inch, and their vertical diameter, inclusive of the part imbedded in the inter- 
mediate substance, was in some 7, in others 6, in others 5 and 4 inches. Each 
of these narrow subsidiary plates had an uniform breadth, and the setae, which 
were often more than 6 inches long, arose not from the sides, but only from 

" Although, the rows of plates were counted without difficulty in the greater part of the wreath, 
yet at the posterior end, and at the front, of the mouth the exact enumeration was attended with con- 
siderable difficulty, owing to the bristle-like baleen being arranged in less definite rows than were the 
blades of this substance. 

VOL. XXVI. PART I. 3 K 



214 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

the free end. Whilst the setae generally had the same deep black colour as the 
plates, in some cases they had more of a deep soot brown tint. The baleen at 
the inner end of each transverse row consisted, not of plates, but of short bristles, 
similar to those already referred to at the anterior end of the series. As the 
vertical diameter of the plates and the length of the setae were so much greater 
in the outer than in the inner parts of each transverse row, it followed that the 
lower bristle-fringed aspect of each wreath arched, from without, obliquely 
upwards and inwards, so that the roof of the mouth presented a considerable 
concavity from side to side. 

The plates were all imbedded at their attached palatal borders in a dense 
semi-elastic, slate-coloured material, the intermediate substance or "gum" of 
the whaling seamen. This substance varied in its thickness from its attached 
to its free surface to from 1 to 4 inches in different parts of the wreath, and was 
thinner along the outer and inner borders than in the intermediate portions. It 
was continuous, along the inner border of the wreath, with the cuticle investing 
the palatal mucous membrane, and along the outer border, with the coronary 
or wreath-band already referred to. The free surface possessed an irregular 
softened, water- worn appearance. 

After decomposition had begun the baleen and intermediate substance, 
intimately connected together, could be readily peeled off the surface of mucous 
membrane from which they grew, and their mode of growth and structure could 
be examined. 

All anatomists know, who have studied the structure of whalebone, that, 
when a blade is carefully detached from the surface of the palate, the edge or 
base of attachment is cleft along the line of its transverse diameter into two 
laminae. If these laminae be drawn asunder numerous holes are seen at the 
bottom of the cleft, which open into tubes or canals that traverse the substance 
of the plate in the vertical direction. It has been pointed out by Eschkicht 
and Reinhardt, that in the short baleen plates of the Rorquals or fin whales the 
length of these tubes is comparatively greater than in the much longer plates 
of the Greenland Right whale. In the Longniddry whale, the deep black colour 
of the baleen made the plates so opaque, that the existence of the tubes could 
only be surmised by the longitudinal markings visible on a surface examination, 
and it was not until after sections were made in the vertical or transverse direc- 
tion, that the tubes could be distinctly seen. 

In vertical sections the tubes were cut longitudinally, and could be followed 
for some distance (Plate VII. fig. 19). They contained a delicate, brownish- 
yellow substance, which could be easily drawn out of the tube. In the part of 
the plate which surrounded the tubes numerous black pigment granules were 
distributed in such a manner as to give to the section the appearance of 
longitudinal striation. 



STRANDED AT LONGNIDDEY 215 

Transverse sections of the plates, examined with low magnifying powers, 
were, however, the more instructive (fig. 20). The number and size of the 
tubes was by no means uniform in the different parts of the same trans- 
verse plane. Sometimes a single comparatively large tube was alone met with ; 
at others two, or even a larger number, occupied the antero-posterior diameter, 
and in this case the tubes were considerably smaller. The soft brownish- 
yellow contents were readily recognised, and in many of the sections this sub- 
stance was seen to be perforated with holes, which looked like transversely- 
divided small blood-vessels. 

The solid portion of the plate was spotted with black pigment, and dis- 
tinctly striated. The striae ran in two different directions, and indicated a 
laminated arrangement. One set of striae or lamellae surrounded, in a concentric 
manner, the individual tubes, and in their arrangement might be compared 
with the lamellae surrounding the Haversian canals in a transverse section of 
bone. They may be called the tubular lamellae ; and the tube, its contents, 
and the lamellae surrounding it, might be termed a tubular system. The other 
lamellae were situated on the peripheral part of the plate, and formed a sort of 
envelope enclosing the tubular system of lamellae. These may be called the 
peripheral or cortical lamellae ; and they formed that part of the plate which has 
been called the cortical layer or " enamel" of the whalebone. When examined 
with higher powers of the microscope, the lamellae were seen to be composed of 
elongated and flattened cells, each containing a distinct nucleus, and more or 
less black pigment (fig. 21). These cells were obviously peculiarly modified 
epithelial cells. The intervals between the outermost lamellae of adjacent 
tubular systems were filled up by cells, which presented less of a flattened and 
more of a fusiform or rod shape ; these cells, though interstitial in their position, 
were apparently continuous with the cells of the cortical layer. 

Transverse sections through the setae displayed in each a central tube or canal, 
surrounded by the usual arrangement of concentric tubular lamellae (fig. 22). 
The tube within the seta contained a similar soft brownish material to that 
found in the tubes within the blade itself. Each seta represented, therefore, 
a single tubular system. 

When vertical sections through the intermediate substance, in which the 
bases of the plates were imbedded, were examined with low powers of the 
microscope, the deep surface attached to the palate was seen to be much more 
highly charged with pigment than the more superficial parts, and so regularly 
was it disposed, that it might almost be described as a special pigmentary 
layer of the structure. The deep surface had an uniform rich black colour, and 
was perforated by numerous apertures, which in the vertical sections were seen 
to lead into clefts which passed some distance into the intermediate substance 
(fig. 23). The black pigmentary layer was prolonged along the walls of these 



216 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

clefts. Under higher powers of the microscope, the intermediate substance 
was seen to consist of flattened cells, epithelial in character (fig. 24), and the 
black pigmentary layer was due to a special accumulation of pigmentary 
granules in the deepest cells of this substance. This layer may be considered 
therefore as comparable to the Rete Malpighii of the human cuticle. 

The intermediate substance was intimately united to the laminae formed by 
the cleavage of each plate at its base ; so close indeed was this union that it was 
impossible to separate them from each other without injury to the latter. It 
not unfrequently happened, in tearing away the substance from between the 
plates, that a portion of the cortical layer of the adjacent part of the plate 
peeled off along with it. A distinct horizontal lamination was seen on the 
surface of vertical sections made through the intermediate substance. 

In my further researches into the structure of the baleen, I have derived 
considerable assistance from the examination which I made of the baleen of a 
recently killed, lesser Pike whale, B. rostrata, about 18 feet long, which was 
captured at Burntisland in September last. In this animal the plates were for 
the most part white, or yellowish- white, but, when quite fresh, a distinct pink 
or rosy colour was seen, more especially in that part of the blade which lay 
within and next to the intermediate substance. Some days after death the 
pink or rosy colour became converted into purple. 

When a fresh blade was examined in a good light, the pink colour was 
found to be not on the surface, but within the substance of the plate, and 
arranged in regular lines, which ran parallel to each other from the attached 
border to the free border fringed with setae, and in many cases it extended even 
into and along the latter. When a pocket lens was used in the examination, 
the colour was seen to be due to a red fluid contained in the numerous tubes 
which traversed the plate in its vertical diameter. Sometimes the fluid formed 
an unbroken column of one, two, or three inches in length ; but at others the 
column was much subdivided, and reminded one of the appearance presented 
by a broken-up column of mercury in a barometer tube when out of repair. In 
some of the tubes, more especially those situated near the outer and inner 
edges of the plate, the red fluid was either absent, or extended only a short 
distance down the tube. Many of these tubes appeared as if subdivided by 
little septa passing across their canals, not unlike the arrangement one has 
seen in the medullary part of a hair. When the baleen plate was cut across 
transversely, and forcibly squeezed between the finger and thumb, the red 
fluid oozed out of the divided tubes, and when collected on a glass slide was 
examined microscopically. Under a high power numerous circular, disk-shaped, 
non-nucleated corpuscles, which possessed the optical characters of blood cor- 
puscles, were found in it (fig. 25), and along with these were three-sided pris- 
matic crystals, probably the triple phosphate, and numerous actively moving 



STRANDED AT LONGNIDDRY. 217 

vibriones. It was clear, therefore, that the pink tint of the baleen in' the Pike 
whale was due to the blood"" situated in the tubes which traversed its substance 
in the vertical direction. 

I am not aware that any explanation has previously been given of the cause 
of the pink colour of the baleen in the lesser Pike whale. Indeed many 
writers seem to have paid but scanty attention in their descriptions to the 
existence of this tint. 

Both in the Longniddry and the Pike whales the surface of the palate, from 
which the baleen grew, possessed numerous transversely elongated folds of the 
palatal mucous membrane (the pulp-blades of Eschricht and Reinhardt), 
corresponding in their arrangement and transverse diameter to the different 
sizes of the baleen plates in the various transverse rows, and fitting into their 
cleft basal edges (fig. 26). The largest of these folds in the former animal pro- 
jected as much as r^ths of an inch from the general palatal surface. The free 
lower edge of each fold was fringed with multitudes of well-marked elongated 
filiform papillae, which fitted into and indeed filled up the tubes in the 
plates and setae already described. These may be called the tubular papillae. 
If great care was taken in stripping off the plates, the papillae could be drawn 
out of the tubes, and in fig. 26 a view of a number of these structures from 
the interior of the tubes of a plate of the Longniddry whale is given. The 
tubular papillae varied in length in this preparation, some being 3 inches long, 
whilst others were considerably shorter ; but none of these papillae represented 
the full length of the tubes they originally occupied, as they always broke short 
in the act of removal. They varied also in thickness, in correspondence with 
differences in the bore of the tubes ; and they were thicker at their attached 
than free extremities. 

Folds and papillae of this character have been described with more or less ful- 
ness of detail by Hunter, Ravin,! Rosenthal,! Knox,§ Owen,j| Eschricht and 
Reinhardt,^ Flower,** and MALM,tt in connection with the baleen in the 
different whales which they have examined ; and in the Anatomical Museum of 
the University of Edinburgh are several specimens, prepared, I believe, in the 
year 1843, by the late Professor Goodsir, which furnish very illustrative views 
of the folds and larger papillae of the baleen plates. They have been regarded 
as the nidus, matrices or pulps, from, and in connection with, which the specially 

* As confirmatory evidence of this fluid being blood, I may state that I requested my friend, Dr 
Arthur Gamgee, to apply the cbemical test for blood. He found that the fluid gave with guaiacum 
and peroxyde of hydrogen the characteristic greenish-blue colour of haemoglobin. 
"f" Ann. des Sc. Naturelles, 2 Ser. t. v. 

X Abhand. der Akad. der Wissensch. zu Berlin, 1829, p. 127. § Catalogue, op. cit. 

|| Odontography, p. 312. 1F Ray Society's Translation, op. cit. 

** Proc. Zool. Soc, 1865, Nov. 28. 
tt Monographie Illustree du Baleinoptere, Stockholm, 1867. 

VOL. XXVI. PART I. 3 L 



218 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

modified, horny, epithelial cells of the baleen plates were developed. The 
vascularity of the folds and of the papillae has also been recognised by these 
anatomists, but no exact description of the arrangement of the vessels has 
as yet been given. 

The fresh condition of the baleen in the B. rostrata led me to think that it 
might be possible to inject its papillae, and to obtain a more complete view of 
the arrangement of their vessels than had yet been described. I accordingly 
carefully detached the entire palatal mucous membrane, with its baleen wreaths, 
from the upper jaw; and after introducing injecting pipes into several of the 
palatine arteries, I succeeded with the aid of my assistant, Mr Stirling, whose 
skill as a minute injector is so well known, in injecting the vessels of the baleen. 
But before proceeding to describe their arrangement, it will be necessary to speak 
of two other groups of papillae, which appear hitherto to have been overlooked by 
anatomists. When the surface of the palatal mucous membrane, situated be- 
tween the bases of the transverse folds, was examined with a pocket lens, it was 
found to be studded with short papillae, which fitted into clefts similar to those 
already described (fig. 23), as extending into the intermediate substance from 
its deep attached surface. These papillae we will call intermediate. Similarly, 
when the sides of the transverse folds were also examined with a pocket lens, they 
were seen to give origin to numerous minute papillae, which passed into minute 
apertures in the inner wall of each of the laminae, produced by the cleavage of 
the baleen plate at its base. These laminae were continuous with the cortical 
layer of the plate to which they belonged, and their papillae may be called peri- 
pheral or cortical. 

In the injected preparations, the following appearances were seen in vertical 
sections (fig. 27). The palatal mucous membrane was highly vascular, and the 
principal vessels ran parallel to the horizontal plane. They gave origin to 
smaller vessels, which were distributed to the three groups of papillae. Those 
which passed to the intermediate papillae, occupying the spaces in the attached 
surface of the intermediate substance, did not enter the transverse folds or pulp 
blades ; they were very slender, but formed distinct loops (fig. 27). The vessels for 
the other papillae entered the transverse folds. Those destined for the peripheral 
or cortical papillae formed a well-defined superficial network of small vessels, 
which gave off, at intervals, capillaries which entered these papillae, and formed 
loops in the usual maimer. The vessels for the elongated, filiform, tubular 
papillae were considerably larger. As a rule, two entered the base of each papilla, 
and extended along its axis into the tube. These vessels preserved their size 
for a very considerable distance down the tube, and occasionally anastomosed. 
They were easily recognised by the naked eye, both in vertical and transverse 
sections of the plates and setae ; and it was in them that the blood was contained 
which conferred on the baleen of B. rostrata its characteristic pink markings. 



STRANDED AT LONGNIDDRY. 219 

When the papillae were carefully extracted from the tubes, and examined 
with high powers of the microscope, they were seen to consist of a delicate, 
wavy, connective tissue, the filaments of which lay parallel to the long axis of 
the papilla. The nucleated corpuscles of the connective tissue were distinctly 
recognised after the papilla had soaked some time in glycerine. On the free 
surface of the papillae a very distinct layer of flattened polygonal cells, with 
their borders in close contact with each other, like epithelial cells on a free 
surface, was met with. These cells were soft and delicate, and were evidently 
the youngest layer of epithelial cells lying next the papillae, which had not 
yet undergone the horny transformation. In some of the papillae I saw, more 
especially at their broader attached ends, elongated fibres, having a double 
contour, which I believe to have been medullated nerve fibres. 

The baleen of the foetus of the Longniddry whale possessed some features 
of interest, to which I may now refer. Only the wreath, which was met with 
early in the dissection of the mother, was preserved, for the opposite wreath, 
which had also been shed from the palatal surface, was lost in the course of the 
dissection. The wreath was 4 feet long, and 3^ inches in its greatest transverse 
diameter. The anterior end had been broken away, and lost, but the posterior 
end was flattened, and terminated in an obtuse angle. Notwithstanding the 
loss of its most anterior portion, as many as 335 transverse rows were counted 
in the wreath, and they were slightly curved with the convexity forwards. 
Owing to the comparative thinness of the intermediate substance, the interval 
between any two adjacent transverse rows was not more than j^th of an inch. 
Here, as in the adult, the outer or labial plate in each transverse row was by far 
the largest ; indeed, those internal to it were little more than short bristles in the 
foetus. In the greater part of the wreath seven, eight, or sometimes nine plates 
or bristles were counted in each transverse row. Towards the anterior end 
only five were counted ; but posteriorly, where the external plate, like those 
internal to it, consisted of a mere bristle, — the number of bristles in the row 
had increased to about thirty, and at the same time the rows increased very 
materially in their obliquity. Quite at the posterior end the bristles were so 
feeble as scarcely to be visible. 

In the foetal wreath I recognised not only the transverse arrangement just 
described, but also a distinct antero-posterior or longitudinal arrangement of 
the baleen. The outer longitudinal row was formed by the series of large plates, 
whilst those internal consisted of the bristle-like baleen. The number of longi- 
tudinal rows varied, however, in different parts of the wreath, where variations 
occurred in the number of elements in the transverse rows. 

The baleen had not the rich black colour so characteristic of the plates in 
the older animal. The plates were dark grey, intermingled with black. The 
setae were light grey, and the intermediate substance had a similar tint. The 



220 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

substance bore a greater proportionate thickness to the vertical diameter of the 
entire plate than in the older animal. In one of the largest unequally four- 
sided plates, whilst the greatest vertical diameter was 2\ inches, the padding 
at its thickest part was 1 "6 inch ; but at the inner and outer border of the plate 
it was only - 8 inch. The greatest transverse diameter of this plate at its 
attached border was 2*3 inches. The longest setae projecting from the free 
lower border of the plate measured 1\ inch. The foetal baleen plates had a 
distinctly fibrous appearance, and, from the thinness of the cortex, could be 
readily torn along the vertical diameter into numerous fine parallel horny 
fibres, which in each plate corresponded in number to the setae, and consisted of 
the tubular systems, with their contained papillae. The openings into the 
tubes were visible in the cleft between the basal laminae of attachment of the 
plate. No transverse rings, such as have been described in the older animal, 
were seen on the surface of the fcetal baleen plates, a circumstance which adds 
to the probability of the view entertained by Eschricht and Reinhardt, that 
the rings indicate a periodical change in the formation of the cortical part of 
the blade. When transverse sections through a plate were examined micro- 
scopically, the tubes, the tubular lamellae, and the peripheral lamellae were 
seen, but on a much smaller scale ; the peripheral lamellae especially being 
thinner, and not so distinct as in the older animal, so that the entire plate 
was consequently much thinner. The intermediate substance readily tore up 
in the vertical direction, and the torn surface was longitudinally streaked, to all 
appearance, in conformity with the development of its epidermal cells, in con- 
nection with the basal papillae. Numerous black pigment granules were scat- 
tered through both the plates and intermediate substance. 

The surface of the palatal mucous membrane, from which the fcetal baleen 
had been shed, presented folds or pulp-blades, which, in their general plan, 
though with some modifications in form, agreed with those already described 
on the palate of the mother. A series of transversely elongated folds corre- 
sponded to, and fitted within, the clefts at the bases of attachment of the large 
external plates of the transverse rows. Internal to these, owing to the baleen 
having so much more of a bristle than a plate-like form, the elevations of the 
mucous surface were not transversely elongated, but had more the shape of sub- 
conical papillae (Plate VI. fig. 15). The corresponding surface of the baleen 
wreath, instead of presenting a series of transversely, elongated, short clefts, 
as in the mother, possessed polygonal pits, mostly of a regular hexagonal form 
(fig. 16), into which these sub-conical papillae fitted. Towards the anterior part of 
the palate, the folds were so faintly marked as to be recognised with difficulty. 

As the violence which had occasioned the rupture of the uterus, and the 
displacement of the foetus, had in all probability, also, been the cause of the 
separation of the baleen wreaths from the palate, the elongated tubular papillae 



STRANDED AT LONGNIDDRY. 221 

had, for the most part, been torn off the folds of the palatal mucous membrane, 
and were included within the tubes of the baleen plates. In some localities, 
however, some of these papillae still retained their proper attachments to the 
folds ; and they presented an appearance which reminded one, though on a 
smaller scale, of that which has already been described and figured in the older 
animal. 

John Hunter, in his account of the mode of growth of whalebone, 
pointed out very clearly that a baleen plate is formed upon a thin broad pro- 
cess of a vascular substance, which fits into the hollow at the base of the 
plate, and that the first part of the growth takes place on the inside of the 
hollow. He was also of opinion that the cortical layer of the baleen, and the 
intermediate substance arose on the surface of the vascular membrane, and 
were continuous with each other. He showed their relations to hair, nails, and 
other epithelial structures, and stated that the free surface of the intermediate 
substance softens like the old cuticle of the sole of the foot when steeped in 
water. Eschricht and Reinhardt described epidermic cells as continually 
forming, not only on the pulp-blades, but on the smooth intervals of the palatal 
membrane between the blades, the cells of the latter constituting the compara- 
tively soft intermediate substance, whilst those of the former hardened into the 
horn-like material of the baleen plate. The medullary or tubular portion of the 
plate formed on the free lower edge of the pulp-blade, and on the numerous, 
soft, elongated, filamentous papillae which fringe it, whilst the cortical layer of 
the baleen plate formed on the free lateral surfaces, and inner and outer edges 
of the pulp-blade, which it ensheaths. 

This description by the distinguished Scandinavian anatomists is, I believe, 
as far as it goes, perfectly accurate ; but the observations which have just been 
recorded enable me to supplement it with some new and important particulars. 
For, in addition to the elongated, filamentous, vascular papillae of the tubes, 
two other sets of vascular papillae have been observed — a cortical and an inter- 
mediate — each of which has its appropriate epithelial investment. Hence we 
may now state, that each of the three great groups of epithelial cells found in 
the baleen wreath takes its rise from, and constitutes the epithelial investment 
of, a distinct set of vascular papillae. The cells which form the tubular lamellae, 
are the cornified epithelium of the filamentous tubular papillae : those which 
form the peripheral or cortical lamellae are the cornified epithelium of the cor- 
tical papillae ; whilst the softer intermediate substance consists of the epithelial 
cells, which invest the sides and summit of the intermediate papillae. 

Many anatomists, in discussing the characters and morphological position 
which whalebone occupies amongst the textures, have compared it with the 
teeth, and have regarded it as a special modification of the dental tissue, 
springing from the surface of the palate. But it seems to me, that a more exact 

VOL. XXVI. PART. I. 3M 



222 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

comparison may be found in the well-marked vascular folds of mucous mem- 
brane, covered by epithelium, which lie transversely across the palate in the 
Ruminantia. In the giraffe, for example, these folds are very strong, and they 
are, moreover, fringed along the free edge with well-defined papillae, which are 
also covered with an epithelium. If we were to suppose these papillae con- 
siderably elongated, their epithelium cornified, and the whole series of papillae, 
springing from any single fold, bound together by a cortical, cornified, epithelial 
layer, we should then have an arrangement of parts closely corresponding in 
structure to that of a plate of whalebone. But the Balaenoidea are not the only 
placental mammals in which a cornified epithelium is developed in connection 
with papillary growths from the surface of the buccal mucous membrane. For, 
as is well known, in the Carnivora, the papillae on the dorsum of the tongue are 
invested with a horny epithelium arranged in the form of retroverted spinules. 

I am also of opinion that we must assign to the baleen a more important 
function than that of the mere hair sieve or filter, with which it is most usually 
compared. For structurally it is much more highly organised than hair. It is 
highly vascular, and, I believe, also nervous, and can therefore play the part of a 
whole series of tactile organs, by means of which the animal would be enabled 
to estimate the amount and character of the food which it receives into the 
cavity of the mouth. 

As Geoffrey St Hilaire* and Robert KNOXt had discovered rudiments of 
the teeth in the gum of the very young foetus of the Balcena mysticetus, and as 
EschrichtJ had also observed them in the fcetal stage both of Megaptera and 
Balcenoptera, I removed the gum from the edges of both the upper and lower 
jaws, with the view of examining if the rudiments of these organs still existed 
in the almost fully developed foetus of the Longniddry Finner. I found in con- 
nection with the periosteal surface of each gum a well-defined band, which 
corresponded precisely with the margin of the jaw, and which received a number 
of arteries coming through foramina in the bones. This band, from its position, 
was obviously the part in which the teeth, if present, ought to have been found. 
A careful examination, however, both of the band and of the tissue on each 
side, failed to discover the smallest rudiment of a tooth. Hence it follows that 
in the Balaenoidea not only do the teeth not pierce the gum, but all trace even 
of their rudiments disappear before the termination of foetal life. 

Alimentary Organs. — Owing to the wide sweep of the lower jaw, the cavity 
of the mouth was of great size, and the space included between the two halves 
of the lower jaw reminded one of a huge barge ; indeed it was no uncommon 

* Aimales du Museum. Vol. x. p. 364. 

f Catalogue, op. cit. p. 22. Knox's preparations are in the Anatomical Museum of the University 
of Edinburgh. 

t Die Nordischen Wallthiere, 1848. 



STKANDED AT LONGNIDDRY. 223 

thing, when the animal was lying on the beach, to see a number of persons 
standing within the left mandible on the dorsum of the tongue as it was exposed 
by the falling over of the beak to the right side. The roof of the mouth was 
formed by the palate and baleen plates ; its sides corresponded to the great 
antero-posterior cleft between the upper and lower jaws ; its floor was formed 
by the dorsum of the tongue included within the two halves of the mandible. 
The dorsum of the tongue was almost flat near the front of the mouth, but 
somewhat further back it presented a considerable elevation, which arose like 
a hillock, and fitted within the concavity of the roof of the mouth between the 
opposite wreaths of the baleen. The tongue was very compressible and elastic. 
The mucous membrane on its surface was of a dark slate colour, and was at 
once reflected from the dorsum at the tip and sides of the tongue to the inner 
surface of the lower jaw, so that the tongue was tied to that bone, and obvi- 
ously could not be protruded from the mouth. The surface of the mucous mem- 
brane was firm and tough ; it was marked by ridges and furrows, which, for the 
most part, were placed longitudinally, though some extended in the transverse 
direction. 

The mouth rapidly narrowed towards the posterior buccal orifice. In the 
adolescent animal the diameter of this orifice was 10 inches. The mucous 
membrane was, in this locality, brownish-yellow in colour, and spotted with 
patches of brown and black pigment. Numerous rounded or somewhat oblique 
orifices opened on its free surface. These communicated with pits, the largest 
of which formed depressions -fths of an inch deep in the mucous membrane, 
big enough to admit peas ; these were obviously the mouths of gland follicles. 
The upper boundary of the orifice was formed by the soft palate, which was 
about an inch and a half thick, and distinct muscular fibres entered into its 
construction. 

In the foetus the posterior buccal orifice was much more constricted, for its 
diameter was only 2 inches. It was bounded above by a broad, well-defined velum, 
which extended backwards for 6^ inches, and possessed a broad attachment on 
each side to the pharyngeal wall, sending also a posterior pillar backwards on 
each side as far as a line opposite the arytenoid cartilages (Plate VIII. fig. 30). 
The greatest breadth of the soft palate was 7 inches. Its position was almost 
horizontal ; mucous membrane covered its upper and lower surfaces and posterior 
border, and from the latter no uvula projected. The absence of an uvula in the 
lesser Pike "Whale had previously been noticed by Drs Carte and Macalister.* 
Owing to the breadth of the attachment laterally of the velum, the passage from 
the mouth to the pharynx was much more in the form of a canal, which may be 
termed the bucco-pharyngeal canal, than a simple opening. This canal gradually 

* Philosophical Transactions, 1868, p. 232. 



224 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

widened in its backward passage, for whilst only the tips of the four fingers could 
be introduced into its buccal orifice, the fist could be readily passed through it 
from the pharyngeal end. The mucous membrane surrounding the buccal orifice 
and lining the bucco-pharyngeal canal, was spotted with pigment, and with pits, 
such as have been described in the same region in the older animal. The mucous 
membrane was also thrown into faint transverse folds, which corresponded in 
their direction with the fibres of the well defined palato-glossus muscle. The 
part of the pharynx situated immediately above the velum was greatly dilated, 
and measured 24 inches in circumference. It constituted the nasal subdivision 
of the pharyngeal chamber. The antero-posterior diameter of the pharynx from 
the posterior border of the soft palate to the commencement of the oesophagus 
was 9 inches. In its general form it was funnel shaped ; for whilst the transverse 
diameter just behind the attachment of the velum was 7^ inches, it rapidly nar- 
rowed behind, where it joined the oesophagus to a tube, If inch in diameter. 

"When the interior of the pharynx was more completely exposed by a mesial 
longitudinal incision, not only could the posterior buccal orifice be more clearly 
seen, but the relations of the superior laryngeal opening were exposed (Plate VIII. 
fig. 31). In front of this opening was the elongated, tongue-like flexible epiglottis, 
which projected forward and upward. It was invested by mucous membrane, 
and from its anterior surface a well-defined hyo-epiglottidean fold of mucous 
membrane passed forwards to the body of the hyoid. Projecting from the 
middle of its posterior surface was a vertical rounded elevation, which obviously 
corresponded to the " cushion" described by Czermak on the back of the human 
epiglottis, and which, doubtless, like that cushion, plays an important part in 
the closure of the laryngeal orifice during deglutition. From each side of the 
epiglottis a strong aryteno-epiglottidean fold of mucous membrane passed back- 
wards to the lappet-like processes of mucous membrane which invested the 
horns of the arytenoid cartilages, which formed the posterior boundary of the 
orifice. These lappets were separated by a median cleft. No hood-like fold 
of mucous membrane, such as Drs Carte and Macalister have described in 
B. rostrata, as affording protection to the orifice of the larynx during degluti- 
tion, existed in this animal. The superior orifice of the larynx was large 
enough in the foetus to admit both fists at the same time. 

The muscular wall of the pharynx was formed of the constrictors, the fibres 
of which passed from below upwards, to be attached to the superior mesial 
raphe of the pharynx. The fibres of at least two pairs of constrictor muscles, 
arising from the hyoid bone and thyroid cartilage, were distinctly recognised. 
The muscular coat of the oesophagus was comparatively thin, and presented the 
longitudinal and circular arrangement. 

Numerous glands existed in the submucous coat of the pharynx. The posi- 
tion of many of these was marked, more especially on its lateral and anterior 



STRANDED AT LONGNIDDEY. 225 

walls, by crypt-like depressions in the mucous membrane, some of which were 
large enough to admit a kidney bean, others not bigger than a pea (figs. 30, 31). 
These crypts were collected into groups, the best marked of which were situated 
close to the junction of the anterior border of the soft palate with the anterior 
wall of the pharynx. 

In studying the method by which this and other whalebone whales collect 
their food in their huge mouths prior to deglutition, it should be kept in mind 
that they are not provided either with teeth, or with a protrusible tongue by 
which to grasp the prey. It is probable that when in search of food, the animal 
swims about with its mouth wide open, until a sufficient quantity of food is 
collected on the dorsum of the tongue, in the space between the two halves of 
the mandible, prior to being swallowed. 

Though the depression of the lower jaw in the act of opening the mouth 
is doubtless due to muscular action, yet, when once open, the jaw may, I 
believe, remain depressed without the continued action of muscles. The huge 
fibrous columns, which pass, one on each side, from the base of the skull to the 
condyles of the lower jaw, so suspend that bone, as to support it without the 
need of calling into action any muscle ; for it was observed, as the animal was 
floating at high water, that the lower jaw was open, and swayed gently to and 
fro with the movements of the waves. To draw the jaw back prior to degluti- 
tion, the temporal and other elevator muscles must be called into action ; and, as 
the jaw is raised, the tongue is pressed upwards against the lower edges of the 
baleen, and the water contained in the cavity of the mouth is forcibly squeezed 
out between the rows of plates. The food retained in the mouth by the sieve- 
like fringes of the baleen, is then forced back through the bucco-pharyngeal 
canal, doubtless by the action of the tongue, into the pharynx, when the con- 
strictors grasp it and force it back into the oesophagus. Here the soft palate 
acts as a valve to prevent its passage upwards to the nose, and the superior 
laryngeal orifice is closed by the co-aptation of the epiglottis, arytenoid cartilages, 
and aryteno-epiglottidean folds of mucous membrane, so that it cannot enter the 
larynx. In these respects, therefore, the mechanical arrangements for prevent- 
ing the passage of the food into the respiratory passages, closely remind one 
of the structures found in the corresponding locality in the human subject. 
As it is also important that water should not pass from the mouth into the 
pharynx whilst the animal is collecting its food ; and as the respiratory process 
is performed, not by the mouth but by the nose, the contraction of the fibres of 
the palato-glossal sphincter would effectually close up the bucco-pharyngeal 
canal at the time when these processes were going on. 

The stomach was so injured in various places by the men engaged in flensing 
the animal, that little more was ascertained in connection with it, than that it 
was subdivided into at least four compartments, which communicated with each 

VOL. XXVI. PART I. 3 N 



226 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

other by valvular orifices. One of these valves was secured, and reminded one 
on a large scale of the human pyloric valve, or of the valve I described and 
figured some time ago* at the end of the fifth compartment of the stomach of 
Globiocephalus svineval. The stomach was to all appearance empty. 

An omentum was in connection with the stomach, which, when stretched 
out, was big enough, in the mother, to cover the floor of a large room. It was 
made up of fibres, composed of connective tissue, which crossed each other so 
as to form a most elegant lace-work pattern, with distinct perforations in the 
meshes of the net. Blood-vessels were seen in the larger bands of fibrous tissue 
which traversed the net. Scarcely any adipose tissue was found in it, which is 
the more remarkable, when we remember the enormous quantity of fat situated 
as a sort of inner padding for the wall of the abdominal cavity. 

The intestinal canal was of great length, and by far the longer part of its 
extent consisted of huge coils, of which as many as fifteen were counted, though 
it is probable that a greater number existed. The hinder end of the gut, as 
it passed backward to the anus, was almost straight, and about 20 feet long. 
No accurate measurement of the length of the intestine could be taken, but it 
was estimated at about 80 feet, for the various coils, as soon as they were 
removed from the abdomen, were carted away to the manure heap. The 
circumference of the tube was not uniform throughout, varying in different 
localities from 20 to 30 inches. Extending along the border of the intestine 
at the line of reflection of the mesentery was a very remarkable looking tube 
with thick walls, which exhibited an alternating series of dilatations and con- 
strictions, which gave it a beaded appearance (Plate VIII. fig. 32, m). This 
tube gave off a number of branches, which ramified in the subserous areolar 
coat of the gut, and formed there a complex anastomosing network. Along 
with this moniliform tube was a large vein (v), and accompanying it was a 
nerve (n), considerably larger than the human pneumo-gastric, which gave off 
branches to the wall of the intestine. This nerve was obviously a large offshoot 
of the sympathetic. The intestine possessed a distinct peritoneal coat (p), 
which rested on the subserous areolar tissue. The muscular coat was thick, 
and the longitudinal and circular arrangement of fibres was strongly marked. 
A distinct submucous coat was present. The mucous membrane was brownish- 
yellow, and thrown into strong valvules conniventes, some of which extended 
two-thirds, others half round the canal of the gut. The largest valvulge pro- 
jected at least one inch into the canal. Numbers of parasites were attached to 
the surface of the mucous membrane. I have not as yet had time properly to 
examine them, but they are in general appearance like the Echinorynchus brevi- 
collis which Malm found in the intestine of the Balcenoptera which he examined. 

* Journal of Anatomy and Physiology. Vol ii. p. 73. 



STRANDED AT LONGNTDDRY. 227 

I can say nothing more of the anatomy of the liver than that it was subdivided 
into two lobes. The pancreas was not recognised in the course of the dissection. 

Organs of Circulation. — My observations on the arrangement of the heart and 
blood-vessels were made chiefly on the foetus, but in several points were supple- 
mented by a reference to the corresponding structures in the adolescent animal. 
The heart was contained in a well-formed pericardium. In the mother it was of 
enormous size ; and in the foetus it was considerably larger than the heart of an ox. 
It presented externally the usual arrangement of grooves, which marked its sub- 
division into four chambers, and in these grooves the coronary vessels ramified. 

In the foetus the right auricle, when opened into, showed a smooth inner 
surface for the most part, but the anterior wall and the interior of the appendix 
had well-defined fleshy columns projecting into the cavity. In the intervals 
between these columns the auricular wall was dilated, and formed a number of 
pouch-like recesses. The superior cava, large enough to admit five extended 
digits, opened into the anterior and external part of the cavity, and had no 
valve at the orifice. The inferior cava, large enough to admit the fist, opened 
into the posterior and external part of the auricle. No trace of an Eustachian 
valve was seen at its mouth. The mouth of the coronary sinus readily admitted 
the tips of three fingers, and opened between the inferior cava and the auriculo- 
ventricular orifice, and was also without a valve. 

In the interauricular septum an almost circular foramen readily admitting 
five extended digits was situated. Surrounding this opening, and attached to 
its edge, a loose, membranous, annular fold, formed by a duplication of the 
endocardium was seen. When put on the stretch it projected into the auricle, 
and the projecting border was free and pierced with large fenestras Although 
this fold was situated in the right auricle, when I opened into that cavity, yet 
it could without difficulty be passed through the foramen into the left auricle. 
At the attached border, again, the membrane was almost entire, and most per- 
fect in its anterior, external, and posterior portions, where the depth from the 
attached to the free borders was 4 inches. This membranous fold was situated 
at some distance from the mouth of the inferior cava, so that it could not be 
regarded as the Eustachian valve in the sense in which it is customary to use 
that term. From its position it would, however, seem to have served some pur- 
pose in connection with the flow of blood from one auricle to the other during 
foetal life ; but it is possible that, by growth both in thickness and surface, it 
might, after the birth of the creature, have closed up the orifice and completed 
the auricular septum. I think it probable that the structure described by Dr 
Knox [Catalogue, p. 24), in the heart of a foetal mysticetus, as " a membranous 
sac, the size of a full-sized thimble, presenting at the bottom a delicate reticu- 
lated net-work, and projecting into the left auricle," was similar to the annular 
fold observed in this foetal Balwnoptera. 



228 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

A well-defined tricuspid valve was placed at the right auriculo ventricular 
orifice. The cusps had the same relative position as in the human heart, and 
the arrangement of the carneae columnar, musculi papillares, and chordae ten- 
dineae was closely similar. In the older whale one of the cusps measured 10 
inches in width at its base, and the depth from base to apex was 8^ inches. 
Some of the chordae tendineae were 12 inches long, and the girth of one of the 
largest of these, where it arose from a papillary muscle, was 2^ inches. As it 
subdivided before it joined the cusp, the size of its branches was very ma- 
terially smaller. 

The pulmonary artery arose from a distinct conus arteriosus. It ran for- 
wards and to the left, and divided into two branches for the right and left 
lungs. Its left branch gave origin in the foetus to a widely patent ductus 
arteriosus, which joined the arch of the aorta immediately behind a spot oppo- 
site the origin of the left subclavian artery (Plate VII., x). 

In the mother a strong, fibrous, rounded cord, 5 inches long, passed between 
the pulmonary artery and aorta in the place of the ductus arteriosus. Its 
circumference at its aortic attachment was about 6 inches, and it was some- 
what thicker at its opposite extremity. When transversely divided it was seen 
to be distinctly laminated, and extending along its axis was a canal readily 
admitting a large sized catheter. This canal widened out into a funnel-shaped 
passage at its two extremities, where it opened into the aorta and pulmonary 
arteries. Hence, even in the adolescent animal the arterial duct was patent, 
though, from the small size of the canal, any intermixture of blood which might 
have occurred would be so small as not to affect the characters of the enormous 
volume of that fluid contained in the arterial system. It is interesting also to 
note that Knox found a pervious ductus arteriosus in the great Rorqual which 
he examined, and Dr Murie observed it in an adult Balcenoptera musculus* 
The trunk of the pulmonary artery in the mother was 3 feet 7 inches in internal 
circumference, and its coat, which was distinctly laminated, varied in thickness 
from 1^ inch to fths of an inch. The internal circumference of one of the 
primary branches was 1 foot 5 inches, the thickness of its coat -|th of an inch. 
The internal circumference of one of the pulmonary veins was 19 inches. 

The left auricle, in the mother, had much thicker walls and a redder 
colour than the right ; but in both, the appendages were large, and the fleshy 
columns within them, and on the adjacent part of the auricular wall, were enor- 
mously developed, one of the largest measuring 5 inches by 3, another 6 inches 
by 2, and so on. The pouch-like dilatations, already referred to in the descrip- 
tion of the foetal auricle, between these columns readily admitted one or both 
fists. From the mode in which the columns intersected each other, they and 
the pouches gave to this part of the auricle quite a cavernous character. The 

* Proc. Zool. Soc, Feb. 14, 1865. 



STRANDED AT LONGNIDDRY. 229 

muscular wall at the bottom of some of the pouches was often so thin as to be 
translucent when held up to the light. Many of these pouches were situated 
parallel and close to the auriculo-ventricular groove. 

The left ventricle had thicker walls than the right, and, in connection with 
its walls and auricular opening, carnese columnar, musculi papillares, chordae 
tendinese, and a bicuspid valve were seen. 

The arch of the aorta in the mother rivalled in its calibre one of the main 
pipes for the supply of water to a district of a large city. The internal circum- 
ference of its ascending part was 3 feet 2 inches, whilst its coat varied in thick- 
ness from 1^ to 1^ inch. The coat was distinctly laminated, of a yellow colour, 
and very elastic. A well-defined inner membrane lined it and the other parts of 
the arterial and venous systems. The external circumference of the aorta in 
the foetus was 10 inches. It then dilated prior to giving origin to the great 
branches of the arch, and immediately beyond these vessels it diminished 
materially in size as it became the posterior thoracic aorta. The external cir- 
cumference of the innominate artery in the mother was 1 foot 9 inches. 

The aorta arched to the left over the root of the lung (Plate VII. fig. 28). 
A pair of coronary arteries (a) arose from the commencement of its ascending 
part, one passing on each side of the root of the pulmonary artery. Each 
coronary immediately subdivided into three branches, the largest of which 
turned round its own margin of the heart in the auriculo-ventricular groove, and 
supplied the corresponding auricle and ventricle. The second branch of the 
right coronary entered the wall of the right auricle ; the third turned round the 
root of the pulmonary artery. The second branch of the left coronary artery 
descended in the anterior inter- ventricular groove ; the third passed to the 
substance of the left ventricle. In the mother each coronary artery was as 
large as the posterior aorta of an ox. 

From the anterior surface of the transverse part of the arch three large 
branches arose, the brachio-cephalic, left carotid, and left subclavian (b, c, d). 
The right branch, by far the largest, was the arteria innominata or brachio- 
cephalic (a). Five inches (in the foetus) from its origin it bifurcated into a right 
common carotid (e) and right subclavian (/). The right subclavian gave off, 
one inch from its origin, a large branch, the right posterior thoracic [g), which 
was traced into the great thoracic rete mirabile. One inch and a-half further 
on the subclavian bifurcated into the axillary (h) and internal mammary (i) 
arteries, the latter of which was somewhat the larger of the two, and supplied 
the inferior wall of the chest. The axillary passed in front of the first rib, 
immediately above the scalenus anticus muscle ; but before doing so it gave off 
a considerable branch which ran forwards along the side of the neck. The 
axillary was traced into the flipper, and, in the dissection of the fore-arm, 

VOL. XXVI. PART I. 3 O 



230 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

branches of this artery were found lying, along with distinct nerves, in con- 
nection with the flexor and extensor muscles of the digits. 

The right common carotid (e) ran forwards for 6 inches and then bifurcated. 
The branches should, I think, be regarded as the cervico-facial (k) and internal 
carotid (/) arteries. The cervico-facial, much the larger, passed to the deeper 
parts of the head, but gave off also a large branch to the face. The internal 
carotid was torn across ; but branches arose from it which passed to a rete 
mirabile in the neck. The state of the parts prevented me from tracing out to 
their termination the branches of the right common carotid artery. 

The second branch of the transverse part of the arch was apparently a left 
common carotid artery (c). It gave off a small branch to the side of the neck, 
and then bifurcated 7 inches from its origin. The larger branch of bifurcation 
was the cervico-facial (m), which divided into many branches for the head and 
face. The smaller branch was apparently the internal carotid (n). 

The third branch of the transverse part of the arch was the left subclavian 
artery (d). It gave off a large branch, the left posterior thoracic (o), to the great 
thoracic rete, and then divided into the left axillary (])) and internal mammary (q) 
arteries. The rete mirabile was not confined to the thoracic cavity, but ex- 
tended upwards into the neck, and prolongations were traced through the inter- 
vertebral foramina into the spinal canal. The large foramina at the roots of the 
transverse processes of the cervical vertebrae were also occupied by considerable 
masses of this highly vascular network. 

The posterior thoracic aorta ran backwards, and gave off the series of inter- 
costal arteries. It then entered the abdomen and supplied the various viscera ; 
but the distribution of its branches, owing to the injured state of the viscera, 
could not be followed out. It was noticed that in the foetus the hepatic artery 
was as large as the human common iliac. The abdominal aorta was prolonged 
backwards as the great caudal artery, which was protected by the series of 
arches formed by the chevron bones. From the caudal artery, opposite the 
body of each vertebra in the foetus, two branches, which entered the middle of 
its ventral surface, were traced into the ossifying centrum of each vertebra. 

It may not be out of place to refer to what has been stated as to the arrange- 
ment of the great arteries, which arise from the transverse part of the arch in 
some of the other Cetacea, where the vessels have been carefully dissected. 
Knox,* EscHRiCHT,t and Carte and MacalisterJ have all pointed out that in 
the Balaenoptera rostrata, three great arteries, the brachio-cephalic, left carotid, 
and left subclavian arise from the transverse part of the arch. Knox also states 
that, in his great Eorqual, the arrangement of the vessels arising from the arch 

* Catalogue, p. 18. + Die Nordischen "Wallthiere, p. 104. 

% Philosophical Transactions, 1867, p. 245. 



STRANDED AT LONGNIDDRY. 231 

followed closely that of man ; and he refers to brachio-cephalic, left carotid, and 
left subclavian arteries ; and Malm observed a similar disposition in his 
Balwnoptera. It seems, therefore, that these great arteries have a similar mode 
of origin in different species of Finners. In Delphinus and Globiocephalus, how- 
ever, the great arteries arise in the form of two brachio-cephalic arteries, and 
the left posterior thoracic arises usually quite independently ; but as I have on 
former occasions * described these arrangements, I need not in this place enter 
into any further details. 

It will be necessary now to give an account of the very remarkable monili- 
form tube, which I have referred to in the description of the intestine of the 
adolescent animal. It was found along the entire length of the mesenteric 
attachment of the gut, and extended back along the rectum. It exhibited an 
alternating series of dilatations and constrictions, which varied in their dimen- 
sions in different parts (Plate VIII. figs. 32, 33). The dilatations were some- 
times globular, at others ovoid in form, and in some cases were flattened on 
their surfaces. The largest measured as much as 1 foot 6 inches in transverse 
external circumference, whilst the smallest were only 8 or 9 inches. When the 
dilatations were ovoid the elongation was mostly in the direction of the long 
axis of the tube, in which direction the circumference of the dilatation was 
therefore somewhat greater. The constrictions also varied in size, the smallest 
being about 4 inches in external circumference, the largest 1 or 2 inches more. 
The tube possessed very strong and dense walls, which varied in thickness in 
different parts. In the larger dilatations the thickness was as much as 1^ inch, 
but in the smaller not more than ^ inch. The walls were white, tough, and 
very resisting. Examined microscopically, the tissue which composed them 
was seen to be chiefly the white fibrous, but mingled with it were elastic fibres. 
The inner surface of the wall presented a corrugated appearance, owing to the 
presence of a number of permanent, circular folds, wrinkles or ridges, which 
passed quite around the inner surface of the tube (fig. 33). In many places 
these folds were situated close together ; but elsewhere they were separated by 
intervals in which the inner wall of the tube was comparatively smooth. These 
ridges were in part formed of a folding of the lining membrane of the tube, and 
in part of the fibrous tissue of the wall. Some of the largest of these folds 
projected as much as 1 inch, or even more, into the lumen of the tube, and as 
this projection was carried all round the inner wall, the lumen was necessarily 
much constricted in these localities, and in the smaller divisions the bore was 
sometimes reduced to a hole in the middle of the fold less than 1 inch in 
diameter, whilst on each side of it the tube might perhaps dilate into a space 
2, 3, or more inches in its diameter. Hence the dilated and constricted 

* British and Foreign Medico-Chirurgical Review, October 1862, p. 479, and Journal of Anatomy 
and Physiology. Vol. ii. p. 66. 



232 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

character of the tube visible externally was an index of important internal 
arrangements. Numerous branches, into which an injection was readily thrown, 
arose from the moniliform tube, and passed directly into the subserous coat of 
the gut. They were about the size, at their origin, of the human brachial artery, 
and ran straight and parallel to each other for some distance, giving off but 
few branches ; then they altered their direction, and formed, by anastomosing, a 
series of arches from which numerous branches arose, which ran towards the 
free margin of the intestine, again to anastomose, and give rise to still smaller 
branches, which penetrated the muscular and mucous coats of the gut. 

In connection with the exterior of some of the dilatations of the moniliform 
tube a peculiar structure was dissected. It consisted of a number of closely 
crowded lacunae, varying in size from a pea to a walnut (Plate VIII. fig. 34), 
separated more or less perfectly from each other by septa formed of a delicate 
smooth membrane, similar to that which also lined the interior of the lacunae. 
The arrangement to some extent corresponded with that of a multilocular cyst, 
the loculi of which communicated with each other. In one spot a distinct tube, 
the size of the stem of a common tobacco pipe, was seen to open into a group of 
these lacunae. In some places, more or less elongated, and sometimes ovoid, bodies 
of a dark brown colour, were situated immediately beneath the delicate semi- 
transparent lining membrane. These bodies had the appearance of lymphatic 
glands, and this view of their structure was confirmed by a microscopic examina • 
tion, for, notwithstanding that the specimen had been for sometime in spirits 
of wine, distinct, pale, circular, lymphoid corpuscles were seen to enter in large 
numbers into the structure of these bodies. I did not succeed in tracing out 
any connection between this lacunary system and the wall of the intestine, 
though it is possible that the small tube, just referred to, may have proceeded 
from or to the wall of the gut. 

It was unfortunate that in the portions of intestine, with the moniliform 
tube attached, which were sent over to the Anatomical Museum for examination, 
none of the expanded part of the mesentery had been preserved. I was con- 
sequently unable to trace the branches which proceeded from the proximal 
surface of this tube to their origin. I have little doubt, however, but that they 
were derived from the mesenteric artery. 

In the foetus the intestine was, as a rule, so softened by putrefaction that it 
could not be preserved. One or two coils were, however, somewhat more per- 
fect, and after being hardened in strong spirits of wine, I was enabled to effect a 
partial examination. 

The mesenteric artery did not possess that complete series of arterial 
arcades, which we are familiar with in man. It branched comparatively seldom, 
and its branches ran towards the border of the intestine. Those which arose 
nearest the gut did not enter directly the intestinal wall, but passed to an 



STRANDED AT LONGNIDDRY. 233 

elongated structure, which lay parallel to and next its mesenteric border. This 
structure occupied the position of the moniliform tube in the parent whale, but 
did not possess its beaded appearance. Indications, in places, of a tube travers- 
ing its long axis were seen ; but in the greater part of its extent it was appa- 
rently subdivided into a large number of minute spaces, so that the surface of 
section had quite a cavernous aspect. From this structure numerous fine 
branches arose, which passed into the subserous coat of the intestine, to be 
distributed there like the branches of the moniliform tube in the parent animal. 
It would seem, therefore, that in the foetus the moniliform tube is not developed 
in the same precise manner as in the adolescent whale, but that a series 
of inter-communicating spaces occupy the position in which it subsequently 
appears. The formation of the moniliform tube, out of this lacunary system, 
would be occasioned by a great increase in size of those lacunas which lie in 
the same longitudinal series, and by the great hypertrophy of their originally 
delicate walls. It is probable that the lacunas described on the surface of some 
parts of the dilated tube in the parent (fig. 34), represented in it the original 
condition of the mesenteric lacunary system of the foetus. 

In the Cetacea, important arrangements, in connection with the vascular 
system, exist in various parts of the body for the purpose of modifying and 
equalising the force of the blood current. The great cervico-thoracic rete 
mirabile, with its numerous offshoots into the spinal canal and cranial cavity, is 
the arrangement which has been most carefully studied by different anatomists. 
But in considering the function of this network, it is not sufficient to regard it 
as merely a reservoir, or huge sponge, which contributes,- by its complex rami- 
fications, to produce an enormously extended area for the reception of the blood, 
when the whale dives to a great depth from the surface of the ocean. It serves, 
I believe, the purpose, by minutely subdividing the arterial stream, of distribut- 
ing and equalising the force of the blood current before it reaches those delicate 
organs the brain and spinal cord. It may be regarded, therefore, as the teleo- 
logical equivalent of the arteries in the human pia mater, of the circle of Willis, 
of the tortuosities in the vertebral and internal carotid arteries, and of the rete 
mirabile in connection with the intra-cranial arteries in ruminants and in 
the pig. 

With what, then, are we to associate the large moniliform tube in the me- 
sentery of this whale ? From its beaded character it might at the first glance 
be supposed to belong to the lymphatic system ; but the careful consideration 
of the distribution of its branches, and of its relations to the mesenteric arteries, 
have led me to the conclusion that it is a remarkable modification of the mesen- 
teric arterial system, which serves the same office, for the intestine, that the rete 
mirabile does for the brain and spinal cord. 

The great size of the aorta and of the trunk of the mesenteric artery, the 
VOL. xxvi. part i. 3 P 



234 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

paucity of the system of arterial arcades, the proximity of the intestine to the 
aorta, the pressure, from the elastic recoil of the arterial wall, of the enormous 
column of blood in the aorta, would seem to render some mechanical arrange- 
ments necessary, by means of which that pressure may be distributed and 
regulated before the blood enters the slender arteries within the wall of the 
intestine. 

The structure of the moniliform tube admirably adapts it for this purpose. 
The blood flows through it on its way to the intestinal arteries, and is diffused 
into the numerous dilatations or bays which bulge out from its sides. The 
transverse inflexible folds on its inner wall diminish at intervals the lumen of 
the tube, and where they project so far as to leave but a narrow aperture in 
the axis of the tube, they act as strictures in retarding the flow of the current. 
At the same time their circular arrangement enables them to act as internal 
girders, and to strengthen the walls so as to prevent over distension of the tube* 

I have already referred to the analogy between the rete mirabile in the cetacea, 
and the network in connection with the intra-cranial arteries in the pig. I may 
now allude to a modification which the pig exhibits in the arrangement of its 
mesenteric arterial system. The arteries subdivide in the middle of the mesen- 
tery, and form there a compact network — a rete mirabile — from which numer- 
ous small arteries radiate outwards to the intestine.t These radiating vessels 
closely correspond in appearance to those which I have described as arising 
from the moniliform tube in the Longniddry whale. The Cetacea, therefore, 
present affinities to the Pachydermata, not only in the diffused character of the 
placenta, but in the possession of closely allied modifications of the cerebral 
and intestinal arterial systems. 

The presence of a moniliform tube, in connection with the intestine, does 
not seem to have been previously recognised in the Cetacea by anatomists. 

The superior vena cava was formed by the junction of the two innominate 
veins, on the right of the ascending aorta. Each innominate vein began at the 
root of the neck in the form of a dilated sinus, into which the veins from the 
neck, flipper and inner wall of the chest opened. The inferior cava received 
a number of hepatic veins before it pierced the diaphragm. The umbilical vein 
was 27 inches long in the foetus in its course from the umbilicus to the 
liver. 

The portal vein in the foetus had a diameter of 3 inches before it entered 

* My colleague, the Professor of Engineering, Professor Fleeming Jenkin, to whom I pointed out 
the structure of this tube, concurs in the opinion of its function expressed in the text. 

t The mesenteric rete in the pig has long heen known to anatomists — see Barclay on the 
Arteries, Edinburgh, 1812; T. J. Aitki in Reports of Edinburgh Meeting of British Association, 
1834, p. 681 ; Owen, Comparative Anatomy of Vertebrates, vol. iii. ; Gurlt, Anatomie der Haus- 
saugethiere, Berlin, 1860. The complexity of the rete in the pig is due to the plexiform arrangement 
of both the mesenteric vein and artery. 



STRANDED AT LONGNIDDRY. 235 

the liver. In the coil of intestine from the adolescent animal, from which 
fig. 32 was taken, a vein larger than the human inferior cava, ran close and 
parallel to the great moniliform artery of the intestine, and received numerous 
veins, the rootlets of which took their origin within the coats of the gut. In 
the foetus a vein lay along with the artery in the expanded part of the me- 
sentery. 

At the upper part of the cavity of the thorax in the foetus, close to the 
apex of the pericardium, a well-defined, though small, thymus gland was found. 
It was subdivided into two lobes, each of which was brown in colour, thin, 
and flattened in form, and 5 inches in length by 4f inches in its greatest 
breadth. The lobes were subdivided into distinct lobules by intermediate con- 
nective tissue, and they received numerous blood-vessels. In proportion to 
the size of the animal the gland was obviously smaller than might have been 
anticipated. The thyroid gland, supra-renal capsules and spleen were not re- 
cognised during the dissection. 

Organs of Respiration. — When the cavity of the thorax was opened into, by 
the removal of the inferior wall, the lungs were exposed. In the foetus each 
lung was an elongated, flattened organ 2 feet 8 inches in length. It was in- 
vested by a distinct and smooth pleura, and was not subdivided into lobes by 
fissures. A similar absence of fissures and lobes I have also seen in the lung 
of B. rostrata. The pulmonary artery, veins, and bronchus entered its substance 
through the hilum on its mediastinal surface. When the lung was removed and 
washed with a jet of water, the softened pulmonary substance broke down, and was 
washed away, and the arrangement of the intra-pulmonic part of the bronchus 
could be seen. This tube, as a rule, branched in a dichotomous manner, though 
collateral offsets sometimes proceeded from it. It was accompanied by the pul- 
monary and bronchial arteries, and by bronchial nerves of some size. 

The cartilaginous framework was much more perfect than in the human 
bronchus. The tube was hooped with cartilaginous, spirally arranged, ring-like 
plates ; in the larger tubes usually not more than once and a-half, but in the 
smaller tubes a greater number of times (fig. 35). Sometimes in these latter the 
cartilage formed perfect rings, and both in them and in the larger tubes 
the cartilaginous plates not unfrequently bifurcated. The branching of 
the plates was always well-seen at the angle of the bifurcation of the tubes. 
The plates were invested by a well-defined perichondrium. The hoop-like and 
spiral coils of these cartilaginous plates have an important office in connection 
with the respiratory process in this animal. They not only aid in keeping the 
tubes open, but, by their elasticity, aid in the recoil of the lung during the great 
expiratory effort which the whale makes in the act of blowing. The diameter 
of the right bronchus in the foetus was 2 inches, that of the left 2^ inches ; in 
the mother one of the bronchi was 7 inches in diameter. 



236 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

Three inches in the foetus, above the place of bifurcation of the trachea, that 
tube gave off a supplementary bronchus, 1^ inch in diameter, to the right lung, 
which seems to be, as Sandifort and Eschricht have pointed out, the usual 
arrangement in the cetacea, the Greenland right whale being excepted.""" The 
trachea had three, somewhat irregularly formed, cartilaginous hoops immediately 
above the bifurcation ; but from the highest of these up to the arytenoid carti- 
lages, a distance of 6^ inches, which corresponded to two somewhat subdivided 
tracheal rings, and to the interval between the separated inferior borders and 
plate-like processes of the cricoid, the cartilage was deficient inferiorly, and the 
ventral wall of the wind-pipe was formed of fibrous membrane. The mucous 
membrane of the trachea, more especially on the anterior wall, was marked by 
numerous fine reticulated folds, the chief of which ran parallel to the long axis 
of the tube. The diameter of the trachea was about 5 inches. 

The cartilaginous framework of the larynx consisted of a thyroid, a cricoid, 
a pair of arytenoid cartilages, and an epiglottis. The form, arrangement, and 
connections of these cartilages were examined in the foetus (Plate VIII., figs. 
36, 37, 38). 

The thyroid cartilage consisted of a median and two lateral portions. It 
was a comparatively thin plate, and possessed two surfaces, a superior and in- 
ferior, which were flattened, and two margins, an anterior and a posterior. The 
median part, tongue-like in form, was bifid at its hinder border, and projected 
for some distance backward ; a deep notch marked its superior border ; from 
this notch, to the end of the forks of the tongue-like part, the diameter was 4^ 
inches. The lateral portion curved outwards, and was then prolonged back- 
wards, as the elongated and somewhat rounded posterior cornu to be articulated 
by a moveable joint with the outer surface of the cricoid. The anterior cornu 
was continuous with the anterior border of the cartilage ; it was short and rudi- 
mentary. The cartilage was connected to the body and great cornua of the 
hyoid bone by a strong membrane, and a pair of thyro-hyoid muscles passed 
between them. 

The cricoid cartilage was an incomplete ring ; suj)eriorly, it formed a thick 
mass of cartilage 7 inches in its antero-posterior diameter. Its surfaces were 
curved, and it turned round the sides of the wind-pipe towards its ventral 
aspect, and ended in the greater part of its extent in a free rounded border. 
From the hinder part of this inferior border, however, five plates, similar in 
form to the cartilaginous hoops of the trachea, arose and turned round the 
side of the larynx to the ventral surface ; but the plates from opposite sides 
did not meet in the mesial line. An interval, varying in its transverse diameter 

* Die Nordischen Wallthiere, p. 148, Ray Society's translation of Memoir on Greenland Whale, 
p. 103. 



STRANDED AT LONGNIDDRY. 237 

from 3 to 4 inches, separated the opposite inferior margins from each other. 
It was filled up by a strong fibrous membrane, which was continuous laterally 
with the perichondrial investment of the cricoid and its plate-like offshoots, 
anteriorly with the perichondrium investing the posterior horns of the two 
arytenoid cartilages, and posteriorly with the membrane which filled up the 
interval between the ventral borders of the first two cartilages of the trachea. 
This membrane, which may be called the inferior crico-tracheal membrane, was 
of great importance as completing the wall of the windpipe on its ventral aspect. 
The posterior margin of the cricoid was comparatively narrow; the anterior 
margin possessed at each lateral angle a broad surface for articulation with the 
body of the arytenoid cartilage, distinct capsular and synovial membranes con- 
nected the two cartilages. 

Each arytenoid cartilage, irregular in form, consisted of a body and two 
cornua. The body formed a thick plate of cartilage. The anterior cornu 
curved upwards and forwards into the lappet-like fold of mucous membrane 
behind the superior laryngeal opening. The posterior cornu curved back- 
wards and inwards within the area enclosed by the sides of the cricoid ; it 
almost reached the mesial plane, where a transverse fibrous ligament connected 
it by the tip to its fellow. The two posterior horns formed an imperfect hoop, 
invested by the mucous membrane of the larynx, which was prolonged directly 
backwards and downwards to form the mucous lining of the laryngeal sac. 
The free rounded border of the cricoid was connected to the posterior cornu 
of the arytenoid by the inferior crico-tracheal membrane. A crico-thyroid 
muscle existed also on each side, and muscular fibres were seen to occupy the 
position of the crico-arytenoidei postici and arytenoideus. 

The epiglottis contained a bar of yellow fibro-cartilage, which passed back- 
wards along the axis of the entire structure, to be attached to the superior 
surface of the middle portion of the thyroid cartilage. In the older animal, 
from which it had been removed without much injury," 5 - the entire organ 
measured 25 inches in length, whilst its breadth at the base was about 10 
inches ; it was thick and massive, and rounded in form at its free end. The 
fibro-cartilage was covered by mucous membrane, which was prolonged back- 
ward as the aryteno-epiglottidean folds, and forward as the hyo-epiglottidean 
fold. When this membrane was removed from the hinder surface of the epi- 
glottis and its arytenoid connecting folds, a strong aryteno-epiglottideus muscle 
was exposed, which curved upwards and inwards, decussating with its fellow 
in the substance of the epiglottis, and obviously was arranged to act as a 

* The other laryngeal cartilages were so much injured during their removal from the adolescent 
whale, that I was unable to examine them satisfactorily. I may, however, refer to their great size and 
thickness, more especially of the cricoid and body of the arytenoid. The cartilage was traversed in 
various directions by very distinct vascular canals. 

VOL. XXVI. PART I. 3 Q 



238 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

powerful sphincter for closing the glottis during deglutition. A deeper set 
of fibres of the same muscle was exposed by the removal of the thyro-hyoid 
membrane. 

There were no true vocal cords passing from the thyroid to the arytenoid 
cartilages, or laryngeal ventricles, but a slight fold of the mucous membrane, 
extended obliquely in the antero-posterior direction within the aperture of the 
glottis, on each side, a short distance below the free edge of the aryteno- 
epiglottidean folds. These might, perhaps, be regarded as rudimentary false 
vocal cords. 

One of the most interesting structures connected with the larynx was the 
great laryngeal pouch or cul-de-sac. It was 10 inches in length in the foetus, and 
extended backward from the thyroid cartilage, in close relation to the ventral 
surface of the inferior crico-tracheal membrane, to within 2 inches from the 
bifurcation of the trachea. Its outer wall was formed by a powerful muscle, 
which arose from the superior surface of the median tongue and adjacent lateral 
plate of the thyroid, from the inferior free border of the cricoid, and from the 
body of the arytenoid. The fibres were arranged in transverse rings around 
the walls of the pouch, and they formed a thick mass at its posterior end. The 
pouch was lined by a mucous membrane, which was continuous with the general 
mucous lining of the larynx, by extending upwards on the inner surface of the 
bodies of the arytenoid cartilages, and by passing round the free border of the 
hoop formed by their posterior horns. The mouths of numerous large crypts 
opened on the surface of this membrane. 

Owing to the peculiar arrangement of the arytenoid cartilages and the 
presence of this pouch, the laryngeal chamber might be regarded as subdivided 
into three compartments. The supero-anterior which formed the glottis proper, 
was bounded by the epiglottis, the aryteno-epiglottidean folds, and the anterior 
horns and bodies of the arytenoid cartilages with their investing and intermediate 
mucous membrane. The posterior was bounded above and to the sides by the 
cricoid cartilage, in front by the two posterior horns of the arytenoids, which 
ran obliquely from above backwards and downwards ; through the fissure 
between these horns it communicated with the glottis, whilst behind it was con- 
tinuous with the canal of the trachea. The inferior was the laryngeal pouch 
above described, which communicated directly and freely with the glottis at 
the base of the epiglottis, but with the posterior chamber through the fissure 
between the arytenoid horns. This pouch is often regarded as occasioned by a 
deficiency in the ventral part of the ring of the cricoid cartilage. But from 
the description of the arrangement of these parts, and from the figure 37, it 
will be seen that although this plate of cartilage is defective, yet that the ring 
is completed ventrally by the strong inferior crico-tracheal fibrous membrane, 
beneath which the pouch is situated. The laryngeal sac is rather to be regarded 



STRANDED AT LONGNIDDRY. 239 

as a diverticular prolongation of the mucous membrane between the thyroid 
and cricoid cartilages, accompanied by an imperfect development of the crico- 
thyroid membrane. 

The air entering the lungs during inspiration would have to pass from the 
glottis into the trachea through the fissure between the posterior horns of the 
arytenoids ; but the air, entering the laryngeal pouch, would pass into it below 
these two horns. The close approximation of these cornua would aid in the 
closure of the glottis, and in the retention of the air in the lungs when the whale 
has dived to a depth from the surface. 

The presence of a laryngeal pouch or sac in the B. rostrata, which he dis- 
sected, had not escaped the acute observation of John Hunter. In his 
account of that animal he says,* " The arytenoid cartilage on each side sends 
down a process, which passes on the inside of the cricoid, being attached to a 
bag which is formed below (behind) the thyroid, and before (below) the cricoid ; 
these processes cross the cavity of the larynx obliquely, making the passage at 
the upper part a groove between them." Sandifort t then pointed out and 
described its arrangements in two foetuses of Balcena mysticetus. Knox ob- 
served it \ not only in B. rostrata, and B. mysticetus, but in his great northern 
Rorqual, and he specially directed attention to the mode in which it was 
supported by the posterior horns of the arytenoid cartilages. Eschricht has 
also recognised this sac not only in the foetus of B. rostrata, but in that of 
the Megaptera longimana§ and Reinhardt and he have anew carefully 
described it in the Greenland Right Whale. A description, with several 
figures, of the sac in B. rostrata has recently been published by Messrs Carte 
and Macalister.|| 

Of these authors the last named alone discuss the probable use of this very 
remarkable pouch. They consider, that by the contraction of its muscular walls, 
it may expel the contained air so as to augment the power of, and to sustain the 
expiratory current. They suggest that it might aid in the production or modu- 
lation of sound, if the whales possessed such a faculty, but think that the size 
of its aperture, and the absence of all constricting bands, or apparatus, militate 
against that view of its use. 

The powerful muscular wall of the sac is unquestionably for the purpose of 
permitting the contraction of the wall on the contents, and as the pouch com- 
municates above directly with the glottis, a rapid contraction of the investing 
muscle would aid the expiratory act. But there is another purpose to which 
this sac may be applied. It may serve the office of a reservoir in which a 

* Structure and Economy of Whales. 

•f* Nieuwe Verhand. van Wetensch. te Amsterdam, 1831. 

\ Catalogue, pp. 11, 17, 23. § Die Nordischen Wallthiere, p. 103, e. s. 

|| Op. cit., p. 236, e. s. 



240 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNNER WHALE 

quantity of oxygenated air may be stored up to be made use of when the animal 
remains for some time below the surface, by permitting an interchange, by 
diffusion, to take place between the pure air in it and the carbonised air within 
the lungs. 

It has been customary to consider, that because the Balcenoidea have no 
vocal cords, therefore they have no voice, and cannot produce sound.""" But 
although they do not possess a pair of elastic bands, extending horizontally 
across the larynx between the arytenoid and thyroid cartilages, such as we see in 
the mammalia generally, yet in the posterior horns of their arytenoid cartilages, 
united by the transverse ligament, they possess a pair of structures which can 
be approximated or divaricated, and by the vibration of which, as the air 
passes between them, into or out of the lungs, sounds may very probably be 
elicitecl.t Their vibration would, without doubt, be assisted by their close 
relation to the air-filled laryngeal pouch. 

The nares consisted of two vertical passages, separated by a cartilaginous 
septum, which opened superiorly on the dorsum of the head by the external 
apertures or blow-holes, whilst by their deeper orifices they communicated with 
the nasal part of the pharynx. "When looked at from below (fig. 39), the 
mucous membrane was seen to be pitted with the mouths of numerous gland 
follicles, and to cover the surface of an oval fibro-cartilage which formed a 
considerable convexity in the outer and anterior wall of the passage, and in 
contact with the outer surface of which was a muscle. When the external 
orifice was widely opened, a fold, occasioned by the position of a large postero- 
external cartilage, fitted into a corresponding depression on the antero-external 
wall (fig. 40). A muscle, apparently a dilator, lay beneath the skin to the 
outer side of the aperture, and was attached to the cartilage at its postero- 
external angle. It is clear that the nostrils can be readily and widely opened, 
and also forcibly and completely closed, during the respiratory movements, so 
as to retain the air within the windpipe and lungs when the animal dives below 
the surface of the water. 

Genito-urinary Organs. — In fig. 9, the form and relation of the penis 
in the foetus are represented. As all that portion of the organ in front of the 
crescentic folds was invested by integument, the penis in this animal seemed in 
its flaccid state, not to be altogether retracted within a sheath, but to be in part 

* Dr Marttn, in a paper published in the Proc. Roy. Soc, London, 1857, ascribed the supposed 
absence of the voice in the cetacea to the absence of a thyroid gland ; but as I pointed out in a memoir 
published, in 1860, in the Transactions of this Society, a thyroid gland exists both in Phocama and 
Delphinus. 

t Whilst this memoir is passing through the press, Dr Murie has published in the " Journal of 
Anatomy and Physiology," November 1870, an interesting paper on Grampus rissoanus, in which he 
points out that a laryngeal sac of moderate capacity exists in the toothed whales in the angle of junc- 
tion between the enlarged epiglottis and the thyroid cartilage. He also describes a pair of folds within 
the larynx of Risso's grampus, which he regards as representatives of the vocal cords. 



STRANDED AT LONGNIDDRY. 241 

pendulous from the ventral wall. The organ consisted of a distinct corpus 
spongiosum urethree, and of a strong corpus cavernosum. These bodies 
extended backwards for eight inches behind the crescentic folds above referred 
to. The corpus cavernosum then subdivided at a very obtuse angle to form 
the crura penis, which were firmly connected to the perichondrial investment 
of the larger and more rounded end of the rudimentary and still cartilaginous 
ossa innominata, which represented, therefore, the ischial elements of the 
pelvis.* 

A strong muscle, which must be regarded as the erector penis, arose from 
the ischium, close to the attachment of the crus, and passed forward to be 
inserted into the corpus cavernosum. Large vessels and nerves were also seen 
passing to the different subdivisions of the penis. From the posterior border 
of each diverging crus, and from the sides of a tendinous raphe, which extended 
backwards from the end of the corpus spongiosum, a broad and strong muscle 
arose, which passed backwards along the side and under surface of the hinder 
end of the rectum, and ended close to the anus. This muscle was apparently 
the retractor penis. The corpus spongiosum had unfortunately been torn 
across, where the crura diverged, and the rest of the urethra, the bladder, 
testicles, &c, were not distinguishable, owing to the soft and injured state of 
the parts. 

The arrangement of the parts at the entrance to the female passage has 
been described on p. 201. The vagina was traced forwards for six feet from the 
external orifice. Numerous irregularly arranged, and much subdivided, folds 
of the mucous membrane projected from its surface into the canal. The uterus 
was not recognised with any certainty, but a bag-like membranous organ, a 
part of which was seen to project through a long cut in the wall of the 
abdomen, on the day on which the baleen wreath of the foetus was found loose 
in the abdominal cavity, was supposed to be a portion of that organ. 

The kidneys possessed the lobular construction so characteristic of the form 
of those organs in the cetacea. 

I shall reserve for another communication the description of the skeleton and 
joints, and such observations on the arrangement of the muscles as I was 
able to record. I may, however, state that the vertebral formula, both in 
the foetus and in the mother, was — Cervical, 7 ; Dorsal, 15 ; Lumbo-caudal, 41 ; 
in all, 63. The outline of the cranial beak was in conformity with that of the 
head, which is so well represented in fig. 10 from the foetus. 

The following are a few measurements of the skull, taken with a tape-line, 
which may be of service in comparing it with the crania of other described 
whales : — 

* I have described and figured the innominate bones and the sternum in the " Journal of Ana- 
tomy and Physiology," May 1870. 

VOL. XXVI. PART I. 3 R 



242 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 



From anterior border of foramen magnum over vertex to tip of beak, 

From nasal process of superior maxilla to tip of beak, 

From anterior border of foramen magnum to nasal process of superior 

maxilla, ..... 
Breadth across upper ends of nasal processes, 
Breadth of a single nasal process. 
Breadth of dorsum of beak — 

3 feet in front of nasal end of superior maxillaries, 



5 ,',' 






6 „ 




" » 


h 






* » 




>1 1! 


8 ,. 




» » 


9 „ 




>> >■> 


10 „ 




» » 


11 „ 




17 1) 


12 






1 - » 




Jl •! 


13 „ 




>! >1 


14 „ 




» )! 


15 „ 




J5 IJ 


Breadth at the tip of the beak, 


Breadth 


between the orbits, . 


Length 


of lower ja'w 


' along the convexity, 


» 


>> 


in a straight line, 


Depth of ramus at coronoid process, . 


Length 


of humerus 


. 


>> 


radius, 





Feet. 


Inches 


20 


3 


16 


6 


3 


9 


1 


8 





6 


7 





6 


10 


6 


8 


6 


61 


6 


u 


6 


H 


5 


9 


5 


4 


4 


10 


4 


5 


3 


8 





Hi 


2 


l 





7 


9 


3 


21 


2 


19 


5 


2 


6 


2 


2 


3 


9 



Comparison with other Finners. — In instituting a comparison between the 
Longnidclry whale and the other Fin whales which have been described by 
different authors, with the view of determining the species to which it should be 
referred, there is no need to compare it with either the Balamoptera rostrata, or 
the Balamoptera laticeps. For these animals never, apparently, exceed the length 
of 35 feet, and they differ so materially from the Longniddry whale in the number 
of vertebrae and ribs, that there can be no possibility of confounding it with 
either of them. My remarks, therefore, will be restricted to a consideration of 
those described specimens of fin whales which have reached the length of 40 
feet and upwards. As I have not yet given an account of the skeleton of 
this large Finner, I shall almost entirely confine myself, on this occasion, to an 
examination of the external characters of these animals. 

a. Sir R. Sibbald, in his observations on rare whales cast on the Scottish 
coast,* describes two fin whales. One, he says, rostrum acutum habet, et plica s 
in ventre ; the other maxillam inferiorem rotundam, et superiore multo latiorem 
habuit. The one with a sharp beak was cast ashore in 1690 near Burntisland, 
and measured 46 feet in length. It was in all probability an immature 
specimen of the Razor-back. The other with the rounded lower jaw, much 
wider than the upper, was stranded on the south side of the Forth, near the 
old castle of Abercorn, in 1692. It was a male, 78 feet long, and possessed 



* Phalainologia nova. 



Edinburgh, 1692. 



STRANDED AT LONGNIDDRY. 243 

various points of resemblance to the Longniddry specimen. From the greater 
width of the lower jaw than of the upper, the latter was received within the cir- 
cumference of the former. The upper jaw was contracted in front so as to 
terminate in a sharp end. The baleen was black, the longest plates having a 
vertical diameter of 3 feet, and they were fringed with black hairs. The 
bristles near the front of the palate were also black, and the intermediate 
substance was similar in character. The flipper was 10 feet in length, and 2^ 
feet in its broadest part. The dorsal fin was 2 feet high, and in it was a 
rounded hole made by a leaden ball. Through this hole in its fin the whale had 
been recognised by the herring fishermen for nearly twenty years, and was called 
by them the Hollie Pyke. The back was black and the belly whitish. The 
blubber was 4^ inches thick on the sides, and one foot on the head and neck. 

Although it is customary for cetologists to regard this broad-jawed whale, 
described by Sibbald, as the Balcenoptera musculus* yet the characters which I 
have just related are much more those of the species to which the Longniddry 
whale will have to be referred. 

b. The best known of the large fin whales is the common Eazor-back, the 
Balcenoptera musculus, or Physalus antiquorum of Gray, upwards of thirty 
specimens of which have come under the notice of, and been more or less perfectly 
described by, naturalists. Between the common Razor-back and the Long- 
niddry whale there are many characteristic features of difference. In the 
former the beak is much more pointed than in the latter, and its width rapidly 
contracts from base to apex, instead of the borders forming a gentle convex curve; 
the flipper also is absolutely and relatively shorter in proportion to the length 
of the animal. In the B. musculus, captured near Gravesend, described by Dr 
MuRiE,t whilst the animal was 60 feet, the length of the pectoral limb along 
the anterior curve was only 6 feet 3 inches ; in the specimen 67 feet long, stranded 
at Pevensey, described by Professor Flower,J the flipper was 6 feet 9 inches ; 
and in the specimen 61 feet long, beached last year at Langston harbour,§ the 
flipper had the length of 5 feet 4 inches. The external or labial baleen plates 
are in the common Finner neither so long nor so broad ; their colour is slate- 
coloured, mottled, or striped with yellow, or white, or brown, or pale horn 
colour, the setae are white, or yellowish-white ; the palatal mucous membrane 
is pale, whilst in the Longniddry whale all these structures had a rich deep 
black colour. In the Razor-back, whilst the back is black, the belly is white or 
yellowish-white, instead of being mottled with silver-grey, or milk-white, tints. 
The blubber also is very much thinner in the common Razor-back, — not more 

* Eschkicht, "Die Nordischen Wallthiere." Van Beneden and Gebvais," Osteographie des Cetaces," 
p. 188. Dr Gray in his Catalogue says, probably it may belong to this species, 
t Proc. Zool. Soc, Feb. 14, 1865. 
\ Idem., Nov. 28, 1865. § Idem., Dec. 9, 1869. 



244 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

than four tons of oil were extracted from the Gravesend specimen, — so that the 
animal possesses very little commercial value, whilst several hundred pounds 
have been realised by the sale of the oil from the Longniddry animal. Further, 
it is very doubtful if the Balwnoptera muscuius exceeds the length of 70 feet ; 
the Gravesend and Pevensey specimens, already mentioned, were both adult 
males, and yet they did not reach that length. Several specimens which have 
been referred to this species are, it is true, stated to have been longer than 70 
feet ; but of these, some, I believe, belong to another species, whilst it is 
doubtful how far the others have been measured with sufficient exactness. More- 
over, the vertebrae in B. muscuius are not so numerous, and do not apparently 
exceed sixty-one. 

It is not necessary to compare the Longniddry whale with the Physalus 
Duguidii, described by Mr Heddle * and Dr GRAY,t as that animal is appa- 
rently nothing but a young specimen of the B. muscuius. 

c. In the year 1827 a fin whale, said to have been upwards of 80 feet long, 
was found floating on the North Sea, and towed into the harbour of Ostend, 
from which circumstance it has been customary to term it the Ostend whale. 
Unfortunately, no satisfactory account of the dimensions and external charac- 
ters of this animal have been recorded, and the descriptions of the skeleton are 
in some respects imperfect. Zoologists, therefore, are by no means at one as 
to the genus or even species to which this whale ought to be referred. Dr 
Gray places it in his genus Sibbaldius, and calls it S. borealis ; Eschricht has 
termed it the Balcenoptera gigas, or Pterobalwna gigas ; whilst Van Beneden 
and Gervais, in their Osteographie, have regarded it as merely an unusually large 
specimen of the B. muscuius. Owing to the very imperfect data at my com- 
mand, I cannot make any exact comparison between its external form and 
that of the Longniddry whale. I may state, however, that the length of the 
pectoral fin is said to have been about 10 feet ; the distance from the point 
of the snout to the dorsal fin 61 feet ; from the point of the snout to the 
genital organs 55 feet ; that the back was black, and the belly whitish, the 
outer surface of the pectoral fin was black, and the baleen setse also black.| 
In these respects it more closely approaches the Longniddry whale than it does 
the B. muscuius. It must be admitted, however, that the measurements, which 
have been recorded by those who have described the animal, are not of a very 
reliable character, for, whilst Van Breda states its length to be about 84 feet, 
Dubar makes it as much as 105 feet. I shall have again to refer to the Ostend 

* Proc. Zool. Soc. 1856. t Catalogue, p. 158. 

X The notices of this animal which I have read, and from which the above statements are drawn, 
are by M. Van Breda in Cuvier's " Hist. Nat. des Cetaces," p. 328 ; by Eschricht in " Die Nordischen 
Wallthiere," p. 176 ; by Lilljeborg in the Memoir translated for the Kay Society, p. 262; by Dr 
Gray in his " Catalogue of Seals and Whales ;" and by Dubar in his " Osteographie de la Baleine." For 
the opportunity of consulting Dubar' s scarce pamphlet, I am indebted to my colleague Professor 
Kelland. 



STRANDED AT LONGNIDDRY. 245 

whale when I describe the skeleton of the Longnidclry whale, and to point out 
certain other points of correspondence between them. I may on this occasion, 
however, state that the small number of vertebrae, 54, described in the former 
animal is obviously owing, as Dubar's figure shows, to the loss, in the prepared 
skeleton, of several vertebrae in the caudal series. And there is good reason 
for believing that the double headed condition of the first rib which Dubar 
figured in this creature, and on the presence of which Dr Gray has to a large 
extent based his genus Sibbaldius, is merely an individual peculiarity, and may 
occur as a variety in more than one species of whale, just as it occasionally 
occurs as a variety in the human subject. 

d. In the month of October 1831, a fin whale was observed floating dead 
on the surface of the sea off" the mouth of the Firth of Forth, and was brought 
ashore near North Berwick, 23 miles from Edinburgh. It was purchased and 
anatomised by Dr and Mr Frederick Knox. The skeleton was carefully pre- 
pared and publicly exhibited, and now forms the most noticeable object in the 
Natural History Department of the Museum of Science and Art, Edinburgh. 
Unfortunately no systematic description of this animal was ever published ; but 
from one or other of the publications mentioned below * I have gathered the 
following particulars. The animal was a male, and measured 80 feet in length. 
The length of the head over the vertex was 21 feet ; the pectoral limb 11 feet 
long ; the circumference behind the pectoral limbs 34 feet, and even 52 feet when 
greatly distended with gas ; the breadth of the tail 20 feet ; the distance from the 
anus to the fork of the tail 21 feet.t The whole baleen, with its fringed edge, 
was of a clear shining black, and the longest plate measured 2 feet 2 inches in 
length, by 15 inches in breadth. Nothing is said as to the colour of the skin 
or the thickness of the blubber; but it is stated in the "Account," that "the 
fluid oil in the abdomen, particularly, was in very considerable quantity, and 
often gave a covering to the sea as far as the eye could reach." 

Knox named the animal the Great Northern Rorqual, or Balcena maximus 
borealis. 

In July 1847, Dr J. E. Gray stated to the Zoological Society of London, J 

* Abstract of a paper on the " Anatomy of the Rorqual (a Whalebone Whale of the largest 
magnitude)," by Dr Robert Knox (Proc. Roy. Soc. Edin., March 18, 1833). " Account of the Gigantic 
Whale or Rorqual, the Skeleton of which is now exhibiting in the great rooms of the Royal Institution, 
Princes Street," by Frederick John Knox, surgeon, Edinburgh, 1835. " Catalogue of Anatomical pre- 
parations illustrative of the Whale, particularly the Great Northern Rorqual," by F. J. Knox, Edinburgh, 
1838. Although the name of Mr Frederick Knox is attached to the catalogue, yet it would appear 
that the best part of it was from the pen of Dr Knox (" Life of Knox," by Dr Lonsdale, p. 168). For 
the opportunity of consulting this scarce and valuable catalogue, to which I have referred on various 
occasions in the text, I beg to express my acknowledgments to my friend Dr John Alexander Smith. 
The skeleton of this animal is figured in Jardine's " Naturalist's Library," vol. vi., Edinburgh, 1837. 

t The Gravesend B. musculus was only 11 feet 1 inch between the points of the tail. The 
Pevensey Razor-back, about 13 feet ; the Langston harbour specimen 11 feet. In the Pevensey whale 
the distance from the end of the tail to the middle of the anal aperture was 1 7 feet 9 inches. 

% Proceedings, Part xv. p. 117. 

VOL. XXVI. PART I. 3 S 



246 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

that he had examined, though without being able to take any measurements, on 
account of its position, the skeleton of this animal. He considered it to be a 
Physalus, very nearly allied to the Physalus antiquorum, though it differed from 
a specimen of that animal taken at Plymouth in some of the characters of its 
cervical vertebrae. Since that time it has been customary to describe this great 
whale as the Balamoptera musculus, or Physalus antiquorum* 

A comparison of the measurements, which I have quoted, with those of the 
Longniddry whale, given in the early part of this paper, and the very decided 
statement made as to the clear, shining, black baleen and setae, will, I think, 
suffice to show that in its general proportions, and the colour of its baleen, the 
North Berwick whale resembled closely the Longniddry whale, and differed, 
therefore, in many most material points from the common Razor-back, so that 
it can no longer be regarded as of that species. The shape of its cranium, 
also, differs most materially from that of the B. musculus. Knox, in his cata- 
logue, has given a few measurements of its skeleton, which, if compared with 
those of the Longniddry animal, will show that a close resemblance exists be- 
tween these animals in this part also of their frames. The breadth between the 
orbits was 10 feet ; the length of the base of the cranium measured in a straight 
line, 19 feet ; the length of the lower jaw, 21 feet 4 inches ; circumference of 
ramus about the middle, 4 feet ; depth of ramus at coronoid process, 2 feet 7 
inches ; depth of body of hyoid, 8^ inches ; between the ends of the great 
cornua, 2 feet 6^ inches ; length of the humerus, 1 foot 11 inches ; of the 
radius, 3 feet 10 inches. But it is right also to mention that there are differ- 
ences in the skeleton, especially in the form of the sternum and the pelvic 
bones, and whilst the North Berwick whale has thirty ribs, it possesses as many 
as sixty-five vertebrae. The more complete comparison of the skeletons of 
these two animals I shall reserve for the second part of this memoir. 

e. In 1847 Dr Gray described,t by the name of Physalus Sibbaldii, from 
the skeleton of an immature animal 47 feet long, in the museum of the Hull 
Literary and Philosophical Society, a new species of Finner, the baleen of which 
possessed a uniform deep black colour. In 1864 Professor Flower J dis- 
covered in the collection of the late Professor Lidth de Jeude, of Utrecht, 
the skeleton of a young finner about 44 feet long, which differed from the 
common Razor-back in possessing a much broader beak. He named it Physalus 
latirostris.^ Subsequently, on examining the skeleton in Hull, which Dr Gray 
had observed, he came to the conclusion that the animals were of the same 
species, and he withdrew his specific name in favour of the prior one given by 

* Dr Gray, " Catalogue of Seals and Whales," p. 144 ; Van Bexeden and Gervais, " Osteographie," 
p. 172 ; and various other writers on the cetacea. 
■f" Proc. Zoological Soc., June 8th. 
% Idem, Nov. 8, 1864, and June 13, 1865. 
§ This skeleton has since been acquired by the British Museum. 



STRANDED AT LONGNIDDRY. 247 

Gay.r Since then Dr Gray has changed the generic name to Cuvierius, and 
terms the animal C. Sibbaldii* Those zoologists who do not break up the 
great genus Balwnoptera into several smaller sub-genera, prefer to call the 
animal Balwnoptera Sibbaldii. The Hull and Utrecht skeletons agree in pos- 
sessing each 64 vertebrae ; but whilst the former has 16 pairs of ribs, the latter 
has only 15 pairs. No information existed as to the external characters of 
either of the animals from which these skeletons were obtained, so that it was 
difficult to identify them with any of the species of whales known to zoolo- 
gists, up to that time, only by their external appearances. 

In 1867, however, Professor Reinhardt published an important memoir, in 
which he gave an account,! from notes furnished him by Mr Hallas, surgeon 
to a whaling ship, of a Finner of which the Danish whalers had captured several 
specimens. This whale was known to the Icelanders as the Steypireythr. The 
back was blackish grey ; down the sides the colour was lighter ; the belly, behind 
the plicae, was uniformly grey, the ridges blackish grey ; the furrows between 
them, light grey ; the caudal fin, blackish grey on both sides ; the pectoral fins, 
blackish grey, spotted with lighter specks on the outer surface, but milk White 
on the inner. The baleen was uniformly black. The animal was about 80 feet 
long, and was said to have a dorsal fin not more than 7 inches high.J No measure- 
ments are given of the caudal or pectoral fins, or, indeed, of the proportions of 
the other parts of the body. Mr Hallas also forwarded the skull, hyoid bone, 
and atlas of this animal, of which Reinhardt gives figures. Further, he states 
that the animal possessed 64 vertebrae and 15 pairs of ribs. In his remarks on 
this whale, Reinhardt compares it both with the Balwnoptera musculus (Physalas 
antiquorum) and B. Sibbaldii, and considers that from its osteological characters 
it should be referred to the latter species. 

By these observations, it was clearly established that a well-defined species 
of Finner exists in the northern seas, which differs from the common Razor-back, 
in possessing a greater number of vertebras, a broader beak to the cranium, a 
greyish and not a whitish belly, and a uniform black baleen, instead of one 
mottled with various tints. In the distribution of the tints of the skin, in the 
uniform black colour of the baleen, and in the length of the animal, the Stey- 
pireythr obviously closely corresponds with the Longniddry whale. But what is 
even more important for the determination of the species, the cranium, atlas, and 
hyoid, as far as one can judge from Reinhardt's figures, are almost identical in 

* Appendix to Catalogue of Seals and Whales, p. 380. 

t Vidensk. Meddelelser fra den Naturhist, Forening iKjbbenhavn, 1867. Translated in " Annals 
of Nat. Hist.," November 1868. 

| Although the end of the dorsal fin had been removed from the adolescent Longniddry whale 
before my measurements were taken, yet sufficient had been left to show that this fin had been more 
than 12 inches high. Consequently, T do not think that the shortness of the dorsal fin is so definite 
a character as Reinhardt supposes. 



248 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE. 

form with the corresponding bones in the Longniddry whale. Hence we arrive 
at the conclusion, that the Longniddry whale is a specimen of the Balcenoptera 
Sibbaldii, or Physalus Sibbaldii of Gray. 

Two years before the publication of Reinhardt's memoir, a fin whale, about 
54 feet long, came ashore alive at Gothenburg, on the west coast of Sweden. 
It was secured by Professor Malm, the superintendent of the Museum in that 
city, and was carefully examined by him. He published an elaborate mono- 
graph, with numerous photographic illustrations, descriptive of the capture of 
the animal, its form, colour, proportions, and dimensions, with a detailed ac- 
count of the skeleton, and a number of observations on its visceral anatomy.* The 
animal was a male, and had not reached its full growth. Its colour was a deep 
slate tint, with somewhat paler tints on the sides, whilst the lower surface was 
mottled with patches of milk white, of different sizes and shapes. The flippers 
were white on the inner surface, and the lobes of the tail at the under part 
whitish. The distance from the anterior part of the base of the flipper to its 
free extremity, measured in a straight line, was 7 feet 4 inches, whilst the dis- 
tance between the extreme points of the tail was about 11 feet. The baleen 
was uniformly of a deep black slate colour, whilst the hairs at the free margins 
of the plates were of a brown soot colour. The vertebrae were 63 in number, 
and there were 15 pairs of ribs. Malm considered it to be a new species, and 
named it Balcenoptera Carolina?. 

From a comparison of its osteological characters with those of the B. Sib- 
baldii, more especially the resemblance in the breadth of the beak, the form of 
the nasal bones, the relative and absolute length of the metacarpals and phalanges, 
and the spine of the axis, as well as from the uniform dark colour of the baleen, 
Professor Flower came to the conclusion,! that Malm's whale ought not to be re- 
garded as a distinct species, but was merely another immature specimen of the 
Balamoptera [Physalus) Sibbaldii. In this conclusion he has been supported 
by Professor Reinhardt, who states \ that, in his opinion, " Eschricht's ' Tun- 
nolik,'tke 'Steypireythr ' of the Icelanders, and, finally, the whale described by 
Malm, are only one and the same species, which appears to be one of the most 
common in our northern seas, and the systematic name of which must be 
Balcenoptera Sibbaldii." 

If I am correct in regarding the Longniddry whale as the B. Sibbaldii, then — 
Professors Flower and Reinhardt being also correct in their supposition — its 
characters should closely correspond, allowance being made for the different sizes 
of the two animals, with those of Malm's whale. In the colour, both of the skin 
and the baleen ; in the shape of the tail and pectoral fin ; in the relative pro- 

* " Monographie illustr^e du Baleinoptere," Stockholm, 1867. For the opportunity of consulting 
this work, three copies only of which are, I believe, in this country, I am indebted to my friend, Mr J. 
W. Clark, of Cambridge. 

f Proc. Zool. Soc, March 12, 1868. J Memoir, cited above. 



STRANDED AT LONGNIDDRY. 249 

portions of these parts to the length of the entire body ; in the form of the beak ; 
and in the curve of the lower jaw, the resemblances are very striking. The 
osteological characters have also much in common ; but the consideration of 
these I shall not enter into on this occasion. 

The comparison I have now made between these different specimens of 
Finners, leads me to the conclusion that the following should be referred to 
the Balcenoptera Sibbaldii : — 

The North Berwick whale. 

The Hull skeleton. 

The Utrecht skeleton, now in the British Museum. 

The Gothenburg whale. 

The Steypireythr. 

The Longniddry whale. 

And, in all probability, the Ostend whale, and Sibbald's " Balsena tripinnis 
quae rnaxillam inferiorem rotundam, et superiore multo latiorem habuit." 



EXPLANATION OF THE PLATES. 

With the exception of fig. 1 Plate V., of figs. 19, 20, 21, 22, 23, 24, 25, 27, 28, Plate VIL, and of 
fig. 29 Plate VIII., the illustrations have been very carefully drawn, under my superintendence, by Mr 
J. B. Abercrombie, from nature. Eig. 27 was drawn by Mr Coughtrey, fig. 28 by Mr Foulis, and 
figs. 19 to 25 inclusive, and fig. 29, were sketched by myself from microscopic preparations. As far as 
possible, the specimens from which the drawings were taken have been preserved in the Anatomical 
Museum of the University of Edinburgh. When not otherwise stated, the drawings represent portions 
of the adolescent animal. 

Plate V. 

Figure 1. Side view of the Longniddry Whale. This drawing was constructed from photographs, 
from pencil sketches, and from a water-colour sketch by Mr Sam. Bough. The 
lower jaw is represented somewhat out of position so as to give a side view of the baleen 
and of the dorsum of the tongue. 

Figure 2. The falcate dorsal fin of the foetus. 

Figure 3. The horizontal tail of the foetus. 

Figure 4. The abdominal plicse of the foetus, showing bifurcations of the ridges. 

Figure 5. Supero-anterior surface of the left flipper of the foetus. The outlines of the bones of the 
antibrachium and of the four digits are represented. The posterior edge of the flipper 
was much thinner than the anterior. 

Plate VI. 

Figure 6. The clitoris, below which is the opening of the urethra, and the folds of mucous membrane, 

on the floor of the vestibule. The labia majora have been drawn asunder to expose these 

parts. 
Figure 7. The orifice of the nipple fossa, displaying the nipple with the pedunculated papillae at its 

summit. 
Figure 8. The anal orifice, with the ruga? of the integument converging to it. 
Figure 9. The ventral wall of the foetus, displaying the penis with the crescentic folds of skin at its 

root, the median perineal raphe, with a rudimentary nipple fossa on each side, and, more 

posteriorly, the anal orifice. 

VOL. XXVI. PART I. 3 T 



250 PROFESSOR TURNER'S ACCOUNT OF THE GREAT FINNER WHALE 

Figure 10. Dorsum of the beak of the foetus. The curved outline of the beak; the dorsal median 
ridge ; the form and direction of the blow-holes, which are partially open, and the inter- 
mediate groove are all represented. 

Figure 11. A portion of the mammary gland to show the rugose character of the mucous lining of the 
duct, one-half the size of nature. 

Figure 12. One of the large, irregularly quadrilateral, labial, baleen plates, much reduced in size. 

Figure 13. A vertical section through the intermediate substance of the baleen, displaying its laminated 
appearance. The subsidiary blades are shown, two of which have been cut short. On 
the upper or palatal surface, the clefts between the lamina? of the plates, into which the 
palatal folds of mucous membrane fit, may be seen. 

Figure 14. The baleen plates and intermediate substance of the foetus, the size of nature. One of the 
plates, with the thin layer of intermediate substance on each side, has been partially sepa- 
rated from the others. 

Figure 1 5. Portion of the palatal mucous membrane of the foetus. At the upper end of the figure is 
the lip ; lower down the elongated folds for the larger labial baleen plates, and at the lower 
end the subconical papillae from which the bristle-like subsidiary plates arise. The tubular 
papillae are not represented in the drawing, as they had all been broken off before the 
drawing was made. 

Figure 16. Palatal surface of a part of the foetal baleen wreath, with a side view of one of the plates. 
The elongated clefts between the laminae of the labial plates and the polygonal pits for the 
sub-conical papillae are shown ; as the tubular papillae are still within the blades, their 
broken ends may be seen in part occupying the clefts and pits. 

Plate VII. 

Figure 17. Portion of the foetal membranes ; a, the non- villous surface of the chorion ; b, villous sur- 
face. Between a and b the elongated marginal folds of the chorion may be seen. 
e, Divided end of one of the arteries of the chorion. 

Figure 18. A large triangular fold of the chorion, displaying the reticulated arrangement of the villi on 
its surface. 

Figure 19. Vertical section through a portion of a baleen plate to show the tubes, with the lamella- 
and black pigment granules. x 40 diam. 

Figure 20. Transverse section through a portion of a baleen plate. The entire antero-posterior diameter 
is represented. The tubes are divided transversely. Some are empty, others contain the 
tubular papillae, and in some of these the transversely divided ends of the contained blood- 
vessels may be seen. Both the tubular and cortical lamellae, with numerous black pig- 
ment granules, are represented in the drawing. x 40 diam. 

Figure 21. Epithelial cells from the outer layers of two adjacent tubular systems. At the lower part 
of the drawing some interstitial cells are represented. x 200 diam. 

Figure 22. Transverse section through one of the setae of a baleen plate. The shaded central portion 
represents the soft papilla, in which a transversely divided blood-vessel is represented, 
x 40 diam. 

Figure 2 3. Vertical section through a portion of the intermediate substance ; the clefts extending into 
its substance, in which the intermediate papillae are lodged, are seen at the upper part of 
the section. x 40 diam. 

Figure 24. Epithelial cells from the intermediate substance. x 200 diam. 

Figure 25. Red blood corpuscles from the blood in the vessels of the baleen plate of the B. rostrata. 
x 1200 diam. 

Figure 26. Portion of one of the elongated folds (pulp-blades) of the- palatal mucous membrane. The 
tubular papillae are dependent from the lower edge of the fold. Size of nature. 

Figure 27. Vertical transverse section through the pulp-blades, intermediate substance, and imbedded 
parts of the baleen plates of B. rostrata, the blood-vessels of which have been injected ; i, 
the vessels of the intermediate papillae; c, the vessels of the cortical papilla; t, the elongated 
vessels of the tubular papillae. 
Figure 28. Arch of the aorta and great vessels of the foetus, x, the ductus arteriosus ; a, right 
coronary artery; b, brachio-cephalic ; c, left carotid; d, left subclavian; e, right carotid ;/, 
right subclavian ; g, right posterior thoracic ; h, right axillary; i, right internal mammary ; 
k, right cervico-facial ; and I, right internal carotid ; m, left cervico-facial ; and n, left in- 
ternal carotid ; o, left posterior thoracic ; p and q, left axillary and internal mammary 
arteries. 



STRANDED AT LONGNIDDRY. 



251 



Plate VIII. 

Figure 29. Vertical section through the integument. It shows the elongated papillae, the comparatively 
thin cuticle containing a quantity of black pigment, and the subcutaneous tissue, -with the 
small arteries entering the bases of the papillae. x 20 diam. 

Figure 30. Dorsal surface of the pharynx and commencement of the oesophagus of the foetus ; p h, the 
pharynx displaying the fibres of the constrictors and the longitudinal raphe. The upper 
part of the pharynx has been cut across, and the soft palate v is displayed ; passing under 
it is an arrow lying in the bucco-pharyngeal canal. Immediately behind the velum a por- 
tion of the epiglottis is visible. 

Figure 31. The interior of the cavity of the pharynx of the foetus opened into by a posterior median 
incision ; v, the velum ; e, the epiglottis, the letter is placed on the cushion, which corre- 
sponds in position to the bar-like rod of fibro-cartilage ; I, the lappet-like fold of mucous 
membrane which invests the superior horn of the arytenoid cartilage, the outline of which 
may be seen in the figure. The upper arrow is in the bucco-pharyngeal canal, the lower 
is in the windpipe. 

Figure 32. Portion of the intestinal tube, v, the superior mesenteric vein which receives numerous 
rootlets from the gut ; m, the moniliform tube, giving off numerous small arteries to the 
wall of the intestine ; n, the sympathetic nerve, also sending branches to the gut ; p, the 
peritoneal coat turned down. At the right cut edge of the intestine the valvules conni- 
ventes of the mucous coat are shown. 

Figure 33. A portion of the beaded mesenteric vessel, displaying the series of dilatations and constric- 
tions. At the right side the tube has been opened, and the corrugated folds of the inner 
wall may be seen. 

Figure 34. One of the dilated portions of the beaded vessel. The lacunary system on its surface is 
represented. The darkly shaded, elongated, and globular bodies, I I, are the small lym- 
phatic glands. 

Figure 35. Annular and spirally arranged plate of cartilage from a bronchial tube. 

Figure 36. Front view of the larynx and hyoid apparatus ; h, the body of the hyoid with the stylo- 
hyal and great cornu on each side. Immediately above the hyoid body is the orifice of 
the bucco-pharyngeal canal, the arrow lying in which has emerged below through the 
oesophagus ; th, the thyro-hyoid muscle ; sh, the stylo-hyoid muscle ; t, the thyroid 
cartilage ; c, the cricoid ; cm, the constrictor muscle of p, the laryngeal pouch. The bifur- 
cation of the trachea and the supplementary right bronchus are seen, and the arrow 
passed through the left bronchus emerges superiorly, immediately behind the posterior 
horn of the left arytenoid cartilage. 

Figure 37. Front view of the larynx and trachea ; the laryngeal pouch has been removed and the cartilages 
dissected, t, the thyroid cartilage ; c, the cricoid with its plate-like processes ; a, the body ; 
s, the anterior, and i, the posterior cornu of the arytenoid cartilage ; ct, the inferior crico- 
thyroid membrane. The barb of the arrow passed through the left bronchus, lies im- 
mediately behind the posterior horn of the left arytenoid cartilage, and in front of the body 
of the cricoid, which is in deep shadow. 

Figure 38. View of the interior of the larynx from behind, obtained by cutting through and turning 
outwards the body of the cricoid, and the membrane connecting the anterior horns of the 
two arytenoid cartilages ; e, the epiglottis ; c, the cricoid ; I, the lappet of mucous mem- 
brane enclosing s, the anterior horn of the arytenoid ; i, the posterior horn. To the inner 
side of the anterior horn is the fold of mucous membrane, which may represent a false vocal 
cord. 
Figure 39. The posterior nares viewed from below. 
Figure 40. The anterior nares or blow-holes viewed from above ; the walls are separated to show the 

internal foldings. 
Fig\ires 35 to 40 inclusive are from the foetus. 



Yol.XX.VI. 



Plate IX. 







ty.soc Eam 1 vol. xxvr 



Plate I. 







(253) 



XII.— On some Points in the Structure 0/ Tubifex. By W. C. M'Intosh, M.D., 

F.R.S.E. (Plates IX., X.) 

(Eead 2nd May 1870.) 

At least two species of Tubifex are abundant in Scotland, one of which is, 
perhaps, more prevalent in streams, the other in lakes. The former is common 
at the margin of the river Tay, when the water is low, in sandy tubes of little 
tenacity, and often in tunnels formed amongst the wet sand under stones, just 
as many of the marine annelids occur. Its length varies from three-fourths of 
an inch to an inch and a-half when stretched, and the segments range from fifty 
to seventy, the average number probably being sixty. The body is of various 
shades of dull fawn or pale madder-brown, somewhat interrupted by the pale 
bands at the junctions of the segments, and streaked by the reddish dorsal 
vessel ; or, in summer, marked anteriorly by the whitish mass of the reproductive 
organs. It is easily recognised amongst its fellows by its faintly purplish or 
lilac hue, as well as by its peculiar mode of progression ; and not a few are 
observed with reproducing heads and tails. This form, perhaps, has most claim 
to be called Tubifex rivulorum. 

The body is tapered towards head and tail, distinctly segmented, and much 
shorter and stouter than the succeeding species. Moreover, the length of the 
bristles does not equal the diameter of the body. The snout is somewhat- 
conical, with the puckered mouth at its posterior margin, near the first crenation, 
which indicates its separation from the succeeding segment. There are many 
motionless microscopic processes on the surface of the snout in well-developed 
specimens, and the same organs occur on the bristle-papillse and the caudal 
segment. Such have generally been regarded as tactile papillae. Though 
analogous, they are not quite homologous with similar processes in the Turbel- 
laria. The second segment bears a long bristle at each side dorsally, and three 
hooks, one of which is small. The third segment has two bristles and three 
hooks on each side superiorly ; ventrally four hooks on each side. Generally 
the inferior hooks are five or six in number on each side, one being short and 
in process of development. The bristles (Plate IX. fig. 1) seem slightly stouter 
than those of the longer form, and no serrations are visible on the sides. M. 
d'Udekem noticed in his form a bristle with a brush-like tip, and has figured 
the same,* but though Mr Lankester has seen such in examples of Tubifex 

Hist. Nat. du Tubifex, &c. ; Mem. couronnes et Mem. des sav. etrangers, &c. ; l'Acad. Roy. de 
Belgique, torn. xxvi. p. 11, Plate II. fig. 8. 

v qL. XXVI. PART II. 3 U 



254 DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

from the Thames, they have never occurred in those found in this neighbour- 
hood. The number of pairs of bristles in front ranges from twenty-one to 
twenty-three. The hooks are gently curved organs, with a bifid tip, and a dis- 
tinct swelling or shoulder about the upper third, from which point they taper 
towards the base. Those accompanying the bristles anteriorly (Plate IX. fig. 1) 
slightly differ in their curvature from those of the ventral series (Plate IX. fig. 2). 
In the other and longer form (with about 150 segments) from the lakes, the 
fourth segment has a pair of bristles, and the latter increase in length till the 
twelfth segment is reached, after which they gradually diminish and disappear 
about the fortieth. There is a small papilla where each bristle-bundle passes 
through the skin, and the tips of the hairs are delicately serrated or roughened, 
the serrations being directed distally. In this form the bristles are larger than 
the diameter of the body, and hence it differs from Nais scotica and the Nais 
lacustris of Dalyell. The hooks commence with the bristles, and besides 
those accompanying the latter, form two rows, as usual, inferiorly, which rows 
in front consist of groups of four hooks. Those accompanying the bristles 
(Plate IX. fig. 3) are more closely forked at the tip, and if examined under a 
power of 700 diameters show certain processes in the fork (a), a fact first 
pointed out to me by Mr Lankester, whose larger specimens from the Thames 
exhibited this and other peculiarities in a marked manner. These are also 
less shouldered, less curved, and somewhat more elongated than the inferior 
hooks. The latter in each form of Tubifex continue after the last bristle- 
bundle, and thus form four rows posteriorly, the terminal segment only being 
bare. M. d'Udekem's representations of the hooks,"" though easily recognisable, 
deviate a little from the foregoing, and the same may be said of M. Claparede's 
figures of the hooks of his Tubifex papillosus.f 

Body- Wall. — M. d'Udekem speaks of the epidermis as being separable from 
the chorion by the aid of an alkaline solution, but I have not been able to dis- 
engage it as a distinct layer either by the action of chemicals in the fresh animal, 
or in transverse sections of the body- wall. M. Claparede does not mention 
the superficial layer as a distinct coat, but groups it with the subjacent, under 
the name of cuticle.! The cuticular surface (or layer) is quite homogeneous, 
but the chorion which is incorporated with its inferior surface is distinctly 
cellulo-granular, as described by Gruithuisen in Nais (Chcetog aster), and by 
Buchholz in Enchytraeus. This is most distinctly marked at the snout and 
tail, where the layer is thickened. The other layers in Tubifex are a belt of 
circular muscular fibres, and a longitudinal muscular coat. M. Claparede 
gives an ideal section of Limnodrilus, a form which differs from Tubifex in the 

* Op. cit. PI. II. figs. 6 and 7. 

t Beobach. fiber Anat. u. entwicklung. &c, p. 25, Pi. XIII. fig. 15. 

£ Rechercbes Anat. sur les Oligocbetes, p. 7. 



DP M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 255 

absence of the bristles and other points, in which he shows the longitudinal 
muscular coat separated into six divisions, viz., — two dorsal, two lateral, and 
two ventral. I have not been able to see this arrangement in the transverse 
sections of the minute forms of Tubifex, and even the separation at the bristle- 
sacs is comparatively indistinct. This ambiguity is no doubt due to the small 
size of the specimens. In the living animals, however, certain rows of papillae 
may occasionally be observed, which probably mark the dorsal and ventral lines. 
The circular muscular coat is much thinner than the longitudinal. The latter 
forms in transverse section numerous well-defined fascicles, and in the fresh 
condition these are bounded internally by a membranous layer with many cells. 
At the period of reproductive activity the neighbourhood of the eleventh seg- 
ment becomes almost opaque from a cellular covering. This appears to be due 
to an increased development of the cellulo-granular elements of the chorion. 

Adhering by short stalks to the walls of the body posteriorly in both forms, 
were numerous parasitic vorticellse (Plate IX. figs. 4 and 5), having an active 
crown of cilia, and numerous globules and granules in their interior. In some 
examples these were very numerous, often in groups of three or four, but they 
rarely occurred on the terminal segment, except in decomposing individuals. 
In contraction the base becomes finely corrugated. The free motion of the tail 
of the worm in the water places these organisms under very favourable condi- 
tions for aeration and food. Fungi, also, may frequently be seen growing on the 
disorganised anterior segments, while the posterior are in full activity. Fresh water 
annelids, indeed, are prone to have such growths, just as young salmon are 
under similar circumstances. The anterior part of the body becomes first 
attacked, dissolving into a granular mass swarming with fungi and infusoria. 
The segment immediately behind the decayed portion shows its integument 
corrugated and thrown into transverse rugae, while the perivisceral corpuscles 
and the blood have disappeared. The next septum is strongly contracted, and 
in marked contrast to the succeeding segment, within which are many perivisceral 
corpuscles of the ordinary appearance, and whose dorsal vessel pulsates 
vigorously. 

Perivisceral Fluid and Corpuscles. — The perivisceral fluid occupies, as usual, 
the space within the body- wall all round, from the tip of the snout to the tail, sur- 
rounding and bathing the digestive and other structures contained therein. In 
Tubifex rimdorum, the perivisceral corpuscles (Plate IX. fig. 6, a), are very con- 
spicuous, and differ characteristically from those of the succeeding form from 
the lakes* They are rounded bodies filled with circular granules of consider- 

* Whatever result more extended investigations may give with regard to the specific value of 
characters derived from the shape of these bodies, it is right that the name of Dr Thomas "Williams 
should be honourably remembered in conjunction therewith. Vide his paper on the " Blood-proper 
and Chylaqueous Fluid of Invertebrate Animals," Philos. Trans. P. II., 1852. 



256 DE M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

able size, and in the living animal undergo various changes in shape by pres- 
sure against each other, the body-wall and viscera of the worm. On extrusion 
into the surrounding water they become very transparent, and their broken 
contained granules collect together at one point (Plate X. fig. 1). Tincture 
of iodine and chromic acid colour them deep yellow, while sulphuric ether 
does not materially affect them. Dilute glycerine first corrugates, and then 
causes them to burst, giving exit to the contained clear granules (Plate IX. 
fig. 7), which measure about e-oVoth of an inch in diameter. Some of the 
corpuscles are smaller, and their contained granules less in proportion. Besides 
the foregoing, there are many elliptical, curved, and granular corpuscles (Plate 
IX. fig. 8) in the perivisceral space. In the elongated form the perivisceral 
corpuscles are less conspicuous both as regards number and size. The larger 
bodies in this case are rounded cells (Plate IX. fig. 9), filled with much more 
minute granules than in the preceding form, and many show a granular nucleus. 
The other corpuscules (Plate IX. fig. 10) are elliptical or fusiform, flattened, trans- 
parent and non-granular, and often longer than the diameter of the ordinary 
granular corpuscle just described. As contrasted with a gland-cell from the 
intestinal wall, the perivisceral corpuscle in the former case is widely different, 
while in this it has much smaller granules, is pale, and easily distinguished from 
the other with its highly refracting yellowish granules. In a form occurring 
abundantly in certain lakes with the latter, and referable to M. Claparede's 
genus Limnodrilus, the perivisceral corpuscles are remarkably developed. They 
are larger than usual, very transparent, and frequently show a somewhat 
puckered outline within the body of the worm. They also have the peculiarity 
of adhering here and there in considerable numbers to the intestinal coating. 
Few or none of the ordinary fusiform or other bodies are present. On ex- 
truding these corpuscles into the water they swell out, and show a large 
granular nucleus, the rest of the cell being quite translucent. Moreover, both 
cells and nuclei have a nearly uniform diameter throughout the fluid. On con- 
trasting these corpuscles (Plate IX. fig. 11) with the gland-cells from the 
intestine (Plate IX. fig. 12), a very marked difference is observable. The for- 
mer are quite transparent — with the exception of the nucleus, becoming slightly 
granular only after remaining many hours in the water. They have nuclei 
of definite size and structure, which retain their shape and appearance after the 
bursting of the cell-wall. Acetic acid and ether only show the structure just 
described more clearly. On the other hand, I have watched the gland-cells 
from the intestine under water and various reagents side by side with the others, 
and for a considerable time; but I do not feel able to say that nuclei or 
other contents than the refracting granules have been detected. The gland-cell 
may be set in motion, rolling over and over, so as to expose it all round, yet 
not a trace of a nucleus is seen. In all the forms there is thus a considerable 






DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 257 

histological difference between the two sets of cells ; and both differ very 
much from the cells on the inner surface of the intestinal wall (Plate IX. 
fig. 13.) 

I have been somewhat minute in observing this point, because it has 
generally been stated that the perivisceral corpuscles have their origin from, or 
are closely connected with, the gland-cells which cover the intestine and dorsal 
vessel. M. d'Udekem is stated by Mr Lankester, in his recent paper on 
Chsetogaster,* to have connected the two in his memoir on Tubifex, but such is 
not my impression. It is true the author describes two hinds of " glandules " 
covering the intestine and the dorsal vessel, viz., nucleated brownish " glandules," 
and colourless " glandules " having oily contents, and says they represent the 
liver of the higher animals, — secreting a liquid for assisting digestion. In speak- 
ing of the perivisceral fluid, moreover, he omits all notice of the origin or rela- 
tionship of the corpuscles ; and adds that the number and large size of these 
" globules lymphatiques " constitute one of the differences between the young 
Tubifex, on its extrusion from the egg, and the adult. He hints at no connec- 
tion between the two structures. Mr Lankester, also, in the same paper does 
not fully express the published opinions of M. Claparede on this point. He 
says, " There is a very distinct relation between the abundance of the perivisceral 
granules and cells, and the abundance of the brownish granules which surround 
in masses the dorsal vessel and its ramifications on the stomach or intestine. 
Claparede, in his 'B-echerches sur les Oligochetes,' has spoken of the brown-yellow 
' hepatic ' tissue of the intestine in Lumbricus being continued to and surround- 
ing the dorsal vessel, and has hinted (but only obscurely) at some connection 
between the perivisceral cells and the supposed hepatic tissue. "t Now, in the 
first place, in the memoir alluded to, M. Claparede did not specially refer to 
Lumbricus so much as to those genera included under his family of " Oligochetes 
Limicoles" (Tubifex, Limnodrilus, Clitellio, Lumbriculus, Stylodrilus, Enchytrwus, 
&c), whose structure formed the text of his work. Chcetogaster, of course, 
would come under the same head. M. Claparede states that the pigment- 
cells of the intestine have generally been considered as hepatic, and points out 
that the said cells have as much connection with the dorsal vessel as with the 
intestine ; that in Lumbriculus variegatus, for example, the cellular coating, 
which ceases to cover the intestine at the sixth segment, continues on the 
dorsal vessel to the fourth, and, moreover, the coating follows certain branches 
of the dorsal vessel. Further, he adds, that the intimate connection between 
the supposed hepatic structure and the vascular system is extremely evident in 
the true Lumbrici, and concludes with the following :— " II est done tres-im- 

* Trans. Linn. Soc. vol. xxvi. p. 637. 

f" Mr Lankester has altered his views here. — Vide his paper in the Quart. Jour, of Micros. Sc. 
vol. v. N. S. p. 109. 

VOL. XXVI. PART. II. 3 X 



258 DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

probable que ces cellules versent de la bile clans la cavite" de l'intestin. II est 
beaucoup plus vraisemblable qu'elles deVersent leur contenu dans la cavite" 
pe>iviscerale." He reiterates this opinion in his recent beautiful and accurate 
memoir on the Histology of the Earthworm.* Dr Gruithuisen, indeed, 
clearly anticipated most of the subsequent observers in regard to the connection 
between this glandular coating and the perivisceral fluid, which he termed the 
chyle. In describing the glands which envelope the intestine of his Nais 
(Chsetogaster) diaphana, he observes, "Diese Drlis'chen bilden das, was bei 
hohern Thieren die Chylusdrtisen sind, und ergiessen den Chylus unmittelbar 
in den Eaum zwischen der musculosen Haut und dem Darmcanale."t This 
author, moreover, notes the peculiarity that in a single " Mutternaide " of 
Chcetog aster diastropha, he found in December that the chyle-corpuscles were 
larger than usual, and seems to think that there is a connection between chyli- 
fication (referring to the perivisceral fluid) and generation. Dr Thomas 
Williams, \ again, was strongly of opinion that the long coils of the blood- 
vessels anteriorly in his Nais filiformis (probably Tubifex) and the perivisceral 
branches elsewhere in the body of this worm, were specially intended for 
absorbing from the perivisceral (his " chyl-aqueous ") fluid elements by which 
the blood-proper is formed and replenished. It will therefore be seen that the 
supposition thrown out by my friend Mr Lankester that " the yellow glandular 
tissue" surrounding the alimentary canal "may have but little to do with the 
secretion of digestive juices, or, at any rate, may have an additional and most 
important connection with the production of the corpuscles of the perivisceral 
fluid, and may serve to place that fluid in organic relation with the liquid of the 
closed vascular system of the intestine, and the contents of the digestive tract," 
is by no means new. It appears, indeed, to be the result arrived at by Dr 
Fritz Batzel from an examination of the literature of the Oligochetes previous 
to the appearance of the foregoing ; the author, moreover, assigning the peri- 
visceral fluid the function of a communicating medium between the digestive and 
circulatory systems. Further, I have not seen anything to support the idea of 
Mr Lankester that the abundance or scarcity of the "granules" in the perivis- 
ceral fluid depends on the condition of the glandular coating of the intestine 
and dorsal vessel. The glandular investment presents the same appearance 
whether the corpuscles be few or many, and the agglomerations of granules 
shown by him most readily take place in such a highly coagulable fluid. For 
my part, I have no objection to offer to any of the theories advanced on this 
subject, so far as they rest on actual observation and not on mere conjecture. 
In Tubifex and its allies the perivisceral fluid is an eminently coagulable and vital 

* Zeitsch. f. wiss. Zool. Ed. xix. (18G9), p. 614. 

t Ueber die Nais diaphana, &c, Nova Acta Acad. Leop. Carol. Tom. xiv. Pt. i. p. 411. 

% Report Brit. Assoc. 1851, p. 182 ; and Philos. Trans. Part ii. 1852, p. 625. 



DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 259 

fluid, and, as has long been supposed, doubtless performs important functions 
in the animal economy; as, indeed, the observations of Frey and Leuckart, De 
Quatrefages, and Dr Williams, show it does in other invertebrate animals. 
I think, however, that too little attention has been bestowed upon the in- 
herent properties of the fluid itself. Perhaps the remarkable corpuscles 
contained therein are the products of such inherent properties, and not 
necessarily derived from its surroundings. If the glands covering the intestine 
discharge their contents into the perivisceral fluid, as most authors believe, such 
a discharge probably only furnishes materials for the evolution of the special 
properties of the liquid. It is well to bear in mind, also, that in the clearly 
defined group of the Nemerteans, a fluid identical in appearance, coagulable 
nature, and in the presence of definite corpuscles, occurs within . a special 
muscular sheath on the dorsum of the intestine. This chamber has smooth 
walls, and contains, besides, the proboscis, which, as it were, is invaginated 
within it. The glandular elements, which exist in vast numbers in the walls of 
the digestive tract, cannot thus communicate directly with the fluid. 

In the perivisceral space of one example was a curious parasitic larva 
(Plate X. fig. 2) which moved backwards and forwards in its chamber. It 
lengthened its body into the shape shown at a, then contracted itself as in b, 
forming a club with a large rounded head, and finally assumed the appearance 
figured at c; after which it again elongated itself and repeated the same con- 
tractions. Its structure was minutely granular, with a streak at the anterior 
end. It appears to be the same form as that described subsequently from the 
lobule of the testis (p. 265). 

Digestive System. — Granular Glands. — Anteriorly there are some finely 
granular glands at the sides of the oesophagus ; and by-and-by numerous larger 
glands cover the entire external surface of the alimentary canal, and envelope 
the dorsal blood-vessel. These are somewhat pedicled structures, consisting of 
a fine external membrane containing numerous distinct granules of an orange 
or pale brownish hue (Plate X. figs. 3 and 4). When these bodies are extruded 
into the water, the contained granules show very evident molecular movements, 
and in a short time escape by the bursting of the cell- wall, their movements con- 
tinuing in the surrounding fluid. The yellowish granules also occasionally 
group themselves together, and larger granules are formed here and there, ap- 
parently by the union of several. All the granules refract the light very strongly. 
The gland-cells are rendered more translucent by acetic acid, which, however, 
does not affect the granules. On the addition of sulphuric ether the residue 
clearly shows that their composition is of a fatty nature. Dr Buchholz* is of 
opinion that the pigment-granules of these cells in Lumbriculus variegatus is a 

* Beitrage zur Anat. der Gattung Enchytrceus, &c. Schriften der Physik. okonom. Gesellschaft 
in Konigsberg, 1862, p. 108. 



260 DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

modification of chlorophyll. This author, moreover, shows a distinct nucleus 
in all his figures of the gland-cells of the same worm, and M. Claparede 
describes a nucleus in those of Lumbricus. So long as the cell is filled with the 
granules, it would be a very difficult thing to make out a nucleus, and the large 
number of nucleated cells from other parts which get mixed up with these in 
the field of the microscope necessitates some caution in observing. As pre- 
viously stated, I have not succeeded in seeing a nucleus while the granules 
were within their investment, nor on watching their extrusion has such been 
observed. The same result was arrived at after a careful scrutiny of highly 
favourable longitudinal and transverse sections of the alimentary canal of 
Tubifex, and after manipulation of the fresh specimens with carmine. 

Amongst the sandy mud and Diatomacese in the intestinal canal, are nume- 
rous examples of an Opalina (Plate IX. fig. 14, a, b, c, d). Some are about ^th 
of an inch long, and had the various shapes shown in the figures. The species is 
probably identical with that found in other minute fresh-water annelids. A few 
had a swollen anterior end covered with fine striae like a Pecten or Lima, while 
the posterior or caudal portion was filiform. The usual clear granules and 
vesicles were present. An elongated granular structure like a canal was occa- 
sionally visible in the central line, but this could not be traced throughout 
the entire length of the animal. When freed by laceration of the worm, they 
rush through the surrounding water very actively by aid of their cilia, for it is 
to be remembered they are but in their native medium, since the intestinal 
canal is ciliated, and often gives passage to currents of water. Although a 
little glycerine is added to the water, their cilia continue in active motion, and 
the contained globules are very distinct. 

In a few specimens minute parasitic Nematode worms (Plate IX. fig. 15) 
were coiled at the sides of the intestine near its termination. There is a streak 
at the snout, and some faint central markings along the body. They appear to 
be undeveloped or partially developed Anguillulidse, numerous examples of 
which are frequently found in Lumbricus. 

Circulatory System. — The following observations on the circulatory system 
are in the main confirmatory of the investigations of M. Claparede, who added 
considerably to the descriptions of M. d'Udekem. In Tubifex rivulorum the 
course of the blood-vessels is very regular, and I have met with very few 
abnormal arrangements. There is a large contractile dorsal vessel which is 
thrown in the usual state of the animal into many zig-zags or figure of eight 
crossings, from the fibrous contractions at the septa. A ventral vessel less in 
calibre and paler in colour has a similar direction, but lies on the opposite side 
of the alimentary canal. The dorsal trunk, in conjunction with the alimentary 
canal, is covered by the gland-cells previously described, while the ventral is 
free. The course of the dorsal vessel is as follows : — 



DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIPEX. 261 

At the posterior end of the worm it is joined by the ventral (in a similar 
manner to that shown in Plate X. fig. 5) and proceeds forwards as a deep red 
trunk, the depth of its colour being, perhaps, due more to the larger calibre of 
the vessel as contrasted with the ventral, than to its thicker coats. In this 
region, moreover, it pulsates with a swift and clear stroke from behind forwards 
— the action being noticeable in the penultimate segment. The ventral trunk, 
on the other hand, so far as I could observe, remained of the same calibre at 
this part, except when affected by the wave of perivisceral fluid. In the stasis 
following the introduction of chloroform, the dorsal vessel becomes moniliform 
posteriorly, being constricted, apparently, by the spasm of the septal fibres ; 
while the perivisceral corpuscles rush with great vehemence through the 
narrowed apertures. From the colour of the central region of the last segment, 
it would seem that, before joining, the ventral and dorsal vessels form a slight 
plexus, and, from the vigorous motions usually occurring in this part, there 
could be no better region for the aeration of the blood. 

In each segment two great branches pass off from the dorsal and ventral 
vessels respectively. Towards the posterior border a large trunk (the perivis- 
ceral) springs on each side from the dorsal, and, proceeding outwards towards 
the body- wall, divides into numerous capillary branches, which again unite to 
form a trunk, nearly as large as the original, that on each side enters the ventral 
vessel. The extensive coils formed by the perivisceral branch of the dorsal 
provide ample freedom of motion, an arrangement so necessary during the con- 
tortions of the worm. The coils are especially distinct towards the posterior 
part of the body. About the middle of each segment, again, the ventral vessel 
on each side gives off a branch, which passes upwards round the intestine ; but 
whether it terminates by anastomosing with its fellow of the opposite side, or 
by joining the dorsal, could not be determined. Certainly no branch of any 
size joined the dorsal in this region. 

In some views there are, besides the perivisceral branch of the ventral, one 
or two vessels towards the anterior part of the segment, which course outwards 
from the ventral, and anastomose on the body-wall with branches of the peri- 
visceral. Such a branch or branches are not strictly "intestinal," for they like- 
wise send twigs to the body- wall. I must also add that in one specimen the 
ventral main trunk was observed to bend outwards in a simple curve, without 
being fixed in the centre by any vessel or fibrous tissue. The "intestinal" 
branch thus does not always attach the main trunk closely to the alimentary 
canal. After the addition of a little aconite (which causes spasm of the fibres 
at the septa, so as to render the worm moniliform) the dorsal and ventral 
vessels become much contracted posteriorly, while the periviscerals remain 
well filled, indeed, so as to constitute a broad red bar across the segment. 
Anteriorly some of the intestinal branches are similarly distended. 

VOL. XXVI. PART II. 3 Y 



262 DR M/INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

In the eighth segment the perivisceral branch is considerably enlarged, and, 
curving outwards and downwards, enters the ventral as a large trunk, only 
slightly less than at its commencement. The dorsal half of the vessel pulsates ; 
the ventral does not. It would thus seem that the vessel, probably where fixed 
to the body- wall, ceased to pulsate. This arrangement constitutes the so-called 
" hearts" of these annelids, and in this species both contracted simultaneously. 
The perivisceral branches of the seventh and ninth segments acted similarly, 
though in a less conspicuous manner. The perivisceral vessel of the latter 
(ninth) segment is often noticed to give off large branches at the body- wall. 

In specimens whose generative organs are much developed, the periviscerals 
of the ninth and tenth segments are of considerable size, but neither approach 
the periviscerals of the eleventh, which are enormously dilated, indeed, nearly 
as large as the main trunk itself. This enlarged perivisceral sends branches 
over the succeeding segments, sometimes as far backwards as the twenty-third 
in ripe animals (Plate X. fig. 6, e, e). The periviscerals of the twelfth segment 
under the same circumstances are also dilated, and those of the thirteenth 
more so, three large branches being directed forwards. The arrangement of 
these trunks would seem to countenance my view of the circulation in the 
ordinary condition, viz., that the periviscerals as a rule do not proceed as con- 
tinuously cylindrical trunks into the ventral, but that they communicate by 
their branches on the body-wall. 

Continuing forwards, the main trunks (dorsal and ventral, Plate IX. fig. 17) 
have the same arrangements in the fifth and sixth segments as previously de- 
scribed, the only noteworthy change being an occasional abnormality in the 
origin of the intestinals — one coming off before the other, and thus affording a 
better view of their distribution. It is to be observed, also, that the ventral 
trunk has in this region faint contractions, which render the vessel pale ; it then 
fills again. The periviscerals of the fourth segment are somewhat smaller than 
usual. At a point corresponding to the posterior border of the third segment, 
the dorsal gives off two large trunks, doubtless the homologues of the perivis- 
cerals, though they generally slant obliquely forwards and outwards rather 
than transversely, and divide into many small branches towards the margin of 
the body. The dorsal then pursues its course straight forwards, again gives 
off two branches behind the mouth — the branches subdividing and inosculating 
with others in front and behind, and finally terminates by forking in the snout 
in front of the mouth. The two divisions thus formed split, after bending 
backwards, into numerous twigs, which unite with the capillaries that go to 
form the feeders of the main ventral vessel. The latter originates, by the 
junction of the two great branches constituted by the feeders just mentioned, 
towards the posterior border of the third segment. In many positions under 
pressure, the whole anterior part of the animal is one vast series of vascular 



DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 263 

reticulations. The latter quite differ from the long simple coils described and 
figured by Dr Williams* in Nais filiformis, but doubtless he was misled by 
their complexity. 

In some views, where congestion had been produced by the addition of 
chloroform, atropine, or muriate of morphia,t the intestine was observed to 
be covered by an extensive series of minute blood-vessels, longitudinal and 
circular. This arrangement was due to the presence of two or three vessels in 
each segment winding round the canal, and sending off lateral branches to meet 
others from the adjoining trunks, as shown on the supero-lateral surface of 
the intestine in Plate X. fig. 7, the ventral vessel in this case not being seen. 
A series of nearly parallel anastomosing branches course from the secondary 
trunk in a longitudinal direction. A lateral view of the seventh segment after 
the addition of chloroform (Plate X. fig. 8) exhibits a much coarser reticulation, 
in which the main trunks arise from the ventral. In such experiments, of 
course, the trunks do not remain of their normal calibre, but are irregularly con- 
tracted. These statements with regard to the vascular ramifications on the 
surface of the intestine are fully borne out in the transverse and longitudinal 
sections of the worm, the former exhibiting a complete mesh-work of blood- 
vessels surrounding the alimentary canal in certain positions. The same has 
been noticed by M. Perrier| in Dero obtusa, one of the Nais-grovop, and he 
aptly compares the arrangement to a very elegant trellis with rectangular open- 
ings. According to Mr Lankester they would appear to be more easily 
observed in Chcetogaster. Under the action of chloroform, also, many fine 
cutaneous branches were seen in Tubifex forming a network and a series 
of parallel longitudinal vessels. These ramifications remained comparatively 
still during the motions of the worm, and were probably fixed branches of the 
perivisceral. Some of the twigs (which extended over most of the body-wall) 
coursed towards the septa, and inosculated with the same set of vessels in the 
adjoining segments. There is thus a series of vascular communications between 
segment and segment independently of the main trunk. It would also appear 
that some of the branches, which proceed from the dorsal towards the ventral, 
do not join the latter trunk, but inosculate with twigs from the opposite side of 
the body. 

The circulatory system in the elongated form (Plate X. fig. 9,) much 
resembles that of the foregoing, though it is proportionally more developed. 
The swollen periviscerals or " hearts " occur in the eighth segment, and 
pulsate vigorously and alternately from eight to twelve times per minute. Very 
slight contraction of the tissues anteriorly causes the mobile vessels to assume 

* Report Brit. Assoc, p. 182, PL III. fig. 8. 

The addition of a small quantity of this drug in solution was speedily fatal to ciliary action. 
\ Ann. Nat. Hist. 4th Se. vol. 6, p. 264 (Extr. Comptes Rendus). 



264 DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

so many curves and spirals that it is impossible to unravel them, (vide Plate 
IX. fig. 16), until a more favourable condition of extension ensues. It is a fact 
of interest, that while the vascular distribution is more apparent in this species, 
the perivisceral corpuscles are less developed. 

Generative Organs. — The first swollen segmental organ in the shorter form 
(Tubifex rivulorum), as M. Clapakede observes, occurs in the eighth segment. 
In one specimen the dilated portion of tjbie organ was at the anterior border, 
and on the same side the coils of the duct had entered the seventh; while on 
the other side neither coils nor dilated portions were visible in either seventh 
or eighth segments, but both were present on that side in the ninth. Consider- 
able room, therefore, exists for misunderstandings. The segmental organs 
(Plate IX, fig. 18, from behind the middle region,) vary a little in shape, and 
some in developed specimens are tinted brownish by transmitted light. The 
shorter tube (a) is attached to the septum in front, opening through the mem- 
brane by a slightly dilated and ciliated opening. The long coil, again, opens 
externally, also by a very slightly enlarged extremity, at a point a little posterior 
to the former, but in the same segment. 

The sexual pore lies a short way behind the ventral bristles of the eleventh 
segment, and has the form of a conical papilla (Plate X. fig. 10), which is per- 
forated at the summit. Occasionally spermatozoa are observed to issue from 
the tip. In this instance the copulating organ is slightly protruded. 

The integuments, as already noted, from the tenth to the fifteenth segment 
become at the reproductive season very opaque, and hence the difficulty in 
making an accurate description is much increased. The tenth and eleventh 
segments especially swell out, and become opaque white at the period of 
perfection. 

Male Organs. — In those with undeveloped (or only slightly developed) 
generative organs the testicles are found at the anterior border of the tenth 
segment, and the segmental organ in the eleventh is small, showing that it only 
becomes enlarged with the other structures subsequently. Under the same 
circumstances coils of the ciliated duct of the segmental organ are found at the 
posterior border of the twelfth segment. At a further stage of development 
the testicles form large opaque-whitish masses, which are at first granular 
(Plate X. fig. 19). What appears to be a further stage is shown in fig. 20, 
Plate IX., the cells being filled with a vast number of awl-shaped bodies, 
measuring l2 1 50 of an inch long, rounded at one end, and having a slender style 
at the other. There are also numerous minute ovoid granules in the cell, their 
long diameter ranging from b J- 6 o to 6 J 0o of an inch. The bodies represented 
in fig. 6, b, c, d, Plate IX., are probably also stages in the development of these 
structures. 

In their fully developed state the spermatozoa resemble wavy or zig-zag 



DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 265 

lines (Plate IX. fig. 21), sometimes with attached globules or loops resembling 
heads, but more frequently without them. They do not swim actively about 
on escaping through a wound, but spread themselves insensibly over the field 
of the microscope. They often, as M. d'Udekem shows, surround a sperm- 
cell so completely as to resemble a seed with its downy pappus. 

The first testicle, in those with developed organs, occupies to a greater 
or less degree one side of the ninth segment; and occasionally it is little 
developed while the second stretches to the sixteenth segment. I have also 
seen the first testicle slip entirely out of the ninth segment, and lie towards 
the posterior part of the tenth. It is attached to the septum between the 
ninth and tenth segments, in the angle next the intestine (in ordinary views, 
c, fig. 6, Plate X.) In a large specimen there was the unusual appearance of a 
glandular organ resembling a testis with sperm-cells in the fifth segment, and 
the seventh and eighth had each two of a similar nature. The ninth had the 
vas deferens with its trumpet-shaped aperture fixed in the septum between it 
and the eighth. The developed organ (testis), moreover, stretched from the 
bulged septum last-mentioned to the fifteenth segment. The ordinary condition, 
however, is that the first testis occurs in the ninth segment, the receptacles in 
the tenth, the ovaries in the eleventh, and the second testis in the twelfth 
segment. 

The eleventh segment also holds the large coils of the vas deferens (Plate 
X. fig. 6, b), which, moreover, often slip into the twelfth. The trumpet-shaped 
aperture is connected with the septum between the tenth and eleventh segments. 
It (vas deferens) is clearly a development of an ordinary segmental organ, as 
indeed most authors state. 

In the sixteenth segment of one example there was a large parasite (Plate X. 
fig. 11) in the lobule of the testis, and extending throughout the entire length 
of the division. Its interior was filled with cellulo-granular matter, and in 
contraction its sides were distinctly crenated, while the body was crossed by 
transverse rugae, like a larval cestode. There is a short median furrow passing 
from a notch in its anterior or smaller end. It is not ciliated. 

Female Organs.- — In the early condition the ovaries are observed at the 
anterior border of the eleventh segment, attached on each side to the septum, 
close to the dorsal vessel and intestine (Plate X. fig. 12, a, b). In this state 
they are composed of granular cells. The developed organs (sometimes of an 
orange colour) stretch to the fourteenth, fifteenth, and subsequent segments, 
and when compressed give exit to a vast mass of fatty granules. 

The seminal receptacles (Plate X. fig. 6, a) are amongst the most distinctly 
marked organs in the developed animal, and are at once distinguished by the 
lively contractions which ensue when they are filled with spermatozoa. They 
occupy nearly the whole of the tenth segment, and the apertures have the form 

VOL. XXVI. PART II. 3 Z 



266 DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 

of trumpet-shaped organs, one on each side anteriorly. When empty the sacs 
have a somewhat coarse granular appearance, and do not show the rolling 
contractions. 

In a specimen with largely developed ovaries, a curious ovoid organ (Plate 
X. fig. 13) occurred at the anterior part of the eleventh segment, and another 
at the anterior part of the twelfth. Externally there was a dense capsule, and 
internally a minutely granular mass altogether different in appearance from the 
structure of the ovaries or their contents. They measured about ^th to r^th 
of an inch in diameter, and were of so unyielding a nature that they soon 
escaped by rupture through the body-wall of the worm. 



EXPLANATION OF THE PLATES. 
Plate IX. 

Figure 1. Bristle and dorsal hook of Tubifex rivulorum, from the anterior segments. x 350 diam. 
Figure 2. Ventral hooks of the same species. x 350 diam. 

Figure 3. Anterior hooks (accompanyingthe bristles) of the elongated form from the lakes ; a, pro- 
cesses in the fork. x 350 diam. 
Figure 4. Body-wall (a) of T. rivulorum, with parasitic Vorticellae. x 210 diam. 
Figure 5. One of the parasitic Vorticellas in a partially expanded state. x 350 diam. 
Figure 6. Perivisceral corpuscles of T. rivulorum ; a, cells in the ordinary condition; b, a cell from 

the perivisceral chamber after the addition of chloroform ; c and d, the contents of the 

latter more highly magnified. In all probability, however, this (b) is only a sperm-cell in 

course of development. x 350 diam. 
Figure 7. The same after the action of dilute glycerine, with extruded clear granules. x 350 

diam. 
Figure 8. Variously shaped corpuscles from the perivisceral fluid. x 350 diam. 
Figure 9. Perivisceral corpuscles of the elongated Tubifex from the lakes. x 280 diam. 
Figure 10. Elliptical and other corpuscles from the same fluid. x 350 diam. 
Figure 11. Perivisceral corpuscles of a species referable to Clap arede's genus Limnodrilus. x 850 

diam. 
Figure 12. Gland-cells from the intestinal wall of the same species. x 350 diam. 
Figure 13. Ciliated epithelial cell from the interior of the digestive tract of the same animal. x 850 

diam. 
Figure 14. a, b, c, d. Various forms of the Opalina parasitic in the alimentary chamber ; b represents 

an outline of the anterior end of a large specimen, the cilia being omitted, x 210 diam. 
Figure 15. Parasitic Nematode worm from the same region. x 400 diam. 
Figure 16. Anterior region of the elongated Tubifex from the lakes, showing the dense coiling of the 

blood-vessels anteriorly in the semi-contracted condition ; a, dorsal blood-vessel ; d, 

ventral. 
Figure 17. Anterior segments of Tubifex rivulorum in a somewhat contracted and flattened condition, 

exhibiting the arrangement of the , vascular system ; a, fissure at the mouth ; d, dorsal 

blood-vessel ; v, ventral. The figures indicate the segments. 
Figure 1 8. Segmental organ of the same species from behind the middle region of the bod}- ; a, the 

septum. 
Figure 19. Sperm-cell in the granular stage. x 350 diam. 
Figure 20. Awl-shaped bodies and granules from a sperm-cell in course of development. x 400 

diam. 
Figure 21. Spermatozoa of T. rivulorum. x 350 diam. 



DR M'INTOSH ON SOME POINTS IN THE STRUCTURE OF TUBIFEX. 



267 



Plate X. 



Figure 1. Perivisceral corpuscles from Tubifex rivulorum after extrusion into the water. x 210 

diam. 
Figure 2. a, b, c, Various forms assumed by the parasitic larva from the perivisceral chamber of 

Tubifex. x 210 diam. 
Figure 3. Granular glands from the wall of the digestive cavity in situ. x 350 diam. 
Figure 4. Isolated gland-cells similarly magnified. 
Figure 5. Posterior end of the Tubifex from the lakes, showing the junction of the dorsal and ventral 

blood-vessels ; a, cuticle ; b, chorion and muscular coats ; c, ending of dorsal blood-vessel ; 

c, last perivisceral ; d, perivisceral and other corpuscles. x about 50 diam. 
Figure 6. Portion of Tubifex rivulorum at the reproductive season ; a, seminal receptacle in the tenth 

segment ; b, coils of ciliated duct (vas deferens) ; c, testicle ; d, atrium (?) with a double 

outline under pressure ; e, e, elongated vascular branches from the eleventh and other 

segments for the supply of the developed generative products. x 55 diam. 
Figure 7. Vascular ramifications on the supero-lateral surface of the intestine ; a, dorsal blood-vessel ; b , 

septum. x 210 diam. 
Figure S. A lateral view of the seventh segment after the addition of chloroform ; d, dorsal vessel ; v, 

ventral ; p, perivisceral. x 210 diam. 
Figure 9. Anterior portion of the elongated form from the lakes, showing the circulating system ; a 

dorsal blood-vessel ; b, ventral ; c, enlarged pulsating cavities or " hearts "of the peri- 

viscerals in action ; d, forking of ventral vessel. 
Figure 10. Tip of the copulating organ protruding through the sexual pore ; a, hooks. x 210 diam. 
Figure 11. Larval parasite from the lobule of the testis. x 210 diam. 

Figure 12. The eleventh segment, showing the development of the ovaries; a, cellulo-granular con- 
tents ; b, investing membrane ; c, perivisceral corpuscles ; d, granular glands of intestine, 
x 210 diam. 
Figure 13. Curious ovoid structure from the anterior part of the eleventh segment of a specimen with 

largely developed ovaries. x 210 diam. 



( 269 ) 



XIII. — On the Place and Power of Accent in Language. By Professor Blackie. 

(Read 6th March 1871.) 

On the subject of accent and quantity as elements of human speech, there has 
been such an immense amount of confusion, arising from vague phraseology, 
that in renewing the discussion nothing seems more necessary than to start 
with a careful and accurate definition of terms ; and that a definition not taken 
from books, and the dumb bearers of a dead tradition, but from the living facts 
of nature, and the permanent qualities belonging to articulated breath. Now, 
if we observe accurately the natural and necessary affections of words in human 
discourse, considered merely as a succession of compact little wholes of arti- 
culated breath, without regard to their signification, we shall find that all the 
affections of which they are capable amount to four. Either (1), the mass 
of articulated breath which we call a word, is sent forth in a comparative^ 
small volume, as in the case of a common gun, or it is sent forth in large 
volume, as in the case of a Lancaster gun ; this is a mere affair of bulk, in virtue 
of which alone it is manifest that any word rolled forth from the lungs of a 
Stentor must be a different thing from the same mass of sound emitted from 
a less capacious bellows. In common language this difference is marked by 
the words loud and low. A broader wave of air impelled against the acoustic 
machinery of the ear will always make a more powerful impression independent 
of any other consideration. But (2), an equal or a stronger impression may 
be made on the ear by a less volume of sound, if it be sent forth with such 
an amount of concentrated energy and force as to compensate for its deficiency 
in mass. A more sharp and intense clap of thunder, for instance, may in this 
way affect the ear more powerfully than a greater peal less vigorously sent 
forth and more widely spread. The affection of sound brought into action here 
is what in language we generally call stress or emphasis ; and it depends altogether 
on the intensity of the projectile force, and gives to speech the qualification of 
more or less forcible. But (3), this force may often be, and very naturally is, 
accompanied with another affection of sound altogether distinct, viz., the 
sound may be deep and grave, or high and sharp, corresponding to what in 
music we call bass and treble notes. The analogy between music and articulate 
speech is here so striking, that it has passed into common use ; as when we talk 
of a person speaking in a high or a low key, in a monotone, or in a deep low 
sepulchral tone, and so forth. And in reference to single words, we are 

VOL. XXVI. PART II. 4 A 



270 PROFESSOR BLACKIE ON THE 

accustomed to say, that the acute accent stands on syllables pronounced in an 
elevated tone, and the grave on those pronounced with a low tone. The only 
difference between the musical scale and the scale of articulate speech in this 
view, is that the latter, besides being much narrower in its compass, rises or 
sinks, not by mathematically calculated intervals, but by a mere upward or 
downward slide, not divided by any definite intervals. The true connection of 
these slides with the general doctrine of accent has been well set forth by Mr 
Walker, the author of the Pronouncing Dictionary, in a separate treatise.* 
(4). The fourth affection of articulated sound is that which is familiarly known 
to scholars and schoolboys under the name of quantity, and signifies simply the 
greater or less duration of time during which the sound continues to impress 
the ear. For it is manifest that any sound may be produced either by a sudden 
stroke, or jerk, or by a traction prolonged to any extent. In grammar a short 
vowel corresponds to a quaver or semiquaver in music, and a long vowel to a 
crotchet or minim, according to the ratio of the movement. 

Now it should seem to be pretty plain at the outset, to all persons whose ears 
have been exercised in a very slight degree to discern the differences of articulate 
sounds, that what is called accent in grammar has to do only with the second 
and third of the above four elements, and not at all with the first or fourth ; in 
other words, that the accent of a word is totally distinct both from the volume 
of voice with which the word is enunciated, and the length of time during which 
the speaker dwells on the syllable. Nevertheless, such is the confusion which 
learned writers have introduced into this subject, that it is necessary at the very 
outset to enter a caveat against a very prevalent notion that the placing of the 
acute accent on a syllable, naturally or necessarily implies a prolongation of 
the sound of the accented vowel ; or, in other words, that to accent a syllable 
withoutmaking it long is impossible. In music no performer ever dreams that 
the rhythmical beat on the first, we shall say, of three quavers — that is jig time — 
necessarily turns the quaver into a crotchet. A musician making such an 
assertion would simply be deemed drunk or mad ; nor does it make the slightest 
difference in the quantity of the note receiving the musical accent, whether in 
respect of elevation of tone it stands high or low in the scale. It is understood 
by every girl who fingers the piano, that the elevation of the note, the duration 
of the note, and the rhythmical emphasis upon the note, are three essentially 
different things which never interfere with one another. But the moment we 
transfer this case to the analogous domain of spoken accent, — the certus quidam 
dicendi cantus, as Cicero called it, — we find ourselves involved in a region of con- 
fusion and contradiction with regard to the simplest matters, than which few 
things can be imagined more humiliating to human reason. For however diver- 

* A Key to the Classical Pronunciation of Greek and Latin Proper Names ; with Observations 
on the Greek and Latin Accent and Quantity. By John Walker. London, 1827. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 271 

gent the printed opinions of the learned may sound, that the relative facts are 
exactly the same in the case of spoken speech, as of song or played notes, is 
beyond question. A single example will make this evident. The first syllable 
of po' -tent, for instance, according to a well-known rule in the English language 
is long ; but the first syllable of the Latin word from which the English comes 
is short, pot' -ens, while the accent is on the same syllable in both languages. 
Now, it surely will not be alleged, in obedience to the dictates of any sane ear, 
that in pronouncing the Latin word I am obliged to call it pb'-tens, after the 
English fashion, on account of the tyrannic force of the acute accent. It seems, 
nevertheless, that British schoolmasters and professors have acted under the 
notion that some compulsion of this kind exists ; for as a rule they say bo'-nus, 
and not Ion' -us, though they know very well that the first syllable of this word is 
not long, as in the English word po'-tion, but short, as in mor'-al. Such confusion 
of ideas on a very simple matter is a phenomenon so strange, that some reason 
may justly be demanded for its existence ; and on reflection I find two reasons 
principally that seem to account for it. The first is the confounding of a really 
long quantity with that predominance of a sound to the ear which is a necessary 
element of all accentuation. Thus, when I take the word tep'-id, and form the 
abstract substantive from it — tepid'-ity, by changing the place of the accent from 
the first syllable of the adjective to the second, I certainly have given a pro- 
minence to the short i which it did not possess before, and a prominence, no 
doubt, which though it consists principally in force, emphasis, or stress, may 
also carry along with it a certain dilatation of the tenuous vowel, so that it is 
really longer in the substantive, being accented, than when it was slurred over 
without emphasis in the adjective. But though this is quite true, it is altogether 
false to say that the vowel has been made long according to the comparative 
value of prosodial quantity ; for, if the second syllable of tepl'd-ity be compared, 
not with the last syllable of the adjective tepid, but with the same syllable of 
the substantive, as mispronounced by some slow, deliberate Scot — tepi-dity, 
tepee-dity — we shall see that the vowel i, for all rhythmical purposes, still remains 
short. The other cause which presents itself to explain the confusion of 
English ears on this subject, is the doctrine of what the Greek and Roman 
grammarians call length by position. According to this doctrine, a vowel 
before two consonants is long. What this means we may clearly conceive by 
the example of such words as gold, ghost, in English, or Ptibst or Obst in German ; 
but though the vowels in these words are unquestionably long in both 
languages, they are so only exceptionally, the rule both in English and German 
being that a vowel before two consonants is short. Of this rule the word 
shoi't itself may be taken as an excellent example ; which, if it occurred in a 
Greek chorus, by the law of position, would be sung short, with the o prolonged, 
like o in shore. Now, with this classical analogy in their ears, or rather in their 



272 PROFESSOR BLACKIE ON THE 

head (for it is by no means certain that all those authors who have written on 
this subject did use their ears), when I pronounce such a word as prtm'-rose or 
el' -bow, it is not at all uncommon for English scholars to say, and obstinately to 
insist, that the accent on the first syllable of these words is necessarily accom- 
panied by a prolongation of the vowel. But this is a judgment of the question, 
not by the living fact of the sound, but by the doctrine of an old book about 
the sound. And as to what the old book says, we in fact do not know whether 
length by position meant a habitual prolongation of the vowel sound in common 
discourse, as in our words gold, told, sold, ghost, most, or only a poetical license ; 
that is to say, whether the genitive plural of av-qp, of which the penult is short, 
was really pronounced awndro'ne or dndrbne in prose. I for one am strongly 
inclined to think that the latter is the true fact of the case ; for, if it had been 
otherwise, would it not have been a more correct phraseology in the grammarian 
to say, that a vowel before two consonants is naturally long ? But when they 
tell us that a vowel which is naturally short becomes long when two consonants 
follow, this looks rather like an artificial exception than a natural rule. And I 
am inclined to think that such an exceptional rule was introduced from sheer 
necessity, like the long o in certain comparatives, such as ao^ajrepos, because, 
without such a license, really long syllables in sufficient abundance would not 
have been found in the language for the necessities of the early dactylico- 
spondaic poetry. As to any inherent natural necessity in the rule, such an idea 
cannot be entertained for a moment ; for the vowel is then most easily pro- 
longed — as in the English words pb'-tent, no-tion, na'-tion, pa' -tent, where it is kept 
separate in spelling from the influence of the succeeding consonant or con- 
sonants, which, as in por'-tion, rather act by cutting the breath short, and pre- 
venting the prolongation of the vowel. The influence of the consonant in 
shortening the vowel will be apparent in comparing the words nom-inal and 
Leb'-anon with no'-tional and la'-bial; nor does the addition of a second consonant 
in any perceptible way alter the case. If the first syllable in prim is manifestly 
short, it is certainly not made long by the addition of the long syllable rose in 
the noun pi^tm'rdse — a word which, in the relative values of its final and penult 
syllables, corresponds exactly to a whole host of Greek words which usher in a 
long final by a short accented penult, as in UXdrcov, the name of the great 
philosopher of Idealism, in Anglicising which, we, besides attenuating the 
vowel, elongate the short penult, according to the practice of our own language. 
It will now be distinctly understood, as a starting-point to the present 
inquiry, that by accent I mean merely a certain predominance, emphasis, or stress 
given to one syllable of a word above another, in virtue of a certain greater 
intensity of force in the articulated breath ; this increased intensity being natu- 
rally in many cases, but not necessarily in all cases, accompanied by an elevation 
in the key of the voice. My observations do not include either rhetorical accent, 



PLACE AND POWER OF ACCENT IN LANGUAGE. 273 

which affects whole sentences and clauses, or national accent, which, in addition 
to rhetorical accent, often includes some favourite sound, note, or vocal man- 
nerism characteristic of different peoples. 

The general question to which we shall now attempt a scientific answer is 
the following — What are the great leading principles on which accent, as a 
phenomenon of articulate speech, depends ? Are there any such principles, or is 
it a matter of mere arbitrary association, fashion, and habit ? and in the com- 
parison of different languages what is the standard of value in respect of their 
accentual character % Does sesthetical science contain any general rules which 
might enable us to measure the value of accents, as we do the value of sounds in 
language, when, for instance, we say that Italian is a more harmonious language 
than Gaelic, and Greek a more euphonious language than Latin % In answering 
this question, I would remark, in the first place, that there is no such thing as 
a language altogether without accent ; only a machine could produce a con- 
tinuous series of sounds in undistinguished monotonous repetitions like the Mm, 
turn, tlim of a drum ; a rational being using words for a rational purpose to 
manifest his thoughts and feelings, necessarily accents both words and sentences 
in some way or other. When, therefore, we find it stated in Adam Smith's 
Essay on Language, and other English writers, that the French have no accent 
in their words, this is either a gross mistake, or it must be understood to mean 
that the French do not give such a decided and marked preponderance to one 
syllable of the word as the English do ; which is very true, as any man may see in 
comparing the English velocity with the French velocite. But this is merely a 
difference in the quantity and quality of accent, not a contrast betwixt accent 
and no accent. The second postulate of all rational discussion on this subject 
is, that the significant utterance of articulate breath, like every other mani- 
festation of reason-moulded sense, is a part of sesthetical science, and subject 
to the same necessary laws which determine the excellence of a picture, a poem, 
or a piece of music. No doubt in the enunciation of words, as in all the fine 
arts, fashion may often prevail to such an extent, as in some cases to usurp the 
place of reason and propriety; but the prevalence of false taste in any depart- 
ment of art does not effect the certainty of the eternal principles by which it is 
regulated, any more than the prevalence of murders or lies amongst any people 
can take away from the essential superiority of love to hatred, and of truth to 
falsehood in all societies of reasonable beings. We are, therefore, justly entitled 
to look for a standard of excellence in the matter of orthoepy, no less certain 
than the standard of truth in morals or mathematics ; as, indeed, all things in 
the world being either directly or indirectly the necessary effluence of the 
Divine reason, must, in their first roots and foundations, be equally rational and 
equally necessary. Now, in looking for the necessary conditions on which the 

VOL. XXVI. PART II. 4 B 



274 PROFESSOR BLACKIE ON THE 

comparative excellence of accentual systems may depend, we find that they may 
be reduced to the four following heads : — 

1. Significance. 3. Variety. 

2. Euphony. 4. Convenience. 

And first, that Significance must be a main point in all accentual systems, 
is manifest from the very nature of accent. For why should a man give pre- 
dominance to one syllable in a word more than to another, unless that he means 
to call special attention to the significance of that syllable ? Nay, it may often 
be essential to the effect intended to be produced by the word, that its most sig- 
nificant syllable should be emphasised — as when Lord Derby lately said that the 
adoption of the Prussian system of making every citizen a soldier, would not 
be a progression but a retrogression. No doubt, in order to express such an 
accentual contrast as this, the English language departs from its usual fashion 
of accenting these words ; but this only proves that the English method of 
accentuation in this case is a mere fashion, founded on no natural law, and 
which accordingly must yield to the higher law of emphatic significance, when 
nature, like murder, will out. And here we may observe that the English, as a 
merely derivative and mixed language, is by no means a favourable one for ex- 
hibiting the natural and normal laws of a rational accentuation. Neither, so 
far as I know, is there any language whose orthoepy presents so many anomalies, 
and where changes entirely reasonless and arbitrary, require only the stamp of 
aristocratic or academic whim to give them currency. With regard, however, 
to the natural preponderance of the contrasting element in compound words, 
the Saxon part of our language affords obvious examples of its recognition, as, 
when we say, out' -side and in -side, back'-ivards and for' -wards, up-hill and down'- 
hill, male and female. So in the names of the Highland clans, as MacBain, 
MacDonald, MacGrigor, &c.,the emphasis does not lie on the common element, 
the Mac, but on the distinctive element to which the other is attached ; and in this 
view our Saxon pronunciation of Macintosh and Maclntyre, affords two very 
good examples of words where custom and fashion have inverted the natural 
and significant place of the accent. In the Greek language, this most natural 
of all accentual laws, operates in all such compounds, as aKapiros, aVcus, o-uVoSos, 
7rapoSo5, with which we may contrast the English fruitless, childless, where the 
accent is on the root, and not where it ought naturally to be on the contrasting 
element of the compound. In the same category with this I am inclined to 
place the accent on the augment in Greek, as in erv\\ta, reru/x/xat; for it is the 
augment here manifestly that contains the element of past time which is dis- 
tinctive of the tense, being equivalent in effect — whatever its original meaning 
may have been — to / did strike, as opposed to / am striking. The same desire 
to call attention to the distinctive element may have determined the Greeks to 



PLACE AND POWER OF ACCENT IN LANGUAGE. 275 

accent the penult of all diminutives, contrary to their usual practice in words, 
with a short final syllable, as in natSiov, 7rcuSicr/<:os, k.t.K. 

Under this head I am sorry to record my dissent from a German writer of 
acknowledged excellence on this subject — Dr Karl Gottling.* This learned 
writer lays down the maxim in the first place, that in the Greek language the 
accent falls on the syllable containing the principal idea of the word ; and, 
accordingly, he says that in Xeyco and other verbs not pure it falls on the penult, 
because this syllable is the root, and the root, as containing the principal idea of 
the word, is naturally emphasized. Now, looking back to the first framers of a 
language, I cannot see in this case any reason why the root syllable should have 
received the accent rather than the termination, which, for the sake of distinc- 
tion and contrast, is added to the root. If we say aKapiros, because we wish to 
call attention to the negative particle, why should we not say Xeyw calling 
attention to the personal pronoun ; as, in fact, we do say in English, quoth T, 
quoth he ? And in the same way with regard to nouns, as the terminations of 
the cases were originally expressions of relation, attached to the noun for the 
sake of emphasis and contrast, I do not see why the schoolboy fashion of declining 
dominus-i-o '-um — should not have been the original one. And so in the case 
of the German brauerii and the Scotch brewer^ as contrasted with the English 
breivery ; for though no doubt it may be said, that as the root brew contains the 
principal idea, the accent should naturally be there, and this is what Goettling 
says, yet it may with more right be said, that what is intended to be emphasized 
here is not mere brewing, but a place for brewing, and that the syllable denoting 
the place receives the accent as appropriately as the terminations r)piov, elov, 
and oiv, when used for the same purpose in Greek. Only so much truth, 
therefore, can I perceive to lie in Goettling's principle, as to admit that, so soon 
as the original signification of terminations is lost, and people commence to 
supply their place by prepositions, pronouns, and other separate words, whose 
significance is felt — then, and not till then, can the accent on the root syllable be 
regarded as natural and normal in language. Thus, when the German says 
Hdbe, laying the stress on the first syllable of the first person singular present 
indicative of the verb to have, it is natural and normal, because the termina- 
tion e has no significance to him, and could receive an accent only from 
a senseless fashion, not from a natural propriety. On the other hand, in 
A'bgdbe, Hingdbe, Zugabe, and similar compounds, the accent is properly placed 
on the contrasting element of the compound, of which the significance is strongly 
felt. 

The next element we have to take into consideration in measuring the value 
of different accentual systems is Euphony. The simple mention of this word 
will suffice to show how very one-sided a notion it was in Goettling, that the 

* Elements of Greek Accentuation, from the German. London : Whitaker. 1831. 



276 PROFESSOR BLACKIE ON THE 

accent, as a general principle, should always be on the root syllable, as being 
the most significant. If man were only a logical animal, this might be all very 
well as an a priori ideal of a perfect accentual system ; but he is also, if not 
always at starting, certainly when fairly developed, an sesthetical animal, who 
may be allowed on occasions to sacrifice the significance of ideas to the luxury 
of sounds. And if this is true of man generally, it is certainly so a fortiori of 
the Greeks, whose whole culture grew out of music, and remained in the closest 
connection with it to the very end of their classical period. Supposing, 
therefore, that with this most musical and artistic of all peoples a regard to the 
mere luxury of sound had, in certain cases, determined the position of the accent, 
let us ask in what way this determination would naturally manifest itself ? The 
answer is obvious. In richly terminational languages such as the Greek, where 
the terminations are not insignificant little short vowels or syllables as in the 
German Gabe, Buche, Briider, &c, but deep, full-rolling, prolonged vowel- 
syllables such as cov, ot5, ao, acov, and oio, there might exist a very natural 
tendency to place the accent on these syllables, — not, of course, because there is 
any necessary connection, as some persons say, between accenting a syllable 
and lengthening it, but because when a syllable by the presence of a long vowel 
actually is long, the placing of the accent on it, is the most certain way both to 
bring out the full length of the vowel, and to ensure the permanence of the full 
musical value of the syllable, so long as the language lasts. For whatever 
other syllables of a word may from carelessness, or .haste, or reasonless fashion, 
be cheated of their natural quantity, the accented syllable will always most 
stoutly maintain its rights, even if it be a short syllable, much more if it be 
a long. To illustrate this by a familiar example ; in the famous Homeric line 
(II. i. 49), in which the twang of Apollo's bow is described : — 

" Seivrj Se Kkayyrj yiver dpyvpeoio yStoto," 

it is manifest both that the euphony of the line lies mainly in the two termi- 
nations in oio, though these syllables are certainly not the significant ones in the 
verse ; and further, that this verse is much more beautiful when recited with the 
rhythmical accent on both the full-sounding penults, than when, according to 
the prose accentuation, it emphasizes only the 61 of the last word. The coinci- 
dence of the termination with the accent therefore is favourable to music ; and 
it is favourable also as a bar to the injury which time is always ready to inflict 
on final unaccented syllables. Now, with this principle to guide us, we shall have 
no difficulty in seeing the cause of one peculiar excellence which the ancient 
Roman critics recognised in the Greek, as contrasted with their own tongue, in 
respect of the accentual system. For, as the Romans in no word placed the 
accent on the last syllable, it followed that they could enjoy the rich auricular 
luxury of a grand terminational unison of accent and quantity, only in the case 



PLACE AND POWER OF ACCENT IN LANGUAGE. 277 

of words whose terminations are dissyllabic. Thus, they dealt largely in final 
trochees — trochees both by accent and quantity, in such words as sermb'nis, 
penndrum, domino' rum, legis, probd'vit, voluptd'tem, and so forth, but could not 
say domino's, or Macend's, or any word accented in the same way as in English 
our engineer, volunteer, evdde, capsi'ze, theori'se. On the other hand, the Greek 
terminational accent is pretty equally divided between trochaic terminations, 
such as olo, <f>ikov<ri, TV(f>6ei(ra, [jivdos, cr<y//,a, jjlolWov, and oxytone endings, such 
as ayadwv, \a/3a>v, Tv^deis, </>t\et9. Of the prevalence of the oxytone accent in 
Greek, especially in large groups of adjectives and substantives, not to mention 
the whole army of prepositions, and certain familiar parts of verbs, any one may 
convince himself by taking a sentence at random from a Greek book ; and the 
effect of this on the music of the sentence will be evident to the dullest ear. 
Sometimes a whole sentence runs on with a succession of accented terminational 
syllables, a peculiarity which, without any rhetorical intention, arises naturally 
from the number of oxytone substantives and adjectives, and the additional 
fact that all substantives of the first declension, whatever the accent of their 
termination may be, receive a long rolling accent on the last syllable of the 
genitive plural, while all monosyllables of the third declension, by a law common 
both to Greek and Sanscrit, transfer the accent from the radical syllable to 
the termination in the genitive and dative cases of both numbers. Take a 
passage from Plato's Kepublic as an example : — 

" Ot re dyjpevTal iravTes, ol re p,ipjr)Toi, 7ro\\ot fxev ol irepl to. o-yr\p,wra. re /cat 
Xpaj/xara, ttoWoI Se ol nepl jjLOvcriKrjv, iroirjTai re /cat tovtwv virripeTai, paxfjcoSoi, 
vnoKpLTai, -^opevrai, ipyoXdfioi, o~Keva>v re TravTooawcop oyjjjLiovpyol, tcov re akXcov /cat 
Tbtv wepl top yvvaiKeiov koct/jlov, /cat orj kgu oiaKOvoiv tt\^l6vu>v oerjo-ojJLeda. ^ ov So/cei 
Serjcreiv Tra&ayaiywv, tltOoiv, Tpo(f>a>v, KOfx^oiTpLOiv, Kovpiav, /ecu av oxJjoitoiojv re /cat 
jxayeipov ; £tl Se /cat o-v/3(i)Tcjv TrpocrSe^croue^a.""'" 

Greek, therefore, is superior to Latin in this respect, just as an instrument 
with a larger is superior to one with a smaller compass of notes. And taking 
Italian, under this point of view, into the comparison, we observe that the few 
oxytone accents which that beautiful language possesses all arise out of Latin 
words, with an accented penult, whose last syllable has fallen away; thus, 
podestd from potestate, amo from amavit, and so forth. The same is the case 
with the French, as in mlocite, variete, valetir ; and most of our English oxy- 
tones, whether Latin or Greek, are merely curtailed forms of a final trochaic 
accent, as evdde from evddo, volunteer from volontiefre, proceed from procefdo, 
theorise from #ecopt£a>. And it is this systematic curtailment by the way, caused 
by the dropping of the final unaccented vowel both in Latin and Saxon words, 
which has produced that lamentable deficiency in trochaic endings which makes 
our rhythmical language so much narrower in compass than that of Greek, 

* Eep. ii. 373, B. 
VOL. XXVI. PART II. 4 C 



278 PROFESSOR BLACK1E ON THE 

Latin, German, and Italian. Only for short lyrical efforts can we manage the 
rhymed trochaic ending with graceful effect ; all attempts to go beyond this 
natural limit have ended either in a manifest artificial strain, or an admixture 
of the comic element which is fatal to the effect of serious composition.* 

If this rich and various disposition of the accent on terminational syllables 
is thus manifestly a plain element of euphony, that accentuation, on the other 
hand, will be justly esteemed cacophonous which, by drawing the accent back 
to the beginning of the word, that is to the third, fourth, or even fifth syllable 
from the end, has a tendency to cheat the ultimate or penultimate syllable of 
its full musical value ; we say a tendency, because it is only in this tendency that 
the evil lies ; for, if by careful elocution the tendency is corrected, the blot may 
be turned into a beauty on a principle to be mentioned under the next head. 

The remark here made is a very serious consideration for us English, as our 
predominant accent is decidedly antepenultimate, and the fashion seems to be 
increasing of throwing back the accent from the penult to the antepenult, and 
from the antepenult sometimes to the fourth syllable from the end. Thus we 
used to say contemplate and illustrate, whereas we say now con'template and 
illustrate, disputable has become disputable, and contemplative, of course, must 
become con'templatite. The tendency of this practice to deprive our syllabifica- 
tion of its natural melody is obvious enough. In such words, for instance, as 
signify and purify, the tendency to rob the final y of its natural long quantity 
is strong, while in co'lumbine, brogardine, from the fuller quality of the final 
syllable it is less. But if the danger be great in the case of the final syllable of 
such words, it is greater in the case of the penult, that is, the syllable imme- 
diately following the accented antepenult ; for, in the case of the final syllable, a 
secondary accent may come in to save the prominence of the vowel, while the long 
unaccented penult lies under the double disadvantage of a sinking inflexion 
and a feeble stress, after the combined force, it may be, of an elevated accent 
and a long quantity. From this cause it is that in vulgar speaking the second 
syllable of the verb educate is so liable to be shortened and turned into edlcate ; 
and so strong is this tendency, that many English scholars will tell you that to 
pronounce the Greek word avOpcoTros, with the accent on the first syllable and 
the second syllable long, is impossible ; and it is no doubt true that it is not so 
easy as saying avOpoiros, which the modern Greeks generally do ; but as to the 
alleged impossibility, we have only to look to such words as landholder, codl- 
hedver, com' dealer, to see that it exists only in the unpractised orthoepic organs 
of the objectors. Of all languages that I know, the Gaelic is that whose euphony 
has suffered most from the habit of throwing the accent back to the beginning 
of the word. Of this there cannot be a more striking instance than words com- 

* This is one among half-a-dozen reasons for the general want of success in our English hexa- 
metrical experiments. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 279 

pounded with the element mor, signifying great, which may be divided into two 
classes, those in which the termination mor, recognised in its full significance, is 
accented, and those in which it falls under the category of the German lich and 
our y — in Gliicklich and lucky — being used for flexional purposes without a distinct 
appreciation of its meaning, and therefore naturally unaccented. Of the one class 
of words, Liosmor and Ben More, i.e., large garden send great mount, may serve as 
familiar examples; of the other, sultmhor,/at,})ronou.ncedsvltur, sendgrasmhor, 
gracious, pronounced grdsvur, are excellent illustrations. For in these two last 
words we see that the adjective mor, in losing its separate significance, loses both 
its quantity and its natural accent ; and the compound word becomes a paltry 
pyrrhic s-, instead of a respectable iambus, ~— , or a majestic spondee, -. 

Under this head it only remains to mention the extraordinary theory of 
Bopp with regard to the place of the accent both in Sanscrit and Greek. 
That illustrious philologer, in a work entitled " System of Comparative 
Accentuation, or concise Exhibition of the Points of Agreement between Greek 
and Sanscrit in the Doctrine of Accent, Berlin, 1854," lays it down as a ruling 
principle, that the most perfect kind of accentuation generally, and that which 
prevailed originally in the Sanscrit language, was that in which the acute 
intonation is placed as nearly as possible to the beginning of a word, however long. 
Into the historical proofs of any such system of accentuation ever having existed, 
of course only a profound student of the Vedas could enter. I am authorised, 
however, by Professor Max Muller and Professor Aufrecht to say, that the 
theory of Bopp is universally recognised as baseless ; and this is just what 
might have been expected. The mere assertion of such a principle to a man 
whose ears have been trained to a rich and various orthoepy is monstrous. If the 
accentuation of the first syllable, as in the well-known case of the Greek voca- 
tives of the third declension, Yldrep, "AttoXKov, and such like, may well be 
explained by the eager energy with which the call was made ; it does not there- 
fore follow either that eager energy is the only thing to be looked at in a good 
orthoepy, or that such oxytone words as ayadrj and #ed? may not be so enun- 
ciated as to carry an intense expression of energy to the ear of the hearer. Let 
this notion of Bopp, therefore, stand as only another instance of the great 
blunders to which great wits are subject, and which, as large experience teaches, 
are the natural consolation of the dunces. 

That variety is a necessary element of all aesthetic presentation of the highest 
order, needs no special proof. Variety is both an indication of wealth and a 
preventive of monotony ; and as such is no less a natural source of delight to 
the recipient of aesthetic pleasure than of just boast to the producer. 

Alles in der Welt lasst sich ertragen, 
Nur nicht eine Reihe von schoncn Tacjen 
says Goethe, 



280 PROFESSOR BLACKIE ON THE 

and what the Weimarian sage here says of beautiful days, is equally true of 
beautiful verses or of beautiful words. Hence arises the sure canon — 

That language is superior in point of accentual effect which gives no partial 
predominance to any one accentual place, but gives the rising inflexion free play 
over all the syllables of a word, so far as the range is consistent with a full 
vocalisation. Now, when we compare the Greek and Latin language by this 
rule, we find a decided and universally admitted superiority in favour of the 
Greek ; for this language admits of the acute on any one of the three last 
syllables, while Latin allows it to fall only on the penultimate and the antepen- 
ultimate. English, on the other hand, in this view, asserts one point of decided 
superiority over both the classical languages ; for words so accented as 
Idmentable and heritable, on the fourth syllable from the end, are not at all 
uncommon with us, while the Greeks and Romans, who had no such accents, 
fell into the very natural error of thinking that they were contrary to nature. 
But, though with help of this peculiarity we are able to marshal a much larger 
army of what the ancients called proceleusmatic feet in words than either Greeks 
or Romans, we have gained this small advantage at a great risk in point of 
general weight and majesty ; and we may be thankful to the graceful pedantry 
of our classical scholars, who, in retaining the penultimate accent of many 
Latin words, have done something to balance our habit of flinging the principal 
accent far back and skipping over the remaining part of the word. The next 
canon deducible from the test of variety is, that of any two compared languages 
that is the more rich and beautiful in respect of accent, in which the acute accent 
is placed not on the long syllable but on the short, so that, while the accent gets 
fair play in one syllable, the quantity stands out in another, and thus a richer 
and more various melody is distributed over every part of the word. For this 
reason such words as columbine, renegade, are more beautiful than glb'rious and 
victorious, engineer and volunteer, because in these last words, whether oxytone 
or proparoxytone, all the wealth of sound is spent upon one syllable, while the 
others remain comparatively weak and ineffective. On the same principle the 
Greek avOpamos is richer than the same word accented in the Latin way, 
auOpuiTos, and ' Apia-TO(f>dv7]<; is more beautiful than Aristophanes, if, as the English 
habit has generally been, the final es of the word is pronounced short. 

On the fourth principle, by which the comparative excellence of accents 
may be determined, I place very little value. No doubt, as languages, like 
buildings, are intended for use, convenience as well as theoretic excellence must 
be consulted ; but as utilitarian considerations have changed many an archi- 
tect's noble plan for a great building into a grand incongruity, so considerations 
of mere convenience have spoiled many a fine language. For convenience, 
really, in a great majority of cases, means haste and carelessness, or sloth and lazi- 
ness, and in all such cases proves eventually a hostile and destructive force acting 



PLACE AND POWER OF ACCENT IN LANGUAGE. 281 

against all excellency of organism in articulate speech. We shall only say 
generally, therefore, that it is always an imperfection in language when words 
are so accented as to produce a lumbering unwieldy heaviness in the march of 
syllables ; and we may say also that accents ought, if possible, to be so placed 
as to admit of suffixes or prefixes being added without changing the intonation 
of the word. In this view, contemplative is a more convenient accentuation 
than contemplative, because it admits of a substantive contem'plativeness, and an 
adverb contemplatively, being formed from it, without the necessity of either 
advancing the accent or allowing it to remain on the fifth syllable from the end 
of the new word, where its influence on the following syllables must naturally 
be feeble in proportion to their remoteness from the point of vocal energy. 

Of the effect of fashion and whim and caprice, in determining the accent of 
certain words, and even of whole classes of words, contrary to every principle 
whether of significance, euphony, or convenience, I say nothing, because such 
arbitrary freaks belong not to the domain of scientific knowledge, and are 
merely noticeable as casual aberrations or monstrosities. 

Such are the grand principles of the general doctrine of accents, so far as I 
have been able to discover them. It will be observed that they are based 
on a wide induction, and apply to Latin and Greek as well as to Gaelic or 
Italian. It is, however, a point which has been long maintained in the 
learned world, that the Greek accents have something altogether peculiar, and 
not peculiar only, but peculiarly mysterious about them, which prevents 
them from being used along with examples from any modern language as illus- 
trations of general propositions about accent. It is against this notion — a notion 
peculiarly English, and prevalent in high quarters — that I must proceed now 
to make a distinct and deliberate protest ; for, till it be removed, it will be impos- 
sible to say a single sensible word on the doctrine of accents, from which the most 
interesting language in the world shall not be withdrawn as an example. I pro- 
ceed, therefore, to show, both from the nature of the case and from the most 
authoritative evidence, that there is not the slightest ground for the imagination 
that accent in the classical languages meant anything substantially different from 
what it means in English, or Italian, or modern Greek ; and, as a natural sequel 
to this, I will trace the long course of scholarly opinion on the subject, from the 
doctrine of Erasmus to that of Professor Munro, Mr Geldart, and other English 
scholars ; and conclude by showing practically, what I have proved in the actual 
work of teaching, how all the strange contradictions of this singular controversy 
can be reconciled, and all the imaginary difficulties be made to disappear. 

As a foundation for all argument on this subject, we may assume — what no 
well-instructed scholar in the present state of learning will question — that the 
accentual marks now seen in every Greek book were first invented by Aristo- 
phanes of Byzantium, about 250 b.c, for the very same purpose that the marks 

VOL. XXVI. PART II. 4 D 



282 PROFESSOR BLACKIE ON THE 

of emphasis stand in our pronouncing dictionaries, viz., to ensure a correct 
orthoepy in the reading and recitation of the language. The assertion once 
boldly flung forth by the early opponents of Greek accents, that they were pro- 
perly marks of musical intonation, having nothing to do with spoken eloquence, 
can now be hazarded by no philologer. Whatever the accents meant, they 
were intended to direct the reading of prose ; had they been anything else 
indeed, it is impossible to understand how they ever found their way into 
the familiar notation of prose. But for the sake of those who may not be 
familiar with the evidence on which this point rests, we shall here set down 
the testimonies of two eminent grammarians : first, Dionysius Thrax, who 
lived at Rome about 80 B.C., and whose re^i? ypappaTLK-rj, quoted by Sextus 
Empiricus (Adv. Math., i. 12), has been recently printed in the second volume 
of Bekker's Anecdota (p. 629). This grave authority tells us that the art ot 
grammar, as it was then practised, consisted of six parts — 

1. avayvoxTLs ivTpijSrjs Kara irpoo-o&lav — assiduous reading, according to accen- 
tuation. 

2. Explanation of the meaning, according to the significance of the tropes 
used by the writers. 

3. Explanation of the historical facts and of the glosses or peculiar words. 

4. Etymology. 

5. Consideration of linguistical analogies. 

6. A critical appreciation of the work expounded, in its beauties and defects. 
Now, there can be no doubt here as to what Trpoacp&ia means ; for, though 

the plural of this word sometimes is used in a wider sense, as we talk of the 
Hebrew points, so as to include aspirations, pauses, quantities, and every affec- 
tion of which spoken and written words are capable, when used in the singular 
as a special technical term, it signifies accent, and nothing else. The second 
grammarian whom I quote is Theodosius, who lived in the time of the Emperor 
Constantine, and whose treatise on grammar was published by Goettling in 
the year 1822. This author, in the chapter (p. 58) entitled Trios XPV wayiy- 
vaxTKeLv, says that good reading consists in three things — 

1. vTTOKpiaris, dramatic expression, arising out of a sympathetic conception 
of character. 

2. rrpoo-oxtia — or reading Kara tov<; aKpLfieis tovows — according to the exact 
accents — irpoo-a&ia yap 6 tovos — for accent and tone, are the same. 

3. SiacTToXrj, attention to pauses and punctuation. 

Now, if any person further inquires whether the ancients did not read their 
prose according to quantity also, I answer that of this there can be no doubt ; 
but that the prominence in correct reading is naturally given to accent, because 
quantity is the specialty of poetry, and unless where we talk specially of poetry, 
by the word reading we are understood to mean prose. But that correct read- 



PLACE AND POWER OF ACCENT IN LANGUAGE. 283 

ing of prose included quantity also, is evident from what the same grammarian 
says a sentence or two below, viz., that under irpoo-G&la, in a wider sense we 
understand both accent and quantity, and in this wider sense correct prosodial 
reading arises e/c tov Trapa^vXarreiv tou? tovovs koll tov<; ypovows, from observing 
the tones and the times, and all the other affections of articulate speech. Now, 
as there was an uninterrupted succession of grammatical teachers, from the age 
of the Alexandrian Ptolemies to the time of the Roman Emperors, and from the 
establishment of the Eastern Empire by Constantine to the taking of Constan- 
tinople by the Turks, no historical fact can be more certain than this, that the 
living accentuation with which Greek was spoken in the great seats of learning 
and culture in the third century before Christ, and by which a just ortheopy in 
reading was determined, has been handed down to us in an unbroken chain of 
the most authoritative testimony. If this is not true, there is nothing now 
credited in the wide sphere of linguistic tradition that rests on a surer basis. 

If, then, the ancient Greeks both spoke and read by the rule of those 
accents which we now see on our printed books, what are we to understand by 
that accent ? Now, here the field of definition is happily well narrowed. That 
Greek accent did not mean quantity, every page of tradition on the subject 
distinctly testifies ; that it did not mean mere volume of mass of articulate 
sound is equally certain ; and no man, ancient or modern, ever dreamt that it 
did. There remain, therefore, under which it may fall to be subsumed, only 
the other two affections of articulate speech with which we started, viz., eleva- 
tion of tone and intensity of utterance. Greek accent must be either the one 
or the other of these, or both together. That it means the first, viz., elevation 
of tone, is plain from the mere terms ofus and /3apu<?, sharp and heavy, or high 
and low, by which the two familiar accents are designated. It is also distinctly 
stated by both Greek and Roman grammarians that accent implies change of 
tone in the voice, by alternate elevation and depression. The phraseology, 
indeed, of this matter was borrowed by the grammarians from the musicians, 
and had reference to the high and low notes in the musical scale, these minute 
speculators having justly observed that, as the voice in music rises or falls by a 
series of measured intervals, so in articulate speech it rises and falls by a suc- 
cession of slides, what our great orthoepic teacher calls the rising and falling 
inflexions. Either, therefore — the acute accent of the Greeks, which is the 
accent properly so called — means the rising inflexion of the voice on particular 
syllables of a word, or it means this, plus a stress or emphasis on a certain 
syllable of a word, produced by the greater force, or stretch, or tension of 
the voice on that particular syllable. Now that it does not mean elevation of 
the voice merely, but also, and at the same time, that greater stretch or tension 
of the voice which produces the emphatic syllable of a word, will, I think, be 
evident from the following six considerations : — 



284 PROFESSOR BLACKIE ON THE 

1. From the natural difficulty of elevating the voice, and not at the same 
time giving an increased emphasis to the elevated vowel ; or, may I not say, 
rather the natural impossibility — for, though it is certainly possible to give a 
great emphasis to a syllable, and keep the voice at a low key, that is to say, 
though stress does not necessarily imply elevation — it certainly does not seem 
very natural or very easy to raise the pitch of the voice without accompanying 
that high pitch with a certain emphasis. I may, for instance, pronounce the 
Greek word avarokq, with a stress on the last syllable, and yet with the 
whole pronounced in monotone ; but, if I raise my voice on that syllable, it will 
be difficult for' me to withhold from the syllable the stress which naturally 
accompanies the act of elevation. 

2. But that Greek accent implies stress as well as elevation is manifest 
from the natural and obvious meaning of the terms used by the grammarians 
in describing the phenomena of accent. For what does racris mean but stretch 
or tension ? and is it not quite plain that as contrary as light is to darkness, so 
contrary is eVtracrts to avecris, — i.e., intension to remission, strain to slackness of 
sound — the constant phraseology of the grammarians with regard to this matter. 
The word Kpovu^a, also signifying beat or strike, which is sometimes used, of 
the acute accent,"" sufficiently indicates its analogy to the emphatic note in a 
musical bar, which certainly does not signify elevation or depression. 

3. The analogy of the ictus metricus in rhythmical composition, suggested by 
the word Kpovcrfxa, supplies another argument to prove that the Greek and 
Roman accent meant stress as well as elevation. For there are some places in 
the poets where we can observe that a word naturally short is made long for no 
other reason that can be seen than that the spoken accent on the syllable 
favoured the poetical license, just in the same way that the rhythmical accent 
sometimes does. Mere elevation has no effect on quantity ; but stress or 
emphasis can easily be so manipulated by the voice as to pass over into a long 
syllable, or, to use the language of the grammarians, eViVao-is may become 
€ktol(ti5, intension may spread itself out into extension. 

4. That the acute accent meant stress is plain from the inherited intonation 
of the modern Greeks ; for accent is one of the most obstinate affections that 
belong to spoken speech ; and no man can hear such words as kcl\6 ttcuSC, 2ko7to, 
and Ylapvacrao in the mouth of the living Greeks without feeling that the dead 
mark on our books has here received its living interpretation ; and, if any per- 
son objects that the modern Greek not only acutes the last syllables of these 
words, but makes their quantity long, this is all in favour of my argument ; 
for the length arose and could arise naturally only from an exaggeration of 
that tension of voice which was the necessary accompaniment of the accent. 

* Theodosius, Goettling, p. 61 ; KpovariKorepa ycyvof^evrj rj \e£t? o^vvercu, Scliol. Dionys. 
Thrax. Bekker, ii. p. 690. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 285 

With regard to the modern Greek dialect generally, I would observe that 
though the place of the accent has been changed in a few classes of words, in 
the great majority of cases it has been retained ; and that in the case of cur- 
tailed words, as fids for ifxa<s, Trio-oi for ottlo-o), i//api for oxpdpiov, naiBi for iraiZiov, 
Bev for ovSev, &a, it is the stress upon the medial accented syllable which has 
secured its permanence after the initial or final unaccented syllable had 
dropped off. 

But the most incontestable proof that accent means emphasis lies in the 
doctrine of Enclitics ; for in Greek as in English there are certain little words, 
such as the pronouns or the negative no, which in common cases are purposely 
kept unemphatic, and pronounced so rapidly as to appear to lean upon {ijKkivoi), 
or be taken up by the previous or following word ; but the moment that the 
necessity of speech demands these words to become prominent, they receive 
the accent, and become emphatic. Thus we say, "give me the book," like datemi 
in Italian, as one word, but " give me the book," that is, give it to me, not to 
you. Now, there could not be a stronger fact than this to prove that Greek 
accent meant emphasis ; for this use of the acute accent to emphasize in 
particular cases otherwise unemphatic words is quite common, as, for example, 
in the case of the negative particle fxa Aia ovk eycoye, contrasted with ovtgjs Aeyeis 
rj ov, do you say so, or do you not ? 

6. Lastly, the analogy of the modern Italian compared with the ancient 
Eoman, plainly shows us both the obstinacy of accent as a fact in the life of 
language, and what accent really meant in ancient Rome and "Greece, as in 
modern Rome. For nothing is more certain than that, though its special laws 
were different in the two learned languages, accent, as an accident of articulate 
speech, did not mean one thing in Greece and another thing in Borne ; but 
the Greek and Latin accent were in their nature and operation identical ; so 
that what is predicated of the essence of the one must be considered as predicated 
of the essence of the other. If, therefore, the modern Italian accent, in its position 
and power so evidently identical with the old Latin, possesses the element of 
stress as a prominent feature, it is a legitimate conclusion that the Greek accent 
did so too. Altogether, it may be remarked as a very extraordinary fact, and in- 
dicative of the operation of some strange deluding prejudice, that, while the most 
formidable artillery of erudite arguments have been brought to bear against pro- 
nouncing Greek with Greek accents, no learned Latinist has yet written a book 
to prove that Latin ought not to be pronounced with Latin accents. When 
reading Latin we put the stress on the accented syllable exactly where Cicero, 
and Quinctilian, and Priscian say it was placed ; but the moment a Hellenist 
gives the natural predominance to the accents which he finds marked on his 
books, he is immediately told that accent does not mean stress, but means some- 
thing that no man can understand or make use of. Whence this inconsistency ? 

VOL. XXVI. PART II. 4 E 



286 PROFESSOR BLACKIE ON THE 

Having thus proved, by what may surely seem sufficiently strong arguments, 
that accents mean nothing in Greek, which they do not equally mean in Eng- 
lish, or Latin, or Italian, there remains only to take a bird's-eye view of the 
somewhat remarkable literature of this subject, from the revival of letters 
down to the present hour. Such a review will at once be the best justification 
of the principles above set forth, and will place vividly before the reader the 
partial and inadequate points of view from which the opposing doctrines have 
taken their rise. 

Now, in tracing the stream of confusion which this matter exhibits to its 
fountain head, it is most natural that we should, in the first place, turn to 
Erasmus, both because he was the most prominent scholar of European reputa- 
tion in the eventful age to which he belonged, and because it is quite certain that 
before his time no learned man ever dreamt or could have dreamt of disown- 
ing the pronunciation of the Greek language, which Europe had received as a 
common legacy from the Constantinopolitan Greeks. The early scholars, indeed, 
were occupied with matters of far more serious import than the exact accen- 
tuation and quantification of syllables. They read the Greek books for the 
information they contained : Herodotus for history, Strabo for geography, 
Thucydides for political wisdom, Plato for philosophy, Aristotle for science. 
So long as this appetite for the stores of Hellenic thought and knowledge was 
the one thing needful, no man had either leisure or desire to put curious ques- 
tions to himself with regard to the auricular luxury of a just orthoepy. 
But the time' must come when this matter also would be examined : Homer 
and Sophocles could not be read in their mother tongue by men who used 
their ears as well as their eyes, without provoking questions as to the best 
method of bringing out the full music of that most musical of human languages 
which it was the happy fortune of these great poets to employ. If Greek was 
the language of the gods, there seemed a manifest impiety in allowing it to be 
enunciated by a confused, degraded, and irrational elocution. And, if such 
questions were to be raised, Erasmus was precisely the man, who, from his fine 
genius, cultivated taste, and broad human sympathies, was best fitted to raise 
them. Accordingly, in the famous dialogue, " Be recta Latini, Grcecique 
sermonis pronuntiatione," published at Basle in the year 1528, the whole subject is 
brought under review ; and the text of his discourse is in the broadest terms, that 
" nunc totafere pronuntiatio depravata est tarn apud Grcecos, quam apud Latinos " 
and this is proved in a very exhaustive style in an argument extending to above 
two hundred pages. The powers of the different letters are critically discussed, 
and the relation of accent and quantity illustrated both by learned rules and 
by living examples. With regard to the vowel sounds, which is the first point 
handled, he had an easy task to prove that the slender sound the characteris- 
tic of the Byzantine Greeks could not have been the original sound of so 



PLACE AND POWER OF ACCENT IN LANGUAGE. 287 

many distinct vowels and diphthongs. Signs of different vowels were certainly 
not made originally to confound, but to distinguish. The confusion in this case 
is always of a later birth. What Erasmus, however, failed in here, and what, 
from want of materials, he could not but fail in, was to show at what period 
this confusion commenced ; for, as the most polished nations in modern times 
display in their speech abnormal tendencies and depravations of all kinds, 
which are consecrated by usage and fashion, so there is no reason why the 
itacism of the theologians of Byzantium should not have been practised by the 
philosophers of Alexandria, and even, to a certain extent, by the orators of the 
Periclean and Demosthenic age. However, this was not curiously looked into ; 
and the result was that, by this assault of Erasmus, the faith of scholars in the 
orthoepic traditions of the Byzantine elders was shaken in all the most learned 
countries of Europe, and every nation set up vocalizing Greek according to 
what seemed good in its own eyes. Hence the motley babblement of Greek 
which now prevails. The old foundations were removed before the ground was 
opened, or the materials ready, to make new ones. And thus it has happened 
that an orthoepic reform, well intended, and in so far conducted on rational 
principles, has issued in an extremely irrational and altogether unsatisfactory 
result. So much for Greek vocalisation. With regard to that other matter 
with which we are specially concerned here, we do not find, what we might per- 
haps have expected to find, that the great modern innovation of disowning Greek 
accents in reading Greek, receives the slightest countenance from Erasmus. 
On the contrary, part of the bad pronunciation which it was his object to reform 
was precisely the ignorance or loose observance of the proper accents in Greek 
and Latin, according to the characteristic laws of each language. He saw also 
everywhere amongst careless, tasteless, or ignorant speakers, that confusion of 
things so distinct as accent and quantity, which from the same causes prevails 
so largely at the present day. Scholars still tell you that accent and quantity 
annihilate each other, and cannot both be observed, meaning only, in fact, that 
for their particular ill-tutored and perverted auricular organs, it has become 
difficult, and is perhaps impossible. It certainly is impossible for a sharp, hard 
Aberdonian to speak with the rich silvery mellowness of a high-bred English 
lady ; but the difficulty lies in bad habit, not in Scottish nature. On the super- 
induced habitude which erudite ears have so often displayed in not being able 
to distinguish accent from quantity, there is a passage in the Erasmian tractate, 
which we shall be excused for inserting at length : — 

" Sunt quidam adeo crassi, ut non distinguant accentum a quantitate, quum sit 
longe diver sa ratio. Aliud est enim acutum, aliud diu tinnire: sicut aliud in- 
tendi, aliud extendi: quanquam nihil vetat eandem syllabam et acutum habere 
tonum, et productum tempus, velut in vidi, et legi prwteritis. At eruditos novi, qui, 
quumpronunciarent Mud avexpv koX anexpv, mediam syllabam, quoniam tonum habet 



288 PROFESSOR BLACKIE ON THE 

acutum, quantum possent producerent, quum sit natura brevis, vel brevissima 
potius. Etfere qui Grceca legunt, accentus observatione confundunt spatium mora?, 
sic enunciantes pevekaos, quasi penultima sit brevis, et jxev£>7)ixo<; quasi duo? postre- 
ma? sint breves, quemadmodum in deoScopos TrapaKk-qTos, etSwXa, aliisque innumeris. 
Nee ita multis contingit sonare Grceca, ut accentuum simul et morarum rationem 
observent, vel in carmine. Loquor autem non jam de vulgo, sed de eruditissimis 
quoque. Minus est erroris in Latinis, sed tamen illic quoque tonus acutus ac in- 
flexus obscurat coeterarum sonum, ut in videbimus, congruit accentus cum quanti- 
tate, at in legebamus, sola penultima videtur esse producta, quum secunda sit ceque 
longa : in amaveVimus sola antepenultima, quum ea sit brevis, secunda producta. 
LE. Omnino sic obtinuit usus, quern dediscere difficillimum est. UR. Atqui qui 
degustarunt musicam, nullo negotio distinguunt inter longam, brevem, et inter acu- 
tam et gravem. Nihil enim est aliud pronunciatio, quam modulatio quondam 
vocum numerosa. Est enim et in oratione soluta pedum ratio, licet non perinde 
certis astricta legibus ut in carmine : qua? si confundatur, non magis erit oratio 
quam cantio in qua graves cum acutis, longa? cum brevibus tenure confunduntur. 
Unde quidam priscorum grammaticorum non inscite dixerunt, accentum esse ani- 
mam dictionis. Et tamen hodie talis est etiam eruditorum pronunciatio, qualis 
esset ilia ridicula cantio. Scis opinor canere cithara. LE. Utcunque. UR. 
Nonne frequenter imam chordam pulsans producis sonos, et summam tangens 
brevibus insonas aut contra ? LE. Frequenter, quanquam hoc discrimen eviden- 
tius est in flatili musica. UR. Unde igitur nos sumus usque adeo a/xovcroi, ut 
omnes acutas syllabas sonemus productiore mora, graves omnes corripiamus ? Vel 
ab asinis licebat hoc discrimen discere, qui rudentes corripiunt acutam vocem, 
imam producunt. LE. Ldem propemodum facit cuculus." 

The only other interesting point, with regard to the present matter, which 
requires to be mentioned here, is that Erasmus distinctly teaches that verses, 
both in Greek and Latin, are to be read with an accurate observance both of accent 
and quantity. The difficulty and alleged impossibility of doing this, so much 
spoken of by modern scholars, he supposes to arise only from the gross neglect of 
the art of elegant reading in modern education. How far he is right in apply- 
ing the spoken accent thus sweepingly to the rhythmical recitation of poetry, 
we shall have occasion to consider afterwards. 

But what to the fine genius and well-trained ear of Erasmus presented no 
difficulty, to the gross majority who take everything without discrimination in 
broad masses was so formidable, that they do not even seem to have had the 
courage to look the difficulty in the face, but quietly settled down into a habit 
of confounding accent and quantity, and making all accented syllables long. 
This is distinctly mentioned by the next champion in the field, Adolph von 
Meetkerche (vulgarly Mekirch), a Flemish nobleman, born at Bruges in the 
very year when Erasmus' book was published, and well known in high circles 



PLACE AND POWER OF ACCENT IN LANGUAGE. 289 

in England, from his having lived and died at London as an attache* of the 
Belgian ambassador at the court of Elizabeth. He was, besides an able diplo- 
matist, an accomplished scholar, and in the year 1576 published a Discourse " de 
vera et rectd pronuntiatione linguae Greece"* which seems to have given the first 
impulse to the paradoxical movement which caused the Greek accentuation, so 
laboriously preserved by the Alexandrian grammarians, to be thrown overboard 
in the general practice of scholars, and the vulgar Latin accentuation substi- 
tuted in its place. The principal part of this work is occupied with the ques- 
tion which then loomed most large, whether the Byzantine vocalisation should 
be retained, or a reformed one introduced, as suggested by Erasmus ; but, in a 
short appendix, the doctrine of accents is stated succinctly, and, what is more 
important, the author's practice with regard to their observance. In the first 
place, he tells us the important fact that, in his day, Greek was so read by 
many, confounding accent and quantity, as altogether to destroy the perception 
of any poetical rhythm. " Manifestos est eorum error qui tonos cum temporibus 
confundunt, ita ut qucecunque acuenda vel Jlectenda est syllaba, earn producant : 
qucecunque deprimenda vel cequabiliter pronuncianda, earn corripant. Ex quo Jit 
ut in Grcecd oratione vel nullum vel potius corruptum numerum intelligas, dum 
multas breves producuntur, et contra plurimce longce corripuntur ; ut pcene prcesti- 
terit Groeca vel Latina non legere quam ita /cede depravare" (p. 175). And no 
wonder ; if, as he says, the accent was allowed such a power that, in the second 
line of the Iliad, zd-qKtv was read as a dactyle, and the two final syllables of 
ovXofxevrjv as a spondee. And then he tells us of a general practice of school- 
masters, which by the way prevails in England almost universally to the present 
hour. " Solent enim pcedagogi vulgo ita suos erudire ut in omnibus dissyllabis 
penidtimam producant." Just as in Eton and Harrow the boys had, till very 
recently, if indeed they are not still, taught or carelessly allowed to say, bonus, and 
not bonus. He then goes on to show how this practical assumption that a penul- 
timate accent must necessarily lengthen the vowel has no foundation in the real 
nature of accent and quantity, of which the one expresses the quality of the 
sound, the other the dimensions. And then anticipating an objection often 
made in modern times, he goes on to say, " Neque tamen nego brevi syllaba? 
temporis aliquid accedere, quando acuto signo signatur, quantum scilicet necesse 
est in acuenda syllaba consumi ; $ed, ut minus sit brevis quam antea, minime tamen 
consequitur habendam esse pro longd, sicutab Us habetur qui malus arbor em a malo 
adjectivo non distinguunt" (p. 178). This is exactly what Erasmus had said ; and 
one should think it would be sufficiently patent to all ears, except those of stupid 
schoolmasters, careless schoolboys, and bookish scholars, whose learning is all in 
their eyes, and not in their ears. But things easy in speculative thought become 
in the hasty practice of life, sometimes tolerably difficult ; and, in fact, a just 

* Reprinted in " Havercamp's Sylloge." 1736. Vol. i. p. 9. 
VOL. XXVI. PART II. 4 F 



290 PROFESSOR BLACKIE ON THE 

and true pronunciation, even in the case of the mother tongue, is not attainable 
without a certain amount of trouble. Meetkerche accordingly finds that 
his argument for accents, however just, is liable to be met with the objection 
which nullified so many of Solon's well-conceived legislative reforms. The 
laws were no doubt very good, but they were too good for the people. The 
best for them was not the best absolutely, but the best which they could endure. 
"At enim," he continues, " dices, ista (i.e., the right pronunciation both of quan- 
tity and accent) esse perdifficilia, etfortassis etiam dSvvara, Us quidem qui diversce 
pronuntiationi assueverunt. Id ego vero fateor, et in me ipso non invitus agnosco. 
Sed nihil vetat rectam viam aliis ostendere, etiam ut illam ingredi non possis. 
Certe Veritas mihi dissimulanda non fuit, ut paullatim meliora probare et sequi 
condiscamus. Ergo, ut libere dicam quod sentio, vel tonos prorsus sublatos esse 
velim, tantis per dum depravata ilia pronunciatio tonorum pro temporibus emen- 
detur (quum prcesentim veteres constet istos apices in scribendo non usmpasse) vel 
nullam eorum rationem haberi."* Which simply means that he is in favour of 
suspending the operation of Greek accents till such time as schoolmasters — 
proverbially not a very teachable race — shall have learned to distinguish 6s, a 
bone, from 6s, a mouth, and that cctn'o is a possible combination of articulate 
sounds, as much as caiv'no or caeno. 

The next important work which falls to be noticed indicates plainly by its 
title — " De Poematum cantu et viribus Rhgthmi;" Oxon. 1673 — from what 
quarter the attacks of a section of the learned world were now to be directed 
against the traditional sway of Greek accents. The author of this tract was 
the celebrated Isaac Vossius, " unquestionably," to use the words of Markland, 
" a very learned man, but whose whimsicalness and love of paradox scarce 
leaves room for him to be considered a reasonable one."t Vossius, like Meet- 
kerche, had got his ear possessed with a genuine living appreciation of the 
beauty of measures and rhythm in poetry, which justly resented the barbarism 
of those scholars who read ancient verse by accents, just as if it was so 
much German or English verse. In expressing his indignation strongly against 
these systematic murderers of the regal majesty of Latin, and the luxu- 
riant swell of Greek verse, Voss did well ; but, when he went farther, and 
not content with the interim act of suspension passed by Meetkerche, 
stood up in violent revolt against the whole .accredited system of accentua- 
tion in the Greek language, and cast it, to save the ship, like a Jonah 
overboard, he committed a great mistake, and kicked vehemently against 
the pricks, where he could only wound his own legs. He declared roundly that 
the whole system of Greek accents, as we now have them, was a modern 
invention, or, at least, a corruption, or a monstrous compound of both ; 

* Havercamp's Sylloge. Ludg. Bat., 1836. Vol. i. p. 179. 

t Letter to Foster in the Essay on Accent and Quantity. 3d edit. London, 1820. P. 207. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 291 

that accents were originally musical marks, and had nothing to do with 
the pronunciation of the language ; that the best proof of this was the un- 
rhythmical jar which they produced, when actually applied to the recitation 
of verse, whether Greek or Latin ; and that therefore the only course left to the 
scholar of taste was to disregard them altogether, and use only such accent as 
was manifestly dictated by the march of the metre. While, however, this 
ingenious scholar found it comparatively easy work to pronounce a dictatorial 
sentence of eternal exclusion against Greek accents, of which few had any real 
knowledge, he found himself obstinately met by an obvious objection from the 
familiar practice of the Latin tongue, which, while it distinctly disowns (except 
in a very few exceptive cases) all oxytone accentuation, nevertheless, in verse, 
constantly uses an emphasis, which falls with marked effect on the last syllable 
of one or more words in the verse. In answering this objection, Voss fell upon 
an aspect of the case, which, if he had applied it to Greek poetry, might have 
saved him from the trouble of beating vainly against the strong bulwarks of 
Alexandrian and Roman and Byzantine tradition in the matter; for he distinctly 
says that singing is one thing and reading another, and that the Romans may 
have followed a different law of accentuation with regard to each. " Quare non 
qiddem multum refragabor, si quis in recitatione Latinorum poematum ultimas 
syllabas unquam productas fuisse negaverit : sed vero in Cantu id ipsum fieri 
potuisse si quis contendat, idem etiam merito affirmet et Latinos canere nescivisse."* 
Close upon the traces of Vossius comes a German, Henry Christian Hennin, 
whose work entitled " 'EXA^ta-joto? dpOcpSos, Traject ad Rhenum, 1684," with a 
great flourish of trumpets on its title-page, proclaims itself to prove " Grcecam 
linguam secundum accentus, ut vulgo ab omnibus hucusque fieri consuerit, pronun- 
ciandam non esse." The inspiration of this book — for it is full of fervour and 
emphasis, and a sort of lofty protestation — manifestly is the same as that of 
Voss' treatise ; a certain school of scholars with whom the writer had been 
familiar, or it may be all the scholars of his time and place had got into a habit 
of sacrificing the rhythmical recitation of Greek poetry to the traditional accen- 
tuation of Greek prose, a usurpation, no doubt, of a most gross kind, and which 
it was obvious to think could best be got rid of by not only dethroning the 
usurper and telling him to keep to his proper place, but by killing him outright, 
and casting him down among the dead men with a triple volley of curse and 
execration. It was a procedure akin to that in political history, when democracy 
dethrones despotism, and acts ten times more despotically than the tyrant whom 
it overthrew. In conducting his indictment against the accents, the author com- 
mits in the outset the very transparent blunder of confounding the marks of the 
accents in printed books, with the living accents in the mouth of the people who 
spoke the Greek language. These marks, whether present or absent in books, 

* Deviribus rhythmi, p. 44. N.B. — By productas in this passage he evidently means accented. 



292 PROFESSOR BLACKIE ON THE 

do not in the slightest degree affect the question ; they do not exist in English 
books, and yet English words have a well-known accent in the voice of the 
English people, and as made visible artificially to the eye in the pronouncing 
dictionaries of Walker and other orthoepists. The next great error made by 
Hennin lies in the theory — for it is a mere baseless theory — that the accents were 
invented by Aristophanes of Byzantium, for some purpose quite different for that 
which they now subserve. This is simply to leap over the testimonies of the 
most learned Greek grammarians from the time of the Alexandrian scholars to 
the taking of Constantinople by the Turks. And in order to make such a 
hypothesis possible and even plausible, he draws a flaming picture of the 
barbarism which corrupted the Greek language at a fever pace from the 
Roman to the Turkish conquest. All this, however, is purely imaginary, as any 
person who has looked even superficially into Byzantine literature must con- 
fess. Whatever changes in the course of time naturally might take place in 
the spoken language of the Greeks, the last element that would be touched by 
the change was the accentuation ; and that not only from its own natural 
obstinacy, but from the very fact that the proper place of the accent visible in 
most written books presented a stereotyped norm, that checked all arbitrary 
deflexion in the start. Any other arguments that make a parade in Hennin's 
book are based on the fact of which we hear so much in these days, that certain 
persons could not pronounce avOpoi-rros without saying avOpoTros, and certain 
other persons imagined that it was impossible to do so. After overleaping 
heroically the bristling fence of historic testimony on the matter, the author 
proceeds to lay down four rules of accentuation, which, both in the Greek and 
Latin languages are, " sine alld exceptione ceternce veritatis" These rules are 
as follows : — 

(I.) " Omnis vox monosyllaba modulationem habet in sua vocali ut 0&Js, vov%, 
mons, pons." 

(II.) Omnis vox dissyllaba modulationem habet in syllabd priori, ut Xo'yoi, 

OOOL, <p(t)V7]. 

III. " Omnis vox polysyttaba penultimam longam modulatur ut avOpco-rros 
TVTTTcoixev, Grcecorum, jucunda, Romanorum. " 

IV. " Omnis vox polysyllaba, penidtima brevi, modulatur antepenidtimam ut 
d6minas, dXoyov." 

This is certainly one of the most cool pieces of insolent one-sided dogmatism 
that the history of learning presents, the whole affair being simply an assertion 
that the particular method of accentuation in the Latin language, which the 
author had inherited from secular and ecclesiastical Rome, should be stilted up 
into an eternal norm of accentuation for all languages, while the most plain and 
obvious facts, both in ancient Greek and modern English, which contradict the 
theory are held as non-existent, and excluded from the calculation ; an instructive 



PLACE AND POWER OF ACCENT IN LANGUAGE. 293 

example of the truth of Goethe's remark, that truth is often disagreeable to us, 
because it limits the despotic sweep of our one idea, while error is grateful for 
this, above all other reasons, because it prostrates fact and thought and 
history before the triumphant march of our infallible conceit. 

It was not to be supposed that the sweeping dictatorial dogmatism of this 
book of Hennin, backed as it substantially was by the high authority of Voss, 
would pass without comment from the learned of the Continent ; and accordingly 
we find that in the year 1686 it received a long and able reply from John 
Rudolph Wetstein, professor of Greek in the university of Basle. Wetstein's 
book, by an overwhelming array of historical testimony, enforced by sound 
argument, demonstrates the utter untenableness of the proposition of his 
adversary, unwarrantable equally in the wholesale swamping of the Greek by 
the Latin accent, and in the elevation of this latter into a rational norm of 
accentuation, by which the excellence of all articulate speech is to be measured. 
With regard to the main difficulty which had staggered Meetkeeche, the Basle 
professor quietly reminds his antagonist, in the words of Quinctilian, that the 
recitation of verse is in many respects different from the speaking of prose, 
" imprimis lectio virilis et cum suavitate quddam gravis, et non quidem prosw 
similis, quia carmen est." 

The infection of this notable dispute now comes to England, and the first 
oracle to whom we feel inclined to propound the question for solution is, of 
course, the great Bentley. This massive and masculine scholar, in the short 
treatise on metres prefixed to his edition of " Terence," has the following 
passage : — " Tarn vero id Latinis comicis, qui fabulas suas populo placere 
cuperent magnopere cavendum erat ne contra linguae genium ictus seu accentus in 
quoque versu syllabas verborum ultimas occuparent. Id in omni metro, quoad 
limit, observabatur ; ut in his 

' Ar'rna vinimque cano, Trojae qui primus ab oris, 
Italiam fato profugus, Lavinia venit 
Litora ; multum ille et terris jactatus et alto 
Vi siiperum, saevae memorem Junonis ob iram.' 

Qui perite et modulatae hos versus leget sic eos, ut hie accentus notantur, pro- 
nuntiabit, non ut piteri in scholis, ad singulorum pedum initia ; 

Italiam fat6 profugus, Lavinaque venit, sed ad rhythmum totius versus. " 
Now, it in no wise concerns us to discuss the value of the remark here 
made as to the practice of the Latin poets ; that is a delicate matter, we believe, 
not so easily settled as the stout Cantab seems to have imagined. The only 
significance of the passage for our present inquiry is, that the writer believed that 
in some way or other the structure of Latin verse was regulated by a regard to 
the spoken accent, and not simply by the law of quantity and the metrical beat, 

VOL. XXVI. PART II. 4 G 



294 PROFESSOR BLACKIE ON THE 

What truth there may be in this notion will appear in the sequel ; meanwhile 
it is quite plain that it leaves the matter in a state of considerable uncertainty, 
an uncertainty which is not at all diminished by the unquestionably rash 
assertion in the letter to Mill, that Greek accents were an invention of later 
times, which could only mislead the accurate scholar.""" An obiter dictum of 
this kind, even from a Bentley, on a confessedly difficult question, cannot be 
regarded as having any real weight. It may, however, along with other causes, 
have contributed to produce that strange aversion to Greek accentuation so 
characteristic of English scholarship. 

We now advance by a long stride into the middle of the great battle of 
accent and quantity that was fought in this country about the middle of the 
last century. The protagonist of this warfare is the Rev. Henry Gally, a 
Kentish Doctor of Divinity, and chaplain to His Majesty King George IT. 
His dissertation against Greek accents was first published in the year 1754, 
seventy years after the famous works of Henninius and Wetstein ; and quite 
recently on the back of two treatises on the same subject, which had appeared 
in Rome.t Dr Gally wrote, quite aware of the achievements of his predecessors, 
but convinced that their attempts to untie the Gordian knot were unsatisfactory, 
and that his own method was altogether new and original ; and so it is, no 
doubt, in some things, but novel only in the daringness of its assertions and the 
glaringness of its absurdity. Its absurdity consists mainly in the writer's 
belief that he can overturn the whole principles and practice of the Greek 
accentuation, by simply saying that it is irrational and absurd, as if some 
famous philosopher, some thousand years after this, when the English orthoepy 
may have become a field for learned debate, were to say that Macintosh and 
Mac'Intyre could not have been pronounced with the accent on the first syllable, 
because it is irrational to place the accent on the common element of the Mac, 
instead of on the distinguishing element, the clan; which rational method of pro- 
nunciation, as above remarked, exists not only in all the other Macs, but in all 
the Saxon names ending in son, as An'derson, Peterson, not Anderson , Peterson. 
A writer belonging to a people whose pronunciation is in all points so various, 
so arbitrary, and so dependent on fashionable caprice as the English, might 
surely have spared himself the inconsistency of such an argument. In the 
other parts of this learned divine's book we find merely a repetition of what had 
been said by Meetkerche, Henninius, Vossius, and others. Accents, we are told, 
were entirely musical, and had nothing to do with the intonation of colloquial 
speech : then it is broadly asserted that accent necessarily constitutes quantity, 

* " Eotse accentuum quorum omnis hodierna ratio prsepostera est atque perversa." Works by 
Dyce, vol. ii. p. 362, 

f (1) Sarpedonii dissertatio de vera Atticorum pronunciatione. Romae, 1750. (2) Velaste disser- 
tatio de literarum Grsecarum pronunciatione. Romae, 1751. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 295 

and therefore must be wrong ; and that, whatever the advocates of accents 
might preach in theory, in practice they never did, because they never could 
observe the accents without destroying the quantity. This practical difficulty 
is, in fact, the gist of his whole treatise, as is manifest from the very notable 
words with which he concludes : — " If, therefore, we would observe uniformity, 
and keep to what we can safely rely on, we must not admit of any use of 
accents in the pronunciation of the ancient Greek language but what is con- 
sistent with quantity ; and if we have lost the nicer part of the ancient pronun- 
ciation, we have the more reason to adhere to the essential part which still 
subsisteth." And this way of putting the case, viewed as an argumentum ad 
hominem addressed to the great mass of the English scholars and teachers, is no 
doubt perfectly just ; for these gentlemen had got into a monstrous and irrational 
habit of writing Latin and Greek verses with much labour and wonderful 
dexterity, by help of their understanding only, against the verdict of their 
ears, and treated both accent and quantity as an affair of dead rules, not of 
living vital action." 

But English scholarship — whatever might be the absurdities of professional 
pedagogy — was not destined to surrender one of the strongholds of venerable 
philological tradition at the trumpet-blast of such a windy dogmatist as Dr 
Gally. In the year 1767, a reply to his pretentious heresy was sent forth from 
Eton, by Foster, in which, so far as the learning of the subject is concerned, 
he showed himself as superior to Gally as Wetstein was to Henninius. 
He proved, beyond all possibility of denial, that accent had always been a 
recognised element in Greek orthoepy, and was in no sense the barbarous 
creation of a decadent age and a degraded taste. He stated also most distinctly 
that, while elevation of tone was the most characteristic element in Greek 
accent, it also necessarily included the element of stress — which Dr Gally also 
saw clearly — but that this stress or emphasis was in no case to be confounded 
with the length or duration of syllables. Hence, indeed, the great superiority 
of his argument to that of the Kentish D.D. ; for he not only maintained that 
accent was not to be confounded with quantity, but that, from the very nature 
of the case, the intense energy of the acute accent might, in many cases, have a 
tendency to shorten rather than to prolong the emission of breath by which it 
was enunciated.t With regard to the main difficulty, however — the practice of 
the theory, which, as we have seen, was the stumblingblock of Dr Gally — he 
does not seem to advance the matter far. Hear his words : — 

" Nor let it be said, if we should retain these sounds, we can never apply 

* On this notable inconsistency of those champions of quantity who denounce accent, Mr Foster 
is justly severe ; ch. x., on accent-quantity. 

\ On this point he produces a remarkable passage from Suidas, in voce o£u, vol. ii. p. 1136. 
Bernhardt. 



296 PROFESSOR BLACKIE ON THE 

them to their proper use in practice. Who can affirm that with certainty \ An 
English voice was capable of doing this in the time of Henry VIII., and why 
not now ? Sir John Cheke declares it not only practicable, but that it was 
actually practised, and that he knew many persons who could express these 
sounds consistently with accent and quantity perfectly well. I know one 
person who, after a few trials, is now able to do the same." By this one 
person, the reader will naturally suppose that he means himself, though it is a 
pity he did not say so in a manner that could not admit of ambiguity. But who- 
ever the individual might be who in the year of grace 1761 had solved this 
easy vocal problem, curiously imagined to be so difficult, schoolmasters who 
sinned against this high ideal of classical recitation might well reply, that to 
attempt to indoctrinate the ears of schoolboys with such delicate distinctions 
would prove as hopeless as to bring out the beautiful harmony of one of 
Handel's operas from a hurdy-gurdy. On another point also, Foster's Essay, 
though victorious against Gally, did perhaps more harm than good to the 
question of orthoepic reform in the great schools. He does not always suffi- 
ciently distinguish between the emphasis, or stress, or intensity of utterance, 
which he rightly considers to belong essentially to accent, and the prolongation 
of sound with which that intensity may sometimes be accompanied. Hence he 
speaks of the effect of the accent in English being habitually to lengthen the 
syllable ; whereas, if we attend to our ears, words like vdjy'id and rap'id, are just 
as common in our language as po'tent and pa' tent, and no person feels himself 
under any tendency or compulsion to assimilate the pronunciation of the first 
two words to that of the other pair. 

Three years after the appearance of Mr Foster's Essay, the " Accentus 
Redivivus" of Primatt appeared, the title of which seems sufficiently to indicate 
that in England at least Meetkerche, and Voss, and Gally, had practically 
won the day, and that accents had retired from the schools, and even from the 
typographic theatre in Oxford ; for in the year 1759 an edition of Aristotle's 
Rhetoric, without accentual marks, had appeared under the imprimatur of 
Thomas Randolph, Vice-Chancellor of the University. How many more 
Greek books, in the same nude fashion, may have issued from the same quarter 
about the same time, I do not know ; but there was certainly just cause for the 
champions of accents to take the alarm ; and so Mr Primatt marched forth, an 
accentual cataphract, bristling all over with Alexandrian and Byzantine erudi- 
tion, through which it was impossible to pierce him. In his learned work, he 
first shakes himself free from the notion flung out by Vossius, and the extreme 
men of the rhythmical party, that accents, however they might have been 
observed afterwards, were originally a musical, and not an orthoepic notation. 
He then shows, by a long historical deduction, that the reading of Greek prose 
always was accentual, and that nothing can be more illegitimate than to 



PLACE AND POWER OF ACCENT IN LANGUAGE. 297 

transfer to prose the laws of quantitative rhythm, which belong to poetry. But 
in this second proposition unfortunately, he is only half right, and entangles 
himself and the whole subject in a network of the most hopeless confusion ; 
for, in defining accent, besides asserting with Fostee, that there is an over- 
bearing tendency in English to lengthen all accented syllables, and an invariable 
rule in Latin to accentuate long penults, he lays it down in the strongest terms 
that the acute accent necessarily lengthens the syllable on which it falls, 
and that, in fact, when properly read, every accented syllable in Greek prose is 
long. Nay, more, so confused are his ideas on the whole terminology of the 
subject which he treats, that he actually tells us "we can hardly read a verse 
in Viegil or Homee in which the rhythm does not more than once break in upon 
the quantity" (p. 157), a sentence which, according to the usage of all who 
write intelligibly on such subjects, is pure nonsense, or true only of such 
accented verse as we have in English and other modern languages. This ex- 
traordinary confusion of two things by the ancient grammarians, kept so 
distinct as accent and quantity, rendered his whole discourse nugatory. To 
accept accent according to this theory was to make a formal transference of 
quantity from one syllable to another, and to acquire a habit of reading prose, 
which, in the point of quantity, would require to be reversed the moment a 
scholar threw down Plato, and took up Sophocles. In a country where the 
most elegant scholars, under the guidance of such a Titan as Bentley, had 
already begun to look with a curious preference on everything connected with 
metrical composition, such a startling doctrine could not be expected to make 
converts. 

After these violent but practically ineffective efforts, the great strife about 
accents in England stopped for thirty years, when in the year 1796 another re- 
markable combatant entered the lists in the person of Samuel Hoesley, one of 
the most notable of the singular army of erudite polemical bishops of which 
the Anglican Church has been so fertile.'" Into the weakness and utter mi- 
tenableness of the received method of reading Greek in this country the Bishop 
casts a piercing eye, and with an outspoken emphasis calls black black, and 
white white in the matter, after a fashion to which it might have been expected 
that in a country where the Church has so much to say in the school, some 
serious attention might have been given. " A practice" he says, " is adopted 
in this country of reading Greek verse with the Latin accent, and this is most 
absurdly called reading by quantity ; and having adopted this strange practice of 
reading one language by the rules of another, it is not unnatural that we should 
wish to prove the practice right" (pp. 26, 27). This is indeed hitting the nail on 
the head ; but the strange practice, like many strange things in England, still 

* On the Prosodies of the Greek and Latin Languages. Lond. 1796. The author's name was 
not given on the title page. 

VOL. XXVI. PART II. 4 H 



298 PROFESSOR BLACKIE ON THE 

continues, and we still make ourselves ridiculous by awkward endeavours to 
prove that what is altogether unnatural and monstrous is justifiable and even 
beautiful. How is this ? Not only, I believe, because the patient was self- 
willed and obstinate, but because the physician who pronounced a most scien- 
tific diagnosis of the disease had not the sagacity to discover the proper cure. 
He suggested a cure more flattering to his own ingenuity than true to the 
state of the case, or beneficial to the patient. He was as original as Dr 
Gally, in a more subtle indeed, but not in a more practical way. Gally's 
originality, as we have seen, consisted simply in calling everything on the doc- 
trine of Greek accents irrational and absurd which was contrary to his 
orthoepic habits or fancies, and nonsuiting it, without more ado, as a defaulter in 
foro rationis. Horsley, with that respect for historical fact and erudite testimony 
which became a bishop and a theologian, admitted the doctrine of accent in its 
full weight, as an element of which no sane reasoner on the matter of Hellenic 
orthoepy could get rid ; but, in order to explain its operation as part of the 
harmony of Greek verse, he invented a theory altogether novel and altogether 
arbitrary, which nobody had ever proposed before, and which nobody, we may 
feel pretty certain, will ever propose again. This theory consists simply in 
acknowledging the Greek accents, as we find them in the books, as the law for 
the pronunciation of the separate words, but refusing to allow them their 
natural force under certain rhythmical conditions. Thus, he says, that at the 
end of a hexameter verse such a word as edrjKe must be pronounced i9t]Ke, 
because the last syllable of a hexameter verse being long, the accent, according 
to a well-known canon of Greek orthoepy, must fall on the penult ! Now, the 
objection to this theory is threefold — (1.) It is not true that the last syllable of 
hexameter verse, as idrjKe, is long ; it is short, and the time is filled up by the 
pause which belongs to the end of the line, like a rest in music ; (2.) The theory 
proceeds on a supposed connection between prose accent and rhythmical 
emphasis, which is fundamentally false ; and (3.) The whole theory is a figment 
spun out of the brain of the writer, without a shadow of authority from ancient 
grammarians and metricians. This being so, the natural consequence fol- 
lowed ; — the book explained nothing, and changed nothing. If everybody 
could not answer it, nobody cared to understand it. 

Immediately upon the back of the learned Bishop's treatise, in 1797, appeared 
a little book entitled " Metron Ariston; or, a neiv Pleasure Recommended," 
with a ruffed and bearded effigy of Meetkerche fronting the title-page, and a 
motto which sufficiently indicates the temper and direction of the writer— 

" Tollite barbarum 
Morem. perpetttum, dulcia barbare 
Laedentem metra, quoe Venus 
Quintet parte sui nectaris imbuit." 



PLACE AND POWER OF ACCENT IN LANGUAGE. 299 

This book was not written by a scholar, but by a man of taste and 
vivacity, and a gay self-reliance which stands him in good stead against a 
whole host of scholastic cuirassiers. In point of tendency and contents, this 
book is nothing more than a repetition of Meetkerche and Voss, and 
those writers who have maintained the right of rhythmical as opposed to the 
accentual recitation of Greek and Latin verse ; but the striking fact which 
the title of the book suggests is, that the masters and teachers of the great 
English schools, who certainly could not be accused of paying any partial 
attention to accent, were the very persons who had so thoroughly ignored the 
practice of rhythm in their teaching, that it was a discovery to the author of 
the book to find that there was such a thing as rhythmical reading of classic 
verse ; and this discovery, with a prompt philanthropy, he hastens to com- 
municate to the ingenuous youth of the nation under the inviting name of " a 
new pleasure." This entirely agrees with the complaint which we have just 
heard the right reverend Bishop make with regard to the absurdity of reading 
Greek poetry with Latin accents and calling it reading by quantity. No wonder 
that clever schoolboys on occasions should begin to dream that the learned and 
reverend doctors, by whom their ears had been indoctrinated in the unpleasant 
mysteries of long and short syllables, at bottom knew less about the matter 
than they might have known themselves with the help of a little unsophisticated 
juvenile instinct. And accordingly the writer of " Metron Ariston " tells us 
that " he always indeed had an idea that our very anomalous and irrational 
way of reading Greek and Latin poetry was founded on error ; yet, from indo- 
lence, he had conformed, though reluctantly, to the general practice, because it 
was not his business to examine the error and seek its remedy." But what he 
did not seek for, he goes on to tell us, like Worcester's rebellion, came in his 
way, and he found it ; and the good Hermes, on whom he stumbled to direct 
him in his rhythmical wanderings one day, was a learned Italian ecclesiastic, 
while they were walking together in the Campo Vaccino at Rome one morning, 
and talking of Horace, and quoting the well-known line — 

" Ibam forte via sacra sicut mens est nws." 

The full musical weight with which the learned Italian recited this verse struck 
the Englishman with a pleasant surprise ; whereupon the priest, divining the 
cause of his satisfaction, began to expound to him the correct theory of classical 
recitation according to Meetkerche, "the great ambassador of a little state." 
Against this true doctrine, without which verse had no meaning, and lost more 
than half of its suavity, the English scholars and schoolmasters were in the 
systematic habit of sinning, by pronouncing equities, for instance, a horse, as if it 
were aequus, equitable — by shortening the final syllables of all words, and pro- 
nouncing dom'inos as if it were dominos and sacra, the ablative singular, like 



300 PROFESSOR BLACKIE ON THE 

sacrd the nominative plural ; and by turning anapests into clactyles, dactyles into 
tribrachs, spondees into trochees, iambi into pyrrhics — in fact, doing everything 
that could be clone systematically to turn order into disorder in this region, and 
" by this most abominably absurd custom, destroying at once both sound and 
sense, and seeming to sin from a love of the very ugliness of sinning." These 
are hard words, but not, in fact, one whit more strong than those which we 
have quoted from the English Bishop ; nor is it possible, indeed, to conceive 
anything at once more unscientific, more tasteless, and more unpractical than 
the way in which prosody and rhythm have been handled in the great English 
classical schools up to the present hour. On this point, certainly, the author of 
" Metron Ariston," a single light horseman, could triumphantly ride up and 
attack without fear a whole army of big blundering and self-contradictory 
hoplites. As to accents, however, about them he wisely said nothing ; but 
allowed them quietly to lie in the state of suspended animation to which they 
had been condemned by his patron-god Meetkerche. If these mute, mysterious, 
little oblique and curved lines were ever to revive into speaking significance 
at the touch of some philological wizard, the author of "Metron Ariston" 
certainly did not possess the secret for their disenchantment ; nor, indeed, if he 
had possessed it, would he have cared to use it ; for the accents, whatever 
virtue they might possess, could add but little to the luxury of the new 
rhythmical pleasure which he had discovered. 

But what were the great German scholars doing all this while, — the Heynes, 
the Wolfs, and the Hermanns, the founders of that stable and splendid edifice of 
philological learning which has placed Germany in the van of erudite and 
thoughtful research during the whole of the present century ? In the preface 
to the second edition of his Odyssey, Wolf remarks that in the matter of the 
accents, " the editors of the previous centuries had shown a great laxness of 
procedure, a fault which had commenced with so illustrious a name as Henry 
Stephanus, who in this respect had declined from the accuracy of his prede- 
cessors, Chalcondylus and Aldus." And after a few remarks on points of 
detail, follows a remarkable witness to the practical disuse into which accents 
had fallen in Germany just as in England towards the end of the last century. 
" In fact, no person now-a-days — and for many centuries back — ever hears 
a Greek accent ; and only a few, indeed, seem to believe that the doctrine of 
the grammarians on this subject is a thing that belongs to a complete course of 
teaching."* This passage is decided as to the general disuse of accents among 
the Germans in Wolf's time; but the phrase seit vielen Jahrhunderten is certainly 
too strong ; for the works of Meetkerche, Vossius, and Henninius, are sufficient 
to prove the living predominance of the Byzantine tradition in respect to 

* These extracts are taken from an historical review of the opinions of scholars about accents in 
Wagner's "Accent Lehre." Helrnstadt, 1807. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 301 

accents in the scholastic practice of their time. An equally emphatic declaration 
in favour of accents is made by Hermann in his famous work " De emendandd 
ratione Grammatices Grcecce ; * " but whether these two illustrious scholars 
contented themselves with publishing an authoritative manifesto on the neces- 
sity of maintaining accents as an inherited doctrine of genuine Hellenic ortho- 
doxy, or took any steps to put their views into that practical shape which alone 
could give them significance to articulate-speaking mortals, I have not been 
able to learn. Certain it is, however, that the stagnant waters of the schools — 
in Germany much more apt than in England to deduce practice from principle — 
began to be moved in this matter ; and, according to information which I 
have from continental scholars of high reputation, the accents are now pro- 
nounced in a great number of the best German gymnasia. I myself, some 
forty years ago, heard Professor Boeckh, in Berlin, reading the Iambic verse of 
the tragedians with a distinct and well-marked observance both of accent and 
quantity. The matter appears to have been left pretty much to the arbitration 
of the scholastic world ; and we may feel perfectly convinced that the natural 
conservatism of teachers would have resisted all change in this matter, unless it 
had been incontestably proved that the change carried with it the double 
advantage of scientific truth and practical convenience. Whilst the matter was 
thus not only fairly ventilated, but to a large extent embodied in the scholastic 
practice of Germany, in England not a single step seems to have been taken 
either to the recognition of the principle or the settlement of the practice of 
Greek accents. The well-known declaration of Porson, no doubt, in a note to 
the Medea,t gave the imperial imprimatur to certain traditional marks as a fact 
on paper, and of course put a stop for ever to the inchoate practice of printing- 
Greek books without such marks ; but it was a fact which seemed to remain as 
mysterious as a row of hieroglyphics on an obelisk before the great decipherment 
of Champollion. In fact, to use Scripture language, notwithstanding the authori- 
tative dictum of the great Cantab, the doctrine has remained in England up to the 
present hour a meaningless thing, " having a name to live while it is dead." In 
Scotland, indeed, a country too much accustomed slavishly to follow English 
authority in classical matters, twenty years ago I published a short protest 
against the gross inconsistency and grave practical grievance of inculcating 
rules about a host of mysterious marks which gave neither ideas to the intellect 
nor direction to the ear ;J it had become clear to me as sunlight, not only from 
meditation on the nature of the case, but from an accurate study of the ancient 

* Ch. xiii. De accentu. 

t " Si quis igitur vestrum ad accuratam Grcecarurn litterarum seientiam aspirat, is probabilem 
sibi accentuura rationem quam rnaturrime comparet in propositoque perstet, scurrarum dicacitate et stul- 
torum derisione immotus." 

| The Pronunciation of Greek : Accent and Quantity ; a Philological Inquiry. Edinburgh, 
1852. 

VOL. XXVI. PART II. 4 I 



302 PROFESSOR BLACKIE ON THE 

grammarians, that Greek accents contained the two elements of elevation and 
stress of voice, and are, in fact, practically identical with the accents in English, 
Italian, German, and other modern languages. And this truth I have carried 
out in practice for twenty years with increasing profit and satisfaction. In 
England, however, as was to have been expected, no attention was paid to a 
Greek argument coming from the north side of the Tweed ; and, accordingly, in 
the next work, that of Chandler,"- which issued from the Oxford press, we find 
the whole subject flung back into a grim limbo of despair, and involved in a 
mantle of impenetrable darkness. In the preface to his work, this author goes so 
far as to assert that neither Porson nor any other scholar, " while sanctioning 
the practice of accentuating Greek by their example, has condescended to 
justify it by sound and conclusive reasons. Porson specially, it is hinted in 
terms more vigorous than polite, " gave assertion for proof in the matter, 
actuated partly by his contempt for Wakefield, who happened to entertain a 
different opinion from his own." Then he goes on to proclaim the utter hope- 
lessness of being able to arrive at any certainty with regard to the meaning of 
accents ; it is not even certain that they did not " indicate the length or short- 
ness of syllables ; " he denounces " the absurdity of those who perpetuate in 
writing a something to which they never attend in reading, and who persist in 
ornamenting their Greek with three small scratches, the very meaning of which 
is doubtful and perhaps unknown," and laments in the most pathetic terms his 
own evil destiny in having had anything to do with the tangled disorder of 
" these troublesome appendages." 

" There 's something wrong iri accents — cursed spite 
That ever I was born to set it right ! " 

In fact, it appears not a little extraordinary that a writer who uses such 
strong language, should not have followed out consistently the practice of his 
predecessor Hennlnius, and flung the whole cargo of Byzantine lumber over- 
board ; for what task can be imagined more irksome and more fruitless than to 
spend long months of painful inquiry, with fret of brain and vexation of vision, 
upon every mappik and dagesh of a gospel in which the writer does not believe ? 
Almost contemporaneously with this remarkable book of Mr Chandler, ap- 
peared an interesting paper on accent and quantity by Professor Munro of 
Cambridge.! The occasion of this discourse was a Latin inscription in accentual 
hexameters from Cirta in Numidia, and supposed by the professor to belong to 
the third century of our era. In commenting on these verses, of course, the 
writer was led to explain both what accent meant, and how it came to pass 

* A Practical Introduction to Greek Accentuation. By H. W. Chandler, M.A. Oxford, 1862. 
t On a Metrical Latin Inscription, copied by Mr Blakeslet, at Cirta. — " Transactions of the 
Cambridge Philosophical Society," vol. x. part 2. 1861. 



PLACE AND POWER OF ACCENT IN LANGUAGE. 303 

that accentual verse, at so very early a date, came to usurp the place of quanti- 
tative, which only we now acknowledge as classical. In making this explana- 
tion, Professor Munro lays down the following propositions : — 

(1.) That the acute accent of the ancients was a mere elevation of the voice, 
without any stress on the accented syllable. 

(2.) That in the composition of Greek and Latin verse, the metre was 
determined by quantity alone, and that accent had no influence on it direct or 
indirect. 

(3.) That, nevertheless, the quantity of syllables was a matter which swine- 
herds in the days of Homer, and ploughmen in those of Plautus, had imbibed 
with their mother's milk, and could discriminate with the nicest precision. 

(4.) That by some strange and, to us, unaccountable process, the nature of 
the Greek and Roman accent was suddenly changed in such fashion that, from 
being a mere raising or sharpening of the tone, "it became a stress," "a mere 
stress," " a stiff and monotonous stress," a stress which is always accompanied 
with " the lengthening of the quantity," having nothing in common with the 
genuine classical accent except the name ; and that by this strange and inexpli- 
cable plunge, the accentual poetry of the mediaeval hymns, and the whole of our 
modern metrical system, so early as the third century had started into recog- 
nised existence. 

So much for the theory of the matter. With regard to the strange and un- 
scientific practice of the English great schools and colleges, the following 
passage is notable : — 

" It appears from what has been said, that we English, in reading Latin, 

place the accent generally, but by no means always, on the proper syllable. 

But then, we have entirely changed its nature, making it a mere stress, instead 

of a simple raising of the tone, without any lengthening of the quantity. And 

Pr^ecilius and his cotemporaries already did the same. From them, and their still 

more degraded descendants, the Italians, and other western nations, we inherit 

this debased accent, which had usurped and overthrown the rights of quantity. 

In the second line of the iEneid we read Italiamfdto profugus with the accent 

on the right syllable ; but on the same principle we ought to say — and Pr^ci- 

lius, indeed, and the Romans for centuries after him, did say — Lavindque, with 

the accent on the second a. We flatter ourselves that we thus preserve the 

quantity, but that is a mere delusion. It we feel by a mere mental process. 

Whether we pronounce profugus or profugus, quantity is equally violated. In 

the same way we read Greek with this debased Latin accent, and fancy that 

we preserve the quantity while sacrificing the accent. The modern Greeks 

read old Greek with the ancient Greek accent, debased in the same way into a 

mere stress. We think them, they think us, in the wrong ; and in different 

ways we are both equally in the wrong. M.r)va> aei'Se dia in an English or 



304 PROFESSOR BLACKIE ON THE 

Italian, and \ir\vw aeiSe 6ed in a modern Greek mouth, are equally remote from 
the accent and quantity given to the words by Homer or Demosthenes." 

It will be observed that this passage touches exactly on the same absurdity 
which, sixty years earlier, had roused the sprightly indignation of the author of 
" Metron Ariston," and the grave episcopal censure of Dr Horsley. 

In the "Cambridge Journal of Philology," vol. i., for 1868, appeared an 
article on the English pronunciation of Greek, by W. G. Clark, then public 
orator, Cambridge. Mr Clark is a scholar particularly well entitled to 
speak on this subject, both from his general accomplishments, which are far 
from being confined to the ordinary routine of an English classical scholar, and 
specially from his having travelled in Greece, and taken note of the actual 
accents of the language, as at present spoken by the people. In theory, Mr 
Clark entirely agrees with Professor Munro, that the ancient Greek accent 
consisted merely in the elevation of the tone, while the accent of the modern 
Greek includes " a stress precisely like our own, which is given by prolonging 
the sound, as well as by raising the note." When it falls upon a syllable it 
lengthens the vowel except before a double consonant. Thus Xoyos is pro- 
nounced Xvyos, 6Vo? iovos, and so forth. With regard to scholastic practice, Mi- 
Clark is of opinion that, while our English Greek vocalisation is altogether 
anomalous and indefensible, and must be abandoned, the present system of 
reading Greek with Latin accents should not be touched, because the modern 
system of accentuation is widely different from the ancient, and its adoption 
could only tend " to confuse such ideas as we at present possess of the rhythm 
of ancient Greek verse." And again, "It is impossible in practice to recur to 
the ancient system of accentuation, supposing that we have ascertained it in 
theory. Here and there a person may be found with such an exquisite ear, 
and such plastic organs of speech, as to be able to reproduce the ancient dis- 
tinction between the length and tone of syllables accented and unaccented, and 
many not so gifted may fancy that they reproduce it when they do nothing of 
the kind. For the mass of boys and men, pupils as well as teachers, the dis- 
tinction is practically impossible." So Mr Clark leaves us, so far as action is 
concerned, in a plight little better than that in which we were left by Chandler, 
— not enveloped, indeed, in impermeable mystery, but clogged with impracticable 
fetters, and groaning under a yoke of grammatical tradition which neither we 
nor our fathers were able to bear. 

A strange and a grateful contrast to the general current of English scholar- 
ship on this subject is presented by Mr Geldart, of Balliol College, Oxford, in 
his interesting and ingenious book, entitled " The Modern Greek Language in 
its Eelation to Ancient Greek; Oxford, 1870." In the third chapter of this 
work, the author states views with regard to accent and quantity which lift 
him completely out of what has always appeared to me the sort of enchanted 



PLACE AND POWER OF ACCENT IN LANGUAGE. 305 

circle of confusion and delusion in which English scholars are involved the 
moment they approach this subject. Mr Geldart is a decided advocate for 
accents, both in theory and practice, and he says roundly that " our prejudice 
against accents is for the most part insular, and deepened, to boot, by the pecu- 
liarities of our own insular pronunciation." He blows to the wind in a single 
sentence the vulgar error of English scholars, so often noticed in these pages, 
that accent has the necessary effect of lengthening the syllable on which it 
falls, the accented syllable in English being, in fact, as often short as long, as in 
get' -ting, plck'-ing, while a long syllable is often unaccented, as flndncial, fertile, 
a priori, in which last the first syllable is nearly always pronounced long, in 
spite of the fact that it is short in Latin. It is accordingly a complete delusion 
to imagine " that the Latin accent is either an indispensable or an infallible 
device for marking the right quantity of Greek syllables." With regard to 
accent, he makes the just remark that the raising of the note, and the increase 
of the stress generally go together. He farther denies altogether — and on this 
point he is a witness of great authority — that the modern Greeks always, or 
even in a majority of cases, lengthen the syllable on which the accent falls ; 
and in regard to the relation of accent and quantity, he shows that neither is 
modern poetry always governed by the mere spoken accent, nor is ancient poetry 
altogether regardless of it, but that the real regulator, both of ancient and of 
modern poetry, though in very different ways, is Rhythm, which is determined 
by the musical beat. How far the spoken accent was heard, as it were, through 
the rhythmical movement, depended principally upon whether the verse was 
sung or recited. In pure singing there might be heard only a faint glimmer of 
the spoken accent ; in prose it was the prominent element, and directed the 
flow of the period ; while between these two extremes there might be several 
intermediate styles of utterance in which the spoken accent was more or less 
prominent, according to the greater or less approach of the style of recitation 
to colloquial prose. 

It will not be difficult, after this long and strange historical survey, to sum 
up the conclusions to which, by the consideration of the various facts and argu- 
ments, we are inevitably led. We find ourselves, in fact, after more than three 
centuries of confusion, one-sidedness, and hallucination, arrived at a point of 
view where no fact or principle, necessary to a just conclusion, is concealed, 
and all apparent contradictions find a happy conciliation. In particular, the 
whole history of the controversy displays the fact that in one form or another 
quantity is the bugbear, and that from Voss and Meetkerche, to Munro, 
Chandler, and Clark, a sacred regard for the rights of metre is the apology 
for the monstrous invasion of the province of Greek by Roman accents. But 
those who have attended to the course of our argument and historic survey will 

VOL. XXVI. PART II. 4 K 



306 PROFESSOR BLACKIE ON THE 

easily perceive that the interference of Greek accents with the laws of Greek 
metre is a pure hallucination ; inasmuch as — 

1. It has been amply proved that in the case of individual words the pre- 
dominance given to one syllable by the stretch, stress, or emphasis of the voice 
with which the acute accent is naturally accompanied, has no necessary tendency 
to lengthen the syllable on which it is laid. Through the whole argument of 
those who oppose Greek accents a confusion runs between two things, which 
in this matter must be kept carefully apart — a confusion between a short sylla- 
ble unaccented compared with the same syllable accented, and a short accented 
syllable with a long syllable accented. When the three terms rjpipa, r)p.l'pa, 
and r) fir)' pa are compared, the middle syllable of the middle term, while it is more 
prominent, and may be in some degree longer than the same syllable of the 
first term, is decidedly short when compared with the same syllable of the 
third term. If, therefore, any short syllable, whether in Greek or English, on 
which the accent falls, is in danger of being pronounced long, it arises not 
from the nature of the case, but from the ignorance, carelessness, or stupidity 
of the teacher ; and, in fact, a great part of the strange confusion which has so 
long prevailed on this subject may not unreasonably be traced to the want of the 
directing presence of a living rhetorical and musical culture in our great English 
schools and colleges. 

2. The second great element of confusion which has been introduced into 
this matter is the gratuitous and altogether unauthorised assumption, that 
because our metrical composition follows the laws of spoken accent, therefore 
in Greek and Latin the same law was necessarily observed. In the writings of 
Hyphaestion and of those who lay down the canons of classical verse, there is 
not a single word said about the spoken accents ; and the sure inference is, that 
in metrical composition they were, as Professor Munro justly remarks, systema- 
tically ignored, or, if attended to at all, only in a subordinate, exceptional, inci- 
dental, and even accidental way. Nothing, therefore, could be more mistaken 
than the attempt of Horsley to give a new theory of Homeric scansion, founded 
on the doctrine of the spoken accents. On what principle, then, it will be 
asked, was the v Greek poetry written % Can it be supposed that a nation of 
refined taste and high culture could be delighted with the barbarism of pronounc- 
ing words, one way in prose, and another way in verse % We answer, there is 
nothing at all strange in this supposition ; and that, whether it appear strange 
or not, it was certainly the fact. To understand this, instead of transferring 
the laws of our modern poetry wholesale to the poetry of the Greeks, let us 
rather transfer ourselves from an age of books, reviews, newspapers, and read- 
ing-rooms into an age where there was no such thing as books or reading at 
all, where prose composition was altogether unknown, and where every com- 
position, not purely ephemeral, was made to be sung, and had its existence 



PLACE AND POWER OF ACCENT IN LANGUAGE. 307 

only in the element of music. Now, we need not at the present day set forth a 
formal proof that Homer and the pre-HoMERic teachers of Greece were not 
avayaxTTdt, but doiSot, and that all hexameter verse, the current form of the 
oldest Greek metrical compositions, was originally sung, and not recited. 
Under these conditions, it naturally conformed to the laws of musical compo- 
sition ; and what these laws were, especially in relation to spoken accent, it is not 
difficult to realise. What music principally demands from poetry is a mass of 
rich and full vocalisation, to correspond with the measured flow of the notes ; for 
the vowels are the musical element in human speech, and especially the deep 
broad vowels pronounced long, and not rapidly rattled over. This element, 
therefore, was naturally preserved in the first place : that is to say, Hellenic 
poetry was founded on quantity. But what of accent ? The rhythmical march 
of speech adapted to music, as every one knows, is secured by the element of 
equality expressed in the succession of equal spaces of sound, marked by recur- 
rent emphasized pulsations ; these pulsations constitute what is called the 
musical accent, or beating of time, as it is vulgarly called. Now, it certainly 
might have been desirable to make this rhythmical accent of the music cor- 
respond in every case with the spoken accent of the words ; but this was not 
done, for the very simple reason that the choice of poetical language would 
have been too much fettered by the constant double demand on the poet of 
conformity in every case, both with the spoken quantity and the spoken accent. 
Nor should this appear at all strange. As it is, we see how often Homer — as 
in aOavaros and other words — is obliged to put an artificial length upon tribrachic 
feet in order to get them admitted into the dactylic march of his verse ; and how 
impossible it would have been to compose a long poem under the strict law of 
both quantitative and accentual conformity, we may see from the fact, that, in 
our own poetry, we have contented ourselves with fettering one of the elements 
and leaving the other free ; that is to say, that, while we never, or very rarely, 
allow our spoken accent to clash with the rhythmical beat, we constantly take 
the liberty in our sung psalms and songs of drawing out short syllables to any 
length, and skipping over long ones with any amount of metrical celerity. 
Here, therefore, the Gordian knot is untied : the Greek poetry made to be 
sung is governed by quantity, the musical element of language ; the modern 
poetry made to be read is governed by accent, the colloquial accent. What 
Nature, or rather the necessities of Art, have kept asunder, let no man bring 
together. Let no man imagine that colloquial accents, whether Greek or 
Roman, can possibly come into collision with the laws of a poetry so essentially 
musical in its character as the Greek. 

3. But the ancients, it will be said, though their poetry was all musical in 
its birth, and a verse had no meaning except as sung, certainly did recite their 
poetry at an early period. Of course ; and in this case it is obvious, that a 



308 PROFESSOR BLACKIE ON THE 

poetry constructed as part of the musical art was to a certain extent put out 
of Nature the moment it was translated into the region of spoken verse. In 
this case a collision between the musical beat and the accented syllables was 
unavoidable, and some sort of compromise would naturally be the result. This 
compromise, however, would on the whole be decidedly to the advantage of the 
musical rhythm, as opposed to the colloquial accent. For metre, as we have 
seen, was metre only in virtue of the regularly recurrent musical beat ; and to 
abolish this was to destroy metre, and to turn verse into prose, as, in fact, we 
often hear English schoolboys do, when reading Horace, and as the modern 
Greeks do when they read Homer accentually. But that the ancients could 
not have done this is manifest both from the prominence of music in their 
national culture and from the effect of the rhythmical stroke in lengthening the 
shortest vowels, even in the verse of Virgil, which certainly was not sung. 
The poet who wrote 

Liminaque' laurusque Dei, 

must have had his ear tuned to the march of a verse which gave that marked 
preponderance to the first syllable of a foot, which is musically given to the first 
note of a bar, and which allowed the license of lengthening a short vowel in such 
a position after the example of Homer, specially before a word beginning with 
a liquid. Meetkerche and Voss were therefore right in reading classical verse 
mainly by this rhythmical beat, and practically disregarding the spoken accent. 
It does not follow, however, that though the rhythmical accent remained 
dominant even in spoken verse, it therefore exercised an exclusive sway. In 
many cases, of course, there would be no clash, and this, indeed, regularly 
happened in the two last feet of a Latin hexameter. But in other cases, where 
a clash did occur, the occasional bringing forward of the spoken accent might 
serve to break the monotony of a merely musical rhythm, and cause it to 
approach nearer to the march of dignified prose eloquence. Thus, the first line 
of Virgil may either be accented 

Arma viumque cano' Trojce' qui primus ah oris, 
or 

Arma viumque cdn'o Tro'jde qui primus ah oris ; 

and in both cases the true quantities are preserved ; but in the second method 
the spoken accent is allowed to control two words to the prejudice of the 
musical beat, by whose regular recurrence the hexameter verse was originally 
framed. In this way it was quite easy to recite Latin hexameters or Greek 
iambics in such a manner that, while the rhythmical beat mainly ruled, and no 
short syllable was ever heard where the music had a long note, the spoken 
accent to which the ear had been habituated in conversation did neverthe- 
less generally shine through, and in special cases assert itself with that natural 



PLACE AND POWER OF ACCENT IN LANGUAGE. 309 

emphasis which subordinates rhythm only to aid expression, and to prevent 
monotony. 

4. It will now be evident how entirely Professor Munro was mistaken when 
he expressed surprise at the fact, that, while the rudest boor in the days of 
Plautus was familiar with the exact laws of quantitative metre, even well- 
educated gentlemen of the middle class before the time of Constantine were 
apparently unable to write anything but accentual metre, constructed on the 
same principle as the Byzantine 0-1-9(01 tto\ltlkoL The rudest boor, no doubt, 
could distinguish a long syllable from a short, and could discriminate the penul- 
timate vowel in pat'er and mater in a way that seems impossible to the gross 
ears of some of our English teachers. Our own peasants will distinguish gdt 
from goat, or god from goad, exactly in the same way ; but it will require more 
than a rhetorical flourish from Cicero to prove that the peasants of Italy, or 
even Attica, at any time were perfectly master of the complete doctrine of 
quantity as taught in the musical schools. For it must always be borne in 
mind that the practice of these schools was to a certain extent artificial ; it 
was founded on certain concessions which the currency of common life had 
made to the necessities of art ; and the common people, whose ears were 
trained mainly by the spoken accent, could . not be expected either to 
compose verses in neglect of that accent, or to sympathise fully with its 
neglect in the case of verses composed by cultivated poets, except in so far 
as their own education had kept them in living connection with those schools 
of music from which the cultivated poetry had emanated. Now, in the best 
ages of Greece this living connection naturally existed ; and the effect of custom 
and association would be such, that no other verses but those composed on the 
original quantitative principle would be recognised as legitimate even by the 
vulgar ear. But the moment that a great national decay commenced, and 
schools of popular culture were neglected, from that moment the common 
people, left to themselves, if ever they tried poetical composition, could do so 
only in obedience to the instinct which governs all poetry not intimately associated 
with the musical art. Poetry now became a species of measured conversation to 
which laws were given by the spoken accent, and where the fixed musical 
recurrence of long and short syllables was systematically ignored. In this 
change there is nothing strange or mysterious ; on ■ the contrary, it was the 
natural, and, we may say, necessary consequence of passing from a musical to a 
colloquial epoch in literature ; and as a fleet-footed man, when he leaves the 
ice and takes off his skates, passes to a kind of locomotion governed by different 
conditions and subject to different laws, so a people, shaken loose from all 
musical tradition and left to form a poetry for itself, will infallibly fall upon a 
form of verse in which the musical value of vowels will be sacrificed to the 
familiar control of accentually preponderant syllables. 

5. One word remains on the question of scholastic practice, which has 

VOL. XXVI. PART II. 4 L 



310 PROFESSOK BLACKIE ON THE 

been such a bugbear to our teachers. Now, with regard to this problem, it is 
one of those to which, as Geldart says, the old adage applies, solmtur ambulando. 
What appears impossible in theory, is often easy in practice. If you wish to 
learn how to use your legs, just rise up and walk. If you imagine that there is 
any difficulty in saying Soj/cpaV^s without saying S^/cpaV^s, or bon'us without 
saying bonus, just put yourself under a master of elocution for five minutes, and 
you will shortly be drilled out of your difficulty. But why should the ears of 
teachers be haunted by such a hallucination as that by placing the Roman 
accent on the penult of all dissyllabic words, they are furnished with some sure 
spell against the violation of quantity ? Is it not quite evident, rather, that the 
short quantity of the first syllable of /8109, a bow, is much more easily preserved 
by the natural oxytone accent than by the Latin accent /3i'os on the penult ? 
And if the quantity of the long penult in the verb Scarpi'Su is more effectively 
brought out by the accent on that syllable than if it had been on the last, is it 
not manifest that the same syllable, being short in the substantive BiarplQij, is 
more certainly pronounced short — according to the argument of the Latinising 
Hellenists themselves — with the native oxytone accent than with the imported 
Latin one % Take, again, the word /capapa, a vault, where all the vowels are 
doubtful, and where, of course, the quantity of each syllable can be recognised 
only by utterance. According to the current method, the accent, laid on the first 
syllable of this word, should inform me, that the syllable is long by virtue of the 
stress, and it does inform me also, if I am to believe my ears, that the other two 
syllables are short. But three parts of the information thus given are false ; for 
the accent is not on the first syllable, and the quantity of the first syllable is short, 
and that of the last long. On the other hand, if I pronounce the same word 
according to the principles laid down in this paper, I learn not only where the 
accent is, but that the two first syllables are short, and the last long. The fact of 
the matter is, that, while the Greek accent, rightly placed, informs the ear rightly 
both as to the accent and the quantity of the syllables of which a word is com- 
posed, the Latin accent inverts and perverts both, and teaches, with regard to 
accent and quantity, only what must be unlearned. The opponents of accents, 
who absurdly call their Latinising method the quantitative pronunciation of 
Greek, ought to bear in mind that, in practical teaching, next to pronouncing 
the long syllables long and the short short, the best way to teach quantity is to 
pronounce the accent, which either stands upon the long syllable and favours 
its prolongation, or stands in such a definite relation to that syllable that the 
quantity of the unaccented syllable is known from the place of the accented. 

But the great practical difficulty to which teachers allude is, perhaps, rather 
rhythmical than prosodiacal. The pronunciation of the Latin accent, says Mr 
Clark, is the only way we have of teaching our pupils to appreciate the 
measure of classical verse. Abolish the Latin accentuation of Greek prose, 
and you turn the organ of Homer into a hurdy-gurdy. Now, with regard to 



PLACE AND POWER OF ACCENT IN LANGUAGE. 311 

this matter, I would observe, in the first place, that if the young gentlemen 
who usually come to our universities were to lose all the rhythmical apprecia- 
tion of Greek verse that really lives in their ears, and not merely in their 
understanding, they would lose little that is worth keeping. For what are the 
facts of the case % The observation of the Latin accent facilitates the rhythmical 
reading of the two last feet of a hexameter verse ; this is an accident of the 
Latin language, that is all. But not even in the reading of Latin does the 
reading, according to the Latin prose accents, prevent the constant occurrence 
of a clash between the spoken accent and the rhythmical beat. In the Ovidian 
pentameter such a clash must always occur twice, and in the two most marked 
places of the verse, And, if the absence of the oxytone accent causes this 
opposition in Latin, is it not strange that we should banish this same accent 
from its natural place on a Greek word, in order, as we say, to avoid, but 
actually in a great number of cases to produce, a collision between the rhyth- 
mical beat and that accent ? Take, for instance, this second line from " the 
Wasps " of Aristophanes — 

" <£>v\aKr)v KaTokveiv WKTepivrjv SiSacr/co/AezA," 

and it is plain that in the only two places where a clash does occur between 
the spoken accent and the rhythmical beat, according to the Latinised accent, 
that clash disappears the moment the words are read according to their natural 
Greek accentuation. And so, not only in Iambic verse, but in every verse whatever, 
the introduction of the Latin accent must jar with the rhythmical flow of the 
line wherever the rhythmical stroke falls, as it constantly does, on the last 
syllable of a word. This practical objection therefore vanishes in smoke. That 
gross-eared and ill-trained persons may be enabled to receive the harmonies of 
the two last feet in a Homeric line, with a little less trouble, or with no trouble 
at all, no wise educator can deem a sufficient reason for invading the whole 
inherited intonation of the finest language in the world, with sounds which, 
however proper on the banks of their native Tiber, on the banks of the Ilissus 
must be felt to be a gross barbarism. The rhythmical objection from the prac- 
tical side is, in fact, only an ingenious apology to cover carelessness, to prop 
prejudice, and to mask with an attitude of apparent utility a pedagogic pro- 
cedure, alike unscientific in principle and self- contradictory in practice. 

Finally, if those who delight themselves in exaggerating imaginary difficul- 
ties have any honest desire to see how they disappear in the actual business of 
teaching, let them come to me ; for I am a practical man, and speak from the 
experience of half a lifetime. I teach Greek on the principle that the ear is the 
natural and legitimate organ which must be addressed in the first place. I 
pronounce every word according to its just accent and quantity, allowing its 
own natural emphasis to sway the proper syllable of the Greek word, just as 
the Latin accent emphasizes the proper syllable of the Latin word, taking 



312 PROFESSOR BLACKIE ON THE 

special care at the same time that in no case shall the emphasis of the accent 
be drawn into a prolongation of a short vowel. In the matter of quantity, I 
allow length by position to be pronounced short, according to the English habit, 
partly because I do not feel sure that this length was anything but a metrical 
license unknown to prose, partly because I should not think it advisable to 
encumber the English lighthorseman with a greater weight of heavy Spondaic 
armour than he can conveniently carry. On the elevation of tone which natu- 
rally accompanies the stress, and indeed always seems to have done so at the 
end of a clause, I do not curiously insist, the accent being sufficiently 
marked without it. As little do I endeavour to distinguish between a long 
accented syllable, as in nrjvr), and a circumflex, as in {xaXkov, though I have not 
the slightest difficulty myself in bringing out the combination of rising and falling 
inflexion on the same syllable which the circumflex properly denotes. Thus, in 
the reading of prose, which should be continued assiduously for six months or 
a year before poetry is meddled with : I then take up Homer, and forthwith 
intimate to my students that, as the whole doctrine of Greek metres was a part 
of the science of music, it necessarily followed the laws of that science, and 
can be understood only by an entire subordination or sinking of the spoken accent 
in the first place, and a recitation according to the regularly recurrent beats of 
the rhythm. This, which teachers imagine to be so difficult, is one of the 
easiest things in the world. Most human beings have ears, and can beat time. 
Even serpents, and elephants, and dancing bears can do this. And in order 
that the rhythm may be thoroughly worked into the ear, I have no objec- 
tion even to what may be called a little sing-song at starting ; but the pupil, of 
course, as he advances, must be trained to counteract the monotony of mere 
rhythm by that variety which a proper attention to expression and punctuation 
produces. In this way, the whole perplexing and tedious doctrine of accent 
and quantity is learned from beginning to end by the ear • the pain of prosody 
becomes a pleasure ; accent and quantity learn to observe their proper bounds, 
each, happy in his recognised domain, forgetting all thought of making a hostile 
invasion into the territory of the other. The only difficulty in the matter arises 
from the necessity of teaching a number of thoughtless and idle young men to 
unlearn all that lumber of false quantities and false accents which has either been 
systematically built up, or carelessly allowed to accumulate in the schools ; but 
this is a difficulty which it is in the power of schoolmasters, and of schoolmas- 
ters alone, radically to remove. And I feel convinced that, so soon as a radical 
reform in this matter shall be seriously undertaken by teachers, not only will 
the inculcation of classical Greek be much facilitated, but the organs of utter- 
ance being rendered more flexible and more amenable to training, will accom- 
modate themselves to the characteristic peculiarities of German, French, and 
other living orthoepies, with an aptitude the want of which is now so frequently 
lamented. 



(313) 



XIV. — On the Average Quantity of Rain in Carlisle and the Neighbourhood. 
By Thomas Barnes, M.D., F.RS.E. 

(Read 17th April 1870.) 

In the year 1827, I communicated to the Royal Society of Edinburgh some 
meteorological journals, kept at Carlisle by the late Mr Pitt, extending over a 
period of twenty-four years, viz., from 1801 to 1824 inclusive. An abstract of 
these journals, with explanatory remarks and tabular results, were drawn up 
by me, and read before the Society, and were afterwards published in their 
Transactions. I now beg to offer some remarks to the Society on journals 
kept by Dr Carlyle, in the city of Carlisle, from 1757 to 1783 inclusive, by the 
Eev. Jos. Golding at Aikbank, near Wigton, Cumberland, fourteen miles west 
of Carlisle, from 1792 to 1810 inclusive, and by myself at Bunkers Hill, two 
and a half miles west of Carlisle, which is situate 184 feet above the sea level, 
according to the late Ordnance Survey, from 1852 to 1870 inclusive. I shall 
confine my remarks to the quantity of rain that fell during the several periods 
of our journals. The accompanying tables show the quantity of each month and 
year included in these periods. I regret much that I am not able to give a 
description of the instruments used by Dr Carlyle and Mr Golding ; but as 
they both were gentlemen of considerable ability and of liberal education, and 
devoted much time and attention to meteorology, there is no reason to doubt 
either the quality of their instruments or the correctness of their observations. 
Dr Carlyle's rain-gauge was placed in his garden, near the head of Abbey 
Street, and is about the same height as the ground on which the Cathedral 
stands, eighty-two feet above the level of the sea. My own rain-gauge consists 
of a copper funnel, twelve inches in diameter at the top, and is inserted into a 
strong tinned iron vessel, placed in a box on my garden wall, the height of the 
funnel being six feet above ground. It is examined from time to time, and 
particularly after a fall of rain. The water is measured by means of a glass 
tube of half an inch diameter, with an attached scale of inches and tenths. By 
this means, the rain that falls on a circular area of twelve inches diameter is 
collected on an area of half an inch diameter, so that inches and tenths in the 
tube correspond to g-^-g- and 5-7^ of an inch of rain on the surface of the gauge. 
To prevent waste by evaporation, the communication between the funnel and 
the receiver is very narrow; and to prevent the rain that falls within the gauge 
from splashing over, the upper edge or rim of the funnel is turned upwards 
from the inclined direction of the under part, so as to stand vertically, and the 

VOL. XXVI. PART II. 4 M 



314 



DR BARNES ON THE AVERAGE QUANTITY OF 



top of the gauge is parallel to the horizon. I have abstracted from the journals 
the quantity of rain that fell at Carlisle, Aikbank, and Bunkers Hill, during 
the periods they were kept, and have drawn up in a tabular form the quantity 
of rain for each month and year of these periods. I have also taken the aver- 
ages of the observations, and have found some remarkable coincidences in the 
results. By these tables we observe the wet and dry months of every year for 
long series of years ; we also observe the wet and dry years, and the wet and 
dry seasons of every year. 



A Table exhibiting the 


Quantity 


of Eahs 


■ of each Month and Yeae 


, for Twenty-Seven Years, taken fromi 


the Meteorological Journal 


of the late George Carlyle, M.D., 


kept at Abbey Street, Carlisle, from 


1757 to 


1783. 












, 














Years. 


Jan. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Annual j 
Quantity of 
each Year. 


1757 


•44 


1-097 


2-117 


2 


23 


2 


206 


1 


014 


2 


•005 


3-102 


•544 


1 


•457 


2-703 


Mil 


20-026 


1758 




832 


2-9 


1 


319 


1 


•59 


1 


152 




759 


5 


•66 


1-774 


2-254 


2 


•46 


2-196 


3-354 


26-250 ; 


1759 


1 


348 


•284 


2 


099 


1 


479 




668 


3 


•773 


1 


76 


2-368 


3-016 


4 


•137 


1-494 


•525 


22-951 


1760 


1 


722 


2-519 




445 




687 


1 


■106 


2 


795 




577 


4-166 


3-442 


3 


■433 


3-903 


3-848 


28-643 


1761 




357 


2-808 


1 


534 




■96 


1 


925 


2 


322 


2 


617 


1-976 


5-079 


1 


•432 


3-698 


1-735 


26-443 


1762 


2 


327 


1-487 


1 


386 


2 


157 




905 




648 


2 


271 


•96 


4-393 


1 


•348 


2-296 


•36 


20-538 


1763 




291 


1-608 


1 


094 


1 


884 


1 


909 


3 


018 


3 


668 


3-261 


2-412 


2 


16 


1-844 


5-204 


28-353 


1764 


4 


181 


2-538 


1 


497 




718 


1 


568 




772 


2 


764 


2-097 


1-897 


2 


565 


2-525 


1-04 


24-162 


1765 


2 


079 


•596 


3 


343 


2 


368 




408 


1 


575 




386 


2-195 


1-903 


2 


147 


1-572 


•814 


19-386 


1766 




173 


1-257 




259 


1 


371 


2 


927 


3 


316 


2 


241 


1-794 


2-948 


2 


566 


1-541 


1-079 


21-472 1 


1767 


1 


647 


2-426 


1 


586 




211 


3 


41 




559 


3 


941 


2-03 


3-065 


2 


954 


4-084 


•624 


26-537 1 


1768 




893 


6-504 




654 


1 


73 


1 


114 


3 


475 


4 


49 


1-43 


3-236 


2 


578 


3-099 


2-598 


31801 H 


1769 


1 


016 


1-557 




902 


1 


447 




886 


1 


753 


1 


488 


3-427 


5-138 


1 


37 


1-242 


1-577 


21-803 H 


1770 


1 


111 


1-505 


1 


521 


1 


32 


1 


277 


4 


009 


1 


969 


•831 


3-8 


1 


299 


2-77 


371 


25122 1 


1771 


1 


58 


•476 




632 




805 


1 


894 




694 


3 


027 


3-619 


1-728 


4 


374 


2-887 


2-266 


23-982 


1772 


1 


365 


1-398 


1 


8 




772 


1 


239 


2 


679 


3 


035 


3-256 


3-517 


3 


09 


4-991 


1-376 


28-518 \ 


1773 


2 


927 


1-24 


1 


077 


1 


993 


1 


897 




835 


1 


460 


1-9 


5-62 


5 


24 


2-378 


1-666 


28-233 


1774 


2 


01 


2'222 




565 


1 


481 


1 


859 


1 


757 


2 


212 


1-953 


2-006 




737 


•947 


1-595 


19-344 j \ 


1775 


3 


136 


2-958 


2 


099 




902 


1 


154 




645 


2 


857 


3-903 


3-489 


4 


104 


2-58 


1-305 


29-132 j} 


1776 




625 


2-373 




713 




59 




857 


1 


93 


3 


645 


3-237 


3-252 


1 


531 


1-336 


1-601 


21-6901 


1777 




725 


•69 


1 


152 


1 


593 


1 


1 


3 


308 


2 


606 


2-771 


•962 


4 


392 


2-3 


•416 


22-015 I 


1778 


1 


405 


•691 


1 


861 




42 


2 


688 


2 


154 


4 


177 


2-179 


T504 


3 


519 


2-328 


3-36 


26-286 } 


1779 




258 


•626 




324 


1 


607 


2 


49 


1 


376 


4 


058 


roi 


5-829 


4 


5 


1-651 


3-643 


27-372 B 


1780 




5 


•988 


2 


303 


1 


799 


2 


137 


1 


347 


2 


043 


•833 


3-561 


3 


161 


1-591 


•722 


20-9851 


1781 




824 


2-081 




551 


1 


024 


1 


075 


1 


417 


1 


891 


3-16 


•833 




63 


4-403 


1-517 


19-406 


1782 


3 


531 


•678 


2 


041 




767 


2 


104 


1 


362 


1 


674 


4-229 


3-392 


3 


608 


•840 


1-271 


25-497. 


1783 


2-076 


1-774 


•458 


•17 


1-931 


1-981 


2-11 


3-676 


3-592 


2-743 


1-684 


•576 


22-771 


Totals fori 
27 years,/ 


39-379 


47-281 


35-332 


34-075 


43-886 


51-273 


70-632 


67-137 


82-412 


73-535 


64-883 


48-893 


658-7181 


Means for) 
27 years/ 


1-458 


1-751 


1-309 


1-262 


1-625 


1-899 


2-616 


2-486 


3-052 


2-723 


2-403 


1-812 


24-396 





















































RAIN IN CARLISLE AND THE NEIGHBOURHOOD. 








31 


5 




Table exhibiting the Quantity of Rain of each Month for Nineteen Years, and the Annual Quantity 
of each Year, taken from the Eev. Joseph Golding's Meteorological Journal, kept at Aikbank, near 


Wigton, Cumberland, from 1792 to 1810. 




Years. 


Jan. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Annual 
Quantity of 
each Year. 


1792 


1-599 


1-41 


2-348 


3 


578 


3 


067 


1 


979 


3 


757 


4 


968 


5 


843 


2 


623 


1 


781 


4 


495 


37 


448 


1793 


1 


388 


4-1 


2-405 




901 


1 


620 


2 


095 


1 


594 


5 


328 


1 


617 


2 


426 


2 


034 


2 


988 


28 


496 


1794 


2 


594 


4-255 


1-426 


3 


357 


1 


948 




995 


2 


564 


2 


594 


3 


207 


4 


813 


2 


675 


2 


862 


33 


290 


1795 




682 


3-505 


3-256 


2 


503 


1 


342 


3 


377 


1 


836 


4 


117 




674 


6 


216 


6 


830 


6 


022 


40 


360 


1796 


6 


505 


2-502 


•928 


1 


559 


3 


515 


3 


31 


5 


633 


1 


192 


3 


027 


3 


558 


1 


988 


1 


627 


35 


344 


1797 


3 


776 


•655 


1-437 


1 


646 


3 


757 


1 


921 


4 


146 


4 


336 


5 


668 


3 


239 


3 


534 


4 


458 


38 


573 


1798 


3 


294 


2-715 


1-401 


1 


671 


1 


15 


1 


193 


4 


604 


3 


053 


3 


349 


3 


775 


2 


847 


1 


731 


30 


783 


1799 


2 


781 


2-379 


1-276 


2 


717 


2 


357 




558 


3 


657 


8 


476 


5 


228 


4 


777 


3 


916 




242 


38 


364 


1800 


3 


267 


•880 


2-368 


3 


499 


3 


559 




647 


1 


641 


1 


362 


4 


659 


5 


243 


4 


813 


1 


929 


33 


867 


1801 


3 


117 


3-953 


4-898 


1 


19 


1 


257 




318 


5 


544 




857 


4 


459 


5 


321 


2 


394 


3 


915 


37 


223 


1802 


2 


564 


3-429 


1-611 


3 


441 




394 


2 


627 


6 


883 


3 


368 


2 


597 


5 


199 




501 


3 


260 


35 


874 


1803 


1 


398 


3-007 


1-734 


1 


849 


4 


612 


3 


41 




694 


3 


794 


3 


17 


2 


158 


2 


715 


3 


192 


31 


733 


1804 


6 


101 


1-695 


2-543 


1 


811 


2 


189 


2 


164 


1 


758 


4 


324 


2 


013 


5 


699 


2 


028 


1 


463 


33 


788 


1805 


2 


934 


3-404 


2-769 




946 


1 


75 


2 


938 


3 


628 


2 


31 


3 


011 




235 




547 


4 


869 


29 


341 


1806 


4 


88 


2-669 


•73 


1 


253 


1 


744 


1 


956 


3 


97 


6 


896 


4 


87 


1 


639 


5 


424 


5 


18 


41 


211 


1807 


1 


385 


4-77 


•967 


2 


129 


3 


069 


1 


628 


4 


246 


3 


179 


6 


415 


4 


16 


3 


893 


2 


743 


38 


584 


1808 


3 


839 


1-595 


•267 


1 


662 


2 


942 


1 


773 


3 


269 


3 


816 


2 


103 


5 


162 


3 


478 


1 


886 


31 


792 


1809 


3 


963 


2-967 


•636 




887 


4 


547 


3 


194 


2 


194 


7 


386 


4 


036 




562 


1 


525 


5 


492 


37 


389 


1810 


1-886 


1-348 


5T23 


•719 


•642 


1-386 


5-174 


3-046 


1-254 


3-033 


2-976 


3-771 


30-358 


'talsfor) 
9 years/ 


57-953 


51-238 


38123 


37-318 


45-461 


37-469 


66-792 


74-402 


67-200 


69-838 


55-899 


62-125 


663-818 


Jans for) 
) years/ 


3 05 


2-697 


2-006 


1-964 


2-393 


1-972 


3-515 


3-916 


3-537 


3-676 


2-942 


3-27 


34-938 


It is 


worthy of remark that Dr Miller states in his " 


Synopsis of the Fall 


of Rain, 


&c, in the English Lake and Mountain Distric 


t in the year 1853," 


that—" 


Among several abnormal and opposite atmospheric 


conditions presented 


by the i 


fears 1852 and 1853, the departure from the aver 


age in the rain fall is 


the mos 


st obvious and remarkable. While the former was the wettest, the 


latter was the driest year since the experiments were begun in 1844. In 1852 


tl 


ie 


depl 


:h of ^ 


r ater j 


>re 


cipii 


tat 


ed a 


X i 


5eat 


tlW 


aite 


W 


as e 


qu 


rival 


en 


t to 


15674 


cir 


iche 


s, 





and, in 1853, to 113*69 inches — a difference of 43 inches, corresponding to the 
average annual fall at Whitehaven in the last ten years." A similar departure 
from the average rain-fall took place at Bunkers Hill— the greatest fall during 
the period of my journal being in 1852, and the least in 1853, as appears by the 
accompanying Table — 31-825 inches in the former year, and 19*613 inches in 
the latter. 



316 



DR BARNES ON THE AVERAGE QUANTITY OF 



A Table exhibiting the Quantity of Rain of each Month for Nineteen Years, and the Annual Quanttt 
of each Year, taken from a Meteorological Journal kept at Bunkers Hill, near Carlisle, by Thoma 


Barnes 


, M.D., 


from 1852 to 1870. 




















Years. 


Jan. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Annual 

quantity o 
each year 


1852 


3-571 


1-360 


•625 


1-189 


2-363 


4-88 


2-114 


3-446 


1-947 


2-694 


2-192 


5-444 


31825 


1853 


3-033 




732 


•621 


1 


303 


•881 


2 


151 


2-814 


1-904 


2-07 


2351 


1-243 


•51 


19-613 


1854 


1-665 




788 


•81 




072 


343 


3 


447 


1-501 


3277 


1-817 


2-326 


1-895 


2-178 


23-206 


1855 


•097 




746 


1-449 


1 


442 


1-486 


2 


718 


2-819 


3-098 


1-197 


4-322 


1-375 


•598 


21-347 


1856 


2-072 


1 


843 


•062 


1 


152 


2-829 


3 


906 


1-277 


4-140 


2-175 


2-706 


1-137 


3-618 


26917J 


1857 


1-657 




753 


2-47 


1 


18 


1-138 


2 


413 


2-347 


1-934 


2-895 


2-263 


2-09 


2-003 


23143 


1858 


1-027 




458 


1-75 


1 


055 


2-965 


2 


157 


3-402 


3-276 


3-718 


3-072 


1-158 


1-75 


25-788 


1859 


2-004 


1 


222 


2-59 


1 


984 


•05 


1 


531 


3-111 


2-407 


4-185 


1-378 


3611 


2-361 


26-434H 


1860 


3-381 




854 


2-588 


1 


187 


1-807 


3 


114 


14 


3-684 


1-06 


4-5 


1-25 


2-187 


27-0ll 


1861 


1-093 


1 


42 


2-944 




564 


1-223 


1 


916 


4-02 


3-407 


4-623 


1-815 


6-704 


1-935 


31664 


1862 


2-593 




781 


1-756 


2 


218 


3-066 


2 


854 


4-159 


3-469 


2-609 


4-145 


1-698 


2-312 


31-66 j 


1863 


3-572 


1 


371 


•468 


2 


593 


2-376 


2 


61 


•625 


2-583 


4-711 


4-003 


3-177 


2-274 


30-36,- 


1864 


2-0 


1 


781 


2-966 


1 


156 


1-868 


2 


388 


•541 


1-72 


4-607 


3-407 


1-921 


1-935 


26-29 1 


1865 


1-374 


1 


656 


1-093 




796 


4-311 




783 


1097 


3-671 


•89 


5-0 


2-631 


1-412 


24-7141 


1866 


3-772 


2 


184 


1-593 




684 


1-064 


1 


937 


2-967 


4-0 


3-965 


1-281 


3-592 


3457 


30-49t 


1867 


2-281 


1 


718 


1-407 


2 


92 


2-49 


1 


16 


3416 


1-665 


2-31 


1-857 


•577 


1-27 


23-07: 


1868 


2-393 


2 


01 


3-355 


2 


5 


1-993 




986 


•281 


3125 


2-116 


2-187 


1-646 


4-408 


27-0 


1869 


2-225 


3 


•062 


•468 


1 


871 


2-02 


1 


17 


•743 


•871 


4-25 


1-92 


3057 


2-239 


23-89ij 


1870 


2-673 


1-7 


■468 


•998 


1-354 


1-629 


•859 


2333 


1-436 


3-868 


2-21 


•972 


20-5 | 


Totals for) 
1 9 years, j 


42-483 


26-439 


29-483 


26-864 


38-714 


43-75 


39-493 


54-01 


52-581 


55-095 


43-164 


42-863 


494-93 1 


Means for) 
1 9 years, J 


2236 


1-391 


1-552 


1-414 


2-037 


2-303 


2-078 


2-843 


2-767 


2-9 


2*272 


2-256 


26-04 



The Tables from Dr Carlyle's and Mr Golding's Journals, I made nearly 
forty years ago, but they were never published. Mr Golding set a great value 
upon his Journals, and, for their safe keeping, gave them into the custody of 
the Rev. Richard Matthews of Wigton Hall, with a request that he would 
place them in his library. Mr Matthews died many years ago ; his library was 
sold after his death ; and Mr Golding's Journals disappeared. They have 
probably been torn up as waste paper. Dr Carlyle's family are all dead, and 
what has become of his Journals I know not. 

On comparing the averages of our observations with those of Mr Pitt, which 
I have also added, I find in three out of four, viz. — in Dr Carlyle's, Mr 
Golding's, and Mr Pitt's, April to be the driest month of the year. According 
to my own, February was the driest, and April stands next on the list. July, 
August, September, and October were wet months, according to all the Journals. 

The following are the averages or mean quantities of rain for the several 
months of the year, during the different periods. They are arranged in the 
progressive order of the increasing quantity of rain in each month, according to 






RAIN IN CARLISLE AND THE NEIGHBOURHOOD. 



317 



the several Journals, beginning with the driest month, and proceeding to the 
wet months : — 



Dr Caelyle's 


Journal. 


Mr Golding's 


Journal. 


Mr Pitt's Journal. 


Dr Barnes' Journal. 


27 Tears Mean. 


19 Years Mean. 


24 Years Mean. 


19 Years Mean. 




Inches. 




Inches. 




Inches. 




Inches. 


April, . 


1-262 


April, 


1-964 


April, . 


1-56 


February, 


. 1-391 


March, . 


1-309 


June, 


1-972 


June, 


1-96 


April, 


1-414 


January, 


1-458 


March, . 


2-006 


January, 


2-128 


March, . 


1-552 


May, 


1-625 


May, . 


2393 


March, . 


2-209 


May, . 


2-037 


February, 


1-751 


February, 


2-697 


February, 


2-308 


July, 


2-078 


December, 


1-812 


November, 


2-942 


May, . 


2-355 


January, 


2-236 


June, 


. 1-899 


January, 


3-05 


November, 


2-797 


December, 


2-256 


November, 


2-403 


December, 


3-27 


December, 


. 2-809 


November, 


2-272 


August, . 


2-486 


July, . 


3515 


September, 


2-827 


June, 


2-303 


July, . 


2-616 


September, 


3-537 


October, 


3-061 


September, 


2-767 


October, 


2723 


October, 


3676 


August, . 


3-24 


August, . 


2-843 


September, 


3-052 


August, . 


3916 


July, . 


3-317 


October, 


2-9 



From the averages it appears that about twice as much rain falls in each of 
the latter months of the Table, as in the month of April ; and about one-third 
less rain falls in the first six months of the year, than in the last six months. 

This distribution of rain answers wise and important purposes in the economy 
of nature. Were the reverse the case, i.e. did more rain fall in spring than in 
autumn or winter, very disastrous consequences would ensue. The great benefit 
of dry weather in spring to agriculture is obvious ; the value of an ounce of March 
dust is proverbial. The great fall of rain in the latter months of the year may, 
I think, in some measure be accounted for by the cold increasing as the sun 
recedes from us in autumn, and the vapours, which had been raised by the heat 
of summer, are then condensed and precipitated in the form of rain. 

Mr Golding, whom I had the pleasure of numbering among my friends, on 
seeing the comparative Table I had drawn up of the mean quantities of rain for 
the several months of the year, made the following remarks : — 

"This mode of exhibiting the subject is both curious and useful; and not- 
withstanding the great attention which I formerly paid to the phenomena of 
the weather, I confess that till now I never knew that April was the driest 
month of the year. April showers are so frequently mentioned as to give a 
general idea that it is rather a wet month than otherwise ; but it may be remarked 
that the showers in April are seldom stormy, or attended with great falls of 
rain, as some of the summer months are after the solstice is turned. This dryness 
of April is most probably occasioned by the less development of the electric 
fluid at that particular season of the year ; for when by means of the summer 
heats the air begins to be more strongly electrified, then it is that the showers 
become heavy, and often send down immense quantities of rain in a very short 
space of time. This it is which makes July and August generally the wettest 
months of the year; and happy it is for us poor mortals, that such is the 

VOL. XXVI. PART II. 4 N 



318 DR BARNES ON THE AVERAGE QUANTITY OF 

arrangement of nature ; for if there were not very heavy falls of rain during the 
excessive heats of summer, the ground would be exhausted of moisture, and 
vegetation entirely at a stand." 

There is a remarkable difference between the Journals of the late Dr 
Carlyle and Mr Pitt, in regard to the mean annual quantity of rain. Both 
Journals were kept at Carlisle, and both of the gentlemen, I have reason to 
believe, were careful and accurate observers. According to Dr Carlyle's 
Journal, the average annual quantity of rain is 24396 inches, and according to 
Mr Pitt's it is 30*571 inches. How is this to be accounted for ? Has the 
climate of this country undergone some change % It is evident from an inspection 
of the Journals, or of the Tables formed from them, that the quantity of rain is 
different in different years, and that sometimes there are a few wet years and 
sometimes a few dry years in succession. Is this the case with long periods of 
time ? So that Dr Carlyle's Journal may have been kept when there was a 
dry series of years, and Mr Pitt's when there was a wet series % Perhaps the 
difference may be explained by their rain-gauges being placed in different 
situations. Dr Carlyle's gauge was placed at the head of Abbey Street, 82 
feet above the sea-level, higher than Mr Pitt's, which was kept in Shaddongate, 
40 feet above the sea-level. It has been frequently remarked, that when one 
rain-gauge is placed on the top of a high tower, and another at the bottom, more 
rain falls into the lower gauge than into the higher one. But there is another 
reason which may be assigned for the difference. The situation of Dr Carlyle's 
rain-gauge was in the vicinity of his dwelling-house, which would occasionally 
prevent some rain falling into the gauge. It was placed on a wall on the S.W. 
side of his house. This I am inclined to consider the principal cause of the 
difference of the two Journals. Still the difference of altitude between Abbey 
Street and Shaddongate might have considerable effect, and may in some 
measure account for the different results. These causes, however, would have 
very little influence on the comparative monthly averages of the fall of rain. 

The Cumberland Infirmary stands on elevated ground on the S. side of the 
river Eden, 30 feet above the bed of the river, and about one mile N.W. of my 
garden at Carlisle, which is nearly of the same height as the site of the Cathedral. 
For several years I kept a rain-gauge at each place, constructed on the plan 
recommended in Brewster's Cyclopedia, and I always found a greater fall of 
rain at the former than at the latter place. The following is the quantity 
registered at each place in the years 1837 and 1838, and shows the difference 
of rain-fall at these two places in these years : — 



RAIN IN CARLISLE AND THE NEIGHBOURHOOD. 



319 





Jan. 


Feb. 


March. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 


Annual 
quantity of 
each year. 


1837 
rmary, . 


2-278 


1-866 


•91 


•535 


1-0 


2-38 


5-537 


4-53 


2-28 


3-12 


3-17 


3-66 


30-972 


den in \ ■ 
astle St., J 


1-59 


316 


1-02 


1-2 


1-13 


2-23 


4-37 


1-67 


•98 


2-9 


•82 


1-78 


22-85 


1838 
rmary, . 


1-215 


•59 


2-436 


1-51 


1-49 


4-69 


3-195 


3-45 


2-28 


2-65 


2-47 


•78 


26-756 


den in ) 
astle St., J 


1-05 


•09 


•976 


1-384 


1-69 


3-172 


1-85 


1-08 


1-035 


1-38 


1-4 


1-15 


16-257 



With regard to the difference that exists between the annual mean quantity 
of rain of Mr Golding's and Mr Pitt's Journals, Mr Golding's being 44 inches 
more than Mr Pitt's, I shall give you the explanation of the former gentleman 
in his own words, contained in a letter written by him many years ago : — 

" I find that the annual quantity of rain, according to my diary, is somewhat 
greater than that shewn by Mr Pitt's ; and this might naturally be expected 
from the difference of situation, for my observations were chiefly made at 
Aikbank, which borders on the hilly part of the country, — and it is well known 
that in a hilly, and more especially in a mountainous district, there is much 
more rain than in a level one. Besides, Carlisle has a further cause of exemp- 
tion from rain :— It lies nearly in the direction of the Solway Firth, and when 
storms come from off the Irish Sea, as they frequently do, the vapour on entering 
the Firth is attracted either by the Scotch or the English mountains, which 
will occasion more rain to fall on each side of the Firth, than in the direction 
of the Firth itself." 



Trans Roy. Soc. Edm r Vol XXVI 



Plate XI . 



FIG. I. w. 




1 3 



;/®^ 



i d, 



FIG. 5. 



'•^©S 





ff 



J Bell PetWrew, M I lal ; 



W.K.M! T«Uin,L:th' Earn? 



Trans. %. Soc Edm 1 Vol. XXVI 



Plate X: 



r. 




Fl G .7. 




b 



c 



FIG. 8 







Yn- 



1 '''*\W" 




FIG. 12 . 




FIG. 10. 




FIG. II 



JBellPstligrew.MI del 4 



W. H .W Tan-lane, Litti* Elm* 



Trans Hoy. Soc.Eam 1 Vol. XXVI. . 



Plate XIII 




"W.K M'Farlane.Lith 1 E3m* 



TiansEoj Soc ~EM Vol. XXVI 



Plate XIV 




J BsllTettigrew.lO iel* 



W.H.M'T 



Trans. Roy. Soc Edm 1 Vol. XXVI 



Plate XV. 




Trans. Roy. Soc.Edtf Vol.XXYl 



Plate XVI 




( 321) 



XV. — On the Physiology of Wings, being an Analysis of the Movements by 
which Flight is produced in the Insect, Bat, and Bird. By James Bell 
Pettigrew, M.D., F.R.S., Pathologist to the Royal Infirmary of Edinburgh, 
and Curator of the Museum of the Royal College of Surgeons of Edinburgh. 
Communicated by Professor Turner. (Plates XL to XVI.) 

(Received 2d August 1870. Read 16th January 1871.) 

INTRODUCTORY REMARKS. 

(For Table of Contents see end of Memoir.) 

In order to determine with exactitude the movements made by the wings in 
flight, and the part which the air plays in modifying them, I was induced several 
years ago to collect a large number of facts, and to undertake an extensive 
series of experiments with natural and artificial wings. My observations and 
experiments, I may remark, were not wholly confined to flight. On the con- 
trary, I traced the analogy between flying, swimming, and walking ; a circum- 
stance which compelled me to pay particular attention to the size, shape, and 
movements, not only of wings, but also of the travelling surfaces of quadru- 
peds, amphibia, and fishes. By adopting this method, I obtained suggestions 
which have proved of the utmost importance to me in my attempts at elucidat- 
ing the very intricate problem of flight. 

As there are, strictly speaking, only three highways in nature (the land, the 
water, and the air), so there are three principal varieties of locomotion. There 
are, however, a limited number of mixed forms, the animal in such cases being 
furnished with travelling surfaces, modified in such a manner as to enable it to 
progress upon, or in, two essentially different media. The mixed movements are 
alike interesting and instructive, as they prove that movements apparently very 
dissimilar are in reality only links of a great chain of motion, which drags its 
weary length over the land, through the water, and extends skyward. That, 
therefore, is not wanting which connects the motions peculiar to walking- 
animals with those peculiar to swimming and flying animals. Thus the seal 
furnishes the link between the land and water, and the galeopithecus between 
the land and air ; while the flying fish supplies the link between the water 
and the air. 

On making a careful examination of the structure and movements of the 

VOL. XXVI. PART II. 4 O 



322 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

great pectoral fins or pseudo-wings of the flying fish, I felt persuaded that a 
close analogy existed between the flippers, fins, and tails of sea mammals and 
fishes on the one hand, and the wings of insects, bats, and birds on the other ; 
in fact, that theoretically and practically these organs one and all formed 
flexible helices or screws, which, in virtue of their rapid reciprocating action, 
operated upon the water and air after the manner of double inclined planes. 

Guided by these indications, I especially directed my attention to the 
twisting flail-like movements of the wings of insects ; of the flippers and tails 
of sea mammals, and of the fins and tails of fishes. These I found all acted 
upon the air and water by curved surfaces, the curved surfaces reversing, 
reciprocating, and engendering a wave pressure, which could be continued 
indefinitely at the will of the animal. 

In order to prove that sea-mammals and fishes swim, and insects, bats, and 
birds fly, by the aid of curved figure of 8 surfaces, which exert an intermittent 
wave pressure, I constructed artificial fins, flippers, and wings, which curved 
and tapered in every direction, and which were flexible and elastic, particularly 
towards the tips and posterior margins. These fins, flippers, and wings were 
slightly twisted upon themselves, and when applied to the water and air by 
a sculling or figure of 8 motion, curiously enough not only reproduced the 
curved surfaces referred to, but all the other movements peculiar to the fins 
and tail of the fish when swimming, and to the wings of the insect, bat, and 
bird when flying. 

History of the Figure of 8 or Wave Theory of Flying. 

The Wing a Tivisted Lever or Helix. — I announced this view in a lecture 
delivered at the Royal Institution of Great Britain in the early part of 1867. 
An abstract of the lecture appeared in the Proceedings of the Institution under 
date the 22d of March 1867.* At pages 99, 100, and 101 of the abstract in 
question, the spiral conformation of the wing in the insect and bird is adverted 
to at length, and there described as a twisted lever or helix, which owes its 
peculiar elevating and propelling power in a great measure to its shape. Par- 
ticular emphasis is also placed upon the partial rotation of the wing on its long 
axis during extension and flexion, and to its screwing and unscrewing action 
during the down and up strokes, this being a " sine qua non " in flight. In the 
pages alluded to, the subjoined passages occur : — " The wings of insects and 
birds are, as a rule, more or less triangular in shape, the base of the triangle 
being directed towards the body, the sides anteriorly and posteriorly. They are 
also conical on section from within outwards and from before backwards ; this 
shape converting the pinion into a delicately graduated instrument, balanced 
with the utmost nicety to satisfy the requirements of the muscular system on 

* On the Various Modes of Flight in relation to Aeronautics. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 323 

the one hand, and the resistance and resiliency of the air on the other. . . 
The neurse or nervures in the insect's wing are arranged at the axis or root of 
the pinion, after the manner of a fan or spiral stair ; the anterior one occupy- 
ing a higher position than that farther back, and so of the others. As this 
arrangement extends also to the margins, the wings are more or less twisted 
upon themselves, and present a certain degree of convexity on their superior 
or upper surface, and a corresponding concavity on their inferior or under 
surface ; their free edges supplying those fine curves which act with such 
efficacy upon the air, in obtaining the maximum of resistance and the minimum 
of displacement ; or what is the same thing, the maximum of support with the 
minimum of slip. ..... All wings obtain their leverage by presenting 

oblique surfaces to the air, the degree of obliquity gradually increasing in a 
direction from behind forwards and downwards during extension, when the 
sudden or effective stroke is being given, and gradually decreasing in an oppo- 
site direction during flexion, or when the wing is being more slowly recovered 
preparatory to making a second stroke. The effective stroke in insects, and 
this holds true also of birds, is therefore delivered downwards and forwards, 
and not as the majority of writers believe, vertically, or even slightly backwards. 
. . . . To confer on the wing the multiplicity of movement which it re- 
quires, it is supplied at its root with a double hinge or compound joint, which 
enables it to move not only in an upward, downward, forward, and backward 
direction, but also at various intermediate degrees of obliquity. . . . The wing 

of the bird, like that of the insect, is concavo-convex, and more or less twisted 
upon itself. The twisting is in a great measure owing to the manner in which the 
bones of the wing are twisted upon themselves, and the spiral nature of their 
articular surfaces, the long axes of the joints always intersecting each other 
at nearly right angles. As a result of this disposition of the articular surfaces, 
the wing may be shot out or extended, and retracted or flexed in nearly 
the same plane, the bones of the wing rotating in the direction of their 
length during either movement. This secondary action, or the revolving of the 
component bones upon their own axes, is of the greatest importance in the 
movements of the wing, as it communicates to the hand and forearm, and con- 
sequently to the primary and secondary feathers which they bear, the precise 
angles necessary for flight. It, in fact, insures that the wing, and the curtain 
or fringe of the wing, which the primary and secondary feathers form, shall be 
screwed into and down upon the wind in extension, and unscrewed or with- 
drawn from the wind during flexion. The wing of the bird may therefore be 
compared to a huge gimlet or auger, the axis of the gimlet representing the 
bones of the wing ; the flanges or spiral thread of the gimlet the primary and 
secondary feathers." 

The lecture referred to formed part of a memoir which was communi- 



324 DP PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

catecl by Professor Huxley to the Linnean Society, and read before that body 
on the 6th and 20th of June 1867. It is published in extenso in the 26th 
volume of the Transactions of the Society, with upwards of eighty illustrations/"' 
The principal object of the memoir is to establish an analogy between the 
walking surfaces of quadrupeds, the swimming surfaces of fishes, and the flying 
surfaces of insects, bats, and birds. These are all described! and figured \ as 
twisted levers or screws in an anatomical sense (pages 361 and 362, figures 37, 
38, 39, and 40), and as flexible reversing screws in a functional or physiological 
sense (pages 336 and 362, figures 2, 41, 42, and 43). § As a consequence, 
the quadruped and biped || are represented as walking, IT and the seal and 

* On the Mechanical Appliances by which Flight is attained in the Animal Kingdom, &c. 

t Op. eit., from page 199 to page 267 inclusive. 

t Op. cit., Plate XV. figs. 49, 51, 57, 68, 69, 70. Likewise Diagram 18 A d'e'f, a'b', page 253. 

§ Op. cit, Plate XV. figs. 58, 59, 61, 73, 74, and 75. 

|| Op. eit., Plate XV. fig. 78. 

U I think it proper to state that various anatomists have carefully examined the form of the articular 
surfaces of the joints hi the limbs, more especially in man. The researches of the brothers "Weber and 
Professor Meyer of Zurich are so well known, that it may suffice simply to refer to them. I would also 
direct attention to the writings of Langer, Henke, Meissner, and the late Professor Goodsir, Langer, 
Henke, and Meissner succeeded in demonstrating the " screw configuration" of the articular surfaces of the 
elbow, ankle, and calcaneo-astragaloid joints, and Goodsir showed that the articular surfaces of the knee- 
joint consist of " a double conical screw combination." The last-named observer also expressed his belief, 
" that articular combinations, with opposite windings on opposite sides of the body, similar to those in 
the knee-joint, exist in the ankle and tarsal, and in the elbow and carpal joints ; and that the hip and 
shoulder joints consist of single-threaded couples, but also with opposite windings on opposite sides of 
the body." The following are the views of Langer as interpreted by Goodsir : — (Proc. Eoy. Soc. Edin., 
Jan. 18, 1858, and Anatomical Memoirs, vol. ii. p. 231.) " Langer, acting on the happy idea of pro- 
longing the screw by uniting, in one direction, a number of plaster casts of the same articular surface, 
succeeded in forming continued screws from the upper articular surface of the astragalus in the horse, 
panther, and human subject. Langer concludes that the ' go line ' (a line obtained from the scratch of 
a steel point fixed on one of the articular surfaces, and which marks the opposite surface when the joint 
is moved) of the ankle-joint in all the mammalia is a portion of a helix, and that therefore the astraga- 
loid surface is a segment of a cylindrical or conical male screw, while the tibio-fibular surface is a 
segment of the corresponding female screw. The right ankle-joint is a left-handed screw combination ; 
the left ankle-joint a right-handed. "When therefore the foot is conceived to be fixed, the leg, in passing 
from a position of extension to flexion, moves laterally outwards along the axis of rotation, and the sine 
of the angle of inclination of the thread — that is, in proportion to the extent of flexion and the rapidity 
of the screw." Goodsir, in attempting by Langer's method to develop those articular screw-models, found 
that when two casts were united, an apparently satisfactory helix was produced ; but in adding to the 
series, the spire diminished, and the helix closed upon itself ; so that it appeared that not only the 
angle of inclination of the thread, but also the radius of rotation, diminished. He was, therefore, of 
opinion, that the tibio-astragaloid articular surfaces could not be regarded as segments of a cylindrical 
series, and thought it extremely probable that, abstracting the terminal facets, the acting areas on each 
surface consist each of a segment of a conical screw — the convex portions of these two screws being on 
the astragaloid, the concave on the tibial articular surface ; the one screw coming into action in flexion, 
the other in extension. Goodsir's experiments on the knee and ankle-joints, conducted with extreme 
care, by the aid of fresh specimens, casts, and models, led him to conclude that both joints were ' spiral 
in their nature' — that hi fact they were ' screwed structures,' and that the movements of the knee-joint 
are combined gliding and rolling movements of conical screwed surfaces upon one another. The follow- 
ing are his own words : — " The general character of the curves observed, and the corresponding move- 
ments and structure of the joint (knee-joint) leave little doubt in my mind that the flexion and extension, 
combined gliding and rolling movements of the knee, are performed between two conical double-threaded 
screw-combinations, an anterior and a posterior — the anterior being a left-handed screw, and the posterior 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 325 

fish* as swimming in figure of 8, or looped curves. The wings of the insect, 
bat, and bird, are also described and figured as executing figure of 8 movements 
when the animals are hovering before an object, or when their bodies are 
artificially fixed (page 336, figure 2) ;t the figure of 8, as I explained, being 
opened out or unravelled when the animals are flying at a high horizontal 
speed to form a looped and then a waved track (pages 341, 342, 344, and 345, 
figures 10, 13, 14, and 15) .J 

The following brief passages from my memoir in the Transactions of the 
Linnean Society^ will, I hope, serve to elucidate the peculiar figure of 8 move- 
ments made by the wings in flight : — 

The Wing Twists and Untivists during its action. — " That the wing twists upon 
itself structurally, not only in the insect, but also in the bat and bird, any one 
may readily satisfy himself by a careful examination, || and that it twists upon 
itself during its action I have had the most convincing and repeated proofs.H 
The twisting in question is most marked in the posterior or thin margin of the 
wing, the anterior and thicker margin performing more the part of an axis. As 
a result of this arrangement, the anterior or thick margin cuts into the air 
quietly, and as it were by stealth, the posterior one producing on all occasions 
a violent commotion, especially perceptible if a flame be exposed behind the 
insect. Indeed, it is matter for surprise that the spiral conformation of the 
pinion, and its spiral mode of action, should have eluded observation so long ; 
and I shall be pardoned for dilating upon the subject when I state my convic- 
tion that it forms the fundamental and distinguishing feature in flight, and must 
be taken into account by all those who seek to solve this most involved and 
interesting problem by artificial means." The importance of the twisted confi- 
guration or screw-like form of the wing cannot be over-estimated. That this 
shape is intimately associated with flight is apparent from the fact that the 
rowing feathers of the wing of the bird are every one of them distinctly spiral 
in their nature ; in fact, one entire rowing feather is equivalent — morphologi- 
cally and physiologically — to one entire insect wing. In the wing of the martin, 
where the bones of the pinion are short and in some respects rudimentary, the 
primary and secondary feathers are greatly developed, and banked up in such a 

a right-handed screw in the right knee-joint ; the anterior a right-handed, and the posterior a left-handed 
screw in the left knee-joint. The movements which take place round these two combinations are 
alternate, those round the anterior completing extension and commencing flexion, those round the 
posterior completing flexion and commencing extension of the joint." 

* Op. tit., Diag. 2, page 204 ; Plate XV. fig. 76. 

t Op. tit, page 233, Diag. 5 ; Plate XV. fig. 61. 

X Op. tit, page 233, Diag. 6 j Plate XV. fig. 59. 

§ Op. tit, pages 231, 232, 233, and 234. 

|| Op. tit, Plate XV. figs. 68, 69, and 70. 

1 Op. tit., Plate XV. figs. 58, 61, 73, and 74. 

VOL. XXVI. PART. II. 4 P 



326 DP PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

manner that the wing as a whole presents the same curves as those displayed 
by the insect's wing, or by the wing of the eagle where the bones, muscles, and 
feathers have attained a maximum development. The conformation of the 
wing is such that it presents a waved appearance in every direction — the waves 
running longitudinally, transversely, and obliquely. The greater portion of the 
pinion may consequently be removed without essentially altering either its form 
or its functions. This is proved by making sections in various directions, and 
by finding that in some instances as much as two-thirds of the wing may be 
lopped off without materially impairing the power of flight. Thus, in the summer 
of 1866,"" I removed the posterior two-thirds from either wing of a blow-fly, 
and still the insect flew, and flew well. The only difference I could perceive 
amounted to this, that the fly, while it could elevate itself perfectly, flew in 
circles, and had less of a forward motion than before the mutilation. It had 
in fact lost propelling or driving power, the elevating or buoying power remain- 
ing the same. I took another blow-fly and removed the tip or outer-third of 
either wing, and found that the driving-power was the same as before the muti- 
lation, while the elevating or buoying power was slightly diminished. These 
experiments prove that the posterior or thin elastic margin of the wing is more 
especially engaged in propelling, the tip in elevating.! " The spiral nature of 
the pinion is most readily recognised when the wing is seen from behind and 
from beneath,^ and when it is foreshortened. § It is also well marked in some 
of the long winged oceanic birds when viewed from before, || and cannot escape 
detection under any circumstances, if sought for, — the wing being essentially 
composed of a congeries of curves, remarkable alike for their apparent sim- 
plicity and the subtlety of their detail." 

The Wing during its action Reverses its Planes, and describes a Figure of 8 
track in space. — " The twisting or rotating of the wing on its long axis is parti- 
cularly observable during extension and flexion in the bat and bird, and like- 
wise in the insect, especially the beetles, cockroaches, and others which fold 
their wings during repose. In these in extreme flexion the anterior or thick 
margin of the wing is directed downwards, and the posterior or thin one up- 
wards. In the act of extension, however, the margins, in virtue of the wing 
rotating upon its long axis, reverse their positions, the anterior or thick mar- 
gins describing a spiral course from below upwards, the posterior or thin 
margin describing a similar but opposite course from above downwards. 
These conditions, I need scarcely observe, are reversed during flexion. The 
movements of the margins during flexion and extension may be represented 

* Op. cit, pages 219, 220, 221, 222. 

t Eor further experiments in this direction, see footnote to pages 3G1 and 362. 

% Op. cit, Plate XV. figs. 68, 69, 70, 73, and 74. 

§ Op. cit., Plate XV. figs 61 and 62. 

I| Op. cit, page 253 ; Diagram 18 A, a'b', d'e'f.' 



DP, PETTIGREW" ON THE PHYSIOLOGY OF WINGS. 327 

with a considerable degree of accuracy by a figure of 8 laid horizontally."" .... 
It may likewise happen, though more rarely, that the anterior or thick margin 
of the pinion may be directed upwards and backwards during the return or up 
stroke. I infer this from having observed that the anterior margin of the wing 
of the wasp (when the insect is fixed and the wings are being driven briskly) 
is not unfrequently directed upwards and forwards at the beginning of the 
down stroke, and upwards and backwards at the commencement of the up or 
return stroke. A figure of 8, compressed laterally and placed obliquely with 
its long axis running from left to right of the spectator, represents the move- 
ment in question. The down and up strokes, as will be seen from this 
account, cross each other, the wing smiting the air during its descent from 
above, as in the bird and bat, and during its ascent from below, as in the flying 
fish and boys' kite. The pinion thus acts as a helix or screw in a more or less 
horizontal direction from behind forwards, and from before backwards ; but it 
has a third function — it likewise acts as a screw in a nearly vertical direction 

from below upwards If the wing (of the larger domestic fly) be viewed 

during its vibrations from above, it will be found that the blur or impression 
produced on the eye by its action is more or less concave. This is due to the 
fact that the wing is spiral in its nature,t and because during its action it twists 
upon itself in such a manner as to describe a double curve,! — the one curve 
being directed upwards, the other downwards. The double curve referred to is 
particularly evident in the flight of birds from the greater size of their wings. § 
The wing, both when at rest and in motion, may not inaptly be compared to the 
blade of an ordinary screw propellor as employed in navigation. || Thus the 
general outline of the wing corresponds closely with the outline of the propellor, 
and the track described by the wing in space is twisted upon itself propellor 
fashion. The great velocity with which the wing is driven converts the 
impression or blur IT into what is equivalent to a solid for the time being, in 
the same way that the spokes of a wheel in violent motion, as is well under- 
stood, completely occupy the space contained within the rim or circumference 

of the wheel From these remarks it will appear that not only the 

margins, but also the direction of the planes of the wing, are more or less 
completely reversed at each complete flexion and extension ; and it is this 
reversing, or screwing and unscrewing, which enables the wing to lay hold of 
the air with such avidity during extension, and to disentangle itself with such 
facility during flexion, — to present, in fact, a more or less concave, oblique, and 

* Op. cit., page 233, Diagram 5. Compare this diagram with. figs. 59 and 61 of Plate XV. 

t Op. cit., Plate XV. fig. 68. 

X Op. cit,. Plate XV. figs. 58 and 59 a a. Compare with a a of fig. 52. 

§ Op. cit, Plate XV. figs. 73 and 75 b a c. 

|| Op. cit, Plate XV. fig. 52 a a. 

f Op. cit, Plate XV. figs. 58 and 59. 



328 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

strongly resisting surface the one instant, and a comparatively narrow, non- 
resisting cutting edge the next. The figure of 8 action of the wing explains 
how an insect or bird may fix itself in the air, the backward and forward 
reciprocating action of the pinion affording support, but no propulsion. In 
these instances, the backward and forward strokes are made to counterbalance 
each other." 

The Wing, when advancing ivith the body, Describes a Waved Track. — 
" Although the figure of 8 represents with considerable fidelity the twisting of 
the wing upon its axis during extension and flexion, when the insect is playing 
its wings before an object, or still better, when it is artificially fixed, it is other- 
wise when the down-stroke is added, and the insect is fairly on the wing, and 
progressing rapidly. In this case the wing, in virtue of its being carried for- 
wards by the body in motion, describes an undulating or spiral course. * .... 
The down and up strokes are compound movements, — the termination of the 
down-stroke embracing the beginning of the up-stroke, the termination of the 
up-stroke, on the other hand, including the beginning of the down-stroke. 
This is necessary in order that the down and up strokes may glide into each 
other in such a manner as to prevent jerking and unnecessary retardation, — 
the angle made by the under surface of the wing with the horizon during the 
first part of the down-stroke being increased to support and propel the insect, 
and decreased during the second part to prepare it for making the up-stroke, 
and to diminish the friction caused by the wing itself, while it does not inter- 
fere with its sustaining power." .... 

The Margins of the Wings thrown into Opposite Curves diwing Extension 
and Flexion. — " The anterior or thick margin of the wing and the posterior or 
thin margin present different degrees of curvature, so that under certain con- 
ditions the two margins cross each other, and form a true helix (page 361, 
fig. 37). t The anterior margin (r, s) presents two well-marked curves, a corre- 
sponding number being found on the posterior margin (t, u). These curves ma) 7- , 
for the sake of clearness, be divided into axillary curves and distal curves, the 
former occurring towards the root of the wing, the latter towards its extremity. 
The curves (axillary and distal) found on the anterior margin of the wing are 
always the reverse of those met with on the posterior margin, i.e., if the con- 
vexity of the anterior axillary curve be directed downwards (r),\ that of the 
posterior axillary curve (t) is directed upwards,§ and so of the anterior and 
posterior distal curves (s, u). The two curves, axillary and distal, occurring on 
the anterior margin of the wing, are likewise antagonistic, the convexity of the 
axillary curve (r) being always directed downwards,|] when the convexity of the 

* Op. cit, page 233, Diagram. 6. f Op. cit.. Plate XV. figs. 70, 73, and 74. 

| Op. cit, Plate XV. fig. 73, e. § Op. cit, Plate XV. fig. 73, a, c. 

\\ Op. cit., Plate XV. fig. 73, c. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 329 

distal one (s) is directed upwards,""" and vice versa. The same holds true of the 
axillary and distal curves occurring on the posterior margin of the wing 
(t. u)A .... The anterior axillary and distal curves completely reverse them- 
selves during the acts of extension and flexion, and so of the posterior axil- 
lary and distal curves. This reversal of the curves is seen to most advantage 
in the posterior margin of the wing, formed in the bird, by the primary, second- 
ary, and tertiary feathers.;); When the wing is partially flexed the convexity 
of the distal curve (occurring on the posterior margin of the wing) is directed 
downwards (page 362, figure 41 a, &),§ that of the axillary curve upwards (a, c).\\ 
When the wing is rather more than half extended the curves are obliterated, 
the posterior margin of the wing becoming straight (page 362, figure 42 b, c).1F 
It is at this stage of extension that the axillary and distal curves reverse. 
When the wing is fully extended the convexity of the axillary curve is directed 
downwards (page 362, figure 43 a, c),** that of the distal one upwards (a, b),ff 
which is just the opposite of what happens in flexion. This antagonism in the 
axillary and distal curves observed in the posterior margin of the wing of the bird 
is referrible to changes induced in the anterior margin of the pinion, as the 
subjoined paragraph will show." .... 

The Tip of the Bird's Wing describes an Ellipse. — " The movements of the 
wrist are always the reverse of those occurring at the elbow joint. Thus, 
during extension, the elbow and bones of the forearm are elevated, and describe 
one side of an ellipse ; while the wrist and bones of the hand are depressed, and 
describe the side of another and opposite ellipse. U These movements are reversed 
during flexion, §§ so that when the elbow is raised and carried backwards, the 
wrist is lowered and carried forwards, and vice versa." \\\\ .... 

The Wing capable of Change of Form in all its Parts. — " From this descrip- 
tion it follows that when the different portions of the anterior margin are ele- 

" ;: ' Op. tit, Plate XV. fig. 73,/. t Op. tit, Plate XV. fig. 73, a, b, c. 

t Op. tit, Plate XV. figs. 73, 74, 75. § Op. tit, Plate XV. fig. 73, b. 

I] Op. tit, Plate XV. fig. 73, a, e. IT Op. tit., Plate XV. fig. 74, b, c. 

** Op. tit, Plate XV. fig. 75, c. ft QP- dt > Plate xv - fi g- 75 > «, b - 

%\ Op. tit., p. 249, Diagram 14. §§ Op. tit., p. 249, Diagram 15. 

I Similar movements occur in the body and tail of the fish in the act of swimming. " The double 
curve or spiral into which the fish throws itself when swimming may be conveniently divided into an 
upper or cephalic curve,* and a lower or caudal one.f "When the concavity of the caudal curve is biting 
or laying hold of the water, and when the concave surface of the tail is being forced during extension 
with great violence in the direction of the axis of motion, % where the concave surface is suddenly converted 
into a convex one, the concavity of the cephalic curve, i.e., the concave surface of the upper half of the 
fish, is being urged, with less vigour, in the direction of the same line from the opposite side of it. As the 
caudal and cephalic curves are obliterated when the line in question is reached, there is, consequently, a 
period (momentary it must be), between the effective and non-effective strokes, in which the body of the 
fish is comparatively straight, and, consequently, in a position to advance almost without impediment." § 

* Op. cit., Diag. 2, d, p. 204. t Op. tit., Diag. 2, c, p. 204. J Op. tit, Ding. 2, a, I, p. 204 

§ Op. cit., p. 205. 

VOL. XXVI. PART II. 4 Q 



330 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

vated, corresponding portions of the posterior margin are depressed, the dif- 
ferent parts of the wing moving in opposite directions, and playing, as it were, 
at cross purposes for a common good — the object being to rotate or screw the 
wing down upon the wind at a gradually increasing angle during extension, 
and to rotate it in an opposite direction and withdraw it at a gradually 
decreasing angle during flexion. It also happens that the axillary and 
distal curves co-ordinate each other and bite alternately, the distal curve 
posteriorly seizing the air in extreme extension with its concave surface 
(while the axillary curve relieves itself by presenting its convex surface), 
the axillary curve, on the other hand, biting during flexion with its con- 
cave surface (while the distal one relieves itself by presenting its convex 
one). The wing may, therefore, be regarded as exercising a fourfold func- 
tion, the pinion in the bird being made to move from within outwards, and 
from above downwards during extension, in the effective or down stroke ; and 
from without inwards, and from below upwards, during flexion in the up or 
return stroke." 

The Wing during its Vibration produces a Cross Pulsation.- — "This oscillation 
of the wing on two separate axes — the one running parallel with the body of the 
bird, the other at right angles to it — is well worthy of attention, as showing that 
the wing attacks the air on which it operates in every direction, and at almost the 
same moment, viz., from within outwards, and from above downwards, during 
the down or effective stroke ; and from without inwards, and from below upwards, 
during the up or return stroke. As a corollary to the foregoing, the wing may 
be said to agitate the air in two principal directions, viz., from within outwards, 
or the reverse, and from behind forwards, or the reverse, the agitation in question 
producing two powerful pulsations — a longitudinal and a lateral ; the longitu- 
dinal running in the direction of the length of the wing, the lateral in the 
direction of its breadth. As, however, the curves of the wing glide into each 
other when the wing is in motion, so the one pulsation merges into the other by 
a series of intermediate and lesser pulsations. 

The longitudinal and lateral pulsations occasioned by the wing in action 
may be fitly represented by wave-tracks running at right angles to each other, 
the longitudinal wave track being the more distinct." 

Analogy between the Wing in Motion and the Sounding of Sonorous Bodies.— 
" It is a remarkable circumstance that the undulation or wave made by the wing 
when the insect and bird are fixed or hovering before an object, and when they 
are progressing, corresponds in a marked manner with the track described by 
the stationary and progressive waves in fluids,"' and likewise with the waves of 
sound.t This coincidence would seem to argue an intimate relation between 

* Handbook of Natural Phil. (vol. on Electricity, Magnetism, and Acoustics), by Dr Labdneii 
(Lond. 1863), pp. 366-7. f Op. c#.,pp. 378, 379, 380. ' 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 331 

the instrument and the medium on which it is destined to operate — the wing 
acting in those very curves into which the atmosphere is naturally thrown in the 
transmission of sound, in order, as appears to me, to secure the maximum of 
progression with the minimum of slip. Can it be that the animate and inani- 
mate world reciprocate, and that animal bodies are made to impress the inani- 
mate in precisely the same manner as the inanimate impress each other f This 
much seems certain : — The wind communicates to the water similar impulses to 
those communicated to it by the fish in swimming ; and the wing in its vibrations 
impinges upon the air as an ordinary sound would. The extremities of quad- 
rupeds, moreover, describe spiral tracks on the land when walking and run- 
ning ; so that one great law would seem to determine the course of the insect 
in the air, the fish in the water, and the quadruped on the land." 

Various other passages might be adduced in elucidation and support of the 
curve, wave, or figure of 8 theory of flying, as originally propounded by me, but 
a sufficient number have, I trust, been cited to prove that the theory owes its 
origin and development to no hasty generalisation from a few scattered and 
imperfectly known facts, but that it rests upon a broad basis, such, in reality, as 
nature herself supplies. 

In order that the reader may form his own conclusions on this point, I pro- 
pose to lay before him in the course of my subsequent remarks the observations 
and experiments on which the theory was originally founded. The present 
memoir is illustrated by upwards of ninety original diagrams and drawings, the 
intricacy of the subject being such as to necessitate a free use of the pencil. 
The drawings have been made by myself from the life. I have gone into the 
origin and development of the figure of 8 theory of flying somewhat in 
detail ; first, because the passages selected have an obvious bearing on the 
subject of the present communication ; and second, because nearly two 
years after I had made my views known, Professor E. J. Marey (Col- 
lege of France, Paris), published a series of lectures and papers in the 
" Eevue des Cours Scientifiques de la France et de L'Etranger,"* and in 
the " Comptes E-endus hebdomaclaires des Stances de L'Acade"mie des 
Sciences," t in which the figure of 8 theory of wing movements is put 
forth as a new discovery. Professor Marey made no allusion to my 
researches, which was the more remarkable, as an abstract of my lecture, 
already referred to (p. 322), as published in the Proceedings of the Royal 
Institution of Great Britain in March 1867, was translated into French, and 

* Les mouvements de l'aile chez les insectes, p. 171, 13th Eevrier 1869. Mecanisnie du vol chez 
les insectes — comment se fait la propulsion, p. 252, 20th Mars 1869. Du vol des oiseaux, p. 578, 
14 Aout 1869. Du vol des oiseaux (suite), p. 601, 21 Aout 1869. Du vol des oiseaux (suite), p. 
646, 11 Septembre 1869. Du vol des oiseaux (fin), p. 700, 2 October 1869. 

\ Determination experimental du mouvement des ailes des insectes pendant le vol. Par 
M. E. J. Marey. Tome LXVII. p. 1341, Tome LXVIII. p. 667. 



332 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

appeared on the 21st of September of that year in the same Journal"' in which 
Professor Marey's lectures were originally published. Having had my attention 
directed to this circumstance, I addressed a letter to the French Academy on 
the 28th of March 1870, which appeared in the " Comptes Eendus " (p. 875) on 
the 18th of April 1870. In it I claim to have been the first to describe and 
illustrate the following points, viz : — 

That quadrupeds walk, and fishes swim, and insects, bats, and birds fly by 

figure of 8 movements. 
That the flipper of the sea bear, the swimming wing of the penguin, and 
the wing of the insect, bat, and bird, are screws structurally, and 
resemble the blade of an ordinary screw propellor. 
That those organs are screws functionally, from their twisting and un- 
twisting, and from their rotating in the direction of their length, 
when they are made to oscillate. 
That they have a reciprocating action, and reverse their planes more or less 

completely at every stroke. 
That the wing describes a figure of 8 track in space when the flying animal 

is artificially fixed. 
That the wing, when the flying animal is progressing at a high speed in a 
horizontal direction, describes a looped and then a ivaved track, from 
the fact that the figure of 8 is gradually opened out or unravelled as the 
animal advances. 
That the wing acts after the manner of a kite. 

Previous to replying to the foregoing, Professor Marey wrote me, to inquire 
how he could respond to my "juste reclamation," without entering into a dis- 
cussion which Avould needlessly complicate the question. I thereupon asked 
him to admit in a letter addressed to the French Academy my claim to have 
described and illustrated before him the figure of 8 movements made by the 
wings of insects, bats, and birds, when those animals are artificially fixed, and 
of the spiral and undulatory wave tracks made by the wings of said insects, 
bats, and birds, when the animals are flying at a high horizontal speed. This 
he has done, as the subjoined extract from his letter, printed in the " Comptes 
Rendus " for May 16, 1870 (p. 1093), will show :— " J'ai constate" qu' effective- 
ment M. Pettigrew a vu avant moi, et repr^sente" dans son M^moire, la forme 
en 8 du parcours, de l'aile de l'insecte: que la methode optique a laquelle j'avais 
recours est a peu pres identique a la sienne . . . . je m' empresse de 
satisfaire a cette demande legitime, et je laisse entierement la priorite sur moi, 
a M. Pettigrew relativement a la question ainsi restreinte." 

Mode of Investigation pursued by the Author. — I obtained my results by 

* Revue des Cours Scientifiques de la France et de l'Etranger. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 333 

transfixing the abdomen of insects with a fine needle, and watching the wings 
vibrate against a dark background ; by causing dragon-flies, butterflies, blow- 
flies, wasps, bees, beetles, &c, to fly in a large bell jar, one side of which was 
turned to the light, the other side being rendered opaque by dark pigment ; 
by throwing young pigeons and birds from the hand into the air for the first 
time ; by repeated observation of the flight of tame and wild birds ; by stiffen- 
ing, by tying up, and by removing portions of the wings of insects and birds ; 
by an analysis of the movements of the travelling surfaces of quadrupeds, 
amphibia, and fishes ; by the application of artificial fins, flippers, tails, and 
wings to the water and air ; and by repeated dissections of all the parts directly 
and indirectly connected with flight. 

Professor Marey obtained his results by gilding the extremities and mar- 
gins of the wings of the insect with minute portions of gold leaf; by the 
application of the different parts (tip and anterior margin) of the wing of the 
insect to a smoked cylinder rotating at a given speed, the wing being made to 
record its own movements ; by the captive and free flight of birds, which carried 
on and between their wings an apparatus which, by the aid of electricity, regis- 
tered the movements of the wings on a smoked surface, travelling at a known 
speed in a horizontal direction ; and by the employment of an artificial wing, 
constructed on the plan recommended by Borelli, Chabrier, Straus-Durck- 
heim, Girard, and others. 

Professor Marey describes and figures a captive insect (the wasp) with its 
wings forming figure of 8 loops/"" and a free insect, with its wings describing a 
waved track, t precisely similar to what I described and figured in a variety of 
ways in my memoir. J He also shows that the tip of the wing of the bird, 
because of its alternately darting out and in during extension and flexion, 
describes an ellipse. This, curiously enough, is another of the many points in 
which I have anticipated this author, and one which I took special pains to 
establish, § having in my memoir devoted no less than ten figures || to its illus- 
tration. Professor Marey's views may therefore be regarded as confirmatory 
of my own, as the following brief passage, selected from one of his j)apers, will 
show. He writes : — "But if the frequency of the movements of the wing vary, 
the form does not. It is invariably the same — it is ahvays a double loop — a 

* Revue des Cours Scientifiques de la France et de l'Etranger, 13 Fevrier 1869, page 175, figure 
5. Professor Marey represents the wing of the wasp as fanning the air in a vertical direction. In 
reality, the wing of the wasp and of most insects is made to vibrate very obliquely, and in a more or 
less horizontal direction. 

f Revue des Cours Scientifiques et de la France et de l'Etranger, 13 Fevrier 1869, pages 173, 
174, and 176. 

\ Trans. Linn. Society, Vol. XXVI, page 233, Diagrams 5 and 6 ; page 249, Diagrams 14, 15, 
and 16 ; Plate XV. figures 59 and 61. Vide introduction to present memoir. 

§ Op. tit., pages 247, 248, 249, and 250. 

|| Op. at, pages 248 and 249, Diagrams 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16. 

VOL. XXVI. PART II. 4 R 



334 DE PETTIGEEW ON THE PHYSIOLOGY OF WINGS. 

figure of 8. Whether this figure be more or less apparent, whether its branches 
be more or less equal, matters little ; it exists, and an attentive examination will 
not fail to reveal it."""" 

Professor Marey's experiments, I may add, have been repeated and verified 
in England by Mr Senecal. This investigator also represents and describes the 
double loop and figure of 8 movements.^ These two sets of experiments con- 
ducted independently, and after a considerable interval, by M. Marey and Mr 
Senecal respectively, will, I hope, suffice to establish the absolute correctness 
of the " Figure of 8 or Wave theory of Flight." 



NATURAL FLIGHT.} 

Method of Testing the Accuracy of the Figure of 8 Theory of Wing Move- 
ments. — The correctness of the figure of 8 theory of flying may be readily estab- 
lished by a careful study of the rapidly vibrating wing of the wasp or common 
blow-fly. 

If the body of the former be held, and the wing made to vibrate in front of 
a dark screen, it will be found that not only the tip but also the margins of the 
wing describe a figure of 8 track in space. 

It will further be observed that the planes of the wing are as a rule 
reversed during the down and up strokes ; nay, more, that the angles of inclina- 
tion made by the surfaces of the wing with the horizon vary at every stage of 
the wing's progress, this variation in the angles being accompanied by a varia- 
tion in the curves occurring on the anterior and posterior margins, as already 
explained. As a consequence, the wing is moving in all its parts at the same 
time — a somewhat remarkable occurrence, and calculated, it appears to me, to 
excite the curiosity, if it does not rivet the attention of physiologists. The wing 
of the insect is, with few exceptions, more flattened than that of the bat and 
bird, a circumstance which enables it, when it is made to vibrate in a more or 
less horizontal direction, and when its planes are reversed at the end of each 
stroke, to apply its under or ventral surface to the air when it is urged 
from behind forwards, and its upper or dorsal one when urged from before 
backwards (figures 3 and 4, page 338). It sometimes happens that the 
posterior margin of the wing is rotated in an upward direction at the end 
of the forward stroke, and in this case it is the under surface of the wing which 
is effective during the backward stroke (vide g h ij k I of figure 19, page 351). 

* Mechanisnie du vol des insectes — comment se fait la propulsion. Eevue des Cours Scientifiques 
de la France et de l'Etranger, 20th March 1869. 

t Fifth Annual Eeport of the Aeronautical Society of Great Britain for 1870, pages 42-47. 
Figures 1,2; Diagrams 1-4. 

\ Artificial flight is described at page 402. 



DR, PETTIGREW ON THE PHYSIOLOGY OF WINGS. 335 

When the wing acts in this manner, it is the under or ventral surface which is 
effective both during the forward and backward strokes. The wing, during 
the back stroke occasions very little friction, from its being placed in a more 
or less horizontal position — this position being favourable to its affording a 
maximum of support. The upper and under surfaces of the wing are applied 
to the air alternately, more particularly when the insect is fixed, or when it is 
hovering in one spot. When it is flying at a high horizontal speed, and when 
the wing is made to oscillate in a slightly vertical direction, as in the butterfly 
(figures 29, 30, 31, 32, 33, and 34, page 360) and dragon-fly (figures 35, 36, 37, 
and 38, page 361), it is the under or concave surface of the pinion which does 
the principal part of the work, this attacking the air both during the down or 
forward stroke and the up or backward stroke, like a boy's kite, as explained 
at pages 349 and 350, figures 16 and 17. The direction of the stroke varies 
slightly according to circumstances, but it will be quite proper to assume that 
the wing of the insect is made to vibrate in a more or less horizontal direction, 
and that of the bird and bat in a more or less vertical direction. By a slight 
alteration in the position of the body, or by a rotation of the wing in the 
direction of its length, the vertical direction of the stroke is converted into 
a horizontal direction, and vice versa. The facility with which the direction of 
the stroke is changed is greatest in insects ; it is not uncommon to see them 
elevate themselves by a figure of 8 horizontal screwing motion, and then, sud- 
denly changing the horizontal screwing into a more vertical one, to dart rapidly 
forward in a curved line. The horizontal screwing movement is represented at 
figures 2, 3, 4, 5, 6, 7, and 10, pages 336, 338, 340, and 341 ; and the vertical 
screwing at figures 12 and 13, page 342. The horizontal action of the insect's 
wing is described at pages from 336 to 341 inclusive, and the vertical action at 
pages from 347 to 355 inclusive. The vertical action of the bat and bird's wing 
is described at page 342, and at pages from 366 to 397 inclusive. Whether the 
wing is made to vibrate vertically or horizontally, it, practically speaking, in 
progressive flight, strikes doivnwards and forwards during the down stroke, and 
upwards and forwards during the up stroke, as fully explained at pages 344 
and 345. 

Compound Rotation of the Wing. — The wing during its vibration rotates 
upon two separate centres, the tip rotating around the root of the wing as an 
axis (short axis of wing), the posterior margin rotating around the anterior margin 
(long axis of wing). This compound rotation goes on throughout the entire 
down and up strokes, and is intimately associated with the power which the 
wing enjoys of alternately seizing and evading the air. 

The Wing inclined Fomvards at the End of the Doivn Stroke and Backwards 
at the End of the Up Stroke. — I had my attention first strongly directed to the 
screwing figure of 8 action of the wing by closely observing the twisting figure 



336 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



of 8 movements made by the pectoral fins and tails of fishes, and from finding that 
in the beetle, blow-fly, and wasp (anterior wings), the posterior margin and body 
of the wing were inclined forwards (fig. 1 a) with reference to the head of the 
insect, at the end of the down stroke, and backwards (fig. 1 b) at the end of the 
up stroke. 




The Wing Rotates upon its Long Axis. — This at once suggested a rotation of the 
wing upon its long axis along its anterior margin, or, what is practically the 
same thing, a folding and plaiting of the posterior or thin yielding margin of 
the wing around the anterior semi-rigid and comparatively unyielding margin 
— a certain amount of rotation, or what is equivalent thereto, being necessary 
to reverse and change the planes of the wing at each stroke. 

The Wing Twists and Untwists during its action. — I further observed that the 
planes of the wing were not only changed at the end of each stroke, but that the 
wing at this juncture was twisted upon itself, the outer portion of the posterior 
margin of the wing at the end of the down or forward stroke being inclined 
forwards (g of fig. 2), while the inner portion was inclined backwards (r of fig. 2) ; 
whereas at the termination of the up or backward stroke, the outer portion of 
the posterior margin was inclined backwards (a of fig. 2), while the inner 
portion was inclined forwards (s of fig. 2). 



»C4 




The Image produced on the Eye by the Wing in Motion is Concavo-Convex, 
and Twisted. — I likewise discovered that the blur or impression produced on the 
eye by the rapidly oscillating wing was tivisted upon itself {fig. lcdh,eg f), and 
more or less concave above (c d e fig. 1), and convex below (fgh fig. 1), a circum- 
stance which, while it strongly corroborated the opinion that the wing rotated 
upon its long axis during its vibration indicated that the twisting and reversal 



DR PETTIGKEW ON THE PHYSIOLOGY OF WINGS. 337 

of the planes of the wing occurred more especially at the end of the down and 
up strokes. I inferred this from observing that the angle made by the wing 
with the horizon is greater towards the termination than towards the middle of 
the strokes. This could readily be ascertained by looking at the blur produced 
by the oscillating wing edgewise, and this view revealed what is perhaps the 
most important feature in wing movements, viz., that the tip of the wing during 
its vibrations describes a scooped out (cde fig. 1) figure of 8 track as repre- 
sented at 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14 of fig. 2. 

The Direction of the Stroke of the Wing in the Insect — ivhat Effective and what 
Non-effective — the Kite-like Action of the Wing. — This view also showed that the 
wing of the insect is made to vibrate in a more or less horizontal direction (figs. 
3 and 5, page 338, Plate XI. fig. 4), in which respect it differs somewhat from 
the wing of the bat and bird, these being worked more or less vertically (Plate 
XI. figs. 5 and 6, and Plate XIV. figs. 18 and 19). The oblique action of the 
pinion is necessary to avoid the resistance of the air during the up stroke, the 
wing of the insect being in one piece, and having in many cases no adequate 
apparatus for diminishing its area during its ascent. One great advantage 
gained by the wing of the insect reversing its planes at the end of each stroke 
consists in the great length of the effective stroke — the wing flying backwards 
and forwards like a true kite, and tacking upon the air so suddenly as to 
occupy very little either of time or space."" The period occupied by the wing 
in reversing does not apparently amount to more than one-eighth of the time 
taken up by one entire stroke, so that something like seven- eighths of the 
area mapped out by the rapidly vibrating wing represents buoying area — the 
remaining eighth slip. This, put in other words, simply means that in one 
passage of the wing from behind forwards (down stroke) the pinion is effective 
in seven- eighths of its course and non-effective in one-eighth, the same remark 
being applicable to the passage of the wing from before backwards (up stroke). 

The Wing Attacks the Air at various Angles. — It is just possible that even less 
than one-eighth is devoted to slip, from the fact that the wing when it is being- 
reversed is slowed and applied to the air at an increased angle — a surface 
which makes a large angle with the horizon, giving, when forced against the 
air at a low speed, as much support as a similar surface whose inclination is 
less, but whose speed is higher. As the wing attacks the air during the down 
and up strokes at various angles, those angles being greatest when the wing 
travels slowest, and least when the wing travels most rapidly, it follows that the 
wing adapts itself to the resistance opposed to its passage by the air, and always 
extracts the maximum of support from it. The wing, in this respect, differs 

* The movements of the wing somewhat resemble those of a sailing ship. The wing and ship 
both tack upon the wind, and both change their tack or reverse abruptly. The changing of the tack 
is moreover always accompanied by a slowing or diminution of the speed. 

VOL. XXVI. PART II. 4 S 



338 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



widely from the screw propellors at present in use — the blades of these propel- 
lors always striking at a given angle and in the same direction. The advantage 
in favour of the wing as compared with the screw as employed in navigation 
is very great, and not at present understood.'" The area mapped out by the 
wing during the effective stroke and while reversing; the various angles made 
by the surfaces of the wing with the horizon in its passage to and fro ; the 
rotating and twisting of the posterior or thin margin of the wing round the 
anterior or thick margin ; and the figure of 8 track made by the tip of the wing 
during its action, as seen in the wasp, are shown at figs. 3, 4, 5, and 6. 




fh Cf 



Fig. 3. 




Fig. 4. 



—X 




Analysis of the Movements of the Wing of the Wasp, Reversal of the Planes 
of the Wing, Reciprocating Action, <$c. — In the wasp the wing commences the 
down or forward stroke at a of figures 3 and 5 ; and it will be observed that 
the angle which it makes with the horizon (x of fig. 5) is something like 45°. 
At b (figures 3 and 5) the angle is slightly diminished, partly because of a rota- 
tion of the wing along its anterior margin (long axis of wing), partly from 
increased speed, and partly from the posterior margin of the wing yielding to a 
greater or less extent. 

At c the angle is still more diminished from the same causes. 

At d the wing is slowed slightly, preparatory to reversing, and the angle 
made with the horizon (x) increased. 

At e the angle, for the same reason, is still more increased; while at /the 
wing is at right angles with the horizon. It is, in fact, in the act of reversing. 

* For specific differences between the screws formed by the wings and the propellors employed in 
navigation, see memoir by the author, Trans. Linn. Society, vol. xxvi. pages 228, 229, 230, and 231. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 339 

At g the wing is reversed, and the up or back stroke commenced. 

The angle made at g is, consequently, the same as that made at a (45°), with 
this difference, that the anterior margin and outer portion of the wing, instead 
of being directed forwards, with reference to the head of the insect, are now 
directed backwards. 

During the up or backward stroke all the phenomena are reversed, as shown 
at ghijkl of figures 4 and 6 ; the only difference being that the angles made by 
the wing with the horizon are somewhat less than during the down or forward 
stroke — a circumstance which facilitates the forward travel of the body, while it en- 
ables the wing during the back stroke still to afford a considerable amount of sup- 
port. This arrangement permits the wing to travel backwards when the body 
is travelling forwards ; the diminution of the angles made by the wing in the 
back stroke giving very much the same result as if the wing were striking 
in the direction of the travel of the body. The slight upward inclination of 
the wing during the back stroke permits the body to fall downwards and for- 
wards to a slight extent at this peculiar juncture, the fall of the body, as will be 
more fully explained hereafter, contributing to the elevation of the wing. 

If figure 5, representing the down or forward stroke, be placed upon figure 
6, representing the up or backward stroke, it will be seen that the wing crosses 
its own track more or less completely at every stage of the down and up strokes. 
As, moreover, the wing draws a current after it, and is pursued in its passage 
from above downwards by a stream of air which it meets in its passage from 
below upwards, it follows that the pinion, during the down or forward stroke, 
creates a current on which it operates during the up or backward stroke, and 
vice versa; hence the reciprocating action of the wing. 

The wing reciprocates most perfectly, and the figure of 8 is most dis- 
tinct when the insect is fixed artificially, or when it is hovering of its own accord 
in a given spot, as is well shown at a b c d efghijklm n op of fig. 8, 
p. 340, where the wing is represented as screwing steadily downwards. 

Points wherein the Wing differs from the Scull of the Boatman. — The down- 
ward screwing movement of the wing somewhat resembles the action of an oar 
in sculling, as represented at a b, c d, x s, of fig. 7, the 
cross movement occasioned by the rotation of the 
wing on its long axis as it darts to and fro being 
shown at m n, o p, q r. There is, however, this 
marked difference. It is the upper surface of the oar 
which is effective in sculling, whereas it is the under 
surface of the wing which is effective in flying." This 
is accounted for by the fact that the oar simply propels Fi g 7. 

— the boat being buoyant, the wing propelling and 

* A precisely similar difference is found to exist between the aerial or flying wing and the subaquatic 
VOL. XXVI. TART II. 4 T 




340 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



likewise elevating. There is this further difference. The margins of the blades of 
the oar are of the same thickness, the axis of rotation running midway between 
the two ; the anterior margin of the wing, on the contrary, is much thicker than 
the posterior one, the axis of rotation corresponding to the former. The oar, as 
far as the margins of its blade are concerned, is as it were concentric, the wing 
eccentric. As the downward screwing movement of the wing, in virtue of the 
action and reaction of the wing and air upon each other, is at once converted 
into an upward screwing movement, as shown at a! b' c d! e' '/' ' g' h' i'f k' V m' nf 
o' p' of fig. 9, it follows that the body of the insect is rapidly but steadily elevated 
in an almost vertical wave-line. The impulse is communicated to the wing at 
points corresponding to the heavy portions of the line in figure 8, and the 
corresponding upward recoil is indicated at similar points in figure 9. 





Fig. 9. 



Hoiv the Figure of 8 is Unravelled, and becomes a Waved-Track. — When the 
insect flies in a horizontal direction, and the speed attained increases with the 
duration of flight, the wing reciprocates less and less perfectly, because the figure 
of 8 sweeps described by it are converted into a looped and then a waved track, 
as represented at # & c d efg h ij k I m n o p q r s t of figure 10 (p. 341); the cor- 
responding looped and waved track clue to recoil being shown at similar letters 
of figure 11 (p. 341). When the horizontal speed attained by the insect is high, 



or diving wing. In the gannet, cormorant, merganser, grebe, &c, which fly under the water, it is the upper 
or dorsal surface of the pinion which gives the effective stroke, whereas in aerial flight it is the under or 
ventral surface. This is proved by the fact that in the penguin and great auk, which are incapable of flying 
out of the water, and confine their efforts to diving or swimming under it, the wing is actually twisted 
round, so that the dorsal surface of the pinion occupies the position normally occupied by the ventral surfaces 
in all other birds. This is necessitated by the fact that a diving bird, seeing it is of lighter specific 
gravity than the water, must always fly downwards ; in other words, it must counteract buoyancy 
as the flying bird counteracts gravity — buoyancy forcing the diving bird to the surface of the water in 
the same way that gravity drags the flying bird to the surface of the earth. Levity and weight are 
therefore separate forces, and act under diametrically opposite conditions, levity being quite as useful to 
the diving bird as weight to the flying one. The wings of diving birds are applied to the water 
precisely in the same manner as the flippers of the seal, sea bear, walrus, turtle, porpoise, whale, manatee, 
&c. All these animals are lighter than the water, and, as a consequence, their travelling surfaces 
to be effective must act from below as in the case of the scull. It is the reverse in the air, the 
travelling surfaces acting invariably from above. Eor further development of this view see footnote to 
page 371. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



341 



the wing is successively and rapidly brought into contact with innumerable 
columns of undisturbed air. It consequently is a matter of indifference whether 
the wing is carried at a high speed against undisturbed air, or whether it operates 
upon air travelling at a high speed (as, e.g., the artificial currents pro- 
duced by the rapidly reciprocating action of the wing). The result is the same 
in both cases, inasmuch as a certain quantity of air is worked up under the 
wing, and the necessary degree of support and progression extracted from it. 
It is, therefore, quite correct to state, that as the horizontal speed of the body 
increases the reciprocating action of the wing decreases, and vice versa. In 
fact, the reciprocating and non-reciprocating function of the wing in such cases 
is purely a matter of speed. If the travel of the wing is greater than the hori- 
zontal travel of the body, then the figure of 8 and the reciprocating power of 
the wing will be more or less perfectly developed, according to circumstances. 
If, however, the horizontal travel of the body is greater than that of the wing, 
then it follows that no figure of 8 will be described by the wing, that the 
wing will not reciprocate to any marked extent, and that the organ will describe 




Fi«. 10. 




Fig. 11. 



a waved track, the curves of which will become less and less abrupt, i.e., longer 
and longer in proportion to the speed attained. The downward looped track 
represented at fig. 10, is at once converted into an upward looped track, as shown 
at figure 11, in virtue of the action and reaction of the wing and air upon each 



342 



DR PETTTGREW ON THE PHYSIOLOGY OF WINGS. 



other, the body of the insect being carried along a waved line obliquely upwards 
and forwards (q r s t, fig. 11, p. 341). The waved track made by the wing is gene- 
rated by the figure of 8 loops being gradually opened out, these becoming less and 
less distinct as the insect advances, as is more especially shown at nopqrst of 
both figures (10 and 11, p. 341). The impulse is communicated to the wing at 
ac egikmo qsoi fig. 10, and the upward recoil at corresponding letters of fig. 11. 
The waved track formed by the ascent and descent of the wing of the bat 
and bird is originated in a similar manner, but in this case the figure of 8 
loops are disposed more vertically, because of the more vertical direction of 
the stroke, as shown at efg h ij k I of figure 12. ( Vide also Plate XL figures 
5 and 6). In this figure (12) the oar, as seen at a b, x s, and cd, represents the 




Fig. 12. 

wing of the bat and bird at the beginning, middle, and termination of the 
down stroke — the little oar, m n op q r, indicating the cross action of the wing. 
The large oar is more especially engaged in elevating, the little one in pro- 
pelling. The manner in which the figure of 8 loops made by the wing of the 
bat and bird during its ascent and descent are opened out or unravelled by the 




Fiff. 13. 



horizontal travel of the body is shown at a b c d efg h ij klmnop of figure 13 ; 
the completed waved track being seen at s t u v w of the same figure. 



DR FETTIGREW ON THE PHYSIOLOGY OF WINGS. 343 

When the Wing Ascends the Body Descends, and vice versa. — As the body 
of the insect, bat, and bird falls forwards in a curve when the wing ascends, and 
is elevated in a curve when the wing descends, it follows that the trunk of the 
animal is urged along a waved line, as represented at 1, 2, 3,4, 5 of figure 14, p. 344, 
the waved line ac eg i of the same figure giving the track made by the wing. 
I have distinctly seen the alternate rise and fall of the body and wing when 
watching the flight of the gull from the stern of a steam-boat. 

The direction of the stroke in the insect (figs. 3, 5, and 8, pp. 338, 340), as 
I have already explained, is much more horizontal than in the bat or bird (figs. 
12 and 13, p. 342). In either case, however, the down stroke must be delivered 
in a more or less forward direction. This is necessary for support and pro- 
pulsion. A horizontal to and fro movement will elevate, and an up and down 
vertical movement propel, but an oblique forward motion is requisite for pro- 
gressive upward flight." 

The Wing during its Vibrations moves on the Surface of an Imaginary 
Sphere. — All wings are convex above and concave below. This shape is neces- 
sary to enable the wing to evade the air during the up stroke, and to seize it 
during the down one. The concave surface is presented during the up stroke, 
and the concave one during the down stroke — the resistance experienced by a 
concave surface when compared with a convex one being something like two to 
one. The resistance is further increased by the wing being made to descend 
with greater rapidity than it ascends. In whatever direction the wing turns 
during the up stroke its movements are calculated to evade the air, and in 
whatever direction it turns during the down stroke they are calculated to 
seize it. This arises alike from the shape of the wing and the manner in which 
it is applied to the air. Thus, in the insect in progressive flight the wing during 
the up stroke describes a curve which is directed upwards and forwards. In the 
bat and bird, where the wing is drawn towards the body during the up stroke, 
the wing describes a second curve, this curve being directed upwards and inwards 
with reference to the body. The under or concave surface of the wing may, 
therefore, be said to be moving on the surface of an imaginary sphere during 
the up stroke— an arrangement which enables it to avoid the superincumbent 
air by its upper or convex surface, while it affords a certain amount of support 
and ascensional power by its under or concave surface, this latter acting partly 
as a kite and partly as a parachute. The wing may, in fact, be said to climb 
during the up stroke ; and this climbing is so adroitly performed that two objects 
are served by it — the superimposed air being avoided, and the body bearing 
the wing being supported. In the climbing movement the anterior margin of 
the wing cleaves a passage from behind upwards and forwards for the body 

* On the Mechanism of Flight, by the Author, Trans. Linn. Society, vol. xxvi. pages 214, 255, 
and 256. 

VOL. XXVI. PART II. 4 U 



344 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



and posterior margin, the root in like manner cleaving a passage from without 
inwards and upwards for the body and tip. It is in this way that the wing 
presents a sharp cutting edge during the up stroke, a remark which applies even 
to the rowing feathers (quill feathers) of the wing of the bird. The ascent of 
the wing, as will be subsequently explained, is favoured by the reaction of the air 
on its under surface, and by the downward and forward fall of the body. If 
the wing was not concavo-convex in form, and made to oscillate on the surface 
of an imaginary sphere, it would be impossible for it alternately to avoid and 
seize the air while it is rising and falling. When the wing descends or 
makes the down stroke, as it is termed, it also rotates on the surface of the 
imaginary sphere in question. In this case, however, it is the concave or under 
surface of the wing which is active, and the rolling takes place in such a manner 
(it is outwards, downwards, and forwards) as actually greatly to increase the sup- 
port afforded — the air, which was dispersed and avoided during the up stroke, 
being now collected together and seized with avidity. It would be difficult to 
conceive a more simple or effective arrangement. 

The Natural Wing, ivlien Elevated and Depressed, must move Fomvards. — It 
is a condition of natural wings, and of artificial wings constructed on the prin- 
ciple of living wings, that when forcibly elevated or depressed, even in a strictly 
vertical direction, they inevitably dart forward. This is well shown in figure 14. 




Fig. 14. 

If, for example, the wing is suddenly depressed in a vertical direction, as 
represented at a b, it at once darts downwards and forwards in a curve to c, thus 
converting the vertical down stroke into a doivn oblique forward stroke. If, 
again, the wing be suddenly elevated in a strictly vertical direction, as at c d, the 
wing as certainly darts upwards and forwards in a curve to e, thus converting 
the vertical up stroke into an upivard oblique forward stroke. The same 
thing happens when the wing is depressed from e to /, and elevated from g to 
h. In both cases the wing describes a waved track, as shown at e g, g i, which 
clearly shows that the wing strikes downwards and fomvards during the down 
stroke, and upwards and forwards during the up stroke. The wing, in fact, is 
always advancing, its under surface attacking the air like a boy's kite. If, on 
the other hand, the wing be forcibly depressed, as indicated by the heavy waved 
line a c, and left to itself, it will as surely rise again, and describe a waved 
track, as shown at c e. This it does, in virtue of its flexibility and elasticity, 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 345 

aided by the recoil obtained from the air. In other words, it is not necessary 
to elevate the wing forcibly in the direction c d to obtain the upward and for- 
ward movement c e. One single impulse communicated at a, causes the wing 
to travel to e, and a second impulse communicated at e, causes it to travel to i. 
It follows from this that a series of vigorous down impulses would, if a certain 
interval was allowed to elapse betiveen them, beget a corresponding series of up 
impulses, in accordance with the law of action and reaction, the wing and the 
air under these circumstances being alternately active and passive. I say if a 
certain interval was allowed to elapse between every two down strokes, but 
this is practically impossible, as the wing is driven with such velocity that 
there is positively no time to waste in waiting for the purely mechanical 
ascent of the wing. That the ascent of the pinion is not, and ought not to be, 
entirely clue to the reaction of the air, is proved by the fact that in flying 
creatures (certainly in the bat and bird) there are distinct elevator muscles and 
elastic ligaments, delegated to the performance of this function. The reaction 
of the air is therefore only one of the forces employed in elevating the wing ; 
the others, as I shall show presently, are vital and vito mechanical in their nature. 
The falling downwards and forwards of the body when the wings are ascending 
also contribute to this result. 

The Wing acts as a true Kite both during the Down and Up Strokes. — If, as 
I have endeavoured to explain, the wing, even when elevated and depressed in 
a strictly vertical direction, inevitably and invariably darts forward (figure 14, p. 
344), it follows as a consequence that the wing, as already partly explained, flies 
forwards as a true kite, both during the down and up strokes, as shown at 
cdefghijklmoi fig. 15, and that its under concave or biting surface, in 
virtue of the forward travel communicated to it by the body in motion, is closely 
applied to the air, both during its ascent and descent, a fact hitherto overlooked, 
but one of considerable importance, as showing how the wing furnishes a per- 
sistent buoyancy, alike when it rises and falls. 




Fig. 15. 



In figure 15 the greater impulse communicated during the down stroke is 
indicated by the double dotted lines. The angle made by the wing of the bat and 
bird with the horizon [a b of figure 15) is constantly varying, as in the insect wing, 
as a comparison of c with d, d with e, e with /, and /with g of figure 15 will 
show, these letters having reference to supposed transverse sections of the 



346 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

wing. Figure 15 also shows that the convex or non-biting surface of the wing 
is always directed upwards, so as to avoid unnecessary resistance on the part 
of the air to the wing during its ascent, whereas the concave or biting surface is 
always directed downwards, so as to enable the wing to contend successfully 
with gravity. 

On comparing c d efg of figure 15, p. 345, with a be dot figures 3 and 5, p. 338, 
it will be seen that the principle involved in the flight of the wing of the insect, 
bat, and bird is essentially the same. The wing is, in short, in every instance, a 
true kite, and flies forward in accordance with natural laws. 

Where the Kite formed by the Wing differs from the Boy's Kite. — The natural 

kite formed by the wing differs from the artificial kite only in this, that the former 

is capable of being moved in all its parts, and is more or less flexible and elastic, 

thelatter being comparatively rigid. The flexibility and elasticity of the kite formed 

by the natural wing is rendered necessary by the fact that the wing is articulated 

or hinged at its root ; its different parts travelling at various degrees of speed in 

proportion as they are removed from the axis of rotation. Thus the tip of the 

wing travels through a much greater space in a given time than a portion nearer 

the root. If the wing was not flexible and elastic, it would be impossible to 

reverse it at the end of the up and down strokes, so as to produce a continuous 

vibration. The wing is also practically hinged along its anterior margin, so that 

the posterior margin of the wing travels through a much greater space in a 

given time than a portion nearer the anterior margin. The compound rotation 

of the wing is greatly facilitated by the flexible and elastic properties of the 

pinion. It causes the pinion to twist upon its long axis during its vibration, as 

already fully explained (see g, r and a, s of fig. 2, p. 336). The twisting 

referred to is partly a vital and partly a mechanical act ; that is, it is occasioned 

in part by the action of the muscles, and in part by the greater momentum 

acquired by the tip and posterior margin of the wing, as compared with the 

root and anterior margin ; the speed acquired by the tip and posterior margin 

causing them to reverse always subsequently to the root and anterior margin, 

which has the effect of throwing the anterior and posterior margins of the 

wing into figure of 8 curves. It is in this way that the posterior margin of the 

outer portion of the wing is made to incline forwards at the end of the down 

stroke (fig. 2 g, p. 336), when the anterior margin is inclined backwards, and 

that the posterior margin of the outer portion of the wing is made to incline 

backwards at the end of the up stroke (fig. 2 a, p. 336), when a corresponding 

portion of the anterior margin is inclined forwards. 

The Angles formed by the Wing in Action. — Not the least interesting feature 
of the compound rotation of the wing, of the varying degrees of speed attained 
by its different parts, and of the twisting or plaiting of the posterior margin 
around the anterior, is the great variety of kite-like surfaces developed upon 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 347 

its dorsal and ventral aspects. Thus the tip of the wing forms a kite 
which is inclined upwards, forwards, and outwards, while the root forms a 
kite which is inclined upwards, forwards, and inwards. The angles made by 
the tip and outer portions of the wing with the horizon are less than those 
made by the body, and those made by the body less than those made by 
the root and inner portions. The inclined surfaces peculiar to any portion of 
the wing become more inclined as the speed peculiar to said portion decreases, 
and vice versa. The wing is consequently mechanically perfect, the angles made 
by its several parts with the horizon being accurately adjusted to the speed 
attained by its different portions during its travel to and fro. From this 
it follows that the air set in motion by one part of the wing is seized upon 
and utilised by another, the inner and anterior portions of the wing supplying, 
as it were, currents for the outer and posterior portions. This results from the 
wing always forcing the air outwards and backwards. These statements admit 
of direct proof, and I have frequently satisfied myself of their exactitude by 
experiments made with natural and artificial wings. 

In the bat and bird the twisting of the wing upon its long axis is more of a 
vital and less of a mechanical act than in the insect, the muscles which regulate 
the vibration of the pinion in the former (bat and bird), extending quite to the 
tip of the wing. 

The Body and Wings move in Opposite Curves. — I have stated that the wing 
advances in a waved line, as shown at a c eg i of figure 14, p. 344 ; and the same 
remark holds true, within certain limits, of the body as indicated at 1, 2, 3, 4, 
and 5 of the same figure. Thus, when the wing descends in the curved line 
a c, it elevates the body in a corresponding but minor curved line, as shown at 
1, 2 ; when, on the other hand, the wing ascends in the curved line a e, the body 
descends in a corresponding but smaller curved line (2, 3), and so on ad infinitum. 
The undulations made by the body are so trifling when compared with those 
made by the wing that they are apt to be overlooked. They are, however, 
deserving of attention, as they exercise an important influence on the undula- 
tions made by the wing, the body and wing swinging forward alternately, the 
one rising when the other is falling, and vice versa. Flight may be regarded 
as the resultant of three forces : — the muscular and elastic force, residing in 
the wing, which causes the pinion to act as a true kite, both during the down 
and up strokes ; the iveight of the body, which becomes a force the instant 
the trunk is lifted from the ground, from its tendency to fall downwards and 
forwards; and the recoil obtained from the air by the rapid action of the wing. 
These three forces may be said to be active and passive by turns. 

Analysis of the Down and Up Strokes in the Insect — the Terms Extension and 
Flexion defined. — As considerable confusion exists in the minds of most inves- 
tigators as to the precise changes induced in the wing during the down and up 

VOL. XXVI. PART II. 4 X 



348 DE PETTIGEEW ON THE PHYSIOLOGY OF WINGS. 

strokes respectively, and in especial as to the manner in which the wing is 
elevated, so as to avoid the resistance of the air and yet afford support, I have 
felt it incumbent upon me carefully to analyse the movements as observed in pro- 
gressive flight. In insects the wings are variously arranged during the period 
of repose. In some they are elevated above the body, as in the butterfly ; in 
others, they are disposed on the same level with the body, and rest upon the 
dorsal surface of the abdomen, as in the common fly ; in a third, the wings are 
arranged partly on the sides and partly upon the dorsal aspect of the body, the 
anterior or thick margin of the wing being in such cases directed downwards, 
as in the cicada. This is also the position occupied by the wings of the bat and 
bird, the pinions, when not employed in flying, being folded upon themselves to 
economise space. In some insects, as the ephemera or mayfly, the beetles, 
locusts, &c, the wings are also folded upon themselves during the intervals of 
rest. The power which some wings possess of alternately folding, flexing, or 
crushing their component parts together, and of extending and widely separating 
them, has introduced the terms extension and flexion: extension, strictly speak- 
ing, signifying the opening out or spreading of the pinion, and the carrying of 
it away from the body in the direction of the head of the animal ; flexion sig- 
nifying the folding of the pinion, and the drawing of it towards the body in a 
direction from before backwards. The terms extension and flexion, when 
applied to insect wings, which are in one piece, and which consequently do not 
admit of being alternately opened and closed to any great extent, are only 
partly correct, — extension in the insect, signifying the carrying of the 
wing away from the body in a plane nearly on the same level with it in the 
direction of the head ; flexion the drawing back or recovering of the wing until 
it regains its original position. 

The terms extension and flexion have, unfortunately, got mixed up with the 
expressions the down and up strokes, from the fact that the wings of bats, birds, 
and some insects are always extended towards the termination of the up strokes, 
and flexed towards the termination of the down ones. This confusion is the 
more natural as all wings when extended rotate upon their long axes in such a 
manner that their posterior margins are screwed doivnivards %&& forwards. 

In all wings, whatever their position during the intervals of rest, and whether 
in one piece or in many, this feature is to be observed in flight. The wings are 
slewed downwards and forwards, i.e., they are carried more or less in the direc- 
tion of the head during their descent, and reversed or carried in an opposite 
direction during their ascent. In stating that the wings are carried away from 
the head during the back stroke, I wish it to be understood that they do not 
therefore necessarily travel backwards in space when the insect is flying for- 
wards. On the contrary, the wings, as a rule, move forward in curves, both 
during the clown and up strokes. The fact is, that the wings at their roots are 



DE PETTTGREW ON THE PHYSIOLOGY OF WINGS. 



349 



hinged and geared to the body so loosely that the body is free to oscillate in a 
forward or backward direction, or in an up, down, or oblique direction. As a 
consequence of this freedom of movement, and as a consequence likewise of the 
speed at which the insect is travelling, the wings during the back stroke are for 
the most part actually travelling forwards. This is accounted for by the fact 
that the body falls downwards and forwards in a curve during the up or return 
stroke of the wings, and because the horizontal speed attained by the body is 
as a rule so much greater than that attained by the wings, that the latter are 
never allowed time to travel backward, the lesser movement being as it were 
swallowed up by the greater. For a similar reason the passenger of a steam- 
ship may travel rapidly in the direction of the stern of the vessel, and yet be 
carried forward in space, — the ship sailing much quicker than he can walk. 
While the wing is descending, it is rotating upon its root as a centre (short axis). 
It is also, and this is a most important point, rotating upon its anterior margin 
(long axis), in such a manner as to cause the several parts of the wing to 
assume various angles of inclination with the horizon. 

Figures 16 and 17 will supply the necessary illustration. 



x < 




-x 



Fig. 16. 



3 ^r 



a%~ 



Nn^NSXnXxN 




— X 



<- 



Kg. 17. 



//^■//y/ 2 



Vv^^-SsNSs 



m 



If, for example, we take the common blow-fly when reposing we will find 
that the plane of the wing (fig. 16 a) is arranged in the same plane with the 
body, and that both are in a line with the horizon (x #').* When, however, the 

It happens occasionally in insects that the posterior margin of the wing is on a higher level than 
the anterior one towards the termination of the up stroke as shown at a (dotted line) of fig. 16. In 
such cases the posterior margin is suddenly rotated in a downward and forward direction at the 



350 DR PETT1GREW ON THE PHYSIOLOGY OF WINGS. 

wing is made to descend, it gradually, in virtue of its simultaneously rotating 
upon its long and short axes, makes a certain angle with the horizon as repre- 
sented at b. The angle is increased at the termination of the down stroke as 
shown at c, so that the wing, particularly its posterior margin, during its descent 
(A), is screwed or crushed down upon the air with its concavity or biting 
surface directed forwards and towards the earth. The same phenomena are 
indicated at a b c of fig. 17, p. 349, but in this figure the wing is represented as 
travelling more decidedly forwards during its descent, and this is characteristic 
of the down stroke of the insect's wing — the stroke in the insect being delivered in 
a very oblique and more or less horizontal direction, as shown at Plate XL fig. 4. 
The forward travel of the wing during its descent has the effect of diminishing the 
angles made by the under surface of the wing with the horizon. Compare bed 
of fig. 17 with the same letters of fig. 16. At fig. 15, page 345, the angles for a 
similar reason are still further diminished, and this latter figure gives a very 
accurate idea of the kite-like action of the wing both during its descent and 
ascent. The downward screwing of the posterior margin of the wing during 
the down stroke is well seen in the dragon-fly at page 361, fig. 38. (In this 
figure the arrows r s give the range of the wing.) At the beginning of the down 
stroke (dragon-fly) the upper or dorsal surface of the wing (i df) is inclined 
downwards and backivards, the under or ventral surface downwards and for- 
ivards. In other words, the anterior margin (i d) of the pinion is directed 
slightly upwards and forwards, the posterior margin (/) slightly downwards 
and backwards. As the wing descends, which it does in a downward and 
forward direction, the posterior margin (/) is screwed downwards and for- 
wards until it assumes the position indicated by j ; the anterior margin (i d) 
inclining more and more upwards and backwards, as shown at g h. This rota- 
tion of the posterior margin (/) round the anterior margin (g h) has the 
effect of causing the different portions of the under surface of the wing to 
assume various angles of inclination with the horizon, the wing attacking 
the air like a boy's kite. The angles are greatest towards the root of the wing 
and least towards the tip. They accommodate themselves to the speed at which 
the different portions of the wing travel — a small angle with a high speed giving 
the same amount of buoying power as a larger angle with a diminished speed. 
The screwing of the under surface of the wing (particularly the posterior margin) 
in a downward direction during the down stroke is necessary to insure a sufficient 
upward recoil, the wing being made to swing downwards and forwards pendulum 
fashion, for the purpose of elevating the body, which it does by acting upon the air 
as a long lever, and after the manner of a kite. During the down stroke the wing 

beginning of the down stroke — the downward and forward rotation securing additional elevating 
power for the wing. The posterior margin of the wing in bats and birds, unless they are flying down- 
wards, never rises above the anterior one, either during the up or down stroke. 



DB PETTIGREW ON THE PHYSIOLOGY OF WINGS. 35) 

is active— the air passive. In other words, the wing is depressed by a purely 
vital act. This is proved by taking a living or dead blow-fly, and forcibly 
depressing its wing in the direction of the head by the aid of a slender rod. 
This act causes the wing to make various angles of inclination with the horizon, 
as shown at a b cdefg of fig. 18 ; but the instant the rod is removed the wing 
obliterates the angles in question, and flies in an upward and backward direction 
to its original position as indicated at g h ij k Im of fig. 19. 



Fig. 18. Fig. 19. 

This shows very satisfactorily that while a voluntary effort is required to 
depress the wing, it is in some measure elevated, and the various inclined 
surfaces which it makes with the horizon changed by the aid of an elastic 
ligament or spring common to all wings. The down stroke is readily explained, 
and its results upon the body obvious. The real difficulty begins with the up or 
return stroke. If the wing was simply to travel in an upward and backward direc- 
tion from c to a of fig. 16, page 349, it is evident that it would experience much 
resistance from the superimposed air, and undo or negative the advantages secured 
by the descent of the wing. What really happens is this. The wing does not travel 
upwards and backwards in the direction cb a of fig. 16 (the body be it remembered 
is advancing), but upwards and forw ards in the direction c d efg. This is brought 
about in the following manner. The wing is at right angles to the horizon {xx') at c. 
It is therefore caught by the air because of the more or less horizontal travel of 
the body at 2, the elastic ligaments and other structures rotating the posterior 
or thin margin of the pinion in an upward direction, as shown at g h i of figure 
19, page 351, and d efg of figure 16, page 349. The wing by this partly vital 
and partly mechanical arrangement is rotated off the wind in such a manner as 
to keep its dorsal or non-biting surface directed upwards, while its concave or 
biting surface is directed downwards. The wing, in short, has its planes so 
arranged, and its angles so adjusted to the speed at which it is travelling, that 
it darts up a gradient like a true kite, as shown at c d efg of figures 16 and 17, 
page 349. The wing consequently elevates and propels during its ascent as well 
as during its descent. It is, in fact, a kite during both the down and up strokes. 
The ascent of the wing is greatly assisted by the forward travel of the body. 
It is further assisted by the downward and forward fall of the body. This 
view will be readily understood by supposing, what is really the case, that 
the wing is more or less fixed by the air in space at 2 of figure 16, page 349, 
and that the body, the instant the wing is fixed, falls downwards and forwards 

VOL. XXVI. PART II. 4 Y 




352 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

iii a curve, which, of course, is equivalent to placing the wing above, and, so 
to speak, behind the insect — in other words, to elevating the wing prepara- 
tory to a second down stroke, as seen at g of figures 16 and 17, page 349/" 
The Body ascends when the Wing descends, and vice versa. — The manner in 

which the body falls downwards and forwards in 
progressive flight is illustrated at figs. 20, 21, and 
22. 

At fig. 20 the body is represented at a and c, 
the wing at b and d, x supplying the fulcrum or 
• pivot on which the body and wing oscillate. 
I If the body (a) is elevated in the direction 

e, the wing (b) of necessity descends in the direc- 
tion h. If, on the other hand, the body (c) 
descends in the direction /, the wing (d) ascends 
-,//■ in the direction g. The ascent or descent of 

Fig. so. the wing is always very much greater than that 

of the body, from the fact of the pinion acting as 
a long lever. The remarks just made are true more especially of the body 

* When a bird rises from the ground it runs for a short distance, or throws its body into the air 
by a sudden leap, the wings being simultaneously elevated. When the body is fairly off the ground, 
the wings, are made to descend with great vigour, and by their action to continue the upward impulse 
secured by the preliminary run or leap. The body then falls in a curve downwards and forwards, the 
wings, partly by the fall of the body, partly by the reaction of the air, on their under surface, and 
partly by the contraction of the elevator muscles and elastic ligaments being placed above, and to 
some extent behind the bird — in other words, elevated. The second down stroke is now given, and 
the wings again elevated as explained, and so on " ad infinitum," the body falling when the wings are 
being elevated, and vice versa, as shown at fig. 14, p. 344. When a long-winged oceanic bird rises 
from the sea, it uses the tips of its wings as levers for forcing the body up, the points of the pinions 
suffering no injury from being brought violently in contact with the water. A bird cannot be said to 
be flying until the trunk is swinging forward in space and taking part in the movement. The hawk, 
when fixed in the air over its quarry, is simply supporting itself. To fly, in the proper acceptation of 
the term, implies to support and propel. This constitutes the difference between a bird and a balloon. 
The bird can elevate and carry itself forward, the balloon can simply elevate itself, and must rise and 
fall in a straight line in the absence of currents. When the gannet throws itself from a cliff the inertia 
of the trunk at once comes into play, and relieves the bird from those herculean exertions required to 
raise it from the water when it is once fairly settled thereon. A swallow dropping from the eaves of 
a house, or a bat from a tower, afford illustrations of the same principle. Many insects launch them- 
selves into space prior to flight. Some, however, do not. Thus the blow-fly can rise from a level sur- 
face when its legs are removed. This is accounted for by the greater amplitude and more horizontal 
play of the insect's wing as compared with that of the bat and bird, and likewise by the remarkable 
reciprocating power which it possesses when the body of the insect is not moving forwards. ( Vide 
figs. 3, 4, 5, and 6, page 338). When a beetle attempts to fly from the hand it extends its front 
legs and flexes the back ones, and tdts its head and thorax upwards so as exactly to resemble a 
horse in the act of rising from the ground. This preliminary over, whirr go its wings with immense 
velocity, and in an almost horizontal direction, the body being inclined more or less vertically. The 
insect rises very slowly, and often requires to make several attempts before it succeeds in launching 
itself into the air. I could never detect any pressure communicated to the hand when the insect was 
leaving it, from which I infer that it does not leap into the air. The bees, I am disposed to believe, 
also rise without anything in the form of a leap or spring. I have often watched them leaving the 
petals of flowers, and they always appeared to me to elevate themselves by the steady play of their 



DE, PETTIGKEW ON THE PHYSIOLOGY OF WINGS. 



353 



and wing when oscillating on either side of the fixed point x, this furnishing 
the fulcrum on which the body and the wing alternately act. The pecu- 
liarity, however, of the wing consists in the fact that it is a flexible lever and 




Fig. 21. 




^~ I 



Fig. 22. 



acts upon yielding fulcra (the air), the body participating in, and to a certain 
extent perpetuating the movements originally produced by the pinion. The 
part which the body performs in flight is illustrated at fig. 21. At a the body 
is depressed, the wing being elevated and ready to make the down stroke at b. 
The wing descends in the direction c d, but the moment it begins to descend 
the body moves upwards and forwards (see arrows) in a curved line to e. As 
the wing is attached to the body it is made gradually to assume the position/. 
The body is now elevated and the wing depressed, the under surface of the 
latter being so adjusted that it strikes upwards and forwards as a kite would. 
The body now falls doivmvards and forwards in a curved line to g, and in doing 
this it elevates or assists in elevating the wing to /. The pinion is a second 
time depressed in the direction k I, which has the effect of forcing the body 
along a waved track and in an upward direction until it reaches the point 
m. The ascent of the body necessitates the descent of the wing as at n. The 
body and wing, as will be seen from this figure, are alternately above and beneath 
a given line x x. The same points are shown at fig. 22, the only difference 
being that the sweep of the wing is greater and the undulation made by the 
body less abrupt, as seen in vigorous flight. At a the body is depressed/and 
the wing (b) elevated high above the body. The pinion (b) descends in the 
direction c d, and forces the body in an upward curve to e. The body (e) is 
now elevated and the wing (/) depressed. The body (<?) falls doivmvards and 

wings, which, was the more necessary, as the surface from which they rose was in many cases a yield- 
ing surface. The falling forward of the body during flight was indicated in my Memoir " On the 
Mechanism of Flight," Trans. Linn. Society, vol. xxvi. p. 22G. 



354 DR PETTIGREW ON THE PHYSIOLOGY OE WINGS. 

forwards in a curve to g, the pinion (/) by this act being made to describe the 
segment of a circle h % j, its under concave surface being applied to the air like 
a kite all the time. (It is thus that the wing elevates and sustains during the 
up stroke.) The wing (j) is made to descend in the direction k I, and forces 
the body (g) along an upward curve until it arrives at m, its subsequent fall 
elevating the wing (n) in the direction o p. Here again, the body and wing 
play alternately on either side of a given line x x. 

A careful study of figs. 20, 21, and 22 (pages 352, 353) shows the great im- 
portance of the twisted configuration and curves peculiar to the natural wing. 
If the wing was not curved in every direction it could not be rolled on and off 
the wind during the down and up strokes, as seen more particularly at fig. 22. 
This, however, is a vital point in progressive flight. The wing (b) is rolled on to 
the wind in the direction c d, its under concave or biting surface being crushed 
hard down with the effect of elevating the body to e. The body falls to g, 
and the wing (/) is rolled off the wind in the direction h i, and elevated partly 
by the action of the elevator muscles and elastic ligaments, and partly by the 
reaction of the air, operating on its under or concave biting surface, until it 
assumes the position j. The wing is therefore to a certain extent resting 
during the up stroke. The concavo-convex form of the wing is admirably 
adapted for the purposes of flight. In fact, the power which the wing possesses 
of always keeping its concave or under surface directed downwards and more 
or less forwards enables it to seize the air at every stage of both the up and 
down strokes so as to supply a persistent buoyancy. The action of the natural 
wing is accompanied by remarkably little slip — the elasticity of the organ, the 
resiliency of the air, and the contraction and relaxation of the elastic ligaments 
and muscles all co-operating and reciprocating in such a manner that the 
descent of the wing elevates the body, the descent of the body aided by the 
reaction of the air and the contraction of the elastic ligaments and muscles 
elevating the wing. The wing during the up stroke arches above the body after the 
manner of a parachute, and in turn prevents the body from falling. The 
sympathy which exists between the parts of a flying animal and the air on 
which it depends for support and progress is consequently of the most intimate 
character. 

The up stroke (B of figures 16 and 17, page 349), as will be seen from the fore- 
going account, is a compound movement due in some measure to recoil or resist- 
ance on the part of the air — to the contraction of the muscles, elastic ligaments, 
and other vital structures, to the elasticity of the wing, and to the falling of the 
body in a downward and forward direction. The wing may be regarded as rotating 
during the down stroke upon 1 of figure 16, page 349, which may be taken to 
represent the long and short axes of the wing, and during the up stroke upon 
2, which may be taken to represent the yielding fulcrum furnished by the air. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 355 

The same points are illustrated at 1 and 2 of figure 17, page 349, allowance 
being made in this case for the greater horizontal travel of the body during 
the down (A C) and up (B D) strokes, the increased horizontal travel of the 
body, as already pointed out, having the effect of diminishing the angles made 
by the under surface of the wing with the horizon during its vibrations. 

The Wing acts upon Yielding Fulcra. — -The chief peculiarity of the wing, as 
has been stated, consists in the fact that it is a twisted flexible lever specially 
constructed to act upon yielding fulcra (the air). The points of contact of the 
wing with the air are represented at ab c d efg h ij k I respectively of figures 16 
and 17, page 349, and the imaginary points of rotation of the wing upon its long 
and short axes at 1, 2, 3, and 4 of the same figures. The assumed points of 
rotation advance from 1 to 3, and from 2 to 4 (vide arrows marked r and 
s, fig. 17). The actual points of rotation correspond to the little loops ab c def 
g h ij k I of same figure ; the descents of the wing to A and C, and the ascents 
to B and D. When the wing is in the position represented at g of figures 16 
and 17, page 349, it is ready to begin a second down stroke, that is, it is 
screwed in a downward and forward direction. At i the second down stroke 
(C) is completed ; at i the second up stroke is begun, the posterior margin of 
the wing being gradually rotated in an upward direction to prepare it for making 
the return or up stroke (D), as shown at j k I m. A third down stroke (E, fig. 
16) is commenced at m and completed at o. 

Weight contributes to Horizontal Flight. — That the weight of the body plays 
an important part in the production of flight may be proved by a very simple 
experiment. If two quill feathers are fixed into an ordinary cork, as repre- 
sented at fig. 23, p. 356, and the apparatus is allowed to drop from a height, 
the cork does not fall vertically downwards, but downwards and forwards in a 
curve, and for the following reasons. The feathers a b are twisted flexible 
inclined planes, which arch in an upward direction. They are, in fact, true wings 
in the sense that an insect wing in one piece is a true wing. When dragged 
downwards by the cork (c), which would, if left to itself, fall vertically, they 
have what is virtually a down stroke communicated to them. Under these 
circumstances they inevitably dart forward ; a struggle ensuing between the cork 
tending to fall vertically and the feathers tending to travel in a horizontal 
direction. As a consequence, the apparatus describes the curve d efg before 
reaching the earth, h i. This is due to the action and reaction of the feathers 
and air upon each other, and to the influence which gravity exerts upon the 
cork. The forward travel of the cork and feathers, as compared with the space 
through which they fall, is very great. Thus, in some instances, they advanced 
as much as a yard and a half in a descent of three yards. 

When artificial wings constructed on the principle of natural ones (vide fig. 24, 
p. 357), with stiff roots (c, a), tapering semi-rigid anterior margins (a b, c d), and 

VOL. XXVI. PART IT. 4 Z 



356 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



thin yielding posterior margins (ef, g h), are allowed to drop from a height (r), 
they describe double curves in falling, as shown at m n o I, ij k I, the roots of 
the wings (c, a) reaching the ground first, a circumstance which proves the 
greater buoying power of the tips of the wings. I might refer to many other 
experiments made in this direction, but sufficient have been adduced to show 
that weight, when acting upon wings, or, what is the same thing, upon elastic 
twisted inclined planes, must be regarded as an independent moving power. But 




/ e 



,-""f 



■<r 



// 



Fig. 23. 



for this circumstance flight would be at once the most awkward and laborious form 
of locomotion, whereas in reality it is incomparably the easiest and most graceful* 
The power which rapidly vibrating wings have of sustaining a body which tends 
to fall vertically downwards, is much greater than one would naturally imagine, 
from the fact that the body, which is always beginning to fall, is never per- 
mitted actually to do so. Thus, when it has fallen sufficiently far to assist m 
elevating the wings, it is at once elevated by the vigorous descent of those 
organs. The body consequently never acquires the downward momentum 
which it would do if permitted to fall through a considerable space uninter- 
ruptedly. It is easy to restrain even a heavy body when beginning to fall, 
while it is next to impossible to check its progress when it is once fairly 
launched into space and travelling rapidly in a downward direction (see foot- 
note to page 371). 

The importance to be attached to weight in flight is variously explained in my Memoir on the 
subject, Trans. Linn. Society, vol. xxvi. pages 218, 219, 246, 260, and 261. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



357 



Mechanical Theory of the Action of the Insect's Wing as stated by Chabrier. — 
In one instance only, according to Chabrier,* are the muscles of flight in 
insects inserted directly into the root of the wing. This solitary example is 




n 



o '■ 



/ # 



/ J 



! k 



/ 

Fig 24. 

the dragon-fly. Chabrier regards the action of the insect's wing as purely 
mechanical. His argument may be stated in a few words. He observes, 
that whereas the muscles which propel the wings of the insect are, with one 
exception (the dragon-fly), confined to the interior of the thorax, that there- 
fore they exert no direct influence upon the wings. He further gives it as 
his opinion, that the wings are actuated by the muscles only during the down 
stroke, and that the up stroke is entirely due to the reaction of the air — in 
fact, that if the wings only be depressed rythmically, the air will do the 
remainder of the work. Unfortunately for this theory there is no time to 
wait for the reaction of the air, the wings being driven with such velocity as 
necessitates their being partly elevated either by elastic ligaments or elevator 
muscles, in addition to the reaction of the air (vide page 345). Chabrier, as will 
be seen, delegates to the air the task of reversing the planes of the wing, and 
of conferring upon it those peculiar curves which, overlooked by him, I have 



* Memoires du Museum d'Histoire Nat urelle. Tome septieme. Paris, 1821. Essai sur le vol des 
Insectes, par I. Chabrier, p. 297. Plates x. xi. and xii. 



358 DR PETTIGREW ON THE PHYSIOLOGY OE WINGS. 

endeavoured to show are indispensable in flight. In short, he confides to the air 
the delicate task of arranging the details of flight — those details constituting in 
reality the most difficult part of the problem. 

Objections to the Mechanical Theory of Wing Movements. — There are many 
facts which militate against Chabrier's mechanical theory of the movements of 
the insect's wing. I find, for example, that if the wing of the wasp, fly, humble bee, 
or butterfly be depressed by a delicate rod, its posterior margin is made to curve 
downwards, and to make various angles with the horizon (fig. 18, ab cd efg, 
page 351) ; the wing, the instant the rod is removed, being flexed and elevated 
by the action of elastic ligaments which obliterate the angles formed during the 
depression (fig. 19, ghijklm, page 351). This implies the existence of a 
muscular system for depressing the wing, and a fibro-elastic system for elevating 
it, similar to what is found in the bat and bird, to be described presently. It 
also proves that the wing is jointed to the body in such a manner that it cannot 
either descend or ascend without changing the direction of its planes — the air 
taking no part in the change of plane referred to. 

I find, secondly, that insects have the power of vibrating either wing by 
itself in any part of a radius not exceeding a half circle, and that the wing may 
be played above the body or on a level with or beneath it, as circumstances 
demand. These facts argue a much more intimate relation between the muscular 
system and the wings than Chabrier is inclined to admit. 

Thirdly, The wing in most insects is composed of two distinct portions at its 
root (figure 25, a b, p. 359), those portions being endowed with independent move- 
ments, which enable the insect to incline the anterior or thick margin (a cfe)oi 
the wing in one direction, and the posterior or thin margin in another — to twist, 
in fact, the wing upon its long axis. This twisting of the wing upon its long axis 
exerts upon the organ precisely the same influence which the extending and 
flexing of the pinion does upon the wing of the bird and bat (figures 39, 40, 41, 42, 
and 43, p. 362). It in short developes double figure oj "8 curves along the anterior 
and posterior margins, and converts the iving into a, screiv capable of change of 
form. 

Fourthly, In the humble bee and other insects supplied with two pairs of 
wings geared to each other by hooklets, the posterior or thin margin of the first 
wing glides along the anterior or thick margin of the alula or second wing, 
which latter, acting as a long lever, has the power of adjusting the posterior 
or thin margin of the first wing. 

Fifthly, In the wasp the first wing can be distinctly folded upon itself in the 
direction of its length, the alula or second wing folding upon the first wing previ- 
ously folded, so that the area of the two wings is reduced to about one-third of what 
it was before the folding took place. When the wing is so folded it is very compact, 
and presents a well-defined cutting edge, which points in a backward direction. 



DR PETTIGREW ON THE PHYSIOLOGY OE WINGS. 



359 



I am induced to believe that the wing is folded after this fashion in certain 
cases during the back or return stroke, although the action of the pinion is so 
rapid that I have hitherto failed to make it out. The folding of the first wing 
upon itself in the wasp occurs in the line g s of fig. 25 ; the folding of the first 
wing upon itself and of the second upon the first, being seen at fig. 26 (h d) ; 
and the two wings, when folded and ready to make the return stroke, at fig. 
27 (ds). The course pursued by the folded wings during the back stroke is 
indicated at ghijklm of fig. 19, page 351. Figure 28 represents the wing of 





Fig. 25. 



Fig. 26. 




I 9 A 




Fig. 27. 



h 9 



Fig. 28. 



the crane-fly, which has, I believe, a similar action, the thin posterior margin, 
fg h i, being folded during the back or return stroke, and opened out during 
the forward stroke. 

Sixthly, Many insects, such as the ephemera, beetles, locusts, &c, have 
assuredly the power of more or less completely crushing their wings together, 
and of alternately increasing and diminishing the wing area during the down 
and up strokes. The wings of most insects, moreover, are during the up stroke 
thrown into rugae, which are flattened or altogether disappear during the down 
stroke. They further have the power of arching their wings during the up 
stroke, and of opening them out so as to increase their area during the down 
one. The butterfly affords an admirable example. 

The Down and Up Stroke of the Wing of the Butterfly ; Increase and 
Diminution of the Wing Area; Development of Figure of 8 Curves on the Margins 
of the Wing. — In the butterfly, as I have sufficiently satisfied myself, the first 
wing is made to pass above or over the second wing towards the termination of 
the down stroke, the convexity of both wings increasing meanwhile. This 
reduction in the wing area is necessary to destroy the momentum acquired by 
the wings during their descent, and to prepare them for making the up or return 
stroke. In the butterfly the wings strike downwards and forwards, and have 
a more vertical play than in almost any other insect. The wings are elevated 



VOL. XXVI. PART II. 



O A 



360 



DR PETTIGKEW ON THE PHYSIOLOGY OF WINGS. 



in the overlapped arched condition, and towards the end of the up stroke they 
are gradually separated to increase the area and prepare them for making the 
down stroke in a manner precisely analogous to what happens in bats and birds. 
They are then made to descend in their flattened condition, the first wing passing- 
over the second towards the termination of the down stroke as just stated. 
Nor is this all. While the wings are being depressed and made to overlap 
more or less completely, and while they are being elevated and spread out, 
double and opposite curves are being developed along their anterior, posterior, 
and outer margins. This is a somewhat remarkable circumstance, as the butter- 
fly is perhaps the most awkward flying creature that exists. It seems to prove 
that the presence of double or figure of 8 curves, is indispensable to flight. These 
points are illustrated at figs. 29, 30, 31, 32, 33, and 34. At a, of fig. 29, the 





Fig. 29. 



Fig. 30. 





^^^□XQ^ 




Fig. 32. 



Fig. 33. 



Fig. 34. 



concavity of the first wing is directed downwards, the concavity of the second 
wing being directed slightly upwards as at b. The two curves taken together 
give a double or wave curve. In this figure the two wings are separated or 
spread out and ready to give the down stroke. At fig. 30 the two wings are 
separated to the utmost, and in the act of making the clown stroke. Here the 
concavity of both wings is directed downwards as at a, a very small portion of 
the second wing only curving upwards (b). At fig. 31 the down stroke is com- 
pleted, the first wing overlapping the second, and both being deeply concave on 
their under surfaces, as shown at a. They are now in a condition to make the 
up stroke, which is the reverse of the down one, and need not be described. 
The curves produced along the anterior and posterior margins of the wings of 
the butterfly during the up and down strokes are seen at figs. 32, 33, and 34. 
At fig. 32, the curves formed along the anterior (c d) and posterior (ef) margins 
of the first wing at the beginning of the down stroke, are represented. At fig. 
33 the wing is represented, as seen at the middle of the down stroke, and the 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 



361 



curves referred to are nearly obliterated (vide rs, tu). At fig. 34 the wing is 
shown at the end of the down stroke, and the curves are reversed, as a com- 
parison of c d, ef of fig. 32 with g h, ij of fig. 34 will satisfactorily prove. 

In the dragon-fly similar figure of 8 curves are developed along the anterior 
and posterior margins of the wings at the beginning, middle, and termination of 
the down stroke, as an examination of figs. 35, 36, 37, and 38 will show. If 





Fig. 35. 



Fig. 36. 




Fig. 37- 



Fig. 38. 



the letters c d, ef of fig. 35 (dragon-fly) be compared with corresponding letters 
of fig. 32 (butterfly) ; the letters r s, t u of fig. 37 (dragon-fly) with similar letters 
of fig. 33 (butterfly), and the letters gh, ij of fig. 36 (dragon-fly) with the same 
letters of fig. 34 (butterfly), it will at once be perceived that the curves which 
these letters represent are identical in both cases. At fig. 38 the wings are 
represented as seen at the beginning and end of the down stroke, the arrows r, s 
giving the range or play of the wings. The letters df of this figure (anterior 
wing at beginning of down stroke) correspond with df of fig. 35 ; the letters g h 
ij (anterior wing at end of down stroke) corresponding with similar letters in fig. 
36. Fig. 38 shows how the posterior margin of the wing (/) is screwed dowmvards 
and forwards (j) during the down stroke (compare with a, b, c of figs. 16 and 
17, page 349, and read remarks on the dragon-fly's wing at pages 335 and 350).'"" 

* The wing area in insects is usually greatly in excess of what is absolutely required for flight, as 
the following experiments made, with the common white and brown butterfly and dragon-fly will show : — 

1. Removed posterior halves of first pair of wings of white butterfly. Flight perfect. 

2. Removed posterior halves of first and second pairs of wings. Flight not strong but still per- 
fect. If additional portions of the posterior wings were removed, the insect could still fly, but with 
great effort, and came to the ground at no great distance. 

3. When the tips (outer sixth) of the first and second pairs of wings were cut away, flight was in 
no wise impaired. When more was detached the insect could not fly. 



362 



DB, PETTIGKEW ON THE PHYSIOLOGY OF WINGS. 



Curves in all respects analogous to those occurring in the wing of the butterfly 
and dragon-fly are observed in the wing of the bat and bird, as a reference to 




Fig. 39. 




Fi°r. 40. 





Fig. 41. 



Fig. 42. 




Fig. 43. 

figs. 39, 40, 41, 42, and 43 will satisfy. They are also found in the rowing- 
feathers of the wing of the bird, as shown at fig. 50, page 379. 

4. Eeinoved the posterior -wings of the brown butterfly. Flight unimpaired. 

5. Kemoved in addition a small portion (one-sixth) from the tips of the anterior wings. Flight 
still perfect, as the insect flew upwards of ten yards. 

6. Eemoved in addition a portion (one-eighth) of the posterior margins of anterior wings. The 
insect flew imperfectly, and came to the ground about a yard from the point where it commenced its 
flight. 

7. In the dragon-fly either the first or second pair of wings may be removed without destroying 
the power of flight. The insect generally flies most steadily when the posterior pair of wings are 
detached, as it can balance better ; but in either case flight is perfect and in no degree laboured. 

8. Eemoved one-third from the posterior margin of the first and second pairs of wings. Flight 
in no wise impaired. 

If more than a third of each Aving be cut away from the posterior or thin margin, the insect can 
still fly, but with effort. 

Experiment 8 shows that the posterior or thin flexible margin of the wing may be dispensed with 
in flight. It is more especially engaged in propelling. 

9. The extremities or tips of the first and second pair of wings may be detached to the extent of 
one third, without diminishing the power of flight. 

If the mutilation be carried further, flight is laboured, and in some cases destroyed. 

1 0. When the front edges of the first and second pair of wings are notched, or when they are 
removed, flight is completely destroyed. 

This shows that a certain degree of stiffness is required for the front edges of the wings, the front 
edges indirectly supporting the back edges It is, moreover, on the front edge of the wing that the 
pressure falls in flight, and by this edge the major portion of the wing is attached to the body. The 
principal movements of the wing are in addition communicated to this edge. 

Note. — Some of my readers will probably infer from the foregoing experiments, that the figure 
of 8 curves formed along the anterior and posterior margins of the pinion are not necessary to flight, 
since the tip and posterior margin of the wing may be removed without destroying it. To such I 
reply, that the wing is flexible, elastic, and composed of a congeries of curved surfaces, and that so long as 
a portion of it remains, it forms, or tends to form, figure of 8 curves in every direction. 

Figures 39, 40, 41, 42, and 43 si ow the double curves which occur on the anterior (bac) and posterior (dcf) 
margins of the wing of the bat and bird. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 363 

Consideration of the Forces which Propel the Wings of Insects. — Proceeding 
now to a consideration of the forces which propel and regulate the wings of 
insects, I find that in the thorax of the insect the muscles are arranged in two 
principal sets in the form of a cross — i.e., there is a powerful vertical set which 
runs from above downwards, and a powerful antero-posterior set which runs 
from before backwards. There are likewise a few slender muscles which proceed 
in a more or less oblique direction. The antero-posterior and verti'^al sets of 
muscles are quite distinct, as are likewise the oblique muscles. Portions, how- 
ever, of the vertical and oblique muscles terminate at the root of the wing in 
jelly -looking points which greatly resemble rudimentary tendons, so that I am 
inclined to believe that the vertical and oblique muscles exercise a direct 
influence on the movements of the wing. The contraction of the antero-pos- 
terior set of muscles (indirectly assisted by the oblique ones) elevates the 
dorsum of the thorax by causing its anterior extremity to approach its posterior 
extremity, and by causing the thorax to bulge out or expand laterally. This 
change in the thorax necessitates the descent of the wing. The contraction of 
the vertical set (aided by the oblique ones) has a precisely opposite effect, and 
necessitates its ascent. While the wing is ascending and descending the oblique 
muscles cause it to rotate on its long axis, the bipartite division of the wing 
at its root, the spiral configuration of the joint, and the arrangement of the 
elastic and other structures which connect the pinion with the body, together 
with the resistance it experiences from the air, conferring on it the various 
angles which characterise the down and up strokes. The wing may therefore 
be said to be depressed by the contraction of the antero-posterior set of 
muscles, aided by the oblique muscles, and elevated by the contraction of 
the vertical and oblique muscles, aided by the elastic ligaments, and the reac- 
tion of the air. If we adopt this view we have a perfect physiological expla- 
nation of the phenomenon, as we have a complete circle or cycle of motion, 
the antero-posterior set of muscles contracting when the vertical set of muscles 
are relaxing, and vice versa, an arrangement which gives an equal period of 
activity and repose to both sets. This, I may add, is in conformity with all 
other muscular arrangements, where we have what are usually denominated 
extensors and flexors, but which, as I have shown elsewhere," are simply the two 
halves of a circle of muscle and of motion, an arrangement for securing diametri- 
cally opposite results in limbs and the condition of activity and rest in muscles. 
Chabrier's account, which I subjoin, virtually supports this hypothesis : — 
" It is generally through the intervention of the proper motions of the 
dorsum, which are very considerable during flight, that the wings or the elytra 
are moved equally and simultaneously. Thus, when it is elevated, it carries 

On the Mechanical Ajjpliances by Avhich Flight is attained in the Animal Kingdom, Trans. 
Linn. Society, vol. xxvi. pages 200, 201, and 262. 

VOL. XXVI. PART II. 5 B 



364 DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

with it the internal side of the base of the wings with which it is articulated, 
from which ensues the depression of the external side of the wing ; and when 
it approaches the sternal portion of the trunk, the contrary takes place. During 
the depression of the wings the dorsum is curved from before backwards, or in 
such a manner that its anterior extremity is brought nearer to its posterior, that 
its middle is elevated, and its lateral portions removed further from each other. 
The reverse takes place in the elevation of the wings ; the anterior extremity 
of the dorsum being removed to a greater distance from the posterior, its 
middle being depressed, and its sides brought nearer to each other. Thus its 
bending in one direction produces a diminution of its curve in the direction 
normally opposed to it ; and by the alternations of this motion, assisted by 
other means, the body is alternately compressed and dilated, and the wings 
are raised and depressed by turns." * 

Objections to Mechanical Theory of Insect Wing Movements specified. — The 
objections to Chabrier's mechanical theory of the action of insects' wings 
may be briefly stated : — 

First, The movements of the wings of insects are not necessarily absolutely 
synchronous. On the contrary, insects have the power of moving their wings 
independently. 

Second, Insects can twist or plait theirwings at the root— the butterfly having 
the power of causing the one wing to overlap the other when required. 

Third, Insects can increase the convexity of their wings during the up stroke 
and decrease it during the down stroke. 

Fourth, They can in some cases fold and diminish the area of the wing 
during the up stroke and increase it during the down one. 

Fifth, In the dragon-flies we can without difficulty trace the muscles termi- 
nating in the roots of the wings — a presumptive proof that in other insects there 
is a direct connexion between the muscles of the thorax and the wings they 
are destined to move. 

Sixth, All insects have the power of elevating their wings when dressing 
them, so that the reaction of the air is not necessary to the up stroke, although 
it certainly contributes to it in flight. They can, moreover, during the intervals 
of rest, develope figure of 8 curves along the anterior and posterior margins 
of the pinion independently of the air. 

Seventh, There are muscles in the dragon-fly, and I believe in other insects 
also, delegated to elevate as well as depress the wing. 

Eighth, There are elastic ligaments which recover or flex and partly elevate 
the wing when the organ is depressed artificially and not engaged in flight. In 

* " General Observations on the Anatomy of the Thorax in Insects, and on its Functions during 
Flight." By E. T. Bennett, F.L.S., &c. (Extracted chiefly from the " Essai sur le vol des Insectes," par 
J. Chabriee, Mem. du Museum d'Histoire Naturelle. Zool. Journal, vol. i. art. xlvi. 1825.) 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 365 

such cases the air can exert no influence whatever, as the wing is depressed 
gently, expressly to avoid recoil. 

We have therefore the conditions of flight developed to nearly as great an 
extent in the insects as in the bats and birds. That distinct elevator and de- 
pressor muscles exist in the bat and bird, and that these act in conjunction with 
elastic ligaments there can be no doubt whatever, see pages 395, 396, and 397. 

Wings Mobile and Flexible as well as Elastic — Elasticity, Flexibility, and 
Mobility not to be confounded — Mobility and Flexibility necessary to Flight. — 
Much importance has been attached by ancient and modern authors to the 
elastic properties of the wing, and not a few recent investigators are of opinion 
that flight is mainly due to the yielding of the wing to the impact of the air on 
its under surface during the down stroke. That, however, the mere elasticity 
of the pinion, if regarded apart from its mobility and flexibility, avails little 
may be proved in a variety of ways. By mobility I mean that power which 
the wing enjoys of moving at its root in an upward, downward, forward, 
backward, or oblique direction, and likewise the remarkable property which 
it possesses of rotating or twisting in the direction of its length. I also include 
under the term mobility the additional power possessed by bats and birds of 
opening and closing, i.e., of flexing and extending the wings during the up and 
down strokes, as well as the power enjoyed by the bat of moving its fingers, 
and by the bird of moving its individual primary, secondary, and tertiary 
feathers at their roots. By the flexibility of the wing, I mean that power 
which the wing possesses of throwing itself into a great variety of curves during 
its action — these curves being formed, reversed, or obliterated at the will of the 
flying animal. It is necessary to distinguish between mobility, flexibility, and 
mere elasticity, because any rotation of the wing along its anterior or thick 
margin is at once followed by an elevation or depression of its posterior or thin 
margin, which elevation or depression is almost invariably and wrongly attri- 
buted to elasticity. That the wing is elastic throughout, and that its posterior 
or thin margin yields slightly (to prevent shock) when it attacks the air there 
can be no doubt. The yielding, however, is very slight, and it is always accom- 
panied by a certain degree of rotation or torsion. If it were otherwise — if 
the posterior margin of the wing yielded to any marked extent in an upward 
direction when the wing descended, it is evident that the air on which the wing 
depended for support would escape from under it, and flight as a consequence be 
rendered abortive. It is the air more than the wing which yields or gives way 
in flight, and the yielding that occurs in the wings, is to be traced for the most 
part, to a rotation of the wing along its anterior margin — to movements occur- 
ring in the muscles and ligaments, and in the bones and feathers when present, 
particularly at the root of the feathers. These remarks are true of living wings. 
It is not, however, to be inferred from what is here stated that natural wings 



366 DP PETTIGREW ON THE PHYSIOLOGY OF WINGS. 

may not be successfully imitated, both in their structure and moveriients, by 
mechanical appliances in which elasticity plays a very prominent part. On the 
contrary, I am prepared to show further on, that flight may be regarded as a 
purely mechanical problem, and that it admits of a mechanical solution. I am, 
however, desirous of showing in the first place what movements are vital, 
what vito-mechanical, and what mechanical in natural flight. This done, we 
will then be in a position to enter upon a consideration of artificial flight. That 
elasticity of itself will not produce flight may be inferred from the following 
experiments. If, for instance, we lash light unyielding reeds to the anterior 
margins of a pigeon's wings so as to prevent flexion at the elbow-joints, we 
instantly destroy flight. In this experiment the elasticity of the wings, and 
particularly of the rowing feathers, is in no wise impaired ; in reality the 
mobility and flexibility of the wings only are interfered with. A still more 
conclusive proof is to be found in the fact that in insects the most elastic 
portions of the wings can be altogether removed without destroying the power 
of flight. Thus I have cut away as much as two-thirds from the posterior 
margin of either wing of the blow-fly, and yet the insect flew with remarkable 
buoyancy. I have also removed portions of the tips of the wings with impunity. 
I made similar experiments with the dragon-fly, butterfly (pages 361 and 362), 
and sparrow, and with nearly uniform results. 

Analysis of the Down and Up Strokes in the Wing of the Bird and Bat. — 
What was said of the movements of the wing of the insect holds equally true 
of those of the bat and bird, if allowance be made for the more vertical direc- 
tion of the down and up strokes, and for the fact that the wings of the bat and 
bird are in several pieces and jointed."" The joints, like the muscles, extend in 
the direction of the length of the wing ; thus, in addition to the shoulder-joint, 
we have the elbow, wrist, and finger joints. The insect, bat, and bird have the 
shoulder joint in common, and this joint is so constructed that the wing is 
free to move in an upward, downward, forward, backward, and oblique direc- 
tion. It also admits of a certain amount of rotation or torsion in the direction 
of the length of the wing. The joint is in fact universal in its nature. Another 
feature possessed in common by insects, bats, and birds, is the elastic ligaments 
which recover and partly elevate the wing during the up stroke. Those liga- 
ments in the bat and bird are not confined to the root of the wing, but extend 
along its margins even to its tip. 

The presence of those ligaments shows that the wing is not elevated exclu- 
sively by the reaction of the air. There are, moreover, distinct elevator muscles 
in the wing of the bat and bird. The presence of voluntary muscles, and of 
elastic and other ligaments, afford important indications in the construction and 

* The beetles have also their wings jointed. 



DR PETTIGREW ON THE PHYSIOLOGY OF WINGS. 367 

application of artificial wings, and I find that by employing a ball and socket 
joint, and a cross system of elastic bands at the root of the wing, I can imitate 
the movements of the natural wing with remarkable precision. By adopting 
the springs referred to — by making the wing elastic in all its parts, even along 
its anterior or thick margin (natural wings are elastic in this situation), and by 
applying a power which varies in intensity, I can communicate to an artificial 
wing a vibratory motion, completely devoid of pauses or dead points. The 
working of the wing in question is accompanied with very little slip. Indeed, 
the slip is so little that the wing may be said to supply a persistent buoying 
and propelling power. When the wing is made to vibrate briskly in a more or 
less vertical direction, it leaps forward in a series of curves, the down stroke run- 
ning into the up one and vice versa, to form a continuous upward wave track. 
The power applied is greatest at the beginning of the down stroke. It is 
decreased at the end of the down stroke, slightly increased at the beginning of 
the up stroke, and again decreased towards the termination of that act. Those 
changes in the intensity of the driving power are necessary to allow the air 
time to react on the under surface of the wing, and to bring the elastic pro- 
perties of the springs and of the wing into play. The springs should be arranged 
at right angles and obliquely, that is, there should be a superior, inferior, ante- 
rior, and posterior set running at right angles to each other, and between these 
as many oblique springs as are deemed necessary. The springs ought to vary 
as regards their length and their strength. Thus, the superior springs, which 
assist in elevating the wing, ought to be longer and stronger than the inferior 
ones ; and the posterior springs, which restrain the wing from leaping forwards 
during its vibrations, should be longer and stronger than the anterior ones, the 
wing having no tendency to travel backwards. A detailed account of the structure 
and movements of artificial wings will be found at the end of the present memoir. 
In the bat and bird the wing is extended or pushed away from the body prior 
to the down stroke, and folded or drawn towards the body prior to the up stroke. 
The unfolding or extending of the wing prior to the down stroke, as seen in 
the gull, is shown at Plate XI. figures 3, 2, 1, 5 ; Plate XIV. figure 18. 

When the wing is being extended or opened out it is also being elevated, 
as shown at 1, 2, 3 of Plate XL figure 5, and Plate XIV. figure 18. When 
the wing is flexed, as at t p of figure 3, Plate XL, the under surface of the wing 
(s q) is nearly on a level with the horizon (b d). When, however, the wing- 
is partially extended, as at Plate XL figure 2, the angle which its under surface 
makes with the horizon is considerable, c b d representing the angle, and b d 
the horizon. When the wing is fully extended, and ready to give the down 
stroke, the angle which the under surface of the wing makes with the horizon 
is still more increased, as shown at Plate XL figure 1, c b d indicating the 
angle, and b d the horizon. The angle made by the under surface of the root 

VOL. XXVI. PART II. 5 C 



368 DR PETTIGKEW ON THE PHYSIOLOGY OF WINGS. 

of the wing with the horizon considerably exceeds that made by the tip, and 
is much greater than a casual observer would be inclined to admit. It 
is obscured by the curving downwards and forwards of the anterior mar- 
gin of the wing towards the root, as seen at a of figure 7, Plate XII. In 
this figure the apparent angle made by the root of the wing with the horizon 
(ef) is a b d, the real angle being c b d. The wing of the bird rotates in 
opposite directions during extension and flexion. The various angles of 
inclination made by the wing of the gannet in extension and flexion is well 
shown at Plate XIII. figures 16 and 17. 

In figure 17 (flexion) the posterior margin of the wing (s q p o) is on a 
level with the body of the bird ; whereas in figure 16 (extension) the posterior 
margin {qp o) is directed downwards and forwards, as indicated by the arrows. 
The same thing is seen in the pea- wit, at Plate XII. figure 8. In this figure 
the wing to the right of the observer is flexed, and in the act of making the 
up stroke, the anterior margin of the pinion being slightly directed down- 
wards {vide arrow). The wing to the left of the observer is, on the contrary, 
extended, and in the act of making the down stroke, the anterior margin of 
the pinion being directed upwards {vide arrow). 

The rotation of the posterior margin around the anterior as an axis during ex- 
tension, is occasioned by the points of insertion of the pectoralis major and other 
muscles, by the attachments and directions of the elastic and other ligaments, 
and by the spiral nature of the articular surfaces of the bones of the wing — 
the mere act of extension on all occasions involving the rotation in question. 

The Wing of the Bird Descends as a Long Lever. — Let us imagine the wing 
fully extended and elevated, and making a certain angle with the horizon, as 
indicated at c b d of figure 1, Plate XL, at 3 of figure 5, Plate XL, and at 3' of 
figure 18, Plate XIV. The wing is now prepared to make the down stroke, and 
descends in a spiral swoop, successively assuming the position 4 in figure 19, 
Plate XIV., and 4 in figure 6, Plate XL It acts with extreme energy as a long 
lever {vide c d of figure 6, Plate XL), the purchase which it has on the body 
being much greater than is usually anticipated. 

During its descent the angle which the wing makes with the horizon is 
increased, as shown at a b c of figures 16 and 17 (page 349), the horizon in these 
figures being indicated by the straight line x x' . 

In the bird, therefore, as in the insect, the posterior or thin flexible margin 
of the wing is screwed down upon the air while the wing is descending. 

The Rotation of the Posterior Margin of the Wing in a Downward Direction 
increases the Elevating, but diminishes the Propelling Power of the Wing. — The 
additional hold which the bird can cause its wing to take of the air by resorting 
to a greater or less degree of rotation, is truly surprising. If the wing is 
depressed minus the rotation, it darts forward, but takes no very decided catch 



DE PETTIGREW ON THE PHYSIOLOGY OF WINGS. 369 

of the air. As a consequence, the recoil is feeble. If, however, the rotation is 
added, the wing seizes the air with such avidity as in all cases to produce a very 
violent reaction. The tendency of the wing to dart forward is diminished by the 
rotation, but the actual elevating power of the pinion is greatly augmented. 
This point can be readily ascertained by depressing and screwing, in the manner 
described, the wing of the swan or of any other large bird, previously dried, in 
the extended position. In preparing the wing for the experiment care should 
be taken not to destroy the curves peculiar to the natural extended wing. I 
mention this fact because, of many swans' wings prepared by me for this purpose, 
I found one had been inadvertently flattened, and gave quite an indifferent result. 

The Importance to be attached to the Concavo-Convex Form of the Wing in 
Birds.— The downward screwing of the concave or under surface of the wing, 
which is so efficacious in securing a powerful hold of the air during the down 
stroke, is followed during the up stroke by an upward screwing of the convex or 
upper surface, which is not less effective in evading the air. In fact, when the 
wing ascends it is drawn towards the body, and deeply arched, so that it is 
literally made to roll upwards, its convex or dorsal surface being directed 
upwards throughout the entire up stroke. It is thus the wing evades the super- 
incumbent air during the return stroke. This account will be readily under- 
stood by a reference to figures 13, 14, and 15, Plate XIII. 

At figure 15, Plate XIII., the wing is represented as seen in the middle of the 
down stroke. It is widely spread out, and finely arched. At figure 14, Plate 
XIII., the wing is shown as observed towards the end of the down stroke — the 
wing being partly flexed or drawn towards the body, and the arch rendered more 
abrupt, particularly towards the root of the pinion. . At figure 13, Plate XIII., 
the wing is seen quite at the termination of the down stroke. It is fully flexed, 
and drawn still closer to the body. It is, moreover, more deeply arched than in 
either of the other figures. It has, in fact, assumed the shape which offers 
least resistance in an upward direction, and is prepared to make the up stroke. 

The Under or Concave Biting Surface of the Wing of the Bird effective both 
during the Down and Up Strokes. — If, instead of believing that the wing is 
elevated, we believe what, as I have already stated is actually the case, viz., that 
the body of the bird falls downwards and forwards, we at once transfer the 
resistance from the dorsal or convex non-biting surface of the wing to the ven- 
tral concave or biting surface — the body being supported while the wings are 
being elevated by a beautifully arched natural parachute formed by the wings. 
The elevation of the wings is, in