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* 


PROCEEDINGS 


OF 


THE  ROYAL  SOCIETY 

OF 

EDINBURGH. 


VOL.  VIII. 


NOVEMBER  1872  to  JULY  1875. 


EDINBURGH: 

PRINTED  BY  NEILL  AND  COMPANY. 


MDCCCLXXV. 


CONTENTS. 


Opening  Address.  Session  1872-73.  By  Sir  Robert  Chris  tis  on , 
Bart.,  ........  2 

On  the  Philological  Genius  and  Character  of  the  Neo-Hellenic  Dialect 
By  Professor  Blackie,  . . . . . .31 

Laboratory  Notes.  By  Professor  Tait.  Communicated,  in  his  ab- 
sence, by  Professor  G.  Forbes — 

1.  On  the  Delation  between  Thermal,  and  Electric,  Conduc- 

tivity, . . . . . . .32 

2.  On  Electric  Conductivity  at  a Red  Heat,  . . .32 

3.  On  the  Thermo-Electric  Properties  of  Pure  Iron,  . . 32 

Note  on  the  Rate  of  Decrease  of  Electric  Conductivity  with  Increase 
of  Temperature.  By  D.  H.  Marshall,  M.A.,  Assistant  to  the  Pro- 
fessor of  Natural  Philosophy.  Communicated  by  Professor  Tait,  . 33 

Notices  of  deceased  Fellows.  By  David  Milne  Home,  LL.D.,  . 34 

On  a Question  of  Arrangement  and  Probabilities.  By  Professor  Tait,  37 
Laboratory  Notes.  By  Professor  Tait — 

1.  On  the  Stiffness  of  Wires,.  . . . . . 44 

2.  Preliminary  Sketch  of  the  Thermo-Electric  Diagram  for 

Iron,  Gold,  and  Palladium,  . . . .44 

On  the  Muscles  which  open  and  close  the  Mouth,  with  some  Observa- 
tions on  the  Active  and  Passive  Condition  of  Muscles  generally. 

By  Dr  Gamgee,  . . . . . . .47 

Observations  and  Experiments  on  the  Cerebral  Hemispheres  and 
Corpora  Striata  of  Birds.  By  Dr  M‘Kendrick.  Communicated  by 
Professor  Turner,  . . . . . . .47 

Award  of  Makdougall  Brisbane  Prize  to  Professor  Allman,  . . 48 

Report  anent  proposed  alteration  of  Laws,  . . . .48 

On  the  Physical  Constants  of  Hydrogenium.  I.  By  James  Dewar, 

Esq.,  . . . . . . .49 

n the  supposed  Upheaval  of  Scotland,  in  its  Central  Parts,  since  the 
time  of  the  Roman  Occupation.  By  D.  Milne  Home,  LL.D.,  . 49 


IV 


Contents. 


On  the  Anatomy  of  a new  Species  of  Polyodon,  the  Polyodon  G-ladius 
of  Martens,  taken  from  the  river  Yang-tsze-Kiang,  450  miles  above 
Woosung.  Part  I.,  being  its  External  Characters  and  Structure. 
By  P.  D.  Handyside,  M.D.,  ..... 

Note  on  the  Thermal  Equivalents  of  the  Oxide  of  Chlorine.  By 
James  Dewar,  Esq.,  ....... 

On  the  Resemblances  which  Microscopic  Objects  in  Dichroite  and 
Amethyst  have  to  some  of  the  lower  forms  of  Organic  Life.  By  J. 
Scott,  Tain.  Communicated  by  Professor  Kelland, 

Note  on  the  Zodiacal  Light.  By  George  Forbes,  Esq., 

Note  on  Angstrom’s  Method  for  the  Conductivity  of  Bars.  By  Pro- 
fessor Tait,  ........ 

On  the  Thermal  Conductivity  of  Ice,  and  a new  Method  of  Deter- 
mining the  Conductivity  of  Different  Substances.  By  Professor 
George  Forbes,  ....... 

On  the  Formation  of  Coal,  and  on  the  Changes  produced  in  the  Com- 
position of  the  Strata  by  the  Solvent  Action  of  Water  slowly  per- 
colating through  the  Earth’s  Crust  during  long  periods  of  Geological 
Time.  By  R.  W.  Thomson,  C.E.,  F.R.S.E., 

Note  on  Homocheiral  and  Heterocheiral  Similarity.  By  Sir  William 
Thomson,  . . . . . . . 

On  the  Mud  Banks  of  Narrakal  and  Allippey,  two  Natural  Harbours 
of  Refuge  on  the  Malabar  Coast.  By  George  Robertson,  Esq.,  C.E., 
The  Meteorology  of  the  Month  of  May.  By  Alexander  Buchan,  M.  A., 
On  Vortex  Motion.  By  Sir  William  Thomson, 

A Contribution  to  the  yisceral  Anatomy  of  the  Greenland  Shark 
(Lcemargus  borealis).  By  Professor  Turner, 

Additional  Note  on  the  Strain-Function,  &c.  By  Professor  Tait, 
Notice  of  a Singular  Property  exhibited  by  the  Fluid  enclosed  in 
Crystal  Cavities.  By  Edward  Sang,  Esq.,  .... 

On  the  Germ  Theory  of  Putrefaction  and  other  Fermentative  Changes. 
By  Professor  Lister,  ...... 

Notice  of  New  Fishes  from  West  Africa — 

I.  Ophiocephalus  obscurus,  Gunther,  .... 

XI.  Synodontis  Bobbianus,  nov.  spec.  mihi.  (With  a Plate). 

By  John  Alexander  Smith,  M.D., 

On  the  Electrical  Conductivity  of  Certain  Saline  Solutions,  with  a 
note  on  their  Density.  By  J.  A.  Ewing  and  J.  G.  MacGregor,  B.  A. 
Communicated  by  Professor  Tait,  ..... 
On  the  Effect  of  Heating  one  Pole  of  a Magnet,  the  other  being  kept 
at  a Constant  Temperature.  By  D.  H.  Marshall,  Esq.,  M.A.,  and 
C.  G.  Knott,  Esq.  Communicated  by  Professor  Tait.  (With  a 
Plate),  . 

On  the  Physiological  Action  of  Light.  No.  I.  By  James  Dewar, 
Esq.,  and  John  G.  M‘Kendrick,  M.D.,  of  the  University  of  Edin- 
burgh, . 


50 

51 

52 

55 

55 

62 

68 

70 

70 

79 

80 

81 

84 

87 

89 

89 

89 

95 

97 

100 


Contents. 


v 


Notice  of  two  Fossil  Trees  lately  uncovered  in  Craigleith  Quarry,  near 
Edinburgh.  By  Sir  R.  Christison,  Bart.,  President  R.S.E.,  . 104 

On  the  Formation  of  Buds  and  Roots  by  the  Leaves  of  the  Ipecacuan 
Plant  ( Cephaelis  Ipecacuanha).  By  Professor  Balfour.  (With  a 
Woodcut),  ........  108 

On  the  Physiological  Action  of  Light.  No.  II.  By  James  Dewar, 

Esq. , and  John  G.  M‘Kendrick,  M.D.,  . . . .110 

On  the  Thermal  Influence  of  Forests.  By  Robert  Louis  Stevenson, 

Esq.  Communicated  by  Thomas  Stevenson,  Esq.,  . .114 

Observations  and  Experiments  on  the  Fluid  in  the  Cavities  of  Calca- 
reous Spar.  By  Dr  James  Hunter  and  Edward  Sang,  Esq.,  . 126 

On  “ Tait’s  Property  of  the  Retina.”  By  George  Forbes,  Esq.,  . 130 

A Theory  of  Volcanic  Eruptions.  By  Daniel  Vaughan,  . . 133 

On  the  Placentation  of  the  Sloths.  By  Professor  Turner,  . .134 

On  the  Anatomy  of  a new  species  of  Polyodon,  the  Polyodon  Gladius 
of  Martens,  taken  from  the  river  Yang-tsze-Kiang,  450  miles  above 
Woosung.  Part  II.,  being  its  Nervous  and  Muscular  Systems.  By 
P.  D.  Handyside,  M.D.,  ......  136 

On  the  Placentation  of  the  Seals.  By  Professor  Turner,  . .137 

Second  Report  by  the  Committee  on  Boulders  appointed  by  the 
Society.  (With  a Plate),  . . . . . .137 

On  the  Physiological  Action  of  Light.  No.  III.  By  James  Dewar, 

Esq.,  and  John  C.  M‘Kendrick,  M.D.,  ....  179 

On  the  Thermo-Electric  Properties  of  Pure  Nickel.  By  Professor 
Tait,  . . . . . . . .182 

Notice  of  the  Ravages  of  the  Limnoria  terebrans  on  Greenheart 
Timber.  By  David  Stevenson,  Esq.,  Civil  Engineer,  . . 182 

Election  of  Office-Bearers,  ......  207 

Laboratory  Notes.  By  Professor  Tait — 

1.  First  Approximation  to  a Thermo-Electric  Diagram,  . 208 

2.  On  the  Flow  of  Water  through  Fine  Tubes,  . . 208 

Note  on  the  Transformation  of  Double  and  Triple  Integrals.  By 
Professor  Tait,  .......  209 

On  the  Physiological  Action  of  Ozone.  By  James  Dewar,  Esq., 
Lecturer  on  Chemistry,  and  John  G.  M ‘Kendrick,  M.D.,  Physio- 
logical Laboratory,  University  of  Edinburgh,  . . .211 

On  a Compound  formed  by  the  addition  of  Bromacetic  Acid  to  Sul- 
phide of  Methyl,  and  on  some  of  its  Derivatives.  By  Professor 
Crum  Brown  and  Dr  E.  A.  Letts,  . . . .219 

Note  on  the  Various  Possible  Expressions  for  the  Force  exerted  by 
an  Element  of  one  Linear  Conductor  on  an  Element  of  another. 

By  Professor  Tait,  .......  220 

Mdress  on  Ozone,  by  Professor  Andrews,  Hon.  F.R.S.E.,  Vice- 
President  of  Queen’s  College,  Belfast,  ....  229 

A new  Method  of  Determining  the  Material  and  Thermal  Diffusivities 
of  Fluids.  By  Sir  William  Thomson,  ....  229 


VI 


Contents . 


Continuants — A New  Special  Class  of  Determinants.  By  Thomas 
Muir,  M.A.,  Assistant  to  the  Professor  of  Mathematics  in  the 
University  of  Glasgow,  ......  229 

Remarks  upon  the  Footprints  of  the  Dinornis  in  the  Sand  Rock  at 
Poverty  Bay,  New  Zealand,  and  upon  its  recent  extinction.  By 
T.  H.  Cockburn-Hood,  F.G.S.,  . . . . . 236 

Supplementary  Notice  of  the  Fossil  Trees  of  Craigleith  Quarry.  By 
Sir  Robert  Christison,  Bart.,  Hon.  Vice-President,  R.S.E.,  &c.,  . 241 

On  a Method  of  Demonstrating  the  Relations  of  the  Convolu- 
tions of  the  Brain  to  the  Surface  of  the  Head.  By  Professor 
Turner,  . . . . . . . .243 

On  some  Peculiarities  in  the  Embryogeny  of  Tropceolum  speciosum, 
Endl.  & Poepp.,  and  T.  peregrinum,  L.  By  Professor  Alexander 
Dickson,  ........  247 

Notes  on  Mr  Sang’s  Communication  of  7th  April  1873  on  a Singular 
Property  possessed  by  the  Fluid  enclosed  in  Crystal  Cavities  in 
Iceland  Spar — 

1.  By  Professor  Tait,  . . . . , .247 

2.  By  Professor  Swan,  ......  248 

Preliminary  Note  on  the  sense  of  Rotation  and  the  Function  of  the 
Semicircular  Canals  of  the  Internal  Ear.  By  Professor  A.  Crum- 
Brown,  ........  255 

Biographical  Notice  of  J.  S.  Mill.  By  Professor  Fraser,  . . 259 

Obituary  Notice  of  the  Rev.  Dr  Guthrie.  By  the  Rev.  Dr  Lindsay 
Alexander,  . . . . . • • .273 

Obituary  Notice  of  Mr  R.  W.  Thomson.  By  Professor  Fleeming 
Jenkin,  . . . . • • • 278 

Obituary  Notice  of  Archibald  Smith.  By  Sir  William  Thomson,  . 282 
Obituary  Notice  of  the  Very  Rev.  Dean  Ramsay.  By  the  Rev.  D.  F. 
Sandford,  ........  289 

Obituary  Notice  of  Professor  Rankine.  By  Lewis  D.  B.  Gordon, 

C.E.,  . . . • . . .296 

Obituary  Notice  of  Justus  Liebig.  By  Professor  Crum -Brown,  . 307 
Obituary  Notice  of  Gustav  Rose.  By  Professor  Crum-Brown,  .312 
Obituary  Notice  of  the  Rev.  Professor  Stevenson,  D.D.  By  John 
Small,  M.A.,  Librarian  to  the  University  of  Edinburgh,  . . 314 

Obituary  Notice  of  Auguste  De  la  Rive.  By  George  Forbes, 

Esq., 319 

Obituary  Notice  of  Dr  J.  Lindsay  Stewart.  By  Dr  Cleghorn, 
Stravithy,  . . • • • • • • 321 

Obituary  Notice  of  John  Hunter.  By  J.  T.  Bottomly,  Esq.,  Univer- 
sity, Glasgow,  . . . . . . .322 

The  Kinetic  Theory  of  the  Dissipation  of  Energy.  By  Sir  William 
Thomson,  ........  325 

On  the  Stresses  due  to  Compound  Strains.  By  Professor  C.  Niven. 
Communicated  by  Professor  Tait,  . . . . .335 


Contents . 


vii 

On  the  Parallel  Roads  of  Glen  Roy.  By  the  Rev.  Thomas  Brown, 

F.R.S.E., .339 

Note  on  the  Perception  of  Musical  Sounds.  By  John  G.  M ‘Kendrick, 

M.D., 342 

On  the  Establishment  of  the  Elementary  Principles  of  Quaternions 
on  an  Analytical  Basis.  By  G.  Plarr,  Esq.  Communicated  by  Pro- 
fessor Tait,  ........  348 

Preliminary  Note  “ On  a New  Method  of  obtaining  very  perfect 
Vacua.”  By  Professor  P.  G.  Tait  and  James  Dewar,  Esq.,  . 348 

Laboratory  Notes.  By  Professor  Tait — 

1.  On  Atmospheric  Electricity,  ....  349 

2.  On  the  Thermo-Electric  Position  of  Sodium,  . . 350 

On  the  Resistance  of  the  Air  to  the  Motion  of  Fans.  By  James  C. 
Fairweather,  Esq.  Communicated  by  George  Forbes,  Esq.  (With 
two  Plates),  . ......  351 

On  the  Curve  of  Second  Sines  and  its  Variations.  By  Edward  Sang, 
Esq.,  ........  356 

Laboratory  Notes.  By  Professor  Tait — 

On  the  Thermo-Electric  Positions  of  Sodium  and  Potassium,  . 362 
On  a New  Form  of  Mariner’s  Compass.  By  Sir  William  Thomson,  . 363 
Further  Note  on  Spectra  under  exceedingly  Small  Pressures.  By 
Professor  Tait  and  James  Dewar,  Esq. , . . . . 363 

On  the  After-Glow  of  Cooling  Iron  at  a Dull-Red  Heat.  By  George 
Forbes,  Esq.,  .......  363 

On  a Form  of  Radiation  Diagram.  By  George  Forbes,  Esq.,  . 366 

On  the  Semicircular  Canals  of  the  Internal  Ear.  By  Professor  Crum- 
Brown,  . . . . . . . . 370 

On  Last-Place  Errors  in  Vlacq’s  Table  of  Logarithms.  By  Edward 
Sang,  Esq.,  . . . . . . . .371 

Note  on  the  Submerged  Fossil  Trees  of  Granton  Quarry.  By  Sir 
Robert  Christison,  Bart.,  Hon.  V.P.  R.S.E.,  . . . 377 

Note  on  Grouse  Disease.  By  Professor  Maclagan,  . . . 378 

Latent  Heat  of  Mercury  Vapour.  By  James  Dewar,  Esq.,  . .380 

Notes  by  James  Dewar,  Esq. — 

1.  Problems  of  Dissociation,  .....  380 

2.  Formation  of  Allotropic  Sulphur,  ....  380 

3.  Heat  of  Fermentation,  .....  380 

Further  Note  on  Continuants.  By  Thomas  Muir,  M.A.,  F.R.S.E., 
Assistant  to  the  Professor  of  Mathematics  in  Glasgow  University,  380 
On  the  Formation  of  Allotropic  Sulphur.  By  James  Dewar,  Esq.,  . 382 
On  Some  Compounds  of  Dimethyl-Thetine.  By  Professor  Crum- 
Brown  and  Dr  E.  A.  Letts,  . . . . . 382 

On  a New  Example  of  the  Opheliidse  ( Linotrypane  apogon ) from 
Shetland.  By  W.  C.  MTntosh,  M.D.,  ....  386 

Concluding  Remarks  by  David  Milne  Home,  LL.D.,  . , „ 390 


viii 


Contents. 


Election  of  Office-Bearers,  . . . . . .416 

Presentation  of  the  Keith  Prize  to  Professor  Tait,  . . .415 

Opening  Address  on  the  Stability  of  Steady  Motion.  By  the  Presi- 
dent, . . . . . . . 420 

Remarks  on  the  Great  Logarithmic  and  Trigonometrical  Tables  com- 
puted in  the  Bureau  du  Cadastre  under  the  direction  of  M.  Prony. 

By  Edward  Sang,  . . . . . . 421 

On  the  Elimination  of  /3,  y,  from  the  conditions  of  integrability  of 
S uoc^p,  S ufllp,  S uylp.  By  G.  Plarr,  Esq.  Communicated  by 

Professor  Tait, 436 

The  Development  of  the  Ova,  and  the  Structure  of  the  Ovary,  in  Man 
and  other  Mammals.  By  James  Foulis,  M.D.  (Edin.)  Communi- 
cated by  Professor  Turner,  . . . . . .437 

Mathematical  Notes.  By  Professor  Tait — 

1.  On  a singular  Theorem  given  by  Abel,  . . . 440 

2.  On  the  Equipotential  Surfaces  for  a Straight  Wire,  . 443 

3.  On  a Fundamental  Principle  in  Statics,  . . . 443 

Exhibition  and  Description  by  the  President  of  his  Tide  Calculating 
Machine,  also  his  Improved  Tide-Gauge  ; he  also  described  certain 
Capillary  Phenomena,  with  Experiments,  ....  445 
Biographical  Notice  of  Lord  Colonsay.  By  the  Hon.  Lord  Neaves,  . 445 
Biographical  Notice  of  Cosmo  Innes.  By  the  Hon.  Lord  Neaves,  . 453 

Biographical  Notice  of  Francis  Deas.  By  the  Hon.  Lord  Neaves,  . 461 

Biographical  Notice  of  Adam  Black.  By  the  Rev.  Dr  Lindsay 
Alexander,  . . . . . . . .467 

Biographical  Notice  of  Sheriff  Cleghorn.  By  David  Maclagan,  Esq., 

C.A.,  . 468 

Biographical  Notice  of  Henry  Stephens.  By  Professor  Maclagan,  . 469 
Biographical  Notice  of  Christopher  Hansteen.  By  Alexander  Buchan, 

Esq.,  . .473 

Biographical  Notice  of  Jacques  Adolphe  Lambert  Quetelet.  By 
Alexander  Buchan,  Esq.,  . . . . .474 

Biographical  Notice  of  George  Berry.  By  George  Barclay,  Esq.,  . 476 
On  the  Complete  Theory  of  the  Stone  Arch.  By  Edward  Sang, 

Esq.,  ........  479 

On  the  Application  of  Angstrom’s  Method  to  the  Conductivity  of 
Wood.  By  C.  G.  Knott  and  A.  Macfarlane.  Communicated  by 
Professor  Tait,  . . . . . . .481 

Notice  of  Striated  Rock  Surfaces  on  North  Berwick  Law.  By  David 
Stevenson,  V.P.R.S.E.,  Civil  Engineer,  ....  481 

Laboratory  Notes.  By  Professor  Tait — 

a.  Photographic  Records  of  the  Sparks  from  a Holtz  Machine,  484 

b.  Determination  of  the  Surface-Tension  of  Liquids  by  the 

Ripples  produced  by  a Tuning-Fork,  . . . 485 

c.  Capillary  Phenomena  at  the  Surface  of  Separation  of  two 

Liquids,  . . . . . . . 485 


Contents.  ix 

Obituary  Notice  of  Dr  Robert  Edward  Grant,  late  Professor  of  Com- 
parative Anatomy  in  University  College,  London.  By  Dr  W. 
Sharpey,  ........  486 

An  Illustration  of  the  relative  Rates  of  Diffusion  of  Salts  in  Solution. 

By  Professor  Crum  Brown,  ......  490 

On  the  Oscillation  of  a System  of  Bodies  with  rotating  Portions.  By 
Sir  William  Thomson,  ......  490 

Laboratory  Notes.  By  Professor  Tait — 

a.  On  the  Application  of  Sir  W.  Thomson’s  Dead-Beat 

Arrangement  to  Chemical  Balances,  . . . 490 

b.  Photographs  of  Electric  Sparks  taken  in  Cold  and  in  Heated 

Air,  .......  49.1 

c.  On  the  Electric  Resistance  of  Iron  at  High  Tempera- 

tures, .......  491 

Biographical  Notice  of  William  Ewing,  Esq.,  F.R.S.E.  By  Professor 
William  P.  Dickson,  . . . . . .491 

On  a Faulty  Construction  common  in  Skewed  Arches.  By  Edward 
Sang,  Esq.,  . •*  . . . • . . . 497 

On  the  mode  of  Growth  and  Increase  amongst  the  Corals  of  the 
Palaeozoic  Period.  By  IT.  Alleyne  Nicholson,  M.D.,  D.Sc.,  Pro- 
fessor of  Biology  in  the  Durham  University  College  of  Physical 
Science,  ........  498 

Exhibition  of  Diagrams  in  Illustration  of  the  Capillary  Surfaces  of 
Revolution.  By  the  President,  . . ,.  . 500 

Presentation  of  the  Makdougall  Brisbane  Prize  to  Professor  Lister,  . 500 
On  the  Diurnal  Oscillations  of  the  Barometer.  By  Alexander  Buchan, 
M.A.,  . . . . . . . .505 

The  Phenomena  of  Single  and  Double  Vision,  as  shown  in  the  Stereo- 
scope. By  R.  S.  Wyld,  Esq.,  .....  505 

On  the  Products  of  the  Oxidation  of  Dimethyl-Thetine,  and  its  Deriva- 
tives. By  Professor  Crum  Brown  and  Dr  E.  A.  Letts,  . . 508 

Presentation  of  the  Neill  Prize  to  Charles  Wm.  Peach,  . . 509 

On  the  Physiological  Action  of  Light.  Part  II.  By  James  Dewar, 

Esq.,  and  Dr  John  C.  M‘Kendrick,  ....  513 

On  the  Structure  and  Systematic  Position  of  Tristichopterus  alatus, 
Egerton.  By  R.  H.  Traquair,  M.D.,  F.C.S.,  . . .513 

Note  of  Temperature  Measurements  in  the  Great  Geysir  of  Iceland — 
August  1874.  By  Robert  Walker,  Esq.,  ....  514 

On  the  Capillary  Surface  of  Revolution.  By  Sir  William  Thomson 
and  Mr  John  Perry,  . . . . . .520 

On  the  Oscillation  of  a System  of  Bodies  with  Rotating  Portions. 

Part  II. — Vibrations  of  a Stretched  String  of  Gyrostats  (Dynamics 
of  Faraday’s  Magneto-Optic  Discovery),  with  Experimental  Illustra- 
tions. By  Sir  William  Thomson,  . . . . .521 

On  the  Theory  of  the  Spinning-Top,  with  Experimental  Illustrations. 

By  Sir  William  Thomson,  . . . . .521 

YOL.  VIII.  b 


X 


Conten  ts. 


Laboratory  Note — Analysis  of  Titaniferous  Iron  Sand  from  North 
Berwick.  By  James  Davidson,  Esq.  Communicated  by  Professor 
Crum  Brown,  .......  523 

On  some  Permian  Fishes,  hitherto  erroneously  referred  to  the  Genus 
Palceoniscus.  By  Dr  Traquair,  . , . . .525 

Note  on  the  action  of  Bile  Salts  on  the  Animal  Economy.  By  J. 

Graham  Brown,  Esq.  Communicated  by  Dr  M‘Kendrick, . . 525 

Preliminary  Note  on  the  Anatomy  of  the  Pia  Mater.  By  Dr  J.  Batty 
Tuke,  . . . . . . . .534 

Note  on  the  Physiological  Action  of  Light.  By  James  Dewar,  Esq., 
and  Dr  M ‘Kendrick,  ......  534 

On  the  Expiatory  and  Substitutionary  Sacrifices  of  the  Greeks.  By 
Dr  Donaldson,  .......  535 

The  Placenta  in  Ruminants — a Deciduate  Placenta.  By  Professor 
Turner,  . . . . . . . .537 

An  Essay  towards  the  General  Solution  of  Numerical  Equations  of 
all  Degrees.  By  W.  H.  Fox  Talbot,  Esq.,  Hon.  F.R.S.E., . .514 

Note  on  the  Electrical  Conductivity  of  Saline  Solutions.  By  J.  G. 

Macgregor,  M.A.,  B.Sc.  Communicated  by  Professor  Tait,  . 545 

On  High  Flood  Marks  on  the  Banks  of  the  River  Tweed  and  some  of 
its  tributaries,  and  on  Drift  Deposits  in  Tweed  Valley.  By  David 
Milne  Home,  LL.D.,  ......  559 

Observations  on  Mr  Sang’s  Remarks  relative  to  the  Great  Logarithmic 
Table  compiled  at  the  Bureau  du  Cadastre  under  the  direction  of 
M,  Prony.  By  M.  F.  Lefort.  Communicated  by  Mr  Sang,  who 
has  translated  the  pa, per  from  the  French,  ....  563 


Observations  relatives  aux  remarques  publiees  par  M.  Edward  Sang 
dans  les  “ Proceedings  of  the  Royal  Society  of  Edinburgh,  Session 
1874-1875,”  sur  les  grandes  tables  logarithmiques  et  trigono- 
metriques  calculees  au  Bureau  du  Cadastre  sous  la  direction  de 
Prony;  par  F.  Lefort,  Inspecteur  general  des  Ponts  et  Chaussees, 
Membre  Correspondant  de  l’Academie  des  Sciences  des  Naples,  . 564 
Observation  relative  to  Mr  Edward  Sang’s  “ Remarks  on  the  Great 
Logarithmic  and  Trigonometrical  Tables  calculated  in  the  Bureau 
du  Cadastre  under  the  direction  of  Prony,”  published  in  the  Pro- 
ceedings of  the  Royal  Society  of  Edinburgh,  Session  1874-1875, 
by  M.  F.  Lefort,  Inspecteur  General  des  Ponts  et  Chaussees  Corre- 
sponding Member  of  the  Academy  of  Sciences  of  Naples,  . .574 

Reply  to  M.  Lefort’s  Observations.  By  Edward  Sang,  . .581 

Note  on  Electric  Resistance  of  Solutions.  By  William  Durham,  Esq., 
and  P.  R.  Scott  Lang,  M.A.,  .....  587 

On  the  Circumscribed,  Inscribed,  and  Escribed  Circles  of  a Spherical 
Triangle.  By  C.  G.  Colson,  Esq.  Communicated  by  Professor 
Tait,  ........  589 

On  some  Remarkable  Changes,  Additions,  and  Omissions  of  Letters 
in  Certain  Cognate  European  Words.  By  the  Hon.  Lord 
Neaves,  ........  596 


Contents.  xi 

De  l’interpolation  des  fonctions  irrationnelles  en  general,  et  des 
fonctions  logarithmiques  en  particulier,  a l’aide  des  tables  nume- 
riques.  Par  F.  Lefort,  inspecteur  general  des  Ponts  et  chaussees, 
Membre  Correspondant  de  l’Academie  des  Sciences  de  Naples,  . 602 
The  Theory  of  the  Causes  by  which  Storms  Progress  in  an  Easterly 
Direction  over  the  British  Isles,  and  why  the  Barometer  does  not 
always  indicate  real  vertical  pressure.  By  Eobert  Tennent,  Esq.,  . 612 
On  Electric  Images.  By  Professor  Tait,  ....  623 
Laboratory  Notes.  By  Professor  Tait — 

a.  On  the  Origin  of  Atmospheric  Electricity,  . . . 623 

b.  Experiments  on  the  Thermal  Conductivity  of  some  Dialec- 

trics.  By  Messrs  C.  M.  Smith  and  C.  0.  Knott,  . . 623 

A Chapter  on  the  Tides.  By  the  Eev.  James  Pearson,  M.A.,  Vicar  of 
Fleetwood.  Communicated  by  Professor  Tait,  . . . 627 

Farther  Researches  in  very  perfect  Vacua.  By  Professors  Dewar  and 
Tait,  . . . . . . . .628 

On  the  Electric  Resistance  of  Iron  at  a High  Temperature.  By  Messrs 
C.  M.  Smith,  C.  G.  Knott,  and  A.  Macfarlane.  (Plate),  „ . . 629 


'* 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  vm.  1872-73.  No.  85. 


Ninetieth  Session. 

Monday , 2d  December  1872. 

Sir  EOBEET  CHEISTISON,  Bart.,  President,  in  the  Chair. 
The  following  Council  were  elected 

President. 

Sir  ROBERT  CHRISTISON,  Bart.,  M.D.,  D.C.L.,  LL.D. 

Honorary  Vice-President. 

His  Grace  the  DUKE  of  ARGYLL. 

Vice-Presidents. 

The  Hon.  Lord  Neaves.  I Sir  W.  Stirling-Maxwell,  Bart. 

Professor  Sir  William  Thomson.  Professor  W.  J.  Macquorn  Rankine. 
Principal  Sir  Alex.  Grant,  Bart.  | David  Milne  Home,  LL.D. 

General  Secretary — Dr  John  Hutton  Balfour. 

Secretaries  to  Ordinary  Meetings. 

Professor  Tait. 

Professor  Turner. 

Treasurer — David  Smith,  Esq. 

Curator  of  Library  and  Museum — Dr  Maclagan, 

Councillors. 

Rev.  Thomas  Brown. 

James  Dewar,  Esq. 

Professor  Kelland. 

Professor  Lister. 

George  Robertson,  Esq.,  C.E. 
Captain  T.  P.  White. 

A 


James  Donaldson,  Esq. 
Dr  Thomas  R.  Fraser. 

Dr  Arthur  Gamgee. 
Alexander  Buchan,  Esq. 
Prof.  A.  Dickson. 

James  Leslie,  Esq.,  C.E. 

VOL.  VIII. 


2 


Proceedings  of  the  Royal  Society 


Monday , 2 d December  1872. 

Sir  Robert  Christison,  Bart., ’the  President,  read  the 
following  Opening  Address : — 

The  Society  now  enters  into  its  90th  session  since  its  foundation. 
During  the  session  recently  concluded  the  number  of  its  Ordinary 
Fellows  has  increased  from  331  to  343.  Twenty-two  members 
were  admitted  during  last  session.  In  the  twelve  months  ending 
with  the  30th  ultimo,  death  has  laid  his  hands  sparingly  upon 
our  brethren.  During  the  former  year  we  lost  by  death  ten 
Ordinary  and  three  Honorary  Fellows,  several  of  whom  occupied 
during  their  lives  a very  high  position  in  science.  Last  year 
has  deprived  us  of  only  four  Ordinary  Fellows,  and  one  on  our 
Honorary  list ; and  although  these  were  all  men  of  great  esti- 
mation in  their  several  professions,  our  Honorary  Fellow  alone, 
among  them  all,  was  widely  known  as  a successful  scientific 
labourer.  Therefore  the  duty  I have  now  to  discharge  as  their 
biographer  is  evidently  on  two  accounts  a brief  one. 

The  Ordinary  Fellows  who  have  disappeared  from  amongst 
us  during  last  year  are,  Dr  Thomas  Barnes  of  Carlisle,  Dr  Patrick 
Miller  of  Exeter,  Dr  John  Addington  Symonds  of  Clifton,  and 
the  Right  Reverend  Charles  Hughes  Terrot,  Bishop  of  Edinburgh 
in  the  Scottish  Episcopalian  Church.  Our  only  deceased  Honorary 
Fellow  is  Hugo  von  Mohl,  Professor  of  Botany  in  the  University 
of  Tubingen. 

The  three  first  were  graduates  of  the  University  of  Edinburgh, 
each  of  them  distinguished  during  a long  life  by  his  successful 
cultivation  of  medicine,  and  the  pursuit  of  medical  practice  in 
an  important  district  of  England.  It  has  often  been  remarked 
that  there  is  scarcely  in  all  England  an  important  county  town, 
where  for  almost  a century  past  the  leading  physician  of  the 
town  and  surrounding  country  has  not  been  a graduate  of  the 
University  of  Edinburgh.  Drs  Barnes,  Symonds,  and  Miller 
illustrate  a fact  which  the  University  has  always  regarded  with 
allowable  pride. 


3 


of  Edinburgh,  Session  1872-73. 

Dr  Thomas  Barnes  was  born  in  1793,  near  Wigton,  in  Cumber- 
land. He  commenced  bis  medical  studies,  according  to  the  fashion 
of  the  time,  by  becoming  apprentice  to  a medical  practitioner 
in  that  town;  where,  among  other  duties,  he  had  to  supply  physic 
to  horse,  dog,  and  cow,  as  well  as  to  the  human  subject,  to  sell 
pepper  and  coffee,  and  to  look  after  his  master’s  Bosinante. 
Having  thus  cultivated  medicine  in  a practical  way,  he  proceeded, 
in  the  inverse  order,  to  study  the  principles  of  medicine  and  its 
fundamental  sciences  in  the  University  of  Edinburgh  at  the 
age  of  eighteen.  In  more  recent  times  medical  students  carry 
on  their  studies  differently.  Apprenticeship  is  at  a sad  discount 
with  them.  They  study  instead  literature,  philosophy,  and  physi- 
cal science,  then  begin  medicine  at  the  root  of  the  tree,  and 
end  their  school  studies  with  that  of  medical  and  surgical  practice. 
It  was  different  in  the  time  of  Dr  Barnes’  noviciate ; even  in 
my  young  days,  two-and  twenty-years  later,  I was  almost  a 
solitary  example  of  an  unapprenticed  British  student,  working 
till  the  age  of  eighteen  in  the  Faculty  of  Arts  and  at  the  Natural 
Sciences,  instead  of  wasting  the  most  precious  of  his  years  in 
dispensing  drugs,  and  practising  physic  before  learning  it ; and, 
indeed,  there  are  even  still  some  estimable  men,  laudatores  temporis 
acti,  who  sigh  over  the  now  fast  vanishing  old  rule,  and  lament 
the  disappearance  of  medical  apprenticeships,  and  the  loss  of 
apprentices. 

Dr  Barnes,  after  studying  medicine  for  six  years,  partly  in  this 
University  and  partly  in  London,  Paris,  and  Germany,  took  his 
degree  at  Edinburgh  in  1817.  Soon  afterwards  he  settled  as 
a consulting  physician  in  Carlisle,  where  at  first  he  made  only 
that  slow  progress  to  which  those  must  usually  submit  who  choose 
this  the  highest  class  of  medical  practice, — but  where  before  long 
he  became  for  many  years  the  leading  physician  over  a great 
extent  of  the  northern  counties  of  England.  In  this  pursuit  he 
led  a life  of  great  professional  activity  and  usefulness  till  his  56th 
year,  when  failing  health  led  him  to  restrict  his  field.  At  the 
same  time,  he  did  much  good  to  the  place  of  his  residence  by  found- 
ing some,  and  encouraging  and  improving  other,  important  charitable 
establishments.  Nor  did  he  neglect  the  improvement  of  medical 
knowledge.  For,  though  he  never  contributed  any  large  work  to 


4 Proceedings  of  the  Royal  Society 

the  literature  of  medicine,  he  communicated  from  time  to  time 
to  the  professional  journals  many  papers  of  acknowledged  value. 

Like  most  county  and  country  practitioners  of  ability,  he  found 
recreation  in  cultivating  a favourite  branch  of  science,  little,  if 
at  all,  connected  with  his  profession.  This  in  Dr  Barnes’  instance 
was  meteorology.  His  studies  in  this  department  of  natural 
history  were  the  main  cause  of  his  being  associated  with  us  as 
a Fellow  of  the  Boyal  Society.  A paper  by  him  on  “ The  Meteor- 
ology of  Carlisle  for  24  years,”  was  read  to  the  Society  in  1830 ; 
and  in  the  same  year  he  was  elected  one  of  our  Fellows.  Forty 
years  later,  and  therefore  quite  recently,  he  contributed  to  the 
Proceedings  of  the  Society  a continuation  of  his  inquiries  on  the 
same  subject. 

Dr  Barnes  died  in  March  last,  in  the  79th  year  of  his  age. 

Dr  John  Addington  Symonds,  another  county  physician  of  great 
eminence  in  England,  was  born  in  1807  at  Oxford,  where  his 
father  practised  the  medical  profession.  The  opportunities  of  his 
birth-place  gave  him  the  inestimable  advantage  of  an  excellent 
general  education,  which  ever  afterwards  shone  out  in  his  tastes 
and  the  occupations  of  his  leisure  hours.  After  taking  advantage 
for  two  years  of  the  limited  opportunities  which  Oxford  in  these 
days  presented  for  the  study  of  the  fundamental  sciences  of 
medicine,  he  repaired  in  1825,  being  then  in  his  19th  year,  to 
the  University  of  Edinburgh,  where  he  graduated  three  years 
afterwards.  He  was  a very  distinguished  student,  as  I personally 
know,  for  he  was  one  of  my  pupils  in  1827,  when  I was  Professor 
of  Medical  Jurisprudence.  Nor  were  his  studies  confined  to  me- 
dicine,— philosophy  at  that  time  being  also  a favourite  pursuit. 
Returning  to  Oxford,  he  assisted  his  father  in  his  practice  for 
three  years.  But  in  1831  he  was  induced  to  settle  in  Bristol;  and 
there  at  first,  and  afterwards  in  conterminous  Clifton,  he  passed 
his  whole  professional  life. 

Dr  Symonds  attained  great  reputation  as  a practising  physician 
at  an  early  age.  Crowds  were  attracted  to  him  from  all  quarters 
of  Great  Britain,  partly  no  doubt  by  the  salubrity  of  the  climate 
of  Clifton,  but  chiefly  by  the  eminence  of  its  physician.  The 
climate  had  been  long  considered  favourable  for  the  treatment  of 


of  Edinburgh , Session  1872-73.  5 

certain  common  pulmonary  diseases.  Taking  advantage  of  this 
peculiarity,  Dr  Symonds,  while  neglecting  no  corner  of  the  field  of 
medical  practice,  studied  with  great  care  and  success  the  diseases 
of  the  lungs.  In  consequence,  the  suffering  members  of  the 
community  flocked  to  him  in  great  numbers  from  all  parts. 
Many  went  to  him  from  Scotland,  many  from  Edinburgh.  Among 
the  latter  Principal  Forbes,  while  Professor  of  Natural  Philosophy, 
repaired  to  Clifton  at  my  recommendation  ; and  he  derived  so 
much  benefit  from  his  first  residence  there,  under  the  care  of 
Symonds,  that  he  was  able  to  struggle  bravely  with  his  malady 
for  many  years,  and  at  one  time  indeed  seemed  as  if  about  to 
shake  off  his  deadly  enemy  altogether.  Forbes  often  spoke  to  me 
with  admiration  and  gratitude  of  the  Clifton  physician’s  kindness, 
skill,  and  philosophical  acuteness ; and  it  is  no  wonder  that  two 
such  men  continued  fast  and  intimate  friends  ever  after. 

Local  celebrities,  in  positions  similar  to  that  of  Dr  Symonds, 
not  unfrequently  owe  success  to  qualities  different  from  those 
which  ought  alone  to  give  a title  to  it.  Dr  Symonds  was  none  of 
these,  but  in  every  sense  of  the  word  a true  physician  of  the 
purest  dye,  of  excellent  talents,  rare  assiduity,  deep  discernment, 
well-balanced  determination,  unpretentious  bearing,  thorough  con- 
scientiousness in  every  thought  and  act,  a sincere  unostentatious 
Christian, — in  short,  a man  qualified  to  rise  to  a high  rank  wher- 
ever he  might  have  chanced  to  choose  his  path  in  the  medical  pro- 
fession. 

But  Dr  Symonds  was  more  than  a physician.  He  had  a fine 
taste  for  art.  His  classical  training  in  youth  led  him  to  keep  up 
familiarity  with  ancient  literature.  Philosophy,  too,  was  his  frequent 
recreation  from  professional  toil.  It  is  no  wonder,  therefore,  that, 
when  his  part  of  physician  had  been  discharged  and  came  to  an 
end,  that  of  friend  continued  ; and  that  he  thus  enjoyed  through 
life  the  friendship  and  society  of  not  a few  of  the  most  remarkable 
men  in  British  literature,  science,  and  politics  during  the  last 
thirty  years. 

These  his  tastes  are  displayed  in  the.  subjects  he  chose  for 
those  of  his  writings,  which  have  been  collected  and  published 
since  his  death  by  his  son.  He  has  contributed  less  than  he 
might  have  done  to  the  literature  of  the  practice  of  medicine  in 


6 Proceedings  of  the  Royal  Society 

the  strict  signification  of  that  term,  though  his  experience  emi- 
nently qualified  him  to  illustrate  it.  His  works  in  the  posthumous 
collection  of  them  consist  of  Essays  on  topics  of  a general  nature, 
generally  delivered  as  addresses  to  public  meetings,  and  the  titles 
of  which  prove  the  nature  of  his  favourite  pursuits,  and  the 
variety  of  his  endowments.  They  treat  of  the  Principles  of 
Beauty,  of  Waste,  of  Decades  of  great  events  in  the  world’s 
history,  of  Knowledge,  of  Sleep  and  Dreams,  of  Apparitions,  of 
the  Relations  between  Mind  and  Muscle,  of  Habit,  of  the  Criminal 
Responsibility  of  the  Insane,  of  the  Public  Estimate  of  Medicine, 
of  the  Health  of  Clifton,  of  Medical  Evidence ; and  the  last  of 
these  treatises  is  an  address  on  Health,  delivered  at  the  Bristol 
meeting  of  the  Social  Science  Association  in  October  1869. 

There  is  none  of  these  able  essays,  distinguished  alike  by  sound 
sense,  ingenious  views,  logical  discussion,  and  purity  of  style, 
which  might  not  be  analysed  here  with  credit  to  his  memory,  and 
advantage  to  those  now  listening  to  me.  But  I must  remember 
that  brevity  is  the  first  essence  of  this  Presidential  Address ; and, 
therefore,  I shall  confine  myself  to  a single  paper,  probably  indeed 
not  the  most  attractive  of  them  for  the  general  reader,  but  which 
illustrates  well  Dr  Symonds’  ability  as  a statistical  inquirer  and 
critic.  In  an  address  delivered  at  Bath,  he  tells  us  that  “ a severe 
shock  was  inflicted  on  the  sanitary  sensibilities  of  Clifton,”  by 
the  town  being  gibbeted  in  the  “ Times”  newspaper,  on  the  authority 
of  the  Registrar-GreneraPs  mortality  returns,  as  “ the  most  mortal 
of  watering  places,” — because,  while  at  Torquay,  Cheltenham,  the 
Isle  of  Wight,  &c.,  the  annual  death  rate  in  every  1000  of  the 
population  ranged  from  15  to  17  only,  in  Clifton  it  mounted  so 
high  as  24.  The  truth,  as  demonstrated  by  Symonds,  is  an  admir- 
able illustration  of  the  frequent  fallacy  of  statistics,  and  the 
danger  when  rash,  ill- trained  minds  dare  to  deal  with  them.  Dr 
Symonds  shows  that  the  supposed  high  death-rate  is  founded  on 
a single  quarterly  return,  while  the  returns  taken  from  other 
quarters  of  the  same  year,  or  from  other  years,  vary  so  much  as 
from  24  down  to  so  low  as  14-8  in  1000  of  the  population ; and 
he  shows  further  that  the  returns  made  use  of  in  the  4 1 Times” 
do  not  apply  to  Clifton  the  watering-place  at  all,  but  that  the 
newspaper  writer  had  committed  the  ridiculous  mistake  of  con- 


7 


of  Edinburgh,  Session  1872-73. 

founding  with  it  the  “ Clifton  Union,”  a term  including  a far 
more  extensive  and  populous  district,  from  which  the  watering- 
place  is  sharply  defined  by  site  as  well  as  by  structure,  and  which 
adds  to  the  count  a great  mass  of  the  most  needy  population  of 
the  Bristol  suburbs.  Thus,  raking  away  the  rubbishy  statistics 
of  the  newsmonger,  he  proves  by  irrefragable  facts,  on  a scale  of 
several  annual  returns,  that  the  yearly  mortality  of  the  justly 
famous  watering-place  is  no  more  than  17  in  1000. 

Dr  Symonds  published,  in  the  professional  periodicals  chiefly, 
various  valuable  papers  on  various  strictly  practical  subjects, 
which  it  would  be  out  of  place  for  me  even  to  enumerate  here, 
and  much  more  so  to  discuss.  They  were  received  as  they 
successively  appeared  with  approbation  by  his  professional  brethren, 
and  may  be  perused  now  with  profit  by  every  professional  student. 

In  1854  Dr  Symonds  became  a Fellow  of  the  Royal  Society  of 
Edinburgh,  led  to  us  partly  by  his  early  connection  with  the 
University,  and  partly  by  the  close  ties  of  friendship  contracted 
with  many  Scotsmen,  of  whom,  or  of  whose  relatives,  he  had  been 
at  Clifton  the  skilful  and  sympathising  physician. 

In  the  autumn  of  1868  his  health  for  the  first  time  began  to 
fail,  and,  though  he  took  early  warning  and  contracted  greatly  the 
field  of  his  labours,  his  ailments  grew  upon  him,  and  proved  fatal 
on  the  25th  February  1871. 

Dr  Patrick  Miller,  another  eminent  physician  who  practised 
during  a long  life  at  Exeter,  died  there  in  December  1871,  in  his 
90th  year,  Senior  Fellow  of  the  Royal  Society  of  Edinburgh,  and 
also,  I apprehend.  Senior  Gfraduate  of  the  University  of  Edin- 
burgh, where  he  took  his  degree  as  Doctor  of  Medicine  in  1804. 
I cannot  find  satisfactory  evidence  that  any  graduate  of  that  year, 
or  of  those  immediately  preceding  it,  has  survived  him.  In  our 
own  list  there  still  stands  one  name  for  the  year  1818,  in  which 
Dr  Miller  was  elected  a Fellow;  but  for  some  time  past,  on 
careful  inquiry,  no  trace  can  be  discovered  for  identifying  this 
his  contemporary. 

Dr  Miller  was  connected  with  us  by  ties  dear  to  every  member 
of  our  Society.  He  was  grandson  of  the  celebrated  Professor  of 
Mathematics  in  the  University,  Dr  Matthew  Stewart,  and  nephew 


8 


Proceedings  of  the  Boyal  Society 

of  that  Professor’s  still  more  famous  son,  Professor  Dugald 
Stewart.  He  was  educated  here  at  the  High  School  and  Univer- 
sity, under  the  eye,  and  very  much  in  the  family,  of  his  uncle ; 
a precious  privilege,  which,  among  other  advantages,  secured  for 
him  the  early,  and  throughout  life  uninterrupted,  friendship  of 
several  of  the  greatest  men  in  the  subsequent  history  of  our 
country,  such  as  Lords  Palmerston,  Lansdown,  and  Brougham, 
who  were  his  uncle’s  pupils. 

Three  years  after  graduation  he  settled  in  Exeter,  where  he  was 
so  well  received,  that  in  two  years  more  he  was  appointed  physi- 
cian of  the  Exeter  Hospital  for  the  sick.  He  soon  became  the 
leading  physician  of  the  town  and  adjacent  country  ; — a position 
for  which  he  was  eminently  qualified  by  his  large,  highly-culti- 
vated mind,  his  courteous,  kindly,  gentle  manner,  combined  with 
great  energy  and  decision,  high  professional  attainments,  and  a 
strong,  robust,  healthy  frame  and  constitution.  He  was  also 
constantly  employed  in  doing  good  in  other  ways  in  the  city  of 
his  adoption.  He  was  an  original  founder,  or  active  promoter,  of 
every  one  of  the  various  public  institutions,  organised  in  his  life- 
time at  Exeter,  for  the  bodily  care  and  mental  culture  of  the 
labouring  classes,  in  whose  welfare  he  constantly  took  great  interest. 

In  these  days  of  rapid  development  and  change  in  the  medical 
sciences,  and  in  the  details  of  medical  practice,  there  are  not 
many  men  of  Hr  Miller’s  unquestionable  ability,  who,  in  pro- 
fessional positions  parallel  to  his,  have  not  contributed  by  their 
writings  to  some  branch  or  another  of  professional  progress.  But 
Hr  Miller’s  tastes  did  not  lie  in  the  direction  of  medical  publi- 
cation, although  his  wide  and  long  experience  must  have  supplied 
him  with  great  store  of  materials. 

Until  eight  years  before  his  death,  Hr  Miller  continued  to  retain 
great  bodily  activity.  Kheumatism,  however,  then  gradually 
circumscribed  his  powers  in  that  respect ; but  the  faculties  of  his 
mind,  even  his  memory,  are  stated  by  one  who  knew  him  well,  to 
have  been  preserved  unsubdued  till  very  near  the  close  of  his  life. 

He  repeatedly  visited  Scotland  and  Edinburgh,  to  keep  alive 
his  old  associations ; but  for  many  years  past  I fear  he  must  have 
encountered  very  few  to  recall  to  him  his  old  associates.  His 
regard  for  his  University  was  shown  a few  years  ago  by  his  pre- 


9 


of  Edinburgh,  Session  1872-73. 

senting  to  the  University  collection  a valuable  bust  of  his  uncle, 
Dugald  Stewart,  by  the  sculptor  Joseph ; who  has  produced  an 
excellent  likeness  of  the  philosopher,  as  I remember  him  on  the 
only  occasion  when  I ever  saw  him,  in  advanced  old  age,  in  the 
Edinburgh  theatre,  at  one  of  the  early  representations  of  the  late 
Mr  Murray’s  famous  dramatic  conversion  of  “ Rob  Roy.” 

Charles  Hughes  Terrot,  Bishop  of  Edinburgh,  was  a descendant 
of  one  of  the  many  French  families  which  the  revocation  of  the 
Edict  of  Nantes  drove  from  their  native  land  to  seek  a home  in 
this  country.  His  father  entered  the  Indian  army,  and  was  killed 
at  the  siege  of  Bangalore  a few  weeks  after  the  birth  of  his  son, 
which  took  place  on  the  19th  of  September  1790.  To  his  mother 
accordingly  fell  the  charge  of  young  Terrot’s  education,  and  we 
may  attribute  to  the  influence  of  her  powerful  mind  much  of  her 
son’s  subsequent  eminence.  Mentally  as  well  as  personally  there 
was  a striking  resemblance  between  the  two. 

Before  sending  him  to  Cambridge,  Mrs  Terrot  placed  him  with 
one  of  the  good  men  of  his  day,  the  Rev,  John  Fawcett  of 
Carlisle.  In  1808  he  entered  Trinity  College,  Cambridge,  where, 
as  he  was  wont  to  say,  he  obtained  his  real  education  by  daily 
converse  with  such  men  as  Whewell,  Peacock,  Rolfe,  Amos,  Mill, 
and  Robinson,  especially  the  last  two,  with  whom  his  intercourse 
ceased  only  with  life.  He  took  his  degree  in  1812,  obtaining  a 
position  on  the  Honour  list  altogether  inferior  to  what  his  sub- 
sequent appearance  as  a mathematician  would  have  warranted  us 
in  anticipating.  The  fact  is  that  Terrot’s  mind  revolted  at  the 
drudgery  of  acquiring  branches  of  the  science  towards  which  he 
felt  no  inclination.  It  was  characteristic  of  him  to  tread  a small 
circle,  but  to  tread  it  well;  and  he  was  constitutionally  unfitted  for 
stowing  away  in  his  memory,  for  temporary  purposes,  facts  and 
figures  in  which  he  took  no  interest.  Thus  his  degree  examina- 
tion resulted  in  a comparative  failure.  Nevertheless,  on  the 
Fellows  of  his  college  this  failure  made  no  impression.  They  had 
enjoyed  ample  opportunities  of  judging  of  his  accuracy  and  of  his 
acuteness,  and  they  did  not  hesitate  to  elect  him  into  their  body 
in  the  very  year  in  which  he  took  his  degree.  He  did  not  retain 
his  Fellowship  many  years,  having  married  in  1815,  and  settled  ip 

VOL.  VIII.  B 


10 


Proceedings  of  the  Royal  Society 

Haddington.  The  leisure  of  a country  incumbency  permitted  liis 
entering  the  list  of  competitors  for  University  honours  of  a literary 
kind.  In  1816  he  obtained  the  Seatonian  Prize  for  a poem  on 
the  Destruction  of  Sennacherib’s  Army  before  Jerusalem. 

To  have  been  the  author  of  a successful  prize  poem  in  the  Uni- 
versity of  Cambridge  is  not  a little  honourable,  though  it  must 
be  confessed  that  secular  themes  have  enlisted  a higher  display  of 
genius  on  their  side  than  sacred.  Witness  such  names  as  William 
Whewell,  Thomas  Babington  Macaulay,  and  Alfred  Tennyson. 
Still  Terrot’s  poem  is  very  far  from  being  an  ordinary  production. 
Portions  of  it  indeed  are  deserving  of  a high  rank,  and  as  a whole 
it  is  striking  and  effective.  The  finest  part  is  the  night  scene,  in 
which  is  depicted  the  Assyrian  army  encamped  before  the  walls 
of  Jerusalem,  waiting  with  feverish  anxiety  the  first  streak  of 
dawn  to  commence  the  assault.  The  author  introduces  the  reader 
to  a humble  tent,  in  which  lie  two  soldiers,  restless  and  tossing 
through  the  whole  night.  Each  dreams  his  dream.  The  one, 
eager  for  battle, 

“ Dreams  that  with  Jewish  blood  his  spear  is  red.” 

He  has  cleared  the  ramparts,  and  with  his  comrades  is  rushing 
wildly  on  the  devoted  city.  The  other,  “ of  softer  mind,”  is 
carried  away  to  the  home  of  his  affections  on  the  banks  of  the 
Tigris, 

“ To  the  rude  cot  where  dwelt  his  infancy.” 

He  is  welcomed  back  by  his  friends  “ with  a smiling  tear,” 

“ And  she  whom  best  he  loves,  who  loves  him  best, 

Hangs  round  his  neck,  and  weeps  upon  his  breast.” 

The  pleasant  dream  is  broken  by  the  frantic  struggles  of  his 
comrade.  He  awakes, 

“ And  fear  comes  over  him, — he  knows  not  why.” 

The  curtains  of  the  tent  are  shaken  ; 

“ a blast 

From  heaven  moaned  low  and  sadly  as  it  passed.” 

It  is  the  “icy  wind  of  death.”  On  that  blast  rides  the  avenging 
angel,  carrying  “the  last  long  sleep”  to  all  that  slept  that  night 
in  the  Assyrian  host. 


11 


of  Edinburgh,  Session  1872-73. 

The  success  of  this  his  first  poem  seems  to  have  inspired  Terrot 
with  the  ambition  to  try  a more  difficult  theme.  In  1819  he 
published  anonymously  a poem,  with  the  rather  prose-inspiring 
title,  “ Common  Sense.”  In  this  production  the  poets  and  poli- 
ticians of  the  day  were  pretty  freely  criticised  by  a hand  which 
wielded  some  of  the  power  of  the  Dunciad  and  the  Rolliad  com- 
bined. That  the  poem  was  vigorous  and  pointed  no  one  who 
knew  Terrot  can  for  a moment  doubt.  But  it  was  not  the  less  a 
great  mistake  in  the  author  to  attempt  to  weigh  poets  in  the 
balance  of  common  sense ; and  the  attempt  accordingly  failed.  A 
line  or  two  from  the  first  page  may  be  taken  as  a specimen  : — 

“ Time  was  when  bards  were  few  : then  might  you  see 
In  Button’s  room  the  whole  fraternity. 

But  now,  like  Egypt’s  frogs,  on  every  hand 
They  spread,  and  croak,  and  darken  all  the  land.” 

As  a poet,  then,  it  is  clear  that  Terrot  would  have  found  himself 
in  very  unpleasant  society.  He  accordingly  renounced  the  fra- 
ternity, and  carried  his  common  sense,  of  which  he  had  an 
abundant  stock,  to  the  regions  of  theology  and  mathematics. 
With  his  theology  we  have  in  this  place  no  concern.  But  a very 
graceful  recognition  of  its  merits  has  appeared  in  the  sketch  of 
Terrot’s  life  from  the  pen  of  Dean  Ramsay,  who  has  delineated  his 
character  by  a few  well-marked  and  kindly  touches. 

Our  concern  is  only  with  his  mathematics.  To  mathematics, 
when  harassed  by  the  cares  and  vexations  incident  to  his  position, 
he  had  recourse  as  a retreat  from  irritating  thoughts.  His  passion 
for  this  science  was  strong  enough  to  take  possession  of  his  mind, 
and  soothing  enough  to  settle  it  down  to  repose.  Bishop  Terrot 
contributed  several  papers  to  the  Transactions  of  this  Society. 
The  subjects  treated  of  were  the  Properties  of  Numbers;  the 
Square  Roots  of  Negative  Quantities  as  Symbols  of  Direction ; 
and  the  Theory  of  Probabilities.  To  the  papers  on  the  second 
and  third  of  these  subjects  it  may  be  permitted  to  make  more  than 
a passing  allusion. 

In  January  1847  he  read  to  the  Society  a paper,  entitled,  “ An 
Attempt  to  Elucidate  and  Apply  the  Principles  of  Geometry,  as 
published  by  Mr  Warren  in  his  Treatise  on  the  Square  Roots  of 
Negative  Quantities.”  The  subject  here  treated  of  had  been 


12 


Proceedings  of  the  lioyal  Society 

floating  somewhat  dimly  before  the  eyes  of  mathematicians  for 
half  a century,  and  was  just  then  beginning  to  assume  a living 
form  in  the  mind,  and  a living  exponent,  though  a somewhat 
obscure  one,  in  the  writings  of  Sir  W.  R.  Hamilton.  It  was  not 
until  six  years  later  that  the  doctrine  of  Quaternions  of  the  great 
master,  as  developed  in  his  u Lectures,”  swallowed  up  in  its  vast 
amplitude  all  that  had  preceded  it.  Terrot  must  accordingly  be 
considered  as  one  of  the  pioneers  of  the  science.  In  the  paper 
now  referred  to  he  points  out  the  applicability  of  the  method  to 
plane  trigonometry  in  all  its  parts ; but  he  could  see  his  way  no 
further.  Years  after,  when  paralysis  had  laid  him  low,  on  being 
told  that  Symbols  of  Direction  had  been  embodied  by  Sir  William 
Hamilton  into  the  full-grown  science  of  Quaternions,  his  delight 
was  expressed  in  the  form  of  thankfulness  that  enough  of  life  had 
been  spared  him  to  know  that  the  dream  of  his  early  years  had 
been  realised,  even  although  all  power  to  comprehend  it  had 
passed  away  from  him. 

In  1858  Bishop  Terrot  published  in  our  Transactions  a paper 
“ On  the  Possibility  of  Combining  two  or  more  Probabilities  of 
the  same  Event,  so  as  to  form  one  Definite  Probability.”  This 
paper  was  his  best  contribution  to  mathematical  science.  In 
addition  to  its  own  excellence,  it  has  the  merit  of  having  drawn 
forth  the  valuable  paper  of  the  late  Professor  Boole,  “ On  the 
Application  of  the  Theory  of  Probabilities  to  the  Question  of  the 
Combination  of  Testimonies  or  Judgments,”  to  which  the  Council 
of  this  Society  awarded  the  Keith  medal  in  1858.  In  this  paper 
the  conclusions  of  Bishop  Terrot  are  confirmed,  and  a flood  of  new 
light  is  cast  on  the  subject.  It  ought  perhaps  to  be  added,  that 
an  extended  correspondence  between  the  Bishop  and  Boole  had 
preceded  the  publication  of  the  papers  in  question  ; in  which  the 
Bishop  had  steadily  manifested  an  anxious  desire  both  to  promote 
the  advance  of  science,  and  to  aid  Boole  in  his  upward  career. 
Selfish  ends  had  no  place  in  the  Bishop’s  mind. 

In  dismissing  this  brief  notice  of  Bishop  Terrot’s  scientific 
connection  with  the  Royal  Society,  it  may  not  be  amiss  to  add  a 
word  or  two  on  his  personal  connection  with  us.  For  many  years 
of  his  life  he  was  one  of  the  regular  attendants  of  our  meetings  ; 
and  when  not  actively  engaged  in  the  work  going  on,  he  was  an 


of  Edinburgh,  Session  1872-73. 


13 


attentive  listener,  and,  when  occasion  called  for  it,  an  unsparing 
critic.  He  had  a real  love  for  the  Society.  As  he  left  the 
building  for  the  last  time,  he  expressed  himself  to  the  effect,  that 
thenceforth  his  heart  would  be  with  us,  hut  that  the  work  of  his 
hands  was  done.  The  only  part  of  our  proceedings  which  he  did 
not  relish  was  the  tea-drinking  after  the  meeting. 

What  the  Bishop  was  in  private  it  is  for  others  to  tell.  Dr 
Hannah,  one  of  his  most  intimate  friends,  testifies  of  him,  that  he 
rejoiced  in  conversation,  and  never  tired  of  it  so  long  as,  in  his 
own  phrase,  “ the  talk  was  good;”  and  that,  with  the  keenness  of 
his  wit  and  the  quickness  of  his  repartee,  he  united  tolerance  and 
good  nature.  Dr  Fawcett,  who  also,  when  a medical  student, 
knew  Bishop  Terrot  well,  says,  u his  manner  was  short  and  abrupt, 
but  he  was  always  spicing  it  with  something  good.”  Not  a few 
members  of  this  Society  can  likewise  bear  testimony  to  his  won- 
derful felicity  in  conversation.  But  we  are  now  more  concerned 
with  the  impression  which  he  made  on  society  at  large.  He 
was  there  eminently  conversational.  He  did  not  talk  much  ; but 
he  talked  well.  He  had  the  faculty  of  saying  powerful  things  in 
a few  pithy,  pointed  words,  which  always  hit,  and  generally  re- 
mained fixed  in  the  mind.  His  humour  was  dry,  even  caustic  ; 
but  neither  personal  nor  ill-natured.  His  criticisms  of  authors 
were  sometimes  severe,  but  they  were  never  meaningless.  For 
example,  of  one  of  Goethe’s  later  works  of  fiction,  which  to  ordi- 
nary minds  appears  wild  and  extravagant,  Terrot  was  wont  to  say, 
that  Goethe,  having  during  a long  life  inhaled  incense  from  the 
worshippers  of  his  genius,  had  in  his  old  age  become  satiated,  and 
accordingly  gave  the  world  what  he  knew  to  be  worthless,  in  order 
that  the  admiration  it  should  call  forth  might  ascend  as  pure 
incense  direct  to  himself. 

This  remark  of  the  Bishop’s,  whatever  it  may  be  worth,  will 
help  us  to  get  a faint  glimpse  at  a prominent  feature  in  his  cha- 
racter as  a man.  The  feature  in  question  was  a dread  for  himself 
and  a dislike  in  others,  of  appearing  to  assume  that  to  which  they 
had  no  just  title, — of  seeking  out  the  upper  chambers, — even  of 
claiming  a place  to  which  the  world  at  large  would  raise  no  objec- 
tion. This  feeling  rendered  him  sensitive  as  regarded  himself, 
and  critical  in  his  remarks  on  others.  But  his  judgments  were 


14  Proceedings  of  the  Royal  Society 

tempered  with  so  real  an  insight  into  character,  so  just  an  appre- 
ciation of  all  that  was  worthy,  and  withal  were  so  free  from  the 
suspicion  of  envy  or  jealousy,  that  they  never  produced  a rankling 
sore  or  gave  rise  to  a bitter  repartee. 

The  Society  will  kindly  treat  with  indulgence  this  imperfect 
attempt  at  the  portraiture  of  one  of  the  most  noteworthy  of  those 
whom  death  has  recently  removed  from  among  them.* 

Hugo  yon  Mohl,  the  only  Fellow  whom  death  has  struck  off 
our  Honorary  list  during  the  last  year,  was  long  eminent  among 
the  botanists  of  the  Continent  for  his  researches  in  Botanical 
Physiology.  In  his  student  days  medicine  was  his  main  pursuit, 
but  combined  with  the  ardent  cultivation  of  botany  and  geology. 
He  graduated  with  great  distinction  at  Tubingen,  and  was  en- 
couraged to  make  medicine  his  profession  by  his  father,  who 
filled  an  important  office  in  the  Wiirtemberg  Government.  But 
the  son’s  bent  was  turned  more  and  more  to  botanical  investi- 
gation, which  by  degrees  became  his  great  object  in  life,  to  the 
utter  disregard  of  medical  practice.  He  entered  on  his  task  with 
the  great  advantage  of  a mind  highly  cultivated  in  the  collateral 
sciences,  as  well  as  in  the  languages.  With  the  further  advantage 
of  a robust  frame  and  constitution,  he  was  enabled  to  make  at  an 
early  age  frequent  successful  excursions  in  his  own  neighbour- 
hood, and  also  in  the  Alps,  gathering  extensive  collections  of 
plants,  and  accumulating  materials  for  future  study.  He  then 
commenced  his  researches  into  the  anatomical  structure  of  the 
Palms,  Ferns,  and  Cycads.  In  his  twenty-sixth  year  he  was 
appointed  Sub-director  of  the  Imperial  Gardens  at  St  Petersburg; 
next  year,  without  having  taken  up  that  office,  he  was  elected 
Professor  of  Physiology  in  the  Academy  of  Bern,  and  then  in  the 
University  of  that  city;  and  in  his  thirtieth  year  he  was  pro- 
moted to  the  Chair  of  Botany  in  his  own  University  of  Tubingen. 
Eight  years  afterwards,  on  account  of  his  services  to  science,  he 
was  raised  by  the  King  of  Wiirtemberg  to  the  rank  of  nobility. 
A few  years  later,  in  spite  of  his  apparently  robust  constitution, 
he  became  subject  to  catarrhal  affections.  Although  he  succeeded 

* For  the  preceding  sketch  of  Bishop  Terrot’s  life,  the  Society  and  I are 
indebted  to  Professor  Kelland. 


15 


of  Edinburgh , Session  1872-73. 

in  throwing  off  this  enemy,  he  subsequently  suffered  from  pleurisy, 
and  also  from  liver  complaints.  Again  restored  to  health  for  some 
time,  he  was  seized,  in  May  1871,  with  obstinate  giddiness,  which, 
although  it  disappeared  and  left  him  apparently  well,  was  never- 
theless the  presage  of  his  end ; for,  on  the  1st  of  April  last,  he  was 
found  dead  in  bed,  having  to  all  appearance  sustained  an  attack  of 
apoplexy  during  the  night.  He  died  in  the  67th  year  of  his  age. 

Mohl  published  his  researches  chiefly  in  the  form  of  occasional 
papers  or  monographs.  He  is  the  author  of  two  books  only,  the 
one  on  Micrography,  the  other  on  The  Vegetable  Cell.  But  his 
occasional  papers  are  no  fewer  than  ninety  in  number,  the  most 
remarkable  of  which  belong  to  the  domain  of  Vegetable  Histology 
— the  earliest  and  most  important  being  his  treatise  De  Palmarum 
Structura,  published  in  1832,  in  his  twenty-sixth  year.  Many  of 
his  writings  relate  also  to  Vegetable  Morphology  and  Botanical 
Geography,  and  some  to  Botanical  Physiology.  In  every  branch 
his  researches  display  much  originality,  and  have  added  materially 
to  the  structure  of  modern  botanical  science. 

Professor  von  Mohl  was  a tall,  strong  man,  a bachelor,  reserved 
in  manner  and  disposition,  of  retired  and  somewhat  peculiar 
habits,  in  all  things  conscientious  and  upright,  free  altogether 
from  vanity,  regardless  of  all  consequences  in  upholding  the 
truth,  entirely  devoted  to  scientific  research. 

Having  now  discharged  to  the  best  of  my  ability,  within  the 
space  to  which  I am  confined  by  the  necessary  limits  of  this 
address,  the  duty  owing  to  the  memory  of  our  Fellows  who  have 
been  removed  from  among  us  by  death  during  the  twelvemonths 
just  concluded,  I do  not  know  that  I can  apply  the  rest  of  your 
time  this  evening  better  than  by  referring  to  the  present  position  of 
certain  scientific  proceedings  in  which  the  Society  takes  an  interest. 

The  first  subject  I shall  take  the  liberty  of  bringing  under 
your  notice  is  the  present  condition  of  the  Ordnance  Survey  of 
Scotland. 

I am  almost  afraid  to  say — in  the  year  1872 — when  the 
Government  Survey  of  our  division  of  the  United  Kingdom  was 
commenced;  hut  it  had  made  some  progress  when  I witnessed  a 
demonstration,  by  the  chief  surveying  engineer,  of  the  construe- 


16  Proceedings  of  the  Royal  Society 

tion  and  powers  of  Ramsden’s  great  theodolite,  stationed  on  the 
Dalton  Hill  in  the  year  1817  or  1818.  Now  in  the  present  year, 
as  we  may  gather  from  the  catalogue  of  published  maps  which 
appeared  by  authority  on  the  8th  of  May  last,  there  remains  to  be 
published  about  two-fifths  of  the  sheets  of  the  25-incli  survey; 
fully  one-half  of  those  on  the  6-inch  scale ; and  of  those  on  the 
1-inch  scale — the  scale  most  generally  desired  by  the  public  at 
large — no  less  than  two-thirds  of  the  whole.  In  the  course  of  a 
life  which  has  not  been  short  I have  witnessed  the  completion  of 
one-third  part  of  the  Survey.  At  this  rate,  some  grandson  of  the 
youngest  among  you,  if  he  be  fortunate  enough  to  attain  a great 
age,  may  be  also  so  lucky  as  to  see  the  whole  maps  before  he 
dies;  and  yet  I cannot  guarantee  even  him  that  pleasure. 

To  the  1-inch  map  of  Scotland  the  index  map  of  the  May 
Report  assigns  120  compartments  or  sheets;  but  Orkney  and 
Shetland,  which  are  left  out,  will  require  three  more.  Of  the 
whole  number,  only  44  were  published  on  the  8th  of  last  May — 38 
of  them  shaded,  and  6 in  outline.  These  embrace  all  Scotland 
south  of  the  Forth  and  Clyde,  and,  to  the  north  of  that  boundary, 
the  counties  of  Fife,  Clackmannan,  Stirling,  and  Dumbarton, 
most  of  Perthshire,  all  Forfar  and  Kincardine,  a little  corner  of 
Aberdeen,  the  island  of  Arran,  and,  far  apart  from  all  other  com- 
pleted work,  the  “ Ultima  Thule  ” of  the  west,  the  island  of 
Lewes.  Since  8th  May  there  have  been  issued  separate  slips, 
showing  what  has  been  added  since,  viz.,  two  sheets,  one  of  which 
is  an  outline  map  of  a small  portion  of  the  coast  line  of  Aber- 
deenshire, and  the  other  the  small  corner  of  that  county  already 
mentioned,  with  a conterminous  part  of  Kincardineshire,  con- 
verted from  outline  into  a shaded  map.  The  Society  will  judge 
for  themselves  how  much  remains  to  be  done,  and  what  is  the  rate 
of  progress  of  the  1-inch  maps. 

The  misery  of  the  want  of  two-thirds  of  these  maps  is  enhanced 
by  the  minute  accuracy  and  admirable  execution  of  those  which 
we  do  possess.  Permit  me  to  illustrate  this  statement  by  a single 
incident.  This  was  no  more,  indeed,  than  an  incident  in  the 
holiday  life  of  a wanderer  in  quest  of  recreation ; but  numberless 
analogous  occurrences  must  happen  to  others  engaged  with  more 
important  objects.  Four  years  ago  I made  a long  day’s  excursion 


of  Edinburgh , Session  1872-73. 


17 


from  Arrochar,  with  an  English  friend,  round  the  base,  up  to  the 
summit,  down  again  a great  way,  then  up  again  over  a lofty  spur 
into  an  upland  valley,  of  one  of  the  neighbouring  mountains, 
Ben-Arnen ; which  is  very  seldom  visited,  although  it  is  very 
interesting  in  structure,  and  3050  feet  in  height,  and  commands  a 
magnificent  view  in  all  directions.  Descending  into  the  heart  of 
the  valley,  in  which  there  are  many  fine  precipices,  we  twice  came 
suddenly  near  the  brink  of  these,  as  a stranger  is  apt  to  do  in 
going  down  hill  on  such  mica-slate  mountains ; but  the  instinct  of 
experience  forewarned  us  of  our  approach  to  danger,  and  enabled 
us  to  avoid  it  by  a flank  route.  On  returning  to  town,  I tried  to 
trace  this  excursion  on  the  best  of  our  ordinary  maps,  hut  in  vain ; 
for  in  some  our  mountain  was  not  to  be  seen  at  all,  while  in  others 
it  was  put  in  evidently  ad  libitum , and  in  not  one  was  it  named. 
In  the  Ordnance  shaded  1-inch  map,  however,  every  valley,  every 
spur,  ravine,  grassy  slope  and  precipice  is  given  so  precisely  that  I 
am  sure  I could  furnish  any  stranger  to  the  mountain  with  a route 
upon  that  map  by  which  he  could  safely  follow  our  track.  All 
praise,  therefore,  to  Sir  Henry  James  and  his  faithful  assistants, 
who  could  little  have  thought  that  their  work,  in  so  remote,  wild, 
and  little  known  a corner,  would  he  subjected  to  such  minute 
criticism  from  so  improbable  a quarter.  It  is  not  in  his  depart- 
ment that  the  blame  lies  for  the  hideous  delay  in  the  progress  of 
the  Ordnance  Survey  of  Scotland,  and  for  our  not  having  long  ago 
reaped  all  the  advantages  of  its  completion.  Very  far  from  it. 
But  what  are  we  to  say  of  the  blindness,  and  deafness,  and  mis- 
placed economy  of  successive  Governments,  who,  possessing  such 
an  admirable  instrument  as  the  Ordnance  Survey  Office,  refuse  to 
make  use  of  it,  to  the  full  extent  of  its  power,  in  one  of  the 
most  important  and  most  attractive  of  all  branches  of  civil 
administration  ? And  what  has  become  of  the  nobility,  gentry, 
men  of  science,  and  others  in  Scotland,  who  in  former  days 
did  not  sit  so  tamely  under  disregard  of  their  just  claims  upon 
the  State? 

The  publication  of  the  maps  upon  the  6-inch  scale  is  somewhat 
farther  advanced.  These  include,  besides  the  country  mapped  on 
the  1-inch  scale,  all  Perthshire,  most  of  Aberdeen,  all  Banff  and 
Nairn,  Can  tyre,  and  the  southern  half  of  the  other  peninsula  of 


VOL.  VIII. 


18  Proceedings  of  the  Royal  Society 

Argyllshire,  which  is  bounded  by  Loch  Long  and  Loch  Fine, 
with  the  island  of  Bute. 

The  maps  on  the  25-inch  scale  ai;e  advanced  still  farther, 
especially  when  it  is  considered  that  this  large  scale  is  not 
applicable  to  a great  extent  of  mountainous,  unproductive  land 
throughout  the  Highlands  and  Islands  of  Scotland.  In  northern 
parts  they  include,  besides  the  counties  mentioned  above  as  por- 
trayed on  the  6-inch  scale,  that  of  Elgin,  a third  part  of  Inver- 
ness, most  of  the  Argyllshire  mainland,  but  none  of  its  islands ; 
and,  very  far  north  indeed,  the  Survey  now  extends  to  a small 
patch  comprising  the  central  parish  of  Watten  in  Caithness, 
which  thus  hangs  “en  1’air,”  far  remote  from  every  other  indica- 
tion on  the  index  map  of  Ordnance  Survey  operations.  Very 
singular  are  the  omissions  in  the  more  southerly  counties.  Fife  is 
altogether  excluded  ; so  is  Kinross,  and  so  are  Mid-Lothian  and 
East  Lothian,  four  of  the  most  purely  agricultural  counties;  to 
which  must  he  added  the  more  chequered  shires  of  Kirkcudbright 
and  Wigtown.  Perhaps  these  rich  districts  are  already  so  far 
provided  with  every  desideratum  which  an  accurate  and  minute 
survey  is  intended  to  promote, — roads  are  so  abundant  and  perfect, 
railways  so  numerous,  water-supply  so  complete,  field-drains  so 
perfect,  estates  so  well  surveyed  by  their  possessors, — that  such 
counties  may  be  left  by  Government  to  look  after  themselves. 
But  there  should  be  better  reasons,  I imagine,  for  districts  of  so 
great  importance  being  left  so  long  unprovided  with  that  scale  of 
survey  and  map  for  which  they  are  peculiarly  fitted. 

A single  word  more  on  this  subject.  How  is  the  25-inch  survey 
to  be  made  accessible  in  Scotland?  By  individuals  purchasing 
such  of  the  separate  maps  as  they  severally  need  ? But  there  are 
various  professions  whose  members  may  require  to  consult  very 
many,  and  to  have  access,  at  one  time  or  another,  to  all.  But  no 
such  individual  can  afford  to  pay  L.1500,  the  price  of  a complete 
set  of  25-inch  maps,  or  the  space  for  preserving  them  conveniently 
accessible.  It  would  surely  be  no  unreasonable  demand  on  the 
parental  care  of  Government  that  a complete  set  should  be  made 
accessible  to  the  public  at  Edinburgh,  Glasgow,  and  Aberdeen. 
I understand  that  some  such  boon  has  been  asked  for,  but 
declined. 


19 


of  Edinburgh,  Session  1872-73. 

I have  here  pointed  out  a line  of  action  in  which  the  Royal 
Society  may  usefully  exert  itself.  It  has,  indeed,  done  so  without 
avail  before  now;  but  that  was  a number  of  years  ago.  Govern- 
ment may  at  last  be  roused  to  do  justice  if  repeatedly  appealed  to  ; 
and  it  should  be  remembered  that  we  have  to  knock  at  a door, 
which  in  general  must  be  well  battered  before  it  can  be  opened. 

Having  considered  the  present  occasion  an  apt  one  for  remind- 
ing you,  and  through  you  the  public  at  large,  of  the  great  desire 
expressed  by  this  Society  about  eighteen  months  ago  to  obtain  a 
thorough  catalogue  and  scrutiny,  and  general  concurrence  in  the 
preservation,  of  the  most  remarkable  boulders  in  Scotland,  I have 
asked  the  chairman  of  our  Boulder  Committee  whether  he  could 
supply  me  with  any  information  for  the  Society  as  to  the  progress 
made  in  this  matter  since  the  printing  of  the  very  full  and  able 
report  of  the  Committee  last  April.  Mr  Milne  Home  agreed 
with  me  that  the  time  and  occasion  are  opportune,  and  has 
therefore  kindly  furnished  me  with  some  interesting  particulars 
and  general  views,  which  I am  sure  you  will  approve  of  my 
having  elicited,  and  which  I shall  now  present  very  much  in  his 
own  words. 

Mr  Milne  Home  continues  to  receive  from  abroad  assurances  of 
warm  sympathy  on  the  part  of  Continental  associations  engaged 
in  the  same  work.  He  has  not  yet  received,  in  reply  to  the 
invitations  issued  by  our  Committee,  any  communications  from 
geologists  and  others,  who,  in  their  wanderings  last  summer  and 
autumn,  must  have  had  opportunities  for  adding  to  the  Com- 
mittee’s stock  of  facts.  But  may  I not  hope  that  this  appeal  may 
even  still  elicit  a favourable  reply?  In  the  meanwhile  Mr  Milne 
Home  has  himself  acquired,  by  his  personal  exertions,  so  much 
new  information,  that  we  shall  scarcely  feel  this  year  the  want  of 
communications  from  others. 

Desirous  of  carrying  through  in  some  measure  the  inspection  of 
known  boulders  asked  for  by  the  Committee,  Mr  Milne  Home 
made  a tour  “ through  the  districts  indicated  by  the  following 
towns,  viz.,  Callender,  Aberfeldy,  Pitlochrie,  Dunkeld,  Perth, 
Forfar,  Aberdeen,  Forres,  Elgin,  Nairn,  Inverness,  Tain,  Kin- 
gussie, Lochaber,  Fort  William, -Grlenelg,  Tyndrum,  and  Killin. 


20 


Proceedings  of  the  Royal  Society 

11  Many  of  the  boulders  in  these  districts  are  entered  in  the  list 
of  the  Committee’s  Preliminary  Eeport ; but  Mr  Milne  Home  also 
fell  in  with  many  others  which  will  be  detailed  in  the  next  Report. 
The  present  sketch  will  be  mainly  confined  to  some  points  bearing 
on  the  probable  mode  of  transport  of  the  boulders. 

“ 1.  The  first  inquiry  was  the  quarter  whence  the  boulder  had 
come,  when  the  rock  composing  it  was  different  from  the  rocks  of 
the  adjoining  district.  In  all  the  districts  visited  the  parent 
rock  seemed  situated  in  a direction  between  north  and  west  from 
the  boulder.  This  fact  did  not  surprise  me  in  regard  to  those  in 
the  counties  of  Stirling,  Perth,  Forfar,  and  Kincardine ; — situated 
as  they  were  principally  in  the  low  grounds  south  and  east  of  the 
Grampians,  which  undoubtedly  produced  them.  These  boulders 
had  probably  come  down  the  valleys.  Put  boulders  were  also 
found  in  the  counties  of  Moray  and  Nairn,  which  apparently  had 
come  from  the  same  direction,  viz.,  from  points  between  north 
and  west.  Here  the  same  explanation  was  impossible ; for  they 
must  have  travelled  across  a considerable  extent  of  sea.  In  these 
two  counties,  there  are  boulders  of  granite,  gneiss,  and  a very 
compact  conglomerate,  which  came  most  probably  from  Caithness, 
Ross,  and  Cromarty ; and  besides  these  rocks,  of  which  great 
mountains  exist  in  the  north-west,  there  are  to  be  seen  smaller 
boulders  of  oolite, — a rock  forming  a narrow  fringe  along  the  eastern 
shore  of  Ross  and  Caithness. 

“ This  point  being  of  some  importance  with  reference  to  the 
mode  of  transport,  one  or  two  other  facts  may  be  mentioned  which 
seem  to  confirm  the  conclusion  that  the  boulders  of  Moray  and 
Nairn  had  come  from  the  north-west.  1.  The  rocks  of  the  hills 
on  or  near  which  they  lie,  had  manifestly  been  shaven,  ground 
down,  polished,  and  scored  by  some  powerful  and  wide-spread 
agent  passing  over  them  from  the  same  direction.  2.  In  most 
cases  the  boulders  lie  on  hill-slopes  facing  the  north-west,  as  if 
arrested  in  their  farther  course  by  the  high  ground.  I could 
not  help  concurring  in  the  remark  of  a farmer,  who  was  point- 
ing out  to  me  four  or  five  huge  boulders  on  the  same  hill- 
slope,  that  1 in  takkin’  the  hill,  they  had  stuck  on  it.”  3.  In  most 
cases  the  boulders,  when  long-shaped,  lie  with  their  longer  axis 
in  a north-west  direction,  and  also  with  their  sharper  end  towards 


21 


of  Edinburgh,  Session  1872-73. 

the  same  quarter,  as  if  moved  into  that  position  by  some  agent 
which  had  been  flowing  past  them.  These  facts  seem  to  indicate 
conclusively,  that  some  powerful  agent  had  passed  over  this  part 
of  the  earth’s  surface,  crossing  what  is  now  an  arm  of  the  sea,  the 
Moray  Firth,  carrying  great  masses  of  rock,  and  dropping  them  at 
considerable  distances. 

“In  the  counties  of  Moray  and  Nairn,  the  boulders  are  at  all 
heights,  from  the  sea-level  close  to  the  shore,  up  to  the  height  of 
about  500  feet.  But  in  other  districts  they  are  to  be  seen  as 
high  up  as  2500  feet  above  the  sea.  Many  of  them  are  perched 
on  hill-tops,  or  very  near  the  tops,  and  many  are  in  such  positions 
as  to  indicate  that,  whatever  was  the  transporting  agent,  they 
could  not  have  fallen  from  any  height.  These  positions  are  rocky 
hill-sides,  where  the  slope  is  so  considerable  that  the  boulders  could 
easily  have  slid  down  with  a very  small  amount  of  force  applied. 

“ The  angular  form  of  the  boulders  is  also  instructive.  Thus 
there  is  one  huge  cubical  block  of  old  conglomerate  on  the  border 
of  Nairn  with  Inverness,  called  “ Tom  Riach,”  to  which  Captain 
White  first  called  attention,  each  side  measuring  almost  exactly  21 
feet.  It  lies  on  nearly  horizontal  beds  of  Old  Red  Sandstone,  in  a 
wide  valley,  with  no  cliff  near  it.  There  can  be  no  doubt  that  this 
boulder,  weighing  betwixt  600  and  700  tons,  must  have  been  brought 
from  a great  distance — and  otherwise  than  by  rolling  or  pushing, 
because,  from  the  sharpness  of  its  angles,  it  evidently  had  undergone 
no  friction.  There  are  hundreds  of  boulders,  which,  lying  on  the 
open  surface  of  the  country,  sometimes  on  bare  rocks,  sometimes 
on  gravel  deposits,  give  similar  proofs  that  they  must  have  been 
transferred  by  some  agent,  without  friction.  The  boulders  referred 
to,  are  generally  single  ; but  there  are  two  districts  where  they  are 
huddled  or  grouped  together  in  such  a way,  as  to  indicate  that 
they  had  been  all  brought  to  the  spot  by  one  transporting  agent 
which  went  no  further  in  its  forward  course.  One  of  these  places 
is  to  the  south  of  Inverness,  at  or  near  the  mouths  of  two  valleys 
which  unite  at  their  lower  ends.  It  is  just  beyond  the  mouths  of 
these  two  valleys  that  the  boulders  occur  in  enormous  numbers, 
composed  of  rocks  existing  in  the  valleys,  to  the  west  and  north 
west.  Another  place  is  Lochaber,  where  there  are  long  thick 
lines,  or  trainees,  of  boulders,  forming  parts  of  a semicircle  or  horse- 


22 


Proceedings  of  the  Royal  Society 

shoe,  the  concave  sides  facing  a valley,  from  which  the  boulders 
appear  to  have  issued.  In  this  locality  there  are  also  elongated 
mounds  of  rubbish,  running  more  or  less  parallel  with  the  lines  of 
boulders, — very  similar  to  the  moraines  so  common  in  Switzer- 
land. The  impression  made  on  the  mind  by  an  inspection  of  these 
two  localities  was  that  the  transport  of  the  boulders  found  there 
was  due  to  glaciers. 

“ There  is  a third  class  of  boulders,  distinguished  from  the  two 
classes  just  referred  to.  The  latter  are  generally  angular,  and 
lie  on  the  upper  surface  of  the  land.  The  third  class  are  rounded 
in  shape,  and  imbedded  in  gravel  or  clay.  They  are,  in  short, 
huge  pebbles,  having  evidently  undergone  tremendous  friction  by 
being  pushed  or  forced  along  an  uneven  surface,  in  contact  with 
other  stony  materials. 

“ Some  of  the  boulders  belonging  to  the  first  and  third  classes 
have  been  carried  great  distances  ; and  when  it  is  considered  that 
they  had  to  pass  across  valleys,  ranges  of  hills,  and  arms  of  the 
sea,  the  difficulty  of  the  problem  as  to  the  mode  of  transference  is 
vastly  increased.  For  example,  there  are  in  the  county  of  Berwick 
several  granite  and  mica-slate  boulders,  which, — if  they  came  from 
the  Highland  hills,  as  they  probably  did, — must  have  crossed  many 
ranges  of  hills,  and  at  least  one  arm  of  the  sea,  and  one  large 
valley,  that  of  the  Firth  of  Forth. 

“ Until  many  more  facts  have  been  ascertained,  it  would  be  a 
pity  to  form  very  decided  opinions  as  to  the  agency  of  transport. 
Instructive  as  some  districts  are  among  those  referred  to  above, 
there  are  others  probably  even  more  so  on  the  west  coast  of  Scot- 
land, and  on  the  Hebrides.  It  is  desirable  that  the  boulders 
reported  from  these  quarters,  should  be  visited  scientifically ; for  in 
size  and  peculiarity  of  position,  they  are  said  to  be  even  more 
remarkable  than  those  now  described.  The  Boulder  Committee 
have  in  their  custody  schedules  representing  the  place,  size,  and 
other  particulars  of  these  boulders,  which  they  will  lend  willingly 
to  any  geologist  who  will  inspect  them  and  report  on  them. 

The  Committee  had  two  duties  assigned  to  them.  Besides 
ascertaining  the  position  of  remarkable  boulders,  they  were  to 
endeavour  to  secure  the  preservation  of  the  most  interesting. 
They  have  not  yet  proceeded  to  the  fulfilment  of  this  second  duty, 


23 


of  Edinburgh,  Session  1872-73. 

except  in  a single  case,  where,  at  the  special  request  of  a parish 
minister,  they  applied  to  the  proprietor,  on  whose  lands  the 
boulder  lay,  to  prevent  the  destruction  of  it  by  the  tenant ; and 
this  application  proved  successful.  When  the  Committee  proceed 
further  in  discharge  of  the  same  branch  of  duty,  they  may  expe- 
rience some  difficulty.  It  may,  therefore,  be  not  out  of  place  to 
state  now  what  has  beenylone  by  the  Boulder  Committees  of  France 
and  Switzerland  on  this  point. 

“ These  Committees  have  adopted  several  plans  of  conservation. 
In  some  cases,  they  have  acquired  a right  of  property  in  the 
boulder,  by  means  of  a regular  deed,  signed  by  the  proprietor  of 
the  land.  In  some  cases,  the  proprietor  has  granted  this  right 
only  for  his  own  lifetime.  The  identification  of  the  particular 
boulder  was  matter  of  difficulty ; but  this  has  been  got  over  by 
describing  the  land  on  which  it  stands,  and  cutting  out  on  one  of 
its  sides  the  letter  F for  France,  or  S for  Switzerland. 

“The  success  of  the  Swiss  Committee  has  been  most  gratifying. 
In  the  Canton  of  Soleure  upwards  of  200  boulders  have  been 
secured  from  destruction, — one  of  these  being  a magnificent  block 
at  Steinhof,  weighing  about  5000  tons.  It  was  purchased  by  the 
Communal  Council  for  L.16,  and  given  to  the  Natural  History 
Society  of  Soleure.  The  famous  ‘ Pierre  a Bot,’  near  Neufchatel, 
a granite  boulder  from  Mont-Blanc,  weighing  about  2000  tons, 
now  belongs  to  the  Communal  Council  of  the  Canton.  The  blocks 
of  £ Monthey,’  which  Principal  Forbes  described  in  this  Society, 
have  been  gifted  by  the  proprietor  to  the  Helvetic  Society  of 
Natural  Science.  From  the  list  appended  to  Professor  Favre’s 
Fourth  Report  of  last  year,  it  appears  that  the  Swiss  Committee 
have  succeeded  in  insuring  the  preservation  of  several  hundred 
boulders; — not  all  of  gigantic  size,  but  each  interesting  for  some 
other  reason,  such  as  position,  historical  association,  or  traditionary 
name  or  legend,  or  for  having  been  made  triangulation  points  by 
a government  survey,  or  marking  the  boundary  between  parishes 
or  cantons,  or  because  named  after  distinguished  alpine  travellers, 
such  as  Charpentier,  von  Buch,  and  Venetz. 

“ It  is  interesting  to  see  how  cordially  the  objects  of  the  Swiss 
Committee  are  sympathised  with,  not  only  by  the  government, 
local  as  well  as  general,  but  likewise  by  the  people  at  large.  Pro- 


24:  Proceedings  of  the  Royal  Society 

fessor  Favre  mentions  in  his  last  Report,  that  the  Town  Councils 
of  Bienne,  Bondry,  and  Soleure,  and  the  Cantonal  Councils  of 
Berne,  Friburg,  Aargau,  and  Neufchatel  have  aided  the  Committee 
in  various  ways ; and  in  a previous  Report,  he  stated  that  the 
public  purse  had  been  freely  opened  to  defray  the  expenses  of  the 
Committee. 

“ It  would  not  be  right  to  conclude  without  adding,  that  the 
Swiss  Committee  in  their  last  Report  have  been  pleased  to  take 
favourable  notice  of  our  own  similar  movement  in  Scotland,  ob- 
serving that  it  has  received  not  only  the  support  of  the  Royal 
Society  of  Edinburgh,  but  likewise  the  -approval  of  the  British 
Association  for  the  Advancement  of  Science,  and  that  the  course 
of  proceeding  in  Scotland  is  the  same  as  that  followed  in  Switzer- 
land. 

“ Whether  our  Committee  will  adopt  the  Swiss  plan  of  acquiring 
a right  to  property  in  any  of  the  Scottish  boulders  is  a question 
for  consideration.  Already  good  has  been  done  by  the  inquiries 
which  the  Committee  has  instituted,  and  by  their  explanation  of 
the  scientific  value  and  historical  interest  of  the  boulders ; a dis- 
position to  preserve  them  has  been  thereby  created  which  did  not 
previously  exist.  The  press  has  also  noticed  with  approval  the 
appointment  of  our  Boulder  Committee,  and  has  no  doubt  influenced 
public  opinion.” 

The  Society  will  have  no  difficulty  in  perceiving  with  what  view 
I have  given  on  the  present  occasion  this  detailed  communication 
from  Mr  Milne  Home  to  me.  I trust  that  the  public  may  be 
encouraged  to  aid  in  the  preservation  of  our  boulders.  I hope 
that  geologists  will  without  delay  aid  the  Committee  in  visiting 
and  investigating  them.  And  it  may  be  a question  whether  our 
own  Council  may  not  consider  that  they  could  scarcely  expend 
more  profitably  a portion  of  our  moderate  funds,  than  in  sending 
out  some  young  but  competent  geologist  to  some  of  these  distant 
parts  of  the  country  indicated  by  Mr  Milne  Home,  where  there 
are  remarkable  boulders,  which  have  not  yet  been  described  or 
investigated,  or  even  scientifically  visited. 

In  the  address  delivered  to  the  Society  at  the  opening  meeting 
in  December  last,  I brought  before  you  some  observations  on  the 


25 


of  Edinburgh,  Session  1872-73. 

Temperature  of  the  Water  at  Great  Depths  in  Loch  Lomond,  as 
exemplifying  that  of  the  deep  fresh-water  lakes  of  Scotland 
generally.  I afterwards  communicated  other  observations  made 
in  the  middle  of  April  last,  on  the  first  approach  of  weather 
warmer  than  that  of  the  preceding  winter  months;  which,  however, 
were  unusually  open  and  free  from  frost.  The  result  was  that 
between  the  middle  of  September  1871,  to  the  middle  of  April 
1 872,  in  parts  of  Loch  Lomond,  varying  between  about  500  and 
600  feet  in  depth,  there  is  constantly  at  the  bottom  a great  sheet 
of  water  from  250  to  350  feet  in  thickness,  the  temperature  of 
which  remained  steadily  at  42°,  whatever  might  be  the  temperature 
of  the  surface-water,  or  that  of  the  air  immediately  over  it.  I beg 
now  to  supplement  these  observations  very  briefly  with  a few 
made  since,  in  continuation  of  them. 

But  allow  me,  in  the  first  instance,  to  do  justice  to  others  who 
had  previously  made  observations  somewhat  similar,  and  whose 
results  were  last  year  imperfectly,  and  some  of  them  altogether, 
unknown  to  me. 

So  early  as  1767,  Horace  Benedict  de  Saussure  made  thermome- 
trical  observations  in  the  lake  of  Geneva,  finding  the  temperature 
at  82  feet  to  be  550,6,  when  at  the  surface  it  was  78°.  This  was 
in  the  middle  of  August. 

In  1774,  Mallet  and  Pictet,  in  a deeper  part  of  the  lake,  opposite 
the  Castle  of  Chillon,  found  at  a depth  of  300  feet  a temperature  of 
51°,  while  that  near  the  surface  in  August  was  76°.  This  result, 
says  Saussure,  “ is  very  remarkable  ; for  51°  is  two  degrees  and  a 
half  below  the  mean  temperature  of  the  earth  at  Geneva.” 

De  Saussure  afterwards  extended  his  researches  greatly.  But,  in 
the  first  place,  not  being  acquainted  with  any  available  register- 
thermometer  for  such  observations,  he  laboured  to  construct  one 
which  should  retain,  when  hauled  up,  the  temperature  it  had 
attained  at  the  bottom.  He  at  last  succeeded  in  constructing  such 
an  instrument  by  using  a thermometer  whose  bulb  was  an  inch  in 
diameter,  surrounding  it  with  a non-conducting  coat  of  wax,  resin, 
and  oil  three  inches  thick,  encasing  the  whole  in  a wooden  box, 
two-thirds  of  an  inch  in  thickness,  and  securing  the  whole  with 
tight  iron  ferrules.  His  instrument,  which  was  thus  a cylinder 
above  seven  inches  in  diameter,  had  the  lamentable  defect  of 


vol.  vnr. 


26  Proceedings  of  the  Boy  at  Society 

requiring  to  remain  twelve  hours  at  the  bottom,  to  arrive  at  the 
temperature  of  the  surrounding  water.  But  the  zeal  and  patience 
of  the  philosopher  were  a match  for  this  trial,  and  his  construction 
had  probably  the  advantage  of  securing  his  bulb  and  tube  against 
the  disturbing  influence  of  pressure,  which  must  have  been  great  in 
some  of  his  experiments,  but  which,  as  he  never  refers  to  it,  must 
not  have  occurred  to  him  as  a condition  to  be  provided  against. 
He  then,  between  1779  and  1784,  made  a number  of  observations 
on  the  lakes  of  G-eneva,  De  Joux,  Annecy,  Thun,  Bourget,  Brienz, 
Lucerne,  Constance,  and  Lago  Maggiore;  always  reaching  the 
bottom  at  depths  varying  from  80  English  feet  to  163,  240,  335, 
350,  370,  500,  600,  620,  and  950  feet.  His  observations  were 
generally  made  at  midsummer,  a few  in  February,  and  a few  also 
in  October.  Excluding  the  experiment  in  Lac  de  Joux,  whose 
depth  of  80  feet  excludes  it  from  the  category  of  deep  lakes,  and 
that  of  Maggiore  in  a warmer  latitude  and  locality  than  the  Swiss 
lakes,  we  find  that  he  never  got  a higher  temperature  than  42°T, 
and  once  he  got  it  so  low  as  39°-6.  The  deepest  lakes  on  the 
whole  gave  the  lowest  temperatures,  but  by  no  means  always  in 
exact  proportion.  In  the  lake  of  G-eneva  the  bottom  temperature 
at  950  feet  was  410,7  ; and  in  that  of  Lake  Constance  it  was  39°*6, 
at  370  feet  only.  He  thought  the  time  of  the  year  made  little 
difference ; but  he  did  not  try  the  same  lake  in  the  same  place  in 
different  months.  He  tries  to  show  that  locality  did  not  much 
affect  the  question  of  temperature.  But  this  is  surely  a mistake; 
for  the  vicinity  of  snow-clad  mountains,  and  the  hard  winter  they 
occasion,  are  the  probable  causes  why  the  cold  at  the  bottom  of 
the  deep  lakes  there  is  greater  than  is  observed  in  so  much  higher 
a latitude  as  Scotland. 

In  fact,  the  deep  temperature  of  a very  deep -lake  must  be  ruled 
far  more  by  the  cold  of  winter  than  by  the  heat  of  summer.  The 
cold  water  must  continue  to  descend  as  long  as  the  cold  months 
last.  The  colder  these  months  are,  the  longer  that  cold  lasts,  the 
greater  must  be  the  cold  at  the  bottom,  and  the  thicker  the 
stratum  of  cold  water.  The  warmth  of  the  air  in  summer  and 
autumn  acting  only  on  the  water  by  conduction,  cannot  move  the 
deep  cold  substratum  upwards.  The  only  other  heating  influence 
from  above,  a far  more  penetrating  influence,  is  the  sun’s  rays. 


27 


of  Edinburgh,  Session  1872-37. 

But  the  water  of  Loch  Lomond  is  scarcely  transparent  enough  to 
allow  the  sun’s  heating  rays  to  penetrate  so  deep  as  500  or  600  feet, 
and  the  transparency  of  the  lake  of  Geneva  is  not  so  much  greater 
as  to  permit  us  to  assume  that  the  heating  portion  of  the  sun’s 
rays  can  penetrate  to  620  and  950  feet.  It  may  be,  nevertheless, 
that  a slight  effect  may  be  produced  even  at  these  great  depths 
in  this  way. 

But  there  is  still  another  heating  power  available  for  raising  the 
cold  substratum  of  water,  and  that  is  the  heat  of  the  earth  at  the 
bottom.  At  Loch  Lomond,  at  600  feet,  this  ought  to  be  about  60°. 
At  the  bottom  of  the  lake  of  Geneva  it  ought  to  be  about  72°.  It 
is  true  that  the  conducting  power  of  the  rocky  exterior  of  the 
earth  is  too  feeble  to  allow  of  much  effect  from  this  heating  power, 
but  it  must  have  some  influence,  however  small.  In  one  way  or 
another, — by  heat  from  the  sun’s  rays,  or  heat  from  the  bosom  of 
the  earth,  or  by  the  joint  action  of  both, — it  may  be  that  the 
cooling  influence  of  the  atmosphere  will  be  to  some  little  extent 
counteracted.  If  so,  the  amount  of  this  counteracting  effect  will 
vary  according  to  the  severity  or  mildness  of  the  winter  months. 
In  short,  the  bottom  temperature  will  rise  a little  in  autumn  after 
a very  open  winter ; and  it  will  not  stand  so  high  after  a very 
severe  one. 

We  have  had  an  excellent  opportunity  of  testing  this  view 
during  the  past  summer  and  autumn,  on  account  of  the  uncommon 
deficiency  of  cold  weather  last  winter, — so  great  a deficiency  that, 
as  stated  in  my  communication  last  spring,  the  mean  atmospheric 
temperature  of  the  six  cold  months  was  at  Loch  Lomond,  by  the 
calculations  of  Mr  Buchan,  10,4  higher  than  the  average  for  thir- 
teen preceding  years. 

Has  this  circumstance  had  any  effect  on  the  bottom  temperature 
of  Loch  Lomond  in  deep  soundings  ? 

On  10th  April,  as  stated  in  the  Proceedings  of  the  Society,  the 
temperature  at  594  feet,  as  near  as  possible  to  the  place  of  obser- 
vation in  September,  October,  and  November  last,  was  42°, — exactly 
as  in  these  months.  On  0th  May , much  intervening  sunshine 
having  prevailed  for  nearly  four  weeks,  but  with  a cold  atmosphere, 
the  surface-temperature  at  the  same  place  had  risen  only  from  43° 
to  44° *5  ; and  the  bottom  temperature  was  42°*1.  I did  not  attach 


28 


Proceedings  of  the  Royal  Society 

any  consequence  whatever  at  the  time  to  this  difference.  It 
might  have  been  an  error  of  observation  ; but  three  competent 
observers  agreed  in  marking  the  index  as  at  42°-l.  I had  unhappily 
no  opportunity  of  making  any  observation  during  the  remaining 
summer  months,  which  I now  greatly  regret.  But  on  8th  August 
I went  from  Loch  G-oil  to  visit  Dr  Bennett  at  Loch  Lomond,  and 
with  his  assistance  as  an  observer,  got  the  following  results,  with 
the  same  thermometer  as  in  former  observations,  viz.,  near  the 
surface,  610,5 ; at  200  feet,  44° ; at  250  feet,  42°*6 ; at  300  feet, 
42°*5 ; at  the  bottom,  in  594  feet  soundings,  42°-5.  I returned  on 
22d  August,  and  again,  with  Dr  Bennett’s  check,  obtained  at  the 
surface,  64°*5 ; at  300  feet,  42°*5 ; at  600  feet,  420,4.  A third  time  I 
returned  on  19th  September,  and  obtained  at  the  surface,  57°*0 ; at 
200  feet,  43*0°;  at  582  feet,  at  the  bottom,  42  -66. 

Here  then  is  an  appreciable  rise, — as  to  which  I know  not  where 
a mistake  can  exist, — since  the  autumn  of  lagt  year,  and  taking 
place  during  the  warm  months  only. 

It  would  be  rash  to  draw  deductions  from  the  observations 
alone  of  two  such  autumns  as  those  of  1871  and  1872,  the  one 
following  a rather  hard,  the  other  an  uncommonly  open  winter. 
But  do  not  these  observations  establish  some  hope  that  a single 
good  observation,  made,  let  us  say,  in  the  middle  of  August,  of 
September,  and  of  October,  may  be  found  to  denote  the  relative 
quality  of  our  winters,  and  to  mark  out  cycles  of  it  ? 

Everything  here  depends  on  the  fidelity  of  the  observer  and 
the  accuracy  of  his  instrument.  On  this  account,  and  for  the  sake 
of  those  who,  I trust,  will  repeat  these  observations  from  year  to 
year,  I have  to  remark  that  the  thermometer  I used  was  always 
the  same,  a protected  thermometer,  by  Casella,  instrument-maker 
to  the  Admiralty ; that  its  scale  at  60°  and  40°  agreed  exactly  with 
three  others  intended  by  their  respective  makers  to  be  exact,  one  of 
them,  indeed,  made  by  Casella  himself ; and  that  I had  an  oppor- 
tunity of  ascertaining  two  days  ago,  that  it  is  proof  against 
pressure,  in  an  excellent  machine,  constructed  for  Professor 
■Wyville  Thomson’s  expedition  by  the  able  engineer  Mr  Milne. 
Marking  55o,0  in  the  air,  it  came  out  after  being  exposed  to  a 
pressure  equivalent  to  that  of  3000  feet  of  water,  marking  66°  by 
the  mercury  in  both  limbs ; and  in  the  minimum  side  the  index 


29 


of  Edinburgh,  Session  1872-73. 

remained  exactly  at  55°,  while  the  index  in  the  maximum  side 
stood  in  close  contact  with  the  mercury  at  66°.  This  instrument 
is  subject  to  an  alternative  inconvenience,  requiring  nice  adjust- 
ment of  the  force  of  the  spring  attached  to  the  indices.  If  they 
are  too  tight,  they  may  stick  beyond  the  force  of  the  magnet  to 
move  them,  or  so  that  the  mercury  may  pass  instead  of  pushing 
them.  If  they  are  too  loose,  a slight  shock  may  alter  their  posi- 
tion. To  avoid  this  risk,  the  simplest  precaution  is  to  paint  the 
last  eighteen  feet  of  the  line  white.  As  the  rest  becomes  deep 
brown  in  the  water,  the  winder-up  of  the  reel  is  at  once  apprised 
of  the  necessity  of  gradually  slowing  his  speed  before  the  instru- 
ment appears  near  the  surface.  The  time  necessary  for  the 
thermometer  to  assume  a new  temperature  is  considerable,  and 
ought  to  be  ascertained  experimentally.  Mine,  instead  of  twelve 
hours,  like  that  of  De  Saussure,  takes  seven  minutes  to  move  six 
degrees  in  a gentle  current  of  uniform  temperature.  It  had 
seldom  to  pass  through  so  many  degrees  between  one  observation 
and  another  ; but  I allowed  it  always  eight,  and  generally  ten 
minutes,  and  in  important  observations  near  the  bottom  even 
fifteen  or  twenty  minutes,  for  absolute  security.  But  I believe 
ten  minutes  to  be  in  all  circumstances  more  than  sufficient. 

The  late  Mr  James  Jardine,  civil  engineer,  and  during  his 
lifetime  a prominent  Fellow  of  this  Society,  made  in  1812  and 
1814  observations  in  Loch  Lomond,  Loch  Katrine,  and  Loch 
Tay  similar  to  De  Saussure’s  and  my  own.  These  valuable 
observations  have  been  recovered  by  Mr  Leslie,  in  the  form  of  the 
original  draught,  and  have  been  communicated  to  the  Society 
by  Mr  Buchan;  but  I find  that  most  of  them  had  appeared  in  Sir 
John  Leslie’s  article  Climate , in  the  “ Encyclopaedia  Britannica,” 
and  again  in  an  octavo  collection  of  Sir  John’s  treatises  in  that 
work,  edited  in  1838  by  the  late  Principal  Forbes.  Jardine’s 
observations  may  yet  turn  out  more  valuable  than  he  could  have 
anticipated,  and  already  seem  to  me  of  such  interest  as  to  deserve 
further  notice. 

His  experiments  were  made  early  in  September.  In  Loch 
Lomond,  in  1812  he  found  near  the  surface  a temperature  of  59°*3 ; 
at  240  feet,  410,3;  at  the  bottom,  in  600  feet  soundings,  41  T°.  On 
Loch  Katrine,  the  day  previous,  he  found  570,3  near  the  surface; 


30  Proceedings  of  the  Royal  Society 

at  210  feet,  41°T ; at  480  feet,  close  to  the  bottom,  41o,0  Again,  on 
Loch  Katrine  in  1814,  fonr  days  earlier  than  in  1812,  he  found 
near  the  surface,  56°#4;  at  180  feet,  410,9;  at  the  bottom,  410,3.  On 
Loch  Tay,  in  August  1812,  he  found  at  the  surface,  570,2;  at  210 
feet,  43°*2 ; at  the  bottom,  420  feet,  41°*9.  These  results,  if  we 
could  only  know  exactly  how  they  were  obtained,  are  singularly 
interesting  as  comparative  with  mine,  got  about  sixty  years  after- 
wards. If  they  be  quite  accurate,  they  indicate  a bottom-tempera- 
ture decidedly  below  what  I have  always  obtained;  and  this  is 
quite  intelligible  under  the  view  I have  taken  of  the  probability  of 
annual  change,  according  to  the  character  of  the  preceding  winter; 
for  all  the  winters  preceding  the  times  of  Mr  Jardine’s  observa- 
tions were  uncommonly  severe.  Or,  taking  a different  view  of  the 
facts,  these  comparative  observations  give  no  countenance  to  the 
fanciful  announcement  by  some  late  meteorological  alarmists,  that 
the  climate  of  G-reat  Britain  is  undergoing  progressive  deterioration 
by  descent  of  the  polar  ice.  Accurate  deep-water  observations  in 
our  deep  lakes  will  in  time  very  easily  test  this  hypothesis ; if 
Jardine’s  and  my  own  be  both  correct,  they  may  denote  certainly 
no  deterioration,  but,  if  any  change,  a slight  improvement  rather. 
But  I have  shown  how  the  difference  probably  arose  from  a 
temporary  peculiarity  of  the  climate  of  each  year  observed.  As  to 
Mr  Jardine’s  observations,  we  cannot  now  learn  exactly  how  he 
worked,  and  we  can  trust  for  their  correctness  only  to  the 
character,  universally  allowed  him  during  his  life,  of  being  a 
singularly  acute,  exact,  conscientious  observer  of  all  physical  facts 
and  phenomena. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  viii.  1872-73.  No.  86. 


Ninetieth  Session. 

Monday , 16^  December  1872. 

Sir  ALEXANDER  GRANT,  Bart.,  Vice-President, 
in  the  Chair. 

The  following  Communications  were  read  : — 

1.  On  the  Philological  Genius  and  Character  of  the 
Neo-Hellenic  Dialect.  By  Professor  Blackie. 

The  Author  showed  by  a historical  review  of  the  fortunes  of 
Greece,  through  the  Middle  Ages,  and  under  the  successive  in- 
fluences of  Turkish  conquest  and  Turkish  oppression,  how  the  Greek 
language  had  escaped  corruption  to  the  degree  that  would  have 
caused  the  birth  of  a new  language  in  the  way  that  Italian  and  the 
other  Roman  languages  grew  out  of  Latin.  He  then  analysed  the 
modern  language,  as  it  existed  in  current  popular  literature  before 
the  time  of  Coraes,  that  is,  from  the  time  of  Theodore  Ptochopro- 
dromus  to  nearly  the  end  of  the  last  century,  and  showed  that  the 
losses  and  curtailments  which  it  had  unquestionably  suffered  in  the 
course  of  so  many  centuries,  were  not  such  as  materially  to  impair 
the  strength  and  beauty  of  the  language,  which  in  its  present  state 
wras  partly  to  be  regarded  as  a living  bridge  betwixt  the  present  and 
the  past,  and  as  an  altogether  unique  phenomenon  in  the  history  of 
human  speech. 


VOL.  VIII. 


32 


Proceedings  of  the  Royal  Society 


2.  Laboratory  Notes.  By  Professor  Tait.  Communicatee!, 
in  his  absence,  by  Professor  G.  Forbes. 

1.  On  the  Eelation  between  Thermal,  and  Electric,  Conductivity. 

Reference  was  made  to  a previous  paper  by  the  author  (Proceed- 
ings, 1867-8,  p.  309),  in  which  an  attempt  was  made  to  apply  to 
this  subject  the  Theory  of  Dissipation  of  Energy. 

Some  years  ago,  a bar  of  German  silver  was  procured,  at  the 
expense  of  the  British  Association,  for  the  purpose  of  ascertaining 
whether  its  thermal,  like  its  electric,  conductivity  is  little  altered  by 
change  of  temperature.  With  this,  Forbes’  experiments  have  been 
carried  out  carefully  through  very  great  ranges  of  temperatures. 

The  exceedingly  laborious  calculations  necessary  to  a complete 
determination  are  not  yet  carried  out;  hut,  by  a rough  graphic 
method,  it  lias  been  ascertained  that  the  alteration  of  conductivity, 
by  rise  of  temperature,  is  at  least  very  small  compared  with  that 
observed  in  iron  under  the  same  circumstances. 

2.  On  Electric  Conductivity  at  a Red  Heat. 

This  was  a mere  preliminary  notice  of  what  promises  to  be  at 
once  an  interesting  and  an  extended  inquiry,  to  which  I have  been 
led  by  some  recent  results  in  thermo-electricity.  At  present,  it  may 
be  stated  that  at,  and  above,  a red  heat  the  electric  conductivity  of 
iron  seems  to  fall  off  much  faster  with  increasing  temperature  than 
that  of  platinum.  To  such  an  extent  does  this  take  place,  that  I 
have  endeavoured  (as  yet,  however,  unsuccessfully)  to  form  a cir- 
cuit in  which  the  main  resistance  is  an  iron  wire,  and  to  obtain  a 
maximum  current  by  gradually  shortening  the  wire.  The  fall  in 
conducting  power  seems  so  very  marked  that  some  of  it  will  re- 
main, even  I believe  when  allowance  is  made  for  the  oxidation  of 
the  iron.  I have  ordered  a special  apparatus  for  the  purpose  of 
avoiding  this  source  of  uncertainty. 

3.  On  the  Thermo-Electric  Relations  of  Pure  Iron. 

By  the  kindness  of  Dr  Russell,  of  Bartholomew’s  Hospital,  I have 
been  enabled  to  experiment  upon  a ribbon  of  pure  iron  prepared  by 


of  Edinburgh , Session  1872-73.  33 

the  late  Dr  Mattkiessen.  I reserve  details  until  I can  obtain  the 
history  and  mode  of  preparation  of  the  specimen  examined,  hut  I 
may  state  now  that,  when  formed  into  thermo-electric  circuits  with 
various  alloys  of  Platinum  and  Iridium  (Proceedings,  1871-2,  p.  773) 
it  gives  results,  as  to  the  position  of  neutral  points,  not  differing 
more  from  those  given  under  the  same  circumstances  by  various 
iron  wires  of  commerce,  than  the  latter  do  among  themselves.  Thus 
it  appears  that,  in  the  thermo-electric  diagram,  the  line  even  for 
pure  iron  is  sinuous ; and  that  the  specific  heat  of  electricity 
in  it  changes  sign  somewhere  about  a low  red  heat. 


3.  Note  on  the  Bate  of  Decrease  of  Electric  Conductivity 
with  Increase  of  Temperature.  By  D.  H.  Marshall,  M.  A., 
Assistant  to  the  Professor  of  Natural  Philosophy.  Com- 
municated by  Professor  Tait. 

These  experiments  were  undertaken  in  order  to  determine  how 
closely  the  hypothesis  “ that  the  electric  resistance  in  a pure  metal 
is  directly  as  its  absolute  temperature  ” holds  for  various  metals 
at  two  easily  ascertained  temperatures, — that  of  the  air  in  the  room, 
and  the  boiling  point  of  water.  The  apparatus  used  was  a Wheat- 
stone’s bridge ; one  coil  of  wire  kept  in  a vessel  of  water  at  the 
temperature  of  the  air  in  the  room  being  put  against  another,  which 
could  be  heated  up  to  100°  C.  The  experiments  showed  that  the 
rate  of  increase  of  resistance  with  temperature  was  different  for 
hard  and  soft  specimens  of  the  same  metal,  being  always  less  in 
the  hard.  This  was  further  proved  by  additional  experiments, 
which  showed  that  sudden  cooling  always  diminished  the  rate  of 
increase  of  resistance,  whereas  if  the  metal  were  allowed  to  cool 
slowly  after  being  boiled,  the  rate  of  increase  of  resistance  was 
always  sensibly  increased. 

The  first  two  columns  of  figures  give  the  ratio  of  the  resistances 
at  the  two  temperatures ; the  first  and  third  give  the  ratios  of  the 
temperatures  themselves  in  absolute  scale  ; the  fourth  is  the  differ- 
ence between  the  second  and  third,  which  will  therefore  show  the 
amount  and  direction  of  deviation  from  the  above  hypothesis. 
When  the  number  in  the  fourth  column  is  +,  the  rate  of  increase 


34 


Proceedings  of  the  R oyal  Society 


of  resistance  with  temperature  is  less  than  it  would  be  according  to 
the  hypothesis  ; when  ~ , greater. 


Soft  Crown  Cu. 

374 

280 

284-4 

- 4-4 

5? 

283 

284-1 

- 1-1 

» • 

55 

281 

283-6 

- 2-6 

Soft  C.  Cu 

374 

288-6 

287 

+ 1-6 

. 

55 

285-6 

285 

+ -6 

,,  .... 

286-7 

285-8 

+ ‘9 

Hard  C.  Cu 

374 

319 

288-1 

+ 30-9 

. 

321 

288-5 

+ 32'5 

,,  . . . 

» 

319-6 

288 

+ 31-6 

Soft  Pt 

374 

303-9 

288-8 

+ 15-1 

» 

303-9 

289  2 

+ 14-7 

Hard  Pt 

374 

356 

288-2 

+ 67-8 

Cd 

374 

291-5 

295-7 

- 4-2 

„ ..... 

>5 

285 

292-9 

- 7-9 

„ ..... 

286-2 

293-3 

- 71 

Au 

374 

301-7 

292-7 

+ 9-0 

„ ... 

55 

304 

292-2 

+ 11-8 

55 

302-4 

293-1 

+ 9-3 

Ag.  . . . . 

374 

302-3 

291-5 

+ 10-8 

„ ..... 

« 

303-1 

291*8 

+ 11-3 

304-7 

292-9 

+ 11-8 

Zn 

374 

294-1 

294-1 

o-o 

))  ..... 

55 

290-3 

294-2 

- 39 

55  • ' * 

55 

288-6 

293-6 

- 5-0 

Fe 

374 

283-8 

292-8 

- 9-0 

Monday , 6th  January  1873. 

DAVID  MILNE  HOME,  LED.,  Vice-President,  in  the  Chair. 

The  Chairman  said : — Before  the  papers  in  our  to-night’s  pro- 
gramme of  business  are  taken  up  there  is  a statement  which,  at  the 
special  request  of  the  Council  of  this  Society,  I have  to  make  from 
the  chair.  I have  been  requested  to  allude  to  the  deaths  of  three 
much  esteemed  Fellows  of  this  Society,  which  have  occurred  since 


35 


of  Edinburgh , Session  1872-73. 

our  last  ordinary  meeting — Professor  Macquorn  Rankine  of  Glasgow 
University;  the  Very  Rev.  Dean  Ramsay,  Edinburgh  ; and  Archi- 
bald Smith  of  Jordanhill.  The  Council  think  that  it  is  only  a 
fitting  tribute  to  the  memory  of  our  deceased  colleagues  that  I 
should  express  regret  at  the  loss  which  we,  in  common  with  others, 
have  sustained,  and  that  I should  also  briefly  allude  to  their  con- 
nection with  this  Society  and  with  science,  leaving  to  a future 
occasion  the  duty  of  giving  a fuller  biographical  account  of  each. 
Professor  Ranking,  when  he  died,  was  one  of  our  vice-presidents, 
having  joined  the  Society  in  the  year  1850.  Important  scientific 
investigations  were  carried  on  by  him,  and  were  the  subjects  of 
numerous  papers  read  at  our  meetings,  and  published  in  our  Trans- 
actions. A series  of  six  papers  “ On  the  Mechanical  Action  of 
Heat  ” gained  for  him  our  Keith  prize  in  the  year  1853.  Our 
Transactions  also  contain  papers  by  him  “On  the  Centrifugal  Theory 
of  Electricity,”  “On  the  Specific  Heat  of  Water  at  various  Tem- 
peratures,” “On  the  Absolute  Zero  of  the  Gas  Thermometer,”  and 
“On  the  Thermal  Efficacy  of  Molecular  Vortices.”  Professor 
Rankine  was  not  only  the  most  eminent  Professor  of  Engineering- 
known  in  Great  Britain,  but  he  was  also  distinguished  for  his  know- 
ledge of  pure  science.  His  merit  as  a man  of  science  was- recognised 
by  the  British  Association  when  he  was  chosen  to  be  president,  once 
of  their  mathematical,  and  twice  of  their  mechanical  sections. 
Glasgow  University  has  by  the  death  of  this  eminent  man  lost  one 
of  her  most  useful  professors,  so  that  in  many  quarters  the  utmost 
regret  will  be  felt  at  his  death.  The  Very  Rev.  Dean  Edward 
Bannerman  Ramsay  was  an  M.A.,  an  LL.D.,  and  Fellow  of  our 
Society.  In  the  years  1828  and  1829  he  was  one  of  the  secretaries 
of  our  ordinary  meetings,  and  in  the  years  1859  to  1861,  he  was 
one  of  our  vice-presidents.  In  the  year  last  named,  at  the  special 
request  of  the  council,  he  gave  an  opening  address  from  this  chair 
on  the  commencement  of  the  winter  session,  which  address  was 
published  in  our  Proceedings.  The  only  paper  read  by  him  to  the 
Society  on  a particular  subject  was  a biographical  memoir  of  the 
Rev.  Dr  Chalmers,  with  whom  he  had  been  on  terms  of  friendship  ; 
and  the  memoir  was  published  in  our  Transactions.  I may  add, 
that  one  of  the  last  public  acts  of  the  Dean,  other  than  professional, 
was  to  convene  a meeting  in  this  city,  to  obtain  funds  for  a monu- 


36 


Proceedings  of  the  Royal  Society 

raent  to  Dr  Chalmers,  and  this  movement,  I may  add,  proved  so 
successful,  that  as  the  result  of  it,  a colossal  statue  of  that  eminent 
man  is  now  being  executed,  and  will  soon,  I hope,  adorn  one  of  the 
principal  streets  of  our  city.  This  is  neither  the  occasion  nor  the 
place  for  referring  to  Dean  Bamsay’s  usefulness  and  reputation  as 
a divine,  or  as  a pastor  of  a large  and  attached  congregation. 
Neither  can  I do  more  here  than  allude  to  the  many  excellent  dis- 
courses and  treatises  on  religious  subjects,  of  which  he  was  the 
author.  But  I cannot  forbear  mentioning,  and  with  special  emphasis, 
the  Dean’s  geniality  of  disposition,  his  large-heartedness,  and  his 
entire  freedom  from  sectarian  jealousy,  which  enabled  and  disposed 
him  to  acccept,  and  even  to  seek,  the  society  and  friendship  of  any 
person  of  worth,  though  not  belonging  to  his  own  branch  of  the 
Christian  Church.  May  I be  permitted  to  express  a wish  and  enter- 
tain a hope  that  the  example  he  set,  approved  of  as  it  is  by,  I believe, 
all  classes  of  this  community,  may  not  be  without  good  effect. 
Dean  Bamsay,  though  faithful  and  assiduous  in  the  performance  of 
his  professional  duties,  found  time  for  acquiring  information  and 
pursuing  studies  in  other  fields.  He  was  extremely  fond  of  music, 
and  his  knowledge  of  it,  even  in  its  scientific  aspects,  was  well  shown 
in  two  lectures  which  he  delivered  before  the  Philosophical  Institu- 
tion of  the  city  “ On  the  Gfenius  and  Works  of  Handel.”  His 
knowledge  of  botany  was  shown  in  a memoir  which  he  published  of 
the  discoveries  and  works  of  his  friend  Sir  J.  E.  Smith.  But  the 
literary  work  which  carried  his  name  farthest,  and  will  preserve  it 
longest,  at  least  among  his  countrymen,  was  his  “ Beminiscences 
of  Scottish  Life  and  Character.”  It  is  a striking  proof  of  the 
general  appreciation  of  this  book,  that  it  went  through  twenty 
editions,  and  that  only  a fortnight  before  his  death,  the  venerable 
Dean  was  revising  the  proof  sheets  of  a twenty-first  edition.  Dean 
Edward  Bamsay  was  a Scotchman  of  whom  his  country  has  reason 
to  be  proud,  and  who  will  live  in  the  hearts  of  all  who  had  the 
happiness  to  possess  his  personal  acquaintance.  Archibald  Smith, 
of  Jordanhill,  was  an  LL.D.  and  F.B.S.  of  London  and  Edinburgh. 
He  first  distinguished  himself  as  a student  of  Glasgow  University, 
and  afterwards  in  Cambridge,  having,  at  Trinity  College  there, 
acquired  the  high  position  of  Senior  Wrangler  and  first  Smith’s 
prizeman.  Though  he  became  by  profession  an  English  barrister, 


37 


of  Edinburgh,  Session  1872-73. 

In's  tastes  were  for  mathematics  and  physics.  lie  was  employed  by 
Government  to  make  a reduction  of  important  magnetic  observa- 
tions carried  on  by  two  Government  ships  in  the  Antarctic  regions. 
He  was  employed  at  the  suggestion  of  Sir  Edward  Sabine  and  Pro- 
fessor Airy,  both  of  whom  were  well  acquainted  with  his  mathe- 
matical powers.  The  chief  value  of  his  services  lay  in  his  correct- 
ing the  effect  on  the  magnetic  observations  due  to  the  iron  in  the 
ships.  He  afterwards,  under  the  sanction  of  Government,  drew  up 
and  published  an  “Admiralty  Manual  for  the  Deviation  of  the  Com- 
pass,” a work  greatly  appreciated,  and  which  has  been  republished 
in  various  languages.  Mr  Smith  received  from  the  Eoyal  Society 
of  London  one  of  its  Royal  Medals;  from  the  Emperor  of  Russia,  a 
beautiful  compass  set  with  diamonds;  and  from  our  own  Govern- 
ment, a gift  of  L.2000,  in  acknowledgment  of  his  important 
scientific  services.  The  three  individuals  to  whom  I have  now  re- 
ferred were  each,  in  their  different  vocations,  distinguished  by  high 
character,  superior  talents,  and  useful  lives;  and  I am  sure  that  all 
present  will  approve  of  the  tribute  of  respect  to  their  memory, 
which  in  name  of  the  Council  I have  now,  however  imperfectly, 
attempted  to  offer. 

The  following  Communications  were  read  : — 


1.  On  a Question  of  Arrangement  and  Probabilities. 

By  Professor  Tait. 

Many  of  the  common  illustrations  of  probabilities  are  taken 
from  games  in  which  each  hand,  or  trick,  must  necessarily  be  won 
by  one  player,  and  lost  by  the  other.  It  becomes  an  interesting 
question  to  inquire  what  modification  is  introduced  if  we  contem- 
plate the  possibility  of  a hand,  or  trick,  being  drawn — i.e.  not  won 
or  lost  by  either  player.  The  only  difficulty  lies  in  taking  account 
of  the  limiting  conditions. 

In  the  game  of  golf,  for  instance,  where  each  hole  separately 
may  be  won,  halved,  or  lost,  we  have  the  following  question. 
When  a player  is  x holes  “up,”  and  y “to  plajq”  in  how  many 
ways  may  he  win  ? 


38 


Proceedings  of  the  Royal  Society 


Let  this  number  be  represented  by  P^  y . Then  obviously 

Par+l.y+l  = Par+2,y  + Par+l,y  + Pa?,  y • 

If 

Vx-y  = axb>J 

be  a particular  integral,  we  have 

ah  = a2  -+-  a + 1 , 

so  that 

P*,!,  = SCa*(a  + l + -|)!'  . 


Now  the  conditions  are  obviously 

P x,y  = 1 , if  oc>y\ 

and 

P —x,y=  0,  if  x>y  . 

Failing  in  several  attempts  to  determine  fully  the  special  form  of 
P x,y  from  these  conditions,  I bad  recourse  to  a graphical  method, 
which  will  he  given  below.  But  before  I do  so,  I take  another 
mode  of  integration,  which  leads  easily  to  special  numerical  re- 
sults. 

Suppose  y = x + n , 
then  the  equation  becomes 


AP*,  x+n  — P#+2,  x+n  4~  P#+l,  x+n 

from  which  it  appears  that  if  we  can  find  expressions  for  PX:X+m 
and  P#+i,  x+m  we  can  deduce  by  summation  that  for  Px-iiX+m. 

Let  us  first  put  n — 0 ; we  have 

AP#,  # = P#-|-2,  x + Px+l,x  =r  2 , 


since,  obviously,  each  of  these  quantities  is  unity.  Integrating, 
we  have 

P X,X  ~ 2# , 

no  constant  being  added,  since  it  is  clear  that 
Po,o  = 0 . 

Again,  by  the  fundamental  equation,  putting  n = 1,  we  have 


AP^,a:-(-i  — P x+2,x+l  + P#  + l,x+l 
= 1+  2(®  + 1) 

Px,  x+1  = os  + ^(^+1)  -f-  G 

= O + l)2  = x[x  + 1)  + (x  -f  1) 


39 


of  Edinburgh,  Session  1872-73. 
for  we  have  obviously 

Po,i  = 1 • 

Next, 

£d?x,x+2  = Px+2,ar+2  + P#+l,>+2 

= 2(x  + 2)  + (x  -f  2)  + (x  + 1)(#  -f  2)  . 

?x,x+2  = |(>  + 1)0  + 2)  + |#0  + 1)0  + 2), 

no  constant  being  added,  for 

Po,  2 = 3 . 

Similarly, 

?x>x  + z=^(x+l)(x+2)(x+S) +±(x+2)(x+S)  + ±x(x  + l)(x+2)  («+3), 
for 

Po,3  = Pi, 2 + Po,2  4-  P—1,2  = 4 + 3 + 1 = 8. 

Fx,  X + 4=|(* ■ + 2)  (®  ■ + 3)  (x  + 4)  4-  + 1)  (re + 2) (x + 3)  (x + 4)  + i x (x  4- 1) (x + 2) (x  + 3)  (x  + 4) 

for 

Po,4  = Pi, 3 + Po,3  + P — 1,3  = 11  + 8 + 4 = 23. 

We  may  now,  in  conformity  with  these  expressions,  assume 

P*,  x+  n = { K + — + 7 — — rr  + . . . ]•  + 1 . • .X  + n 

( x x(x+l)  ) 

Now,  if  y = x + n,  the  original  equation  of  differences  gives 

AP x,x+n  r=Pa?+2 , x+n  + P#+l  ,x+n 


where  A refers  to  x and  not  to  n.  By  the  assumed  value  of 
Pff,  x+n  this  becomes 


j~  (n  + 1)  A n 

L~ 


nBn 

(»-  1)0, 

J XX  + 1 

x(x  + 1) 

+ x(x  + 1)04-  2)  + * 

Bn_2 

o_2  i 

| X 4-  2 

x + 2 

+ (x  + 2)  (a?  + 3)  + J 

Bn— l 

o-i  | i 

X 1 

X + 1 

0 + 1)0  + 2)  J 

VOL.  VIII. 


40 


Proceedings  of  the  Royal  Society 
Whence,  equating  coefficients  of  like  factorials,  we  have 
(rc  + l)Ara  = An_i  , 

■=  Bw — i 4-  An — 2 j 

( n - 1)  Cn  = Cn_i  + Bw_2  , 

(n-  2)  Dn  = Dw_i  + Cn_2,  Ac.,  Ac. 

Let 

| n + 1 An  = a«,  I /Z  Bn  = fin  , I ??  - 1 Crc  = yft,  Ac. 
then  these  equations  become 


Otra  — CLn — i 

1 = fin  4-  aw_i 

y«+i  = y»  + /?n-i 
Sw+1  = 8n  4-  yw_i 

Thus  we  have 


M>n  ~ SO. 

/L.  = Sare_i  = jyan 
yn  — %fin—l  — p.  ^ ra 


= Syw— i = py»j  &c. 


x(x  + 1)  . . (x  + n) 


_ f an  fin  s n , 1 /2\2  „ . ) 

" l [ n + l+x  | njf  + 4r  + l)  |H-l(p)a  J 

_ / n + 1%  n+ln  f%\2  )#(#4-l)  . (#  + ?2) 

( X D a?(a?+l)\D/  J 1.2  . . .(n+1) 

= 1 i-2  + 12--  \d/)  + ••••}“'■ 

W 


Sy  + » 

SV-1  0 


.M) 

d) 


v 

for  no  negative  powers  of  *—  are  to  be  retained,  as  a»  is  a mere 
constant. 

The  trouble  of  carrying  out  this  process  is  considerable,  depend- 


41 


of  Edinburgh,  Session  1872-73. 

ing  on  the  determination  of  the  constants  in  each  finite  integral 
so  as  to  satisfy  the  limiting  conditions  of  the  problem.  To  a few 
terms  we  have 


| x + n 
| x- 1 | n+ 


- j 2 + (2rc-l)lL±-1  + {n-  2)2(-  + 1)n  . 

1 \ x x(x  + 1)  ) 


By  a slight  modification  of  the  preceding  process  we  get  in 
succession 


A?  — x,  x + n — p — (x  + 1),  x-\-n  + P— 


(x  + 2) , X + n , 


■X,  X + 


I g+J:  U I /-  I'^-I  , 1)(»-2)(»- 1)  , 

[ x f 1 \ n- 1 ( v ,x  + 2 2 (x  + 2)(x  + Z) 


The  graphical  method  to  which  I referred  above  consists  simply 
in  supposing  the  various  values  of  Fx>  y to  be  written  each  at  the 
point  whose  co-ordinates  are  the  values  of  a?  and  y.  If,  to  fix  the 
ideas,  we  suppose  the  axis  of  x to  be  horizontal  and  that  of  y 
vertically  downwards,  then  the  fundamental  equation  shows  that 
by  adding  together  any  three  contiguous  numbers  in  a horizontal  line , 
we  'produce  the  number  immediately  under  the  middle  one  of  the  three. 

The  limiting  conditions  show  that  all  the  numbers  along  the 
line 

x + y = 0, 

and  those  between  it  and  the  negative  part  of  the  axis  of  x , are 
zeros  ; while  those  along 

y = x - 1 , y = x - 2 , y + x = 1 , 
are  each  equal  to  1 . 

Hence  we  have  the  figure 

0000001100  0 0....X 

00000  1211000 
00001  3441100 

00014  8 11  96110 

0 0 1 5 13  23  28  26  16  8 1 1 
0 1 6 19  41  64  77  70  50  25  10  1 


&c.  y &c. 


• («) 


42 


Proceedings  of  the  Royal  Society 

where  the  numbers  printed  in  darker  type  are  inserted  by  the  rule 
given  above.  This  is,  of  course,  in  one  sense  a complete  solution 
of  the  problem ; but  the  results  may  easily  be  put  in  an  analytical 
form. 

Had  we  had  zeros  along  the  line 

V = x - 2 

we  should  have  had  the  following  scheme  instead  of  that  above : 

0 1 0 • . x 

0 1110 

0 1 2 3 2 1 0 . . (6) 

013676310 
0 1 4 10  16  19  16  10  4 1 0 

i 

&c.  y &c. 

Hence  the  part  added  by  the  units  along  the  line 

y = x - 2 
is 

0 . . x 

0 1 

0 112 

0 1 2 4 3 3 . . (c) 

01379  10  64 

1 

y &c. 

This,  again,  differs  from  (6)  shifted  one  place  downwards,  by 
0 . . x 

0 0 
0 0 1 

0 112  . . (d) 

1 2 4 3 3 

y &c. 

But  it  is  obvious  that  this  is  a repetition  of  the  same  one  place 
diagonally  downwards  to  the  right. 


43 


of  Edinburgh,  Session  1872-73. 

Also  ( b ) is  obviously  the  coefficients  of  the  powers  of  a in 

a (a  +-  1 +-  — 

V a 

for  the  several  positive  integral  values  of  y.  Call  the  term  in  ax 
in  this,  i.e.,  the  coefficient  of  ax~ 1 in  + 1 +-  , A^y,  and 

that  at  x,  y in  the  scheme  (c)  Q^y , then 

Q x,y  Q x— 1,  y — 1 — A x,y — 1 • 

and  thus 

P#,  y — A.x,  y "b  Q#,  y 

— Ax,  y + A#,  y — 1 4-  A#  — 1,  y — 2 ”b 

This  points  to  a very  simple  way  of  constructing  the  values  of 
P*,  y from  those  of  y . 

In  scheme  (b),  add  to  the  number  in  any  position  that  im- 
mediately above  it,  and  also  those  lying  in  the  left  handed  upward 
diagonal  drawn  from  the  last  named,  their  sum  is  the  number  in 
the  corresponding  position  in  (a).  Thus  16  + 6 + 3 + 1=  2 6. 

If  D refer  to  x and  D'  to  y,  we  have 

p / 1 , 1 , 1 , V 

y — ( 1 + jy  j)jy2  "1"  J)2D/3  ' ' ' ’ y » 

= (*  + DD'-l)A"r’!'\ 

It  is  to  be  observed  that,  since  if  one  player  wins  the  other  must 
lose,  P_ x,  y is  the  number  of  ways  in  which  a player  may  lose, 
when  he  is  x “ up”  and  y u to  play.” 

The  number  of  ways  in  which  the  game  may  be  drawn  is  also  a 
solution  of  the  same  equation  of  differences  ; but  the  limiting  con- 
ditions are  now  obviously  independent  of  the  sign  of  x : and  are, 
taking  it  positive, 

Ptf,y  = 1 if  X = y , 

Ptf,  y = 0 if  x > y . 


44 


Proceedings  of  the  Boycd  Society 

Hence  the  values  are  represented  by  the  following  scheme — 

0 10....* 

0 1110 
0 1 2 3 2 1 0 

0 13  6 7 6 3 10 

&c.  y &c. 

Thus  the  value  of  P x,y  in  this  case  is  the  coefficient  of  ax  in 

Hence  the  number  of  different  modes  in  which  the  game  may 
finish,  when  one  of  the  players  is  x u up,”  and  there  remains  y “ to 

/ l\y 

play”  is,  calling  R#,  the  coefficient  of  ax  in  I a + 1 + - J , 

C(D  + d)(1  + DD'-l)  + 

while  the  number  of  different  ways  of  finishing  if  the  whole  y holes 
are  played  out  is  3y. 

There  are  many  very  curious  properties  of  the  numbers  we  have 
denoted  by  P#,  y , A*,  y , Qx,  y . Thus,  for  instance,  it  is  easy  to 
see  that 

Ql,  2 = Q2,  2 - 1 Qo,  2 = Q3,  2 + 1 

Qi,  3 = Q2, 3 + l Qo,  3 = Q3, 3 - l 

all  of  which  are  included  in 

Qx,y  = Q 3-x,y  + (-i  f+V  . 


2.  Laboratory  Notes.  By  Professor  Tait. 

1.  On  the  Stiffness  of  Wires. 

The  following  are  the  results  of  some  experiments  made  for 
me  by  Mr  W.  M.  Ogilvie  with  Amontons’  apparatus;  chiefly  with 
the  view  of  testing  the  accuracy  with  which  it  can  be  applied,  but 
incidentally,  with  the  view  of  obtaining  an  idea  of  the  relation  be- 
tween tension  and  stiffness  in  the  same  wire  or  cord. 


45 


of  Edinburgh,  Session  1872-73. 


(a)  Fine  Iron  Wire. 


Weight  on  each 
end  of  Wire. 

Weight  required 
to  overcome  stiff- 
ness of  Wire. 

4,000  grains 

170  grains 

5,000  „ 

200  „ 

7,000  „ 

230  „ 

Roller  used  is  1J  in.  diameter. 

12,000  „ 

270  „ 

15,000  „ 

280  „ 

22,000  „ 

300  „ 

(6)  Fine  Copper  Wire,  annealed  over  a gas  flame. 

1000  grains 

27  grains 

2000  „ 

40  „ 

3000  „ 

50  „ 

4000  „ 

56  „ 

5000  „ 

60  „ 

8000  „ 

64  „ 

The  results  which  immediately  follow  were  obtained  from  annealed 
and  unannealed  wires,  of  the  same  gauge,  of  two  very  different  kinds 

of  copper — crown 

being  of  very  high,  C of  very  low,  thermal  and 

electric  conductivity. 

(0 

Soft  C Wire. 

5,100  grains 

1240  grains 

9,100  „ 

1300  „ 

22,100  „ 

1370  „ 

40,100  „ 

1400  „ 

Soft  Crown  Wire. 

5,100  grains 

1340  grains 

9,100  „ 

1400  „ 

22,100  „ 

1500  „ 

40,100  „ 

1560  „ 

(«) 

Hard  C Wire. 

5,100  grains 

1400  grains 

12,100  „ 

1540  „ 

22,100  „ 

1740  „ 

41,100  „ 

1900  „ 

46 

(/) 


Proceedings  of  the  Royal  Society 


Weight  on  each 
end  of  Wire. 

5.100  grains 

9.100  „ 

22,100  „ 
40,100  „ 


Hard  Crown  Wire. 

Weight  required 
to  overcome  stiff, 
ness  of  Wire. 

1500  grains 
1600  „ 

1800  „ 

2000  „ 


(9) 


Same  Wire  as  (e),  after  several  experiments  with  it. 


10.000  grains 

30.000  „ 

50.000  „ 

60.000  „ 


1340  grains 
1600  „ 
1800  „ 
1900  „ 


(h)  Soft  Wire,  another  specimen  of  ( d ),  after  a good  number 
of  trials,  and  taking  the  average  of  the  last  three. 


10,000  grains 

1000  grains 

30,000  „ 

1190  „ 

50,000  „ 

1360  „ 

60,000  „ 

1460  „ 

-) 

Same  Wire  as  last  doubled. 

10,000  grains 

2300  grains 

No  great  precautions  were  taken 

30,000  „ 

2470  „ 

in  this  experiment  to  secure  the 

50,000  „ 

2640  „ 

weight  being  equally  distributed 

60,000  „ 

2740  „ 

over  both  wires. 

No  proper  results  could  be  got  by  doubling  any  of  the  unannealed 
wires. 


(0 


Whip  Cord. 


10,000  grains 

130  grains 

20,000  „ 

240  „ 

30,000  „ 

400  „ 

40,000  „ 

o 

CO 

lo 

50,000  „ 

630  „ 

60,000  „ 

700  „ 

47 


of  Edinburgh,  Session  1872-73. 

With  one  exception  these  results  indicate  a logarithmic  relation 
between  the  stiffness  (S)  and  the  tension  (T)  of  the  form 

S0-  S oc  a~T  . 

Here  S0  is  the  stiffness  when  the  tension  is  very  great. 

Thus,  taking  the  numbers  in  experiments  (b)  and  (Z)  above,  we 
obtain  the  following  comparison  with  experiment  of  the  formula — 


68  - S = 6P5  x (§)100° . 

T 

1950-8  = 1987  x (1-08)  ,0'““ 

Experiment. 

Formula. 

Experiment. 

Formula. 

41 

41 

182 

184 

28 

27*3 

171 

170 

18 

18*2- 

155 

158 

12 

12-1 

142 

146 

8 

8 

132 

135 

4 

2-4 

125 

125 

Considering  the  excessively  uncertain  nature  of  such  experi- 
ments, these  results  may  be  looked  upon  as  agreeing  well  with  the 
law  suggested. 

2.  Preliminary  Sketch  of  the  Thermo-electric  Diagram  for 
Iron,  Gold,  and  Palladium. 


3.  On  the  Muscles  which  open  and  close  the  Mouth,  with 
some  Observations  on  the  Active  and  Passive  Condition 
of  Muscles  generally.  By  Dr  Gamgee. 


4.  Observations  and  Experiments  on  the  Cerebral  Hemi- 
spheres and  Corpora  Striata  of  Birds.  By  Dr  M‘Kend- 
rick.  Communicated  by  Professor  Turner. 

Surgeon-Major  Black  exhibited  twenty-five  large  photo- 
graphic views  of  the  late  eruption  of  Mount  Vesuvius,  which 
had  been  executed  by  his  brother,  John  Melton  Black,  Esq. 


VOL.  VIII. 


48 


Proceedings  of  the  Royal  Society 


Monday , 20 th  January  1873. 

Sir  WILLIAM  STILLING  MAXWELL,  Bart., 
Vice-President,  in  the  Chair. 

The  Council  of  the  Loyal  Society  have  awarded  the  Makdougall 
Brisbane  Prize  to  George  James  Allman,  M.D.,  F.L.S.,  Emeritus 
Professor  of  Natural  History  in  the  University  of  Edinburgh,  for 
his  memoir  “ On  the  Homological  Kelations  of  the  Coelenterata,” 
published  in  the  Transactions  of  the  Society  for  1870-71. 

In  selecting  this  memoir  for  the  prize,  they  took  into  consideration 
not  merely  its  own  importance  as  a contribution  to  zoological 
science,  but  the  author’s  elaborate  and  beautifully  illustrated 
monograph  “On  the  Gymnoblastic  or  Tubularian  Hydroids,”  pub- 
lished in  two  large  folio  volumes  by  the  Kay  Society,  of  which  it 
forms  a leading  chapter. 

This  monograph  comprises  a most  extensive  series  of  researches 
into  the  morphology,  development,  minute  structure,  and  physiology 
of  an  interesting  group  of  invertebrated  animals,  as  well  as  a 
careful  consideration  of  their  zoological  position  and  classification. 

It  contains  the  observations  and  conclusions  of  many  years  of 
laborious  research,  and  whilst  serving  as  a memorial  of  the  industry, 
artistic  skill,  and  scientific  acumen  of  its  author,  forms  a most 
important  contribution  to  natural  history  science. 

The  following  Eeport  was  submitted  to  the  Society  : — 

Report  by  the  Council  of  the  Loyal  Society  of  Edinburgh  on  the 

proposed  alterations  of  the  laws  as  to  the  Election  of  Ordinary 

Fellows  : — 

The  Council  have  carefully  considered  the  proposed  alterations 
in  the  laws  as  to  the  election  of  Ordinary  Fellows  which  were 
remitted  to  them  by  the  Society  for  re-consideration  on  3d  June 
last,  and  have  agreed  to  recommend  to  the  Society  that  there 
should  be  no  limitation  in  the  number  of  Fellows  annually  elected, 
and  that  the  following  alterations  should  be  adopted : — 


of  Edinburgh,  Session  1872-73. 

That  Laws  IX.  and  XIII.  should  be  altered  as  follows  : — 


49 


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. 


XIII. 

The  election  of  Ordinary  Fellows  shall  only  take  place  at  the 
first  Ordinary  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,  provided  twenty-four  Fellows  be 
present  and  vote. 

The  Society  adopted  these  alterations  of  the  Laws. 

The  following  Communications  were  read  : — 

1.  On  the  Physical  Constants  of  Hydrogenium.  I. 

By  Mr  James  Dewar. 

2.  On  the  supposed  Upheaval  of  Scotland,  in  its  Central 

Parts,  since  the  time  of  the  Roman  Occupation  By 

D.  Milne  Home,  LL.D. 

No  abstract  of  this  paper  is  given  in  the  Proceedings,  as  the 
paper  will  appear  in  the  Transactions. 

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


50 


Proceedings  of  the  Royal  Society 


Monday,  3 d February  1873. 

Sir  EOBEET  CHEISTISON,  Bart.,  President,  in  the 
Chair. 

The  following  Communications  were  read  : — 

1.  On  the  Anatomy  of  a new  Species  of  Polyodon,  the 
Polyodon  gladius  of  Martens,  taken  from  the  river  Yang- 
tsze-Kiang,  450  miles  above  Woosung.  Part  I.,  being  its 
External  Characters  and  Structure.  By  P.  D.  Handy  side, 

M.D. 

The  position  of  this  new  species  of  Ganoid,  under  our  commonly 
accepted  classification,  the  author  gave  as  follows 


Division  .....  Vertebrata. 

1st  primary  section,  . . Ichthyopsida. 

1st  class, Pisces. 

3d  sub-class, Ganoidei. 

2d  order,  Chondrostei. 

1st  family, Acipenseridm. 

2d  family,  Polyodontidm. 

Genus,  Polyodon. 

1st  species, P.  folium. 

2d  species, P.  gladius. 


After  referring  to  the  Polyodon  folium  of  Lac^pede  (the  P.  reticu- 
lata of  Shaw,  the  Planirostra  spatula  of  Owen),  the  paddle-fish  or 
spoon-bill  sturgeon  of  the  Ohio  and  Mississippi  and  their  tributaries, 
as  a well-known  species  of  the  genus  in  question,  Dr  Handy  side  went 
on  to  state  that  the  new  species  now  to  be  described  was  first 
observed  on  a Chinese  fishmonger’s  stall  at  Woosung,  12  miles  from 
Shanghai,  and  had  since  been  found  in  the  Yang-tsze-Kiang,  and, 
as  was  alleged,  in  the  northern  Japanese  sea.  He  then  sketched 
the  history  of  the  Polyodontidae  family,  and  narrated  the  researches 
of  Lac6pede,  Von  Martens,  Blakiston,  Kaup,  and  Dumeril. 

He  next  exhibited  to  the  Society — first , a small  entire  specimen 


of  Edinburgh,  Session  1872-73.  51 

of  the  P . gladius,  measuring  26^  inches  = 652  millimeters ; secondly , 
an  opened  specimen  measuring  40  inches  = 1070  millimetres; 
thirdly , three  pieces  of  an  adult  fish  that  measured  fully  9 feet  long 
= 2720  millimetres;  and  fourthly , apiece  of  an  almost  adult  fish 
that  was  not  measured.  He  showed  also  four  large  drawings,  and 
twenty-four  smaller  ones  (including  nineteen  microscopic  views), 
illustrative  of  his  description  of  the  External  Characters  and 
Structure  of  the  fish,  under  the  ten  following  heads : — 

1st,  Its  size,  weight,  &c.;  2d,  its  form;  3d,  its  surface  and 
colour ; 4th,  its  fins ; 5th,  its  proportional  parts ; 6th,  its  lateral 
line  and  system  of  muciparous  pores ; 7th,  its  exo-  or  dermo-skele- 
ton  and  tegumentary  system;  8th,  its  spatula,  rostrum,  or  snout; 
9th,  its  eyes,  mouth,  and  teeth ; and  10th,  its  branchiae,  pseudo- 
branchiae, and  spiracula. 

In  the  course  of  his  paper,  the  author  -remarked  that  a specimen 
had  been  seen  by  Mr  H.  Gr.  Hollingworth,  resident  at  Kiu-Kiang, 
on  the  same  river,  reaching  to  the  length  of  15  feet,  and  weighing 
133  lbs.;  that  in  regard  to  edible  properties,  the  young  fish  was 
said  to  be  very  delicate  eating;  that  the  body  was  compressed, 
elongated,  and  tapering  towards  the  tail,  like  the  sturgeon  family 
generally.  The  head  was  projected  beyond  the  mouth  into  an 
elongated  muzzle  or  spatula.  This  snout  was  thin  at  the  margins, 
but  thick  and  keeled  in  the  centre ; in  young  specimens  it  was 
sharp  at  the  point,  but  it  afterwards  got  blunted  and  rounded  off  by 
digging  among  the  silt  of  the  river  bottom.  The  eyes  of  the  fish 
were  of  very  small  size,  and  it  was  supposed  that  the  sensibility  of 
the  spatula  compensated  for  the  want  of  larger  ones. 

The  2d  Part  of  Dr  Handyside’s  paper  will  consist  of  an  anato- 
mical description  of  the  nervous  and  muscular  systems ; the  3d 
Part  of  the  viscera  of  organic  life ; and  the  4th  Part  of  the  articular’ 
system  and  the  endo-skeleton  of  the  Polyodon  gladius . 

2.  Note  on  the  Thermal  Equivalents  of  the  Oxide  of 
Chlorine.  By  James  Dewar,  Esq. 

Two  years  ago  the  author  submitted  to  the  British  Association 
a preliminary  report  on  the  subject,  which  has  not  been  prosecuted, 


52 


Proceedings  of  the  Royal  Society 


owing  to  the  exhaustive  investigations  of  Professor  Thomsen  of 
Copenhagen,  on  thermal  values.  In  the  paper  referred  to,  the  results 
are  calculated  on  the  assumption  of  hydriodic  acid  evolving  15,000 
heat  units  for  equivalent  in  aqueous  solution.  The  above  num- 
ber is  much  too  high,  according  to  Thomsen’s  recent  experiments, 
who  gave  13,170  as  the  true  number.  If  my  former  results  are  re- 
calculated with  the  new  value  for  hydriodic  acid,  the  following 
numbers  are  obtained: — 

Formation  of  Iodic  acid  in  aqueous  solution  = 25,000  heat  units. 


These  results  show  clearly  that  the  stability  of  the  series  in- 
creases as  we  ascend,  and  not  the  reverse,  as  has  been  generally 
supposed,  from  the  thermal  values  obtained  by  Favre.  No  known 
series  of  bodies,  therefore,  diminishes  in  stability,  or  has  a regular 
increment  of  absorption. 

3.  On  the  Ptesemblances  which  Microscopic  Objects  in 
Dichroite  and  Amethyst  have  to  some  of  the  lower  forms 
of  Organic  Life.  By  J.  Scott,  Tain.  Communicated  by 
Professor  Kelland. 

When  examining  with  the  one  inch  object-glass  of  a compound 
microscope  some  pieces  of  Strathpeffer  Albert  coal,  I happened  to 
place  on  the  stage  a crystal  of  dichroite,  and  was  surprised  to 
observe  its  surface  covered  with  circular  impressions.  Their 
resemblance  to  some  which  I had  previously  noticed  on  iron  pyrites 
associated  with  Albertite,  led  to  a further  inspection,  which  showed 
that  they  were  due  to  globular  bodies  of  various  colours  distributed 
throughout  the  crystal  in  layers  parallel  to  the  respective  faces. 

By  means  of  sections  cut  parallel  to  these  faces,  I observed  that 
the  lower  side  of  each  layer,  namely,  that  looking  towards  the 
interior  of  the  crystal,  differs  essentially  in  its  structural  peculi- 
arities from  the  upper.  On  that  side  each  object  has  a conical 
form  like  a limpet  shell,  and  usually  consists  of  three  or  four  easily 


Chlorine  ,, 

Peroxide  of  chlorine 
Chlorous  acid 
Hypochlorous  acid 


-18,000 
= - 9,800 
= -21,000 
= - 28,000 


(Thomsen.) 


53 


of  Edinburgh,  Session  1872-73. 

defined  zones  surrounding  a well-marked  central  apex.  With 
higher  optical  powers  a greater  number  of  segmentary  zones  are 
brought  out,  and  radial  and  transverse  stride  in  exquisite  detail. 

Besides  these  individual  characteristics,  they  exhibit  composite 
relations  of  a peculiar  kind,  but  in  reality  the  development  of  a 
very  simple  principle.  Whenever  an  increase  of  size  has  produced 
the  contact  of  two  or  more  individuals  of  a group,  further  enlarge- 
ment has  taken  place  by  the  formation  of  a common  investing  border. 

From  the  deposition  of  the  objects  in  successive  layers,  with  their 
conical  extremities  resting  on  what  had  been  at  some  stage  of  the 
crystal’s  formation  one  of  its  faces,  they  must  have  obtained  their 
position  whilst  the  crystal  was  in  the  act  of  formation. 

Sections,  either  perpendicular  or  at  an  oblique  angle  to  a face  of 
the  crystal,  by  presenting  a side  view  of  the  objects,  show  that  the 
hemispheroidal  upper  and  the  conical  lower  extremities  were 
generally  connected  by  a cylindrical  body,  whose  comparative 
length  varied  considerably  in  the  different  individuals. 

The  same  sections  also  exhibit  a remarkable  structural  relation 
between  the  superimposed  layers  which  occupy  the  successive 
laminae  of  the  crystal.  When  the  objects  can  be  traced  from  the  in- 
terior towards  the  surface,  they  are  found  to  have  a linear  arrange- 
ment symmetrically  round  axes  perpendicular  to  the  respective 
faces.  These  structural  features  can  be  well  observed  in  sections 
through  the  terminal  pyramid  of  some  specimens  of  amethyst,  in 
which  they  constitute  a number  of  groups  equal  to  the  sides  of  the 
pyramid,  each  group  consisting  of  a series  of  highly  ornate  beaded 
columns  perpendicular  to  the  same  plane,  and  therefore  parallel  to 
one  another. 

The  individual  objects  in  the  same  axial  line  or  column  are  often 
joined  so  closely  that  they  may  be  considered  as  segments  of  a con- 
tinuous whole,  but  in  other  instances  the  connection  is  a mere 
microscopic  filament.  In  parts  of  the  crystal  a whole  series  of 
columns  terminates  on  the  same  lamina,  where  the  last  segment  of 
each  has  spread  out  to  an  extent  which  gives  the  structure  the 
appearance  of  a disc  with  a long  beaded  handle  attached  to  its 
centre.  This  last  circumstance  indicates  one  or  both  of  two  con- 
ditions— a period  of  retardation  in  the  increase  of  the  crystal,  or  of 
rapid  acceleration  in  the  growth  of  the  objects.  Irrespective  of  the 


54 


Proceedings  of  the  Boyal  Society 

structural  features  which  the  individual  objects  possess,  their  mode 
of  succession  in  linear  directions  perpendicular  to  the  planes  of  the 
crystal  displays  a conformity  to  law,  which  could  not  have  resulted 
from  any  chance  deposition  of  coloured  particles,  whether  solid  or 
liquid,  on  the  surface  of  the  crystal  during  the  process  of  forma- 
tion. They  must  therefore  belong  to  some  peculiar  crystalline 
form,  or  to  some  order  in  the  organic  world. 

The  mode  of  aggregation  just  described  has  obviously  a close 
resemblance  to  some  of  those  animal  structures  produced  by  con- 
tinuous gemmation,  as  for  instance  some  of  the  compound  Fora- 
minifera. 

But  the  agreement  between  the  objects  and  organic  bodies  is 
not  confined  to  form  and  other  structural  resemblances — it  extends 
to  the  changes  through  which  they  must  have  passed  before  they 
were  enclosed  in  the  substance  of  the  crystal.  Whatever  their  ori- 
ginal nature,  so  completely  have  they  become  impregnated  with  the 
inorganic  elements  of  the  crystal,  that  the  more  opaque  layers  are 
often  viewed  through  the  silicified  casts  of  their  successors.  Before, 
however,  their  condition  became  thus  permanently  fixed,  there  is 
evidence  of  continued  and  varied  change.  Specimens  of  amethyst 
contain  whole-layers  from  which  the  upper  or  globular  end  of  each 
object  has  entirely  disappeared,  and  their  interior  become  occupied 
with  silica  so  transparent  that  the  delicate  structural  features  of 
the  conical  extremity  can  be  equally  well  seen  when  viewed  on 
either  side  by  transmitted  light.  In  other  instances  nothing 
remains  except  portions  of  concentric  annuli. 

The  objects  that  retain  their  structural  features  most  entire  are 
opaque,  and  as  seen  in  a small  section  of  dichroite  appear  of  a 
brilliant  white  on  the  lower  side,  and  of  a somewhat  silvery  lustre 
on  the  upper.  The  same  section  also  exhibits  the  changes  on  the 
external  envelope,  including  its  partial  and  complete  removal.  In 
one  group  it  has  disappeared  from  the  one  side,  while  it  remains 
quite  entire  on  the  other,  producing  a well-marked  boundary  line, 
which  passes  over  many  of  the  individual  objects,  displaying  in 
striking  contrast  the  difference  between  the  outside  shell  and  the 
matter  of  the  interior.  Whenever  divested  of  this  covering,  as  is 
generally  the  case,  the  bodies  are  seen  to  be  in  groups  of  various 
colours,  namely,  red,  orange,  yellow,  browns  of  various  tints,  and 
dark  blue. 


of  Edinburgh,  Session  1872-73. 


55 


4.  Note  on  the  Zodiacal  Light.  By  George  Forbes,  Esq. 

A peculiarity  was  observed  about  the  vernal  equinox  in  1871 
in  the  shape  of  the  zodiacal  light,  which  deserves  to  be  recorded. 
The  appearance  resembled  a thin  cone  (such  as  is  usually  seen), 
extending  to  a great  height,  and  rising  out  of  a broad  low  cone 
situated  at  its  bj.se.  This  was  not  an  effect  of  sunlight,  for  it  was 
visible  hours  after  sunset.  It  was  not  peculiar  to  any  time  or 
place,  for  it  was  seen  constantly  in  all  parts  of  the  south  of  Europe, 
viz.,  in  the  Bay  of  Biscay,  all  along  the  Mediterranean,  in  Malta, 
and  in  Sicily.  It  seems  not  unlikely  that  there  are  periodic 
changes  in  the  appearance  of  the  zodiacal  light.  Hence  it  is  well 
to  mention  any  such  peculiarity.  I have  also  to  confirm  what  has 
so  often  been  stated  by  other  observers,  that  the  direction  of  the 
axis  of  the  cone  is  not  always  in  the  direction  of  the  ecliptic,  but 
changes  its  direction  from  night  to  night. 

Monday,  11th  February  1873. 

Sir  ROBERT  CHRISTISON,  Bart.,  President, 
in  the  Chair. 

The  following  Communications  were  read  : — 

1.  Note  on  Angstrom’s  Method  for  the  Conductivity 


If  we  assume  the  excess  of  temperature  above  that  of  the  air,  v, 
to  be  the  same  throughout  a transverse  section  of  the  bar,  the 
equation  for  the  flux  of  heat  is — 


where  cp  is  the  water  equivalent  of  unit  volume  of  the  bar,  h its 
thermal  conductivity,  a its  side,  and  hv  the  quantity  of  heat  lost  by 
radiation  and  convection  from  unit  surface  of  the  bar  per  unit  of 
time,  when  the  excess  of  temperature  is  v. 


of  Bars.  By  Professor  Tait. 


VOL.  VIII. 


56 


Proceedings  of  the  Royal  Society 


Angstrom  writes  this  in  the  form — 


dv 

dt 


assuming  the  conductivity  to  be  unaffected  by  temperature,  so  that 
it  is  necessary  that  the  range  of  temperature  in  his  experiments 
be  small.  As  the  method  consists  essentially  in  so  applying  the 
heat  as  to  bring  the  bar  to  a periodic  state  of  temperature  at  each 
point,  the  solution  must  be  of  the  form — 

v=Y  + cos  (»  ^ - q„x + pj , 

where  T is  the  period,  and  V is  the  mean  temperature  or  non- 
periodic part  of  the  solution.  Substituting  in  the  equation,  we 
have — 

d2Y 

0 = Kjf-RV, 


~ (ji  — — ) 

0 = K(rf-22)-H. 

The  second  of  these  is  equivalent  to  Angstrom’s  exceedingly  simple 
expression  for  K in  terms  of  the  experimental  data.  Angstrom, 
however,  goes  farther  than  this,  for  instead  of  the  formula  for  v 
just  given,  he  uses  a more  restricted  one,  which  assigns  very  simple 
forms  for  the  quantities  jpw,  qn,  viz., — 

Vn^gjn,  qn  = g'Jnf 

where  g and  gf  are  absolute  constants,  depending  on  K,  H,  T alone. 
If  this  were  admissible,  it  seems  that  we  should  have  not  only, 
with  Angstrom, 


but  also  the  impossible  relation, 

0 = Kn  (g2  - g'2)  - H , 


* There  are  several  serious  misprints,  both  in  the  original  {Pogg.  1862)  and  in 
the  English  translation  (Phil.  Mag.  1863,  I.)  In  fact,  in  the  expression  for  v, 
V x appears  instead  of  x , alike  in  the  exponential  and  in  the  argument  of  the 
cosine. 


of  Edinburgh , Session  1872-73.  57 

where  all  the  quantities  are  constants  except  n,  which  may  be  any 
positive  integer. 

It  is  obvious  that,  as  the  difference  of  the  squares  of  pn,  qn , is 
constant,  while  their  product  varies  as  n , their  values  will  ulti- 
mately be  equal  for  very  great  values  of  n.  We  may  therefore 
assume,  as  an  approximation,  for  large  values  of  n — - 

Pn~-  \/ + 2»=\/ 

where  the  square  of  e is  negligible.  This  satisfies  the  first  of  our 
conditions,  and  the  second  gives 

HT 

e - 47m  ' 

This  remark  does  not,  of  course,  affect  Angstrom’s  deduction  of 
the  conductivity  from  the  term  of  full  period  ; but  it  must  materially 
affect  the  others,  and  thus  it  is  certainly  remarkable  how  glosely 
the  results  he  has  obtained  from  the  second  and  third  harmonic 
terms  agree  with  these  simple  forms. 

I have  not  as  yet  managed  to  control  by  this  process  my  results 
deduced  by  Forbes’s  method  {Trans.  R.S.E.),  though  I hope  soon 
to  do  so  The  difficulties  are  of  two  kinds:  ls£,  in  the  strictly 
periodic  application  of  very  hot  sources,  without  a great  range ; 
2d,  in  the  procuring  of  thermometers  which  will  give  with  great 
accuracy  small  differences  at  very  high  temperatures.  In  the 
meantime,  with  the  assistance  of  several  of  my  laboratory  students, 
especially  Messrs  G-reig  and  M‘Leish,  I have  studied  the  periodic 
state  of  temperature  in  bars  of  copper  (of  two  very  different  kinds), 
iron,  and  German  silver,  produced  by  applying  for  fifteen  minutes 
at  a time,  and  with  fifteen  minute  intervals,  a powerful  Bunsen 
burner  to  one  end.  The  ranges  of  temperature  thus  produced  are 
so  great  that  the  differential  equation  assumed  above  can  hardly 
be  regarded  as  even  a rough  approximation  to  the  law  of  the 
phenomenon.  Still,  the  results  possess  considerable  interest, 
especially  in  the  contrast  between  the  various  substances;  indicating 
the  great  differences  not  merely  in  conducting  power,  but  also  in 
its  rate  of  change  with  temperature  The  bars  employed  were  all 
1^-inch  square,  and  the  thermometers  were  inserted  at  3-inch 
intervals. 


td  t> 


58 


Proceedings  of  the  Royal  Society 

Copper — C. 

High  Temperature . 


I. 

100  + 
4-3 
29-1 
58*6 
78-7 
91-8 
68- 


40  + 


Bi  = 


A3— 

b3= 


II. 

100  + 
1-55 
7'2 
26-9 
43- 
55 -5 
51-4 


III. 

90  + 

7-8 

5-3 

16* 

28-5 

38-8 

41-6 


IV. 

80  + 
11-6 
6-6 
10-7 
18-6 
26-8 
32-1 


41- 

32-6 

31-7 

28-5 

21*2 

16-7 

20-2 

21-4 

A0=  149-087 

A'0=  129-33 

A 0 

= 113-737 

A'"0  — 99-537 

A1=- 38-916  ’ 

A'1=-  25-95 

A'7! 

= -15-634 

A'"^  - 7-813 

B1  = 7-688 

B'1=-  4-589 

= - 8-874 

B"\=  - 9-453 

= 39-668 

a\  = 26-3524 

«"i 

= 17-977 

cc"\  = 12-263 

=168°'83 

0'i  = 190° -02 

A 

= 209°-57 

&"1  =230° -42 

A,=  - 0-875 
Bs=-  0-7 

A'2r=-  0-612 
B'a  = - 0-275 

= 1-5052 

A0X  = 21° -19 

ec2  = 1-12 

02  = 218°'65 

a'2  = 0'68 

0'2  = 240°-12 

«i 

a i 

= 1-4658 

£(Z\  = 19°‘55 

A3^-  4-834 
B3=-  1112 

A'3=-  1*025 
B'3=-  1-74 

a i 

°LA 

- = 1-4659 

A (Z\  = 20°-85 

a3  = 4-96 

«r3  — 2 "02 

a'"] 

L 

03  = 192°-95 

0'3  = 239° -49 

a 3 

= 2-455 

a 03  = 46° '44 

40  + 


Copper — C. 
Low  Temperature. 

II.  III. 

40  + 


IY. 


40  + 


32-4 

21- 

12-15 

5- 

27- 

20-6 

13-9 

7-1 

18-7 

15-7 

11-45 

6-65 

12-5 

10-8 

8- 

4-5 

7'55 

6-8 

5- 

2-4 

13-55 

7-3 

3-65 

•6 

22-5 

12-9 

6-5 

1-35 

29- 

18-1 

10-05 

3*7 

60-4 

A'0  = 54-25 

A"o 

= 48-83 

A 0_ 

43-91 

11-507 

A\=  7-1915 

A\ 

= 3-9618 

A"\  = 

: 1-6576 

- 1-489 

B\=  1-7606 

b"i 

= 2-687 

B'\  = 

. 2-6154 

11-603 

«!  = 7-4038 

<*"  i 

= 4787 

*"i  = 

: 3-097 

352°*63 

0'i  = 373° -75 
A'2=  - *2 

= 394°-14 

= 

; 417°-63 

- -3125 

- -2375 

B'a  = - -25 

°h 

= 1-5671 

= 21°-12 

•3925 

a 2 = -335 

<x1 

217°-24 

0'2  = 231°-34 

Or.  i 

= 1-5466 

= 20°-39 

1 

•918. 

A'Jj  - -09156 

*"l 

•4108 

B'3  = -3606 

= 1-5459 

A0"i 

= 23°-49 

1- 

a 3 =z  *372 

k"- 

L 

; 384°-10 

03  = 464° -25 

h 2-688 

^3 

© 

00 

II 

59 


of  Edinburgh,  Session  1872-73. 

Copper — Crown. 


High  Temperature. 


I. 

11. 

III. 

iy. 

100  + 

100  + 

80  + 

80  + 

64-1 

55-5 

53-5 

37*8 

36-2 

34-4 

39-4 

30-2 

16-6 

17'7 

25-7 

19-8 

2-2 

4- 

14-2 

10-2 

32* 

15- 

15-3 

6-6 

60' 

36-2 

29-3 

14-6 

791 

53-1 

43' 

24-6 

92'6 

651 

54- 

33-6 

> 

11 

00 

Cn 

A'0=  135-285 

A"0  = 114-3 

A'"0  = 102-15 

AM  19-798 

A\  = 20-696 

A"XJ  18-371 

A"\  = 14-694 

B1  = -35-8127 

B'1=  -20-05 

B\=-  9-5398 

B,/,1=  - 2-58 

= 40-9152 

*\'=  28-8153 

«"x  = 20-7006 

*'"!  = 14-9187 

0X  = 298° -94 

0'x  = 315°-91 

d\  =3  32° -56 

0"x  = 350° -05 

a2=  -i 

A'9=  - '075. 

B2  = '35 

B'2  = -375 

= 1-42 

A0X  = 16°-97 

«2  = -47 

«'2  = -382 

«i 

d,  = 74°-05 

0'a  = 101°-57 

4 = 1-392 

A (i\  = 16° -65 

A:H-  3-748 

A'3=-  -358 

« x 

B3  = - 4-563 

B'3=-  2-27 

= 1-3875 

A0"x  = 17° -49 

«3  = 5-905 

«3  = 2-298 

a 1 

03  = 230° -65 

0'8  = 261° -48 

- 2-455 

a 3 

a/33  = 30°-83 

Copper- 

— Crown. 

Loir  Temperature. 

I. 

IT. 

III. 

IV. 

40  + 

30  + 

30  + 

30  + 

•1 

9-6 

8-2 

7- 

7-2 

12- 

8-6 

5-9 

14-4 

17-4 

12-1 

8-45 

19-7 

21-9 

15-6 

11-2 

23-6 

25-4 

18-65 

13-65 

16-9 

23- 

18-7 

13-7 

9-65 

17*7 

15- 

11-45 

4- 

13- 

11-1 

8-65 

A0=  51-94 

A'0  = 47-5 

A"0  = 43-49 

© 

Tin 

II 

<1 

A1=- 10-365 

A\  = -7*4678 

A"1=  -5*1934 

A#,/1=  -3-492 

Bx  = 2-248 

B'1=-  -42123 

B^m  1-715 

B//,1=  - 1-678 

«!  = 10-606 

«i  = 7-5856 

«"x  = 5-4692 

A I 3-874 

0i  - 167°-76 

0'x  =183° -22 

0"x  - 198°-27 

0"'x  = 205° -6  6 

A2=  - -0875 

A'a=-  -025 

b2=  -i 

B'2  = - -025 

% = 1-398 

A0X  = 15°-  46 

«2  = -132 

«2  = -035 

« i 

02  = 131°‘19 

0'2  =135°-0 

-i-  - 1-387 

A0'x  = 15° -05 

A3=-  1-38 

A'3  = - -432 

« ! 

B3=  - -127 

B'3=-  -296 

= 1-412 

A0"x  = 7° -39 

«3  = 1 -39 

«3  = *523 

« i 

yS3  = 185° -25 

03  =21 4° -42 

= 2-663 

a/33  = 29° -17 

«3 

60  Proceedings  of  the  Royal  Society 


Iron. 


1. 

II. 

III. 

IV. 

130  + 

110  + 

80  + 

70  + 

16-2 

6-6 

10- 

2-6 

35-1 

9-7 

7-9 

•9 

52-3 

17- 

9-3 

•1 

65-65 

24-5 

12-3 

•7 

62- 

29-9 

15-85 

2-1 

41-5 

28-1 

17-7 

3-6 

25- 

21- 

16-9 

4-1 

8-2 

12-5 

13-85 

3-7 

A0  = 168-24 

A0=  128-66 

A0=  92-95 

A0=  72-225 

Ax=-  22-737 

A1=- 11-1989 

A1=-  2-921 

A,  = -178 

B,  = 15-85 

Bx=  - 2-1312 

Bx  = =3-906 

Bx  = - 2-007 

= 27-7161 

*\  = 11-49 

*\=  4-8773 

*"\=  2-015 

/3X,=  145°-12 

= 190°-77 

fh\  = 233° -20 

A,/,1=  275°' "07 

A2  = -225 

A2=  - -375 

B,=  -68 

B2=  '2 

^ = 2-413 

a/5x  = 45°-65 

«a  = '716 

«'8=  -425 

“i 

|S2  = 7l°-69 

0'2  = 151° -93 

^ - 2-335 

A/^x  = 42  "43 

A3  = - -163 

A3=  - -451 

a l 

> 

"G3 

II 

00 

*<T 

B3  = 2-2 

Bo=-  -1314 

^ = 2-421 

a 3=  2-21 

1-47 

a l 

03=  94°-24 

196° -24 

German  Silver. 

I. 

II. 

III. 

1Y. 

120  + 

100  + 

70  + 

79.4 

39-1 

13-8 

60- 

53-5 

34-6 

16-4 

59- 

29-6 

25-5 

15-45 

57-3 

10-2 

14-5 

11-9 

55-7 

20-7 

6-5 

7-1 

55-15 

48-5 

9-5 

4-1 

56-05 

73-1 

20- 

4-8 

57-65 

91-65 

32- 

8-4 

59-3 

A0=  170-83 

A0=  122-71 

A0=  80-24 

A0  = 

57-52 

Ax=  29-957 

Ax  = 15-6806 

AXJ  3-2304 

Ax  — 

2-37 

Bx=-  24-39 

Bx  = 2-7185 

Bx  = 5-4555 

Bj  = 

'2024 

«x  = 38-63 

= 15-915 

6-340 

/A  __ 

a i — 

: 2-378 

j3x  = 320° -85 

=368° -84 

d\=  419° -37 

= 475°-12 

A2=  - -65 

a — .nos 

-£*-2 — \j  ciO 

B2=  -0375 

B2=-  -6 

«2  = -651 

«'2  = -6 

=4.  = 2-427 

A/3i 

= 48° 

p>.2  = l76°-7 

/3 'a  = 358° ‘62 

«i 

41  = 2-510 

A/3'i 

= 50°-53 

A3  = - -607 

A3—  -62 

« x 

Bo=  - 2-64 

B3=  - -0315 

" 

«3'=  2-708 

«'3  = -62 

= 2-665 

A/3"i 

= 55°*75 

j83  = 256°-75 

iS'3  = 357°-1 

61 


of  Edinburgh,  Session  1872-73. 

The  thermometers  were  read  once  a minute  when  the  periodic 
state  was  arrived  at,  the  corresponding  curves  were  traced ; and 
from  the  curves  so  drawn,  eight  values  of  the  temperature  were 
deduced  for  successive  intervals  of  three  and  three-quarter  minutes. 
It  was  easy  from  these  to  calculate  the  coefficients  of  the  harmonic 
terms  up  to  the  fourth  inclusive,  in  the  following  expression — 

v = A0  + Ax  cos  ^ t + cos  2 ~ t + . . . 

+ Bx  sin  t + B2  sin  2 ^ t + . . . . 

From  these  again  were  calculated  sets  of  values  of  a and  (3  by  the 
formulae 

a = J A2  + B2,  tan  /3  = • 

In  the  preceding  tables  the  dashes  refer  to  the  position  on  the  bar, 
the  suffixes  to  the  order  of  the  harmonic.  It  will  he  seen  that  the 
co-efficients  of  the  even  harmonics  are  too  small  to  give  any  trust- 
worthy results. 

As  the  thermometers  were  read  successively  by  one  observer,  the 
whole  process  occupying  twenty  seconds  or  g1^  of  a period,  the 
values  of  the  phase  must  be  diminished  by  0°,  1°,  2°,  3°,  respectively, 
i.e.,  the  differences  of  phase  must  each  be  diminished  by  1°. 


62 


Proceedings  of  the  Royal  Society 


2.  On  the  Thermal  Conductivity  of  Ice,  and  a new  Method 
of  Determining  the  Conductivity  of  Different  Substances. 
By  Professor  George  Forbes. 

The  value  of  the  coefficient  of  conductivity  for  ice  is  an  impor- 
tant desideratum  in  several  branches  of  physics;  and  it  derives 
additional  importance  from  an  application,  explained  in  the  second 
part  of  this  communication,  to  the  determination  of  the  thermal 
conductivity  of  different  substances  in  absolute  measure.  The 
brilliant  researches  of  Neumann,*  and  some  ingenious  experiments 
by  M.  Lucien  De  La  Bive,t  afford  us  at  present  the  only  two  deter- 
minations that  we  possess  of  this  important  quantity.  The  value 
found  by  Neumann  is  0T14,  while  De  La  Bive  makes  it  0T38. 
The  discrepancy  justifies  the  publication  of  experiments  on  a some- 
what large  scale,  which  gives  us  a close  approximation  to  the  truth. 

Sir  William  Thomson  suggested  the  method  of  imitating  the 
freezing  of  a lake  by  means  of  a freezing  mixture,  and  to  deduce 
the  conductivity  from  measures  of  the  thickness  of  the  ice  formed 
in  a definite  time.  In  order  to  carry  out  this  idea,  I ordered  an 
apparatus  to  be  constructed  by  means  of  which  a disc  of  ice  could 
be  formed  twelve  inches  in  diameter  by  a freezing  mixture  placed 
above  a vessel  of  water  kept  constantly  at  0°  0.  A means  was 
devised  for  measuring  the  thickness  of  ice  formed  at  successive 
intervals  of  time.  The  freezing  mixture  was  drained  constantly 
during  the  course  of  each  experiment  by  means  of  a syphon. 
Temperature  was  read  frequently  at  the  base  of  the  vessel  in  which 
it  was  contained.  It  was  found  possible  to  read  the  thickness  of 
ice  formed  to  within  ^-th  of  an  inch.  The  experiments  lasted  from 
four  or  five  hours  to  twenty-one  hours,  a watch  being  kept  continually 
on  the  drainage  and  temperature  of  the  mixture  for  the  first  six  or 
eight  hours  in  experiments  of  long  duration.  The  ice  formed  was 
quite  uniform,  very  clear,  and  when  cloven  by  planes  perpendicular 
to  the  plane  of  freezing,  split  easily,  showing  the  crystalline  struc- 
ture with  great  clearness. 

Six  whole  days  of  frosty  weather  were  employed  in  perfecting  and 
completing  the  series  of  observations,  during  which  time  seventy-two 
readings  were  taken,  capable  of  giving  a value  for  the  conductivity ; 

* Phil.  Mag.  1863.  t Soc.  de  Ph.  d’Hist.  Nat.  de  Geneve,  1864. 


63 


of  Edinburgh,  Session  1872-73. 

but  the  early  determinations  were  rejected  for  obvious  reasons,  and 
the  ultimate  determination  was  made  from  a mean  of  fourteen 
readings,  the  experiments  having  been  performed  in  this  case  with 
extraordinary  care,  and  with  all  the  experience  derived  from 
previous  trials. 

Let  the  heat  required  to  raise  1 gramme  of  water  1°  C.  be 
taken  as  our  unit  of  heat.  Assuming  that  in  the  formation  of  the 
ice  a statical  state  of  temperature  has  been  reached,  we  have 


x 


when  F = the  flux  of  heat,  h = the  coefficient  of  conductivity, 
SO  = — (the  temperature  of  the  freezing  mixture), 
x = the  thickness  of  ice. 

Jc  is  assumed  to  be  the  quantity  of  heat  which  crosses  an  area  of  ice 
1 square  centimetre  section  in  1 minute,  the  thickness  of  ice  being 
1 centimetre,  and  the  difference  of  temperature  of  the  two  sides  of 
the  ice  being  1°  0. 


But  F = the  quantity  of  water  raised  1°  Cent.,  in  1 minute, 
over  a surface  of  1 sq.  centimetre. 


= (volume  of  ice  formed  in  centimetres)  x (latent 
heat  of  water)  x (specific  gravity  of  ice). 


dt 


S.L. 


S.L.  • ~ 

n dt 

kse.t  = s.l f 


Employing  this  formula  in  the  series  of  experiments  alluded  to 
above  as  being  worthy  of  the  greatest  confidence,  fourteen  values 
of  h were  found  corresponding  to  different  values  of  x.  Now,  for 
small  values  of  x an  error  in  the  value  of  x will  introduce  an  error 
into  the  value  of  h greater  than  for  large  values  of  x.  The  value 


VOL.  VIII. 


64 


Proceedings  of  the  Royal  Society 

of  an  observation  is  almost  exactly  proportional  to  x.  After  giving 
to  each  result  a weight  proportional  to  x,  the  mean  thus  obtained 
was 

k = 0-134. 

This  is  given  in  terms  of  the  units  mentioned  above,  to  which  also 
Neumann’s  and  De  La  Rive’s  results  have  been  reduced.  Other 
experiments  confirmed  this  result  when  reduced  in  the  same 
manner. 

In  the  course  of  these  experiments  some  facts  were  noted,  which, 
though  not  belonging  exactly  to  the  subject  of  this  communication, 
are  yet  worthy  of  being  recorded. 

1 st,  A number  of  measurements  were  made  in  the  temperature  of 
salt  and  fresh  snow,  mixed  in  different  proportions,  with  the 
following  results  : — 


4 parts  (by  weight)  of  salt  + 1 

part  of  snow  gives  - 20°*3  C. 

2 „ 

>> 

„ + 1 

„ - 21-1 

1 „ 

)> 

» +1 

>j  >> 

„ - 21-4 

1 

» 

>>  +2 

>>  >> 

„ - 21-66 

1 

>» 

„ -f  3 

„ - 21-72 

1 „ 

» T 

» + 4 

>> 

„ - 21-4 

2d,  The  blocks  of  ice  formed  were  frozen  in  a cylinder,  with  air 
above  and  water  below.  These  blocks  were  cut  out  by  means  of  a 
chisel  and  hammer.  In  spite  of  the  great  force  used,  there  was  not 
the  slightest  tendency  in  the  ice  to  split  when  thus  compressed  by 
the  walls  of  the  containing  vessel,  although  the  finest  point  split 
the  ice  with  great  ease  when  the  block  had  been  cut  out. 

Having  completed  the  investigation  with  respect  to  ice, it  occurred 
to  me  to  extend  the  same  process  by  means  of  a slight  modification 
to  the  conductivity  of  other  substances.  The  method  employed  was 
as  follows  : — A tin  canister  of  about  3 inches  diameter  was  filled 
with  a freezing  mixture  whose  temperature  was  frequently  read. 
This  was  placed  above  the  substance  to  be  examined,  which  itself 
was  laid  in  a flat  tin  dish  resting  on  supports  in  water  cooled  to  0° 
cent.  If  the  substance  examined  were  a powder  or  soft  material 
like  cotton  wool,  it  was  made  to  rise  to  the  level  of  two  pieces  of 
glass  laid  on  the  flat  dish.  So  soon  as  ice  began  to  be  formed, 
it  was  considered  that  the  statical  state  of  temperature  was 


65 


of  Edinburgh , Session  1872-73. 


reached ; accordingly  the  ice  was  then  scraped  off  from  the 
bottom  of  the  flat  dish,  and  the  time  noted.  An  experiment 
usually  lasted  about  one  hour.  The  thickness  of  the  substance 
was  measured  and  also  that  of  the  ice  formed. 

Let  01  be  the  temperature  of  the  ice-cold  water,  0o  that  of  the 
freezing  mixture,  and  0 that  of  the  boundary  between  the  substance 
examined  and  the  ice  formed. 


Let  x = the  thickness  of  ice  formed, 

a = „ substance  examined, 

h = conductivity  of  ice, 

,,  the  other  substance. 


Then  the  flux  of  heat  being  F, 


F = k a = k 
a 


0,-0 

x 


0,  - go S0_ 

a x ~ a x 

k + \ l + k. 


Also,  adopting  the  same  notation  as  before, 


F = — ■ S.L. 
dt 


. SO  dx 
a x ~ dt 
ic  + hx 


tSO  __  a 

sx. = ix  + w, 


k = 


ax 

tSO  x?_ 

SX.  “ 2 A 


The  last  term  in  the  denominator  is  always  small  for  a non- 
conductor, and  if  ever  it  becomes  large,  we  may  be  sure  that  this 
mode  of  experimenting  is  not  available,  since  the  temperature  will  , 
not  be  in  a permanent  state. 

In  examining  solid  bodies,  it  is  well  to  immerse  the  solid  body 
itself  in  the  water.  Moreover,  in  this  case  I employed  a convenient 
vessel  to  contain  the  freezing  mixture,  consisting  of  a funnel-shaped 


66 


Proceedings  of  the  Royal  Society 

glass  vessel,  4 inches  diameter  at  the  top  and  3 inches  at  the 
bottom,  and  being  open  at  the  two  ends;  its  narrow  end  was 
closed  by  a tightly-stretched  membrane,  thus  securing  good 
contact. 

In  this  way  a large  number  of  bodies  was  examined,  with  follow- 
ing results  : — 


Ice,  along  ax.  . = 

134 

Kamptulikon  . 

•00660 

Ice,  perp.  to  ax.  = 

128 

Vulcanised  India-rubber 

•00534 

Black  marble  . 

106 

Horn 

•00522 

White  marble  . 

0691 

Beeswax  . 

•00522 

Slate 

0486 

Felt 

•00522 

Snow 

0432 

Vulcanite 

•00500 

Cork 

0430 

Haircloth 

*00241 

Glass  . 

0300 

Cotton  wool  (divided) 

•00260 

Pasteboard 

0272 

„ (pressed) 

•00201 

Carbon 

0243 

Flannel  . 

•00213 

Roofing  felt 

0201 

Coarse  linen 

•00179 

Firwood  (parallel  to  fibre) 

0180 

Quartz,  along  axis  . 

•0553 

„ (across  fibre  and 

99 

•0745 

along  the  radius) 

00529 

99  99 

•0340 

Boiler  cement  . 

! ) „ n flC 

00975 

99  99 

•0498 

raramn 

00843 

Sand  (very  fine) 

00788 

„ Perpendicular 

•240 

Sawdust  . 

00736 

•265 

With  regard  to  some  of  these  substances,  I may  say  that  the 
white  marble  comes  from  Italy,  though  I know  nothing  more 
about  it. 

The  slate  is  that  commonly  used  for  roofing. 

The  snow  was  frozen,  and  in  consequence  did  not  compress  very 
evenly. 

The  cork  was  cut  so  that  the  conduction  was  along  the  fibre. 

The  pasteboard  was  the  thick  brown  material  often  called  mill- 
board. 

The  carbon  was  kindly  lent  me  by  Professor  Tait. 

The  roofing  felt  was  that  commonly  known  as  asphaite  roofing 
felt. 

The  firwood  was  thoroughly  seasoned. 

The  boiler  cement  is  that  supplied  by  Messrs  Fleming,  23  St 
Vincent  Place,  Glasgow,  and  was  kindly  given  to  me  along  with 
several  other  materials. 


67 


of  Edinburgh , Session  1872-73. 

The  paraffin  is  that  kind  which  has  its  boiling  point  at  45°  C. 

The  sand  was  very  fine,  nearly  pure  silica,  being  that  used  for 
sand-baths. 

The  sawdust  was  that  of  common  firwood,  and  was  compressed. 

The  flannel  was  of  the  very  coarse  kind  usually  known  as  wash- 
ing cloth. 

The  coarse  linen  was  of  the  coarsest  possible  texture. 

The  quartz  used  for  conduction  along  the  axis  was  very  thin. 
The  piece  used  for  conduction  perpendicular  to  the  axis  was  a large 
piece  in  the  form  of  a hexagonal  prism. 

With  regard  to  the  numbers,  I must  say,  in  the  first  place,  that 
they  differ  considerably  from  those  of  Peclet  in  nearly  all  the  cases 
that  admit  of  comparison.  Reducing  his  numbers  to  the  units 
employed  above,  we  find — 


Substance. 

Forbes. 

Peclet. 

White  marble 

•0691 

•463 

Glass 

•0300 

T25 

Carbon  . 

•0243 

•827 

Caoutchouc  . 

•00534 

•028 

Sawdust 

•00735 

•Oil 

Cotton  wool  . 

•00530 

•00666 

It  appears  that  there  is  a constant  error  due  to  the  difference  of 

methods.  But  it  may  be  well 

to  remark  that  Peclet  has  found 

very  different  results  at  different  times,  as  may  be  seen  at  once  by 
comparing  the  tables  given  at  pages  355  and  481  of  his  “ Traite  de 
la  Chaleur,”  1843,  vol.  ii .,  and  at  page  406  of  the  second  vol.  of  the 
same  work  as  published  in  1861.  My  experiments  have  at  times 
varied,  and  I have  given  all  the  values  I obtained  for  quartz,  to 
show  how  injudicious  it  is  to  use  a thin  piece  of  a substance  that  is 
not  a very  bad  conductor.  The  surface  resistance  is  in  that  case 
too  great  to  give  good  results.  I intend  to  make  further  experi- 
ments on  the  conduction  along  the  axis  of  quartz,  which,  along 
with  a continuation  of  this  investigation,  I hope  to  have  the 
honour  of  laying  before  the  Society  at  a future  time. 

But  these  remarks  do  not  apply  to  really  bad  conductors,  and  I 
have  every  reason  to  believe  that  the  numbers  given  above  do  not 
differ  widely  from  the  truth. 


68 


Proceedings  of  the  Boyal  Society 

The  experiments  on  firwood  confirm  what  we  know  about  the 
difference  in  conduction  along  the  different  axes. 

The  experiments  on  cotton  wool  by  no  means  refute  what  Peclet 
has  found,  viz.,  that  the  conduction  is  the  same  to  whatever  degree 
the  wool  is  compressed,  thus  leading  to  the  most  interesting  con- 
clusion, that  the  conductivity  of  the  fibre  is  the  same  as  that  of  air, 
and  that  the  conductivity  of  air  is  the  number  given  above.  The 
very  low  conductivity  of  many  of  these  substances  are  proverbial ; 
more  especially  flax,  which  we  find  at  the  bottom  of  the  list.  Horns 
and  hoofs  have  also  a bad  name.  The  makers  of  boiler  cement  are 
well  aware  that  they  could  have  worse  conductors,  but  they  must 
consider  the  expense. 

In  all  these  experiments  I was  much  assisted  by  Mr  James 
Gfuthrie,  one  of  my  laboratory  students. 

3.  On  the  Formation  of  Coal,  and  on  the  Changes  produced 
in  the  Composition  of  the  Strata  by  the  Solvent  Action 
of  Water  slowly  percolating  through  the  Earth’s  Crust 
during  long  periods  of  Geological  Time.  By  R W. 
Thomson,  C.E.,  F.RS.E. 

( Abstract .) 

The  author  commences  by  adverting  to  a very  generally  recog- 
nised geological  difficulty — -viz.,  that  of  accounting  for  the  dis- 
appearance of  the  mineral  from  the  carbonaceous  matter  in  the 
processes  which  have  resulted  in  the  formation  of  coal-beds  as  we 
now  find  them.  Coal-beds  have  undoubtedly  their  origin  from 
decaying  vegetable  matter;  and  the  deposition  is  unquestionably 
traceable  to  at  least  three  different  sources — viz.,  the  carrying 
down  by  rivers  of  drift  wood,  and  its  deposition  in  deltas  and 
estuaries  at  their  mouths;  the  accumulations  of  dead  forest  trees, 
&c.,  falling  for  successive  generations  where  they  had  grown ; and 
the  growth  of  peat.  But  in  all  of  the  three  methods  it  is  clear 
that  the  vegetable  matter  must  have  been  mixed  up  to  a very 
large  extent  with  earthy  matter,  which  earthy  matter  has  since 
disappeared,  so  as  to  leave  carbonaceous  deposits  in  a com- 
parative state  of  purity.  The  explanation  of  this  disappearance 
has  hitherto  completely  baffled  geological  ingenuity,  and  the 


69 


of  Edinburgh,  Session  1872-73. 

author,  in  offering  the  present  solution  of  the  enigma,  ventures  to 
hope  that  he  has  successfully  grappled  with  the  difficulty.  Geolo- 
gists appear  hitherto  to  have  strangely  overlooked,  or  at  all  events 
very  much  underrated,  the  solvent  powers  of  water  in  effecting 
changes  on  strata  during,  inconceivably  long  periods  of  geological 
time,  at  great  depths,  and  consequently  under  greater  pressures 
and  higher  temperatures  than  are  obtainable  at  the  surface  of  the 
earth.  The  author  contends  that  a just  comprehension  of  the 
solvent  action  of  water,  slowly  percolating  through  the  strata 
during  vast  and  nameless  periods  of  time,  and  at  pressures  and 
temperatures  of  unknown  intensity,  will  furnish  the  key  to  the 
elimination  of  the  mineral  from  the  carbonaceous  matter  which 
now  constitutes  our  beds  of  coal.  If  carbon  be  not  actually  in- 
soluble, it  may  be  assumed  that  it  is  practically  so  in  relation  to 
any  known  chemical  action  and  as  compared  with  the  proportion- 
• ately  easy  solubility  of  the  mineral  ingredients,  for  the  extension 
of  which  the  present  explanation  is  offered.  Granting,  therefore, 
the  vast  difference  in  degree  of  solubility,  the  immensity  of  the 
time  since  deposition,  and  the  increased  pressure  and  temperatures, 
with  the  incessant  percolation  of  water  through  the  strata,  it  is 
impossible  to  conceive  any  other  result  than  the  gradual  washing 
out  of  the  soluble  from  the  insoluble  constituents  of  any  particular 
stratum.  The  different  ingredients  would  disappear  in  the  rotation 
of  their  degrees  of  solubility  ; and,  in  the  case  of  coal-beds,  the 
separation  and  carrying  away  of  the  mineral  or  soluble  ingredients 
in  solution  and  the  leaving  the  carbonaceous  or  insoluble  matter 
behind,  wrould  seem  to  be  simply  a question  of  time.  The  author 
touches  upon  several  collateral  features  connected  with  the  solvent 
action  of  water  percolating  through  the  strata,  such  as  the  deposi- 
tion of  chemically-dissolved  matter  in  other  strata  through  which 
the  water  has  to  pass  at  a lessened  temperature,  and  consequently 
with  a diminished  power  of  solution,  the  vast  supplies  of  shell- 
forming substances  constantly  being  carried  into  the  sea,  and  thus 
maintaining  a supply  sufficient  for  the  formation  of  myriads  of 
shells,  and  whole  islands  and  almost  continents  of  coral  reef;  and, 
in  conclusion,  he  submits  that  the  solution  now  offered,  besides 
doing  away  with  the  principal  difficulty,  will  contribute  to  the 
elucidation  of  many  other  obscure  points  in  geology. 


70 


Proceedings  of  the  Royal  Society 


4.  Note  on  Homocheiral  and  Heterocheiral  Similarity. 
By  Sir  William  Thomson. 


Monday,  3 d March  1873. 

The  Hon.  Lord  N EAVES,  Vice-President,  in  the  Chair. 
The  following  Communications  were  read  : — 

1.  On  the  Mud  Banks  of  Narrakal  and  Allippey,  two 
Natural  Harbours  of  Befuge  on  the  Malabar  Coast.  By 
George  Bobertson,  Esq.,  C.E. 

In  the  course  of  an  examination  of  the  harbours  and  river 
mouths  of  India,  which  I have  recently  been  making  for  the 
Government  of  that  country,  instructions  were  sent  me  to  examine 
the  backwater  communication  of  the  Malabar  coast,  with  special 
reference  to  the  possibility  of  taking  advantage  of  the  anchorage 
at  such  localities  as  Narrakal  and  Allippey,  and  opening  out  com- 
munications between  them  and  the  backwaters.  As  these  anchor- 
ages are  so  remarkable,  and  the  phenomena  connected  with  them 
are  probably  known  to  but  few  members  of  this  Society,  and  the 
places  themselves  perhaps  never  visited  by  any  member  present, 
I have  thought  a short  account  of  these  mud  harbours  of  refuge 
would  be  of  some  interest. 

And,  first,  for  a few  words  on  the  backwaters  of  Malabar.  These 
consist  of  a network  of  lakes,  river  mouths,  short  rivers,  and 
artificial  cuts  or  canals,  by  which  cargo  boats  can  travel,  with  but 
one  or  two  interruptions  (now  being  overcome),  from  Buddagherry 
(to  the  north  of  Calicut),  in  lat.  11°*35,  to  Trevandrum,  the  capital 
of  the  state  of  Travancore,  in  lat.  8°*29.  Eventually  the  system 
will  be  continued  almost  to  Cape  Comorin.  The  great  value  of 
this  internal  water  communication  is  best  shown  in  the  south-west 
monsoon,  when  communication  by  sea  is  suspended  for  several 
months. 

The  south-west  monsoon,  which  commences  early  in  June,  is  a 
great  bugbear  to  the  commerce  of  the  west  coast  of  India,  partly 


of  Edinburgh , Session  1872-73.  71 

because  there  are  few  harbours  which  can  easily  be  entered  in  it, 
and  ships  lying  out  at  sea  could  not  communicate  with  the  shore  ; 
and  partly  because  the  native  craft  are  so  ill  found  and  such 
rattle-traps  of  vessels,  that  they  would  go  to  the  bottom.  But  it  is 
simply  a long  continuance  of  tolerably  steady-blowing  strong  winds, 
with  torrents  of  rain,  such  as  we  do  not  have  in  this  country,  and 
not  the  least  formidable  to  properly-found  vessels  or  to  steamers. 
I have  been  at  sea  in  the  worst  burst  of  the  south-west  monsoon, 
and  never  felt  the  slightest  uneasiness,  much  less  serious  thought 
of  danger. 

The  cyclones  in  the  Bay  of  Bengal,  on  the  east  coast,  are  of 
course  very  different. 

. The  rain,  however,  in  the  south-west  monsoon  is  a serious  draw 
back  to  shipping  cargoes. 

I explored  about  200  miles  of  the  internal  water-communication, 
reporting  on  Calicut,  Beypore,  and  Cochin  harbours  for  the  Govern- 
ment of  India,  and  also  on  Quilon,  at  the  request  of  the  Maharajah 
of  Travancore,  and  the  Dewan,  Sir  Madava  Bow.  The  canals  in 
the  northern  position  have  only  2 feet  6 inches  of  water  as  a mini- 
mum, but  in  the  Travancore  state  they  are  all  intended  to  have 
4 feet.  1 advised  that  the  latter  depth  should  be  extended  to  the 
full  distance,  and  the  canals  in  various  places  straitened,  so  that 
the  whole  system  might  be  opened  up  for  small  steamers,  both  to 
carry  passengers  and  to  tow  cargo  boats. 

The  greater  part  of  the  distance  that  Col.  Farewell,  superintend- 
ing engineer,  South  Canara,  and  I travelled,  was  through  cocoa- 
nut  groves,  and  we  had  cabined  boats,  with  from  twelve  to 
twenty  rowers  each,  who  sang  fearful  choruses  almost  the  whole 
way. 

The  scenery  was  very  beautiful,  especially  near  Quilon,  but  the 
heat  often  very  great,  and  always  stifling.  Of  course,  when  we  had 
to  sleep  in  the  boat,  the  mosquitoes  were  very  troublesome. 

The  backwaters  run  parallel  to  the  coast,  and  at  a short  distance 
from  it,  at  times  swelling  out  into  lakes  of  varying  sizes,  the  largest 
being  at  Cochin,  where  the  backwater  is  almost  the  size  of  Loch 
Lomond.  There  are  many  mouths  into  the  sea;  some  being  shut  up 
during  the  dry  weather  by  the  bars  of  sand  which  the  surf  is  con- 
stantly throwing  across  any  opening  in  the  coast  line  ; others,  like 


VOL.  VIII. 


72  Proceedings  of  the  Royal  Society 

the  entrance  at  Cochin,  remaining  open  for  navigation  all  the  year 
round. 

At  Cochin  there  is  always  11  feet  of  water  at  low  water  on  the 
bar ; but  I hope  that  20  feet  will  be  attained  by  the  works  now 
projected,  which  will  make  Cochin  by  far  the  best  harbour  in  the 
south  of  India. 

The  two  mud  banks  I am  going  to  describe  are  most  valuable 
adjuncts  to  Cochin.  Narrakal  is  about  five  miles  to  the  north,  and 
Allippey  nearly  forty  miles  to  the  south. 

Allijppey  is  the  better  known  of  the  two,  and  I therefore  take  it 
first.  In  an  old  book  (I  believe  on  the  voyages  of  Captain  Cope) 
Allippey  is  mentioned  in  a way  which  proves  that  its  peculiarities 
and  advantages  have  been  long  known  and  appreciated.  For  this 
fact — and  indeed  for  almost  all  I know  of  the  mud  bank — I am 
indebted  to  information  obtained  from  Mr  Crawford,  the  com- 
mercial agent  for  the  state  of  Travancore,  a shrewd  Scotchman, 
who  resides  at  the  thriving  and  busy  town  of  Allippey,  and 
occupies  a position  of  great  responsibility.  The  bank  is  spoken 
of  in  that  book  as  “ Mud  Bay,”  and  described  as  one  of  the  most 
extraordinary  harbours  in  the  world. 

From  Hamilton’s  account  of  the  East  Indies,  in  Pinkerton’s 
collection  of  “ Voyages  and  Travels  ” (1673  to  1723),  it  is  thus 
spoken  of,  according  to  a report  by  Mr  Maltby,  the  resident  in 
1860 

“ Mud  Bay  is  a place  that,  I believe,  few  can  parallel  in  the 
world.  It  lies  on  the  shore  of  St  Andrea,  about  half  a league  out 
in  the  sea,  and  is  open  to  the  wide  ocean,  and  has  neither  island 
nor  bank  to  break  off  the  force  of  the  billows,  which  come  rolling 
with  great  violence  on  all  other  parts  of  the  coast  in  the  south-west 
monsoon,  but  on  the  bank  of  mud  lose  themselves  in  a moment ; 
and  ships  lie  on  it  as  secure  as  in  the  best  harbour,  without  motion 
or  disturbance.  It  reaches  about  a mile  along  shore,  and  has  shifted 
from  the  northward,  in  thirty  years,  about  three  miles.” 

There  is  some  discrepancy  in  the  statements  of  the  movements 
of  the  bank  in  former  times  as  to  whether  it  moved  from  north  to 
south  or  from  south  to  north  ; but  there  can  be  no  doubt  about  the 
last  movement,  since  it  has  taken  place  during  Mr  Crawford’s  resi- 
dence at  Allippey. 


73 


of  Edinburgh,  Session  1872-73. 

In  Lieutenant  Taylor’s  chart  of  1859,  the  bank  is  shown  off  the 
town  of  Allippey  in  lat.  9o,30.  But,  since  then,  it  has  moved  four 
miles  to  the  south,  where  it  was  when  I examined  the  place,  along 
with  Mr  Crawford,  in  March  1871.  A letter  from  that  gentleman 
in  1860  to  the  resident  at  Travancore  gives  the  following  account 
of  this  bank,  with  some  of  the  theories  which  have  been  started 
in  connection  with  its  properties : — 

“ Lieutenant  Taylor  attributes  the  smoothness  of  the  water  to 
the  soft  mud  at  the  bottom,  by  which,  when  i stirred  up  by  a heavy 
swell  from  seaward,  the  activity  of  the  waves  is  so  deadened  as  to 
render  the  shore-line  free  from  surf.’  I regret  never  having  met 
Lieutenant  Taylor. 

“ A number  of  years  ago  I brought  to  the  notice  of  G-eneral 
Cullen,  that  the  perfect  smoothness  of  the  water  in  the  roads,  and 
at  the  beach  at  Allippey,  was  attributable,  not  to  the  softness  of  the 
mud  at  the  bottom  so  much  as  to  the  fact  of  the  existence  of  a sub- 
terranean passage  or  stream,  or  a succession  of  them,  which,  com- 
municating with  some  of  the  rivers  inland  and  with  the  backwater, 
become  more  active  after  heavy  rains,  particularly  at  the  com- 
mencement of  the  monsoon,  than  in  the  dry  season,  in  carrying  off 
the  accumulating  water,  and  with  it  vast  quantities  of  soft  mud. 
General  Cullen,  the  resident,  sent  a quantity  of  piping  and  boring 
apparatus  in  order  to  test  the  existence,  or  otherwise,  of  what  I had 
urged.  Accordingly,  I sunk  pipes  about  700  yards  east  from  the 
beach,  and  at  between  50  and  60  feet  depth ; and,  after  going 
through  a crust  of  chocolate-coloured  sandstone,  or  a conglomerate 
mixture  of  that  and  lignite,  the  shafting  ran  suddenly  down  to  80 
feet ; fortunately,  it  had  been  attached  to  a piece  of  chain,  or  it 
would  have  been  lost  altogether.  Several  buckets  from  this  depth 
were  brought  up,  which  correspond  in  every  respect  with  that  thrown 
up  by  the  bubbles  as  they  burst  at  the  beach,  which  I shall  here 
attempt  to  describe  as  accurately  as  I can.  Due  west  of  the  flag- 
staff, and  for  several  miles  south,  but  not  north  of  that,  the  beach 
will,  after  or  during  these  rains,  suddenly  subside,  leaving  a long 
tract  of  fissure,  varying  from  40  to  100  or  120  yards  in  length  ; the 
subsidence  is  not  so  quick  at  first ; but,  when  the  cone  of  mud  once 
gets  above  the  water,  the  fall  is  as  much  as  5 feet  in  some  instances, 
when  the  cone  bursts,  throwing  up  immense  quantities  of  soft  soapy 


74  Proceedings  of  the  Eoyal  Society 

mud,  and  blue  mud  of  considerable  consistence,  in  the  form  of  boul- 
ders, with  fresh  water,  debris  of  vegetable  matter,  decayed,  and  in 
some  instances  green  and  fresh.  These  bubbles  are  not  confined 
to  the  seaboard,  but  are,  I am  inclined  to  think,  both  more  active 
and  numerous  in  the  bed  of  the  roads  with  the  flagstaff  bearing  from 
E.N.E.  to  the  south,  until  it  bears  N.E.  by  N.,  or  even  south  of 
that.  About  five  years  ago,  for  about  four  miles  down  the  coast, 
and  from  the  beach  out  to  sea  for  a mile  and  a half,  the  sea  was  no- 
thing but  liquid  mud,  the  fish  died,  and  as  these  cones  reared  their 
heads  above  the  surrounding  mud,  they  would  occasionally  turn 
over  a dead  porpoise  and  numerous  fish  ; the  boatmen  had  consider- 
able difficulty  in  urging  their  canoes  through  this  to  get  outside  of 
it ; the  beach  and  roads  presented  then  a singular  appearance ; no- 
thing to  be  seen  but  those  miniature  volcanoes,  some  silent,  others 
active ; perfect  stillness  of  all  around  the  ships  in  the  roads,  as  if 
in  some  dock,  with  a heavy  sea  breaking  in  seven  fathoms  outside. 

“ There  are  numerous  deep  holes,  some  of  them  I measured  in 
1852 ; one  in  particular,  just  at  the  end  of  this  canal,  had  as  much 
as  60  feet  in  depth ; these  holes  may,  or  may  not,  communicate 
directly  with  the  roads,  but  X think  it  will  be  found  that  the  prin- 
cipal source  of  active  communication  is  more  inland,  and  the  back- 
water perhaps  only  an  auxiliary.  About  three  miles  above  Ohen- 
ganoor,  in  the  river  of  that  name,  there  are  one  or  two  deep  “ Linns” 
which  I only  had  an  opportunity  of  visiting  twice ; the  first  time 
I had  not  the  means  of  ascertaining  the  depth,  the  next  I lost  both 
lead  and  line. 

“ The  depth  of  this  passage  is  not  so  great  as  you  approach  the 
beach,  as  noticed  above;  for,  while  extending  the  canal  from  the 
Timber  Depot  in  March  last,  about  200  yards  from  the  beach,  at  12 
feet  we  suddenly  and  unexpectedly  broke  through  the  substratum, 
when  a column,  fresh  water,  mud,  and  vegetable  debris,  and  about 
nine  inches  in  diameter,  spouted  up,  which,  when  left  alone,  gra- 
dually subsided  as  the  upper  stratum  of  sand  filled  in  round  the 
column  of  the  spring. 

“ I submit  the  above  information,  as  I feel  that  it  will  be  inte- 
resting, both  to  yourself  and  Government,  to  pursue  the  investiga- 
tion of  this  subject  more  efficiently.  I have  omitted  to  state  one 
important  particular, — that  is,  should  no  rain  fall,  as  has  been  the 


75 


of  Edinburgh,  Session  1872-73. 

case  this  year,  the  sea  in  the  roads  and  at  the  beach  is  not  nearly  so 
smooth ; up  to  this  time  we  have  had  none  of  the  mud  cones  burst- 
ing at  the  beach,  neither  in  the  roads,  as  the  waves  tumble  in  per- 
fectly clear;  there  was  a heavy  surf  from  the  26th  ultimo  to  9th 
instant,  but  never,  in  any  instance,  for  these  last  eleven  years,  has 
the  rain  held  off  so  long  as  in  this,  and  the  roads  and  beach  have 
always,  by  the  end  of  May,  been  perfectly  smooth.” 

Since  that  letter  was  written,  the  bank  has  left  Allippey,  and 
has  shifted  some  four  miles  down  the  coast,  which  considerably 
complicates  the  theories  put  forward.  The  oscillation  of  the  bank 
— for  it  is  said  by  some  to  have  previously  had  a northward  ten- 
dency— is  very  puzzling,  viewed  in  connection  with  any  supposed 
underground  communication  with  the  backwaters.  The  smooth- 
ness in  rough  weather  is  said  to  extend  out  to  about  the  six  fathom 
line.  This  is  a point  worth  noticing,  because,  unless  the  mud  sud- 
denly stops  there,  it  shows  the  extreme  limit  at  which  the  waves  on 
this  coast  have  any  effect  on  the  bottom,  even  when  that  is  com- 
posed of  very  fine  slushy  mud. 

Mr  Crawford  states  that  the  mud  cones  he  describes  take  place 
only  during  the  monsoon.  At  all  events,  I did  not  see  any  in  action 
during  my  visit.  He  told  me,  likewise,  that  during  the  monsoon 
there  is  fresh  water  on  the  Allippey  bank,  but  could  not  say  whether 
it  was  succeeded  by  salt  water  to  the  north  or  south.  This  would 
require  to  be  known,  to  make  the  existence  of  fresh  water  during 
the  rains  at  all  curious.  It  is  possible  that  the  fresh  water  may 
extend  all  the  way  to  Cochin  harbour  entrance,  and  owe  its  existence 
either  to  that  outlet  on  the  north,  or  to  some  other  outlet  to  the 
south. 

Towards  the  formation  of  any  theory  about  the  Allippey  bank, 
it  will  be  useful  to  note  that  Mr  Crawford  has  measured  the  level 
of  the  water  in  the  backwater  during  the  height  of  the  monsoon, 
and  found  it  to  be  3 feet  2 inches  above  the  sea-level.  This  gives  a 
hydrostatic  pressure  from  the  backwater  of  less  than  a pound  and  a 
half  on  the  square  inch.  The  backwater  is  about  two  and  a half 
miles  from  the  sea  at  Allippey. 

Mr  Crawford,  when  I saw  him,  had  an  idea  that  volcanic  action 
has  something  to  do  with  the  mud  cones  described  by  him,  but  was 
unable  to  overcome  the  difficulty  I suggested,  that  it  was  only 


76 


Proceedings  of  tlie  Poyal  Society 

regularly  at  one  time  of  the  year,  and  that  during  the  rainy  and 
windy  season,  that  the  mud  cones  appeared. 

There  is  a curious  circumstance  about  the  Allippey  bank,  which 
I give  also  on  Mr  Crawford’s  authority,  viz.,  that,  in  gales  of  wind, 
vessels  may  he  seen  lying  at  anchor  on  the  hank  with  their  bows 
pointed  in  various  directions,  as  if  influenced  by  eddying  currents 
in  the  sea  of  mud. 

The  weather  being  too  calm,  and  the  time  of  year  being  too 
early,  to  exhibit  the  full  virtues  of  the  bank,  I noticed  none  of  these 
wonders,  but  I saw  enough  to  show  that  there  was  some  extra- 
ordinary virtue  in  the  place.  We  got  into  the  boat  with  some 
difficulty  at  Allippey,  on  account  of  the  surf ; but,  at  the  place 
where  the  bank  now  is,  for  several  miles  there  was  not  only  no 
surf,  but  not  a ripple  at  the  water’s  edge,  and  we  stepped  on  to  the 
shore  from  the  boat  with  the  greatest  ease.  Looking  from  shore 
towards  the  sea  horizon,  one  saw  a crest  of  surf,  or,  more  properly 
speaking,  swell,  all  round  in  a horse- shoe  form,  and  reaching  out  to 
about  three  and  a half  miles  from  land,  enclosing  this  smooth 
pond, — the  swell  being  gradually  deadened  as  it  neared  shore,  till 
it  died  off  into  absolute  quiescence. 

I passed  Allippey  in  a P.  & 0.  steamer  last  autumn  during  the 
height  of  the  S.W.  monsoon ; but,  although  within  sight  of 
land,  we  were  too  far  off  to  notice  the  peculiarities  of  the  mud 
bank. 

The  Narrahal  bank,  at  present  five  miles  to  the  north  of  Cochin, 
has  been  known  for  long,  but  was  almost  forgotten  till  it  was  redis- 
covered (I  may  say)  by  Captain  Castor,  the  master-attendant  at 
Cochin  in  1861,  and  surveyed  by  him  in  1865.  Captain  Castor 
(who  is  a native  and  a very  intelligent  man)  is  now  master-attendr 
ant  at  Coconada,  but  was  ordered  to  meet  me  at  Cochin,  so  that  I 
had  the  advantage  of  his  presence  in  visiting  Narrakal.  Curiously 
enough,  he  is  now  statioued  at  the  only  place  I visited  in  India, 
which  approached  in  character  to  the  peculiarities  of  these  mud 
banks;  for,  at  Coconada,  there  is  a quantity  of  mud  in  the  bay, 
which  to  a considerable  extent  reduces  the  surf.  But  Coconada  is 
a regular  bay,  into  which  the  Gfodavery  river  discharges  its  mud ; 
whilst  the  banks  now  in  question  are  detached  spots  of  a peculiarly 


of  Edinburgh , Session  1872-73.  77 

greasy  mud,  moving  about  on  a straight  coast,  and  away  from  any 
river  mouth. 

In  some  of  the  records  of  the  late  Captain  Biden,  the  then  master- 
attendant  of  Madras,  is  to  be  found  the  following  remark  about 
Narrakal  (date  1841): — “ This  bank  is  situated  at  Pooryapooly  about 
nine  miles  to  the  north  of  Cochin  within  the  Cochin  Circar’s  terri- 
tories ; the  extent  of  it  is  about  six  miles,  and  the  soundings  from 
one  to  seven  fathoms.” 

But  there  is  a much  earlier  reference  to  Narrakal,  in  the  transla- 
tion of  an  old  work  by  a Dutch  navigator,  called  “ Yoyage  to  the 
Cape  of  Good  Hope,  Batavia,  Samarang,  Surat,  East  Indies,  Ac., 
in  the  year  1774  to  1778,”  book  iii.,  cap.  12. 

In  describing  Cochin,  he  says— “ The  coast  is  safe  and  clear 
everywhere  along  the  Company’s  Establishment,  except  at  the 
mouth  of  the  river  of  Cranganore  [about  twelve  miles  to  the  north 
of  Cochin].  South  of  the  above-mentioned  mouth  of  the  river  of 
Cranganore  there  is  a bay  formed  of  mud  banks,  the  banks  form- 
ing which  extend  to  fully  a league  out  to  sea,  and  into  which 
vessels  may  run  with  safety  during  the  bad  monsoon,  and  may  lie 
in  twenty  and  less  feet  of  water,  almost  without  anchors  or  cables, 
in  perfect  security  against  the  heavy  seas  which  then  roll  in  upon 
this  lee  shore,  as  they  break  their  force  upon  the  soft  mud  banks, 
and  within  them  nothing  but  a slight  motion  is  perceived.” 

A better  description  of  Narrakal  could  not  be  given  than  is  given 
by  this  writer  of  a century  ago,  except  that  the  action  of  the  mud 
extends  out  to  the  six  fathom  line,  and  that  the  bank  has  shifted 
south  to  within  five  miles  of  Cochin. 

I heard  nothing  about  mud  cones  in  connection  with  Narrakal ; — - 
either  there  were  none,  or  there  was  no  one  to  observe  them. 

I visited  Narrakal  in  the  pearl  fishery  steamer,  the  “Margaret 
Northcote,”  which  had  been  lent  to  me  for  the  cruise  round  Cape 
Comorin,  and  which  drew  only  five  feet  of  water,  so  that  we  were 
able  to  go  through  the  Paumben  Passage,  and  thus  save  the  voyage 
round  Ceylon.  I may  mention  that  this  last  autumn  I visited 
Paumben  again,  to  report  on  the  proposed  ship  canal  which  will 
shorten  the  voyage  from  Europe  and  Bombay  to  the  Bay  of  Bengal, 
by  three  and  a half  days  on  the  double  voyage.  The  day  we  visited 
Narrakal  there  was  a considerable  swell  on,  and  its  effects  were 


78 


Proceedings  of  the  Royal  Society 


very  marked  on  the  countenance  of  the  Prime  Minister  of  Cochin, 
who  had  ventured  on  the  sea,  probably  for  the  first  time.  In 
return  for  the  compliment,  he  turned  out  the  state  snake-boats  of 
the  Rajah  to  attend  us  next  day.  They  are  very  long  narrow- 
framed canoes,  each  with  some  fifty  rowers,  who  sit  with  their  legs 
dangling  over  each  side  of  the  boat  alternately ; and  they  go  at  a 
great  pace.  The  “ bucksheesh  ” for  so  many  men  came  to  be 
heavy  ! 

I sent  a diver  down  for  a specimen  of  the  mud  (which  I regret 
to  have  lost).  It  is  of  a peculiarly  greasy  nature,  dark  green  in 
colour,  and  sticky  ; a specimen  was  analysed  at  Madras  in  1861, 
and  was  found  to  contain — 

1.  Very  minute  angular  fragments  of  quartz,  the  largest  hardly 
visible  without  a lens ; this  is  the  sand 

2.  Foraminiferous  shells  of  the  genus  Rotalia,  and  a few  frag- 
ments of  larger  shells. 

3.  Upwards  of  twenty  genera  of  Diatomacem. 

4.  A few  specules  of  sponges  and  corals,  very  minute. 

5.  Some  amorphous  matter,  which  was  not  destroyed  after  long 
boiling  in  strong  acids. 

I reported  to  the  Government  against  attempting  to  open  out 
communication  between  either  of  the  mud  hanks  and  the  adjoining 
backwater.  A cut  through  the  neck  of  land  between  would  throw 
an  outwards  scour  during  ebb  tides,  and  during  the  rains  into  the 
centre  of  the  mud  hanks,  and  might  do  a great  deal  of  harm,  and 
indeed  destroy  them,  or  shift  their  position.  During  the  dry 
season,  at  flood  tide  the  mud  would  be  drawn  into  the  backwaters, 
and  choke  them  up. 

If  a lock  were  to  be  put  on  the  canal,  the  channel  leading  to  it 
could  not  be  kept  clean  without  a scour. 

At  Narrakal  there  is  already  a canal  from  the  backwater  to 
within  a few  yards  of  the  shore  ; and  at  Allippey  there  is  a similar 
one,  only  the  mud  bank  has  left  it  and  travelled  south. 

These  natural  harbours  of  refuge  are  too  valuable  to  try  ex- 
periments on ; and  I think  the  whole  phenomena  connected  with 
them  are  well  worthy  of  car ej ul  scientific  investigation. 


of  Edinburgh,  Session  1872-73. 


79 


2.  The  Meteorology  of  the  Month  of  May.  By  Alexander 
Buchan,  M.A. 

Excepting  the  months  of  January  and  July — the  months  of 
extreme  temperatures  for  the  larger  portions  of  the  globe — there 
is  no  month  the  meteorology  of  which  is  so  peculiar,  and  a careful 
investigation  of  which  is  so  likely  to  lead  to  striking  and  important 
results,  as  the  month  of  May.  The  peculiarity  of  the  meteorology 
of  the  month  of  May  is,  that  it  is  the  month  of  the  year  during 
which  the  most  rapid  rise  of  temperature  takes  place  over  the 
greater  parter  part  of  the  northern  hemisphere,  and  the  most  rapid 
fall  over  the  greater  part  of  the  southern  hemisphere ; and  since 
that  rapid  rise  and  equally  rapid  fall  takes  place  at  very  different 
rates,  according  to  the  peculiar  distribution  of  land  and  water  in 
each  region,  the  inquiry  is  calculated  to  bring  out  in  strong  relief 
some  of  the  more  prominent  causes  which  influence  climate,  and 
some  of  the  more  striking  results  of  those  causes.  The  method  of 
inquiry  which  has  been  adopted  was  to  compare  the  average  atmo- 
spheric pressure  of  May  with  that  for  the  year,  setting  the  differ- 
ence of  excess  or  deficiency  in  their  proper  places  on  maps,  and 
drawing  therefrom  lines  of  equal  deviation  from  the  annual  mean, 
for  every  0T00  inch,  and  in  some  cases  for  0-050  inch.  The  winds 
had  been  dealt  with  in  a similar  way — viz.,  by  finding  the  difference 
between  the  average  of  May  and  the  general  monthly  averages  of 
the  year.  From  these  two  elements — distribution  of  pressure  and 
winds — the  rainfall  and  other  elements  of  climate  necessarily 
follow.  The  results  of  the  inquiry  which  has  been  made,  and 
which  was  based  upon  observations  at  upwards  of  600  places,  show 
a diminution  of  pressure  in  May  over  tropical  and  sub-tropical 
regions,  and  also  over  the  north  of  Asia  and  to  the  south  of  South 
America  and  Tasmania.  The  excess  of  pressure  in  the  northern 
hemisphere  prevails  over  North  America  (to  the  north  of  the 
Lakes),  over  Arctic  America,  over  Greenland,  over  the  British 
Isles,  and  to  the  north  of  a line  passing  through  the  English 
Channel,  in  a north-easterly  direction,  to  the  Arctic  Sea.  Excess 
in  the  southern  hemisphere  includes  the  southern  half  of  South 
America  and  of  Africa,  the  whole  of  Australia,  and  the  adjacent 
parts  of  the  ocean.  The  influence  of  land  in  the  southern  hemi- 


VOL.  VIII. 


80  Proceedings  of  the  Royal  Society 

sphere,  where  the  land  at  this  season  is  colder  than  the  surround- 
ing sea,  brings  about  a higher  pressure  for  May ; but  the  influence 
of  land  over  regions  heated  more  immediately  by  the  sun  brings 
about  a lower  pressure — interesting  examples  of  which  are  seen 
in  the  distribution  of  the  differences  of  pressure  over  India, 
the  Malayan  Archipelago,  the  Mediterranean,  Black,  and  Caspian 
Seas.  In  many  such  cases  the  lines  follow  more  or  less  closely 
the  contour  of  the  coasts,  or,  more  strictly  speaking,  the  lines 
resembling  the  contours  lay  some  distance  to  eastwards,  so  that 
there  is  a less  diminution  over  those  seas  than  over  the  land 
surrounding  them.  Nearly  the  whole  of  Asia  shows  a very  large 
deficiency  of  pressure — the  Arctic  regions  to  the  north  of  Europe 
and  North  America  the  maximum  excess  of  pressure.  It  is  to 
the  position  of  Great  Britain,  with  reference  to  the  deficiency 
of  pressure  on  the  one  hand,  and  the  excess  on  the  other,  that 
the  east  winds  at  this  time  of  the  year  are  due.  Those  easterly 
winds  prevail  over  the  whole  of  northern  Europe,  as  far  south 
as  a line  drawn  from  Madrid  in  a north-easterly  direction,  and 
passing  through  Geneva,  Munich,  &c.  To  the  south  of  that 
line  the  diminution  of  pressure  is  less,  and  over  that  region 
the  excess  of  wind  is,  not  easterly,  but  southerly.  Crossing  the 
Mediterranean,  and  advancing  on  Africa,  we  approach  another 
region  of  lower  pressure  ; and  towards  that  region  north-easterly 
winds  again  prevail,  as  at  Malta,  Algeria,  &c.  The  effect  of 
these  different  winds  upon  the  rainfall  is  very  decided.  Southerly 
winds  from  the  Mediterranean  result  in  heavy  rainfall  over  France 
and  Central  Europe  in  the  month  of  May. 

The  effect  of  those  east  winds  upon  diseases  is  very  great. 
They  derange  our  nervous  system,  and  bring  about  a series  of  com- 
plaints, physical  and  mental,  an  inquiry  into  which  would  form  an 
interesting  and  important  subject  of  investigation. 

3.  On  Vortex  Motion.  By  Sir  William  Thomson. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

Andrew  Pritchard,  M.R.I.,  Author  of  a work  on  Infusoria,  Highbury, 
London. 


81 


of  Edinburgh , Session  1872-73. 

Walter  Stewart,  F.C.S.,  Haymarket  Terrace. 

Robert  Tennent,  Esq.,  21  Lynedoch  Place. 

Robert  Walker,  M.A.,  Edinburgh  Academy,  Fellow  of  Clare  College, 
Cambridge. 

William  Boyd,  M.A.,  Peterhead. 

Morrison  Watson,  M.D.,  Demonstrator  of  Anatomy  in  the  University, 
Edinburgh. 

J.  Bell  Pettigrew,  M.D.,  F.R.S.,  Conservator  of  Museum,  Royal 
College  of  Surgeons. 


Monday , Ylth  March  1873. 

Sir  ALEXANDER  GRANT,  Bart.,  Vice-President, 
in  the  Chair. 

The  following  Communications  were  read: — 

1.  A Contribution  to  the  Visceral  Anatomy  of  the  Greenland 
Shark  ( Lcemargus  borealis).  By  Professor  Turner. 

Naturalists  have  recorded  a few  instances  of  the  capture  of  the 
Greenland  shark  in  the  British  seas.  Dr  Fleming  states  that  one 
was  caught  in  1803  in  the  Pentland  Firth,  and  that  one  was  found 
dead  at  Burra  Firth,  Unst,  in  1824.  Mr  Yarrell  refers  to  a speci- 
men caught  on  the  coast  of  Durham  in  1840,  which  has  been  pre- 
served in  the  Durham  University  Museum.  In  May  1859,  a speci- 
men about  ten  feet  long  was  caught  in  the  Firth  of  Forth,  near 
Inchkeith,  the  stuffed  skin  of  which  is  preserved  in  the  Edinburgh 
Museum  of  Science  and  Art.  In  1862  a specimen  was  caught  on 
the  Dogger  Bank,  and  brought  into  Leith.  A brief  description  of 
its  external  character  was  read  by  Mr  W.  S.  Young  to  the  Royal 
Physical  Society  of  Edinburgh.  On  April  27,  1870,  Dr  John 
Alexander  Smith  read  before  the  same  Society  a notice  of  a female 
specimen  caught  about  thirty  miles  east  of  the  Bell  Rock.  It  had 
become  entangled  in  one  of  the  deep-sea  fishing-lines,  many  of  the 
hooks  attached  to  which  had  stuck  into  its  body.  It  measured 
about  15  feet  in  length,  and  3 feet  1 inch  between  the  tips  of  the 
tail-lobes.  The  stuffed  skin  of  this  fish  is  also  preserved  in  the 
Edinburgh  Museum  of  Science  and  Art.  In  the  month  of  February 
of  the  present  year,  three  specimens  were  caught  by  fishermen  at 
sea,  some  miles  east  of  the  Bell  Rock,  and  brought  into  Brough ty 


82 


Proceedings  of  the  Royal  Society 

Ferry.  One  was  taken  to  Dundee  for  exhibition  ; the  others  were 
brought  to  Edinburgh  for  the  same  purpose.  By  permission  of  the 
proprietors,  the  author  was  enabled  to  examine  the  latter  specimens, 
and  to  acquire  for  the  Anatomical  Museum  the  viscera  and  other 
parts.  One  was  a large  female,  11  feet  8 inches  in  length;  the  other, 
a smaller  female,  8J  feet  long.  Colour,  bluish-grey ; sides  of  body 
marked  with  a number  of  transverse  stripes ; lateral  line  distinct. 
The  author  then  recorded  several  measurements  of  the  larger 
specimen,  of  which  the  more  important  were  as  follows : — 


Ft.  in. 

From  tip  of  snout  to  end  of  tail,  . . 11  8 

,,  to  back  of  1st  dorsal  fin, . 6 0 

,,  to  back  of  2d  dorsal  fin,  . 9 0 

„ to  antr.  edge  of  ventral  fin,  7 9 

„ to  antr.  edge  of  pectoral  fin,  3 5 

Height  of  1st  dorsal  fin,  . . . .07 

,,  2d  dorsal  fin,  . .0  5^ 

Between  tips  of  tail-lobes,  . .29 

Length  of  pectoral  fin,  . . . .18 

,,  ventral  fin,  . . . .13 


A specimen  of  the  parasitic  crustacean,  th e Lerneopoda  elongata , 
was  attached  to  one  of  the  eyes  of  the  smaller  specimen. 

The  author  then  gave  an  account  of  the  visceral  anatomy  of  this 
shark ; all  the  measurements  given  being  from  parts  of  the  larger 
specimen.  The  stomach  possessed,  in  addition  to  the  large  sac,  a 
posterior  pyloric  compartment  from  which  the  pyloric  tube  arose, 
which  curving  for  6 inches  forwards,  terminated  by  a very  con- 
stricted orifice  in  the  duodenum. 

The  duodenum  was  a cylindrical  tube,  3 feet  2 inches  in  length. 
It  ran  at  first  forwards  and  then  passed  backwards  to  end  in  a 
dilated  part  of  the  intestine  13  inches  long,  which  contained  the 
transversely  arranged  spiral  valve.  A short  rectum,  7 inches  long, 
passed  from  the  spiral  valve  back  to  the  anus,  and  into  this  part  of 
the  gut  the  duct  of  an  ovoid  glandular  body,  attached  to  the  outer 
coat  of  the  rectum,  opened.  The  biliary  and  pancreatic  ducts 
pierced  independently  the  wall  of  the  duodenum,  where  it  bent  on 
itself,  and  between  their  opening  and  the  pyloric  orifice  two  large 


83 


of  Edinburgh , Session  1872-73. 

C93ca,  one  6 inches,  the  other  18J  inches  long,  opened  by  wide 
mouths  into  the  duodenum. 

The  pancreas  was  a well-developed  organ,  from  which  two  long 
processes  passed  backward  parallel  to  the  duodenum.  The  bile- 
duct,  for  some  inches  before  it  joined  the  duodenum,  was  a single, 
well-marked  tube,  and  had  connected  with  it  a small  bilobed  body, 
from  which  a minute  duct,  parallel  to  the  bile  duct,  ran  towards 
the  liver.  The  spleen  was  17  inches  long  and  6 wide  at  its 
broadest  part.  The  kidneys  lay  parallel  to  the  spine  ; their  ureters, 
about  the  size  of  crow  quills,  opened  into  the  cloaca  behind  the 
anus. 

The  ovaries  were  two  in  number,  and  each  was  23  inches  long  in 
the  larger  shark.  They  consisted  of  parallel  club-shaped  laminae, and 
contained  multitudes  of  ova,  varying  in  size  from  minute  specks  to 
small  bullets.  No  oviducts  were  seen  in  the  abdominal  cavity,  and 
no  oviducal  openings  in  the  region  of  the  cloaca;  but  immediately 
posterior  to  the  mouth  of  the  cloaca,  the  two  rounded  openings  of 
the  abdominal  pores,  which  communicated  with  funnel-shaped 
prolongations  of  the  peritoneal  cavity  were  found. 

The  heart,  with  its  subdivisions  into  auricle,  ventricle,  and 
conus  arteriosus,  was  then  described,  and  the  structural  differences 
between  the  conus  and  the  bulbus  aortas  of  the  osseous  fish  were 
pointed  out. 

The  conus  arteriosus  of  the  heart,  in  addition  to  the  large  three- 
segmented,  semi-lunar  valve  at  its  anterior  end,  contained  four 
tiers  of  valves,  consisting  of  nineteen  cuspidate  segments,  to  and 
from  which,  and  from  the  inner  wall  of  the  conus,  chordas  tendinea? 
proceeded. 

It  was  then  pointed  out  that  the  presence  of  a pyloric  compart- 
ment, and  of  a cylindrical  tubular  duodenum,  the  co-existence  of  a 
pancreas  and  pyloric  caeca,  and  the  absence  of  oviducts,  constituted 
most  important  features  of  difference  between  the  Greenland  shark 
and  the  other  Plagiostomata. 

Attention  was  then  drawn  to  the  differences  in  the  form  of  the 
teeth,  which  had  led  Muller  and  Henle  to  separate  the  Greenland 
shark  from  the  old  Ouvierian  genus  Scymnus,  and  to  make  for  it  a 
new  genus  Lcemargus. 

The  author  then  stated  that  the  anatomical  differences  between 


84 


Proceedings  of  the  Eoyal  Society 

Scymnus  and  Lcemargus  were  very  much  greater  than  those  referable 
to  the  form  of  the  teeth,  on  which  systematic  zoologists  had  hitherto 
relied  in  their  classification.  These  differences,  indeed,  affected 
not  only  the  relations  of  Lcemargus  to  Scymnus , but  to  the  sharks 
generally,  and  called  for  a reconsideration  on  the  part  of  the 
zoologist  of  the  place  which  the  Greenland  shark  ought  to  occupy 
amongst  the  Plagiostomata,  and  required  the  establishment  of  a 
separate  family  for  the  reception  of  the  genus  Lcemargus , w'hich 
family  would  possess  the  following  characters: — 

LjEmargid^:. 

No  nictitating  membrane;  two  dorsal  fins;  no  anal  fin;  duo- 
denum cylindrical ; both  a pancreas  and  duodenal  caeca;  in  the 
female  no  oviducts. 

Lcemargus. — Dorsal  fins  short,  the  second  not  quite  so  high  as 
the  first ; lower  teeth  oblique,  truncate. 

2.  Additional  Note  on  the  Strain-Function,  &c.  By 
Professor  Tait. 

The  author  gave  an  account  of  the  mode  in  which  he  had  treated 
the  Strain-Function  in  an  elementary  Treatise  on  Quaternions, 
soon  to  be  published,  mainly  from  the  pen  of  Professor  Kelland. 

The  coefficients  of  the  cubic  in  <p  are  determined  easily  from  the 
condition  that  homogeneous  strain  alters  the  volume  of  every  part 
of  a body  in  the  same  ratio. 

A careful  examination  is  bestowed  upon  the  case  of  three  real 
roots  of  the  cubic ; especially  with  regard  to  the  distinction  between 
the  results  of  a self-conjugate  strain  and  a rotational  one. 

The  separation  of  the  pure  and  rotational  parts  of  a strain  is  very 
fully  treated ; and  as  special  examples,  the  strain  of  a rigid  body 
and  a simple  shear  are  analysed. 

Finally,  the  following  problems  are  solved : — 

Find  the  conditions  which  must  be  satisfied  by  the  simple  shear , 
which  is  capable  of  reducing  a given  strain  to  a pure  strain. 

Find  the  relation  between  two  linear  and  vector  functions  whose 
successive  application  produces  rotation  merely. 

All  this  is  independent  of  the  differential  calculus,  but  as  the 
following  results  regarding  the  stress-function  require  its  aid,  the 


of  Edinburgh,  Session  1872-73.  85 

cannot  be  introduced  into  the  work  referred  to.  They  will  appear, 
with  extensions,  in  the  second  edition  (now  printing)  of  the  author’s 
Treatise  on  Quaternions. 

At  any  point  of  a strained  body,  let  A,  be  the  vector  stress  per 
unit  of  area  perpendicular  to  i,  jjl,  and  v,  the  same  for  planes  per- 
pendicular to  j and  k respectively. 

Then,  by  considering  an  indefinitely  small  tetrahedron,  we  have 
for  the  stress  per  unit  of  area  perpendicular  to  a unit  vector  to,  the 
expression 

ASz’w  + fxSjo)  + vSko)  = — (pit) , 

so  that  the  stress  across  any  plane  is  represented  by  a linear  and 
vector  function  of  the  unit  normal  to  the  plane. 

But  if  we  consider  the  equilibrium,  as  regards  rotation,  of  an 
infinitely  small  rectangular  parallelepiped  whose  edges  are  parallel 
to  i,  j,  k,  respectively,  we  have 

Y(iX  +ju  + kv)  = 0 , 
or 

%Yi(pi  = 0 , 
or 

Y.V<pp=  0 . 

This  shows  that  <p  is  self -conjugate,  or,  in  other  words,  involves  not 
nine  distinct  constants  but  only  six. 

Consider  next  the  equilibrium,  as  regards  translation,  of  any 
portion  of  the  solid  filling  a simply-connected  closed  space.  Let  u 
be  the  potential  of  the  external  forces.  Then  the  condition  is 
obviously 

fM-Uv)ds+fffdsVu  = 0, 

where  v is  the  normal  vector  of  the  element  of  surface  ds. 

Here  the  double  integral  extends  over  the  whole  boundary  ot 
the  closed  space,  and  the  triple  integral  throughout  the  whole  in- 
terior. 

To  reduce  this  to  a form  to  which  the  method  of  my  paper  on 
Green's  and  other  Allied  Theorems  {Trans.  R.S.E.,  1869-70)  is 
directly  applicable,  operate  by  S.a  where  a is  any  constant  vector 
whatever,  and  we  have 


JJS.paUvds  + fffd&aVu  = 0 


86  Proceedings  of  the  Boy  at  Society 

by  taking  advantage  of  the  self-conjugateness  of  <p.  This  may  be 
written 

jQ7tf<S'.Vpa  + S.a Yu)  = 0 , 


and,  as  the  limits  of  integration  may  be  any  whatever, 

S.V^a  + S.aVw  = 0 ....  (1). 

This  is  the  required  equation,  the  indeterminateness  of  a rendering 
it  equivalent  to  three  scalar  conditions 

As  a verification,  it  may  be  well  to  show  that  from  this  equation 
we  can  get  the  condition  of  equilibrium,  as  regards  rotation , of  a 
simply  connected  portion  of  the  body,  which  can  be  written  by 
inspection,  as 

f/V.ptffyds  +ff/Y.pYuds  = 0 . 


This  is  easily  done  as  follows : — (1.)  Gives 


S.Vf>cr  + S.crVw  = 0, 
if,  and  only  if,  cr  satisfy  the  condition, 


S.p(V)<r  = 0. 

Now  this  condition  is  satisfied  if 

cr  = Yap , 


where  a is  any  constant  vector.  For 

8 .<p{V)Yap  = - S.aV <p(y)p 


= S.aVV^p  = 0 . 

Hence 

fffds($.V(pYap  + S.  apYu)  = 0 , 
or 

ff  dsS.appUv  + fff  d&.apYu  = 0. 

Multiplying  by  a,  and  adding  the  results  obtained  by  making  a in 
succession  each  of  three  rectangular  vectors,  we  obtain  the  required 
equation. 

Suppose  cr  to  be  the  displacement  of  a point  originally  at  p,  then 
the  work  done  by  the  stress  on  any  simply  connected  portion  of 
the  solid  is  obviously 

W =JfS.(p(Uv)crds, 


because  <p(Uv)  is  the  vector  force  overcome  on  the  element  ds. 
This  is  easily  transformed  to 

W = JJfS.Ypcrds . 


of  Edinburgh,  Session  1872-73. 


87 


Monday,  1th  Ajoril  1873. 

Professor  Sir  WILLIAM  THOMSON,  Vice-President,  in 
the  Chair. 

The  following  Communications  were  read  : — 

1.  Notice  of  a Singular  Property  exhibited  by  the  Fluid 
enclosed  in  Crystal  Cavities.  By  Edward  Sang,  Esq. 

The  subject  of  the  following  communication  is  a phenomenon 
unexpected  and  peculiar ; it  presents  analogies  to  the  phenomena 
of  magnetism  and  electricity,  in  so  much  as  it  is  an  exhibition  of 
repulsion  ; but  it  is  distinguished  from  these  by  the  absence  of  at- 
traction, or  what  is  called  polarity.  So  far  as  I am  aware,  it  is  the 
only  known  example  of  repulsion  exhibited  independently  of  mag- 
netic or  electric  excitement,  and  seems  to  open  up  an  entirely  new 
field  for  physical  research.  On  these  accounts  I was  exceedingly 
desirous  to  have  it  brought  without  delay  to  the  notice  of  scientific 
men,  and  I have  to  thank  our  Secretary  for  giving  me  the  present 
opportunity,  although  at  the  inconvenience  to  him  of  it  having  to 
accompany  a long  and  interesting  paper  on  another  subject. 

I shall  confine  myself  this  evening  to  a simple  statement  of  the 
nature  of  the  phenomenon,  to  its  exhibition,  and  to  an  account  of 
the  circumstances  that  led  to  its  discovery,  reserving  for  anothei 
opportunity  a more  detailed  notice  of  those  observations  and  ex- 
periments that  have  already  been  made  in  regard  to  it. 

While  discussing,  along  with  Dr  James  Hunter,  the  occurrence 
of  polished  cylindric  strise  in  calcareous  spar,  and  while  examining 
those  striae  under  the  microscope,  I happened  to  notice  an  air- 
bubble  in  a minute  cavity,  having  a regularly  crystallised  form, 
which  air-bubble  was  found  to  move  when  the  position  of  the  spar 
was  changed. 

Next  forenoon,  while  showing  this,  in  itself  very  interesting, 
matter  to  my  pupil,  Mr  David  A.  Davidson,  I desired  to  mark 
the  position  of  the  speck,  and  applied  the  point  of  my  penknife  to 
scratch  the  spar.  Immediately  the  air-bubble  was  seen  to  move 
rapidly.  My  first  thought  was  to  attribute  this  motion  to  the  pres- 
sure on  the  thin  lamina  of  spar  immediately  above  the  cavity,  but 


VOL.  VIII. 


M 


88 


Proceedings  of  the  Royal  Society 

on  exerting  a much  greater  pressure  by  help  of  a small  pencil  of 
wood,  no  motion  was  perceptible,  yet  on  bringing  the  knife-point 
within  the  field  of  view,  but  without  pressure,  the  motion  was  re- 
newed, and  the  bubble  was  seen  to  approach  the  steel  on  whichever 
side  it  might  be  placed.  The  possible  slight  magnetism  of  the 
steel  suggested  itself  as  an  explanation,  accompanied,  however,  by 
the  unheard-of  occurrence  of  a magnetised  fluid;  and  the  blade 
was  magnetised  first  in  the  one  and  then  in  the  opposite  way  with- 
out any  perceptible  change  of  effect.  Meanwhile  Mr  Davidson 
had  found  that  a piece  of  soft  steel  occasioned  the  same  motions. 
Pieces  of  brass  and  copper  wire,  printing  type,  silver  and  copper 
coin,  all  acted  in  the  same  way  ; but  pieces  of  wood,  glass,  ivory, 
showed  no  effect.  . 

Afterwards,  trials  made  with  compact  oxide  of  iron,  and  with 
sulphuret  of  lead,  gave  no  perceptible  result;  yet,  until  the  trials 
shall  have  been  conducted  with  scrupulous  care  as  to  the  horizon- 
tally of  the  upper  surface  of  the  cavity,  we  cannot  hold  the 
absence  of  action  to  be  proved;  but,  as  present  appearances  go, 
it  seems  that  the  metallic  state  is  essential  to  this  repulsion. 

By  inclining  the  instrument,  we  may  bring  this  repulsion  to 
oppose  gravity,  and  the  degree  of  inclination  affords  a test  of  the 
amount,  so  much  so  that  means  for  determining  the  law  of  its  vari- 
ation by  distance,  and  the  specific  influences  of  different  metals, 
are  brought  within  reach. 

Modifications  in  the  arrangement  of  the  microscope,  so  as  to 
allow  of  the  convenient  exposition  of  specific  masses,  as  well  as  to 
secure  the  measurements  of  the  inclination  and  distance,  are  needed 
before  we  can  obtain  results  reliable  as  to  quantity ; when  these 
modifications  are  completed  I shall  place  the  details  before  the 
Society. 

Boughly  made,  as  at  present,  the  experiments  point  to  a specific 
intensity  for  each  metal,  and  to  a diminution  in  a ratio  higher  than 
that  of  the  inverse  squares  of  the  distances. 

I have  not  been  so  fortunate  as  to  find  among  the  cavities  in 
rock  crystal,  topaz,  and  amethyst,  within  my  reach,  any  containing 
movable  fluid : it  is  desirable  that  physicists,  who  may  be  in  pos- 
session of  such  specimens,  should  examine  whether  this  repulsion 
occur  there  also. 


89 


of  Edinburgh,  Session  1872-73. 

2.  On  the  Germ  Theory  of  Putrefaction  and  other  Fermen- 
tative Changes.  By  Professor  Lister. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society 

John  G.  M'Kendrick,  M.D.,  Assistant  to  the  Professor  of  Physiology  in 
the  University  of  Edinburgh. 

Roeert  Wilson,  Esq.,  Engineer,  Patricroft,  Manchester. 


Monday,  21  st  April  1873. 

Professor  KELL  AND  in  the  Chair. 

The  following  Communications  were  read: — 

1.  Notice  of  New  Fishes  from  West  Africa 

(I.)  Ophiocephalus  obscurus,  Gunther. 

(II.)  Synodontis  Bohbianus,  nov.  spec.  mihi. 

By  John  Alexander  Smith,  M.D. 

The  fishes  now  exhibited  were  brought  by  the  Bev.  Alexander 
Bobb,  D.D.,  from  Old  Calabar,  West  Africa.  They  were  taken  in 
the  fresh  water  of  the  great  Old  Calabar  Biver,  near  Ikorofiong, 
about  a hundred  miles  or  so,  by  the  windings  of  the  river,  from  the 
bar  near  its  mouth.  The  Bev.  Dr  Bobb  resides  at  Ikorofiong, 
which  is  one  of  the  stations  of  the  Calabar  mission  of  the  United 
Presbyterian  Church. 

The  fishes  belong  to  the  great  sub-class  of  the  TELEOSTEI. 

I.  Ophiocephalus  obscurus , Gunther. 

The  first  to  which  I would  call  attention  is  a small  dark- 
coloured  fish  ; it  belongs  to  the  Order  of  the  Acanthopterygij, 
Family  Ophiocephalida:,  and  to  the  Genus  Ophiocephalus. 

Dr  Gunther,  in  his  <£  Catalogue  of  Acanthopterygian  Fishes,” 
vol.  iii.  p.  468,  states  that  the  fishes  of  this  family  have  the  body 
elongate , anteriorly  sub -cylindrical,  and  covered  with  scales  of 
moderate  size;  the  head  depressed  and  snake-like,  covered  with 
shield-like  scales  superiorly.  A.  cavity  accessory  to  the  gill  cavity , 
for  the  purpose  of  retaining  water  in  it,  a superbranchial  organ,  not 


90  Proceedings  of  the  Royal  Society 

being  developed.  One  long  dorsal  and  anal  fin  without  spines. 
u They  are  fresh-water  fishes  of  the  East  Indies,  and  are  able  to 
live  and  move  without  the  water  for  a short  time,  feeding  on  small 
animals.”  “ It  appears,  from  recent  observations,  that  the  amount 
of  air  which  is  in  solution  in  water  is  not  sufficient  for  the  respira- 
tion of  these  fishes,  so  that  they  are  obliged  to  come  to  the  surface 
at  certain  intervals,  to  receive  an  additional  quantity  of  atmo- 
spheric air.” 

The  genus  Ophiocephalus  is  distinguished  by  the  presence  of  ven- 
tral fins.  The  species  of  this  genus  are  common  in  India  and  the 
East;  some  of  them,  as  the  uCoramota ” or  uGachuav  (the  0.  gachua ) 
of  Bengal,  have  excited  considerable  interest  from  making  their 
appearance  during  the  rains  in  unexpected  places,  and  giving  rise 
to  the  popular  belief  that  they  must  have  fallen  with  the  rain  from 
the  clouds;  the  fish  having  left,  for  the  time,  the  muddy  waters 
where  it  resides,  for  the  fresh  wet  grass,  and  the  abundance  of 
animal  food  it  gets  there. 

This  genus  was  believed  to  be  entirely  confined  to  India  and  the 
East  until  Dr  Gunther,  in  the  year  1869.  detected  in  the  collection 
of  fish  made  by  Consul  Petherick  on  the  Nile  one  species  which  he 
has  described  as  the  O.  obscurus.  It  was  captured  at  Gondokoro 
on  the  Upper  Nile,  and  forms  the  only  exception  yet  known  to  the 
Indian  habitat  of  the  genus. 

The  interesting  fact  of  the  great  apparent  correspondence  of  the 
fish  fauna  of  the  Nile  with  the  distant  rivers  of  West  Africa  was 
pointed  out  many  years  ago ; the  fauna  of  the  East  African  rivers 
being  apparently  somewhat  different  in  character.  Dr  Gunther, 
from  a careful  examination  of  a number  of  species  from  the  Nile 
and  West  African  rivers,  comes  to  the  conclusion  that — “the 
Faunas  of  the  Nile  and  the  West  African  rivers  belong  to  the  same 
zoological  district;  that  there  is  an  uninterrupted  continuity  of  the 
fish  fauna  from  west  to  east ; and  that  the  species  known  to  be 
common  to  both  extremities  inhabit  also  the  great  reservoirs  of 
water  in  the  centre  of  the  African  continent.”* 

It  is,  therefore,  with  some  little  interest  that  I am  able  to  add 
this  single  species  of  Ophiocephalus  found  in  the  Upper  Nile,  to  the 

* See  Petherick’s  “Travels  in  Central  Africa,”  vol.  ii.  London,  1869. 
Appendix,  “Fishes  of  the  Nile,”  by  Dr  A.  Gunther. 


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of  Edinburgh,  Session  1872-73. 

list  of  corresponding  species  found  in  the  great  Calabar  river  of 
Western  Africa.  The  specimen  seems  to  correspond  very  closely 
with  Dr  Gunther’s  typical  description  of  the  0.  obscurus,  with  the 
exception  of  some  slight  proportional  details  of  measurements  and 
the  presence  of  one  or  two  more  rays  in  some  of  the  fins.  I forwarded 
the  fish  to  Dr  Gunther  for  his  examination,  and  he  writes  me  that 
“ the  Ojphiocephalus  is  closely  allied  to,  if  not  identical  with,  the 
obscurus , but  it  has  five  or  six  more  dorsal  rays  than  the  type.” 
We  must,  therefore,  perhaps,  wait  for  the  examination  of  additional 
specimens,  to  see  whether  some  of  the  characters  will  require  to  he 
expanded  a little,  in  Dr  Gunther’s  description  of  the  fish. 

(Since  this  paper  was  read  to  the  Society,  Dr  Gunther  informs 
me  that  the  British  Museum  has  recently  received  a specimen 
from  the  river  Congo,  with  thirty  anal  rays.) 

I subjoin  Dr  Gunther’s  description  of  the  Nile  fish,  taken  from 
the  appendix  to  Petherick’s  “ Travels  in  Central  Africa,”  vol.  ii. 
London,  1869,  p.  215.  Dr  Gunther  had,  however,  previously 
described  and  named  this  fish  in  his  general  “Catalogue  of  Acan- 
thopterygian  Fishes,”  vol.  iii.,  London,  1861,  p.  478,  from  a speci- 
men in  the  collection  of  the  British  Museum,  the  locality  of  which 
was  not  known  : — 

“ Ophiocephalus  obscurus , A.  Gunther. 

D.  42.  A.  26-29.  (L.  lat.  70.  L.  trans.  7/14.) 

“ The  height  of  the  body  is  nearly  one-eighth  of  the  total  length,  the 
length  of  the  head  nearly  one-fourth;  the  width  of  the  inter-orbital  space 
is  more  than  the  extent  of  the  snout,  and  one-fourth  of  the  length  of  the 
head.  'The  cleft  of  the  mouth  is  wide,  the  maxillary  extending  behind  the 
orbit.  The  scales  on  the  upper  surface  of  the  head  are  of  moderate  size, 
those  on  the  neck  small;  there  are  thirteen  series  of  scales  between  the 
orbit  and  the  angle  of  the  preoperulum.  The  pectoral  does  not  extend 
on  to  the  origin  of  the  anal,  and  its  length  is  one-half  that  of  the  head; 
the  length  of  the  ventral  is  three  quarters  of  that  of  the  pectoral.  Caudal 
rounded,  its  length  being  six  times  and  one-third  in  the  total.  Blackish, 
lighter  below,  with  dark  stripes  along  the  series  of  scales;  a series  of  black 
blotches  along  the  side;  head  with  two  indistinct  oblique  black  spots  along 
its  base.  Pectoral  and  ventral  variegated  with  blackish.  Chin  black,  with 
white  spots.  Length  seventy-seven  lines.  Collected  at  Gondokoro.” 

The  following  are  some  of  the  slight  differences  in  the  specimen 
got  in  the  Old  Calabar  River  : — 


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Proceedings  of  the  Royal  Society 

Ophiocephalus  obscurus,  A.  G-iinther. 

D.  45.  A.  32.  P.  16.  Y.  6.  (L.  lat.  about  70.  L.  trans.  7/14.) 

Height  of  body,  7£  times  in  total  length  of  fish.  Length  of 
head,  4J  times  in  total.  The  length  of  the  pectoral  fin  is  a little 
more  (J  of  an  inch),  than  half  the  length  of  head.  Length  of  ven- 
trals  rather  more  than  half  that  of  pectorals.  Caudal  fin  is  5J 
times  in  the  total  length.  Head  and  body  above  are  black,  or  a 
very  dark  brown  (in  spirits),  the  sides  show  numerous  black 
blotches;  fins  black,  tail  slightly  mottled  with  lighter.  Below, 
head  black,  blotched  with  lighter,  rest  of  body  dirty  white.  Total 
length,  78  lines  (6J  inches.) 

Collected  at  Ikorofiong,  Old  Calabar  River,  West  Africa. 


II.  Synodontis  Robbianus , nov.  spec.  mihi. 

The  other  fish  belongs  to  the  Order  of  the  Physostomi,  Family 
SiLURLDiE,  and  to  the  G-enus  Synodontis.  All  the  species  of  this 
genus  belong  to  tropical  Africa,  and  at  least  one  species  has  been 
discovered  common  to  the  Upper  Nile  and  the  West  African  rivers. 
They  are  scaleless  fish,  with  an  adipose  fin,  and  the  dorsal  and 
pectoral  fins  have  strong  bony  spines.  Mouth  small,  Teeth  in  the 
lower  jaw  movable,  very  thin  at  the  base,  and  with  slightly  dilated 
brown  pointed  apices.  They  have  six  barbels,  and  broad  dermal 
bones  on  the  head  and  neck.  I have  taken  these  details  of  the 
characters  of  the  genus  from  Ur  G-iinther’s  important  work,  the 
“ Catalogue  of  Fishes,”  vol.  v.,  to  give  a general  idea  of  the  fish, 
and  the  following  are  the  character  of  this  new  species:— 

Synodontis  Robbianus. 

Body. — Height  (behind  dorsal  fin),  about  one-fourth  of  length  without 
caudal  rays.  Greatest  height ; one-third  of  distance  between  posterior 
border  of  orbit,  and  caudal  extremity  without  fin  rays.  Head  about  three 
and  a half  times  in  length  of  body,  without  caudal  fin  ; tapers  quickly 
forwards;  short,  in  front  of  eyes;  distance  from  point  of  snout  to  front  of 
orbit,  about  one-third  of  length  from  snout,  to  posterior  extremity  of 
nuchal  plate.  Snout  short,  rounded  in  front;  distance  between  middle  of 
orbits  rather  less  than  to  front  of  snout.  The  gill  openings  extend  down- 
wards to  before  the  root  of  humeral  process  of  pectoral  fin. 

Teeth: — Mandibular,  rather  numerous,  much  shorter  than  the  eye  (about 
half),  varying  in  length,  the  longest  towards  the  middle;  in  a cluster  on 


2.  Mouth,  showing  teeth  and  roots  of  barbels. 


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Proceedings  of  the  Royal  Society 

the  middle  of  front  of  lower  jaw.  Maxillary  teeth  in  front  of  upper  jaw, 
small,  short,  thickly  set  in  a broad  band. 

Barbels: — Maxillary  barbels , dark-coloured,  much  longer  than  head, 
reaching  more  than  half  way  down  pectoral  spines;  edged  with  a broadish 
membrane  interiorly.  Mandibular  barbels. — Outer,  dark-coloured,  slightly 
fimbriated  or  fringed,  reaching  to  base  of  pectoral  fin.  Inner,  light-coloured, 
about  half  the  length  of  outer,  and  more  distinctly  fringed. 

Dermal  bones  of  head  and  neclc. — Broad,  rough  or  granular  ; terminate 
in  front  of  eyes  in  forked  processes;  broad  behind,  and  extend  in  a pointed 
process  a little  beyond  each  side  of  base  of  dorsal  spine.  Humeral 
process. — Much  longer  than  high,  pointed  behind,  runs  nearly  as  far  back 
as  nuchal  plate,  granular  surface,  a slight  projecting  ridge  along  anterior 
margin,  and  a thick,  somewhat  smooth,  and  tapering  ridge  projects  along 
its  inferior  border. 

Fins  rather  small : — D.  1/8.  A.  12.  P.  1/7.  (V.  7.) 

Dorsal  fin. — Spine  shorter  than  the  head  (fixed  upright),  almost  smooth 
in  front,  showing  only  some  very  obscure  indications  of  a few  short  pro- 
cesses or  teeth  at  upper  part  ; toothed  at  upper  part  behind,  teeth  directed 
somewhat  towards  base  of  spine  ; (a  small  soft  ray  or  filament  inserted  a 
little  below  the  point.)  First  five  rays  (the  third  the  longest)  as  long  as 
spine  and  filament  together.  Adipose  fin. — Elevated;  longer  than  head; 
space  between  it  and  dorsal,  about  equal  to  length  of  base  of  dorsal  fin 
without  spine.  Pectoral  fin. — Spine  larger  and  longer  than  dorsal,  toothed 
on  both  sides ; teeth  small  and  thickly  set  together  on  outside,  directed 
towards  extremity  of  spine;  teeth  larger  and  more  apart  on  inner  side,  and 
point  towards  base  of  spine;  fin  reaches  a little  beyond  base  of  dorsal  fin, 
but  not  to  base  of  ventral  fins.  Ventral  Jins. — Small;  in  length  pass  anal 
opening,  but  do  not  reach  to  base  of  anal  fin.  Anal-fin. — Larger  than 
ventral. 

Tail. — Forked  nearly  half  the  depth  of  rays;  two  uppermost  rays  pro- 
duced about  a third  beyond  others. 

Colour  (in  spirits). — Pale  brown,  slightly  blotched  or  mottled  with 
darker,  especially  on  head,  at  insertions  of  fins  and  tail,  and  on  rays  of  fins 
and  tail.  Ventrals  and  anal  fin  nearly  black.  Spines  light  coloured. 

Total  length  of  fish  without  caudal  rays,  4|  inches;  to  extremity  of 
elongated  caudal  rays,  5-|  inches.  From  point  of  snout  to  posterior  extre- 
mity of  nuchal  plate  (lg  inches),  fully  a third  of  total  length  to  extremity 
of  elongated  caudal  rays.  Total  length  of  specimen,  5-f  inches. 

Captured  at  Ikorofiong,  Old  Calabar  Biver,  West  Coast  of  Africa. 

I have  named  the  fish  after  the  Rev.  Alexander  Robb,  D.D.,  to 
whom  I am  indebted  for  these  specimens,  as  well  as  various  others, 
from  the  Old  Calabar  district  of  tropical  Africa. 

Dr  Robb  tells  me  there  are  great  difficulties  in  the  way  of  getting 


95 


of  Edinburgh,  Session  1872-73. 

specimens  of  natural  history  of  almost  any  kind  in  Old  Calabar ; 
and  one  in  particular  depends  on  the  fact,  that  the  natives  eat  at 
once  all  they  can  capture,  and  are  most  unwilling  to  give  them  up 
for  any  other  than  their  own  gastronomic  purposes. 

The  fishes  of  this  genus  Synodontis,  aud  the  allied  genera,  are 
interesting  to  the  geologist  from  their  possessing  dermal  bony 
plates,  and  also  these  strong  bony  fin-spines,  which  are  analogous 
in  character  to  some  of  those  in  the  fossil  fishes,  and  to  the 
iclitliyodorulites , or  fin  spines,  which  are  found  fossil  in  many  of 
our  older  rocks. 

These  bony  spines  are  useful  to  the  fish  as  weapons  both  of 
offence  and  defence,  and  require  a very  careful  handling  of  some  of 
the  species,  which  grow  to  a considerable  size,  as  they  sometimes 
inflict  serious  wounds,  which  are  said  to  be  poisonous,  even  in  some 
cases  causing  death.  Dr  Robb  says,  the  dangerous  character  of 
the  fish  of  this  genus  is  well  known  to  the  Old  Calabar  natives,  as 
well  as,  doubtless,  to  some  of  the  animals  which  prey  upon  fish. 
Crocodiles  are  abundant  in  the  river,  and  in  some  instances 
make  a seizure  of  one  of  these  fishes  with  the  large  bony  spines, 
and  cases  have  occurred  of  a crocodile  being  found  dead  with  the 
spiny  fish  sticking  in  its  mouth  or  throat.  This  circumstance  has 
probably  given  rise  to  an  Efik  proverb  well  known  among  tbe 
people,  to  this  effect, — “When  the  Crocodile  is  lucky,  he  catches 
Inanga  ” (the  spineless  cat  fish) ; “ when  unlucky,  he  catches  Mkpi- 
kuk-i-kuk  ” (the  native  name  for  this  spiny  fish  or  synodontis ),  the 
etymology  of  which,  Dr  Robb  tells  me,  is  not  very  obvious.  The 
proverb,  indeed,  wonderfully  resembles  our  own  common  saying 
about  “catching  a Tartar,”  and  is  frequently  used  by  them  in  its 
more  general  application,  as  among  ourselves. 

2.  The  Electrical  Conductivity  of  certain  Saline  Solutions,  - 
with  a note  on  their  Density.  By  J.  A.  Ewing  and  J . 
G.  MacGregor,  B.A.  Communicated  by  Professor  Tait. 

(A  bstract ). 

In  the  note  on  the  density  of  the  solutions  prepared  for  the  pur- 
pose of  determining  their  electrical  conductivity,  it  is  shown  that  the 
ratio  of  the  weight  of  salt  dissolved  in  unit  weight  of  water  to  the 

N 


. VOL.  VIII. 


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Proceedings  of  the  Boyal  Society 

excess  of  the  density  of  the  solution  thus  formed  over  that  of  water 
(unity),  is  not  constant,  but  increases,  with  greater  or  less  rapidity, 
from  the  more  dilute  to  the  more  dense.  The  work  of  previous 
experimenters  on  the  electrical  resistance  of  liquids  is  then  reviewed 
at  some  length.  Their  chief  difficulty  has  always  been  the  elec- 
trolytic polarisation  of  electrodes. 

The  solutions  under  investigation  were  put  in  a glass  tube,  which 
was  narrow  along  the  central  part,  but  widened  at  the  ends  for  the 
reception  of  platinum  electrodes;  and  by  means  of  connecting  wires 
it  was  made  to  form  one  of  the  aims  of  a Wheatstone’s  Bridge. 
High  resistances  were  introduced  into  the  other  arms.  The  bridge 
was  so  arranged  that  the  effect  on  the  galvanometer  could  be  ob- 
served the  instant  the  battery  circuit  was  closed,  when  for  an  in- 
definitely short  period  there  is  no  polarisation.  By  successive 
passages  of  electricity,  which  were  alternately  in  opposite  directions, 
and  between  which  the  tube  was  short-circuited,  opportunity  was 
obtained  of  adjusting  the  resistances  in  the  arms  of  the  bridge,  so 
that  at  last  there  was  no  deflection  of  the  galvanometer  needle  due 
to  the  passage  of  the  current.  All  measurements  and  observations 
were  made  at  a temperature  of  10°  C. 

Nineteen  solutions  of  zinc  sulphate  were  examined.  The  re- 
sistances of  very  dilute  ones  are  very  great,  hut  fall  off  rapidly 
as  the  density  increases,  until  it  reaches  about  1*08,  after  which 
they  decrease  much  more  slowly.  At  the  density  1*2891,  the 
specific  resistance  ( i.e .,  the  resistance  between  opposite  faces  of 
a cube,  whose  side  is  1 cm.)  is  28*3  B.A.  units.  The  resistances 
of  solutions  from  this  density  to  that  of  saturation  increase, 
that  of  the  saturated  solution  being  33*7  B.A.U.  That  solu- 
tion, therefore,  whose  density  is  1*2891,  is  the  solution  of  maximum 
conductivity.  By  taking  as  ordinates  the  excess  of  the  density 
of  the  various  solutions  over  unity,  and  as  abscissae  their  specific 
resistances,  the  relation  between  density  and  resistance  is  shown 
graphically.  The  curve  thus  obtained  is  symmetrical,  about  an 
axis  passing  through  the  point  of  maximum  conductivity,  and  the 
part  of  it  which  lies  between  the  origin  and  that  point  is  an 
hyperbola  whose  asymptotes  are  inclined  at  an  angle  less  than  a right 
angle. 

Eleven  solutions  of  copper  sulphate  were  prepared  and  their 


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of  Edinburgh , Session  1872-73. 

resistances  found.  The  spec.  res.  of  the  saturated  solution  is 
29*3  B.A.XJ.  The  solution  of  maximum  density  is  that  also  of 
maximum  conductivity.  The  curve  (described  as  above)  is  an 
hyperbola  whose  asymptotes  are  inclined  at  an  angle  less  than  a 
right  angle. 

Nine  solutions  of  potassium  bichromate,  and  nine  also  of  potassium 
sulphate,  were  investigated.  The  resistances  in  both  decrease  up 
to  the  point  of  saturation,  the  least  being,  in  the  former,  29-6  B.A.U., 
and  in  the  latter,  16'6  B.A.U.  The  curves  are  both  hyperbolas; 
that  of  the  bichromate  has  its  asymptotes  approximately  perpen- 
dicular to  one  another,  and  that  of  the  sulphate  has  them  inclined 
at  an  angle  greater  than  a right  angle.* 

Fifteen  mixtures  of  equal  volumes  of  solutions  of  copper  and 
zinc  sulphates  were  also  examined.  In  all  cases,  the  resistance  of 
the  mixture  is  less  than  the  mean  of  the  resistances  of  its  com- 
ponents. The  lowest  spec.  res.  of  any  of  the  mixtures  prepared,  is 
27*3  B.A.U.,  and  it  consisted  of  equal  volumes  of  the  two  saturated 
solutions.  The  zinc  sulphate  appears  to  exercise  the  greater 
influence  in  the  determination  of  the  spec.  res.  of  the  mixtures. 

3.  On  the  Effect  of  Heating  one  Pole  of  a Magnet,  the  other 
being  kept  at  a Constant  Temperature.  By  D.  H.  Mar- 
shall, Esq.,  M.A.,  and  C.  G.  Knott,  Esq.  Communicated 
by  Professor  Tait. 

The  following  are  a modification  of  some  experiments  conducted 
in  the  summer  of  1871,  and  communicated  to  the  Society  on  the 
15th  of  January  1872.  These  consisted  in  heating  a magnet  uni- 
formly throughout,  and  then  noting  the  change  in  magnetic 
strength.  Those  conducted  this  winter  consisted  in  heating  one 
pole  of  a magnet,  while  the  other  was  kept  at  a temperature  as 
nearly  constant  as  possible,  and  then  noting  the  change  of  mag- 
netic strength  in  both  poles.  The  arrangement  adopted  was  the 
same  in  both  series  of  experiments,  only  being  double  in  the  latter. 
It  consisted  in  having  a magnet  set  magnetically  east  and  west, 
each  end  of  which  passed  through  a cork  fitted  into  a hole  made 
* For  all  four  salts  formulae  are  given,  by  means  of  which  the  conductivity  of 
any  solution  may  be  calculated  if  its  density  is  given. 


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Proceedings  of  the  Royal  Society 

in  the  side  of  a copper  pot,  one  of  which  was  filled  with  oil  and 
heated  by  means  of  a brass  Bunsen,  while  the  other  was  filled  with 
water  at  the  temperature  of  the  air  of  the  room.  The  temperatures 
of  both  ends  of  the  magnet  could  thus  be  ascertained  by  means  of 
mercurial  thermometers. 

In  the  same  line  as  the  magnet  and  on  both  sides  of  it  were  two 
small  magnets.  These  were  cemented  to  the  backs  of  small  con- 
cave mirrors,  suspended  by  single  silk  fibres,  and  placed  in  glass 
cases  to  guard  them  against  currents  of  air.  The  deflections  of 
the  small  magnets  were  measured  exactly  as  in  the  reflecting 
galvanometer;  and  from  the  nature  of  the  arrangement,  and  the 
important  fact  made  out  from  these  experiments,  viz.,  that  even 
when  the  poles  of  a magnet  are  at  different  temperatures  the  mag- 
netic strength  is  the  same  in  each,  it  follows  that  the  absolute 
magnetic  strength  in  either  pole  of  the  large  magnet  is  directly  as 
the  tangent  of  the  angle  of  deflection  of  the  contiguous  small 
one,  and,  therefore,  will  be  measured  by  the  reading  on  the  cor- 
responding scale. 


y*  d + y)*  * 


Te 


/ m m \ 

^v7"(T+yjv 


(m  m \ 

x*  ~ (T  + xf)^ 


/ m m,  > 
\~x2  ~(L  + x)2J 


NS  are  the  poles  of  the  fixed  magnet,  m its  absolute  magnetism. 
N a = x,  N a1  = y,  NS  = Z.  The  couples  indicated  are  those  pro- 
duced by  the  large  magnet  and  the  earth’s  magnetism,  E,  on  the 
small  magnets. 

For  any  deflection  <9,  if  the  lengths  of  the  small  magnets  be 
negligible  compared  with  x and  y,  we  have 


E sin  0 = m ( 

” Q + 

| cos  0 . 

\ m a tan  6 . 

E sin  6 = m j 

r 1 

1 ^ 

1 cos  6 . 

m a tan  0. 

(J+y)  V 

Proc.  Roy.  Sac. 


Voi:  VM.  fSess.  1873-/  3.  j 


TemjrT?  XempT? 

40  SO  JZO  40  50  120 400  560 


4 

X- 

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LB.i 

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J rjbJT  40  120  ZOO  ZOO  320  400  520 

BL  200  2JO  2X0  260  M 260  300  310 


99 


of  Edinburgh,  Session  1872-73. 

Curve  T.  of  each  day’s  experiment  represents  the  rate  of  diminu- 
tion of  the-hot  pole  in  terms  of  its  temperature;  Curve  II.  that  of 
the  cold  pole  in  terms  of  the  temperature  of  the  hot  pole ; and 
Curve  III.  shows  how  the  magnetic  strength  of  the  one  pole 
changes  relatively  to  that  of  the  other. 

Perhaps  the  most  important  fact  made  out  from  these  experi- 
ments was  that  already  mentioned,  viz.,  that  whatever  he  the  tem- 
peratures of  the  ends  of  the  magnet,  the  magnetic  strength  is 
approximately  the  same  in  both  poles.  This  was  shown  by  plotting 
the  deflections  of  the  little  magnets  in  terras  of  one  another;  for 
it  was  then  found  that  the  result  was  a straight  line,  which  proves 
that  the  rate  of  diminution  or  increase  of  magnetic  strength  is  the 
same  in  both  poles  ; and,  therefore,  if  they  be  of  the  same  strength 
at  the  commencement  of  each  experiment,  when  the  magnet  is  of 
the  same  temperature  throughout,  they  will  of  course  remain  the 
same  during  the  whole  experiment,  when  the  poles  are  of  different 
temperatures.  (See  figure  III.  of  each  day’s  experiment.)  When 
the  pole  which  had  been  heated  was  allowed  to  cool  again,  the  line 
obtained  by  plotting  the  deflections  of  the  two  poles  was  still 
approximately  a straight  one,  though  not  exactly  coinciding  with 
that  obtained  for  it  when  being  heated.  This,  however,  is  quite 
satisfactorily  accounted  for  by  the  alteration  of  the  zeros,  which 
was  never  the  same  in  both,  and  therefore  the  measured  strength 
differed  from  the  true  strength  more  in  one  pole  than  in  the  other. 
In  the  first  communication  it  was  pointed  out  how  the  mere  heat- 
ing of  the  pot  produced  in  some  unaccountable  way  an  alteration 
of  zero.  The  fact  that  the  poles  are  the  same  strength  throughout 
also  accounts  for  the  general  similarity  of  Curves  I.  and  II.  for 
each  day. 

It  is  to  be  observed  that  Curves  I.  and  II.  become  smoother  day 
after  day,  as  if  the  boiling  so  altered  the  molecular  constitution  of 
the  steel,  as  to  enable  it  to  conduct  more  easily  a state  of  magnetic 
distribution. 

It  is  interesting  also  to  notice  that  the  rate  of  diminution  of 
magnetic  strength  decreases  on  each  successive  experiment,  and 
that  the  two  branches  of  each  curve  approach  nearer  and  nearer  to 
each  other,  thus  showing  a greater  unwillingness  on  the  part  of 
the  magnet  to  lose  any  of  its  magnetism  permanently  with  heating. 


100  Proceedings  of  the  Royal  Society 

The  curves  of  March  4 represent  an  experiment  in  which  the 
poles  of  the  magnet  were  reversed,  i.e.,  what  was  before  heated  is 
now  kept  at  the  temperature  of  the  room  ; and  these  curves  show 
what  a very  great  permanent  loss  was  produced  by  the  reversion, 
and  also  how  much  greater  the  rate  of  diminution  of  the  mag- 
netism was  than  had  been  in  previous  experiments.  In  after  ex- 
periments, such  as  that  of  March  6,  the  permanent  loss  is  not 
nearly  so  great,  and  there  is  also  a remarkable  decrease  in  the  rate 
of  diminution. 

The  curves  of  March  11  represent  an  experiment  in  which  the 
poles  were  again  reversed  ; and,  from  the  approach  of  the  branches, 
we  see  that  the  magnet,  as  it  were,  becomes  accustomed  also  to 
this  treatment,  and  evinces  great  unwillingness  in  losing  its  mag- 
netism permanently.  In  this  day’s  experiment  there  is  a great 
dissimilarity  between  Curves  I.  and  II.  We  may  look  for  the 
explanation  of  this  in  the  alteration  of  zeros,  which  possibly  may 
be  much  greater  in  the  one  pole  than  in  the  other.  This  supposi- 
tion is  strengthened  on  looking  at  Curve  III.,  where  it  will  be 
seen  the  two  branches  are  very  widely  separated. 

Throughout  these  experiments  we  have  to  acknowledge  the 
assistance  which  W.  Campbell,  Esq.,  has  rendered  us. 


4.  On  the  Physiological  Action  of  Light.  No.  I.  By  James 
Dewar,  Esq.,  and  John  G.  M'Kendrick,  M.D.,  of  the  Uni- 
versity of  Edinburgh. 

The  authors  of  this  communication  have  more  especially  directed 
their  attention  to  the  problem  of  the  specific  effect  produced  on  the 
retina  and  optic  nerve  by  the  action  of  light.  Numerous  hypotheses 
have  been  made  from  time  to  time  by  physicists  and  physiologists  ; 
but  up  to  the  present  date,  our  knowledge  of  the  subject  is  without 
any  experimental  foundation.  For  example,  Newton,  Melloni,  and 
Seebeck,  stated  that  the  action  of  light  on  the  retina  consisted  of 
a communication  of  mere  vibrations ; Young  conjectured  that  it 
was  a minute  intermittent  motion  of  some  portion  of  the  optic 
nerve;  Du  Bois-Reymond  attributed  it  to  an  electrical  effect; 
Draper  supposed  that  it  depended  on  a heating  effect  of  the 


101 


of  Edinburgh , Session  1872-73. 

choroid ; anti  Mosier  compared  it  to  the  action  of  light  on  a sen- 
sitive photographic  plate. 

It  is  evident  that,  in  accordance  with  the  principle  of  the  trans- 
ference of  energy  now  universally  accepted,  the  action  of  light  on 
the  retina  must  produce  an  equivalent  result,  which  may  be 
expressed,  for  example,  as  heat,  chemical  action,  or  electro-motive 
power.  It  is  well  known  that  the  electro-motive  force  of  a piece 
of  muscle  is  diminished  when  it  is  caused  to  contract  by  its  normal 
stimulus,  the  nervous  energy  conveyed  along  the  nerve  supplying 
it ; and  similarly  a nerve  suffers  a diminution  of  its  normal  electro- 
motive force  during  action.  In  the  same  manner,  the  amount  and 
variations  of  the  electro-motive  power  of  the  optic  nerve,  affected 
secondarily  by  the  action  of  light  on  the  retina,  are  physical  ex- 
pressions of  certain  changes  produced  in  the  latter ; or,  in  other 
words,  are  functions  of  the  external  exciting  energy,  which  in  this 
case  is  light.  Considerations  such  as  these  led  us  to  form  the 
opinion  that  the  problem  of  what  effect,  if  any,  the  action  of  light 
has  on  the  electro-motive  force  of  the  retina  and  optic  nerve, 
would  require  for  its  investigation  very  careful  and  refined  experi- 
ment. 

The  inquiry  divided  itself  into  two  parts, — first,  to  ascertain  the 
electro-motive  force  of  the  retina  and  nerve;  and,  second,  to  observe 
whether  this  was  altered  in  amount  by  the  action  of  light.  The 
electro-motive  force  of  any  living  tissue  can  be  readily  determined 
by  the  method  of  Du  Bois-Revmond,  This  great  physiologist 
found  that  every  point  of  the  external  surface  of  the  eyeball  of  a 
large  tench  was  positive  to  the  artificial  transverse  section  of  the 
optic  nerve,  but  negative  to  the  longitudinal  section.  This  he 
accomplished  by  the  use  of  his  well-known  non-polarisable 
electrodes,  formed  of  troughs  of  zinc  carefully  amalgamated,  con- 
taining a solution  of  neutral  sulphate  of  zinc,  and  having  cushions 
of  Swedish  filter  paper  on  which  to  rest  the  preparation.  To  pro- 
tect the  preparation  from  the  irritant  action  of  the  sulphate  of 
zinc,  a thin  film  or  guard  of  sculptor’s  clay,  moistened  with  a '75  per 
cent,  solution  of  common  salt,  and  worked  out  to  a point,  is  placed 
on  each  cushion.  These  electrodes  were  connected  with  a galvano- 
meter, and  the  preparation  was  placed  so  that  the  eyeball,  carefully 
freed  from  muscle,  rested  on  the  one  clay-guard,  while  the  transverse 


102 


Proceedings  of  the  Royal  Society 

section  of  the  optic  nerve  was  in  contact  with  the  other.  By 
following  Du  Bois-Reymond’s  method,  we  have  had  no  difficulty 
in  obtaining  a strong  deflection  from  the  eyes  of  various  rabbits,  a 
cat,  a dog,  a pigeon,  a tortoise,  numerous  frogs,  and  a gold-fish. 
The  deflection  was  frequently  so  much  as  to  drive  the  spot  of  light 
off  the  galvanometer  scale. 

With  regard  to  the  second  question,  namely,  whether,  and  to 
what  extent,  the  electro-motive  force  would  be  affected  by  light, 
we  found  more  difficulty.  The  method  followed  was  to  place  the 
eyeball  on  the  cushions  in  the  manner  above  described,  to  note  the 
deflection  of  the  galvanometer  needle,  and  then  to  observe  whether 
or  not  any  effect  was  produced  on  the  impact  of  a beam  of  light, 
during  its  continuance,  and  on  its  removal.  In  a few  of  our  earlier 
experiments,  we  used  Du  Bois-Reymond’s  multiplying  galvano- 
meter; but  finding  the  amount  of  deflection  obtained  was  so  small 
that  the  effect  of  light  could  not  be  readily  observed,  we  have 
latterly  used  Sir  W.  Thomson’s  exceedingly  sensitive  reflecting 
galvanometer,  kindly  lent  us  by  Professor  Tait.  We  met  also  with 
secondary  difficulties,  such  as  the  dying  of  the  nerve,  the  impos- 
sibility of  maintaining  an  absolutely  constant  zero  and  an  absolutely 
constant  amount  of  polarity,  the  effects  of  heat,  &c. ; but  these 
difficulties  we  have  overcome  as  far  as  possible  by  the  most  approved 
methods.  The  changes  in  polarity  of  the  apparatus  occurred 
slowly,  and  could  not  be  mistaken  for  the  changes  produced  by  the 
action  of  light,  which  we  found  occurred  suddenly,  and  lasted  a 
short  period  of  time.  It  is  also  important  to  state,  that  the  de- 
flections we  observed  do  not  at  present  profess  to  be  absolute,  but 
only  relative  values. 

About  500  observations  were  made  previous  to  the  date  of  this 
first  communication,  and  we  took  every  precaution  to  obtain 
accurate  results.  The  effects  of  heat  were  carefully  avoided  by 
covering  over  the  troughs  on  which  the  eye  under  examination 
rested,  with  a spherical  double  shell  of  glass,  having  at  least  an 
inch  of  water  between  the  walls. 

The  results  we  have  arrived  at  are  as  follow : — 

1.  The  action  of  light  on  the  retina  is  to  alter  the  amount  of  the 
electro-motive  force  to  the  extent  of  from  three  to  seven  per  cent, 
of  the  total  amount  of  the  natural  current. 


of  Edinburgh,  Session  1872-73.  103 

2.  A flash  of  light,  lasting  the  fraction  of  a second,  produces  a 
marked  effect. 

3.  A lighted  match,  held  at  a distance  of  4 or  5 feet,  is  sufficient 
to  produce  an  effect. 

4.  The  light  of  a small  gas-flame,  enclosed  in  a lantern,  and 
caused  to  pass  through  a globular  glass  jar  (12  inches  in  diameter), 
filled  with  a solution  of  ammoniacal  sulphate  of  copper  or  bichro- 
mate of  potash,  has  also  produced  a change  in  the  amount  of  the 
electro-motive  power. 

5.  The  action  of  light  on  the  eye  of  the  frog  is  as  follows : 
— When  a diffuse  light  is  allowed  to  impinge  on  the  eye  of  the 
frog,  after  it  has  arrived  at  a tolerably  stable  condition,  the  natural 
electro-motive  power  is  in  the  first  place  increased,  then  diminished; 
during  the  continuance  of  light  it  is  still  slowly  diminished  to  a 
point  where  it  remains  constant;  and  on  the  removal  of  light,  there 
is  a sudden  increase  of  the  electro-motive  power  nearly  up  to  its 
original  position.  The  alterations  above  referred  to  are  variables, 
depending  on  the  quality  and  intensity  of  the  light  employed,  the 
position  of  the  eyeball  on  the  cushions,  and  modifications  in  the 
vitality  of  the  tissues. 

6.  Similar  experiments  made  with  the  eye  of  warm-blooded 
animals,  placed  on  the  cushions  as  rapidly  as  possible  after  the 
death  of  the  animal,  and  under  the  same  conditions,  have  never 
given  us  an  initial  positive  variation,  as  we  have  above  detailed  in 
the  case  of  the  frog,  but  always  a negative  variation.  The  after 
inductive  effect  on  the  withdrawal  of  light  occurs  in  the  same 
way. 

7.  Many  experiments  have  been  made  as  to  effect  of  light  from 
different  portions  of  the  spectrum.  This  was  accomplished  by 
causing  different  portions  of  the  spectrum  of  the  oxy-hydrogen 
lime-light  to  impinge  on  the  eye.  All  these  observations  tend  to 
show  that  the  greatest  effect  is  produced  by  those  parts  of  the 
spectrum  that  appear  to  consciousness  to  be  the  most  luminous, 
namely,  the  yellow  and  the  green. 

8.  Similarly,  experiments  made  with  light  of  varying  intensity 
show  that  the  physical  effects  we  have  observed  vary  in  such  a 
manner  as  to  correspond  closely  with  the  values  that  would  result  • 
if  the  well-known  law  of  Fechner  was  approximately  true. 


VOL,  VIII. 


104 


Proceedings  of  the  Royal  Society 

9.  The  method  followed  in  these  inquiries  is  a new  method  in 
physiological  research,  and  by  the  employment  of  proper  appliances, 
it  may  be  greatly  extended,  not  only  witli  regard  to  vision,  but 
also  to  the  other  senses. 


Monday , 5 th  May  1873. 

Professor  KELLAND,  Y.P.,  in  the  Chair. 

The  following  Communications  were  read : — 

1*  Notice  of  two  Fossil  Trees  lately  uncovered  in  Craigleith 
Quarry,  near  Edinburgh.  By  Sir  B.  Christison,  Bart., 
President,  K.S.E. 

The  late  Mr  H.  T.  M.  Witham  read  in  1830  to  this  Society,  and 
published  three  years  afterwards  in  greater  extension,  an  inquiry 
of  much  interest  respecting  two  fossil  trees  found  in  Craigleith 
Quarry,  a mile  and  a half  from  the  north-west  outskirts  of  Edin- 
burgh. The  general  points  of  this  inquiry  are,  that  trees  of  very 
great  size  lie,  completely  fossilised,  in  the  very  compact  sandstone 
of  the  quarry,  at  a great  depth  below  the  rock  surface,  slightly 
inclined  to  the  dip  of  the  strata,  with  their  structure  so  finely 
preserved  in  the  fossilising  material  as  to  be  beautifully  shown 
before  the  microscope,  and  recognised  as  that  of  the  Pinaceous 
Family,  and  of  the  section  to  which  belongs  the  existing  Araucaria. 
These  trees  have  been  generally  known  to  fossile  botanists  by  the 
name  of  Araucarioxylon  Withami.  An  opportunity  having  occurred 
this  year  of  confirming  and  extending  the  inquiries  of  Witham, 
it  has  been  thought  right  to  take  advantage  of  it,  again  through 
the  medium  of  the  Eoyal  Society. 

One  of  Witham’s  fossils  (No.  1)  was  found  in  1826,  the  other 
(No.  2)  in  1830;  but  his  researches  regarded  principally  the 
second.  Since  the  latter  year  four  similar  fossils  have  been  un- 
covered by  the  operations  of  the  quarrymen.  One  of  these  (No.  3) 
was  exhibited  for  some  time  to  the  curious  in  a hut  constructed 
over  it  for  concealment.  Another  (No.  4)  was  removed  by  the 
late  Mr  Ramsay  of  Barnton,  behind  whose  mansion  several  large 


1C5 


of  Edinburgh^  Session  1872-73. 

fragments  may  still  be  seen.  The  fifth  is  said  to  have  been  first 
brought  to  light  in  1858,  and  to  have  been  subsequently  covered 
with  the  detritus  of  the  quarry,  till  it  was  lately  uncovered  again 
by  the  operations  of  the  quarry  having  returned  to  its  neighbour- 
hood ; and  it  now  lies  in  its  place  half  displayed  to  the  extent 
of  22  feet.  The  sixth  has  been  found  only  a few  months  ago  in 
the  very  bottom  of  the  quarry,  where,  for  the  present,  little  more 
is  seen  of  it  than  a cross  section,  level  with  the  containing  rock. 
There  was  also  lately  found,  not  far  from  the  second  last  fossil, 
but  not  at  all  attached  to  it,  or  otherwise  proved  to  have  belonged 
to  it,  a “ branch,”  as  the  workmen  thought,  eight  feet  in  length 
and  five  inches  across.  No  trace  has  yet  been  found  of  what 
became  of  No.  3,  or  of  either  it  or  of  No.  4 having  been  examined 
by  any  scientific  inquirer. 

The  succeeding  remarks  relate  cursorily  to  No.  4,  at  Barnton 
House,  but  chiefly  to  those  now  shown  in  the  quarry,  and  to  the 
so-called  “branch.” 

Mr  Witliam’s  fossil  of  1830  lay  with  its  lower  end  downwards, 
without  either  branches  or  roots.  The  lowest  12  feet  are  still 
in  excellent  preservation  in  front  of  the  Botanic  Garden  Herbarium  - 
House ; and  what  appears  to  be  the  next  18  feet  is  in  equally 
good  preservation  before  that  part  of  the  Museum  of  Science  and  Art 
now  building.  The  fossil  now  principally  shown  in  the  quarry  is  some- 
what curved,  apparently  from  several  fractures  occasioned  in  situ. 
It  lies  in  a west  and  easterly  direction,  slightly  southward,  with  the 
cord  of  its  whole  visible  length  inclined  to  the  horizon  at  an  angle 
of  about  60°,  that  of  the  surrounding  rock  being  only  28°.  As  no 
record  remains  of  what  has  been  lost  of  its  upper  part,  and  the 
quarrying  has  not  reached  its  termination  below,  its  position  in 
relation  to  that  of  the  living  tree  cannot  be  positively  settled.  Its 
present  top  must  be  120  feet  under  the  upper  surface  of  the  rock  of 
the  quarry.*  The  other  (No.  6),  of  which  little  more  than  the  cross 
section  is  now  visible,*  seems  to  lie  much  in  the  same  direction  as 

* June  30,  1873. — The  upper  fossil,  No.  5,  has  been  pulled  down,  and  is 
about  to  be  removed  to  the  British  Museum.  Four  feet  of  the  lower  one,  No. 
6,  have  been  conveyed  to  the  Botanic  Garden  of  Edinburgh.  One  block  of 
the  former  is  14  feet  in  girth.  The  latter,  which  is  rudely  cylindrical, 
measures  exactly  8 feet  9 inches  in  circumference.  Its  angle  of  inclination' 
was  accurately  ascertained  before  removal  to  be  61°. 


106  Proceedings  of  the  Royal  Society 

the  last,  and  at  a similar  inclination  of  60°  to  the  horizon,  but 
where  the  clip  of  the  rocky  strata  is  38°;  and  it  must  have  been 
covered  with  at  least  180  feet  of  the  very  hard  Craigleith  sand  - 
stone. 

So  much  of  the  lowest  visible  part  of  No.  5 is  uncovered,  that  its 
girth  may  be  safely  estimated  at  nearly  10  feet;  but  at  11  feet 
higher  up  it  swells  out,  like  some  rugged  old  elms,  and  must 
measure  considerably  more.*  The  girth  of  No.  6,  in  the  bottom  of 
the  quarry,  is  very  nearly  9 feet.  These  are  much  greater  trunks 
than  Mr  Witham’s  of  1830,  which,  at  12  feet  from  its  root,  now 
measures  27  inches  by  17.  It  is  considerably  flattened  along  its 
whole  length;  but  No.  4,  at  Barnton  House,  is  comparatively  little 
flattened;  and  those  now  visible  in  the  quarry  seem  scarcely  flattened 
at  all. 

The  woody  structure  of  the  trees  has  been  more  or  less  perfectly 
preserved  in  all  of  these  fossils.  There  is  nothing  under  this  head 
to  alter  in  the  description  and  delineations  by  Witliam  of  the 
fossil  found  in  1830,  and  little  to  add.  Many  portions  present 
little  remains  of  vegetable  structure,  and  others  the  appearance  of 
mineral  matters  only,  crystalline,  and  without  any  other  structural 
character ; but  many  exhibit  in  perfection  the  minute  microscopical 
woody  structure  represented  in  Witham’s  drawings.  No.  6,  that 
most  recently  discovered,  shows  the  woody  structure  perfect  and 
undeformed,  so  far  as  yet  examined,  from  circumference  to  centre ; 
but  it  also  contains  some  small  cavities  containing  nodules  of 
pearl-spar;  and  one  considerable  cavity  has  been  found,  which 
besides  these  nodules,  has  a lining  of  perfect  crystals  of  calc-spar 
three-quarters  of  an  inch  across.  The  “ branch  ” shows  the 
woody  structure  best  of  all. 

This  specimen,  of  which  there  were  originally  8 feet,  is  now 
reduced  to  18  inches.  Its  transverse  section  is  rudely  semi-oval. 
Its  end  is  ruggedly  pointed.  It  had  been  covered  all  over  with  a 
thin  coat  of  coal,  of  which  more  will  be  said  presently.  Under  this 
the  naked  eye  may  see  the  longitudinal  fibrous  appearance  of  wood. 
A cross  section  takes  on  the  colour  and  polish  of  fine  black  marble ; 
and  on  the  surface  are  dimly  seen  ten  lines,  marking  the  boundaries 
of  annual  layers,  extending  from  the  straight  edge  right  across, 
* See  Note  on  p.  105. 


107 


of  Edinburgh , Session  1872-73. 

from  a tenth  to  half  an  inch  apart,  and  on  the  whole  parallel  to 
one  another.  A thin  section,  made  soon  after  this  notice  was  read, 
proves  that  these  really  are  the  boundary  lines  of  annual  woody 
layers,  the  structure  of  which  is  beautifully  shown  before  a common 
lens.  Hence  the  supposed  branch  is  not  such,  but  a longitudinal 
sector  of  one,  or  possibly  of  a trunk. 

All  these  fossils  are  covered  with  a black  shining  crust  of  brittle, 
caking  coal,  from  a tenth  to  a twentieth  of  an  inch  in  thick- 
ness, easily  detached  from  the  surface  underneath.  This  substance, 
when  heated,  froths  up  very  much,  emits  much  white  dense  flame, 
cakes  firmly,  and  burns  slowly  away,  leaving  only  from  3’5  to  4\5 
per-cent,  of  ash. 

Under  this  crust  the  fossils  are  of  a uniform  grey  colour,  like 
our  ordinary  tertiary  limestone.  In  most  of  them  the  fossilising 
material  is  very  tough,  and  hard  enough  to  strike  fire  with  the 
hammer.  No.  6,  however,  is  dark  grey,  almost  black  indeed,  till  it 
is  thoroughly  dried,  and  not  so  hard  as  the  others.  It  has  evidently 
been  long  soaked  in  the  moist  bottom  of  the  quarry.  In  all  the 
mineralising  material  is  essentially  the  same,  and  totally  dif- 
ferent from  that  of  the  containing  strata.  These  are  all  a ver}' 
pure,  compact,  fine-grained,  extremely  hard,  siliceous  sandstone. 
Witbam  has  given  no  fewer  than  four  analyses  of  bis  fossils,  but 
they  are  all  either  erroneous  or  incomplete.  Silica  occurs,  not 
uniformly,  in  rough  particles,  to  all  appearance  adventitious,  and 
amounting  to  about  05  per-cent  only.  Alumina  is  also  present  to 
about  the  same  amount.  But  the  great  mass  of  fossilising  matter 
consists  of  the  carbonates  of  iron,  magnesia,  and  lime,  each  in 
notable  proportion.  The  relative  proportion  of  these  carbonates 
varies,  even  in  different  parts  of  the  same  fossil,  the  average  being 
about  60  per-cent,  of  carbonate  of  lime,  17  of  magnesia,  and  14  of 
carbonate  of  iron  in  the  form  of  protoxide.  The  proportion  of  the 
last  ingredient  varies  most  of  all,  for  it  sometimes  rises  so  high 
as  28.  The  most  interesting  ingredient,  however,  is  carbonaceous 
matter,  which  is  always  left  after  the  solvent  action  of  acids,  in  a 
proportion  varying  from  2*75  to  9-0  per-cent,  and  in  a state  of 
extremely  fine  division.  This  is  not  coal,  like  the  external  crust, 
but  charcoal,  burning  away  with  a red  glow,  and  no  flame,  and 
apparently  not  possessing  the  properties  of  graphitic  charcoal.  It 


108  Proceedings  of  the  Royal  Society 

sometimes  occurs  loose  in  cavities,  two  of  which  were  found  with 
a considerable  loose  lining  of  it. 

Nothing  has  been  found  on  the  exterior  of  these  fossils  distinctly 
or  even  probably  referable  to  the  bark  of  the  original  trees.  This 
deficiency  is  explicable,  if,  as  various  circumstances  seem  to  indicate, 
the  trees  did  not  grow  where  they  lie,  but  have  been  water-borne, 
so  that  their  bark,  like  their  roots  and  branches,  had  been  worn 
away.  The  outer  crust  of  coal  has  been  thought  to  represent  the 
bark  in  such  fossils,  but  that  cannot  be  here;  for,  in  the  first 
place,  it  covers  large  surfaces  of  the  trunk  of  No.  5,  which  are 
evidently  the  places  from  which  lost  branches  had  sprung ; and, 
secondly,  which  is  more  to  the  point,  it'  uniformly  covers  the  blunt, 
rugged  point,  and  the  complete  circuit,  of  the  split  sector,  which 
was  supposed  erroneously  by  the  quarrymen  to  be  a branch  entire 
in  its  whole  circumference,  and  over  the  greater  part  of  which  it  is 
impossible  that  there  could  have  been  any  bark.  It  is  difficult 
to  say  how  this  crust  was  formed.  It  is  also  a very  difficult  question 
to  settle,  how  the  carbon  of  this  exterior  crust  was  converted  into 
coal,  and  that  of  the  interior  into  charcoal.  But  further  examina- 
tion of  such  fossils  may  supply  the  answer,  and  throw  some  light 
on  the  process  of  formation  of  coal  in  general. 

2.  On  the  Formation  of  Buds  and  Boots  by  the  Leaves 

of  the  Ipecacuan  Plant  ( Gephaelis  Ipecacuanha ).  By 
Professor  Balfour. 

The  rapid  propagation  of  Ipecacuan  in  India  is  an  object  of 
importance,  and  as  such  has  occupied  the  attention  of  the  Indian 
Gfovernment.  The  Edinburgh  Botanic  Garden  has  contributed 
largely  to  the  stock  of  Ipecacuan  plants  now  in  cultivation  in  India. 
The  plan  of  sending  cuttings  of  the  roots  or  rather  rhizomes 
enveloped  in  moss  has  been  very  successful.  We  have  been  able 
in  1873  to  send  these  cuttings  in  small  boxes  through  the  post. 
Dr  Henderson,  the  present  interim  Director  of  the  Botanic  Garden 
at  Calcutta,  reports  most  favourably  of  this  plan.  He  carried  out  to 
Calcutta  in  1872  small  boxes  8 inches  by  2,  containing  germinating 
rhizomes  of  Ipecacuan,  and  roots  of  Jalap.  These  are  now  thriving 
under  his  charge.  This  mode  of  transmission  will  save  much 


109 


of  Edinburgh,  Session  1872-73. 

trouble  and  anxiety,  and  will  insure  an  easy  and  rapid  propagation 
of  the  plants.  We  may  expect  thus  to  secure  for  India  a large 
supply  of  this  invaluable  remedy  for  dysentery. 

In  reference  to  the  Ipecacuan  plants  recently  sent  to  India  in 
Wardian  cases  partly  in  earth  and  partly  in  moss,  as  well  as  in 
boxes  with  moss,  Dr  Henderson  at  Calcutta  reports  (18th  March 
1873)  that  the  120  plants  of  Ipecacuan  taken  by  him  from  the 
Edinburgh  Botanic  Garden,  have  increased  to  620  in  three  and 
a-balf  months  and  are  all  thriv- 
ing. The  smallest  possible  slice 
of  the  rhizome  ygth  of  an  inch 
thick  will  form  a plant.  He  has 
scarcely  lost  a single  cutting. 

Mr  Andrew  T.  Jaffray  at  Dar-  a 
jeeling, writes  on  the  19th  March 
to  the  effect  that  he  has  now 
7000  plants  of  Ipecacuan  in  cul- 
tivation. 

In  my  communication  last 
session  to  the  Boyal  Society  I 
stated  that  Mr  Bobert  Lindsay, 
foreman  in  the  propagating  de- 
partment of  the  Botanic  Garden, 
had  discovered  that  the  petiole  of 
the  leaf  of  the  Ipecacuan  plant 
when  put  into  the  soil  was 
capable  of  producing  roots  and 
buds.  He  has  carried  out  the 
experiment  fully,  and  I have  to 
report  the  results.  He  states 
that  leaves  of  Ipecacuan  plants  were  removed  with  the  petioles 
on  27th  June  1872.  Some  were  taken  off  close  to  the  stem, 
while  others  were  cut  off  above  their  attachment  to  the  stem. 
They  were  inserted  in  sandy  soil,  and  placed  in  a warm  moist 
propagating  house,  and  both  gave  out  roots. 

In  about  three  weeks,  the  end  of  the  petiole  where  it  had  been 
broken  off  or  cut,  was  cicatrised  and  formed  a rounded  pea-like 
swelling.  Shortly  afterwards  small  fibrous  roots  were  produced. 


110  Proceedings  of  the  Royal  Society 

These  after  some  time  presented  an  annnlated  appearance,  as 
shown  in  the  preceding  woodcut.  Buds  then  began  to  arise  from 
the  rounded  end  of  the  leaf-stalk.  In  the  woodcut  a young 
shoot  is  shown  arising  from  the  petiole.  Mr  Lindsay  tried  to 
get  buds  from  the  leaves  by  simply  placing  them  flat  on  the  soil 
(like  those  of  Bryopliyllum  and  Gesnera ),  but  in  this  he  did  not 
succeed.  He  found,  however,  that  if  the  upper  part  of  the  leaf 
was  cut  off  transversely,  and  the  petiole  was  planted  with  only 
the  lower  half  of  the  lamina  attached  to  it,  the  growth  of 
roots  went  on.  But  the  upper  half  of  the  leaf  when  planted 
did  not  root.  He  also  ascertained  that,  by  cutting  the  leaf  longi- 
tudinally through  the  midrib,  and  planting  each  half,  he  was  able 
to  get  roots  and  buds  from  each  of  the  halves  after  the  wounds 
had  cicatrised. 

These  experiments  of  Mr  Lindsay  demonstrate  the  facility  with 
which  Ipecacuan  may  be  cultivated,  and  they  supply  useful  hints 
to  those  who  are  superintending  the  growth  of  Ipecacuan. 

Fresh  specimens  were  produced,  showing  the  result  of  Mr 
Lindsay’s  experiments,  and  drawings  were  exhibited,  which  had 
been  executed  by  Mr  Francis  M.  Caird,  one  of  the  assistants  in 
the  Botanical  Class  of  the  University. 


Explanation  of  Woodcut. 

Ipecacuan  Leaf  with  Petiole,  Annulate!  Boot,  and  young  Plant.  (From 
a drawing  by  Mr  F.  M.  Caird.) 

a.  Lamina  or  blade  of  leaf. 

b.  Petiole  or  leaf-stalk. 

c.  Swelling  at  the  end  of  the  petiole  after  being  placed  in  the  soil. 

d.  Boot  proceeding  from  the  swelling,  showing  an  annulated  form. 

e.  Young  Plant  arising  from  the  swelling  of  the  petiole. 


3.  On  the  Physiological  Action  of  Light.  No.  II.  By  James 
Lewar,  Esq.,  and  John  G.  MTCendrick,  M.D. 

Since  the  date  of  the  first  communication,  we  have  endeavoured 
to  obtain  quantitative  results  involving  time  as  a variable  element 
in  the  case  of  the  action  of  light  on  the  retina  and  optic  nerve. 
We  have  therefore  found  it  necessary  to  construct  a true  graphical 


Ill 


of  Edinburgh,  Session  1872-73. 

representation  of  the  variations  of  the  electro-motive  force  occasioned 
by  the  impact  and  cessation  of  light.  It  is  clear  that  to  register 
minute  galvanometrical  alterations,  the  only  plan  that  could  be 
employed  would  be  to  photograph  on  a sensitive  surface,  covering 
a cylinder  rapidly  revolving  on  a horizontal  axis,  the  alteration 
of  position  of  the  spot  of  light  reflected  from  the  mirror,  just  as 
continuous  magnetic  observations  are  registered.  As  the  apparatus 
required  to  execute  these  observations  is  very  complicated,  and 
would  require  much  preliminary  practice,  we  have  in  the  meantime 
adopted  a simpler  method  of  registration.  This  plan  is  to  note  the 
position  of  the  galvanometer  at  equal  intervals  of  time,  before, 
during,  and  after,  the  impact  of  light  on  the  eye.  In  these  obser- 
vations we  have  used  a seconds’  pendulum  giving  a loud  beat. 
One  observer  reads  aloud  the  galvanometer,  the  other  marks  every 
interval  of  two  and  a half  seconds,  registers  the  numbers  obtained, 
and  regulates  the  supply  of  light.  A little  practice  in  the  method 
above  described  has  enabled  us  to  obtain  very  satisfactory  results, 
agreeing  very  closely  in  different  observations,  and  showing  in  a 
decided  way  the  salient  points  of  the  variation  curve. 

These  curves  show,  that  on  the  impact  of  light  there  is  a sudden 
increase  of  the  electro-motive  force;  during  the  continuance  of 
light  it  falls  to  a minimum  value;  and  on  the  withdrawal  of  light 
there  is  what  we  term  an  inductive  effect , that  is  to  say,  a sudden 
increase  of  the  electro-motive  force  which  enables  the  nerve  to 
acquire  its  normal  energy.  The  falling-off  of  the  electro-motive 
force  by  the  continued  action  of  light  is  the  physical  representa- 
tive of  what,  in  physiological  language,  is  called  fatigue ; the  in- 
ductive effect  exhibiting  the  return  of  the  structure  to  its  normal 
state. 

Occasionally  the  impact  of  light  is  not  followed  by  a rise  in  the 
electro-motive  force,  but  by  a diminution.  This  is  probably  to  be 
explained  by  the  fact,  that  the  death  of  the  retina  and  nerve  is 
indicated  by  a gradual  falling  of  the  electro-motive  force,  and  that 
this  change  frequently  goes  on  so  rapidly  that  the  impact  of  light 
is  unable  to  produce  any  rise.  In  these  circumstances,  the  spot  of 
light,  which  before  the  impact  of  light  was  slowly  moving  down- 
wards, is  on  the  impact  steadied  for  a moment,  and  then  pursues 
its  downward  course  more  rapidly. 


VOL.  VIII. 


112 


Proceedings  of  the  Royal  Society 

We  have  carried  out,  since  last  communication,  several  distinct 
sets  of  observations  : — 

1.  We  have  proved  that  though  there  is  no  difficulty  in  obtain- 
ing a strong  current  from  the  skin  of  the  frog,  this  current  is  not 
affected  by  light.  This  observation  demonstrates  that  the  pigment 
cells  of  the  skin  in  the  vicinity  of  the  cornea  have  nothing  to  do 
with  the  results  obtained. 

2.  The  current  obtained  from  a mass  of  the  pigment  cells  of  the 
choroid  does  not  exhibit  any  sensitiveness  to  light. 

3.  The  subcutaneous  injection  into  the  frog  of  Woorara, 
Santonin,  Belladonna,  and  Calabar  bean,  does  not  destroy  the 
sensibility  of  the  retina  to  light. 

4.  As  to  the  action  of  the  anterior  portion  of  the  eye.  On  care- 
fully bisecting  an  eye  of  a frog,  so  as  to  remove  completely  the 
anterior  portion,  including  cornea,  aqueous  humour,  iris,  ciliary 
muscle,  and  lens,  and  on  bringing  the  retina  into  actual  contact 
with  one  of  the  clay  pads,  we  readily  obtained  a large  deflection, 
which  was  as  sensitive  to  light  as  when  the  whole  eye  was  employed, 
thus  eliminating  any  possibility  of  the  contraction  of  the  iris  under 
the  stimulus  of  light  having  to  do  with  the  results  previously 
obtained. 

5.  On  using  the  anterior  portion  of  the  eye  so  that  the  cornea 
and  posterior  surface  of  the  crystalline  lens  were  the  poles,  we 
obtained  a large  deflection,  which  was,  however,  insensible  to  light. 

6.  The  sclerotic  and  nerve  without  the  retina,  in  the  same  man- 
ner, gave  a large  natural  electro-motive  force,  also  not  sensitive. 

7.  The  distribution  of  the  electro-motive  force  between  the  dif- 
ferent portions  of  the  eye  and  cross  section  of  the  nerve  may  be 
stated  as  follows : The  most  positive  structure  is  the  cornea,  then 
the  sclerotic,  then  the  longitudinal  surface  of  the  nerve ; the  cornea 
is  also  positive  to  the  posterior  surface  of  the  crystalline  lens,  and 
the  retina  itself  seems  to  be  positive  to  the  transverse  section  of  the 
nerve. 

8.  As  to  the  effects  'produced  by  lights  of  different  intensities. — If  a 
candle  is  placed  at  a distance  of  one  foot  from  the  eye,  and  then  is 
removed  ten  feet,  the  amount  of  light  received  by  the  eye  is  exactly 
one  hundredth  part  of  what  it  got  at  a distance  of  one  foot;  whereas 
the  electro-motive  force,  instead  of  being  altered  in  the  same  pro- 


113 


of  Edinburgh , Session  1872-73. 

portion,  is  only  reduced  to  one-third.  Repeated  experiments  made 
with  the  eye  in  different  positions  have  conclusively  shown  that  a 
quantity  of  light  one  hundred  times  in  excess  of  another  quantity 
only  modifies  the  electro-motive  force  to  the  extent  of  increasing  it 
three  times  as  much,  certainly  not  more. 

9.  It  was  apparent  to  us  that  these  experiments  would  ultimately 
bear  upon  the  theory  of  sense-perception  as  connected  with  vision. 
It  is  now  generally  admitted  that  no  image,  as  such,  of  an  external 
object,  is  conveyed  to  the  sensorium,  but  that  in  reality  the  brain 
receives  certain  impressions  of  alterations  taking  place  in  the 
receiving  organ.  The  natural  query  then  arises — are  the  physical 
effects  we  have  described  and  measured  really  comparable  in  any 
way  with  our  sensational  differences  in  light  perception  when  we 
eliminate  all  mental  processes  of  association,  &c.,  and  leave  only 
perception  of  difference  of  intensity?  In  other  words,  are  these 
changes  the  representative  of  what  is  conveyed  to  the  sensorium  ? 
It  would  appear,  at  first  sight,  that  this  problem  is  altogether  beyond 
experimental  inquiry.  There  is,  however,  a way  of  arriving  at  very 
accurate  measures  of  the  variation  of  our  sensational  differences  in 
the  case  of  light,  and  this  has  been  developed  theoretically  and 
experimentally  by  the  justly  renowned  physiologist  Fechner.  Stat- 
ing the  law  of  Fechner*  generally,  we  may  say,  the  difference  of 
our  sensations  is  proportional  to  the  logarithm  of  the  quotient  of 
the  respective  luminous  intensities.  A recent  series  of  experiments 
by  Dalboeuf  f has  entirely  confirmed  the  truth  of  this  law.  If, 
therefore,  the  observed  differences  in  electro-motive  power,  regis- 
tered under  conditions  of  varying  luminous  intensity,  agree  with 
this  law  of  Fechner,  regulating  our  sensational  impressions,  then 
there  can  be  little  doubt  these  variations  are  the  cause  of,  and  are 
comparable  to,  our  perception  of  sensational  differences.  Now,  we 
have  stated  above,  that  with  a quantity  of  light  one  hundred  times 
in  excess  of  another  quantity,  the  electro-motive  force  only  becomes 
three  times  greater.  According  to  Fechner’s  law,  we  may  say  the 
difference  of  our  sensations,  with  that  variation  in  the  amount  of 
luminous  intensity,  would  be  represented  by  2,  the  logarithm  of 
100.  Our  experimental  results  being  as  3 to  13  the  difference  is 

* Fechner,  Elemente  der  Psychophysik.  Helmholtz,  Optique  Physiologique. 

t Recent  Memoir  to  Belgian  Academy. 


114 


Proceedings  of  the  Boyal  Society 

also  2,  thus  agreeing  very  closely.  It  is  to  be  remembered,  how- 
ever, that  these  results  have  been  obtained  by  experiment  on  the 
eye  of  the  frog,  but  similar  changes  have  been  observed  in  the  eyes 
of  mammals.  In  the  latter,  however,  the  amount  of  alteration  is 
not  so  great,  in  all  probability  owing  to  the  rapid  death  of  the  parts. 

10.  When  one  clay-point  is  placed  in  contact  with  the  cornea  or 
nerve,  and  the  other  with  the  section  of  the  optic  lobe,  a current  is 
at  once  obtained,  which  is  sensitive  to  light.  In  this  experiment 
the  eye  is  left  in  the  orbit,  and  the  nerve  is  uninjured.  Thus,  the 
effect  of  light  on  the  retina  has  been  traced  into  the  brain. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society 

Donald  Crawford,  M.A.,  Advocate,  Fellow  of  Lincoln  College,  Oxford. 

M.  M.  Pattison  Muir,  Esq.,  Senior  Assistant  in  the  Andersonian 
Laboratory,  Glasgow. 


Monday , 19  th  May  1873. 

D.  MILNE  HOME,  LL.D.,  Vice-President,  in  the  Chair. 

The  following  Communications  were  read 

1.  On  the  Thermal  Influence  of  Forests.  By  Robert  Louis 
Stevenson, Esq.  Communicated  by  Thomas  Stevenson,  Esq. 
The  opportunity  of  an  experiment  on  a comparatively  large 
scale,  and  under  conditions  of  comparative  isolation,  can  occur  but 
rarely  in  such  a science  as  Meteorology.  Hence  Mr  Milne  Home’s 
proposal  for  the  plantation  of  Malta  seemed  to  offer  an  exceptional 
opportunity  for  progress.  Many  of  the  conditions  are  favourable 
to  the  simplicity  of  the  result ; and  it  seemed  natural  that,  if  a 
searching  and  systematic  series  of  observations  were  to  be  imme- 
diately set  afoot,  and  continued  during  the  course  of  the  planta- 
tion and  the  growth  of  the  wood,  some  light  would  be  thrown  on 
the  still  doubtful  question  of  the  climatic  influence  of  forests. 

Mr  Milne  Home  expects,  as  I gather,  a threefold  result : — 1st, 
an  increased  and  better  regulated  supply  of  available  water ; 2d, 
an  increased  rainfall ; and,  3d,  a more  equable  climate,  with  more 


115 


of  Edinburgh,  Session  1872-73. 

temperate  summer  heat  and  winter  cold.*  As  to  the  first  of  these 
expectations,  I suppose  there  can  be  no  doubt  that  it  is  justified 
by  facts;  hut  it  may  not  he  unnecessary  to  guard  against  any 
confusion  of  the  first  with  the  second.  Not  only  does  the  presence 
of  growing  timber  increase  and  regulate  the  supply  of  running 
and  spring  water  independently  of  any  change  in  the  amount  of 
rainfall,  but,  as  Boussingault  found  at  Marmato,f  denudation  of 
forest  is  sufficient  to  decrease  that  supply,  even  when  the  rainfall 
has  increased  instead  of  diminished  in  amount.  The  second  and 
third  effects  stand  apart,  therefore,  from  any  question  as  to  the 
utility  of  Mr  Milne  Home’s  important  proposal ; they  are  both, 
perhaps,  worthy  of  discussion  at  the  present  time,  but  I wish  to  con- 
fine myself  in  the  present  paper  to  the  examination  of  the  third  alone. 

A wood,  then,  may  he  regarded  either  as  a superficies  or  as  a 
solid ; that  is,  either  as  a part  of  the  earth’s  surface  slightly  elevated 
above  the  rest,  or  as  a diffused  and  heterogeneous  body  displacing 
a certain  portion  of  free  and  mobile  atmosphere.  It  is  primarily 
in  the  first  character  that  it  attracts  our  attention,  as  a radiating 
and  absorbing  surface,  exposed  to  the  sun  and  the  currents  of  the 
air ; such  that,  if  we  imagine  a plateau  of  meadow-land  or  bare 
earth  raised  to  the  mean  level  of  the  forest’s  exposed  leaf-surface, 
we  shall  have  an  agent  entirely  similar  in  kind,  although  perhaps 
widely  differing  in  the  amount  of  action.  Now,  by  comparing  a 
tract  of  wood  with  such  a plateau  as  we  have  just  supposed,  we 
shall  arrive  at  a clear  idea  of  the  specialties  of  the  former.  In  the 
first  place,  then,  the  mass  of  foliage  may  be  expected  to  increase 
the  radiating  power  of  each  tree.  The  upper  leaves  radiate  freely 
towards  the  stars  and  the  cold  inter-stellar  spaces,  while  the  lower 
ones  radiate  to  those  above  and  receive  less  heat  in  return ; con- 
sequently, during  the  absence  of  the  sun,  each  tree  cools  gradually 
downward  from  top  to  bottom.  Hence  we  must  take  into  account 
not  merely  the  area  of  leaf-surface  actually  exposed  to  the  sky, 
but,  to  a greater  or  less  extent,  the  surface  of  every  leaf  in  the 
whole  tree  or  the  whole  wood.  This  is  evidently  a point  in  which 
the  action  of  the  forest  may  be  expected  to  differ  from  that  of  the 
meadow  or  naked  earth ; for  though,  of  course,  inferior  strata  tend 

* Journal  Scot.  Met.  Soc.,  New  Series,  No.  xxvi.,  p.  35. 

t Quoted  by  Mr  Milne  Home. 


116  Proceedings  of  the  Royal  Society 

to  a certain  extent  to  follow  somewhat  the  same  course  as  the  mass 
of  inferior  leaves,  they  do  so  to  a less  degree — conduction,  and  the 
conduction  of  a very  slow  conductor,  being  substituted  for  radiation. 

We  come  next,  however,  to  a second  point  of  difference.  In 
the  case  of  the  meadow,  the  chilled  air  continues  to  lie  upon  the 
surface,  the  grass,  as  Humboldt  says,  remaining  all  night  submerged 
in  the  stratum  of  lowest  temperature ; while  in  the  case  of  trees, 
the  coldest  air  is  continually  passing  down  to  the  space  underneath 
the  boughs,  or  what  we  may  perhaps  term  the  crypt  of  the  forest. 
Here  it  is  that  the  consideration  of  any  piece  of  woodland  con- 
ceived as  a solid  comes  naturally  in;  for  this  solid  contains  a 
portion  of  the  atmosphere,  partially  cut  off  from  the  rest,  more  or 
less  excluded  from  the  influence  of  wind,  and  lying  upon  a soil 
that  is  screened  all  day  from  insolation  by  the  impending  mass  of 
foliage.  In  this  way  (and  chiefly,  I think,  from  the  exclusion  of 
winds),  we  have  underneath  the  radiating  leaf-surface  a stratum 
of  comparatively  stagnant  air,  protected  from  many  sudden  varia- 
tions of  temperature,  and  tending  only  slowly  to  bring  itself  into 
equilibrium  with  the  more  general  changes  that  take  place  in  the 
free  atmosphere. 

Over  and  above  what  has  been  mentioned,  thermal  effects  have 
been  attributed  to  the  vital  activity  of  the  leaves  in  the  transuda- 
tion of  water,  and  even  to  the  respiration  and  circulation  of  living . 
wood.  The  whole  actual  amount  of  thermal  influence,  however, 
is  so  small  that  I may  rest  satisfied  with  mere  mention.  If  these 
actions  have  any  effect  at  all,  it  must  be  practically  insensible;  and 
the  others  that  I have  already  stated  are  not  only  sufficient  validly 
to  account  for  all  the  observed  differences,  but  would  lead  natu- 
rally to  the  expectation  of  differences  very  much  larger  and  better 
marked.  To  these  observations  I proceed  at  once.  Experience 
has  been  acquired  upon  the  following  three  points  : — 1.  The 
relation  between  the  temperature  of  the  trunk  of  a tree  and  the 
temperature  of  the  surrounding  atmosphere;  2.  The  relation 
between  the  temperature  of  the  air  under  a wood  and  the  tempera- 
ture of  the  air  outside;  and,  3.  The  relation  between  the  tem- 
perature of  the  air  above  a wood  and  the  temperature  of  the  air 
above  cleared  land. 

As  to  the  first  question,  there  are  several  independent  series  of 


117 


of  Edinburgh,  Session  1872-73. 

observations ; and  I may  remark  in  passing,  what  applies  to  all, 
that  allowance  must  be  made  throughout  for  some  factor  of  specific 
heat.  The  results  were  as  follows : — The  seasonal  and  monthly 
means  in  the  tree  and  in  the  air  were  not  sensibly  different.  The 
variations  in  the  tree,  in  M.  Becquerel’s  own  observations,  appear 
as  considerably  less  than  a fourth  of  those  in  the  atmosphere,  and 
he  has  calculated,  from  observations  made  at  Geneva  between  1796 
and  1798,  that  the  variations  in  the  tree  were  less  than  a fifth  of 
those  in  the  air ; but  the  tree  in  this  case,  besides  being  of  a 
different  species,  was  seven  or  eight  inches  thicker  than  the  one 
experimented  on  by  himself.*  The  variations  in  the  tree,  therefore, 
are  always  less  than  those  in  the  air,  the  ratio  between  the  two 
depending  apparently  on  the  thickness  of  the  tree  in  question  and 
the  rapidity  with  which  the  variations  followed  upon  one  another. 
The  times  of  the  maxima,  moreover,  were  widely  different : in  the 
air,  the  maximum  occurs  at  2 p.m.  in  winter,  and  at  3 p.m.  in 
summer;  in  the  tree,  it  occurs  in  winter  at  6 p.m.,  and  in  summer 
between  10  and  11  p.m.  At  nine  in  the  morning  in  the  month  of 
June,  the  temperatures  of  the  tree  and  of  the  air  had  come  to  an 
equilibrium.  A similar  difference  of  progression  is  visible  in  the 
means,  which  differ  most  in  spring  and  autumn,  and  tend  to 
equalise  themselves  in  winter  and  in  summer.  But  it  appears 
most  strikingly  in  the  case  of  variations  somewhat  longer  in  period 
than  the  daily  ranges.  The  following  temperatures  occurred 
during  M.  Becquerel’s  observations  in  the  Jardin  des  Plantes: — 
1859. 

rv  . Temperature  Temperature 

of  the  Air.  in  the  Tree. 

O O 


Dec 

.15, 

26-78 

32 

?> 

16, 

19.76 

32 

„ 

17, 

17-78 

31-46 

„ 

18, 

13-28 

' 30-56 

55 

19, 

12-02 

28-40 

„ 

20, 

12-54 

25-34 

55 

21, 

38-30 

27-86 

55 

22, 

43-34 

30-92 

55 

23, 

44-06 

31-46 

* Atlas  Meteorologique  de  l’Observatoire  Imperial,  1867. 


118  Proceedings  of  the  Royal  Society 


A.  moment’s  comparison  of  the  two  columns  will  make  the  prin- 
ciple apparent.  The  temperature  of  the  air  falls  nearly  fifteen 
degrees  in  five  days;  the  temperature  of  the  tree,  sluggishly 
following,  falls  in  the  same  time  less  than  four  degrees.  Between 
the  19th  and  the  20th  the  temperature  of  the  air  has  changed  its 
direction  of  motion,  and  risen  nearly  a degree ; but  the  tempera- 
ture of  the  tree  persists  in  its  former  course,  and  continues  to  fall 
nearly  three  degrees  farther.  On  the  21st  there  comes  a sudden 
increase  of  heat,  a sudden  thaw  ; the  temperature  of  the  air  rises 
twenty-five  and  a-half  degrees;  the  change  at  last  reaches  the  tree, 
but  only  raises  its  temperature  by  less  than  three  degrees ; and 
even  two  days  afterwards,  when  the  air  is  already  twelve  degrees 
above  freezing  point,  the  tree  is  still  half  a degree  below  it.  Take, 
again,  the  following  case  : — 


Date. 

1859. 

Temperature 
of  the  Air. 

Temperature 
in  the  Tree. 

July  13, 

8B92 

76-28 

)> 

14, 

82-58 

78-62 

15, 

8042 

77-72 

?> 

16, 

79-88 

78-44 

? ? 

17, 

73-22 

75-92 

>? 

18, 

68-54 

74-30 

55 

19, 

65-66 

70-70 

order 

reappears. 

From  the  1 

3th  to  the  19th  the  tern- 

perature  of  the  air  steadily  falls,  while  the  temperature  of  the  tree 
continues  apparently  to  follow  the  course  of  previous  variations, 
and  does  not  really  begin  to  fall,  is  not  really  affected  by  the  ebb 
of  heat,  until  the  17th,  three  days  at  least  after  it  had  been  ope- 
rating in  the  air.*  Hence  we  may  conclude  that  all  variations  of 
the  temperature  of  the  air,  whatever  be  their  period,  from  twenty- 
four  hours  up  to  twelve  months,  are  followed  in  the  same  manner  by 
variations  in  the  temperature  of  the  tree  ; and  that  those  in  the 
tree  are  always  less  in  amount  and  considerably  slower  of  occur- 
rence than  those  in  the  air.  This  thermal  sluggishness , so  to  speak, 
seems  capable  of  explaining  all  the  phenomena  of  the  case  without 


* Comptes  Rendus  de  l’Academie,  29th  March  1869. 


119 


of  Edinburgh , Session  1872-73. 

any  hypothetical  vital  power  of  resisting  temperatures  below  the 
freezing  point,  such  as  is  hinted  at  even  by  Becquerel. 

Reaumur,  indeed,  is  said  to  have  observed  temperatures  in  slen- 
der trees  nearly  thirty  degrees  higher  than  the  temperature  of  the 
air  in  the  sun ; but  we  are  not  informed  as  to  the  conditions  under 
which  this  observation  was  made,  and  it  is  therefore  impossible  to 
assign  to  it  its  proper  value.  The  sap  of  the  ice-plant  is  said  to  be 
materially  colder  than  the  surrounding  atmosphere ; and  there  are 
several  other  somewhat  incongruous  facts,  which  tend,  at  first  sight, 
to  favour  the  view  of  some  inherent  power  of  resistance  in  some 
plants  to  high  temperatures,  and  in  others  to  low  temperatures.* 
But  such  a supposition  seems  in  the  meantime  to  be  gratuitous. 
Keeping  in  view  the  thermal  redispositions,  which  must  be  greatly 
favoured  by  the  ascent  of  the  sap,  and  the  difference  between  the 
condition  as  to  temperature  of  such  parts  as  the  root,  the  heart  of 
the  trunk,  and  the  extreme  foliage,  and  never  forgetting  the  un- 
known factor  of  specific  heat,  we  may  still  regard  it  as  possible  to 
account  for  all  anomalies  without  the  aid  of  any  such  hypothesis. 
We  may,  therefore,  I think,  disregard  small  exceptions,  and  state 
the  result  as  follows: — 

If,  after  every  rise  or  fall,  the  temperature  of  the  air  remained 
stationary  for  a length  of  time  proportional  to  the  amount  of  the 
change,  it  seems  probable — setting  aside  all  question  of  vital  heat 
— that  the  temperature  of  the  tree  would  always  finally  equalise 
itself  with  the  new  temperature  of  the  air,  and  that  the  range  in 
tree  and  atmosphere  would  thus  become  the  same.  This  pause, 
however,  does  not  occur : the  variations  follow  each  other  without 
interval ; and  the  slow-conducting  wood  is  never  allowed  enough 
time  to  overtake  the  rapid  changes  of  the  more  sensitive  air. 
Hence,  so  far  as  we  can  see  at  present,  trees  appear  to  be  simply 
bad  conductors,  and  to  have  no  more  influence  upon'the  tempera- 
ture of  their  surroundings  than  is  fully  accounted  for  by  the  conse- 
quent tardiness  of  their  thermal  variations. 

Observations  bearing  on  the  second  of  the  three  points  have 
been  made  by  Becquerel  in  France,  by  La  Cour  in  Jutland  and 
Iceland,  and  by  Rivoli  at  Posen.  The  results  are  perfectly  con- 

* Prof.  Balfour’s  Class-Book  of  Botany,  Physiology,  chap.  xii.  page  670. 


VOL.  VIII. 


Q 


±20 


Proceedings  of  the  Royal  Society 

gruous.  Becquerel’s  observations  * * * § were  made  under  wood,  and 
about  a hundred  yards  outside  in  open  ground,  at  three  stations  in 
the  district  of  Montargis,  Loiret.  There  was  a difference  of  more 
than  one  degree  Fahrenheit  between  the  mean  annual  temperatures 
in  favour  of  the  open  ground.  The  mean  summer  temperature  in 
the  wood  was  from  two  to  three  degrees  lower  than  the  mean  sum- 
mer temperature  outside.  The  mean  maxima  in  the  wood  were 
also  lower  than  those  without  by  a little  more  than  two  degrees. 
Herr  La  Courf  found  the  daily  range  consistently  smaller  inside 
the  wood  than  outside.  As  far  as  regards  the  mean  winter  tempe- 
ratures, there  is  an  excess  in  favour  of  the  forest,  but  so  trifling  in 
amount  as  to  be  unworthy  of  much  consideration.  Libri  found  that 
the  minimum  winter  temperatures  were  not  sensibly  lower  at  Flo- 
rence, after  the  Appenines  had  been  denuded  of  forest,  than  they 
had  been  before.J  The  disheartening  contradictoriness  of  his  obser- 
vations on  this  subject  led  Herr  Eivoli  to  the  following  ingenious 
and  satisfactory  comparison. § Arranging  his  results  according  to 
the  wind  that  blew  on  the  day  of  observation,  he  set  against  each 
other  the  variation  of  the  temperature  under  wood  from  that  with- 
out, and  the  variation  of  the  temperature  of  the  wind  from  the 
local  mean  for  the  month  : — 


Wind,  . . 

N. 

N.E. 

E. 

S.E. 

S. 

s.w. 

w. 

N.W. 

Var.  in  Wood, 

+ 0-60 

+ 0-26 

+ 0*26 

+ 0-04 

-0-04 

-0-20 

+ 0*16 

+ 0-07 

Yar.  in  Wind, 

-030 

1 

-2*60 

-330 

-1*20 

+ 1-00 

+ 1-30 

+ 1-00 

+ 1*00 

From  this  curious  comparison,  it  becomes  apparent  that  the 
variations  of  the  difference  in  question  depend  upon  the  amount  of 
variations  of  temperature  which  take  place  in  the  free  air,  and  on 
the  slowness  with  which  such  changes  are  communicated  to  the 
stagnant  atmosphere  of  woods;  in  other  words,  as  Herr  Eivoli 
boldly  formulates  it,  a forest  is  simply  a bad  conductor.  But  this 

* Comptes  Kendus,  1867  and  1869.  t See  his  paper. 

J Annales  de  Chimie  et  de  Physique,  xlv.,  1880.  A more  detailed  compari- 
son of  the  climates  in  question  would  be  a most  interesting  and  important 

contribution  to  the  subject. 

§ Keviewed  in  the  Austrian  Meteorological  Magazine,  vol.  iv.  p.  543. 


121 


of  Edinburgh,  Session  1872-73. 

is  precisely  the  same  conclusion  as  we  have  already  arrived  at  with 
regard  to  individual  trees ; and  in  Herr  Rivoli’s  table,  what  we  see 
is  just  another  case  of  what  we  saw  in  M.  Becquerel’s — the  diffe- 
rent progression  of  temperatures.  It  must  he  obvious,  however, 
that  the  thermal  condition  of  a single  tree  must  be  different  in 
many  ways  from  that  of  a combination  of  trees  and  more  or  less 
stagnant  air,  such  as  we  call  a forest.  And  accordingly  we  find,  in 
the  case  of  the  latter,  the  following  new  feature  : The  mean  yearly 
temperature  of  woods  is  lower  than  the  mean  yearly  temperature  of 
free  air,  while  they  are  decidedly  colder  in  summer,  and  very  little, 
if  at  all,  warmer  in  winter.  Hence,  on  the  whole,  forests  are  colder 
than  cleared  lands.  But  this  is  just  what  might  have  been  ex- 
pected from  the  amount  of  evaporation,  the  continued  descent  of 
cold  air,  and  its  stagnation  in  the  close  and  sunless  crypt  of  a forest ; 
and  one  can  only  wonder  here,  as  elsewhere,  that  the  resultant  dif- 
ference is  so  insiguificant  and  doubtful. 

We  come  now  to  the  third  point  in  question,  the  thermal  influ- 
ence of  woods  upon  the  air  above  them.  It  will  be  remembered 
that  we  have  seen  reason  to  believe  their  effect  to  be  similar  to 
that  of  certain  other  surfaces,  except  in  so  far  as  it  may  be  altered, 
in  the  case  of  the  forest,  by  the  greater  extent  of  effective  radiating 
area,  and  by  the  possibility  of  generating  a descending  cold  cur- 
rent as  well  as  an  ascending  hot  one.  M.  Becquerel  is  (so  far 
as  I can  learn)  the  only  observer  who  has  taken  up  the  elucidation 
of  this  subject.  He  placed  his  thermometers  at  three  points  : * A 
and  B were  both  about  seventy  feet  above  the  surface  of  the  ground; 
but  A was  at  the  summit  of  a chestnut  tree,  while  B was  in  the 
free  air,  fifty  feet  away  from  the  other.  C was  four  or  five  feet 
above  the  ground,  with  a northern  exposure ; there  was  also  a fourth 
station  to  the  south,  at  the  same  level  as  this  last,  but  its  readings 
are  very  seldom  referred  to.  After  several  years  of  observation, 
the  mean  temperature  at  A was  found  to  be  between  one  and  two 
degrees  higher  than  that  at  B.  The  order  of  progression  of  differ- 
ences is  as  instructive  here  as  in  the  two  former  investigations. 
The  maximum  difference  in  favour  of  station  A occurred  between 
three  and  five  in  the  afternoon,  later  or  sooner  according  as  there 


* Comptes  Rendus,  28th  May  1860. 


122  Proceedings  of  the  Royal  Society 

had  been  more  or  less  sunshine,  and  ranged  sometimes  as  high  as 
seven  degrees.  After  this  the  difference  kept  declining  until  sun- 
rise, when  there  was  often  a difference  of  a degree,  or  a degree 
and  a half,  upon  the  other  side.  On  cloudy  days  the  difference 
tended  to  a minimum.  During  a rainy  month  of  April,  for  ex- 
ample, the  difference  in  favour  of  station  A was  less  than  half  a 
degree;  the  first  fifteen  days  of  May  following,  however,  were 
sunny,  and  the  difference  rose  to  more  than  a degree  and  a half.* 
It  will  he  observed  that  I have  omitted  up  to  the  present  point  all 
mention  of  station  C.  I do  so  because  M.  Becquerel’s  language 
leaves  it  doubtful  whether  the  observations  made  at  thist  station  are 
logically  comparable  with  those  made  at  the  other  two.  If  the  end 
in  view  were  to  compare  the  progression  of  temperatures  above  the 
earth,  above  a tree,  and  in  free  air,  removed  from  all  such  radiative 
and  absorptive  influences,  it  is  plain  that  all  three  should  have  been 
equally  exposed  to  the  sun  or  kept  equally  in  shadow.  As  the 
observations  were  made,  they  give  us  no  notion  of  the  relative  action 
of  earth-surface  and  forest-surface  upon  the  temperature  of  the  con- 
tiguous atmosphere  ; and  this,  as  it  seems  to  me,  was  just  the  crux  of 
the  problem.  So  far,  however,  as  they  go,  they  seem  to  justify  the 
view  that  all  these  actions  are  the  same  in  kind,  however  they  may 
differ  in  degree.  We  find  the  forest  heating  the  air  during  the 
day,  and  heating  it  more  or  less  according  as  there  has  been  more 
or  less  sunshine  for  it  to  absorb,  and  we  find  it  also  chilling  it  dur- 
ing the  night ; both  of  which  are  actions  common  to  any  radiating 
surface,  and  would  be  produced,  if  with  differences  of  amount  and 
time,  by  any  other  such  surface  raised  to  the  mean  level  of  the  ex- 
posed foliage. 

To  recapitulate  : 

ls£,  We  find  that  single  trees  appear  to  act  simply  as  bad  con- 
ductors. 

2 d,  We  find  that  woods,  regarded  as  solids,  are,  on  the  whole, 
slightly  lower  in  temperature  than  the  free  air  which  they  have 
displaced,  and  that  they  tend  slowly  to  adapt  themselves  to  the 
various  thermal  changes  that  take  place  without  them. 

3 d,  We  find  forests  regarded  as  surfaces  acting  like  any  other 

* Comptes  Rend  us,  20th  May  1861. 


123 


of  Edin  b urgh , Session  187 2-7 3 

part  of  the  earth’s  surface,  probably  with  more  or  less  difference 
in  amount  and  progression,  which  we  still  lack  the  information 
necessary  to  estimate. 

All  this  done,  I am  afraid  that  there  can  be  little  doubt  that  the 
more  general  climatic  investigations  will  be  long  and  vexatious. 
Even  in  South  America,  with  extremely  favourable  conditions,  the 
result  is  far  from  being  definite.  Glancing  over  the  table  pub- 
lished by  M.  Becquerel  in  his  book  on  climates,  from  the  observa- 
tions of  Humboldt,  Hall,  Boussingault,  and  others,  it  becomes 
evident,  I think,  that  nothing  can  be  founded  upon  the  compari- 
sons therein  instituted ; that  all  reasoning,  in  the  present  state  of 
our  information,  is  premature  and  unreliable.  Strong  statements 
have  certainly  been  made ; and  particular  cases  lend  themselves  to 
the  formation  of  hasty  judgments.  “ From  the  Bay  of  Cupica  to 
the  Gulf  of  Guayaquil,”  says  M.  Boussingault,  11  the  country  is 
covered  with  immense  forests  and  traversed  by  numerous  rivers ; 
it  rains  there  almost  ceaselessly;  and  the  mean  temperature  of  this 

moist  district  scarcely  reaches  78°  8 F At  Payta 

commence  the  sandy  deserts  of  Priura  and  Sechura ; to  the  con- 
stant humidity  of  Choco  succeeds  almost  at  once  an  extreme  of 
dryness ; and  the  mean  temperature  of  the  coast  increases  at  the 
same  time  by  1°*8  F.”  * Even  in  this  selected  favourable  in- 
stance it  might  be  argued  that  the  part  performed  in  the  change 
by  the  presence  or  absence  of  forest  was  comparatively  small; 
there  seems  to  have  been,  at  the  same  time,  an  entire  change 
of  soil;  and,  in  our  present  ignorance,  ‘it  would  be  difficult  to  say 
by  how  much  this  of  itself  is  able  to  affect  the  climate.  Moreover, 
it  is  possible  that  the  humidity  of  the  one  district  is  due  to  other 
causes  besides  the  presence  of  wood,  or  even  that  the  presence  of 
wood  is  itself  only  an  effect  of  some  more  general  difference  or 
combination  of  differences.  Be  that  as  it  may,  however,  we  have 
only  to  look  a little  longer  at  the  table  before  referred  to,  to  see 
how  little  weight  can  be  laid  on  such  special  instances.  Let  us 
take  five  stations,  all  in  this  very  district  of  Choco.  Hacquita  is 
eight  hundred  and  twenty  feet  above  Novita,  and  their  mean  tem- 
peratures are  the  same.  Alto  de  Mombu,  again,  is  five  hundred 


■#  Becquerel,  “ Climats,”  p.  141. 


124 


Proceedings  of  the  Royal  Society 

feet  higher  than  Hacquita,  and  the  mean  temperature  lias  here 
fallen  nearly  two  degrees.  Go  up  another  five  hundred  feet  to 
Tambo  de  la  Orquita,  and  again  we  find  no  fall  in  the  mean  tem- 
perature. Go  up  some  five  hundred  further  to  Chami,  and  there  is 
a fall  in  the  mean  temperature  of  nearly  six  degrees.  Such  num- 
bers are  evidently  quite  untrustworthy;  and  hence  we  may  judge 
how  much  confidence  can  be  placed  in  any  generalisation  from  these 
South  American  mean  temperatures. 

The  question  is  probably  considered  too  simply — too  much  to  the 
neglect  of  concurrent  influences.  Until  we  know,  for  example, 
somewhat  more  of  the  comparative  radiant  powers  of  different  soils, 
we  cannot  expect  any  very  definite  result.  A change  of  temperature 
would  certainly  be  effected  by  the  plantation  of  such  a marshy  dis- 
trict as  the  Sologne,  because,  if  nothing  else  were  done,  the  roots 
might  pierce  the  impenetrable  subsoil,  allow  the  surface-water  to 
drain  itself  off,  and  thus  dry  the  country.  But  might  not  the  change 
be  quite  different  if  the  soil  planted  were  a shifting  sand,  which, 
fixed  by  the  roots  of  the  trees,  would  become  gradually  covered  with 
a vegetable  earth,  and  thus  be  changed  from  dry  to  wet  ? Again, 
the  complication  and  conflict  of  effects  arises,  not  only  from  the 
soil,  vegetation,  and  geographical  position  of  the  place  of  the 
experiment  itself,  but  from  the  distribution  of  similar  or  different 
conditions  in  its  immediate  neighbourhood,  and  probably  to  great 
distances  on  every  side.  A forest,  for  example,  as  we  know  from 
Herr  Bivoli’s  comparison,  would  exercise  a perfectly  different 
influence  in  a cold  country  subject  to  warm  winds,  and  in  a warm 
country  subject  to  cold  winds;  so  that  our  question  might  meet 
with  different  solutions  even  on  the  east  and  west  coasts  of  Great 
Britain. 

The  consideration  of  such  a complexity  points  more  and  more  to 
the  plantation  of  Malta  as  an  occasion  of  special  importance ; its 
insular  position  and  the  unity  of  its  geological  structure  both  tend 
to  simplify  the  question.  There  are  certain  points  about  the 
existing  climate,  moreover,  which  seem  specially  calculated  to  throw 
the  influence  of  woods  into  a strong  relief.  Thus,  during  four 
summer  months,  there  is  practically  no  rainfall.  Thus,  again,  the 
northerly  winds  when  stormy,  and  especially  in  winter,  tend  to 
depress  the  temperature  very  suddenly ; and  thus,  too,  the  southerly 


125 


of  MjdinOurgk,  /Session  1872-73. 

and  south-westerly  winds,  which  raise  the  temperature  during  their 
prevalence  to  from  eighty-eight  to  ninety-eight  degrees,  seldom  last 
longer  than  a few  hours;  insomuch  that  “ their  disagreeable  heat 
and  dryness  may  be  escaped  by  carefully  closing  the  windows  and 
doors  of  apartments  at  'their  onset.”*  Such  sudden  and  short 
variations  seem  just  what  is  wanted  to  accentuate  the  differences 
in  question.  Accordingly,  the  opportunity  seems  one  not  lightly 
to  he  lost,  and  the  British  Association  or  this  Society  itself 
might  take  the  matter  up  and  establish  a series  of  observations, 
to  be  continued  during  the  next  few  years.  Such  a combination 
of  favourable  circumstances  may  not  occur  again  for  years ; and 
when  the  whole  subject  is  at  a stand-still  for  want  of  facts,  the 
present  occasion  ought  not  to  go  past  unimproved. 

Such  observations  might  include  the  following  : — - 

The  observation  of  maximum  and  minimum  thermometers  in 
three  different  classes  of  situation — videlicet , in  the  areas  selected 
for  plantation  themselves,  at  places  in  the  immediate  neighbour- 
hood of  those  areas  wdiere  the  external  influence  might  be  expected 
to  reach  its  maximum,  and  at  places  distant  from  those  areas  where 
the  influence  might  be  expected  to  be  least. 

The  observation  of  rain-gauges  and  hygrometers  at  the  same 
three  descriptions  of  locality. 

In  addition  to  the  ordinary  hours  of  observation,  special  readings 
of  the  thermometers  should  be  made  as  often  as  possible  at  a change 
of  wind  and  throughout  the  course  of  the  short  hot  breezes  alluded 
to  already,  in  order  to  admit  of  the  recognition  and  extension  of 
Herr  Rivoli’s  comparison. 

Observation  of  the  periods  and  forces  of  the  land  and  sea  breezes. 

Gauging  of  the  principal  springs,  both  in  the  neighbourhood  of 
the  areas  of  plantation  and  at  places  far  removed  from  those  areas. 

* Scoresby- Jackson’s  “ Medical  Climatology.” 


126  Proceedings  of  the  Royal  Society 

2.  Observations  and  Experiments  on  the  Fluid  in  the 
Cavities  of  Calcareous  Spar,  By  Dr  James  Hunter  and 
Edward  Sang. 

At  a recent  meeting  I laid  before  the  Society  a short  notice  of  a 
phenomenon  exhibited  by  the  fluid  contained  in  the  cavities  of 
calcareous  spar.  This  phenomenon  had  been  observed  only  a few 
days  before,  and  the  notice  was  given  for  the  purpose  of  directing 
to  it  the  attention  of  other  observers,  and  particularly  of  those  who 
happen  to  possess  other  minerals  with  analogous  cavities,  and  I now 
propose  to  give  an  account  of  some  .more  recent  experiments  and 
observations  in  regard  to  it. 

Of  all  known  minerals,  carbonate  of  lime  presents  the  greatest 
facility  for  the  study  of  the  laws  of  crystallisation.  We  trace  in  it 
evidences  of  the  stoppage  and  resumption  of  growth  ; we  see  marks 
of  abrasion  and  fracture  on  surfaces  once  external  but  now  covered 
over;  layers  of  mud  and  portions  of  extraneous  bodies  are  seen 
inclosed ; yet  amid  all  of  these  interruptions  the  direction  of  the 
planes  of  crystallisation  are  kept  with  remarkable  persistence. 

The  ultimate  or  outer  surface  of  a piece  of  Iceland  spar  of  any 
great  size  presents  a rough  appearance,  caused  by  the  meeting  of 
many  surfaces  of,  as  it  were,  smaller  crystals;  the  hollows  among 
these  had  not  been  filled  up  when  the  deposition  ceased.  If  now 
there  be  an  accession  of  liquid  holding  lime  in  solution,  and  the 
crystallisation  be  renewed,  these  hollows  may  not  be  filled  up  from 
the  bottom,  but  may  be  covered  over  by  the  new  mineral,  leaving 
the  spaces  full  of  the  mother  liquid,  so  that  when  the  whole  mass 
has  been  cooled  a small  vacuity  is  left.  Sometimes  these  cavities 
are  very  irregular,  at  other  times  their  surfaces  are  beautifully  flat 
and  often  obviously  parallel  to  the  cleavage  planes  of  the  spar. 
Hence,  in  mounting  such  specimens  for  microscopic  observation, 
we  must  be  careful  not  to  heat,  or  at  least  not  to  overheat,  the  spar; 
cold  cement  is  at  all  times  preferable. 

On  looking  at  any  object  in  the  interior  of  a piece  of  spar  we  see 
two  images,  one  belonging  to  the  ordinarily,  the  other  to  the 
extraordinarily  refracted  light.  Now,  in  all  bits  of  spar  containing 
faults,  the  crystallisation  has  been  interrupted  and  carried  on  in 


127 


of  Edinburgh,  Session  1872-73. 

various  conditions  as  to  temperature;  hence  the  direction  of  the 
axis  of  crystallisation  is  not  absolutely  kept,  as  is  obvious  on  any 
of  the  cleavage  surfaces.  Hence  the  path  of  the  extraordinarily 
refracted  ray  is  devious,  and  the  image  blurred ; while  the  path  of 
the  ordinary  ray,  depending  only  on  the  homogeneity  of  the 
substance,  is  straight.  For  the  purpose,  therefore,  of  viewing  any- 
thing in  the  interior  it  is  proper  to  eliminate  the  extraordinary 
light  by  using  a polarising  reflector,  a Nicohs  prism,  or  something 
equivalent.  This  blurredness  of  the  extraordinary  image  is 
common  in  crystals  of  other  substances,  and  is  due  to  the  very 
same  cause. 

When  a piece  of  spar  containing  a flat-faced  cavity  is  placed 
under  the  microscope,  and  a small  coin  or  other  bit  of  metal  is 
brought  near  it,  the  fluid  is  observed  to  take  the  opposite  end  of 
the  cavity.  For  convenience  a type-space  was  mounted  on  the  end 
of  a wire  fixed  to  a stand  so  as  to  be  readily  brought  into  position, 
and  the  same  repulsion  was  observed ; here  it  seemed  obvious  that 
the  metal  and  the  spar  had  both  the  same  temperature  with  the 
room,  and  thus  there  was  no  ground  for  suspicion  that  temperature 
had  to  do  with  the  phenomenon. 

Dr  James  Hunter,  while  repeating  the  trials,  observed  that  a 
coin  freshly  laid  down  acted  well,  but  that  after  some  time  its 
repulsion  was  less;  he  observed  the  same  thing  of  a recently 
rubbed  coin.  This  led  him  to  suspect  the  agency  of  heat,  and  on 
repeating  his  trials  it  became  clear  that  a difference  of  tempera- 
ture is  essential  to  the  exhibition  of  this  repulsion.  He  also  found 
that  any  substance  when  warmed  possesses  the  same  property,  and 
lost  no  time  in  communicating  to  me  the  result  of  his  observations. 
This  led  Mr  E.  Elmslie  Sang  to  suggest  the  trial  of  metal  cooled 
below  the  temperature  of  the  room ; and,  on  returning  home  from 
the  Society’s  last  meeting,  I found  that  Dr  Hunter  and  my  son 
had  completed  a set  of  trials  showing  most  clearly  that  the  fluid 
in  the  cavity  moves  from  a warmer  and  toward  a colder  body. 
This  may  be  very  well  shown  by  placing  a piece  of  metal  heated 
in  the  hand  upon  the  spar,  and  so  sending  the  fluid  to  the  farther 
end.  On  now  wetting  the  metal  with  ether,  so  as  to  cool  it,  the 
fluid  is  seen  to  come  to  the  nearer  end  of  the  cavity. 

This  discovery  by  Dr  Hunter  completely  changed  the  line  of 


VOL.  VIII. 


128  Proceedings  of  the  Royal  Society 

research  in  which  I was  engaged,  and  rendered  any  quantitative 
experiment  excessively  difficult,  because  we  have  no  means  of 
determining  the  temperatures  of  such  small  masses,  and  because  a 
very  slight  difference  of  temperature  is  enough  to  produce  the  ob- 
served effect. 

The  statement  that  when  A is  warmer  than  B we  have  repulsion, 
but  that  when  A is  the  colder  we  have  attraction,  cannot  he  uni- 
versal, because  if  A and  B were  merely  to  change  names  the 
enunciation  of  the  law  would  be  reversed.  Such  a law  can  only 
hold  good  between  members  of  two  distinct  classes,  and,  so  far  as 
we  have  yet  seen,  this  distinction  is  between  solids  and  fluids. 
Reflection  on  this  matter  brought  to  my  mind  a phenomenon  with 
which  I have  been  familiar  for  more  than  half  a century,  and 
whioh  I used  to  refer  to  some  peculiar  variety  of  what  is  called 
capillary  action . In  preparing  a small  drill,  such  as  is  used  by 
watchmakers,  the  little  tool  is  first  hardened  by  being  plunged 
while  red  hot  into  cold  water,  and  is  then  tempered  or  softened  to 
the  proper  degree.  This  tempering  is  done  by  dipping  the  drill 
in  oil  or  tallow,  and  then  heating  the  stock  end  of  it  in  a small 
flame.  The  oil  is  seen  to  gather  in  a drop,  which  moves  rapidly 
towards  the  point,  and  the  ebullition  of  this  drop  serves  to  mark 
the  proper  temperature. 

If  we  coat  a common  smooth  knitting  needle  with  a film  of  oil 
so  thin  that  it  will  not  flow,  and,  holding  the  needle  horizontally, 
bring  the  middle  of  it  to  the  edge  of  a flame,  we  shall  see  a bulg- 
ing mass  of  oil  form  on  each  side  and  move  away  from  the  flame, 
gathering  bulk  as  it  proceeds.  Here  we  have  a variation  of  the 
very  phenomenon  seen  in  the  calc-spar ; the  fluid  is  repelled  by 
the  hotter  metal.  The  experiment  may  be  varied  thus.  Having 
placed  the  middle  of  a cleaned  wire  in  the  flame,  put  a small 
drop  of  oil  on  it  near  to  the  flame;  this  drop  will  be  seen  to 
move  towards  the  colder  part  of  the  wire.  Another  variation  is 
to  prepare  a thin  metallic  plate,  and  to  coat  its  upper  surface  with 
a film  of  oil ; when  the  middle  of  the  plate  is  set  upon  a piece  of 
hot  iron,  the  oil  gathers  in  a wave  all  round  the  hot  part,  and  slowly 
recedes  from  it. 

After  having  assisted  at  these  experiments  with  the  oil,  Dr 
Hunter  made  a very  beautiful  variation,  which  consisted  in  direct- 


129 


of  Edinburgh , Session  1872-73. 

ing  a stream  of  warm  air  upon  the  end  of  the  piece  of  spar  under 
the  microscope.  The  fluid  recedes  from  that  end,  and  the  action  is 
reversed  by  changing  the  position  of  the  current. 

On  holding  horizontally  a glass  tube,  of  which  the  inside  has 
been  thinly  coated  with  coloured  oil,  and  on  heating  a part  of  it, 
the  oil  is  seen  to  leave  the  heated  part  and  become  heaped  up  on 
each  side.  The  same  thing  takes  place  with  water;  hut  on 
making  trial  with  sulphuric  acid,  no  such  effect  was  perceptible. 

The  occurrence  of  so  many  analogous  phenomena  points  to  some 
general  or,  at  least,  comprehensive  law ; and  the  question  arises — 
Whether  is  this  motion  of  the  fluid  dependent  on  actual  contact, 
and  due  to  the  unequal  heating  of  the  adjacent  solid,  or  is  it  a true 
repulsion  between  the  colder  fluid  and  the  warmer  solid,  indepen- 
dent altogether  of  contact  ? 

The  instantaneous  movement  of  the  fluid  when  a warm  body 
is  brought  near  to  without  touching  the  spar,  favours  the  latter 
interpretation  of  the  phenomena,  but  the  former  interpretation 
seems  to  be  more  in  accordance  with  the  other  variations  of  the 
experiments.  If,  when  a warm  body  is  brought  near,  the  action 
be  to  induce  an  unequal  heating  of  the  containing  vessel,  and  if 
the  motions  he  due  to  the  attractions  or  repulsions  between  the 
fluid  and  the  spar,  no  real  repulsion  will  be  shown  between  the 
warm  body  and  the  total  mass.  But  if  the  motion  be  due  to 
a repulsion  between  the  warm  body  and  the  colder  fluid,  the  mass, 
as  a whole,  will  be  repelled.  Hence,  by  poising  the  vessel  contain- 
ing the  fluid  so  delicately  as  to  allow  of  this  repulsion  being 
exhibited  if  it  exist,  we  shall  be  able  to  determine  the  true  nature 
of  the  action.  In  making  the  arrangements  we  must  eliminate 
the  influence  of  aerial  currents  caused  by  the  difference  of  tempe- 
rature. I am  in  hopes  of  being  able  soon  to  decide  the  question 
as  between  the  two  interpretations  by  help  of  an  instrument  of 
sufficient  delicacy. 

In  making  the  experiments  with  glass  tubes,  it  was  noticed 
incidentally  that  when  the  glass  has  been  so  heated  as  to  drive 
the  oil  or  the  water  completely  from  it,  the  surface  has  acquired 
the  property  of  not  being  easily  oiled  or  wet  again.  I show  one 
tube,  over  the  surface  of  which  the  oil  flowed  easily ; it  has  been 
hermetically  closed,  and  has  since  that  been  heated.  The  oil  now 


130 


Proceedings  of  the  Royal  Society 

refuses  to  flow,,  and  remains  aggregated  in  oil-drops  over  the 
surface.  When  the  glass  in  the  proximity  of  one  of  these  drops  is 
heated,  the  oil  is  seen  to  creep  away  from  the  heated  part,  leaving 
behind  it  no  trace  of  oil  on  the  surface. 

3.  On  “ Tait’s  Property  of  the  Eetina.” 

By  George  Forbes,  Esq. 

Professor  Tait  having  asked  me  to  communicate  to  the  Society 
some  experiments  I have  made  from  time  to  time  on  the  property 
of  the  retina  discovered  by  him,  and  communicated  to  this  Society, 
15th  January  1872,  I prepared  the  following  notes.  It  will  be 
remembered  that  he  pointed  out  that  when  the  eye  has  been  rested 
for  a long  time  the  first  impression  of  light  gives  a red  colour. 
Professor  Crum  Brown  stated  at  the  same  meeting,  that  after  Pro- 
fessor Tait  had  told  him  of  the  appearance  he  had  himself  observed 
a like  phenomenon.  Awaking  one  morning  at  grey  dawn,  and 
opening  his  eyes  suddenly,  he  saw  a glare  of  red  on  the  window, 
and  was  so  struck  by  it  that  he  hastily  rose  to  discover  what  house 
was  on  fire. 

The  circumstances  under  which  Professor  Tait  made  the  obser- 
vation were  as  follows : — He  was  suffering  from  sleepless  nights 
owing  to  the  illness  arising  from  re-vaccination.  He  found  that  at 
each  time  of  awaking,  a portion  of  the  wall  feebly  illuminated  by 
a gas-flame  appeared  to  have  a crimson  hue,  and  acquired  its  true 
white  colour  only  after  a few  seconds  of  time. 

I have  very  little  to  tell  the  Society,  except  to  corroborate  the 
evidence  of  Professor  Tait,  and  to  describe  a method  of  observa- 
tion that  removes  the  necessity  for  re-vaccination  or  even  sleepless 
nights.  I have  reproduced  the  appearance,  I suppose,  thirty  times 
during  the  past  winter.  I lower  the  gas  until  there  is  only  a 
small  blue  flame.  This  may  be  done  before  going  to  bed,  and  the 
experiment  made  in  the  morning,  provided  the  window  is  darkened 
by  shutters.  In  the  morning,  on  suddenly  turning  up  the  'gas, 
either  the  gas-flame  assumes  the  crimson  flush,  or  if  there  be  a 
globe  of  ground  glass  on  the  gas,  that  globe  assumes  the  hue.  If 
the  gas  he  quickly  lowered  again,  a short  rest  is  sufficient  before 
repeating  the  experiment.  It  is  never  necessary  (in  my  case)  to 


of  Edinburgh , Session  1 872-7 3.  131 

be  in  the  dark  for  more  than  an  hour  or  so.  But  when  the  time 
of  darkness  is  short,  the  crimson  flush  is  seen  only  for  a small 
fraction  of  a second.  It  is  not  necessary  to  have  just  awoken  from 
sleep,  though  certainly  this  seems  to  favour  the  appearance, 
making  it  more  extended  and  more  lasting.  The  colour  of  this 
appearance  is  the  same  as  that  crimson  flush  which  is  often  seen 
when  the  eyelids  are  closed  and  a light  is  shining  on  them.  This 
struck  both  Professor  Tait  and  myself,  and  led  him  to  test  whether 
it  was  due  to  the  same  cause,  viz.,  the  passage  of  light  through 
the  blood-vessels. 

****** 

I had  proceeded  thus  far,  and  had  moreover  duly  apologised  to 
the  Society  for  offering  them  a communication  with  so  little 
novelty  in  it,  when  accident,  or  rather  an  inexcusable  drowsiness, 
led  me  to  perform  some  experiments  that  I look  upon  as  of  far 
greater  importance,  in  that  they  give  an  extension  to  the  property 
of  the  retina  observed  by  Tait,  in  a direction  quite  unlooked  for. 

When  travelling  in  the  train  from  Edinburgh  to  London  lately, 
I had  my  eyes  closed,  and  frequently  saw  that  crimson  flush  which 
is  so  often  seen  under  such  circumstances,  and  to  which  I have 
already  alluded.  This  has  been  stated  by  Professor  Tait  and  my- 
self to  be  of  the  same  hue  as  that  observed  by  him  in  the  cases 
mentioned  in  his  note.  It  has  always  been  attributed  without 
any  doubt  to  the  passage  of  the  light  through  the  blood-vessels  of 
the  eyelid.  But  I soon  noticed  a remarkable  fact,  viz.,  that  if  the 
light  of  the  sky  remained  of  the  same  brightness,  in  other  words, 
if  the  sun  were  not  flitting  behind  clouds,  this  crimson  flush  gave 
place  to  a dingy  orange  or  even  yellowish  brown  colour.  The 
brilliant  crimson  flush  was  in  these  circumstances  seldom  visible 
on  closing  the  eyelids,  and  it  invariably  gave  way  to  this  dingy 
colour.  On  continuing  to  repeat  this  experiment,  no  doubt  re- 
mained on  my  mind  of  the  fact.  Being  now  convinced  that  the 
appearance  of  white  light  passing  through  the  blood-vessels  of 
the  eyelid  is  of  this  orange  colour,  I was  at  a loss  to  account  for 
the  crimson  flush  that  is  so  often  seen.  I soon  noticed,  however, 
that  when  the  eyes  were  closed,  this  brilliant  colour  never  made  its 
appearance,  except  at  such  moments  as  when  the  sun  burst  out 
from  behind  a cloud,  thus  brightening  the  field  of  view.  I then 


132  Proceedings  of  the  Royal  Society 

covered  my  closed  eyes  with  my  hand,  so  as  to  cause  complete 
darkness.  If  I now  removed  my  hand,  the  eyelids  still  being  closed 
the  crimson  flush  made  its  appearance ; the  darkness  having  been 
continued  for  a considerable  time.  I soon  found  that  if  the  closed 
eyes  were  first  directed  to  a white  handkerchief,  and  then  to  the 
bright  sky,  the  crimson  flush  made  its  appearance.  At  this  stage 
the  true  explanation  of  the  phenomenon  began  to  appear.  It  was 
that  the  colour  of  white  light  that  has  passed  through  the  eyelid 
is  dingy  orange  or  yellowish  brown,  and  that  the  crimson  flush  is 
due  to  T ait’s  property  of  the  retina,  namely,  that  when  the  eye  is 
suddenly  illuminated , or  when  the  illumination  is  suddenly  increased , 
the  retina  first  acquires  the  qjoiver  of  recognising  the  deep  red  ; but  the 
other  colours  usually  follow  so  rapidly  as  to  prevent  this  fact  from 
being  recognised.  I hope  that  Professor  Tait  will  allow  me  to  make 
this  slight  addition  to  his  statement,  as  originally  made. 

According  to  this  theory,  the  reason  why  this  flush  is  only  some- 
times  seen  is,  that  peculiarly  favourable  circumstances  are  neces- 
sary for  observing  it.  These  are  (1),  a very  long  rest  to  the  eye, 
(as  this  is  how  Professor  Tait  and  Professor  Crum  Brown  saw  it) ; 
or  (2),  a very  sudden  illumination  of  the  retina  (this  is  the  experi- 
ment of  the  gas-flame  described  in  the  first  part  of  this  communi- 
cation) ; or  (3),  an  exposure  to  a very  feeble  light  after  the  eye 
has  been  in  the  dark  for  a short  time  (this  is  what  I have  just  de- 
scribed). To  prove  still  further  that  this,  and  not  the  transmission 
of  light  through  blood,  is  the  true  explanation  of  the  crimson  flush 
as  usually  seen,  I tried  the  following  experiment : — A piece  of 
common  whitey-brown  paper,  four  folds  thick,  was  placed  in  front 
of  one  eye  (the  other  being  quite  darkened).  This  shaded  eye  was 
kept  dark  for  a short  time,  then  keeping  it  closed  to  the  skin  to 
prevent  stray  light  from  entering,  the  head  was  raised,  and  the 
eye  opened  pointing  to  the  sky.  The  crimson  flush  was  un- 
precedentedly vivid,  but  soon  yielded  to  the  yellow  colour  of  the 
paper  employed.  Lastly,  six  folds  of  plain  white  glazed  writing 
paper  were  placed  in  front  of  the  eye  in  the  same  manner.  A 
longer  duration  of  darkness  was  necessary  than  in  the  last  case, 
but  then  the  crimson  flush  was  well  shown,  the  colour  then  changed 
to  orange,  and  it  was  some  time  before  it  assumed  its  natural  white 
colour. 


133 


of  Edinburgh,  Session  1872-73. 

These  experiments,  then,  prove  that  the  transmission  of  light 
through  the  blood-vessels  is  not  necessary  for  the  production  of  the 
crimson  flush,  and  that  a long  rest  be  given  to  the  eye  to  per- 
ceive the  phenomenon  described  by  Professor  Tait,  and  that  the 
former  depends  upon  the  latter  effect. 

In  the  experiments  last  described  the  whole  of  the  retina  was 
affected.  There  is  still  one  point  that  requires  explanation.  How 
is  it  that  either  a very  powerful  or  a very  feeble  light  is  the  most 
potent,  either  a gas  flame  or  diffuse  light  that  has  passed  through 
several  folds  of  paper  ? At  first  this  seems  to  militate  against  the 
identity  of  the  two  phenomena,  but  a little  consideration  explains 
- difficulty.  First,  if  the  light  be  very  bright,  e.g.,  a gas  flame,  the 
red  will  certainly  have  a greater  tendency  to  appear,  but  it  seems 
a 'priori  likely  that  the  other  colours  will  also  soon  become  apparent. 
Thus  we  should  expect  with  a powerful  flame  to  see  a very  intense 
redness,  lasting  a very  short  time.  Second,  if  the  light  be  very 
feeble,  e.g.,  diffuse  light  passing  through  paper.  Here  it  is  not 
likely  that  we  should  get  so  brilliant  a red,  but  it  is  certainly  very 
probable  that  it  will  be  much  longer  before  the  other  colours  become 
sensible,  since  they  are  so  feeble.  We  should  expect  then,  in  this 
case,  to  have  a less  powerful  red  lasting  a longer  time,  but  with  the 
gas  flame  a strikingly  brilliant  flush,  lasting  a very  short  time. 
Again,  with  a medium  light  the  green  and  blue  colours  would  be 
added  rapidly,  and  the  crimson  flush  would  not  be  powerful  enough 
to  be  conspicuous  in  that  short  time.  I may  say  that  in  every  point 
this  agrees  exactly  with  the  appearances  as  they  are  really  seen. 

4.  A Theory  of  Volcanic  Eruptions.  By  Daniel  Vaughan. 

From  researches  which  have  much  engaged  my  attention  for 
nearly  twenty  years,  I am  convinced  that  silica  performs^  very  im- 
portant part,  not  only  in  the  formation  of  the  earth’s  crust,  but  also 
in  leading  to  violent  subterranean  movements.  The  low  specific 
gravity  of  silicic  acid,  and  of  the  rocks  in  which  it  predominates, 
would  (if  much  of  the  internal  earth  were  fluid)  give  rise  to  certain 
results,  which  I traced  in  an  essay  published  in  1856,  and  also  in  a 
paper  which  was  brought  before  the  British  Association  for  the 
Advancement  of  Science  in  1861.  In  the  latter,  I have  given 


134  Proceedings  of  the  Boyal  Society 

reasons  for  believing  that  the  invisible  side  of  the  earth’s  crust  is 
very  irregular  in  its  structure ; and  that,  as  pressure  promotes 
solidification,  the  great  internal  mountains  must  constantly  increase 
in  depression  in  consequence  of  the  deposition  on  their  peaks  of 
solid  matter  of  low  density,  and  consisting  either  wholly  or  largely 
of  silicic  acid.  I ascribed  earthquakes  to  the  occasional  instability 
of  such  masses  of  new  rock,  as  their  size  and  buoyancy  causes  them 
to  Jbreak  loose  from  their  fastening,  and  an  ascending  stony 
avalanche  is  driven  against  the  weaker  parts  of  the  earth’s  crust. 

But,  on  taking  into  consideration  the  great  affinity  of  silicic  acid 
for  bases  at  a high  temperature,  volcanic  phenomena  may  be  traced 
to  the  collision  of  these  silicious  avalanches  against  such  sedi- 
mentary rocks  as  contain  carbonic  and  many  other  acids.  Car- 
bonate of  lime,  for  instance,  would  not  be  decomposed  by  heat  under 
the  pressure  it  feels  at  great  depths;  but  if  a stratum  of  limestone 
were  struck  by  a mass  of  incandescent  quartz,  or  of  highly  silicified 
rocks,  the  resulting  fragmentary  mass  would  swell  with  the  evolu- 
tion of  carbonic  acid,  and  give  rise  to  the  various  peculiarities 
observed  in  the  eruptions  and  the  upheaval  of  volcanic  mountains. 

5.  On  the  Placentation  of  the  Sloths.  By  Professor  Turner. 

After  referring  to  the  paucity  of  information  on  the  placental 
characters  of  the  sloths,  and  to  the  various  inferences  which  had 
been  drawn  by  anatomists  from  Carus’s  figure  of  the  placenta  of 
Bradypus  tridactylus,  some  holding  that  it  was  cotyledonary  and 
non-deciduate,  others  that  it  might  have  intermingled  with  it 
maternal  deciduous  substance,  the  author  proceeded  to  describe 
his  dissection  of  the  perfectly  fresh  gravid  uterus  of  a specimen 
of  a two -toed  sloth.  This  specimen,  which  was  presented  to  him 
by  Dr  David  Eidpath,  only  possessed  six  cervical  vertebrae,  and  was 
referred  to  the  Cholcepus  Hoffmanni  of  Peters. 

The  author  had  succeeded  in  obtaining  excellent  injections 
both  of  the  foetal  and  maternal  systems  of  blood-vessels.  The 
placenta  consisted  of  about  thirty  discoid  lobes,  aggregated  to- 
gether, and  occupied  about  fths  of  the  surface  of  the  ovum.  These 
lobes  could  be  peeled  off  the  placental  area  of  the  uterus,  and 
carried  away  with  them  a layer  of  deciduous  serotina,  the  curling 


135 


of  Edinburgh,  Session  1872-73. 

arteries,  utero-placental  veins,  and  a very  remarkable  system  of 
intra-placental  maternal  sinuses,  continuous  with  the  uterine 
vessels,  freely  anastomosing  with  each  other  within  the  substance 
of  the  lobes,  and  lying  between  and  in  contact  with  the  foetal  villi. 
Definite  walls,  distinct  from  the  walls  of  the  foetal  villi,  could  be 
traced  around  the  sinuses.  Crowds  of  red  blood  corpuscles  were 
situated  within  the  sinuses,  and  it  was  observed  that  many  of 
these  seemed  to  be  nucleated,  an  appearance  which  had  been 
recognised  a few  years  ago  by  Kuhne,  Eolleston,  and  Moseley,  in 
the  blood  corpuscles  of  the  Tardigrada.  This  sinus  system  pos- 
sessed a special  interest,  because  it  presented  a gradation  between 
the  capillary  net-work  of  the  uterine  mucous  membrane,  occurring 
in  the  diffused  placenta  of  the  mare  or  the  cetacean,  and  the  freely 
anastomosing  cavernous  maternal  blood  spaces  seen  in  the  highly 
concentrated  human  placenta.  The  amnion  lay  in  close  contact 
with  the  inner  surface  of  the  chorion,  as  in  the  human  foetal  mem- 
branes. The  foetus  possessed  a special  envelope,  like  that  figured 
and  described  by  Welcker,  as  investing  the  foetus  of  B.  tridactylus , 
and  named  by  him  an  Epitricliium.  Numerous  additional  details 
respecting  the  structure  of  the  placenta  and  membranes  are  con- 
tained in  the  memoir. 

The  conclusions  drawn  from  the  examination  of  this  placenta 
were,  that  in  the  sloths  the  placenta  is  not  cotyledonary  and 
non-deciduate  as  in  the  Ruminants,  but  in  the  fullest  sense  of  the 
word  deciduate.  If  the  inference  drawn  by  Huxley  from  Sharpey’s 
observations  on  the  structure  of  the  placenta  of  Manis  be  correct, 
then,  if  the  placental  system  of  classification  is  to  be  of  any  value, 
the  non-deciduate  scaly  ant-eaters  can  no  longer  be  grouped  along 
with  the  deciduate  sloths  in  the  order  Edentata,  which  order  will 
have  therefore  to  be  subdivided.  The  author  then  compared  the 
placentation  of  the  sloth  with  that  of  the  other  deciduate  mam- 
mals, and  pointed  out  a series  of  very  interesting  affinities  between 
its  placenta  and  that  in  the  Primates. 


VOL.  VIII. 


136 


Proceedings  of  the  Royal  Society 


Monday,  2 d June  1873. 

Sir  ROBERT  CHRISTISON,  Bart.,  President,  in 
the  Chair. 

The  following  Communications  were  read: — 

1.  On  the  Anatomy  of  a new  species  of  Polyodon,the  Polyodon 
Gladius  of  Martens,  taken  from  the  river  Yang-tsze-kiang, 
450  miles  above  Woosung.  Part  II.,  being  its  Nervous 
and  Muscular  Systems.  By  P.  D.  Handyside,  M.D. 

( For  a notice  of  Part  I.,  see  p.  50). 

The  author  showed  to  the  Society  a small  entire  specimen  of  the 
P.  gladius , and  next  described,  from  a larger  opened  and  dissected 
one,  and  from  part  of  an  adult  fish,  the  spinal  cord,  the  brain,  the 
organs  of  the  senses,  and  other  parts  of  its  nervous  system.  He 
illustrated  his  remarks  by  exhibiting  four  large  drawings  and  nine 
smaller  ones,  including  six  microscopic  views,  explanatory  of  his 
description  of  the  structure  and  disposition  of  the  spino -cerebral 
axis , the  encephalon  as  viewed  from  above  and  below,  the  ramifi- 
cations of  the  encephalic-nerves,  and  more  particularly  the  struc- 
tures subserving  the  senses  of  smell,  sight,  and  hearing.  A 
cartilaginous  capsule  forms  the  olfactory  chamber,  the  mesial  half  of 
which  is  occupied  by  a fibrous  disk  composed  of  29  septa  which 
radiate  from  a prominent  modiolus,  and  thus  leave  intermediate 
pituitary  pouches,  consisting  of  pigment  cells  and  sarcole,  invested 
with  tapering,  probably  ciliary,  epithelium.  The  choroid  of  the 
eye  is  connected  with  the  exterior  of  the  sclerotic  by  means  of  two 
large  tubular  processes  that  may  be  regarded,  anatomically,  as  a 
modified  form  of  the  vaso-ganglion  or  choroid  gland  found  hitherto 
in  most  osseous  fishes  only.  The  cysticule  and  utricule  of  the 
auditory  apparatus  are  the  only  parts  of  the  labyrinth  that  open  into 
the  cranial  cavity, — differing  thus  from  the  generality  of  bony 
fishes  and  from  sturgeons.  A remarkable  sinus  impar  is  present,  as 
in  some  osseous  fishes;  it  is  situated  in  the  middle  line  of  the  skull, 
and  connects  the  right  and  left  vestibules  through  their  upper  walls. 


137 


of  Edinburgh,  Session  1872-73. 

Numerous  cretaceous  particles,  of  the  nature  of  otolites,  are  studded 
over  the  interior  of  the  walls  of  the  cysticules  and  utricules ; but 
none  are  found  within  the  sinus  impar,  nor  is  the  latter  connected 
with  either  the  air-bladder  or  with  atria  on  the  body  of  the  atlas. 
Time  did  not  permit  of  the  author  reading  to  the  Society  his  paper 
in  full. 

The  third  part  of  Dr  Handyside’s  paper  will  consist  of  an  anato- 
mical description  of  the  viscera  of  organic  life ; and  the  fourth  part, 
of  the  articular  system  and  the  endo-skeleton  of  the  Polyodon 
gladius. 

2.  On  the  Placentation  of  the  Seals.  By  Professor  Turner. 

After  pointing  out  that  the  observations  of  Alessandrini,  Eosen- 

thal,  Eschricht,  and  Barkow  on  the  placentation  of  the  seals 
had  been  limited  to  the  determination  of  the  form  of  the  placenta, 
and  to  the  more  salient  facts  connected  with  the  arrangement  of 
the  foetal  membranes,  the  author  in  this  memoir  proceeded  to 
describe  systematically  the  gravid  uterus,  the  form  and  structure 
of  the  placenta,  and  the  arrangement  of  the  foetal  membranes  of 
the  grey  seal,  Halichoerus  gryphus.  He  was  indebted  to  Dr  M‘Bain 
and  Captain  Macdonald  of  the  cruiser  “ Vigilant”  for  the  oppor- 
tunity of  acquiring  the  gravid  uterus  of  a recently  killed  specimen 
of  this  seal.  The  distribution  of  the  utricular  glands  was  described. 
The  affinities  between  the  placentation  of  the  seals  and  the  proper 
carnivora,  more  especially  the  common  bitch,  were  pointed  out. 
Differences  in  the  degree  of  deciduation  in  the  various  forms  of  pla- 
centae were  considered,  and  it  was  shown  that  the  seal,  as  regards 
its  placental  structure,  occupied  a position  intermediate  between 
the  non-deciduate  mare  and  cetacean,  and  the  more  highly  deci- 
duate forms  of  placenta. 

3.  Second  Keport  by  tlie  Committee  on  Boulders  appointed 

by  the  Society.  (With  a Plate.) 

In  April  1871,  this  Committee  was  appointed  for  two  purposes 
— one  to  ascertain  the  districts  in  Scotland  where  boulders  ot 
interest  were  situated;  the  second,  to  point  out  such  boulders  as 
were  deemed  worthy  of  preservation,  with  a view  to  an  appli- 


133  Proceedings  of  the  Royal  Society 

cation  to  the  proprietors  of  the  land  on  which  they  were  situated, 
to  have  them  preserved. 

The  Committee,  in  fulfilment  of  the  first  of  these  objects,  issued 
a number  of  schedules  to  the  ministers  and  schoolmasters  of  Scotch 
parishes.  The  answers  received  enabled  the  Committee  to  present 
a First  or  interim  Report  to  the  Council  of  this  Society;  which 
Report  was  read  at  a meeting  of  the  Society  in  April  1872. 

The  Committee  have  since  continued  their  inquiries,  and  have 
obtained  a considerable  amount  of  additional  information,  the  sub- 
stance of  which  they  propose  to  give  in  the  following  Second 
Report. 

The  additional  information  has  been  procured  from  three  separate 
sources : — 

ls£,  A considerable  number  of  schedules,  filled  up  by  parochial 
ministers  and  schoolmasters,  have  been  received  by  the  Committee 
during  the  past  year,  several  of  which  have  been  accompanied  by 
sketches  of  the  boulders. 

2d,  Special  reports  on  particular  boulders  have  been  received 
from  surveyors  connected  with  the  Ordnance  and  also  the  Geolo- 
gical Survey.  These  reports  are  particularly  interesting. 

3 d,  Your  Convener,  in  a tour  during  last  summer  through  some 
of  the  eastern  and  northern  districts  of  Scotland,  took  an  oppor- 
tunity of  inspecting  some  of  the  boulders  mentioned  in  the 
schedules  and  reports  received  by  the  Committee,  and  ascertained 
many  important  facts. 

The  Committee,  in  order  to  record  the  information  recently 
obtained,  will  follow  the  plan  formerly  adopted  of  specifying  it  for 
each  county  in  alphabetical  order,  and  in  the  briefest  terms. 

In  now  proceeding  to  explain  the  nature  of  the  information 
received,  the  Committee  desire  to  avoid  as  much  as  possible 
mixing  up  speculations  with  facts.  But  it  is  not  easy  to  abstain 
from  alluding  to  prevalent  theories  regarding  the  transport  of 
boulders ; nor  would  it  be  expedient  to  do  so  altogether,  as  it  is 
desirable  to  show  how  far  those  theories  seem  to  be  supported  or 
disproved  by  the  facts  ascertained. 

I.  Boulders. 

1.  From  the  statements  appended  to  this  and  the  First  Report, 


of  Edinburgh,  Session  1872-73.  139 

it  will  be  seen  that  the  boulders  are  divisible  into  two  classes, — 
rounded  and  angular. 

The  boulders  referred  to  are,  of  course,  all  t(  erratics,”  in  the 
geological  sense  of  the  term,  i.  e.,  they  have  been  transported  for 
considerable  distances  from  a parent  rock. 

The  rounded  boulders  are  generally  composed  of  rocks  extremely 
tough  and  hard,  and  on  this  account  were  capable  of  undergoing 
great  friction  and  rough  usage  without  being  broken  up.  Hence  the 
round-shaped  boulders  most  frequently  consist  of  blue  whin-stones, 
fine-grained  granites,  schists,  limestones,  and  felspathic  rocks. 

The  angular-shaped  boulders,  whilst  embracing  these  rocks 
embrace  also  sandstones  and  conglomerates.  Their  angular  shape 
of  itself  proves  they  could  have  undergone  little  or  no  rough  usage 
by  being  rolled  or  pushed,  for  their  angles  and  corners  are  in 
many  cases  sharp.  Moreover,  the  rocks  composing  them  are  so 
loose  and  friable  in  texture,  that  they  would  have  crumbled  or 
been  crushed  to  pieces  liad  they  undergone  rolling  or  pushing. 

The  difference  in  shape  between  the  two  classes  of  boulders  now 
referred  to  can  be  seen  by  looking  at  figures  I.,  II.,  and  V.,  as 
contrasted  with  figures  IV.,  VI.,  and  XIII.  in  Plate. 

It  may  here,  however,  be  proper  to  explain  that  some  of  the 
boulders  composed  of  the  friable  rocks  just  mentioned,  whilst 
angular  and  rough  on  one  side,  are  sometimes  rounded  and  smooth 
on  the  other, — a fact  apparently  indicating  that  after  being  carried 
to  their  present  position  without  injury  or  mutilation,  they  had 
been  subjected  to  friction  or  attrition  on  the  particular  side  which 
is  now  smooth. 

Some  angular  boulders  are  not  cubical  in  shape,  but  are  longer 
than  they  are  broad ; and  in  that  case,  the  smoothed  end,  when 
there  is  one,  is  almost  always  narrower  or  more  pointed  than  the 
rough  end.  It  was  a remark  of  Hugh  Miller’s,  that  on  examining 
pebbles  lying  in  the  channel  of  a river,  the  great  majority  have 
their  narrow  ends  pointing  up  stream.  When  once  in  that  position, 
they  retain  the  position  longer  than  when  lying  broadside  against 
the  stream.  This  remark  should  not  be  lost  sight  of,  in  drawing 
inferences  from  the  shapes  and  positions  of  boulders. 

Examples  of  these  angular  boulders,  with  one  end  smoothed  and 
pointed,  will  be  noticed  in  Sketches  VIII.  and  X. 


140  Proceedings  oj  the  Itoyal  Society 

It  is  not  difficult  to  understand  bow  boulders,  originally  cubical 
in  shape,  may  undergo  a change  by  the  action  of  a stream  of  such 
a nature  as  to  grind  or  smooth  them.  If  fig.  YIII  represents  a 
boulder  cubical  in  shape  when  deposited,  a stream  coming  against 
it  in  the  direction  of  the  arrow  might  break  off  or  grind  down 
the  portion  a,  b , c,  and  leave  the  rest  a,  c,  /,  e,  d,  in  the  form  of  a 
boulder,  smoothed  and  pointed  at  the  windward,  and  rough  at  the 
leeward  side. 

That  many  of  these  boulders,  after  being  brought  to  their  present 
position,  have  been  subjected  to  great  attrition,  is  further  proved 
by  the  markings  on  their  surface.  Scratches  and  sometimes 
deep  ruts  occur,  not  only  on  their  upper  surfaces,  but  also  occa- 
sionally on  their  sides,  as  if  indicating  the  passage  over  and  along 
them,  of  stones  harder  than  themselves,  and  pressed  against  them 
by  some  powerful  agent  or  body.  These  scratches  and  ruts  are 
most  frequently  in  a direction  coincident  with  the  longer  axis  of 
the  boulder,  and  show  that  the  movement  has  been  towards  the 
boulder  at  its  smooth  and  narrow  end. 

2.  Another  class  of  facts  of  some  interest  is  connected  with  the 
positions  of  the  boulders. 

The  rounded  boulders,  though  frequently  on  the  surface,  are 
also,  and  perhaps  more  frequently,  buried  in  mud,  gravel,  and  sand- 
beds. 

The  angular  boulders  are  occasionally  found  in  these  deposits ; 
but  they  are  much  more  frequently  on  the  surface. 

Angular  boulders  are  very  frequently  on  knolls  or  low  hills, 
perhaps  even  more  so  than  on  lower  levels.  They  are  occasionally 
seen  in  clusters  upon  or  round  these  knolls,  as  if  the  agent,  whatever 
it  was,  which  transported  the  boulders,  had  been  obstructed  in  its 
further  progress  by  the  knolls,  and  had  dropped  them  there. 

As  an  example  of  this  class  of  cases,  reference  may  be  made  to 
the  hill  of  Craigiebarns,  about  1|  mile  north  of  Dunkeld.  This  hill 
is  about  1100  feet  above  the  sea,  and  about  800  feet  above  the  river 
Tay,  which  flows  along  its  base.  Four  or  five  large  boulders,  mostly 
angular,  lie  on  the  top,  or  very  near  the  top,  of  several  rocky  knolls 
which  form  the  ridge  of  that  hill.  In  like  manner,  there  is  a hill 
to  the  south  of  Dunkeld,  also  on  the  east  bank  of  the  Tay,  with 
an  angular  boulder  on  the  top  of  a rocky  knoll. 


141 


of  Edinburgh , Session  1872-73. 

Bounded  boulders  also  occur  on  these  rocky  knolls,  but  not  so 
frequently  as  angular  boulders. 

In  connection  with  the  fact  of  boulders  being  much  clustered 
on  and  round  rocky  knolls,  it  may  be  noticed  that  boulders  of  large 
size,  and  especially  angular  boulders,  are  said  to  occur  more  fre- 
quently at  high  levels  than  at  low  levels. 

On  this  point  reference  may  be  made  to  the  report  by  one  of  the 
Ordnance  surveyors  from  Boleskien  in  Inverness  county,  in  which 
it  is  remarked  that  the  hills  in  Stratherick  reach  to  a height  of 
2900  feet,  that  the  boulders  are  often  perched  on  isolated  hills, 
and  that  few  boulders  occur  there  below  the  level  of  2250  feet.* 

One  of  the  largest  angular  boulders  seen  by  your  Convener  (in 
Grlen  Lyon,  Perthshire,  and  weighing  above  100  tons),  is  at  a 
height  of  2500  feet  above  the  sea. 

It  is  proper,  however,  to  add,  that  clusters  of  boulders  do  likewise 
occur  at  or  bejmnd  the  mouths  of  valleys.  In  the  Lochaber  district, 
opposite  to  Loch  Treig,  in  Spean  Valley,  there  is  a great  accumu- 
lation of  large  boulders.  So  also  in  the  valley  of  the  river  Nairn, 
to  the  east  and  below  the  mouth  of  Flichity  Valley,  there  is  a 
similar  accumulation.  In  both  of  these  cases  the  boulders  lie  on 
the  top  of  debris,  having  all  the  appearance  of  moraines.  These 
accumulations  of  boulders  may  be  ascribed  with  great  probability 
to  the  operation  of  glaciers.  But  that  explanation  cannot  apply 
to  clusters  of  boulders  on  or  near  the  tops  of  hills. 

3.  Special  notice  deserves  to  be  taken  of  the  fact,  that  boulders 
of  all  sizes  occur  on  islands,  though  in  these  islands  no  rock  exists 
of  the  same  nature  as  that  composing  the  boulders. 

In  the  First  Keport  of  the  Committee  several  cases  of  that  kind 
were  reported  from  the  Hebrides,  as  also  from  Orkney  and  Shetland. 

In  the  statements  appended  to  this  Beport,  additional  examples 
are  reported. 

Mr  Campbell  of  Islay,  in  a document  given  in  the  Committee’s 
last  Beport,  says  that  many  of  the  boulders  on  the  western  islands 
are  u perched  on  hill  tops,”  and  have  come  from  the  northward  in 
a direction  “ parallel  to  the  run  of  the  tides.” 

Appended  to  this  Beport,  there  is  a similar  opinion  expressed, 
founded  on  the  appearances  in  the  small  island  of  Foula  (Shetland). 

* See  Inverness,  page  157 


142  Proceedings  of  the  Boyal  Society 

The  gentleman  who  expresses  this  opinion,  and  reports  on  the 
Foula  boulders,  affirms  unhesitatingly,  that  these  boulders  came 
from  the  mainland  of  Shetland,  separated  by  a deep  sea  of  from 
16  to  18  miles  in  breadth ; and  he  even  specifies  the  hill  from 
which  the  boulders  have  come. 

So  also  the  report  from  the  Lewis  is  distinct,  that  there  are 
boulders  on  the  east  shores  of  the  island  which  must  have  come 
a distance  of  at  least  35  miles  across  the  sea  from  the  mainland  of 
Sutherland. 

The  important  bearing  of  these  cases  of  island  boulders  on  the 
nature  of  the  transporting  agent,  is  evident.  It  is  difficult  to  see 
how  glaciers  could  have  been  instrumental  in  carrying  them . 

4.  The  information  recently  obtained  by  the  Committee  throws 
additional  light  on  the  direction  from  which  the  boulders  have 
come. 

(1.)  As  already  mentioned,  some  boulders  appear  to  have  come 
down  valleys,  brought  apparently  on  glaciers.  Two  localities 
are  mentioned,  viz.,  in  Lochaber  and  in  Nairn  Valley,  where  such 
explanation  may  be  accepted. 

There  are  also  probably  places  in  Perthshire,  Forfarshire,  and 
Aberdeenshire,  where  boulders  lie  in  valleys,  or  at  the  mouths  of 
valleys,  which  belong  to  this  class  of  cases.  The  nature  of  the 
rock  composing  the  boulders  being  found  to  be  the  same  as  the 
rocks  in  situ  at  the  head  or  along  the  sides  of  the  valleys,  the 
birth-place  of  the  boulders  may  be  readily  and  correctly  assumed 
to  have  been  there. 

(2.)  But  there  are  hundreds  of  localities  with  boulders,  to  which 
this  explanation  is  inapplicable.  Not  only  boulders  situated  on>. 
islands,  but  boulders  perched  high  up  on  hill-sides  and  near 
mountain-tops,  seem  to  require  a different  explanation. 

On  the  mainland  of  Scotland,  at  least  in  its  eastern  half,  from 
which  the  Committee  have  received  the  fullest  information,  the 
angular  boulders,  and  also  many  of  the  rounded  boulders,  appear 
to  have  come  over  a wide  extent  of  country  in  one  and  the  same 
direction,  viz.,  from  the  north-west,  crossing  valleys  and  ranges  of 
hills. 

This  inference  had  been  drawn,  years  ago,  from  such  facts  as 
the  finding  of  granite  and  mica-schist  boulders  in  the  counties  of 


of  Edinburgh,  Session  1872-73  143 

Fife,  East  Lothian,  and  Berwick,  which  must  have  come  from  the 
Scottish  Highlands.  But  farther  and  more  striking  proofs  of  this 
great  north-west  movement  are  afforded  by  the  large  bouldt  rs  in 
the  counties  of  Elgin,  Nairn,  and  Ross-shire,  of  which  accounts 
are  given  in  the  Appendix  to  this  Report.  From  these,  it  appears 
that  conglomerate  boulders,  from  30  to  50  tons  in  weight,  now 
lying  on  the  hill-sides  and  the  plains  of  Elgin  and  Nairn,  must 
have  been  somehow  transported  from  the  conglomerate  hills  of 
Cromarty,  across  what  is  now  the  Moray  Firth ; and  that  granite 
boulders,  very  little  smaller,  and  many  of  them  angular,  situated 
in  the  district  between  Tarbat  Ness  and  Tain,  at  various  levels  up 
to  1200  feet  above  the  sea,  must  have  been  transported  from 
mountains  far  to  the  north-west. 

The  non-occurrence  of  conglomerate  boulders  in  this  last-men- 
tioned district  is  also  itself  negative  proof  corroborative  of  the 
north-west  movement; — there  being  no  conglomerate  hills  to  the 
north-west  of  the  last-mentioned  places. 

Whilst  the  existence  of  this  north-west  movement  is  indicated 
by  the  birth-places  of  the  boulders,  other  circumstances  confirm  the 
conclusion.  Thus,  most  of  the  boulders  now  referred  to  have  their 
smoothest  and  sharpest  ends  towards  the  north-west;  the  scratches 
and  ruts  on  their  surfaces  and  sides  point  in  the  same  direction ; 
and  where  there  are  striae  on  the  rocks  of  the  district  near  these 
boulders,  these  striae  also,  in  nine  cases  out  of  ten,  are  parallel. 

It  also  deserves  notice,  that  when  boulders  are  on  hills,  they 
evidently  indicate  a preference  for  the  sides  of  those  hills  having 
a north-west  aspect, — a fact  which  seems  to  indicate  the  existence 
and  prevalence  of  some  transporting  agent  which  could  be  more 
frequently  and  effectually  stopped  by  the  sides  of  hills  facing  the 
north-west. 

The  facts  reported  from  Elgin  and  Ross-shire  bearing  on  this 
point  are  corroborated  by  the  position  of  the  boulders  described 
as  on  the  hill  on  the  north  side  of  the  Linnhe  Loch  at  Fort- 
William. 

But  whilst  there  is  strong  evidence,  so  far  as  the  Committee 
have  proceeded  in  their  inquiries,  to  show,  that  in  a great  part  of 
the  mainland  of  Scotland  a general  movement  has  prevailed  from 
the  north-west,  some  facts  indicate  a separate  movement  from 


VOL.  VIII. 


144  Proceedings  of  the  Royal  Society 

the  north-east.  These  are  supplied  partly  from  the  Islands 
(Hebrides,  Orkneys,  and  Shetland),  and  partly  from  the  striations 
of  rocks  in  different  parts  of  Scotland.  (See  .Reports  from  Lanark, 
Elgin,  and  Lochaber.)  This  north-east  movement,  however,  does 
not  appear  to  have  been  so  general  or  so  incisive  as  the  north-west 
movement. 

The  Committee  think  it  premature  to  draw  conclusions  with  any 
confidence.  They  would  only  observe,  that  if  two  separate  move- 
ments have  taken  place  over  the  country,  whereby  rocks  were 
striated,  and  boulders  transported  great  distances  across  valleys, 
mountain  ranges,  and  arms  of  the  sea,  it  is  most  probable  that 
these  movements  took  place  when  the  whole  country  was  under 
the  waters  of  a sea  loaded  with  ice,  and  in  which  strong  currents 
prevailed. 

II.  Beds  oe  Clay,  Gravel,  and  Sand. 

1.  Under  this  head,  the  most  interesting  fact  brought  out  in 
the  Reports  lately  received,  is  the  occurrence  at  very  high  levels, 
of  beds  of  boulder  clay,  gravel,  and  sand.  They  are  to  be  seen  in 
several  parts  of  Scotland  (chiefly  the  middle  and  north),  at  heights 
exceeding  2000  feet  above  the  sea. 

It  can  scarcely  be  doubted  that  the  formation  of  these  beds  is 
due  to  large  bodies  of  water.  No  marine  organisms,  it  is  true, 
have  been  found  in  these  beds  at  or  near  this  height ; but  it  is 
difficult  to  account  for  them,  except  on  the  supposition  that  the 
whole  country  had  been  submerged  to  the  depth  of  2000  or 
4000  feet.  Currents,  probably  loaded  with  ice,  have  acted  on  the 
submerged  mountains,  and  carried  away  from  them  an  immense 
amount  of  debris,  which  has  been  deposited  as  sediment  in  the 
hollows,  and  forming  the  existing  beds  of  sand,  gravel,  and  clay. 

When  the  land  emerged,  and  for  a long  period  after,  there  would 
be  numberless  lakes  in  the  interior,  among  the  mountains,  formed 
of  course  by  the  rain  which  fell  on  their  sides.  In  the  course  of 
time,  the  embankments  of  detrital  matter  which  kept  in  the  lakes 
would  be  cut  through,  and  the  lakes  would  sink  in  level.  Most 
probably,  when  they  so  sank,  beach  lines  would  become  visible  on 
the  sides  of  .the  mountains,  like  the  famed  parallel  roads  of  Glen 
Roy. 


of  Edinburgh,  Session  1872-73.  145 

Of  these  old  beach  lines  there  are  many  examples  elsewhere 
than  Glen  Roy;  and  it  is  important  to  obtain  reports  of  them,  that 
they  may  be  carefully  examined. 

Such  terraces  are  visible  in  several  parts  of  Flichity  Valley, 
about  10  miles  south  of  Inverness ; and  there  also,  the  old  detrital 
embankment  still  exists,  which  appears  to  have  kept  in  the  waters 
of  the  lake.  It  has  been  cut  through  by  the  river  which  now  flows 
through  Flichity  Valley. 

The  whole  of  this  valley  deserves  more  particular  examination, 
both  with  reference  to  these  terraces,  and  with  reference  to  the 
boulders,  which  lie  in  great  heaps  below  its  mouth. 

In  the  valley  of  the  Tay,  between  Pitlochry  and  Killiecrankie, 
there  is  a very  instructive  deposit  of  boulder  clay  and  sand  lying 
on  the  clay-slate  rocks  of  Craig  Ower  hill,  which  forms  here  the 
east  side  of  the  valley.  The  deposit  is  well  seen  in  two  ravines, 
formed  by  mountain  torrents,  which  have  cut  through  the  beds 
down  to  the  rocks  in  one  of  the  ravines,  forming  scaurs  from  50  to 
80  feet  high.  These  scaurs  show  that,  whilst  the  boulder  clay 
presents  only  faint  traces  of  stratification,  if  any,  the  beds  of 
sand,  which  are  in  the  heart  of  the  boulder  clay,  are  distinctly 
stratified.  Following  the  course  of  the  most  northern  of  the  two 
ravines  up  from  the  Pitlochry  road  (about  350  feet  above  sea,  and 
about  150  above  the  bottom  of  the  valley),  he  found  the  above  de- 
posits all  the  way  up,  to  a height  of  about  1350  feet  above  the  sea. 
He  saw  that  this  deposit  was  continued  along  the  valley  towards 
the  north,  and  he  was  informed  by  the  Rev.  Mr  Grant,  of  Ten- 
nandry,  the  minister  of  the  parish,  who  takes  some  interest  in 
these  investigations,  that  similar  deposits  exist  on  the  flanks  of 
Ren-y-gloe,  a mountain  three  or  four  miles  to  the  north-east,  within 
the  limits  of  this  valley,  and  at  levels  several  hundred  feet 
higher. 

This  locality  was  also  visited  by  another  member  of  the  Com- 
mittee, the  Rev.  Mr  Brown,  who  was  much  struck  by  the  beds  of 
sand  and  clay  before  referred  to.  He  states  that  he  made  a minute 
search  for  organisms  in  the  clay,  thinking  that  if  the  beds  resulted 
from  marine  currents,  some  remains,  either  animal  or  vegetable, 
would  exist,  but  he  found  none. 

Whether  these  beds  were  formed  by  the  sea  or  by  fresh  water,  it 


146  Proceedings  of  the  Royal  Society 

may  be  impossible  at  present  to  determine.  But  there  seems  strong 
reason  to  believe  that  the  whole  valley  in  this  quarter  was  originally 
filled  with  detrital  matter,  which  has  since  been  carried  away  by 
the  action  of  streams  and  rivers,  except  at  a few  places. 

2.  A question  of  considerable  difficulty  arises  here  in  connection 
with  the  ancient  glaciers  which  undoubtedly  existed  in  Scot- 
land. 

Take,  for  example,  Flichity  Valley.  If  it  was  filled  with  a 
glacier  which  pressed  on  its  sides,  and  carried  down  debris  to  form, 
moraines,  and  the  huge  boulders  which  now  lie  on  that  debris,  at 
what  period  did  this  glacier  exist?  Was  it  before  or  after  the 
submergence  of  the  country?  If  it  was  after  the  emergence,  is  it 
not  likely  that  all  the  drift  deposits  of  sand  and  gravel  now  on  its 
sides  would  have  been  scoured  out,  and  all  traces  of  the  terraces 
obliterated  ? 

On  the  other  hand,  if  the  glacier  existed  before  the  submergence, 
is  it  likely  that  the  moraines,  in  that  valley,  in  Lochaber,  and 
other  parts  of  Scotland,  would  have  retained  so  distinctly  their 
prominent  features?  Would  they  not  have  been  planed  down  by 
submarine  currents? 

It  is,  however,  a circumstance  in  favour  of  the  existence  of 
glaciers  before  the  submergence,  that  the  stride  on  rocks,  which, 
these  glaciers  are  supposed  to  have  produced,  are  often  covered 
over  by  thick  beds  of  sediment. 

The  Committee  abstain  from  venturing  farther  upon  theoretical 
ground.  They  allude  to  these  questions  only  because  the  facts 
already  ascertained,  and  more  of  which  they  will  search  for  if  they 
are  re-appointed,  seem  calculated  to  throw  upon  these  questions 
important  gleams  of  light. 

III.  Work  still  before  the  Committee. 

1.  The  Committee  think  that  as  so  much  information  has  been 
obtained  from  the  east  half  of  Scotland,  it  would  be  desirable  to 
obtain  similar  information  from  the  west  half. 

It  is  manifest  from  the  Beports,  that  in  the  sea  lochs  of  the 
west  coast,  there  are  houlders  of  large  size,  and  in  most  interesting 
positions. 

They  are  also  particularly  anxious  to  have  as  many  particulars 


of  Edinburgh,  Session  1872-73.  147 

as  possible  regarding  boulders  on  islands,  especially  if  the  boulders 
are  composed  of  rocks  not  existing  in  the  islands. 

IV.  Preservation  of  Boulders. 

The  Committee  have  not  yet  taken  any  special  action  towards 
the  attainment  of  this  object. 

Perhaps  it  may  be  premature  to  do  so,  till  they  have  obtained  all 
the  information  which  they  expect  regarding  the  localities  where 
the  most  interesting  boulders  are  situated. 

Some  doubt  also  is  felt  what  would  be  the  most  judicious  course 
of  procedure.  In  Switzerland,  as  the  Committee  observe  from  the 
printed  Reports  which  Professor  Pavre  kindly  sends  to  them  as 
they  are  issued,  very  many  boulders  have  been  purchased  by  or  for 
natural  history  societies  and  museum  managers ; and  in  one  of  the 
Reports,  a form  of  the  deed  or  conveyance  is  given,  transferring  a 
right  of  property  in  any  particular  boulder. 

From  these  Reports,  it  appears  that  the  boulders  sought  to  be 
preserved  are — ls£,  Those  which  have  a traditional  name.  2d, 
Those  which  have  a legend  attached  to  them.  3 d,  Those  which 
possess  scientific  value, — for  some  reason  which  geologists  point 
out. 

Perhaps  the  Committee,  in  their  selection  of  boulders  to  be  pre- 
served in  Scotland,  could  not  do  better  than  act  on  these  principles. 
But  whether,  to  secure  preservation,  they  will  endeavour  to  obtain 
a transference  of  the  property  of  particular  boulders  in  favour  of 
any  Society,  or  whether  they  will  merely  endeavour  to  obtain  from 
the  proprietor  on  whose  lands  they  are  situated,  a promise  to  pre- 
serve them,  the  Committee  have  yet  to  decide. 

The  Committee  cannot  conclude  their  Report  without  repeating 
the  wish,  which  they  expressed  last  year,  that  some  of  the  many 
tourists  who  are  likely  to  be,  during  the  ensuing  summer  and 
autumn,  in  remote  parts  of  Scotland,  where  large  boulders  still 
exist,  may  visit  the  boulders,  with  a view  to  report  upon  them  to 
the  Committee.  The  Committee,  whilst  desirous  of  obtaining 
additional  information  from  all  parts  of  the  country,  may  be 
allowed  to  acid,  that  there  are  three  classes  of  boulders,  as  regards 
position,  information  about  which  would  be  particularly  accept- 
able : — 


148  Proceedings  of  the  Royal  Society 

First,  Boulders  on  an  island,  at  a considerable  distance  from  the 
mainland,  when  these  boulders  have  evidently  been  transported  to 
the  island. 

Second,  Boulders  at  very  high  levels  on  the  mainland,  or  on  or 
near  the  tops  of  mountains,  to  which  they  have  probably  been 
transported  from  a distance. 

Third,  Boulders  along  the  north-west  coasts  of  Scotland,  say  50 
miles  on  each  side  of  Gape  Wrath,  with  the  view  of  ascertaining 
whether  these  boulders  have  come  from  the  mountains  inland,  or 
whether  (as  believed  by  some  geologists)  they  have  come  from 
some  region  sea-ward. 

The  Committee,  in  drawing  attention  to  the  importance  of  ob- 
taining information  regarding  the  boulders  situated  on  the  north- 
west coast  of  Scotland  and  on  remote  islands,  know  the  difficulty 
of  reaching  these  places  by  any  of  the  means  of  conveyance 
accessible  to  the  general  public.  There  are,  however,  many 
gentlemen  who  have  steam-yachts  frequenting  the  western  shores 
during  the  summer  and  autumn ; and  if  they  are  disposed  to  assist 
this  Committee  in  their  researches,  they  might  perhaps  be  induced 
to  propose  to  a geological  friend  to  accompany  them  on  a cruise 
among  the  Hebrides,  and  give  them  an  opportunity  of  visiting 
boulders  not  otherwise  accessible.  The  Committee  would  be  most 
grateful  for  any  reports  obtained  in  this  manner,  and  would  be 
very  ready  to  acknowledge  the  service  thereby  rendered  to  geological 
research. 

List  of  Boulders , Bocks,  striated  or  smoothed,  and  Kaims,  &c. 

reported  to  Royal  Society  Committee,  arranged  by  Counties  and 

Parishes. 

Aberdeen. 

Kemnay. — Boulder,  a fine  grained  blueish-grey  granite  called  “ The 
Souter’s  Stone,”  lying  apparently  in  muddy  sediment.  Dimen- 
sions above  ground  18  x 14  x 9 feet ; but  believed  that  as 
much  below  as  above  surface.  Height  above  sea  about  500 
feet.  Probably  weighs  270  tons.  This  block  on  S.E.  side  of  a 
hill  running  N.  and  S.  for  500  yards,  about  quarter  mile  dis- 
tant, top  of  which  about  100  feet  above  boulder,  and  lies  S.E. 


149 


of  Edinburgh,  Session  1872-73. 

of  boulders  described  in  Appendix  to  Committee’s  First  Eeport. 
Country  not  suited  for  any  glacier  wliich  could  have  brought 
“ Souter’s  Stone,”  or  any  of  the  others.  If  “Souter’s  Stone” 
came  from  westward,  it  must  have  been  floated  and  swung 
round  by  eddy  into  its  present  position.  All  the  boulders  in 
Kemnay  and  Chapel  Garioch  rounded  and  smooth  on  north 
and  west  ends,  and  rough  at  opposite  ends.  (Sketch  of  Souter’s 
Stone,  Plate  No.  II.) 


Argyle. 

Ardchattan . — Granite  boulder,  14J  x 12  J x 5J  feet,  partially  rounded. 
One  rut  on  top  running  whole  length.  Nearest  rock  of  same 
kind  is  Ben  Yreck,  3J  miles  to  eastward.  Height  above  sea, 
57  feet.  Within  70  yards  of  boulder,  a ridge  of  sand  and 
gravel.  Length,  1|-  miles.  Height  of  ridge  varies  from  50  to 
100  feet.  (Captain  White,  B.E.) 

Ayr. 

Ardrossan. — Near  Hunterston  on  shore,  boulder  5|-xllx6  feet 
and  26  J feet  round,  apparently  grey  compact  granite,  about 
12  miles  from  Arran,  and  opposite  to  Great  Cumbrae  Island, 
1\  miles  distant.  (Robert  Hunter,  Hunterston.) 

Berwickshire. 

Berwick-on  Tweed. — Castle  Terrace.  Boulder  clay  cut  through  for 
water  pipes,  and  many  boulders  found,  all  more  or  less  rounded, 
and  composed  of  very  hard  rocks, — such  as  granites,  gneiss, 
limestone, . blue  whinstone,  greywacke,  &c.  The  granites 
showed  two  varieties, — the  common  small-grained  grey  and 
red.  (Observed  by  Convener.) 

Burnmouth. — Near  the  railway  station,  among  gravel,  over  grey- 
wacke rocks,  a well-rounded  lump  of  pinkish  granite  found  by 
Convener. 

This  variety  recognised  by  him  as  very  similar  to  that  used 
for  a handsome  chimney-piece  in  British  Linen  Company’s 
Office,  Edinburgh.  Having  ascertained  that  this  chimney- 
piece  supplied  by  Macdonald  of  Aberdeen,  Convener  sent  to 
him  a chip  of  boulder,  that  he  might  mention  in  what  parts 


150  Proceedings  of  the  Royal  Society 

of  Scotland  the  rock  was  found  in  situ.  Mr  Macdonald  replied, 
— “ The  light-coloured  pinkish  granite  in  the  British  Linen 
Company’s  Bank  came  from  the  hill  of  Correnie  in  Aberdeen- 
shire, not  far  from  Kemnay.  It  was  cut  from  boulders.  But 
similar  rock  is  to  he  had  quite  near.  Bock  very  much  the 
same  appears  about  Kincardine  O’Neil,  in  Deeside,  and  also 
about  Ballater  and  Braemar.  A similar  stone  is  found  at 
Beaufort,  county  Mayo,  and  most  likely  in  other  parts  of 
Scotland  and  Ireland. 

“ Your  boulder  is  very  much  akin  to  all  these  rocks ; perhaps 
a little  closer  in  the  grain,  but  substantially  the  same. 

“ Many  of  the  ocean-worn  beach  stones  all  along  the  coast 
to  the  south  of  this,  are  of  the  same  granite  as  your  boulder, 
or  very  much  like  it. 

“ I cannot  lay  my  hands  on  a specimen  sent  to  us,  some 
years  ago,  from  the  Island  of  Uist;  but  if  recollection  hears 
me  out  truly,  granite  very  much  of  the  same  character  is  to 
be  got  there.” 

Coldstream. — At  the  Hirsel  (Earl  of  Home).  About  120  feet  above 
sea,  boulder  of  white  chert  about  4 feet  square,  but  very  rough 
and  irregular  in  shape.  Found  in  a bed  of  gravel  in  making 
new  avenue  from  Hirsel  Policy  to  Coldstream.  No  rock  of 
this  nature  known  on  north  side  of  Tweed.  It  occurs  at  two 
or  three  places  along  the  south  of  the  Tweed,  viz.,  at  Carham 
and  Nottylees;  places  bearing  W.  by  S.  from  boulder,  distant 
about  3 miles,  with  Tweed  valley  intervening. 

As  rock  composing  boulder  friable,  and  its  shape  very  angular 
and  ragged,  it  could  not  have  been  rolled  or  pushed  to  its 
present  site,  nor  could  have  been  thrown  down  from  any  great 
height.  Probability  is,  that  when  detached  from  parent  rock, 
it  fell  upon  ice,  which  floated  it  across  valley. 

Dunse. — On  farm  of  Cockburn,  a boulder  of  mica- schist  well 
rounded.  Is  from  2 to  3 feet  in  length  and  breadth.  An 
erratic  from  the  Highlands  of  Scotland,  and  must  have  travelled 
at  least  100  miles  across  many  valleys  and  ranges  of  hills. — 
(First  noticed  by  Mr  Stevenson  of  Dunse.) 

Foulden. — Several  small  boulders  of  coarse  sienite  (lying  on  old 
red  san  Istone),  composed  of  red  felspar,  black  hornblende,  and 


of  Edinburgh,  Session  1872-73. 


151 


small  flakes  of  mica — nearest  hill  where  similar  rock,  Cockbnrn 
Law — 8 miles  to  N.W.  Largest  boulder,  5 x 3 J x 3 feet.  Longer 
axis,  N.W.  Sharpest  end  points  that  way.  (Convener.) 

Greenlaw. — Marchmont  (Sir  Hugh  H.  Campbell).  About  930  feet 
above  sea,  a blue  whinstone  boulder  9 J x 5 x 4J  feet,  with 
faint  striae  on  top,  parallel  with  longer  axis.  Original  position 
of  boulder  slightly  changed  before  being  seen.  Thisbouldermust 
have  come  from  westward.  Rocks  in  situ  Old  Red.  District  not 
favourable  to  glacier  theory.  (Sketch  by  Lady  Hume  Campbell.) 

Hutton. — Boulder  of  whinstone  about  12J  tons  found  in  clay  of 
brickwork.  Longer  axis  W. N.W.  Sharpest  end  towards  that 
direction.  Probably  from  Hardens  Hill,  west  of  Dunse,  10 
miles  distant  W.N.W.  Striae  parallel  with  longer  axis  on  one 
side.  This  boulder  now  in  Paxton  Policy  grounds. 

Buteshire. 

Big  Cumbrae. — Rev.  Mr  Lytteil,  Kilmarnock,  pointed  out  to  Con- 
vener many  boulders  of  mica-schist  on  many  parts  of  island. 
Rocks  of  island  are  Old  Red.  Largest  boulder  seen  is  near 
north  end  of  island,  at  Balloch  Martin,  12  x 6 x 3 feet.  But 
as  much  more  probably  below  ground.  Longer  axis  N.N.E. 
Lies  in  a trough  or  valley  running  N.N.E.  May  have  been 
floated  through  this  valley  from  northward. 

Little  Cumbrae. — Rev.  Mr  Lytteil  conducted  Convener  to  highest 
part  of  island,  north  of  Old  Tower,  400  feet  above  sea.  Rocks 
(claystone  trap)  here  smoothed  by  some  agent  passing  over  from 
N.  by  W.  Found  several  boulders  of  conglomerate  and  Old  Red; 
none  of  mica-schist.  Largest  about  5 feet  square,  and  rests 
on  trap  rock,  by  so  small  a basis  that  it  may  once  have  rocked. 
Known  by  name  of  “ Bell  Stane.”  Mr  Lytteil  supposes  name 
derived  from  “Beltane”  fires  lighted  here  in  Pagan  times. 
Close  to  this  stone,  another  smaller  conglomerate  "boulder,  with 
cup  on  it,  apparently  artificial,  4 inches  diameter  and  £ inch 
deep.  Height  above  sea,  190  feet.  Situated  about  2 miles 
N.W.  of  old  castle  on  east  shore. 

No  old  red  or  conglomerate  rocks  in  island.  Nearest  are 
along  shore  at  Rothesay,  about  20  miles  across  sea  to  N.W. 


VOL.  VIII. 


152 


Proceedings  of  the  Royal  Society 

Visited  “Split  Boulder,”  first  mentioned  by  Smith  of  Jor- 
danhill.  A claystone  trap,  similar  to  rock  of  island.  Lies  at 
sea-level  on  rocks  smoothed  and  striated,  forming  east  side 
of  a trough  or  valley  running  N.E.  by  N.  Strise  run  same  way. 

Dumbarton. 

Luss.  — Mica-schist  boulder  on  west  bank  of  Loch  Lomond, 
26  x 18  x 7 feet;  about  250  feet  above  sea-level.  Situated  on 
a brook  entering  Fruin  Water,  west  of  Callendoun  Farm 
House.  Longer  axis  E.  and  W.,  with  sharp  end  to  west 
and  thick  end  to  east.  Bocks  adjoining,  old  red  sandstone. 
Nearest  mica-schist  hills  to  north  and  west,  about  5 miles  off. 
Keporter  remarks,  that  if  boulder  came  from  W.  or  N.W.,  it 
must  have  crossed  hills  from  1000  to  2000  feet  high.  But  it 
may  have  come  from  north,  down  valley  now  occupied  by  Loch 
Lomond,  on  ice  which  floated  it  so  far  south,  and  then  carried 
it  west  up  Grlen  Fruin. — (B.  L.  Jack,  F.Gr.S.,  Alexandria.) 

Elgin. 

Dyke. — Near  west  end  of  approach  to  Darnaway  Castle,  several 
granite  and  gneiss  boulders  from  2 to  3 tons  each. 

In  same  parish,  near  west  lodge  to  Darnaway  Castle,  a 
kaim,  quarter  mile  long,  running  N.  and  S.  12  feet  above 
general  surface.  (Captain  White,  B.E.) 

Elgin. — Boulder  called  “ Carlin’s  Stone,”  onBogton  farm, — a coarse 
conglomerate,  about  230  feet  above  sea.  Imbedded  pebbles, 
chiefly  flesh-coloured  quartzite. 

About  half  a mile  to  N.W.  a sm  aller  boulder,  called  “ Young 
Carlin’s  Stone.” 

Conglomerate  rock  occurs  in  hills  to  south,  distant  5 or  6 
miles ; but  of  a variety  different  from  that  of  boulders.  Same 
variety  of  conglomerate  as  the  boulders  exists  beyond  Inver- 
ness to  W.,  and  in  Boss-shire  to  N.W. 

From  size  and  shape  of  these  conglomerate  boulders,  evident 
they  must  have  been  carried  or  rafted. 

On  other  hand,  in  this  district  hundreds  of  round  and  smooth 
boulders  of  granite,  gneiss,  mica  slate  clay,  slate,  &c.,  whose 
shape  and  smoothness  indicate  that  they  have  been  pushed 


of  Edinburgh,  Session  1872-73.  153 

or  rolled  over  the  surface.  These  chiefly  imbedded  in  gravel, 
clay,  and  sand. 

To  westward  of  these  boulders  a valley  or  depression  runs 
in  an  E.  and  W.  direction;  Halldon  or  Pluscardine  Hill 
being  on  south,  and  Carden  Hill  on  north  side.  This  valtey 
opens  out  to  westward. 

Pluscardine  Hill  on  its  north  slope  dipping  towards  valley, 
covered  with  boulders  which  apparently  deposited  on  it  from 
some  agent  that  came  from  N.W.,  and  which  obstructed  by 
the  hill. 

Carden  Hill  has  a flat  ridge  running  about  E.  and  W.  This 
ridge  consists  mostly  of  a bare  and  hard  gritty  sandstone  rock. 
It  has  been  evidently  ground  down  and  smoothed  by  hard  and 
heavy  bodies  passing  over  it.  Stride  observed  in  numerous 
places  on  Carden  Hill,  viz.,  W.  by  N.,  N.W.,  N.W.,  N.W. 
by  W.,  N.W.  by  W.,  NW.  by  W.  The  average  direction 
was  N.W.  by  W.,  and  from  the  formation  of  strias,  agent  which 
produced  them,  evidently  came  from  north-westward. 

Numerous  boulders  along  ridge  of  hill  of  granite  (chiefly 
grey,  one  of  red),  gneiss,  &c.  The  red  granite  boulder 
4J  x 2J  x 11  feet.  Its  longer  axis  N.W.  by  W.,  and  its 
sharpest  end  was  towards  that  point. 

Most  of  these  boulders  rounded  and  smooth,  as  if  great 
friction  and  pressure  had  operated  on  them. 

Some  were  lying  along  ridge  on  its  northern  slope,  as  if 
arrested  in  their  further  progress.  Numbers  also  along  ridge 
on  south  slope,  as  if  pushed  over  hill,  and  put  into  positions 
where  beyond  reach  of  pushing  agent. 

At  one  place,  sandstone  rocks  of  ridge  broken  up,  as 
evidenced  by  great  fragments  lying  along  southern  slope, 
where  beyond  the  reach  of  agent  which  broke  and  pushed 
them.  These  sandstone  blocks  lie  at  levels  about  40  to  60 
feet  below  level  of  ridge. 

This  flat  ridge  of  Carden  Hill  extends  for  about  a mile,  and 
is  about  400  feet  above  sea. 

From  ridge  of  this  hill,  the  Carlin  Stone  boulder  above- 
mentioned  seen,  bearing  S.S.E.  about  two  miles  distant.  It 
is  not  probable  that  it  came  over  Carden  Hill.  More  probable, 


154 


Proceedings  of  the  Royal  Society 

that  it  was  floated  through  long  valley  between  Pluscardine 
and  Carden,  in  which  case  its  course  would  be  E.S.E.,  in  con- 
formity with  prevailing  movement  in  this  district.  Bottom  of 
this  valley  from  130  to  140  feet  above  sea. 

At  one  place  on  top  of  Carden  ridge,  N.W.  striae  crossed  by 
striae  from  N.  by  E. ; at  another  place,  W.  by  N.  striae  crossed 
by  striae  from  N.W.  The  N.  by  E.  striae  seemed  the  older. 

These  variations  in  direction  of  striae  more  reconcilable 
with  idea  of  drift-ice  than  with  glaciers. 

Moreover,  in  this  district  no  possibility  of  any  local  glacier 
from  N.W. 

From  Carden  Hill,  Cromarty  Firth  bears  about  N.W.,  dis- 
tant about  20  miles  across  sea.  If  a glacier  brought  these 
boulders  from  Boss-shire,  it  must  have  crossed  Moray  Firth, 
and  risen  over  Carden  Hill,  and  passed  across  valley  on  south 
of  it  obliquely. 

If  land  submerged  beneath  an  Arctic  sea,  and  a N.W. 
current  prevailed,  possible  to  understand  facts  observable  in 
this  district. 

Quarrywood  Hill,  about  200  feet  above  sea,  and  composed 
of  sandstone  striated  on  top.  On  N.W.  slope  four  or  five  large 
conglomerate  boulders  about  140  feet  above  sea.  Apparently 
from  Boss-shire,  and  obstructed  in  further  progress  by  this 
hill.  (Convener  much  indebted  to  Mr  Martin,  Elgin,  for 
pointing  out  facts  above  stated.) 

Forres. — Conglomerate  boulder,  9J  x 8 x 8 feet,  about  44  tons, 
called  “Doupping  Stone/’  from  legend  of  ceremony  in  ad- 
mitting Forres  burgesses;  situated  on  Upper  Caliper  farm, 
about  580  feet  above  sea.  Bock  composing  boulder  evi- 
dently same  as  Carlin’s  Stone,  near  Elgin,  being  charac- 
terised by  liver-coloured  quartz  nodules.  This  boulder  situated 
on  hill-side  fronting  Cromarty,  which  bears  N.W.  by  N.  across 
Moray  Firth  about  10  miles. 

Informed  by  tenant  of  farm,  that  another  boulder  of  same 
kind  higher  up  hill,  but  so  buried  in  earth  that  only  upper 
part  visible. 

Forres  to  Nairn. — Extensive  beds  of  sand  and  gravel,  mostly 
stratified,  shown  in  railway  cuttings.  Pebbles  and  boulders 


of  Edinburgh,  Session  1872-73. 


155 


in  these  beds  always  rounded  and  smooth,  seldom  angular. 
Angular  boulders  apparently  never  imbedded  entirely,  almost 
always  on  surface. 

Lossiemouth. — On  old  sea  margin,  20  feet  above  present  sea  level, 
conglomerate  boulder  same  as  Carlin’s  Stone.  About  1J  miles 
west  of  Caussie  Lighthouse,  a large  boulder  of  silicated  sand- 
stone on  a bill  sloping  to  N.W.  with  N.W.  striae  on  it. 

Inverugie  limestone  quarry,  strata  dip  rapidly  to  north. 
On  surface  of  rock,  striae  running  E.  and  W.  This  deviation 
from  normal  direction  perhaps  caused  by  dip  of  stratum. 

In  boulder  clay  over  limestone  rocks  here,  boulders  of  oolite 
found,  which  probably  came  from  Boss  or  Sutherlandshire 
across  Moray  Firth. 

Portion  of  an  Oolite  boulder  seen  by  Convener,  which 
found  near  Duffus  school-house,  about  125  feet  above  sea. 

“ Witch  Stone,”  about  quarter  mile  west  of  Duffus  school, 
250  feet  above  sea,  viz.,  a large  conglomerate  boulder,  exactly 
similar  to  Carlin’s  Stone,  containing  nodules  of  granite,  gneiss, 
and  purple-coloured  quartz.  Its  longer  axis  N.W.,  and 
sharpest  end  towards  that  quarter.  Hill  on  which  lies,  slopes 
that  way.  Lies  on  bed  of  sand. 

On  Clarkeley  Hill,  1\  miles  eastward  of  Burgh-head,  hard 
sandstone  rocks  striated  N.W.  On  same  hill,  several  boulders 
of  granite  (both  red  and  grey)  and  gneiss,  lying  on  hill  sloping 
to  N.W.  One  of  them,  4x3x2  feet,  has  its  longer  axis  in 
same  direction.  They  could  have  come  only  from  N.W.,  and 
therefore  across  sea.  (Rev.  Dr  Gordon,  Birnie,  pointed  these 
out  to  Convener.) 

Hebrides. 

Iona. — Convener  found  on  east  side  of  island  at  the  shore,  small 
well-rounded  boulder  of  conglomerate.  Heard  that  similar 
boulders  to  be  seen  on  west  shore  of  Iona  in  St  Columb’s  Bay. 
Conglomerate  rocks,  said  to  be  in  situ , at  Inch  Kenneth  Island, 
forming  cliffs  50  feet  high,  about  10  miles  to  N.E.  The  rocks 
in  Iona  are  clay  slate. 

N.E.  of  Cathedral,  on  shore,  hundreds  of  granite  boulders 
(chiefly  red  variety).  Several  exceed  20  tons  in  weight. 

Farther  north,  in  a cultivated  field,  about  50  feet  above  sea, 


156 


Proceedings  of  the  Royal  Society 

red  granite  boulder,  weighing  about  150  tons,  called  the 
11  G-eadh,”  or  “ Goose,”  24  x 18  x 6 feet.  Longer  axis,  S.E. 
(See  Plate,  Sketch  No.  IX.) 

About  J mile  farther  north,  on  east  shore,  another  large 
red  granite  boulder,  about  12  feet  square.  East  end  rests  on 
clay-slate  rocks  of  island.  West  end  rests  on  a smaller  granite 
boulder.  Eocks  below  boulder  decayed  out,  so  that  possible 
to  creep  under  boulder.  Groove  on  bottom  of  boulder  running 
N.E.  as  if  pushed  over  rocks  from  that  direction.  This 
boulder  very  rounded  at  angles,  apparently  from  friction. 

Boulder  of  red  granite  on  side  of  highest  hill  in  island, 
called  “ Dun  Ii.”  Cubical  in  shape,  and  very  angular, 
22x16  x16  feet.  Boulder  lies  against  steep  slope  of  hill 
facing  N.N.W.,  at  height  of  230  feet  above  sea. 

Convener  found  red  granite  boulders  of  smaller  sizfe,  at 
height  of  about  400  feet,  the  highest  point  of  island. 

Mr  Allan  McDonald,  schoolmaster,  says  that  these  granite 
boulders  seem  to  be  of  same  variety  as  that  in  Boss  of  Mull ; 
but  he  thinks  granite  does  not  occur  there  so  high  as  300  feet. 
Boss  of  Mull  bears  from  this  spot  S.S.E.  The  “Dun  Ii  ” hill 
lies  between  Boss  of  Mull  and  this  boulder. 

When  asked  by  Convener  if  any  red  granite  in  Islands  of  Tiree 
or  Ulva,  to  north  of  Iona?  Mr  M‘Donahl  said  there  was  none. 

Bocks  on  Iona  more  smoothed  at  the  highest  levels  than  at 
lower  levels. 

Smooth  faces  of  rocks  front  N.  by  E.  The  rough  faces  all 
front  south. 

At  south  end  of  Iona  a number  of  granite  boulders  (mostly 
red,  but  a few  of  grey  variety)  lying  on  the  high  ground,  from 
200  to  250  feet  above  sea.  One  of  these  standing  up  on 
end,  leaning  against  a rock  on  S.W.  side  of  boulder,  show- 
ing that  boulder  came  from  N.E.,  and  was  obstructed  by  rock  in 
its  farther  progress  to  S.W.  (See  Plate,  Sketch  No.  XI.) 

Most  of  boulders  in  south  end  of  Iona  lie  with  longer  axis, 
N.E.  and  E.N.E. 

Some  of  the  boulders  in  this  district  in  such  positions,  that 
they  could  not  have  come  into  them,  except  by  floating  ice, 
brought  from  northward,  and  by  eddying  currents. 


of  Edinburgh,  Session  1872-73.  157 

in  Boss  of  Mull  granite  of  both  red  and  grey  varieties  ex- 
tensively quarried. 

Heard  of  a large  boulder  on  west  side  of  island,  in  two  frag- 
ments, which  said  to  suggest  idea  of  having  been  broken  by 
falling  from  height. 

Lismore  Island. — Convener  found  several  boulders  of  granite, 
both  red  and  grey,  which  supposed  to  come  from  the  Kingair- 
loch  hills  to  north.  Almost  all  the  large  boulders  broken  up. 

Staffa. — Convener  found  several  small  boulders  of  red  granite  on 
surface.  No  rocks  of  granite  in  situ  here. 

Stornoway. — Boulder  15  x 7 x ? of  old  Cambrian  rock,  very  hard, 
and  close  in  texture.  Boulder  now  blasted.  Bested  on 
gneissic  rock,  and  differed  from  any  rock  in  the  Lewis. 
Height  above  sea,  about  50  feet. 

The  whole  hill  at  back  of  Nether  Pyble  strewn  with  small 
round  stones  of  similar  Cambrian  rock. 

In  parish  of  Ness,  from  Lighthouse  at  the  Butt,  thousands 
of  small  worn  boulders  of  Cambrian  rock  scattered  over  sur- 
face, even  on  highest  points. 

No  Cambrian  rock  in  situ  nearer  than  mainland.  The  rock 
in  situ  gneiss.  (Henry  Caunter,  Stornoway.) 

Inverness. 

BolesJcien , Abertarff. \ and  Doves. — 1.  Granite  boulders  of  red  and 
grey  varieties,  in  great  numbers,  over  district  of  Stratherrick. 
Well  rounded.  Largest,  near  farm-house  of  Hell,  20  x 10  x 7 
feet  above  ground,  and  apparently  as  much  below  ground. 
Longer  axis,  N.  and  S.  Another  near  Fall  of  Foyers,  12  x 6 x 6 
feet  above  ground.  Granite  (grey)  occurs  in  situ. 

2.  On  hills  from  which  rivers  Foyers  and  Ness  rise,  a great 
many  boulders  of  granite  and  schist.  The  granite  boulders 
well  rounded ; the  schist  boulders  angular.  Several  perched 
on  tops  of  isolated  hills. 

Highest  hills  in  district  about  2900  feet  above  sea.  The 
boulders  extend  down  to  a level  of  about  2250  feet.  Few 
below  this  level  except  in  beds  of  streams.  (Captain  White, 
B.E.) 

Culloden  Muir. — Duke  of  Cumberland’s  “ stone,”  a conglomerate 


153 


Proceedings  of  the  Royal  Society 

boulder  with  six  sides,  girth  altogether  not  quite  60  feet,  and 
height  6 feet.  Longer  axis  W.N.W.  Height  above  sea  about 
470  feet;  a few  faint  traces  of  striae  running  W.  by  N. 
Nodules  seemed  similar  to,  but  not  quite  the  same  as,  those  of 
Elgin  and  Nairn  boulders. 

Croy  (Tillage). — About  J mile  to  S.W.,  and  320  feet  above  sea. 
A mica  schist  boulder  17  x 9 x 9 feet.  Lies  on  hill  sloping  to 
N.W.  (Convener.) 

A kaim  begins  here,  which  said  to  run  eastward  through 
counties  of  Nairn  and  Elgin  for  30  miles. 

A conglomerate  boulder  called  “ Tom  Riach  ” (Plate,  Sketch 
I.),  of  following  dimensions  : — West  side,  18  feet;  north  side, 
21  feet;  east  side,  24  feet ; south  side,  21  feet;  height,  20  feet, 
it  stands  in  the  middle  of  a plain  or  flat  valley  through  which 
River  Nairn  flows.  Rocks  in  situ  are  gneiss,  and  boulder  appa- 
rently rests  on  this  rock.  A small  portion  of  its  under  surface, 
resting  on  the  rock,  visible.  It  looks  smooth,  as  if  it  had  been 
pushed  over  the  subjacent  rocks ; and  there  seemed  grooves  or 
scorings  which  coincided  with  axis  of  valley,  which  here  E.  and 
W.  This  boulder  must  have  come  from  distance,  and  been 
carried  by  ice,  of  some  kind.  In  higher  parts  of  valley  in 
which  this  boulder  occurs,  conglomerate  rocks  in  situ  exist. 
Not  probable  that  this  boulder  could  come  from  N.W.,  as  in 
that  case  it  would  be  carried  over  Culloden  Muir,  which  300 
feet  higher  than  boulder.  Yeiy  probable  that  brought  by 
glacier  from  westward.  Ingredients  of  this  conglomerate 
apparently  not  same  as  those  in  Elgin  and  Nairnshire. 

On  high  plateau,  4 miles  south  of  Inverness,  at  height  of 
about  774  feet  above  sea,  another  conglomerate  boulder,  with 
a thin  stratum  of  old  red  sandstone  on  top.  Grirth  about  51 
feet.  Height,  9 feet.  Longer  axis  N.  and  S.  Kaim  of  gravel 
and  sand  to  N.  of  boulder,  about  900  feet  above  sea,  running  E. 
and  W.  being  direction  parallel  with  valley  of  Nairn.  (These 
boulders  shown  to  Convener  by  Mr  Jolly,  Inverness.) 

Dallanossie  (Parish). — Moy  Hall  estate,  Eallry  farm,  Mr  Eraser, 
tenant.  Boulder,  30  x 18  x 9 feet,  apparently  a bastard  granite; 
though  rocks  of  adjoining  district  are  also  granitic,  the  boulder 
much  darker  in  colour.  Nearest  rock  in  situ  S.W.  by  S.  about 


159 


of  Edinburgh,  Session  1872-73. 

a mile  distant  Boulder  split  into  two  unequal  parts.  Its 
Gaelic  name  is  “ Clach  Schuilt” — meaning  “ Cloven  Stone.” 
Height  above  sea,  2090  feet.  (Captain  White,  B.E.) 

Duntelchak  Hill , west  of  Inverness. — Top  about  900  feet  above  sea. 
Bocks  composing  it,  a coarse  conglomerate.  On  N.W.  side  of 
hill,  rocks  ground  down  and  smoothed ; — on  S.E.  side  of  hill 
rocks  rough  and  steep. 

A granite  boulder  lying  on  N.W.  slope  of  this  hill,  about  30 
feet  below  top.  Length  7 feet,  width  4 feet.  Longer  axis 
N.W.,  and  sharp  end  towards  that  quarter.  (Convener.) 

Flicliity  Valley. — Beds  of  sand  and  gravel  seen  on  hills  to  south, 
about  1500  feet  above  sea.  Not  near  enough  to  be  examined. 
At  east  or  lower  end  of  valley,  top  of  a rocky  hill  striated,  in 
direction  parallel  with  axis  of  valley,  viz.,  E.N.E. 

At  Farr,  in  Nairn  Valley,  a continuation  of  Flichity  Valley, 
near  the  Free  Church,  a most  remarkable  assemblage  of 
boulders.  Some  rounded,  but  most  of  them  angular.  Many 
are  about  7 feet  square.  No  conglomerate  boulders  here  ; — all 
gneiss  or  mica  schist.  They  mostly  rest  on  gravelly  detritus, 
which  may  have  been  moraines.  Others  (and  these  are  round 
shaped)  rest  on  a smoothed  rocky  surface  of  gneiss  beautifully 
glaciated,  and  sloping  down  towards  west — i.e .,  looking  up 
valley.  fSee  Plate,  Sketch  No.  XIII.)  This  glaciated  rock — 
smooth  towards  west,  and  dipping  at  angle  of  30° — is  on  its 
east  side  rough  and  vertical.  Very  manifestly  these  rounded 
blocks,  glaciated  rocks,  and  gravelly  debris,  indicated  glacier 
action.  Two  valleys  meet  here,  one  (Flichity)  bearing  due 
west,  the  other  (Duntelchak)  bearing  N.W.  Both  valleys 
deserve  exploration,  with  reference  to  remains  above  specified. 

At  lower  end  of  Flichity  Valley  (about  3 miles  west  of  these 
boulders),  a great  embankment  of  gravel  and  sand,  through 
which  Biver  Nairn  has  cut  passage  about  200  feet  deep. 
Before  this  passage  cut,  a lake  must  have  filled  Flichity  Valley, 
dammed  back  by  the  gravel  accumulation.  That  such  a 
lake  existed,  proved  by  terraces  on  hill  sides  of  valley.  Query , 
If  a glacier  filled  this  valley,  and  brought  blocks  and  moraines 
to  Farr  Church,  when  did  this  occur?  Any  gravelly  embank- 
ment, such  as  now  exists  at  east  end  of  Flichity  Valley,  would 


VOL.  VIII. 


X 


160 


Proceedings  of  the  Royal  Society 

have  been  swept  away  by  a glacier.  Glacier  must,  therefore, 
have  existed,  and  disappeared,  before  embankment  formed. 

The  only  solution  of  problem  seems  to  be,  that  after  glacier 
had  filled  valley,  carrying  down  blocks  and  debris  to  Farr, 
land  sank  under  sea,  destroying  glacier,  but  not  disturbing 
position  of  boulders,  or  carrying  away  much  of  moraines. 

In  this  Flichity  Valley  an  isolated  hill,  about  1620  feet  above 
sea.  Near  the  top  of  hill,  rocks  (gneiss)  on  W.  and  N.W.  sides 
present  an  appearance  of  having  been  rubbed  and  ground  down  ; 
on  its  W.N.W.,  S.E.,  and  E.  sides,  boulders  of  gneiss  attract 
attention,  not  only  from  size,  but  from  very  precarious  positions. 
Boulders  evidently  erratic,  for  though  gneiss,  they  are  different 
kind  of  gneiss  from  that  forming  hill,  and,  being  rounded,  they 
have  undergone  considerable  friction  before  reaching  present 
position.  The  hill  remarkably  precipitous  where  boulders 
situated,  insomuch  that  if  they  had  fallen  from  any  height, 
they  would  have  rolled  down.  To  prevent  this,  boulders  must 
have  been  brought  close  to  side  of  the  hill  where  now  lie,  and 
let  gently  or  gradually  down  upon  hill-side. 

A sketch  is  given  of  one  of  these  boulders,  to  show  how  near 
it  is  to  a precipitous  portion  of  the  hill.  (See  Plate,  Sketch  IV.) 

These  boulders  about  500  feet  above  bottom  of  the  valley. 

In  descending  from  this  hill  top,  along  the  north  side  four 
several  horizontal  terraces  passed,  separated  from  one  another 
by  about  100  feet  less  or  more,  having  appearance  of  old  beach 
lines.  On  these  terraces  the  boulders  more  numerous  than 
elsewhere.  (Mr  Jolly  of  Inverness,  was  guide  to  Convener). 

On  N.W.  of  Craig  Phasdrick  Hill,  Inverness,  the  hard  con- 
glomerate rocks  bared,  rounded,  and  smoothed,  and  sloping 
towards  N.W.,  at  about  500  feet  above  sea;  on  south  side  of 
hill,  same  rocks  rough  and  vertical. 

Transported  boulders  of  gneiss,  &c.,  on  N.W.  side  of  bill — 
none  elsewhere. 

Many  of  these  boulders  have  sides  sloping  down  to  N.W. 

On  several  parts  of  hill,  especially  east  side,  rocks  (old 
conglomerate,  coarse  and  compact)  broken  up  into  huge 
cubical  masses,  similar  to  Tomriach  boulder  (see  page  158) — 
many  much  larger. 


161 


of  Edinburgh,  Session  1872-73. 

Above  Clachnaharry,  grooves  on  rocks,  E.  and  W. — a 
direction  parallel  with  Beauly  Yalley;  might  have  been  made 
by  glacier  descending  valley,  or  by  drift  ice,  if  valley  sub- 
merged. 

A remarkable  boulder  here,  30  paces  in  girth,  and  about  15 
feet  high,  and  roughly  estimated  to  weigh  100  tons;— pro- 
bably that  called  by  Anderson  “ The  Watchman’s  Stone.” 
Name  very  suitable,  as  it  rests  on  a projecting  part  of  coast, 
and  extensive  view  from  it.  Situated  on  what  appears  a ter- 
race of  drift,  about  73  feet  above  sea. 

A very  extensive  sea-terrace,  about  40  feet  above  sea,  girds 
coast  of  Beauly  Firth,  and  seems  to  be  repeated  at  Lentran 
and  Clunes  Railway  stations,  towards  Tain. 

Fort-William,. — Ascended  hill  on  north  side  of  Linnhe  Loch. 
Along  both  sides  of  loch  several  terraces  visible,  running  for 
some  distance  one  above  another, — viz.,  20  feet,  110  or  120 
feet,  and  494  feet  above  sea.  This  hill,  called  Treshlik, 
covered  by  small  pebbles,  indicative  of  aqueous  action. 

This  hill  about  1566  feet  above  sea.  It  forms  a ridge 
about  ^ mile  long,  running  W.S.W.  and  E.N.E.  Bocks  on 
north  and  west  sides  smoothed,  as  if  by  friction  of  some  agent 
passing  over  them  from  W.N.W.  No  such  appearances  on 
any  other  side  of  hill. 

But  these  smoothings  confined  to  a line  along  hill,  not  reach- 
ing lower  than  about  60  feet  from  top,  nor  reaching  higher 
than  about  30  feet  from  top. 

Large  boulder  of  coarse  granite  on  N.W.  angle  of  hill  about 
1494  feet  above  sea.  It  is  about  16  paces  round,  and  about 
8 feet  high.  Boulder  rests  on  the  edge  of  the  stratified  rocks 
of  hill,  viz.,  clay  slate.  (See  Plate,  Sketch  No.  Yl.) 

The  boulder  in  composition  resembles  boulder  on  Cluny 
MTherson’s  lands.  (See  next  page.) 

This  boulder  on  very  precarious  site.  The  hill  here  exceed- 
ingly steep.  Boulder  could  not  have  been  brought  from  any 
eastern  point ; for  in  that  case,  it  would  have  rolled  down  hill. 

It  probably  did  not  come  from  a point  due  west,  because 
Blythe  Hill  bears  due  west,  about  2 miles  distant,  and  forms 
a large  mass  about  2500  feet  above  sea,  which  would  intercept 


162 


Proceedings  of  the  Royal  Society 

any  agent  moving  towards  Treshlik  Hill.  There  are  only 
two  points  from  which  boulder  probably  came,  viz.,  from 
mouth  of  Linnhe  Loch  bearing  from  Treshlik  Hill  S.W.  by 
W.,  or  from  Loch  Eil  bearing  from  Treshlik  Hill  N.W. 

The  preference  must  be  given  to  the  N.W.  quarter,  because 
of  the  numbers  of  other  coarse  granite  boulders  all  along  the 
north  slope  of  hill,  and  of  the  smoothed  rocks  being  on  same  side. 

Highland  Railway  from  Forres  to  Kingussie  cuts  through  immense 
deposits  of  clay,  gravel,  and  sand,  up  to  a height  of  about  800 
feet  above  sea.  Some  of  these  deposits  are  stratified.  They 
are  full  of  rounded  blocks  of  all  sizes. 

At  Dava  station,  on  east  side  of  railway,  about  900  feet  above 
sea,  rocks  facing  N.W.  show  large  extent  of  surface  glaciated. 

At  summit  level,  viz.,  about  1080  feet  above  sea  (north  of 
Kingussie),  stratified  gravelly  drift  abounds. 

At  Kingussie  (about  730  feet  above  sea),  two  sets  of  terraces 
visible  on  the  sides  of  valley,  one  about  50  feet  higher  than 
other,  indicating  existence  of  a lake  at  some  former  period, 
and  which  had  been  drained  by  barrier  confining  it  having 
been  cut  through  by  Spey.  Ruthven  Castle  stands  on  an 
isolated  mass  of  drift,  which  probably  formed  island  in  this 
ancient  lake  at  summit  level  of  railway,  viz.,  between  Dal- 
whinnie  and  Dalnaspidel,  about  1430  feet  above  sea;  beds  of 
sandy  gravelly  detritus  abundant,  apparently  remains  of 
aqueous  sediment;  where  cut  through  by  burns,  they  form 
scaurs  or  cliffs  50  to  60  feet  high.  Mr  Robertson,  factor,  Old 
.Blair,  states,  in  letter  to  Convener,  that  near  summit  level  of 
railway  at  Drumnachdier  and  Dalnaspidel,  there  were  exten- 
sive deposits  cut  through  of  “pure  sand,”  “so  fine  and  soft” 
that  it  could  not  be  used  for  building.  He  adds,  that  at  a 
spot  a little  higher,  viz.,  1480  feet  above  sea,  there  was  found 
(from  surface) — ls£,  A peat  bed,  2 or  3 feet  thick,  containing 
fir  roots ; 2 d,  A layer  of  clayey  gravel  about  2 feet  thick  ; 

3 d,  A peat  bed  with  decayed  branches  of  birch  and  hazel , and 
no  fir;  4:th,  Tilly  gravel. 

On  Cluny  McPherson’s  lands  (about  6 miles  west  of  • 
Kingussie)  two  large  boulders  of  a very  coarse  grained  granite 
on  south  side  of  Spey.  One  boulder  is  11  x 9 x 6 feet.  Plates 


163 


of  Edinburgh , Session  1872-73. 

of  mica  in  boulder  about  1 inch  square.  Felspar,  green  in 
colour.  Longer  axis  E.  and  W.  This  boulder  lies  on  hill 
side  sloping  down  to  west.  Height  above  sea  about  1035  feet. 
The  other  boulder,  about  double  size  of  previous  one,  about 
f mile  N.E.  from  it,  and  at  height  of  about  1080  feet  above 
sea ; also  on  hill  side  sloping  down  to  west.  There  are  other 
boulders  on  this  hill  of  smaller  size. 

Rocks  of  district  are  a variety  of  coarse  clay  slate. 

The  only  hill  in  this  district  is  Craig  Dhu,  situated  to  north 
about  4 miles,  consisting  of  clay  slate,  and  about  2500  feet 
above  sea. 

Nearest  granite  rocks  situated  to  westward.  In  that 
direction  a valley,  down  which  these  boulders  might  have 
come.  The  physical  features,  however,  not  favourable  to 
glacier  theory,  from  absence  of  any  range  of  hills  to  south- 
ward. 

At  Laggan  Free  Church,  a well-rounded  granite  boulder, 
lying  on  a glaciated  and  striated  rock  of  clay  slate,  sloping 
down  to  west,  facing  upper  part  of  valley.  Boulder  9x6x6 
feet;  longer  axis  E.  and  W.,  which  corresponds  also  with 
striae  on  rock,  and  with  general  direction  of  valley  at  this 
place. 

Kingussie . — Boulder  called  “ The  Big  Ordan  Stone,”  said  to  be 
whinstone,  situated  on  hill  5 miles  S.W.  of  Kingussie,  and 
2 miles  from  Newtonmore  Railway  Station,  on  Belville  estate 
and  farm  of  Etteridge.  Shape  angular.  Longer  axis,  S.S.W. 
Has  a deep  hollow  on  top  facing  S.W.  Greatest  length  (viz., 
on  S.E.  side),  13  feet  10  inches.  Breadth  at  top,  8 feet  4 inches. 
Height,  8 feet  10  inches.  No  similar  rock  in  district.  Height 
above  sea  from  950  to  1000  feet.  One  legend  is  that  Fingal 
used  the  stone  for  a putting-stone,  throwing  it  from  Craig 
Dhu,  on  opposite  side  of  river  Spey;  another,  that  when 
Fingal  wished  to  drink  out  of  the  Spey,  he  put  one  foot  on  Craig 
Roy  (a  low  shoulder  of  Craig  Dhu)  and  the  other  on  Ordan 
Hill,  but  finding  Ordan  too  low,  he  threw  the  boulder  from 
Craig  Roy  that  he  might  put  his  foot  on  it.  (John  Robertson, 
Old  Blair.) 

Inverie. — On  road  toward  Arrar,  about  2 miles  to  north,  and  at 


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Proceedings  of  the  Royal  Society 

height  of  about  360  feet  above  sea,  clay  slate  rocks  smoothed 
and  striated  in  a direction  from  N.W.  by  1ST. 

Fell  in  with  two  boulders  lying  near  each  other  on  side  of 
hill,  sloping  down  to  W.N.W.,  where  sea  situated,  about  one 
mile  distant.  In  one  case,  boulder  lying  on  clay  slate  rocks ; 
in  the  other  case,  boulder  so  sunk  that  base  not  visible.  First 
boulder  8 x 6-J  x 4 feet.  Longer  axis  N.W.  Second  boulder 
9x5x4  feet.  (Shown  to  Convener  by  James  Baird  of  Cam- 
busdoon.) 

Both  boulders  apparently  came  from  N.W.,  and  intercepted 
in  further  progress  by  hill. 

Fell  in  with  another  boulder,  which  broken  into  two  frag- 
ments. Configuration  of  district  indicates  that  it  must  also 
have  come  from  N.W.  Smaller  fragment  lies  from  rest  of 
boulder  at  a distance  of  4 or  5 feet  and  to  S.E.  A study  of 
fragments  creates  impression  that  boulder  has  been  broken, 
not  by  action  of  frost,  but  by  falling  from  a height,  which 
caused  concussion. 

On  shore  to  west  of  Inverie  House,  several  boulders  of 
coarse  granite,  similar  to  Fort-William  and  Cluny  MTherson 
granite.  These  Inverie  boulders  supposed  to  have  come  from 
Dunedin  and  Cairnmore  Hills,  about  10  miles  to  eastward,  and 
at  head  of  valleys  opening  to  west  coast.  Opinion  expressed 
to  Convener  that  these  boulders  not  so  likely  to  have  come 
down  the  Dhulochan  valley  as  the  Loch  Nevis  valley. 

At  Invergussern  (about  8 miles  north  of  Inverie),  the  valley 
has  been,  at  its  mouth  near  the  sea,  crossed  by  an  immense 
embankment  of  gravel  and  sand,  about  30  or  40  feet  deep, 
lying  over  rocks. 

The  river  has  cut  through  this  embankment,  and  also  a 
portion  of  the  rocks  covered  by  it. 

This  embankment  probably  terminal  moraine  of  a glacier 
or  a submarine  deposit,  more  probably  the  latter,  as  sandy, 
and  in  some  places  stratified.  Its  ridge  is  about  140  feet 
above  sea.  At  one  time  it  has  served  purpose  of  a dam  to 
keep  in  lake,  the  successive  levels  of  which  are  seen  on  both 
sides  of  valley. 

At  summit-level  between  Inverie  and  Gussern,  viz.,  from  400 


165 


of  Edinburgh,  Session  1872-73. 

to  500  feet  above  sea,  a flat  or  terrace  visible,  with  a number 
of  boulders  on  it. 


Kirkcudbright. 

Borgue. — Boulder  of  red  sienitic  granite.  Oblong  in  shape.  Longer 
axis  N.W.  and  S.E.  Rests  on  a low  hill  of  partially  decom- 
posed trap.  Longest  sloping  side  fronts  N.W.  The  S.E.  end 
vertical  and  rough.  Girth  at  3 feet  above  base  is  23  feet. 
A line  over  and  across  boulder  measures  16  feet.  Rocks  in 
situ  at  and  near  boulder  are  partly  trap,  partly  greywacke. 

No  granite  nearer  than  about  10  miles,  forming  a range  of 
hills  extending  from  Dalbeattie,  east  of  boulder,  to  Creetown, 
west  of  boulder.  (See  Plate,  Sketch  No.  XII.) 

Formerly  many  similar  boulders  in  parish,  all  now  broken 
up.  (Earl  of  Selkirk  and  Rev.  Geo.  Cook.) 

Lanark. 

Glasgow . — Near  Possil,  sandstone  rocks  covered  by  boulder  clay. 
Two  sets  of  striae  on  rocks  under  boulder  clay — viz.,  from 
N.W.  and  from  N.E. ; oldest  from  N.W.,  and  caused  by  a more 
powerful  agent,  judging  by  length  and  depth  of  striae. 
Boulders  in  clay,  recognised  by  Mr  John  Young  (Hunterian 
Museum)  as  from  Kilpatrick  hills  to  N.W.,  and  Campsie  hills 
to  N.E. 

At  Brickwork,  Garscube  Road,  sandstone  rocks  also  striated 
from  N.W.  more  deeply  than  at  Possil.  No  striae  from  N.E. 
Perhaps  striating  agent  here  intercepted  by  a hill  to  N.W., 
quarter  of  a mile  distant,  about  100  feet  high.  At  this  place, 
in  boulder  clay,  numerous  boulders  of  old  conglomerate,  grey 
granite,  schists,  &c.,  from  Bonaw  and  Kilpatrick  hills  to  N.W. 
(Convener.) 

Nairn. 

Auldearn. — 1.  Conglomerate  boulder  called  Grass  Stone,  15  x 9 x 4 
feet,  rounded.  Longest  axis,  N.W.  Height  above  sea,  200  feet. 

2.  Grey  granite  boulder  6x5x4  feet,  a few  yards  S.E. 
of  No.  1,  round  and  quite  smooth. 

3.  Red  granite  boulder,  about  1\  miles  south  of  Nos.  1 and  2. 


166 


Proceedings  of  the  Royal  Society 

Lowest  axis  N.W.  Size  12  x 8J  x 8 feet ; striated  in  various 
directions.  Well  rounded.  350  feet  above  sea. 

The  rocks  of  district  old  red.  Nearest- place,  where  rocks 
same  as  boulders  occur,  is  in  Ross-shire  to  N.W. 

Thousands  of  smaller  boulders,  similar  to  the  above,  scat- 
tered over  district,  used  for  buildings.  (Captain  White, 
R.E.) 

Kahn  of  gravel  and  sand,  with  steep  sides.  Average  direc- 
tion east  and  west,  winding  in  usual  serpentine  way.  Is 
here  continuous  for  f mile.  Average  height  above  adjoin- 
ing ground  30  feet.  Full  of  well-rounded  and  smooth  pebbles 
and  boulders  from  rocks  of  district. 

Auldearn  (Parish). — Brightmoney,  Lathan  Estate,  south  of  Dalmore 
Free  Church.  Five  conglomerate  boulders  all  on  ground, 
sloping  towards  N.W.,  about  200  feet  above  sea,  and  1 mile 
distant.  Partly  buried  in  sandy  drift. 

Their  longer  axis  N.W.  They  slope  towards  that  quarter, 
and  have  a smooth  surface;  whilst  S.E.  ends  rough  and  steep. 
If  these  blocks  were  originally,  when  brought  to  spot,  cubical, 
as  when  detached  from  parent  rocks,  they  would  have  this  shape. 
If  any  strong  current  loaded  with  ice  were  to  come  from  N.W., 
their  angles  on  N.W.  end  might  be  broken  off,  so  as  give 
shapes  they  now  have.  (See  Plate,  Sketch  No.  VII.) 

Cawdor. — Hill  of  Urchany,  composed  of  granite  rocks.  Neverthe- 
less, blocks  of  old  red  sandstone  scattered  over  surface  in  such 
quantities,  that  used  for  building  houses  and  dykes.  These 
must  have  come  from  north,  as  sandstone  rocks  only  in  that 
quarter,  about  2 miles  distant,  and  at  a lower  level. 

The  following  four  conglomerate  boulders  seen  : — 

1.  “Clach  na  Gtillean,”  or  “Young  Man’s  Stone.”  Height  10 
feet,  and  girth  54  feet.  Height  above  sea,  687  feet.  Some 
of  its  corners  angular,  on  crest  or  summit  level  of  Urquhany 
hill.  (See  Plate,  Sketch  No.  V.) 

2.  “Clach  na  Cailleach,”  or  “Old  Wife’s  Stone,”  on  same 
hill,  but  on  side  which  slopes  to  west  by  north.  Height  15 
feet ; girth,  54  feet.  Height  above  sea,  581  feet. 

3.  “ Clach  an  Oglach,”  or  “Boy’s  Stone.”  Lies  at  east  end 
of  a kaim.  Height,  9 feet;  girth,  69  feet ; above  sea,  312 


of  Edinburgh,  Session  1872-73.  167 

feet.  (A  gneiss  boulder  near  it  about  one-fourth  the  size. 
Numerous  smaller  do.) 

4.  Oblong  conglomerate  boulder  lying  on  a bank  facing 
W.N.W.  Longer  axis  W.N.W.,  50  feet  x 24  x 12  feet. 
(Shown  to  Convener  by  Mr  Stables  of  Cawdor  Castle.) 

Orkney. 

Mainland. — Mr  Miller  of  Bin  Scarth  says,  that  a valley  runs  E. 
and  W.  across  the  mainland  of  Orkney,  forming  in  its  course 
the  bed  of  the  Lochs  of  Stennis  and  Stanay.  There  is  no 
large  boulder  in  this  district,  but  on  north  exposure  of  the 
hills,  there  are  small  stones  strewed  over  the  surface,  quite 
different  from  rocks  in  situ.  The  former  are  a white  bastard 
freestone ; the  latter,  old  red  sandstone  or  flag  pavement. 

There  is  evidence  through  all  this  valley,  of  it  having  been 
channel  of  a tidal  strait.  There  are  in  it  hummocks  of  sand, 
mud,  and  water- worn  gravel.  Below  these,  reporter  found 
heaps  of  small  sprigs,  brushwood,  and  hazel-nuts,  preserved 
in  moss,  similar  to  the  submarine  mosses  and  forests  under 
the  bays  of  Otterswick,  Deersound,  &c. 

The  comparatively  recent  elevation  from  under  the  sea  of 
all  this  district,  is  evident.  Traces  also  exist  of  dry  land  with 
forests  and  other  produce  not  now  suiting  climate. 

Beporter  does  not  know  of  any  large  boulder  in  the  Orkneys, 
except  on  Sanday  Island. 

Sunday. — Dr  Smith,  secretary  to  the  Edinburgh  Boyal  Physical 
Society,  sends  to  the  Committee  the  following  extracts  from  a 
MSS.  paper  by  the  late  Dr  Patrick  Neill,  on  the  Shetland 
Islands,  dated  26th  January  1806: — 

“ 1 Moorstone  of  Sanda,’  Island  of  Sanday,  flattest  and 
lowest  of  the  Orkneys.  G-reater  part  only  a few  feet  above 
sea.  Near  a place  called  Saville , and  not  far  from  Burness 
Parish  Church,  stands  a large  isolated  mass  of  primary  rock — 
an  aggregate  of  quartz,  whitish  felspar,  and  black  mica.  These 
disposed  in  layers,  so  that  when  seen  in  the  mass,  they  consti- 
tute a block  of  gneiss.  I did  not  accurately  make  measure- 
ments, but  roughly  estimated  weight  at  12  or  13  tons. 


VOL.  VIII. 


1ft 8 Proceedings  of  the  Royal  Society 

“ Rocks  of  Sanda  are  wholly  secondary  strata, — sandstones, 
sandstone  flag,  breccia,  and  limestone. 

“ The  only  primary  rocks  in  Orkney  are  in  the  largest  islands 
(Mainland  or  Pomona),  close  by  sea- port  of  Stromness,  above 
30  miles  distant  from  Sanda.  Hill  at  back  of  Stromness  seems 
granite,  with  outer  coating  of  gneiss.  The  gneiss,  which  is 
similar  in  quality  to  the  Sanda  Moorstone,  is  traversed  by 
dykes  or  veins  of  granite. 

“ About  a mile  to  N.E.  of  Stromness  secondary  strata  begin. 
From  thence  to  Sanda  only  sandstone  and  limestone  visible. 

“From  Stromness  to  Burness  Church  is  at  least  34  miles  in 
a direct  line. 

“ On  supposition  that  this  gneiss  tumbler  in  Sanda  formed 
part  of  Stromness  hill,  it  must  have  passed  over  15  miles  of 
what  is  land,  and  19  miles  of  what  is  sea,  at  present. 

“The  firths  of  Westra  and  Eda,  between  Stromness  and 
Sanda,  are  of  immense  depth, * through  which  the  waters  of 
the  Atlantic  now  rush  with  indescribable  force  towards  east 
or  German  Ocean,  at  the  ebbing  of  the  tides/’ 

Dr  Neill  adds  that  he  cannot  imagine  how  this  boulder 
transported  from  Stromness  to  Sanda,  except  by  “what  Saus- 
sure  has  termed  a debacle,”  “ the  rush  of  vast  torrents,”  which, 
besides  transporting  the  boulder,  might  “have  also  scooped 
out  those  hollows  which  are  now  the  firths  of  Westra  and  Eda.” 

Stromness  bears  from  Saville  about  W.S.W.,  and  a straight 
line  between  the  two  places  crosses  not  only  several  firths,  but 
several  islands.  If  the  boulder  came  from  Stromness,  as  sup- 
posed by  Dr  Neill,  its  transportation  by  land  ice  is  inconceiv- 
able. 

Statistical  Account  states  that  granite  rock,  passing  into 
gneiss,  runs  through  Stromness  parish,  forming  a tract  about 
a mile  wide,  and  six  miles  long  (vol.  xv.  p.  46) ; and  that  all 
the  rest  of  Orkney  Islands  are  sandstones  of  different  kinds. 
It  is  added,  that  “rolled  blocks  of  granite  are  found  in  these 
islands  far  from  their  original  position”  (page  210). 

Whilst  it  is  very  probable  that  this  Sanda  boulder  came,  as 

* Admiralty  charts  show  depths  of  water  in  these  firths  to  he  from  10  to  20 
fathoms. 


169 


of  Edinburgh,  Session  1872-73. 

Dr  Neill  supposed,  from  Stromness,  it  is  right  to  keep  in  view 
that  granite  and  gneiss  rocks  abound  to  the  N.N.W.  in  the 
Shetland  Islands.  Transportation  by  land  ice  from  these 
remote  islands  seems  also  inconceivable. 

Mr  Miller,  schoolmaster  of  Cross  and  Burness,  reporting  the 
above  boulder  in  Sanda  to  Committee,  says  that  it  is  22  feet  in 
girth,  and  is  round  in  shape. 

Stromness  (Parish). — Two  granite  boulders  lying  on  old  red  sand- 
stone near  manse.  A range  of  granite  hills  six  miles  long 
situated  to  eastward.  One  of  boulders  is  a mile,  the  other 
a quarter  of  a mile  distant  from  these  hills.  One  boulder  50, 
the  other  100  feet  above  sea.  Each  boulder  3 or  f feet  in 
length,  breadth,  and  height.  (Reporter,  Rev.  Ch.  Clouston.) 

Perth. 

Blairgowrie. — Two  miles  west  of  town,  on  road  to  Essendy  Bridge, 
a Druidical  circle  of  5 large  mica-schist  boulders,  about  5 feet 
long,  and  6 or  7 feet  in  girth. 

Another  boulder,  7x5x3  feet,  lies  on  summit  of  steep 
acclivity  on  Woodhead  Farm. — (W.  S.  Soutar.) 

Granite  boulder,  4 x 3|  x 3 feet,  on  side  of  Ericht,  quarter 
mile  N.  of  Blairgowrie,  excavated  in  making  mill  lead.  No 
rock  of  same  kind  nearer  than  30  miles  in  Braemar  range 
of  hills  to  N.W.  Height  above  sea,  200  feet.  Numerous 
granite  blocks  found  in  excavating  for  foundations  of  houses 
in  Blairgowrie. 

Callander. — Gneiss  boulder  called  “Samson’s  Putting  Stone  ” on  top 
of  Bochastle  Hill,  two  miles  west  of  Callander,  14  x 9 x 9 feet. 
Longer  axis  N.N.E.  Lies  on  coarse  old  conglomerate,  viz., 
same  bed  or  stratum  which  crosses  Scotland  from  Dumbarton 
to  Stonehaven.  Boulder,  judging  by  nature  of  rock  com- 
posing it,  must  have  come  from  north-westward,  it  occupies 
precarious  position,  being  close  to  edge  of  a precipitous  face 
of  hill  about  330  above  valley,  fronting  W.S.W.  towards 
Loch  Katrine.  It  may  have  been  lodged  either  by  a 
glacier  which  descended  from  Loch  Katrine,  or  by  floating 
ice,  when  land  submerged.  About  50  feet  below  the  above 
boulder,  and  on  a very  steep  part  of  hill,  another  boulder. 


170 


Proceedings  of  the  Royal  Society 

6x4x4  feet,  very  angular,  of  gneiss,  evidently  also  brought 
from  westward.  Several  quartz  boulders  on  hill,  which  also 
must  have  come  from  westward.  (Convener.) — (See  Plate, 
Sketch  No.  IV.) 

Clunie. — Gneiss  houlder  8x5x4  feet,  with  longer  axis  S.W. 
Gneiss  boulder  10  x 6 x 5 feet,  with  longer  axis  N.W.  Both 
boulders  on  tops  of  knolls,  and  must  have  come  from  Grampians 
5 or  6 miles  to  N.W.  down  a valley.  First  boulder  called 
“ The  Grey  Stone.”  Height  about  320  feet  above  sea.— 
(Robert  MHeish,  schoolmaster.) 

Dunkeld. — Craigiebarns  Hill,  to  N.E.  of  town,  visited;  made  it 
about  1000  feet  above  river  Tay  at  Dunkeld  Bridge,  and  about 
1250  feet  above  sea. 

Several  boulders  of  mica-schists  at  and  near  top  of  hill,  but 
chiefly  on  sides  facing  N.W.  Bocks  in  situ  also  mica-schist, 
but  not  the  same  variety  as  boulders. 

These  boulders  mostly  angular  and  sharp  in  edges ; only  one 
or  two  rounded ; among  these  one  of  a hard  brown  sandstone. 

Greater  number  of  boulders  perched  on  top  or  sides  of  knolls 
than  in  hollows.  Agent  which  transported  them  had  been 
of  such  a nature  as  to  be  interrupted  in  its  progress  by  knolls, 
and  made  to  discharge  its  cargo  of  boulders  on  them.  (One  of 
these  boulders  shown  in  Plate,  Sketch  No.  X.) 

On  this  hill,  rocks  smoothed  and  striated  in  numerous 
places.  These  markings,  when  examined  minutely,  show 
a movement  over  the  rocks,  to  produce  them,  from  N.N.W. 
The  longer  axis  of  boulders,  generally  N.N.W.,  which  is 
towards  head  of  valley.  But  whether  a glacier  occupied  valley, 
or  floating  ice,  not  clear. 

On  Craigiebarns,  gravel  found  at  the  highest  points. 

On  descending  hill  towards  the  river,  observed  on  rocks 
the  following  directions  of  striae,  at  the  height  specified  : — 

At  972  feet  above  river,  striae,  direction  of,  N.  by  W. 

„ 700  ,,  ,,  ,,  N-^-E. 

„ 648  „ „ „ N.  by  E. 

„ 288  „ „ „ N.  by  E. 

The  axis  of  the  valley  at  this  place  N.E. ; therefore  agent 
which  produced  striae,  seems  to  have  been  of  such  a nature 


171 


of  Edinburgh,  Session  1872-73. 

as  to  fill  valley;  this  agent  in  its  upper  part  (where  it  over- 
topped sides  of  the  valley)  moved  obliquely  across  valley,  but 
in  lower  part  (near  the  bottom  of  valley)  it  followed  course 
of  valley. 

Hill  on  east  side  of  Eiver  Tay,  2 miles  S.E.  of  Dunkeld 
about  1200  feet  above  sea.  G-ravel  and  sand  abound  all  over 
it,  to  top. 

On  a knoll  of  clay  slate,  saw  boulder  of  gneiss  about  650 
feet  above  sea.  It  was  on  side  of  knoll  facing  N.N.W. 
Longer  axis  of  boulder  also  N.N.W.,  and  its  sharpest  end  in 
that  direction. 

Saw  another  boulder  of  gneiss  6 x 3 x 2£  feet,  lying  on  well- 
smoothed  slate  rocks.  Longer  axis  N.W.  Height  above  sea 
1000  feet.  Eocks  evidently  smoothed  from  N.W. 

Some  of  rocks  on  this  hill  show  smoothings  from  two  sepa- 
rate directions;  one  from  north  (as  if  down  Tay  Valley),  the 
other  from  west  (as  if  down  Eran  Valley).  The  rocks  of  clay 
slate  are  exceedingly  hard,  so  that  their  smoothing  indicates 
tremendous  friction. 

A very  extensive  flat  stretches  south  from  Dunkeld  about 
260  feet  above  sea.  Eobert  Chambers  notices  it,  and  says  it 
is  280  feet  above  sea.  A terrace  at  about  the  same  height, 
visible  on  hill,  skirting  Tay  on  east  side,  half  a mile  S.E.  of 
Dunkeld.  Probably  the  sea  formed  both. 

Foivlis. — Abercairney  estate.  Granite  boulder  weighing  about  30 
tons;  about  500  feet  above  sea.  Situated  on  north  side  of  a 
valley  running  E.  and  W.  Eocks  in  situ  old  red.  This 
boulder,  and  some  smaller  near  it,  must  have  come  from  north- 
westward. May  have  come  either  by  a glacier  or  by  drift  ice. 
Granite  hills  about  20  miles  to  N.  and  N.W.  (Eev.  Mr 
Hardy,  and  Convener.) 

Glen  Lyon  above  Invervar. — Gneiss  boulder  (called  “ Clach  na 
Salainn,”  from  people  who  brought  trees  out  of  Black  Wood 
of  Eannocli  resting  them  on  the  boulder),  composed  of  six  or 
seven  large  fragments.  The  whole  mass  about  30  yards  round 
and  about  3 yards  high.  May  weigh  about  120  tons.  Eests 
apparently  on  coarse  gritty  sand.  Must  have  been  brought 
to  present  site  by  ice,  and  from  northward.  Height  above  sea 


172 


Proceedings  of  the  Royal  Society 

about  2500  feet.  On  south  side  of  summit  level,  between 
Glen  Lyon  and  Rannoch,  a cliff  called  the  Scaur,  half  a mile 
to  N.W.  of  boulder.  Rochs  in  situ  clay  slate.  If  boulder 
came,  as  seems  probable,  from  W.N.W.,  transporting  agent 
must  have  passed  on  one  side  or  other  of  Scaur.  Configura- 
tion of  hills  here  not  favourable  for  glacier.  Boulder  within 
about  one  mile  of  summit  level,  which  probably  only  200  to 
300  feet  higher  than  it.  Boulder  may  have  been  broken  up 
by  action  of  frost,  or  by  having  fallen  from  transporting 
agent.  First  theory  not  probable,  as  interior  surfaces  of  frag- 
ments appear  as  weathered  as  any  of  the  exterior  sides  of 
boulder. 

About  500  feet  below  boulder,  on  banks  of  river  Yar,  thick 
beds  of  boulder  clay,  sand,  and  gravel,  full  of  rounded  boulders, 
indicating  aqueous  deposits. 

Hill  on  east  side  of  Yar,  facing  west,  much  covered  by 
boulders,  as  if  brought  from  westward  by  some  agent,  whose 
progress  intercepted  by  hill.  One  of  these  boulders,  known 
by  name  of  “ Clach  na  Tarbh,”  or  Stone  of  the  Bull. 

Killiecrankie. — On  east  side  of  Killiecrankie  Glen,  on  Fascally 
Estate,  two  ravines,  parallel  to  one  another,  show  very  high 
cliffs  of  detrital  matter  full  of  large  boulders.  In  the 
southmost  of  the  two  ravines,  the  scaurs  are  about  100  feet  high. 

These  scartrs  in  the  higher  parts  of  the  ravines  show  sections 
of  stratified  sand  and  fine  gravel  to  a large  extent.  Traced 
these  up  to  a height  of  about  1570  feet  above  sea  (by  aneroid). 
Was  told  by  Rev.  Mr  Grant,  of  Tennandry,  that  at  or  near 
the  hill  of  Ben  y Gloe,  there  are  beds  of  sand  and  gravel  at  a still 
higher  level. 

Some  of  the  boulders  in  the  most  northern  of  these  two 
ravines,  which  bad  fallen  out  of  the  drift  deposits,  were  of 
large  size ; one,  on  being  measured,  showed  12x6x5  feet. 

The  following  kinds  noted : — Granite,  grey,  fine  grained ; 
granite,  red,  very  coarse  grained;  gneiss,  quartz,  porphyry, 
limestone,  primitive. 

There  is  a large  angular  limestone  boulder  at  the  Pass  of 
Killiecrankie,  about  \ mile  north  of  Tennandry  mass,  sticking 
in  boulder  clay  about  856  feet  above  sea.  These  limestone 


173 


of  Edinburgh,  Session  1872-73. 

boulders  supposed  to  Lave  come  from  Ben  y Gloe,  or  some  other 
ipountains  to  the  north. 

Killin. — Ascended  hill  west  of,  made  it  1350  feet  above  Loch 
Tay,  and  therefore  about  1650  feet  above  sea.  Sides  of  this 
hill,  at  least  that  facing  eastward,  covered  with  sandy  detritus ; 
but  could  not  discover  whether  stratified  or  not.  This  detritus 
here  reaches  to  foot  of  some  steep  rocky  crags,  at  height 
of  about  1000  feet  above  loch.  But  on  adjoining  hills  des- 
cried through  telescope,  sandy  deposits  at  least  500  feet 
higher. 

At  height  of  about  1090  feet  above  loch,  rocks  of  hill 
exhibited  effects  of  friction  by  action  of  some  body  pressing 
against  them  from  a direction  W.  by  S.,  viz.,  down  the  valley. 
Bocks  facing  east  were  uniformly  rough. 

If  it  was  a glacier  which  effected  this  smoothing,  the  drift 
deposits  on  hill  sides  must  belong  to  a period  subsequent  in 
date,  as  glacier  would  have  scoured  them  all  away. 

On  north  side  of  Loch  Tay,  an  extensive  flat  about  400  feet 
above  loch,  with  appearance  of  a similar  flat  on  opposite  side. 

Schehallion  ascended.— Bock  composing  it,  a very  hard  sandstone. 
The  hill  forms  a long  ridge  running  E.  and  W.,  the  highest 
part  of  which  at  west  end,  viz.,  about  3560  feet  above  sea. 
The  side  of  hill  which  seemed  smoothest,  faces  N.W.  by  W. ; 
but  no  striae,  or  even  any  very  clear  proofs  of  a grinding  action, 
seen.  Gravel,  indicative  of  aqueous  deposition,  seen  up  to  a 
height  of  about  3000  feet. 

Various  small  blocks  of  a fine  grained  grey  granite  scattered 
over  surface  up  to  a height  of  about  3000  feet.  A similar 
rock  said  to  be  in  situ  at  Loch  Sunart  to  N.W. 

On  south  side  of  Schehallion,  at  a height  of  about  2500  feet, 
rocks  apparently  ground  down  and  smoothed,  but  not  above 
this  level. 

In  cliffs  of  the  Burn  courses  on  the  south  side  of  Schehallion, 
boulder  clay  noticed,  up  to  a height  of  1500  feet  above  the  sea. 

All  the  strath  between  Dunkeld  and  Pitlochry  seems  to 
have  been  a lake.  Bottom  of  this  lake  indicated  by  a flat, 
through  which  Bivers  Garry  and  Tummel  have  cut,  to  present 
channels.  This  flat  is  about  50  feet  above  these  river  courses 


174 


Proceedings  of  the  Royal  Society 

at  Ballinluig.  Some  miles  farther  south,  this  flat  is  from  80 
to  100  feet  above  river.  The  barrier  must  have  been  to  north 
of  Dunkeld. 

At  the  lower  end  of  Glen  Tummell,  about  l mile  west  of 
Bonskied  House,  there  is  a large  amount  of  debris,  exceedingly 
like  a terminal  moraine,  with  boulders  lying  upon  it.  But 
there  was  no  opportunity  to  examine  the  locality. 

Struan  Railway  Station. — Two  boulders  of  gneiss  on  southern  slope 
of  hill,  on  left  hank  of  the  river  Grarry,  east  of  station.  Rock 
in  channel  of  Grarry  also  gneiss,  but  not  exactly  same.  One 
boulder  12  x 6 x 7 feet.  Longer  axis  N.E.  and  S.W.  The 
other  boulder  7x8x5  feet.  (John  Robertson,  Old  Blair.) 

Ross. 

Edderton. — Three  large  boulders  of  grey  granite  inspected  by  Con- 
vener, on  hill  south  of  manse,  about  1000  feet  above  sea. 
These  boulders  on  side  of  a hill  sloping  to  N.N  .W. 

No.  1,  about  910  feet  above  sea,  and  about  80  feet  below  a 
col  or  lowest  part  of  the  mountain  range,  called  the  “ Stran- 
ger’s Stone.”  If  land  submerged  2000  feet,  a current  pro- 
bably existed,  which,  if  from  northward,  and  bearing  ice, 
might  carry  boulders,  and  when  ice  touched  hill-side  would 
discharge  them.  Hill-side  very  steep  at  this  place,  so  steep 
as  to  make  it  difficult  to  understand  how  boulder  deposited 
without  rolling  down. 

No.  2 boulder.  About  710  feet  above  sea.  Is  situated  on 
a sort  of  flat  or  terrace.  Its  longer  axis  (about  16  feet)  points 
N.  by  E.  G-eneral  slope  of  hill  here  about  N.E. 

No.  3 boulder.  Translation  of  its  G-aelic  name  is  “ Big  Lair 
ofEox.”  Height  above  sea  about  752  feet.  Situated  on  a well- 
marked  flat  or  terrace,  which  bounded  on  south  by  a steepish 
cliff.  Longer  axis  N.  and  S.  General  slope  of  hill  here  is  to  N. 

The  above  three  boulders  clearly  transported.  Composed  of 
granite — a grey  variety.  Rocks  of  hill  on  which  rest,  old  red 
sandstone. 

Where  have  they  come  from  ? The  surmise  that  they  came 
from  “ Cairn  na  C-unneig”  seems  improbable,  if,  as  alleged,  it 
consists  chiefly  of  red  granite. 


175 


of  Edinburgh,  Session  1872-73. 

The  Rev.  Mr  M‘Ewen,  of  Edderton,  suggested  the  hills  at 
or  near  Rogart,  due  N.  or  N.  by  E.  from  this  spot  about  10  or 
12  miles,  as  the  rocks  there  of  grey  granite. 

These  boulders  not  favourable  to  glacier  theory.  Their 
elevated  positions,  and  the  absence  of  any  hills  to  the  west  or 
north  nearer  than  5 or  6 miles,  are  circumstances  which  render 
that  theory  almost  impossible. 

Rosskeen. — Ardross.  Numerous  large  boulders,  their  longer  axis 
nearly  E.  and  W. 

No.  1.  March  stone  between  Newmore  and  Ardross,  about 
50  feet  in  girth,  and  8 feet  above  ground. 

No.  2.  At  Achnacloich,  at  road-side,  granite  boulder  40  feet 
in  girth. 

No.  3.  About  half  a mile  above  Ardross  Castle,  by  way-side 
in  a dyke,  about  100  feet  in  girth,  and  9 feet  above  ground. 

No.  4.  In  a field  opposite  No.  1,  of  similar  shape  and  size. 

District  between  Tain  and  Tarbet  Ness. — Shows  on  surface  neither 
boulders,  nor  gravel,  nor  sand,  but  traces  of  mud,  and  occa- 
sionally of  boulder  clay,  visible.  At  Fort-George,  boulder 
clay  reported  100  feet  deep  and  more.  Mr  Stables,  of  Cawdor 
Castle,  bored  into  it  for  water  to  that  depth,  and  did  not  get 
through  it. 

If  land  was  submerged  2000  feet,  district  about  Fort-George, 
Moray  Firth,  Dingwall,  Cromarty,  &c.,  would  be  deeper  than 
adjoining  districts,  and  would  be  filled  with  muddy  sediment, 
whilst  shallower  districts  would  be  covered  with  gravelly  and 
sandy  sediment.  The  valley  now  occupied  by  Loch  Ness  and 
Caledonian  Canal  then  a strait  or  kyle,  through  which  tidal 
currents  would  pass ; and  if  icebergs  and  drift  ice  came  from 
westward,  boulders  and  debris  would  be  deposited  on  what  are 
now  the  low  lands  of  Moray,  Banff,  Elgin,  and  Ross,  with  the 
intervening  Firths. 

At  Tarbet  Ness,  Balnabruach  boulder  visited,  in  company 
with  Rev.  George  Campbell ; a coarse  reddish  granite  33 
feet  in  girth,  and  about  7 feet  high.  Longer  axis  E.  and  W. 
This  boulder  and  another,  not  quite  so  large,  near  it,  at  sea 
level.  Supposed  to  have  come  from  “ Carn  na  Cunneig”  hill, 
which  visible  from  boulder,  bearing  W.N.W.  about  30  miles, 


vol.  vnr. 


17(3 


Proceedings  of  the  Poycd  Society 

with  an  area  of  sea  between  Tarbet  Ness  and  coast  near  Tain, 
10  or  12  miles  distant. 

An  old  sea  margin  visible  here,  about  11  feet  above  high- 
water  mark,  with  several  large  boulders  on  it.  When  materials 
of  old  sea-cliff  washed  away  by  sea,  these  heavy  boulders  re- 
mained. Boulders  on  such  terraces,  when  numerous,  are  thus 
indicative  of  aqueous  erosion. 

None  of  the  boulders  at  Tarbet  Ness  are  conglomerates.  If 
transporting  agent  came  from  any  points  between  W.  and 
N.N.W.  in  Ross-shire,  granite  boulders  both  red  and  grey 
could  have  come  to  Tarbet.  The  conglomerate  rocks  are  to 
the  southward  of  the  above  line — viz.,  on  Beauly  River,  higher 
parts  of  Strath  Conon,  Black  Isle,  &c. ; and  lienee  boulders 
taken  from  them,  and  moving  S.E.,  would  not  cross  Tarbet 
Ness,  but  would  be  carried  towards  Nairn,  Elgin,  and  BanfF- 
shires,  where  actually  found. 

One  of  boulders  (near  Fearn  parish  school)  has  attached  to 
it  a G-aelic  legend,  the  translation  of  which  as  follows  : — 

“ Grey  stone  of  the  clay  hollow 
Makes  three  sommersaults 
When  it  hears  the  cock  crow.” 

This  boulder  slopes  downwards  on  its  north  side.  It  is  also 
towards  north,  that  land  most  depressed — viz.,  towards  the  sea. 

Boulder  of  red  granite  2 miles  north  of  Tain , on  road  to 
Edderton,  called  after  Sir  Walter  Scott, — about  70  feet  above 
sea  level, — supposed  to  have  come  from  Cairn  na  Cunneig. 

Shetland. 

Bressay. — A boulder  of  coarse  white  sandstone,  10  x 7 x 4J  feet, 
wholly  unlike  any  other  in  parish.  The  rocks  in  situ  old  red 
sandstone,  and  in  N.W.  of  island  there  is  conglomerate  or 
pudding  stone.  There  was  another  larger  boulder  now  split  up. 

A great  many  smaller  boulders,  viz.,  from  8 to  14  cwt.  each, 
of  the  same  sort  of  rock,  viz.,  a white  coarse  conglomerate  sand- 
stone. These  boulders  are  north  of  Lerwbck,  from  one  to 
two  miles.  (Reporter’s  name  not  attached  to  schedule.) 

Rev.  Dr  Gordon  of  Birnie  (an  experienced  observer)  visited 
Shetland  in  September  1872,  near  Northmaven  (the  extreme 


of  Edinburgh,  Session  1872-73.  177 

north  of  mainland).  When  there,  he  heard  of  large  boulders 
half-way  between  Hillswick  and  Ollabery. 

He  has  procured  for  Committee,  pencil  sketches  of  three 
boulders,  situated  in  extreme  north  of  the  mainland  between 
St  Magnus’  Bay  and  Yell  Sound.  They  are  syenitic,  same 
as  singular  “stacks”  in  that  district  called  the  “Drengs” 
(needles).  One  near  Eela- water,  16x12x6  feet;  another, 
called  “Crupna”  (bent?),  11x8x8  feet;  another,  called 
“ Bonhus,”  situated  between  the  two  others,  is  8 x 10  x 10’8  feet. 

In  two  places,  about  20  miles  asunder,  he  met  with  striae  on 
rocks; — one  a mile  north  of  the  Fishing  Huts  of  Stennis,  on 
N.W.  shore  of  St  Magnus’  Bay,  on  coarse  conglomerate  rock ; 
the  other  at  centre  and  bottom  of  a valley,  about  half  a mile 
wide,  and  bounded  by  hills  200  or  300  feet  high,  near  Maris 
Grind,  in  front  of  farm  house  of  Islebury,  on  quartzose  gneiss. 
At  both  places  striae  were  E.  and  W.  (true).  At  Islebury, 
valley  runs  N.  and  S.,  so  that  the  agent  which  striated  rocks 
there,  crossed  valley  at  right  angles. 

Foula. — Five  boulders  from  3 to  5 cwt.  each,  and  two  boulders 
about  2 tons  each. 

The  five  are  at  Hametown  in  south  end  of  island,  and  lie  on 
the  north  side  of  what  was  a strait,  when  land  submerged,  but 
now  a valley  between  the  Noup  Hill  and  Hill  of  Liorafield. 
“ Of  these  five,  two  are  granite  from  Culswick,  and  three  gneiss 
from  (I  would  say)  the  Delting  Hills.  The  compass  bearings 
of  these  places  from  the  boulders  are  (I  would  say)  N.E. 
These  five  boulders  are  as  smooth  as  if  taken  off  a beach  a 
short  time  ago.” 

The  two  boulders  of  2 tons  each  are  in  middle  of  island, 
and  of  irregular  shape. 

From  middle  of  island  to  south  end,  and  as  high  up  as  700 
feet,  granite  and  gneiss  drift ; but  had  not  time  to  examine  the 
north  end  of  the  island. 

“ The  drift  must  have  come  from  either  Culswick  16  miles, 
Norshaven  30  miles,  or  Delting  30  miles,  borne  along  by  tides 
similar  to  what  we  have  now,  and  which  set  in  the  direction 
of  Foula  from  the  mainland. 

“ I shall  send  by  and  by  a lengthened  report,  on  drift  in 


178 


Proceedings  of  the  Royal  Society 

Walls  and  Sandsting.”  (Rev.  James  Russell,  Parliamentary 
Schoolmaster,  Happyhousel,  Walls.) 

Statistical  Account  of  Foula  states  that  “ Poula  is  com- 
posed of  old  red  sandstone,  with  subordinate  deposits  of  granite, 
gneiss,  and  mica  slate.  (Yol.  xv.  p.  20.) 

Lunna. — Stones  of  Stoffus.  Mr  Irvine,  schoolmaster,  called  on 
Professor  Nicol,  Aberdeen,  and  showed  to  him  specimen 
broken  from  stones.  It  is  ordinary  grey  gneiss,  quite  like 
common  rock  of  the  islands.  He  alluded  to  doubt  whether 
‘‘stones”  transported.  Professor  Nicol  inferred  from  Mr 
Irvine’s  account  they  had  been  transported.  There  is  no 
higher  ground  near  them,  and  they  form  a landmark  from 
the  sea.  They  are  from  20  to  22  feet  high,  and  90  feet 
round.  Height  above  sea  from  100  to  120  feet. 

Professor  Nicol  adds  : — “ When  in  Shetland,  I saw  almost 
no  indications  of  glacier  action,  except  near  the  Grind  of  the 
Navir  in  the  extreme  west,  where  the  rocks  are  distinctly 
striated  and  polished.” 


Explanation  of  Lithographic  Sketches  of  Boulders. 

I.  “ Tom  Riach .”  (See  page  158.) 

II.  “ Souter’s  Stone."  (See  page  149.) 

III.  “ Samson's  Tutting  Stone."  (See  page  168.)  This  boulder  is  near  top 
of  hill,  as  shown  on  Sketch.  The  other  and  smaller  boulder  below 
it,  on  hill  side,  is  also  shown  on  Sketch.  The  shape  of  each  is 
indicated  on  a larger  scale  in  the  Sketch. 

IY.  “ Flitchity  Valley."  Boulders  near  to  top  of  hill,  as  shown  on  Sketch. 
The  shape  of  one,  and  its  precarious  position,  shown  to  right  of 
Sketch  on  a larger  scale.  (See  page  160.) 

Y.  “ Clach  na  Cailleach"  Boulder,  or  “ Old  Wife’s  Stone.”  (See  page  166.) 

VI.  Boulder  on  Treshlik  Hill.  (See  page  161.)  Sketch  shows  position 
of  boulder  near  top  of  hill.  There  is  also  an  enlarged  view,  to 
show  shape  of  boulder,  and  its  precarious  site. 

VII.  Boulder  on  Dun  Ii,  Iona.  (See  page  156.) 

VIII.  Auldearn.  This  Sketch  in  the  dark  shaded  part  shows  general  shape 
of  the  conglomerate  boulders  mentioned  on  page  166.  The  faintly 
shaded  part  is  intended  to  show  what  the  original  shape  of  boulder 
may  have  been.  (See  page  140.) 

IX.  “ Geadh  ” or  “ Goose  ” Boulder,  Iona.  (Page  155.) 

X.  Boulder  of  mica  slate,  on  top  of  a rocky  knoll,  at  Craigie  Barns, 
North  of  Dunkeld.  Length,  7 feet;  width,  5|  feet;  depth,  4 feet. 
The  smooth  and  sharp  end  points  N.  by  W.  The  smooth  surface 


Px  o c . Hoy.  S o c . E din* 


VI. 


Vol.  VIII.  (Sess,  1872-73.) 


M'  TsAms  & Ermine,  lifiZ?  Edit 


179 


of  Edinburgh,  Session  1872-73. 

of  rock  on  which  boulder  rests  slopes  down  also  N.  by  W,  This 
rock  also  mica  slate,  hut  of  a variety  different  from  boulder. 
Height  of  boulder  above  river  Tay  855  feet.  (See  page  169.) 

XI.  Boulder  near  S.E.  end  of  Iona,  standing  upright.  (See  page  156.) 

XII.  Borgue  boulder.  (See  page  165.) 

XIII.  Two  rounded  boulders  lying  on  glaciated  rock.  (See  page  159.) 

4.  Oil  the  Physiological  Action  of  Light.  No.  TIL  By 
Janies  Dewar,  Esq.,  and  John  G.  M'Kendrick,  M.D. 

Since  the  date  of  our  last  communication,  we  have  continued  our 
investigations,  with  the  following  results  : — 

1.  The  light  from  a beam  of  uncondensed  moonlight,  though  of 
weak  intensity,  and  almost  entirely  free  from  heat  rays,  is  still 
sufficient  to  alter  the  electro-motive  power  of  the  nerve  and  retina. 

2.  We  have  examined  the  phenomenon  in  the  eyes  of  the  follow- 

ing animals  : — (1.)  The  common  newt  ( Triton  aquations ).  (2.)  The 
gold-fish  ( Cyprinus  auratus ).  (3.)  The  rockling  ( Motella  vulgaris). 

(4.)  The  stickleback  ( Gasterosteus  trachurus ).  (5.)  The  common 

edible  crab  {Cancer  pagurus).  (6.)  The  swimming  crab  ( Portunus 
puher).  (7.)  The  spider  crab  ( Hyas  coarctatus).  (8.)  The  hermit  crab 
{Pagurus  Bernliardus ),  and  f9.)  The  lobster  {Homarus  vulgaris). 

The  general  results  with  the  eyes  of  these  various  animals  were 
similar  to  those  we  have  previously  described.  The  eye  of  the  gold- 
fish and  rockling,  both  sluggish  fishes,  were  found  to  resemble  each 
other,  inasmuch  as  the  variations  in  the  electro-motive  force  were 
slow,  and  in  this  respect  they  presented  a marked  contrast  to  those 
of  the  active  and  alert  stickleback,  the  eye  of  which  was  very  sen- 
sitive to  light. 

The  experiments  on  the  eyes  of  Crustacea  are  of  importance, 
because  they  show  that  the  action  of  light  on  the  compound  eye  is 
the  same  as  on  the  simple  eye, — namely,  that  it  alters  the  amount 
of  the  electro-motive  force  of  the  sensitive  surface.  The  eye  of  the 
lobster  was  found  to  give  a deflection  of  about  600  galvano-metrical 
degrees  (the  scale  being  placed  at  a distance  of  about  26  inches). 
Light  produced  a variation  in  this  deflection  of  about  60  degrees — 
that  is,  about  10  per  cent.,  the  largest  amount  of  variation  we  have 
yet  observed  in  any  eye.  It  was  also  demonstrated  that  the  effect 
of  light  diminished  in  intensity  by  distance  was  exactly  what  was 
observed  in  the  case  of  the  simple  eye.  For  example,  at  the  dis- 


180  P t oceedings  of  the  Poycd  Society 

tance  of  one  foot,  a variation  to  the  extent  of  about  100  degrees 
was  observed.  At  a distance  of  10  feet,  with  ,-J-g-th  part  of  the 
amount  of  light,  the  effect  was  not  1 degree,  but  20  degrees,  or  £th 
of  the  total  amount  observed  at  1 foot. 

3.  The  action  of  light  on  the  electro-motive  force  of  the  liv- 
ing eye  in  cats  and  birds  (pigeon  and  owl)  has  been  observed. 
In  our  earlier  experiments  we  found  great  difficulty  in  observing 
sensitiveness  to  light  in  the  eyes  of  mammals  and  birds  when  these 
were  removed  with  the  utmost  despatch  from  the  orbit  of  the  animal 
immediately  after  death.  This  was  evidently  owing  to  the  fact 
that  the  sensibility  of  the  nervous  system  in  these  animals  disap- 
pears quickly  after  the  withdrawal  of  healthy  blood.  It  therefore 
became  necessary  to  perform  the  experiment  on  the  living  animal. 
This  was  done  by  first  putting  the  cat  or  bird  under  the  influence 
of  chloroform,  then  fixing  it  by  a proper  apparatus,  so  that  the 
head  was  perfectly  immovable,  and  lastly  removing  the  outer  wall 
of  the  orbit  with  as  little  disturbance  to  the  ciliary  vessels  as 
possible.  The  optic  nerve  was  now  cut,  the  transverse  section 
directed  upwards,  and  the  clay  points  of  the  electrodes  were  now 
adjusted,  one  to  the  transverse  section  of  the  nerve,  and  the  other 
to  the  cornea.  With  these  arrangements  we  at  once  found  a strong 
current  extremely  sensitive  to  light. 

4.  The  effect  was  traced  into  the  optic  lobes  of  a living  pigeon 
under  chloroform.  The  following  were  the  results  of  this  observation: 
(a.)  when  one  pole  was  applied  to  the  left  optic  lobe,  and  the  other 
to  the  cornea  of  the  right  eye,  a deflection  was  obtained,  which  was 
sensitive  to  light;  (b.)  when  the  pole  was  removed  from  the  right  eye, 
and  applied  to  the  cornea  of  the  left,  a smaller  deflection  was  ob- 
tained, also  sensitive  to  light;  and  (c.)  when  light  was  allowed  to 
impinge  on  both  eyes,  while  the  one  pole  was  in  contact  with  either 
eye,  and  the  other  with  the  left  optic  lobe,  the  result  was  nearly 
double  that  produced  by  the  impact  of  light  on  one  eye  alone,  either 
right  or  left.  These  effects  may  be  explained  by  the  decussation 
of  the  optic  nerves  in  the  optic  commissure. 

5.  The  eye  of  a snake  * was  examined,  and  in  its  action  resembled 
that  of  the  frog. 

* Kindly  sent  us  by  Mr  Bartlett  of  the  Zoological  Gardens,  Kegent’s  Park. 
We  have  also  to  acknowledge  the  kindness  of  Mr  Lloyd,  manager  of  the  Crys- 


181 


of  Edinburgh,  Session  1872-73. 

6.  We  are  therefore  now  in  a position  to  state  that  the  law  of 
the  variation  in  the  electro-motive  force  of  the  retina  and  optic 
nerve  holds  good  in  the  following  groups  of  the  animal  kingdom  : 
mammalia,  aves,  reptilia,  amphibia,  pisces,  and  Crustacea. 

7.  Many  experiments  have  been  made  which  prove  that  the 
psycho-physical  law  of  Fechner,  alluded  to  in  previous  communi- 
cations, is  not  dependent  only  on  perception  in  the  brain,  but  in 
part  on  the  structure  of  the  eye  itself.  The  effects  which  occur  on, 
during,  and  after  the  action  of  light  on  the  retina,  also  take  place 
after  the  eye  has  been  removed  from  all  connection  with  the  brain. 
Thus  the  law  of  Fechner  is  not,  as  has  been  hitherto  supposed,  a 
function  of  the  brain  alone,  but  is  really  a function  of  the  terminal 
organ,  the  retina. 

8.  We  have  also  employed  a new  method  of  registering  galvano- 
metrical  variations,  which  may  be  of  service  in  many  physical  and 
physiological  researches.  This  consists  in  placing  at  the  proper 
distance  from  the  galvanometer,  instead  of  the  ordinary  graduated 
scale,  the  surface  of  a cylinder  covered  with  paper,  and  moving  on  a 
horizontal  axis  by  clock-work.  The  spot  of  light  reflected  from  the 
galvanometer  mirror  is  rendered  more  precise  by  having  the  shade 
of  the  galvanometer  lamp  blackened  over  the  entire  surface,  with 
the  exception  of  a spot  about  three  millimeters  in  breadth,  in  the 
centre  of  which  a line  or. cross  is  made  of  soot.  The  image  of  this 
line  or  cross  is,  of  course,  reflected  by  the  mirror  upon  the  cylinder. 
When  the  cylinder  is  set  in  motion  by  the  clockwork,  the  spot  of 
light  may  be  accurately  followed  by  the  hand  of  the  observer,  after 
a little  practice,  with  a fine  brush  moistened  with  ink.  The  cylin- 
der we  employed  performed  a complete  revolution  in  80  seconds. 
This  time  was  divided  into  4 equal  parts,  each  representing  20 
seconds,  by  4 lines  drawn  transversely  at  equal  intervals  across  the 
paper  on  the  cylinder.  The  first  space,  between  lines  1 and  2,  re- 
presented 20  seconds,  in  which  the  eye  was  in  the  dark,  and  in 
which  the  electro-motive  force  is  represented  by  a straight  line; 
the  second  space,  between  lines  2 and  3,  represented  20  seconds, 
during  which  the  effect  of  the  impact  of  light  took  place,  and  in 
which  the  variation  of  the  electro-motive  force  is  indicated  either  by 

tal  Palace  Aquarium,  who  supplied  us  with  three  specimens  of  Eledone  (a 
cuttle-fish,  to  represent  mollusea),  but  none  arrived  alive. 


182 


Proceedings  of  the  Royal  Society 

a curve  to  tlie  right  or  to  the  left;  the  third  space,  between  lines 
3 and  4,  represented  20  seconds  of  continued  action  of  light,  during 
which  the  electro-motive  force  gradually  rises ; and,  lastly,  the  fourth 
space,  between  lines  4 and  1 (the  point  of  starting)  represents  20 
seconds,  during  which  the  electro-motive  force  at  first  rises  on  the 
withdrawal  of  light  and  afterwards  sinks  rapidly. 

5.  On  the  Thermo-electric  Properties  of  Pure  Nickel. 

By  Professor  Tait. 

By  the  kindness  of  M.  de  Boisbaudran  I have  been  enabled  to 
experiment  upon  a specimen  of  nickel,  very  nearly  pure.  Its 
thermo-electric  relations  are  exceedingly  interesting,  and  are  easily 
observed  by  employing  palladium  as  the  second  metal  in  the 
circuit.  The  nickel  line  in  the  thermo-electric  diagram  presents 
nearly  the  same  appearance  as  that  of  iron,  but  its  peculiarities 
occur  at  much  lower  temperatures. 

Speaking  generally,  at  low  temperatures  it  is  nearly  parallel  to 
the  palladium  line,  but  below  it ; the  specific  heat  of  electricity 
being  negative.  The  specific  heat  changes  sign  about  230°  C.,  and 
thereafter  the  nickel  line  intersects  the  palladium.  Shortly  after 
this  intersection  (at  about  340°  C.)  the  specific  heat  again  becomes 
negative,  and  of  nearly  its  first  amount ; so  that  the  lines  are 
again  parallel,  but  nickel  is  now  above  palladium.  These  curious 
facts  are  probably  connected  with  the  magnetic  properties  of  iron 
and  nickel,  possibly  also  with  the  chemical  distinction  of  ferricum 
and  ferrosum.  But  exact  determinations  (which  I hope  soon  to 
make)  are  required  before  such  speculations  can  be  successfully 
carried  out. 

6.  Notice  of  the  Bavages  of  the  Limnoria  terebrans  on 
Greenheart  Timber.  By  David  Stevenson,  Civil 
Engineer. 

In  1862  I communicated  to  the  Society  a notice  of  the  ravages 
of  the  Limnoria  terebrans  on  timber  employed  in  engineering 
structures  exposed  to  the  action  of  the  sea.  In  that  communica- 
tion I stated  that  African,  English,  and  American  oaks,  maho- 
gany, teak,  beech,  ash,  elm,  and  the  different  varieties  of  pine,  were 
found  sooner  or  later  to  become  a prey  to  the  Limnoria.  The 


of  Edinburgh,  Session  1872-73. 


183 


special  object  of  the  notice  was,  however,  to  show  that  timber  sub- 
jected to  preservative  processes  did  not  long  resist  the  attacks  of 
the  Limnoria,  and,  more  especially,  that  thoroughly  creosoted 
timber  is  readily  perforated  by  it,  and  subsequent  experience  has 
fully  shown  that  these  statements  were  correct. 

In  that  notice  I also  said  that  the  timber  known  as  G-reenheart 
has  the  valuable  property  of  resisting  the  attack  of  the  Limnoria, 
a statement  which  occurs  in  many  works  on  Engineering  and 
Botany,  and  has  hitherto  been  universally  believed  to  be  correct. 
Recent  experience,  however,  has  satisfied  me  that  this  conclusion, 
if  not  absolutely  incorrect,  requires  considerable  qualification,  and 
the  object  of  the  present  notice  is  to  communicate  some  facts 
which  have  been  ascertained  since  the  date  of  my  former  notice  to 
the  Society. 

The  Bebeeru  or  G-reenheart  tree,  as  is  well  known,  is  a native  of 
British  Guiana  belonging  to  the  order  Lauraeem,  and  its  bark  pro- 
duces sulphate  of  bebeerine,  which  is  used  medicinally  as  a tonic. 

The  colour  of  the  timber,  as  imported  and  used  in  engineering 
works,  is  generally  light  olive-green  (hence  its  English  name),  with 
occasional  darker  shades  approaching  to  brown.  It  can  readily  be 
got  in  logs  of  from  40  to  50  feet  in  length,  and  10  or  15  inches 
square.  The  timber,  as  sent  to  this  country,  has  very  rarely  any 
sap  wood;  the  logs  are  seldom  straight  grown;  and  the  wood,  which 
is  hard  and  close  grained,  is  extremely  difficult  to  dress  owing  to 
its  tendency  to  split  when  cut  up  into  deals  or  slabs.  Its  specific 
gravity  is  high ; its  weight  being  about  50  lbs.  per  cubic  foot, 
while  that  of  the  best  Memel  does  not  exceed  30  lbs. 

Independently  of  its  supposed  exemption  from  the  ravages  of 
the  Limnoria,  the  fact  that  the  breaking  strength  of  greenheart,  as 
compared  with  Memel,  is  as  1 to  T51,  renders  it  very  suitable  for 
many  engineering  works,  and  particularly  for  staging  in  situations 
of  great  exposure.  It  was,  I believe,  for  the  first  time  employed  for 
staging  at  Wick  Bay,  where  logs  of  pine  could  not  withstand  the 
waves ; and  it  was  on  removing  the  temporary  greenheart  staging, 
that  had  been  in  use  from  two  to  four  years  at  Wick,  that  I first 
became  fully  aware  that  the  Limnoria  would  perforate  that  timber. 
Some  of  these  logs  were  found  to  have  been  attacked  by  the  Lim- 
noria throughout  the  whole  surface,  extending  from  about  low- 

2 A 


VOL.  VIII. 


184 


Proceedings  of  the  Royal  Society 


water  mark  to  the  bottom.  This  discovery  caused  no  little  surprise 
and  regret,  as  engineers  had  always  looked  on  greenheart  as  proof 
against  destruction  by  marine  insects ; but  being  the  first,  and  it 
was  hoped  perhaps  an  isolated  instance,  I did  not  consider  it  neces- 
sary at  once  to  record  the  fact. 

I have  since,  however,  received  a specimen  of  timber  taken 
from  one  of  the  piles  in  the  steamboat  pier  at  Salen,  in  the  Sound 
of  Mull,  which  was  erected  four  years  ago,  the  main  piles  being 
made  of  sound  greenheart,  and  I find  that  in  this  locality  also  the 
Limnoria  has  commenced  to  perforate  the  timber. 

In  both  of  these  instances  sufficient  time  has  not  elapsed  to 
allow  the  wasting  to  make  great  progress,  but  in  both  cases  the 
perforations  have  penetrated  into  what  is  unquestionably  sound 
fresh  timber ; and,  therefore,  this  result  conflicts  with  certain  other 
experiments,  such  as  those  made  at  the  Bell  Bock,  where  the 
greenheart  remained  nearly  sound  after  nineteen  years’  exposure. 

The  joint  paper  of  Dr  Maclagan  and  Dr  G-amgee  on  greenheart 
in  the  “ Society’s  Transactions  ” states  that  by  subjecting  green- 
heart wood  to  a process  identical  with  that  used  for  the  extraction 
of  sulphate  of  bebeerine  from  the  bark , a product  is  obtained  pos- 
sessed of  an  intensely  bitter  taste,  and  not  differing  perceptibly 
from  the  sulphate  of  bebeerine.  This  may  account  for  wounds  pro- 
duced by  a splinter  of  greenheart  not  readily  healing. 

I am  also  disposed  to  think  that  it  is  to  the  existence  of  this  alkaloid 
in  the  timber,  and  not  to  its  hardness,  that  its  undoubted  power  of 
withstanding  in  certain  cases  and  for  a certain  time  the  action  of 
the  Limnoria  is  due,  and  it  would  be  interesting  to  discover  whether 
the  wasted  portions  of  greenheart  at  Wick  and  Salen  produced 
bebeerine  in  a smaller  degree  as  compared  with  sound  timber.  It 
is  possible,  as  suggested  by  Sir  Kobert  Christison,  that  long  pro- 
tracted immersion  in  sea-water  may  so  counteract  the  preservative 
principle  due  to  the  bebeerine  in  the  timber  as  to  render  it  open 
to  attack.  It  is  also  possible  that  the  greenheart  now  imported  in 
such  large  quantities  has  degenerated  like  the  “ Crown  Memel,” 
which,  it  is  well  known,  cannot  be  procured  of  the  same  high 
quality  as  formerly.  Change  of  soil,  moreover,  affects  the  growth 
of  trees,  and  is  perhaps  sufficient  to  account  for  the  great  variations 
in  the  quality  of  foreign  grown  timber. 


185 


of  Edinburgh,  Session  1872-73. 

In  any  view  of  the  case,  however,  it  seems  necessary,  in  connec- 
tion with  my  former  notice,  to  make  known  the  fact  that  green- 
heart  as  now  imported , and  generally  used  in  marine  works,  is  not, 
as  was  hitherto  supposed  to  be  the  case,  wholly  proof  against  the 
ravages  of  the  Limnoria  terebrans , suggesting,  perhaps,  increased 
care  in  its  selection,  although  I believe  it  must  still  be  regarded  as 
the  most  durable  timber  that  can  be  employed  in  such  works.  It 
is  almost  unnecessary  to  add  that  these  observations  refer  to  locali- 
ties where  the  timber  is  exposed  to  what  may  be  termed  sea-water , 
and  not  to  situations  where,  from  admixture  of  fresh  water  or  other 
causes,  the  ravages  of  the  Limnoria  are  greatly  mitigated  or  alto- 
gether unknown. 

The  following  Gentleman  was  elected  a Fellow  of  the 
Society 


Major  Welsh,  Bengal  Artillery. 


186 


Proceedings  of  the  Royal  Society 


Donations  to  the  Society  during  Session  1872-73  : — 

I.  Authors. 

Abbot  (Francis),  F.R.A.S.  Results  of  Five  Years’  Meteorological 
Observations  for  Hobart  Town..  Tasmania,  1872.  4to. — From 
the  Author. 

Anderson  (John),  M.D.  Notes  on  Rhinoceros  sumatrensis,  Cuvier. 
8vo. — From  the  Author. 

On  Manouria  and  Scapia,  two  Genera  of  Land  Tortoises. 

8 vo. — From  the  Author. 

On  some  Persian,  Himalayan,  and  other  Reptiles.  8vo. — 

From  the  Author. 

Further  Remarks  on  the  External  Characters  and  Anatomy 

of  Macacus  brunneus.  8vo. — From  the  Author. 

Anderson  (John),  C.E.,  LL.D.  The  Strength  of  Materials  and 
Structures.  12mo. — From  the  Author. 

Andros  (C.  G.).  Den  Danske  Gradmaaling,  Andet  Bind.  Copen- 
hagen, 1872.  4to. — From  the  Author. 

Ball  (R.  Stowell),  LL.D.  The  Theory  of  Screws.  Dublin,  1872. 
4 to. — From  the  Author. 

Account  of  Experiments  upon  the  Retardation  experienced 

by  Yortex  Rings  of  Air  when  moving  through  Air.  Dublin, 
1872.  4to. — From  the  Author. 

Bert  (Dr  P.).  Recherches  sur  les  Mouvements  de  la  Sensitive 
( Mimosa  pudica,  Linn.).  Paris,  1870.  8vo. — From  the 

Author. 

Notes  d’Anatomie  et  de  Physiologie.  Paris,  1870.  8vo. 

— From  the  Author. 

Influence  des  diverses  couleurs  sur  la  Vegetation.  1871. 

4to. — From  the  Author. 

Recherches  Experimentales  sur  l’influence  que  les  change- 

ments  dans  la  pression  Barometrique  exercent  sur  les  Pheno- 
menes  de  la  vie.  1872.  4to. — From  the  Author. 

— — — Sur  les  Phenomenes  et  les  causes  de  la  mort  des  animaus 
d’eau  douce  que  l’on  plonge  dans  l’eau  de  mer.  4to. — From 
the  Author . 


187 


of  Edinburgh,  Session  1872-73. 

Beverley  (H.).  Report  on  the  Census  of  Bengal.  Calcutta,  1872. 
Fol. — From  the  Author. 

Bloys  (Yan.)  Parthenopeus.  Brussels,  1871.  8vo. — From  the 
Author. 

Broun  (J.  A.),  F.R.S.  On  the  Lunar  Diurnal  Variation  of 
Magnetic  Declination  at  Trevandrum,  near  the  Magnetic 
Equator.  Edinburgh,  1872.  4to. — From  the  Author. 

Carlson  (E.  E.).  Minnesteckning  ofer  Erik  Grustaf  G-eijer.  Stock- 
holm, 1870.  8vo. — From  the  Author. 

Day  (St  John  Vincent),  C.E.  On  some  Evidences  as  to  the  very 
Early  Use  of  Iron.  Edinburgh.  8vo. — From  the  Author. 

Ellis  (George  E.).  Memoir  of  Sir  Benjamin  Thomson,  Count 
Rumford  ; with  Notice  of  his  Daughter.  Philadelphia,  1872. 
8vo. — From  the  American  Academy  of  Arts  and  Sciences , 
Boston. 

Friis  (J.  A.).  Lappish  Mythologi  Eventyr  og  Folkesagn.  Chris- 
tiania, 1871.  8vo. — From  the  Author. 

Handyside  (P.  David),  M.D.  Dissertatio  Physiologica  Inaugu- 
ralis  de  Vasis  Absorbentibus.  Edinburgh,  1831.  8vo. — From 
the  Author. 

On  a Remarkable  Diminution  of  the  Medulla  Oblongata 

and  Adjacent  Portion  of  the  Spinal  Marrow.  8vo. — From  the 
Author. 

On  a Remarkable  Diminution  of  the  Medulla  Oblongata. 

8vo. — From  the  Author. 

Cases  of  Quadruple  Mammae.  8vo. — From  the  Author. 

* — On  Hypospadia.  Edinburgh,  1873.  8vo. — From  the 

Author. 

llarkness  (Wm.)  and  Hall  (Asaph).  Reports  on  Observations  of 
Encke’s  Comet  during  its  Return  in  1872.  Washington,  1872. 
4to. — From  the  Author. 

Henslow  (Rev.  George).  Phyllotaxis,  or  the  Arrangement  of 
Leaves  in  accordance  with  Mathematical  Laws.  8vo. — From 
the  Author. 

Hill  (John),  M.D.  A General  Natural  History,  or  New  and 
Accurate  Descriptions  of  the  Animals,  Vegetables,  and  Mine- 
rals of  the  Different  Parts  of  the  World.  Vols.  I .-III. 
1751.  Fol. — Presented  by  Fbenezer  Murray , Esq. 


188 


Proceedings  of  the  Royal  Society 

Hutton  (Captain).  Lecture  on  the  Formation  of  Mountains.  1872. 
8vo. — From  the  Author. 

Kauffer  (P.).  Steam  in  the  Engine;  its  Heat  and  its  Work. 
1873.  8 vo. — From  the  Author. 

Lawson’s  Pinetum  Britannicum,  Part  XXXIU.  Edinburgh.  Fol. 

■ — From  Charles  Lawson , Esq. 

Liais  (Emmanul).  Climats  G-eologie,  Faune  et  G-eographie 
Botanique  de  Bresil.  Paris,  1872.  Large  8vo. — Presented 
by  the  Brazilian  Government. 

Lieblin  (J.).  Recherches  sur  la  Chronologie  Egyptienne  d’apres 
les  Listes  G-enealogiques.  Christiania,  1873.  8vo. — From  the 
Author. 

Maccormac  (Henry),  M.D.  Consumption  and  the  Breath  Re- 
breathed; a Word  with  Reviewers.  1872.  8vo. — From  the 
Author. 

M‘Cosh  (John),  M.D.  Nuova  Italia;  or  Tours  and  Re-tours  through 
France,  Switzerland,  Italy,  and  Sicily.  London,  1872.  8vo. 
— From  the  Author. 

Mailly  (Ed.).  Tableau  de  l’Astronomie  dans  ^Hemisphere  Austral 
et  dans  l’lnde.  8vo. — From  the  Author. 

Rapport  Seculaire  de  l’Astronomie  dans  l’Academie  Royal 

de  Belgique.  1772-1872.  8vo. — From  the  Author. 

Marsh  (Professor  0.  C.).  On  the  G-igantic  Fossil  Mammals  of  the 
Order  Dinocerata.  8vo. — From  the  Author. 

— On  the  Structure  of  the  Skull  and  Limbs  in  Mosasauroid 

Reptiles.  4vo. — From  the  Author. 

Maxwell  (Prof.  James  Clerk).  A "Treatise  on  Electricity  and 
Magnetism.  Yols.  I.,  II.  8vo. — From  the  Author. 

Meikle  (James).  Observations  on  the  Rate  of  Mortality  of  Assured 
Lives  from  1815  to  1863.  Edinburgh,  1872.  Fol. — From  the 
Author. 

Montgomerie  (Major  T.  G-.),  R.E.,  F.R.S.  General  Report  of  the 
Operations  of  the  great  Trigonometrical  Survey  of  India 
during  1871-72.  Derha  Dun.,  1872.  Fol. — From  the  Author. 

Muir  (J.),  D.C.L.,  LL.D.  Original  Sanskrit  Texts  on  the  Origin  and 
History  of  the  People  of  India.  Yol.IV.  8vo. — From  the  Author. 

Munch  (P.  A.).  Nordens  Aldste  Historie.  Christiania.  8vo. — 
From  the  Author. 


189 


of  Edinburgh , Session  1872-73. 

Munster  (E.  B.).  Forekomster  af  Rise  i Yisse  Skifere  i Norge. 

Christiania,  1873.  4to. — From  the  Author. 

Naumann  (Alexander).  Jahresbericht  iiber  die  Eortschritte  der 
Chemie,  &c.,  fiir  1870.  1871.  8vo. — From  the  Editor. 
Newberry  (Dr  J.  S.).  The  U.S.  Sanitary  Commission  in  the 
Valley  of  the  Mississippi  during  the  War  of  tlie  Rebellion 
1861-G6.  Cleveland,  1871.  8vo. — From  the  Author. 
Nicholson  (Henry  Alleyne),  M.D.  A Manual  of  Palaeontology  for 
the  use  of  Students,  with  a General  Introduction  on  the 
Principles  of  Palaeontology.  8vo. — From  the  Author. 

Orsted  (A.  S.).  Bidrag  Kundskab  om  Egefamilien.  Copenhagen. 
4to. — From  the  Author. 

Ordnance  Survey  of  the  Peninsula  of  Sinai.  Part  1,  Account  of 
the  Survey,  with  Illustrations.  Part  2,  Maps,  Plans,  and 
Sections.  Photographs,  Yol.  I.  Part  3;  Yol.  II.  Part  3; 
Yol.  III.  Part  3.  1869.  Under  the  direction  of  Colonel  Sir 

Henry  James.  Fol. — From  the  Secretary  of  State  for 
War. 

Packard  (A.  S.,  jun.),  M.D.  Record  of  American  Entomology  for 
the  year  1870.  Salem.  8vo. — From  the  Author. 

Plantamour  (E.).  Nivellement  de  Precision  de  la  Suisse  par  la 
Commission  Geodesique  Eederale  sous  la  Direction  de  A. 
Hirsch  et  E.  Plantamour.  4th  Liv.  4to. — From  the 

Author. 

Determination  Telegraphique  de  la  Difference  de  Longi- 
tude entre  des  Stations  Suisses  to  Geneve,  1872. — From  the 
Author. 

Observations  faites  dans  les  Stations  Astronomiques  Suisses. 

4to. — From  the  Author. 

Playfair  (Lyon),  LL.D.  Universities  in  their  Relation  to  Profes- 
sional Education.  1873.  8vo. — From  the  Author. 

Praet  (Yan  Jan).  Speghel  du  Wijsheit  af  Leeringhe  der  Zalichede. 

Brussels,  1872.  8vo. — From  the  Author. 

Quetelet  (Ad.).  Tables  de  Mortality  et  leur  Developpement.  1872. 
4to. — From  the  Author. 

Observations  des  Phenomenes  Periodiques  pendant  l’annee. 

1870.  4to. — From  the  Author. 

Unite  de  l’Espece  Humaine.  8vo. — From  the  Author. 


190 


Proceedings  of  the  Royal  Society 

Rickard  (Major  F.  Ignacio).  The  Mineral  and  other  Resources 
of  the  Argentine  Republic  (La  Plata)  in  1869.  8vo. — From 
the  Author. 

Robertson  (G-eorge).  Report  to  the  Government  of  India  on  Indian 
Harbours.  First  and  Second  Series.  Edinburgh,  1873.  Fol. 
— From  the  Author. 

Ross  (Alexander  Milton),  M.A.,  M.D.  The  Birds  of  Canada,  with 
Descriptions  of  their  Habits,  Food,  Nests,  Eggs,  Times  of 
Arrival  and  Departure.  8vo. — From  the  Author. 

Ross  (Captain  W.A.).  Pyrology  of  Fire  Analysis.  8vo. — From 
the  Author. 

Sars  (G.  0.).  Carcinologiske  Bidrag  til  Norges  Fauna.  Chris- 
tiania, 1870.  4to. — From  the  Author. 

Carcinologiske  Bidrag  til  Norges  Fauna.  I.  Monograph! 

Christiania,  1872.  4to. — From  the  Author. 

On  some  Remarkable  Forms  of  Animal  Life.  Christiania, 

1872.  4to. — From  the  Author. 

Schubeler  (Dr  F.  C.).  Die  Pflanzenwelt  Norwegens  ein  Bejtrag 
zur  Natur-  und  Culturgeschichte  Nord-Europas.  Christiania, 

1873.  4to. — From  the  Author. 

Silliman  (B.).  Mineralogical  Notes  on  Utah,  California,  and 
Nevada.  1873.  8vo. — From  the  Author. 

Smith  (John  Alexander),  M.D.  Notice  of  a Discovery  of  Remains 
of  the  Elk  ( Gervus  Alcest  Linn.,  Alces  Malchis , Gray)  in 
Berwickshire,  with  Notes  of  its  Occurrence  in  the  British 
Islands,  more  particularly  in  Scotland.  Edinburgh.  8vo. 
— From  the  Author. 

Smyth  (R.  Brough),  C.E.  Sketch  of  a New  Geological  Map  of 
Yictoria. — From  the  Author. 

Steen  (Adolph).  Loeren  om  Homogene  Tunge  Yaedskers  Tryk. 

Copenhagen.  4to. — From  the  Author. 

Struve  (Otto).  Tabulae  Quantitatum  Besselianarum  pro  annis 
1875  ad  1879  computatae.  8vo. — From  the  Author. 

Teape  (Rev.  Dr  Charles  R.).  Berkeleian  Philosophy,  with  an 
Appendix  to  Dr  Temple’s  Essay.  Edinburgh.  8vo. — From 
the  Author. 

— Confession  and  Absolution  in  the  Anglican  Church.  Edin- 
burgh. 8 vo. — From  the  Author. 


of  Edinburgh,  Session  1872-73.  191 

Thomson  (Murray),  M.D.,  F.R.S.E.  Report  on  Meteorological 
Observations  in  the  North-Western  Provinces  of  India  for 
1871.  Allahabad,  1872.  Fol. — From  the  Author. 

II.  Transactions  and  Proceedings  of  Learned  Societies, 
Academies,  etc. 

Amsterdam. — Flora  Batava.  Nos.  218-221.  4to„ — From  the  King 
of  Holland. 

Jaarboek  van  de  Koninklijke  Akademie  van  Wetenschappen 
gevestigd  te  Amsterdam  voor  1871.  8vo. — From  the 
Academy. 

Processen-verhaal  van  de  Gewone  Yergaderingen  der 
Koninklijke  Akademie  van  Wetenschappen.  Afdeeling 
Natuurkunde  van  Mei  1871  tot  en  Met  April  1872. 
8vo. — From  the  Academy. 

Verhandelingen  der  Koninklijke  Akademie  van  Wetens- 
chappen. Afdeeling  Letterkunde.  Zevende  Deel.  4to. 
— From  the  Academy. 

Verslagen  en  Mededeelingen  der  Koninklijke  Akademie  van 
Wetenschappen.  Afdeeling  Letterkunde.  Tweede  Deel. 
— Afdeeling  Natuurkunde.  Zesde  Deel.  8vo. — From  the 
Academy. 

Baltimore. — Sixth  Annual  Report  of  the  Provost  to  the  Trustees  of 
the  Peabody  Institute.  1873.  8vo. — From  the  Institute. 

Basel. — Verkandlungen  der  Naturforschenden  Gesellschaft.  Theil 
Y.  Heft  3,  4.  8 vo. — From  the  Society. 

Berlin. — Abhandlungen  der  Koniglichen  Akademie  der  Wissen- 
chaften.  1871.  4to. — From  the  Academy. 

Monatsbericht  der  Koniglich  Preussischen  Akademie  der 
Wissenchaften  zu  Berlin.  1872,  Mai,  Juin,  Juli,  August, 
Septembre,  Octobre,  Novembre,  Decemhre.  1873, 
Januar,  Februar,  Februar  (No.  2),  Marz,  April.  8vo. — 
From  the  Academy. 

Namen  und  Sach-Register  zu  den  Fortschritten  der  Physik. 
Band  I.  bis  XX.  8vo. — From  the  Society. 

Die  Fortscbritte  der  Physik  im  Jahre  1868.  Dargestellt 
von  der  Physikalischen  Gesellschaft  zu  Berlin.  XX I Y. 
Jargang,  1 und  2 Abtheilung.  8vo. — From  the  Society. 

2 B 


VOL.  VII. 


192  Proceedings  of  the  Boyal  Society 

Berne. — Beitrsege  zur  Geologischen  Karte  der  Schweiz  herausge- 
geben  von  der  Geologisclien  Commission  der  Schweiz. 
Naturforsch  Gesellscliaft  auf  kosten  der  Eidgenossen- 
schaft.  Eilfte  Lieferung.  4to. — From  the  Commission. 

Mittheilnngen  der  Naturforschenden  -Gesellscliaft  in  Bern, 
ans  dem  Jahre  1871.  Nos.  745-811.  8vo. — From  the 
Society. 

Bologna. — Indici  Generali  dei  dieci  Tomi  della  Seconda  Serie 
delle  Memorie  dell  Academia  delle  Scienze  dell  Isti- 
tuto  di  Bologna  dol  1862  al  1870.  4to. — From  the 

Academy. 

Bordeaux. — Memoires  de  la  Societe  des  Sciences  Physiques  et 
Naturelles  de  Bordeaux.  Tome  VIII.  No.  4;  Tome  IX. 
No.  1.  8vo. — From  the  Society. 

Boston. — Bulletin  of  the  Public  Library.  Nos.  23-26.  8vo. — 
From  the  Library. 

Brazil. — Climats  Geologie,  Faune  et  Geograpliie  Botanique  de 
Bresil. — 8vo. — From  the  Brazilian  Government. 

Brussels. — Biographie  Nationale  publieepar  L’Academie  Royale  des 
Sciences,  des  Lettres  et  des  Beaux- Arts  de  Belgique. 
Tome  III.  Partie  2 ; Tome  IV.  Partie  1 . 8vo. — From 
the  Academy. 

Bulletin  de  PAcademie  Royale  des  Sciences,  des  Lettres  et 
des  Beaux- Arts  de  Belgique.  Tome  XXXIV.  Nos. 
11,  12;  XXXV.  Nos.  2-7.  8vo. — From  the  Academy. 

Memoires  de  PAcademie  Royale  des  Sciences,  des  Lettres 
et  des  Beaux-Arts  de  Belgique.  Tome  XXXIX.  4to. 
— From  the  Academy. 

Memoires  Couronnes  et  autres  Memoires  publiees  par 
PAcademie  Royale  des  Sciences,  des  Lettres  et  des 
Beaux-Arts  de  Belgique.  Tome  XXII.  8vo. — From  the 
Academy. 

Annuaire  de  PAcademie  Royale  des  Sciences,  des  Lettres 
et  des  Beaux-Arts  de  Belgique.  1872,  1873.  12mo. — 

From  the  Academy. 

Academie  Royale  de  Belgique,  Centieme  Anniversaire  de 
Fondation.  1772  1872.  Tomes  I.,  II.  8vo.— From  the 
Academy. 


of  Edinburgh,  Session  1872-73.  193 

Brussels. — Annuaire  de  l'Observatoire  Royale  de  Bruxelles,  par  A. 
Quetelet.  1872,  1873.  12mo. — From  the  Observatory. 

Annales  de  l’Observatoire  Royale  de  Bruxelles  publies 
aux  frais  de  l’Etat,  par  le  directeur  A.  Quetelet.  Tome 
XXI.  4to. — -From  the  Observatory. 

Calcutta. — Journal  of  the  Asiatic  Society  of  Bengal.  Rart  1.  Nos. 

2-4,  1872;  Part  II.  Nos.  1,  2,  1873.  8vo. — From  the 

Society. 

Proceedings  of  the  Asiatic  Society  of  Bengal.  Nos.  6-10, 
1872  ; Nos.  1-4,  1873.  8vo. — From  the  Society. 

Records  of  the  Geological  Survey  of  India.  Vol.  V.  Parts 
1-4.  8vo. — From  the  Survey. 

Memoirs  of  the  G-eological  Survey  of  India,  Paleeontologia. 

Yol.  IY.  Parts  1,  2.  4to. — From  the  Survey. 

Memoirs  of  the  G-eological  Survey  of  India.  Yol.  VIII. 

Parts  1,  2 ; Yol.  IX.  Parts  1,  2.  8vo. — From  the  Survey. 
Descriptive  Ethnology  of  Bengal.  1872.  Eol. — From  the 
Government. 

California. — Proceedings  of  the  Academy  of  Sciences.  Yol.  IY. 

Part  5.  8vo. — From  the  Academy. 

Cambridge  ( U.S. ). — Bulletin  of  the  Museum  of  Comparative 
Zoology  at  Harvard  College,  Mass.  Yol.  III.  Nos.  5,  6. 
8vo. — From  the  College. 

Canada. — Geological  Survey.  Report  of  Progress  for  1870-71, 
1871-72.  8vo. — From  the  Director. 

Catania. — Atti  dell  Accademia  Gioenia  de  Scienze  Naturali  de 
Catania.  Tomo  Y.  4to. — From  the  Academy. 
Christiania. — Beretninger  om  Amternes  Oeconomiske  Tilstand, 
Aarene  1866-1870.  4to. — From  the  Government  of 

Norway. 

Beretninger  om  Norges  Fiskerier,  i Aaret  1870,  1871.  4to. 

— From  the  Government  of  Norway. 

Beretning  om  Skolevaesenets  Tilstand  i Kongeriget  Norges 
Landdistrikt  for  Aaret  1867-69.  4to. — From  the  Govern- 
ment of  Norway. 

Beretning  om  Sunhedstilstanden  og  Medicinalforholdene  i 
Norge,  i Aaret  1869-1870.  4to. — From  the  Government 
of  Norway. 


194  Proceedings  of  the  Royal  Society 

Christiania. — Norsk  Meteorologiske,  Aarbog  1871.  4to. — From  the 
Meteorological  Institute. 

Nyt  Magazin  for  Naturvidenskaberne.  Bind  XIX.  Hefte 
1,  2.  8vo. — From  the  Royal  University  of  Norway. 

Det  Kon  gelige  N orste  F rederiks-U niversitets  Aaresberetning, 
1872.  8vo. — From  the  University. 

Forhandlinger  i Yidenskabs-Selskabet  i Christiania,  Aar 
1871.  8vo. — From  the  Society. 

Norske  Universitets  og  Skole- Annaler  1872.  8vo. — From 
the  University. 

Budget  for  Marine-Afdelingen  under  Marine  og  Post 
Department.  1872, 1873.  8vo. — From  the  Government  of 
Norway. 

Criminalstatistiske  Tabeller  for  Kongeriget  Norge  for  Aaret 
1866,  1869,  1780.  — 4to.  From  the  Government  of 
Norway. 

Driftsberetning  for  Hamar-Aamot- Jernbane,  i Aaret  1871. 
4to. — From  the  Government  of  Norway. 

Driftsberetninger  De  Offentlige  Jernbanger,  i Aaret  1871. 
4to. — From  the  Government  of  Norway. 

Driftsberetning  for  Norsk  Ho vid- Jernbane,  i Aaret  1871. 
4to. — From  the  Government  of  Norway. 

Fattigstatistik,  1868,  1869.  4to. — From  the  Government  of 
Nonvay. 

Forklaringer  til  Statsregnskabet  for  1871.  4to. — From  the 
Government  of  Norway. 

Kommursale  Forbolde  i Norges  Land-  og  Bykommuner, 
Aarene  1867  og  1868.  4to. — From  the  Government  of 
Norway. 

Oversigt  over  Kengeriget  Norges  Indtaegter  og  Udgifter,  i 
Aaret  1870.  4to. — From  the  Government  of  Norway. 

Tabeller  vedkommende  Norges  Almindelige  Brandforsik- 
rings-Indretning  for  Bygninger,  i Aaret  1864-1870.  4to. 
— From  the  Government  of  Norway. 

Tabeller  vedkommende  Norges  Handel  og  Skibsfait,  i Aaret 
1870.  4to. — From  the  Government  of  Norway. 

Tabeller  vedkommende  Folkemaengdens  Bevsegelse,  i Aaret 
1869.  4to. — From  the  Government  of  Norway. 


195 


of  Edinburgh,  Session  1872-73. 

Christiania. — Tabeller  Skiftevsesenet  i Norges,  i Aaret  1869,  1870. 
4to. — From  the  Government  of  Norway. 

Uddrac  af  Consulatberetninger  vedkommende  Norges 
Handel  og  Skibsfait,  i Aaret  1871.  4to. — From  the 

Government  of  Norway. 

Pflanzengeographische  Kaiteiiber  das  Kongreich  Norwegen, 
1873. — From  the  Royal  University  of  Norway. 

De  Skandinaviske  og  Arktiske  Amphipoder.  4to. — From 
the  University  of  Norway. 

Copenhagen. — Memoires  de  FAcademie  Eoyale  de  Copenhagen. 

5th  Serie,  Yol.  IX.  No.  9 ; Yol.  X.  Nos.  1,  2.  4to .—From 
the  Academy. 

Oversigt  over  det  Kongelige  danske  Yidenskabernes  Selskabs 
Forhandlinger  og  dets  Medlemmers  Arbeider  i,  Aaret 
1871,  No.  3;  1872,  Nos.  1,  2.  8vo. — From  the 
Society. 

Dublin. — Astronomical  Observations  and  Researches  made  at  Dun- 
sink  1872,  Part  2.  4to. — From  the  Provost  and  Senior 

Fellows  of  Trinity  College. 

Journal  of  the  Royal  Dublin  Society.  Yol.  YI.  No.  2.  8vo. 
— From  the  Society. 

Transactions  of  the  Royal  Irish  Academy  (Science).  Yol. 
XXIY.  Parts  16  and  17.  Yol.  XXY.  Parts  1,  2,  and  3. 
4to.  From  the  Academy. 

Edinburgh. — Forty-Fifth  Annual  Report  of  the  Council  of  the 
Royal  Scottish  Academy  of  Painting,  Sculpture,  and 
Architecture.  1872.  8vo. — From  the  Academy. 
Catalogue  of  the  Printed  Books  in  the  Library  of  the 
Faculty  of  Advocates.  Yol.  II.  Civil  Engineering. 
Edinburgh,  1873.  4to. — From  the  Library. 

Transactions  of  the  Highland  and  Agricultural  Society  of 
Scotland.  Yol.  Y.  8vo. — From  the  Society. 

Transactions  of  the  Royal  Scottish  Society  of  Arts.  Yol. 

YIII.  Parts  3,  4.  8vo. — From  the  Society. 

Transactions  and  Proceedings  of  the  Botanical  Society. 

Yol.  XI.  Part  2.  8vo. — From  the  Society. 

Transactions  of  the  Geological  Society.  Yol.  II.  Parts  1,  2. 
8vo. — From  the  Society. 


196 


Proceedings  of  the  Royal  Society 

Edinburgh. — Journal  of  the  Scottish  Meteorological  Society.  Nos. 
36-39.  8 vo. — From  the  Society. 

Quarterly  Returns  of  the  Births,  Deaths,  and  Marriages, 
registered  in  the  Divisions,  Counties,  and  Districts  of  Scot- 
land. Nos.  70-73.  8vo.  Monthly  Returns  of  the  Births, 
Deaths,  and  Marriages  registered  in  the  eight  Principal 
Towns  of  Scotland,  from  July  1872  till  June  J873  (with 
Supplement).  8vo. — From  the  Registrar-General. 

Fifteenth  detailed  Annual  Report  of  the  Registrar-General 
of  Births,  Deaths,  and  Marriages  in  Scotland.  Edin- 
burgh, 1873.  8 vo. — From  the  Registrar-General . 

Report  on  the  Royal  Botanic  Garden  for  1872.  8vo. — From 
the  Regius  Keeper. 

Catalogue  of  the  Exhibition  held  at  Edinburgh  in  July  and 
August  1871,  on  occasion  of  the  Commemoration  of  the 
Centenary  of  the  Birth  of  Sir  Walter  Scott.  4to. — From 
the  Committee. 

Erlangen. — Sitzungsherichte  der  Physicalisch-Medinischen  So- 
cietat  zu  Erlangen.  Heft  3.  8vo. — From  the  Society. 

Frankfort. — Abhandlungen  herausgegeben  von  der  Sencken- 
bergischen  Naturforschenden  Gesellschaft.  Band.  VIII. 
Heft  3,  4.  4to. — From  the  Society . 

Bench t liber  die  Senckenbergische  Naturforschende  Gesell- 
schaft. 1871-1872.  8vo. — From  the  Society. 

Fribourg. — Actes  de  la  Societe  Helvetique  des  Sciences  Naturelles 
reunie  a Fribourg.  Compte  Rendu.  1872.  8vo. — From 
the.  Society. 

Frauenfeld. — Verb  andlungen  der  Sell  weezerischen  Naturforschenden 
Gesellschaft  in  Frauenfeld.  Jahresbericht.  1871.  8vo. — 
From  the  Society. 

Genera. — Memoires  de  la  Societe  de  Physique  et  d’Histoire 
Naturelle  de  Geneve.  Tome  XXI.  Part  2.  Tome  XXII. 
4to. — F'rom  the  Society. 

Glasgow  — Proceedings  of  the  Philosophical  Society  of  Glasgow. 
Vol.  VIII.  No.  2.  8vo. — From  the  Society. 

Gottingen. — Nachrichten  von  der  K.  Gesellschaft  der  Wissenschaften 
und  der  Georg- Augusts-Universitat,  aus  dem  Jahre  1872. 
12 mo. — From  the  University . 


197 


of  Edinburgh,  Session  1872-73. 

Gottingen. — Abliandlungen  der  Koniglichen  Gesellschaft  der  Wis- 
senchaften  zu  G-ottingen.  Band  XVII.  4to. — From  the 
Society. 

Haarlem. — Archives  Neerlandaises  des  Sciences  Exactes  et 
Naturelles  publiees  par  la  Societe  Hollandaise  a Haarlem. 
Tome  YII.  Liv.  4,  5.  8vo. — From  the  Society. 

Innsbruck. — Berichte  des  Naturwissenschaftlich  - Mediziniseben 
Vereines  in  Innsbruck.  Jahrgang  III.  Heft  1.  8vo. — 
From  the  Society. 

Kasan. — Reports  of  the  University  of  Kasan.  1869-1872;  1873, 
No.  1.  8 vo. — From  the  University . 

Leeds. — Proceedings  of  the  Geological  and  Polytechnic  Society  of 
the  West  Riding  of  Yorkshire.  New  Series,  1871-72, 
Part  1.  8vo.— From  the  Society. 

The  Fifty-Second  Report  of  the  Council  of  the  Leeds 
Philosophical  and  Literary  Society,  1871-72.  8vo. — From 
the  Society. 

Leiden. — Annalen  der  Sternwarte  in  Leiden  herausgegeben,  von 
Hr  F.  Kaiser.  Fritter  Band.  4to. — From  the  Obser- 

vatory. 

Leipzig.  — Berichte  liber  die  Verhandlungen  der  Koniglich 
Sachsischen  G-esellschaft  der  Wissenschaften  zu  Leip- 
zig; Mathematisch-Physische  Classe.  1871,  Nos.  4-7; 
.1872,  Nos.  1,  2.  8vo.  — From  the  Loyal  Saxon 
A cademy. 

Bestimmung  du  Langendjfferenz  jzwischen  Leipzig  und 
Wien.  C.  Brulms.  Band  X.  No.  3.  8vo. — From  the 
Royal  Saxon  Academy. 

Berichte  liber  die  Verhandlungen  der  Koniglich  Sachis- 
chen  Gesellschaft  der  Wissenchaften  zu  Leipzig;  Phil. 
Hist.  Classe.  1870,  Nos.  1-23.  8vo. — From  the  Royal 
Saxon  Academy. 

Die  Geschichtschrubung  liber  den  Zug  Karls  V.  gegen. 
Tunis  (1535),  von  Georg  Voigt.  Band  VI.  No.  2.  8vo. 
— Fnom  the  Roycd  Saxon  Academy. 

Der  homerische  Gebraucli  der  Partikel  Ei  Einleitung  und 
Ei  mit  dem  Optativ.  Von  Ludwig  Lange.  Band  VI. 
No.  4.  8 vo. — From  the  Royal  Saxon  Academy. 


198 


Proceedings  of  the  Poyal  Society 

Leiyzic. — Elektrische  Untersucliungen  Neunte  Abhandlungiiber  die 
Thermoelektrischen  Eigenschaften  des  Schwerspathes. 
W.  G.  Hankel.  Band  X.  No.  4.  8vo. — From  the  Royal 
Saxon  Academy. 

Elektrische  Untersucliungen  Zebnte  Abhandlung  liber  die 
Thermoelektrischen  Eigenschaften  des  Aragonites  nebst 
Einer  Ubersicht  liber  die  Entwickelung  der  Lelire  von 
der  Thermoelektrischen  a der  Krystalle.  W.  G.  Hankel. 
Band  X.  No.  5.  8vo.  — From  the  Royal  Saxon 
Academy. 

Uber  die  Bomischen  Triumplialreliefe  und  ih re  Stellung  in 
der  Kunstgeschiclite,  von  Adolph  Philippe.  Band  VI. 
No.  3.  8vo. — From  the  Royal  Saxon  Academy. 

Uber  den  Bedentungswechse  gewisser  die  Zurechnung  und 
den  Ocenomischen  Erfolg  einer  That  bezeichnender 
technischer  latenischer  Ausdrucke,  von  Moritz  Voigt. 
Band  VI.  No.  1.  8vo.  — From  the  Royal  Saxon 
Academy. 

London. — Proceedings  of  the  Society  of  Antiquaries.  Vol.  V. 
Nos.  4—7;  VI.  No.  1.  8vo. — From  the  Society. 

Journal  of  the  Society  of  Arts  for  1872-73.  8vo. — From 
the  Society. 

Memoirs  of  the  Boyal  Astronomical  Society.  Vol.  XXXIX. 

Part  2.  4to. — From  the  Society. 

Monthly  Notices  of  the  Eoyal  Astronomical  Society  for 
1872-73.  8vo. — From  the  Society. 

Observations  of  Comets  from  b.c.  611  to  a.d.  1640.  Ex- 
tracted from  the  Chinese  Annals  by  John  Williams. 
4to. — From  the  Royal  Astronomical  Society. 

Journal  of  the  Royal  Asiatic  Society  of  Great  Britain  and 
Ireland.  Vol.  VI.  Part  2.  8vo. — From  the  Society. 
Transactions  of  the  Royal  Society.  Vol.  CLXII.  Parts  1 
and  2.  List  of  Fellows,  1872.  4to. — From  the  Society. 
Proceedings  of  the  Royal  Society.  Nos.  137-146.  8vo. 
— From  the  Society. 

Royal  Society  Catalogue  of  Scientific  Papers.  Vol.  VI. 
4 to. — From  the  Society. 


199 


of  Edinburgh,  Session  1872-73. 

London. — Transactions  of  the  Eoyal  Society  of  Literature.  Yol. 
X.  Part  2.  8vo. — From  the  Society. 

Journal  of  the  Chemical  Society.  1872,  October,  Novem- 
ber, December  (December  Supplementary  Number) ; 1 873, 
January,  February,  March,  April,  May,  June,  July, 
August,  September.  8vo. — From  the  Society. 

Proceedings  of  the  Eoyal  Geographical  Society.  Yol.  XYI. 

No.  5 ; XYII.  Nos.  1,  2. — From  the  Society. 

Journal  of  the  Eoyal  Geographical  Society.  Yol.  XLI. 
8 vo. — From  the  Society . 

Classified  Catalogue  of  the  Library  of  the  Eoyal  Geogra- 
phical Society  to  December  1870.  8vo. — From  the 

Society. 

Quarterly  Journal  of  the  Geological  Society.  Yol.  XX  YII  L 
Part  4;  XXIX.  Parts  1,  2,  3.  8vo. — From  the  Society. 
Proceedings  of  the  Geologists’  Association.  Yol.  II.  Nos. 
7,  8;  Yol.  III.  Nos.  1,  2.  Annual  Eeport  for  1872. 
8vo. — From  the  Society. 

Journal  of  the  London  Institution.  Yol.  II.  Nos.  16-21. 
8vo. — From  the  Society. 

Proceedings  of  the  Eoyal  Institution  of  Great  Britain. 

Yol.  YI.  Parts  5,  6.  8vo. — From  the  Society. 

Journal  of  the  Linnean  Society.  Yol.  XI.  (Zoology),  Nos. 
55-56;  Yol.  XIII.  (Botany),  Nos.  68-72.  8vo. — From 
the  Society. 

Transactions  of  the  Linnean  Society.  Yol.  XXYIII.  Part 
3;  XXIX.  Parts  1,  2.  4to. — From  the  Society. 
Proceedings  of  the  London  Mathematical  Society.  Nos. 

48-61.  8 vo. — From  the  Society. 

Transactions  of  the  Eoyal  Medical  and  Chirurgical  Society. 

Yol.  LY.  8vo. — From  the  Society. 

Proceedings  of  the  Eoyal  Medical  and  Chirurgical  Society. 

Yol.  YII.  Nos.  2-4.  8vo. — From  the  Society. 

Quarterly  Journal  of  the  Meteorological  Society.  Yol.  I., 
New  Series,  Nos.  4-7.  8vo. — From  the  Society. 

Quarterly  Weather  Eeport  of  the  Meteorological  Office. 
Parts  2,  3,  1871;  1-3,  1872.  4to. — From  the  Meteoro- 
logical Committee  of  the  Royal  Society. 

2 c 


VOL.  VIII. 


200  Proceedings  of  the  Royal  Society 

London. — Report  of  the  Meteorological  Committee  of  the  Eoyal 
Society  for  the  year  ending  31st  December  1872.  8vo. 
— From  the  Royal  Society. 

Transactions  of  the  Pathological  Society.  Yol.  XXII. 
8 vo. — From  the  Society. 

Journal  of  the  Statistical  Society.  Yol.  XXXY.  Part  4; 

Yol.  XXXVI.  Parts  1,  2.  8vo. — From  the  Society . 
Statistical  Report  on  the  Health  of  the  Navy  for  the  year 
1870.  8vo. — From  the  Admiralty. 

Descriptive  Catalogue  of  the  Teratological  Series  in  the 
Museum  of  the  Royal  College  of  Surgeons  of  England 
1872.  8vo. — From  the  College. 

Transactions  of  the  Zoological  Society.  Yol.  YIII.  Parts 
3-5.  4to. — From  the  Society. 

Proceedings  of  the  Zoological  Society.  Parts  2,  3.  1872. 

8 vo. — From  the  Society. 

Index  to  the  Proceedings  of  the  Zoological  Society,  1861— 
1870.  8vo. — From  the  Society. 

Journal  of  the  East  India  Association.  Nos.  3,  4;  1873, 
No.  1.  8vo. — From  the  Association. 

Lund. — Acta  Universitatis  Lundensis  Lunds  Universitets  Ars- 
Skrift  Mathematik  och  Naturvetenskap,  for  ar  1869-1870; 
Philosophi  Sprakvetenskap  och  Historia,  1869;  Theologi, 
1870.  4to. — From  the  University. 

Lyons. — Memoires  de  l’Academie  Imperiale  des  Sciences  Belles- 
Lettres  et  Arts  de  Lyon.  Tome  XIX.  8vo. — From  the 
Society. 

Annales  de  la  Societe  d’ Agriculture,  Histoire  Naturelle  et 
Arts  Utiles  de  Lyon.  Quatrieme  Serie.  Tome  II.  8vo. 
— From  the  Society. 

Manchester. — Proceedings  of  the  Literary  and  Philosophical  Society. 

Yol.  XI. ; Yol.  XII.  8vo. — From  the  Society. 

Melbourne. — Patents  and  Patentees.  Yol.  Y.  1870.  4to. — From 
the  Registrar -General  of  Victoria. 

Milan. — Atti  della  Societa  Italiana  di  Scienze  Naturali.  Yols. 
X1Y.,  XY.  Fasc. '2.  8vo. — From  the  Society. 


of  Edinburgh , Session  1872-73.  201 

Milan. — Memorie  del  Reale  Istituto  Lombardo  di  Scienze  e 
Lettere.  Classe  di  Lettere  e Scienze  Morali  e Politiche. 
Yol.  XII.  Serie  III.  Fasc.  3.  — Classe  di  Scienze 
Matematiche  e Naturali.  Vol.  XII.  Fasc.  5.  8vo. — 
From  the  Institute. 

Rendiconti  Reale  Istituto  Lombardo  di  Scienze  e Lettere. 
Serie  II.  Yol.  Y.  Fasc.  8-16.  8vo. — From  the  Insti- 
tute. 

Pubblicarzioni  del  Reale  Osservatorio  di  Brera  in  Milano. 
Nos.  1 and  2.  1873.  4to. — From  the  Observatory. 

Moscow. — Bulletin  de  la  Societe  Imperiale  des  Naturalistes.  1872, 
Nos.  1-4.  1873,  No.  1.  8vo. — From  the  Society. 

Munich. — Abhandlungen  der  koniglich.  bayerischen  Akad.  der 
Wissenscbaften.  Philosophisch-Philologischen  Classe. 
Band  XII.  Abtli.  3.  — Matbematiscb  - Physikalischen 
Classe.  Band  XI.  Abtli.  1.  4to. — From  the  Academy. 

Sitzungsberickte  der  konigl.  bayer.  Akademie  der  Wissen- 
scliaften.  Inbaltsverzeichniss  zu  Jahrgang,  1860-1870. 
8 vo. — From  the  Academy. 

Sitzungsberichte  der  konigl.  bayer.  Akademie  der  Wissen- 
scbaften. 1872,  Hefts  2,  3. — Philosophiscb-Pliilologischen 
und  Historiscben  Classe.  1872. — Mathematiscli-Physi- 

kalischen  Classe.  8vo. — From  the  Academy. 

Ueber  die  G-escbichtschrubung  unter  dem  Kurfursten 
Maximilian  I.  1872.  4to. — From  the  Academy. 

Yerzeichniss  von  4093  telescopischen  Sternen,  Supp.  Band 
XII.  8vo. — From  the  Royal  Observatory. 

Annalen  der  Koniglichen  Sternwarte  bei  Miincken.  Band 
XIX.  8 vo  — From  the  Royal  Observatory. 

Neucliatel. — Bulletin  de  la  Societe  des  Sciences  Naturelles  de 
Neuchatel.  Tome  IX.  Part  2.  8vo.  — From  the 
Society. 

New  Haven  (U.Si). — Journal  ( American  J of  Science  and  Art,  con- 
ducted by  Benjamin  Silliman.  Yol.  IV.  Nos.  21-32. 
New  Haven.  8vo. — :From  the  Editor. 

New  Zealand. — Reports  of  Geological  Explorations  during  1871— 
72,  with  Maps  and  Sections  by  Dr  James  Hector.  8vo. 
— From  the  Geological  Survey. 


202  Proceedings  of  the  Royal  Society 

New  Zealand . — Sixth  and  Seventh  Annual  Reports  on  the  Colonial 
Museum  and  Laboratory,  by  Dr  James  Hector.  8vo. — 
From  the  Geological  Survey. 

Catalogue  of  the  Echinodermata  of  New  Zealand,  with 
Diagnoses  of  the  Species,  by  E.  W.  Hutton,  Esq.  8vo. 
— From  the  Geological  Survey. 

Nijmegen — Nederlandsch  Kruidkundig  Archief.  Deel.  I.  Stub 
2-3.  8 vo. — From  the  Editors. 

Ohio. — Twenty-sixth  Annual  Report  of  the  State  Board  of  Agri- 
culture, 1871.  Columbus,  1872.  8vo. — From  the  Board. 

Orleans. — Archives  of  Science,  and  Transactions  of  the  Orleans 
County  Society  of  Natural  Sciences.  Yol.  I.  Nos.  4-5. 
8 vo. — From  the  Society. 

Oxford. — Astrononomical  and  Meteorological  Observations  made  at 
the  Radcliffe  Observatory,  Oxford,  in  the  year  1870. 
Yol.  XXX.  8vo. — From  the  Observatory. 

Paris.— Annales  des  Mines.  Tome  I.  Liv.  3e;  Tome  II.  Liv.  4e, 
5e,  6e ; Tome  III.  Liv.  le,  2e,  3e.  8vo. — From  the  Ecole  de 
Mines. 

Publications  of  the  Depot  de  la  Marine,  with  Charts.  8vo. 
— From  the  Depot. 

Annales  Hydrographiques.  Nos.  3,  4.  1872.  8vo. — From 

the  Depot  de  la  Marine. 

Bulletin  de  la  Societe  Geographie.  1872,  Juillet,  Aout, 
Septembre,  Octobre,  Novembre,  Decembre;  1873,  Janvier, 
Fevrier,  Mars,  Avril,  Mai,  Juin,  Juillet.  8vo. — From  the 
Society. 

Bulletin  de  la  Societe  Mathematique  de  France.  Tome  I. 
No.  1.  8vo. — From  the  Society. 

Comptes-Rendus  Hebdomadaires  des  Seances  de  l’Academie 
des  Sciences.  1872-73.  4to. — From  the  Academy. 

Best. — Ergebnisse  der  in  den  Liindern  der  Ungarischen  Krone  am 
aufange  des  jabres  1870,  voltzogenen  Yolhszahlung  sammt 
nachweisung  der  nutzbaren  Hausthiere  in  auftrage  des 
Konigl.  Ungarischen  ministers  fiir  Landwirthschaft, 
Gewerbe  und  Handel  verfasst  und  herausgegeben  durch 
das  Konigl.  Ungarische  Statische  Bureau.  1871.  Fob 
From  the  Bureau. 


202 


of  Edinburgh,  Session  1872-73. 

Philadelphia. — Proceedings  of  the  American  Society.  Vol.  XII. 
No.  89.  8 vo. — From  the  Society. 

Quebec. — Transactions  of  the  Literary  and  Historical  Society. 

Session  of  1871-2.  8vo. — From  the  Society. 

Salem  ( XJ.S. ). — Memoirs  of  the  Peabody  Academy  of  Science.  Vol. 

I.  Nos.  2,  3.  8vo. — From  the  Peabody  Academy  of 

Science. 

Fourth  Annual  Eeport  of  the  Trustees  of  the  Peabody 
Academy  of  Science  for  the  year  1871.  8vo. — From  the 
Peabody  Academy  of  Science. 

The  American  Naturalist.  Yol.  Y.  Nos.  2-12;  Yol.  YI. 
8vo. — From  the  Peabody  Academy  of  Science. 

Shanghai. — Journal  of  the  North  China  Branch  of  the  Eoyal 
Asiatic  Society.  No.  6.  8vo. — From  the  Society. 

St  Petersburg li. — Annalen  des  Physikischen  Centralobservatoriums. 
1870-71.  8vo. — From  the  Russian  Government. 

Memoires  de  l’Academie  Imperiale  des  Sciences  de  St 
Petersbourg.  Tome  XVIII.  Nos.  8-10;  XIX.  Nos. 
1-7.  4to. — From  the  Academy. 

Bulletin  de  l’Academie  Imperiale  des  Sciences  de  St  Peters- 
bourg. Tome  XYII.  Nos.  4-8  ; XYIIL  Nos.  1,  2.  4to. 
— From  the  Academy. 

Stockholm. — Sveriges  G-eologiska  Undersokning ; with  Charts. 

Livs.  42-46.  8vo. — From  the  Bureau  de  la  Recherche 
Geologique  de  la  Suede. 

Ofversigt  af  Kongl.  Yetenskaps-Akademiens  Forhandling;ir 
Tjugondesjette  & Tjugondesjunde  Argangen,  1869-1870. 
8vo .—From  the  Academy. 

Kongliga  Svenska  Yetenskaps-Akademiens  Handlingar  Ny 
Folja  Attonde  Bandet  1869;  Nionde  Bandet  1870.  4to. 
— From  the  Academy. 

Meteorologiska  Jakttagelser  i Sverige  utgifna  af  Kongl. 
SvenskaYetenskaps-AkademiensAnstallda  ochBearbetade 
af  Er-Edlund  Nionde  Bandet  1867  ; Tionde  Bandet  1868  ; 
Elefte  Bandet  1869.  4to. — From  the  Academy. 
Lefnadsteckinngar  ofver  Kongl.  Svenska  Vetenskaps-Aka- 
demiens  efter  ar  1854  Aflidna.  Band  I.  Hefte  2.  8vo. 
— From  the  Academy. 


204  Proceedings  of  the  Royal  Society 

Toronto. — The  Canadian  Journal  of  Science,  Literature,  and 
History.  Yol.  XIII.  N os.  5,  6.  8vo. — From  the  Cana- 
dian Institute. 

Turin. — Atti  della  Eeale  Accademia  delle  Scienze.  Yol.  VII. 
Desp.  1-7.  8 vo — From  the  Academy. 

Bolletino  Meteorologico  dell’  Osservatorio  Astronomico  dell’ 
Universita.  1872.  4to. — From  the  University. 

Utrecht. — Aanteeken  ingen  van  het  Yerhandelde  Sectivergader ingen 
van  ket  Provinciaal  Utreclitsck  Genootsckap  van  Kunsten 
en  Wetenschappen,  1871-1872.  8vo. — From  the  Society. 
Yerslagvan  ket  Yerhandelde  in  dealgemeene  Vergaderingvan 
ket  Provinciaal  Utreclitsck  Genootsckap  van  Kunsten  en 
Wetenschappen,  25  Juni  1872.  8vo. — From  the  Society. 
De  Spectatoriale  Gesckriften  van  1741-1800.  8vo. — From 
the  Society. 

Nederlandsck  Meteorologisch  Jaarkoek,  voor  1868-1871. 
4to. — From  the  Meteorological  Institute. 

Venice. — Atti  del  Reale  Istituto  Yeneto  di  Scienze,  Lettere  ed 
Arti.  Serie  1Y.  Tome  I.  Dispensa  6-10 ; Tome  II. 
Dispensa  1,  2.  8vo. — From  the  Institute. 

Victoria  ( Australia ). — Statistics  of  the  Colony  of  Yictoria,  1871. 
Parts  4,  6-  9.  Fol. — From  the  Registrar-General. 

Census  of  Yictoria  for  1871.  Parts  3-6.  Fol. — From  the 
Australian  Government. 

Vienna. — Sitzungsberichte  der  kaiserlichen  Akademie  der  Wis- 
sensckaften.  Phil.  Hist.  Classe.  Band  LXX.  Heft  1-3 ; 
Band  LXXI.  Heft  1-4.— Math.  Nat.  Classe.  Band  LXY. 
Heft  1-5.— Phys.-Anat.  Band  LXY.  Heft  1-5.— Min. 
Bot.  Zool.  Geo.  Pal.  Band  LXY.  Heft  1-5.  8vo. — From 
the  Academy. 

Denksckriften  der  kaiserlichen  Akademie  der  Wissen- 
sckaften.  Math.  Nat.  Classe.  Band  XXXII. — Phil. 
Hist.  Classe.  Band  XXI.  4to. — From  the  Academy. 
Almanack  der  kaiserlichen  Akademie  der  Wissenschaften. 
8vo. — From  the  Academy. 

Register  zu  den  Banden  61,  bis  70,  der  Sitzungsberichte  der 
Phil.  Hist.  Classe,  der  Kaiserlichen  Akademie  der  Wissen- 
chaften,  Math.  Nat.  61,  bis  64.  8vo. — From  the  Academy. 


205 


of  Edinburgh , Session  1872-73. 

Vienna. — Verhandlungen  der  kaiserlich-Konigliehen  Zoologish- 
Botanischen  Gesellschaft  in  Wien.  Band  XXII.  8vo. — 
From  the  Society. 

General  Begister  der  Bande  XI.-XX.  des  Jahrbuch.es 
und  der  Jahrgange  1860-1870,  der  Verhandlungen  der 
Kaiserlich  - Koniglichen  G-eologischen  Reichsanstalt. 
8yo. — From  the  Society. 

Verhandlingen  der  Kaiserlich-Koniglichen  G-eologischen 
Reichsanstalt.  1872,  Nos.  11,  11-18;  1873,  Nos.  1-6. 
8 vo.— From  the  Society. 

Uber  einen  Neuen  Fossilen  Saurier  aus  Lesina,  von  Dr  A. 
Thornhuber.  Band  V.  Heft  4.  4to. — From  the  Society. 

Jahrbuch  der  Kaiserlich-Koniglichen  Geologischen  Reich- 
sanstalt. Band  XXII.  Nos.  3,  4;  XXIII.  No.  1.  8vo. 
— From  the  Society. 

Warwick . — Thirty-Seventh  Annual  Report  of  the  Warwickshire 
Natural  History  and  Archaeological  Society,  1873. 
— From  the  Society. 

Washington. — Memoir  of  the  Founding  and  Progress  of  the  United 
States  Naval  Observatory.  Appendix  IV.  4to. — From 
the  U.S.  Naval  Observatory. 

On  the  Right  Ascensions  of  the  Equatorial  Fundamental 
Stars  and  the  Corrections  necessary  to  reduce  the  Right 
Ascensions  of  different  Catalogues  to  a Mean  Homo 
geneous  System.  Appendix  III.  4to. — From  the  U.S. 
Naval  Observatory. 

Reports  on  Observations  of  Encke’s  Comet  during  its  Return 
in  1871.  Appendix  II.  4to. — From  the  U.S.  Naval 

Observatory. 

Report  on  the  Difference  of  Longitude  between  Washington 
and  St  Louis.  Appendix  I.  1870.  4to. — From  the  U.S. 
Naval  Observatory. 

Papers  relating  to  the  Transit  of  Venus  in  1874,  prepared 
under  the  direction  of  the  Commission  authorised  by 
Congress.  Part  I.  4to. — From  the  U.S.  Naval  Obser- 
vatory. 

Astronomical  and  Meteorological  Observations  made  during 
the  year  1870.  4to. — From  the  U.S.  Naval  Observatory. 


2C6 


Proceedings  of  the  Royal  Society 

Washington. — Results  of  Washington  Observations,  1858-1860. 
4to. — From  the  U.S.  Naval  Observatory. 

Smithsonian  Contributions  to  Knowledge.  Yol.  XVIII. 
4to. — From  the  Institution. 

Report  of  the  Commissioner  of  Agriculture  for  1871. 

Washington,  1872.  8vo. — From  the  Commissioner. 
Monthly  Reports  of  the  Department  of  Agriculture  for  1872. 
Washington.  8vo. — From  the  Commission  of  Agriculture. 
Wellington  (. New  Zealand). — Results  of  a Census  of  New  Zealand. 
1871.  Fol. — From  the  New  Zealand  Government. 
Statistics  of  New  Zealand.  1871.  Fol. — From  the  Neiv 
Zealand  Government. 

Whitby.— The  Fiftieth  Report  of  the  Whitby  Literary  and  Philo- 
sophical Society.  8vo. — From  the  Society. 

Wisconsin. — Thirteenth  and  Fourteenth  Annual  Reports  of  the 
Trustees  of  the  Institute  of  the  Education  of  the  Blind. 
1862,  1863.  8 vo. — From  the  Institute. 

York— -Communications  to  the  Monthly  Meetings  of  the  Yorkshire 
Philosophical  Society.  1872.  8vo. — From  the  Society. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  viii.  1873-74.  No.  87. 


Ninety-First  Session. 

Monday,  24 th  November  1873. 

Sir  BOBERT  CHRISTISON,  Bart.,  President,  in  the  Chair. 
The  following  Council  were  elected 

President. 

Sir  WILLIAM  THOMSON,  Knt.,  LL.D. 


Honorary  Vice-Presidents. 

His  Grace  the  DUKE  of  ARGYLL. 

Sir  ROBERT  CHRISTISON,  Bart.,  M.D. 


Vice-Presidents. 


Principal  Sir  Alex.  Grant,  Bart. 
Sir  W.  Stirling-Maxwell,  Bart. 
David  Milne  Home,  LL.D. 


Professor  Kell  and. 

Rev.W.  Lindsay  Alexander,  D.D. 
David  Stevenson,  Esq.,  C.E. 


(General  Secretary — Dr  John  Hutton  Balfour. 


Secretaries  to  Ordinary  Meetings. 
Professor  Tait. 

Professor  Turner. 

Treasurer — David  Smith,  Esq. 

Curator  of  Library  and  Museum — Dr  Maclagan. 


Professor  A.  Dickson. 
James  Leslie,  Esq.,  C.E. 
Rev.  Thomas  Brown. 
James  Dewar,  Esq. 
Professor  Lister. 

George  Robertson,  Esq. 

VOL.  VIII 


Councillors. 

Captain  T.  P.  White. 

The  Hon.  Lord  Neaves. 

The  Right  Rev.  Bishop  Cotterill. 
Professor  A.  Crum  Brown. 

Dr  Arthur  Mitchell. 

I George  Forbes,  Esq. 

2 D 


208 


Proceedings  of  the  Royal  Society 


Monday , 1st  December  1873. 

Sir  ROBERT  CHRISTISON,  Bart.,  Honorary  Vice- 
President,  in  the  Chair. 

The  following  Communications  were  read: — 

1.  Laboratory  Notes.  By  Professor  Tait. 

1.  First  Approximation  to  a Thermo-electric  Diagram. 

(This  Paper  will  appear  in  the  Transactions  of  the  Society.) 

2.  On  the  Flow  of  Water  through  Fine  Tubes. 

Dr  Matthews  Duncan  recently  ashed  me  whether  the  flow  of 
blood  under  given  pressure  would  be  affected  by  a considerable 
change  of  form  of  the  section  of  a small  vein  or  artery.  It  ap- 
peared obvious,  from  the  well-known  experiments  of  Poiseuille 
(which  show  that  when  the  bore  of  a capillary  tube  of  circular 
section  is  sufficiently  small,  the  flow  through  it. is  as  the  fourth 
power  of  the  diameter),  that  the  flow  through  a capillary  tube 
of  elliptical  section  must  be  less  than  that  through  a circular 
tube  of  equal  sectional  area.  The  accepted  theory  of  fluid  friction 
might  enable  us  to  obtain,  a solution  for  an  elliptic  tube,  but  the 
assumptions  requisite  for  its  deduction  appear  extremely  unlikely 
to  he  fulfilled  in  practice,  so  that  I asked  Messrs  C.  G-.  Knott  and 
C.  M.  Smith  to  make  some  direct  experimental  comparisons  between 
various  circular  and  elliptic  tubes,  specially  drawn  for  the  purpose, 
and  of  the  same  material.  The  present  preliminary  experiments, 
unfortunately,  refer  only  to  tubes  the  smallest  of  which  has  nearly 
the  bore  of  the  largest  of  those  used  by  Poiseuille. 

The  tubes  were  carefully  calibrated  and  the  worst  rejected.  A 
length  of  twenty  inches  was  cut  from  the  most  uniform  portion 
of  each  of  the  selected  tubes,  and  the  axes  of  the  section  (when 
elliptical)  were  carefully  measured  at  each  end.  This  determina- 
tion was  checked  by  weighing  the  column  of  mercury  employed 
for  calibration.  Water,  at  a fixed  temperature,  was  drawn  under 


20D 


of  Edinburgh,  Session  1873-74. 

fixed  pressure,  for  a given  time,  through  each,  and  its  quantity 
measured.  The  following  are  the  experimental  results  : — 


Weight 

Efflux  per 
min. 

Axes  of  sections 

Ratio  of 

Cal.  weight 

Section. 

of  1 inch 
Hg. 

T. 

P. 

in  hundredths 
of  an  inch. 

axes. 

of  1 inch. 
Hg. 

Elliptic. 

Cub.  in. 

C. 

In. 

I. 

•249 

3-30 

9-4 

23*65 

8-5  ) 1 
8-25  \ \ 

>1-5 
1 1-8 

5-073 

•238 

II. 

•357 

7-87 

9-5 

23-65 

U !! 

| 2-3 
1 2-3 

3-956 

•359 

III. 

•441 

12- 

10- 

23-57 

9-4  / j 
10-1  \ \ 

, 2-6 
1 2-7 

3-679 

•445 

IV. 

•685 

21-77 

10- 

23-57 

ir76|  | 

i 3-1 
3-2 

4-087 

•683 

Circular. 

Diameters  of 

ends. 

I. 

•223 

6-16 

I0‘ 

23-1 

* 3-6  3-6 

•223 

II. 

•301 

9-62 

io- 

23-1 

4-1  4-3 

•304 

III. 

•357 

11-81 

10- 

23-1 

4-4  4-5 

•341 

IV. 

•646 

22-6 

9-9 

23-1 

6-2  6-2 

•661 

V. 

1-213 

52-8 

11-5 

23-2 

8’3  8-6 

1-229 

VI. 

1-632 

67- 

11- 

23-2 

9*6  9-6 

1-587 

The  two  last  were  added  with  a view  of  finding  the  effect  of  still 
farther  increasing  the  section.  A comparison  of  the  first  and 
second  groups  of  four  shows  the  very  considerable  effect  of  the 
elliptic  form  in  diminishing  the  rate  of  flow. 


2.  Note  on  the  Transformation  of  Double  and  Triple 
Integrals.  By  Professor  Tait. 


1.  If  we  have  two  equations  of  the  form 

f(u,  v>  & v)  = 0 , 

PO,  a,  £,  v)  = 0 , 


u and  v are  given  as  functions  of  £ and  rj , or  vice  versa.  Here 
either  u and  v,  or  £ and  rj,  may  be  the  ordinary  Cartesian  x and  y, 
or  any  given  functions  of  them. 

Now,  if  we  write  with  Hamilton,  since  we  are  dealing  with  two 
independent  variables  only, 


4 


. d 

3 dy 


v=v“"+v4=v4+v4 


du 


(i) 


we  have 


210 


Proceedings  of  the  Royal  Society 

The  proof  may  be  easily  given  in  a Cartesian  form  by  operating  by 
S i and  S j separately.  For  the  former  operation  gives 

d du  d dv  d d£  d dr)  d 

dx  ~ dx  du  + dx  dv  ~ dx  dx  dr)’ 

equations  manifestly  true. 

2.  Now,  the  elementary  area  included  by  the  curves  u , u + Su, 
v , v + Sv,  is  easily  seen  to  be 


8u8v 

TY Vu Vv ’ 


Hence  we  have  the  following  transformations  of  a double  integral 
extended  over  a given  area  : — 

a -jfi  -Jfi  tw w,  ■ 

But  by  (1)  we  see  at  once  that 


TVVf  V^  = 


d£  d£ 

du  * dv 
drj  dr) 
du  ’ dv 


TY VwVv , 


whence,  of  course,  the  general  proposition 


d£  di 

du  dv 

du  ' dv 

M \ M 

dr)  dr) 
du  ’ dv 

1 

du  dv 
dr)  ’ dr) 

and  the  common  transformation 


ffidxdy  =fj P 


dx  dx 
du  ’ dv 
dy  dy 
du  ’ dv 


dudv . 


3.  Dealing  with  triple  integrals,  V takes  the  ordinary  Hamil- 
tonian form,  and  an  additional  term  is  added  to  each  of  the  mem- 
bers of  (1),  which  thus  at  once  gives  us  the  mode  of  introducing  V 
into  any  system  of  curvilinear  co-ordinates. 


211 


of  Edinburgh,  Session  1873-74. 

The  element  of  volume  included  by  the  surfaces  u , u + Zu,  v , 
v+  Sv,  w,  w+8w,  is  easily  seen  to  be  expressed  by 

SuSvSw 

~ S . VuVvVw  * 


Hence  we  have  the  following — 


fjfvdxiyth  = -fff P 


dudvdw 

S . VuVv'Vw 


-IIP 


d£drjd£ 

S . V£VrjVi ' 


From  these  we  have,  besides  the  more  complex  transformation 
from  u,  v , w , to  y , £,  the  common  one 


ffpdzdyd*  = -fff. P 


dx  dx  dx 
du  ’ dv  5 
dy  dy  dy 
du'  dv  ' dw 
dz  dz  dz 
du  ’ dv  ’ 


dudvdw  , 


and  also  the  general  theorem 


di  dg  d% 

du  du  du 

du'  dv  ' dw 

df'Jy'T^ 

dy  drj  dy 

dv  dv  dv 

du  ’ dv  ' dw 

df'dy'Tt 

d£  di  di ; 

dw  dw  dw 

du  ' dv  ’ dw 

df'ly'lf 

3.  On  the  Physiological  Action  of  Ozone.  By  James  Dewar, 
Esq.,  Lecturer  on  Chemistry,  and  John  G.  M‘Kendrick, 
M.D.,  Physiological  Laboratory,  University  of  Edinburgh. 

A systematic  investigation  into  the  physiological  action  of  ozone, 
so  far  as  we  are  aware,  has  never  been  undertaken.  Isolated  obser- 
vations have  been  made  by  many  while  engaged  in  the  examination 
of  its  physical  and  chemical  properties,  which  have  chiefly  tended 
to  show  that  it  acts  as  an  irritant  on  the  mucous  membrane  of  the 
respiratory  tract,  and  they  have  also  observed  the  peculiar  odour 
which  it  excites  by  its  effect  on  the  organ  of  smell,  from  which  the 
name  ozone  originated.  Beyond  this  little  has  been  attempted. 


212 


Proceedings  of  the  Royal  Society 

Schonbein,  indeed,  showed*  that  a mouse  imprisoned  in  an  atmo- 
sphere of  ozone  died  in  about  five  minutes.  From  meteorological 
data,  this  observer  also  stated  that  the  quantity  of  ozone  in  the 
atmosphere  and  the  prevalence  of  epidemic  diseases  were  in  an 
inverse  relation  to  each  other  both  as  to  time  and  locality.  This 
statement  has  probably  given  rise  to  the  popular  opinion  that  ozone 
not  only  acts  as  a powerful  oxidising  agent  of  decaying  animal 
or  vegetable  matters,  but  also  that  it  has  a specific  action  on  the 
animal  body. 

With  the  view  of  determining  what  action  ozone  exerts  on  the 
body,  we  commenced  a series  of  experimental  observations,  which 
we  now  beg  to  lay  before  the  Society. 

1.  Mode  of  ‘producing  the  Ozone  (see  fig.). — The  ozone  in  the 
following  experiments  was  made  by  passing  a current  of  dry  air  or 


Description  of  Figure. — a,  glass  chamber  for  reception  of  the  animal;  b , 
gasometer ; the  current  of  air  or  gas  passed  from  right  to  left  of  diagram  ; 
c (to  the  right),  bulb-tube  containing  sulphuric  acid;  c (to  the  left),  bulb-tube 
containing  caustic  potash  or  water  ; d , U tube;  e , wire  from  — pole  of  induc- 
tion coil  continuous  with  platinum  wire  within  the  U tube;  f wire  from  -f- 
pole  of  induction  coil  continuous  with  copper  wire  coiled  round  U tube. 

oxygen  from  a gasometer  (5)  through  a narrow  glass  tube,  bent  for 
convenience  like  the  letter  Tj  ( d ),  about  3 feet  in  length,  and  con- 
taining a platinum  wire  2 feet  in  length,  which  had  been  inserted 
* British  Association  Reports,  1848. 


213 


of  Edinburgh,  Session  1873-74. 

into  the  interior  of  the  tube,  and  one  end  (e)  of  which  communi- 
cated with  the  outside  through  the  wall  of  the  tube.  Round  the 
whole  external  surface  of  this  U*shaped  tube  a spiral  of  copper 
wire  was  coiled,  and  the  induction  current  from  a coil  giving  |-inch 
sparks  was  passed  between  the  external  copper  (/)  to  the  internal 
platinum  wire  (e),  so  as  to  have  the  platinum  wire  in  the  interior 
of  the  tube  as  the  negative  pole.  After  the  current  of  gas  was 
ozonised  by  the  passage  of  the  induction  current,  it  was  washed 
by  passing  through  a bulb-tube  (c  to  the  left  of  the  U tube)  con- 
taining caustic  potash  when  air  was  employed,  or  water  when  pure 
oxygen  was  used,  in  order  to  eliminate  any  traces  of  nitrous  and 
nitric  acids.  To  the  right  of  the  U tube  another  bulb-tube  (c)  was 
placed  containing  pure  sulphuric  acid,  for  removing  aqueous 
vapour  from  the  air,  or  gas  passed  through  it.  By  means  of  the 
gasometer,  the  volume  of  gas  passing  through  the  apparatus  could 
be  ascertained. 

2.  Method  of  Experiment. — It  was  necessary,  in  the  first  place, 
to  determine  the  action  of  ozone  on  the  living  animal  imprisoned 
in  an  atmosphere  containing  a large  proportion  of  ozone ; and,  in 
the  second,  to  determine  What  action,  if  any,  it  exerted  on  the  indi- 
vidual living  tissues  of  the  body. 

Observations  were  made  on  frogs,  birds,  mice,  rabbits,  and  on 
ourselves. 

Frogs. — Numerous  experiments  were  made  on  frogs,  and  the 
general  effect  on  these  animals  is  as  follows  : — About  thirty  seconds 
after  introducing  the  animal  into  the  chamber,  through  which  a 
steady  current  of  ozonised  air  was  passing,  the  animal  manifested 
symptoms  of  distress.  The  eyeballs  were  retracted,  so  as  to  be 
deeply  sunk  in  the  orbits,  and  the  eyelids  were  firmly  closed.  It 
rubbed  its  nose  occasionally  with  its  fore  pawrs.  At  first  somewhat 
restless,  the  frog  became  lethargic,  and  the  movements  of  respira- 
tion were  reduced,  both  in  frequency  and  force,  to  at  least  one- 
half  the  normal  amount.  On  pushing  the  frog  with  a wire  it 
might  be  excited  to  move,  but  usually  it  remained  motionless.  The 
position  of  the  animal  was  peculiar — the  neck  arched,  the  head 
flattened,  and  it  remained  in  a crouching  attitude.  This  condition 
of  lethargy  has  been  observed  to  continue  during  a period  of  an 
hour  and  a half,  at  the  end  of  which  time  the  animal  died.  When 


214 


Proceedings  of  the  Royal  Society 

common  air  was  introduced  into  the  chamber  instead  of  ozonised 
air,  or  if  the  frog  was  taken  out  of  the  chamber,  it  quickly  recovered. 
These  effects  may  be  seen  in  the  following  experiment : — 

A large  healthy  frog  was  introduced  into  the  air-chamber,  through 
which  a current  of  air  was  passing  sufficient  to  fill  a litre  flask 
in  three  minutes.  At  the  end  of  two  minutes,  the  respirations  were 
96  per  minute.  The  induction  machine  was  then  set  to  work,  so  as 
to  mix  ozone  with  the  air,  the  current  passing  through  the  chamber 
at  the  same  rate.  In  half  a minute  the  eyes  were  affected,  and  the 
respirations  were  reduced  to  8 per  minute.  At  the  end  of  six 
minutes,  the  animal  was  quite  motionless,  and  the  respiratory 
movements  had  entirely  ceased.  Pure  air  was  then  introduced. 
In  half  a minute,  there  was  a slight  respiratory  movement,  and  in 
eight  minutes,  the  respirations  numbered  85  per  minute.  At  the 
end  of  other  twelve  minutes,  ozone  was  again  turned  on,  with  the 
same  results.  The  animal  in  this  experiment  was  then  subjected 
to  atmospheres  of  common  air  and  air  mixed  with  ozone  alter- 
nately, each  period  of  immersion  in  the  atmosphere  consisting  of 
ten  minutes,  with  invariably  the  same  effect.  At  the  end  of  two 
hours  it  was  removed  from  the  chamber,  and  recovered. 

In  the  case  of  the  frog  which  died  after  being  exposed  to  an 
atmosphere  of  ozonised  air  for  an  hour  and  a half,  the  heart  was 
found  pulsating  after  systemic  death.  It  was  full  of  dark-coloured 
blood.  The  lungs  were  slightly  congested.  In  every  part  of  the 
body  the  blood  was  in  a venous  condition. 

In  two  experiments,  frogs  were  exposed  to  the  action,  not  of  air 
mixed  with  ozone,  but  to  a stream  of  oxygen  mixed  with  ozone, 
and  the  results  were  somewhat  different  from  those  just  narrated. 
The  effects  were  not  so  well  marked.  When  a frog  was  introduced 
into  an  atmosphere  of  pure  oxygen,  the  animal  was  lively  and 
vivacious,  the  eyes  were  wide  open,  and  the  respiratory  movements 
were  greatly  accelerated.  But  when  the  oxygen  contained  a con- 
siderable quantity  of  ozone,  the  eyes  were  closed,  the  respiratory 
movements  did  not  entirely  cease,  but  were  reduced  from  100  or 
110  to  8 or  12  per  minute,  and  the  creature  was  in  a dormant  con- 
dition. After  exposure  for  a period  of  one  hour,  the  web  and  the 
skin  assumed  a purple  hue.  After  keeping  the  animal  in  such  an 
atmosphere  for  If  hour,  it  was  in  the  same  condition. 


215 


of  Edinburgh,  Session  1873-74. 

Birds. — A green  linnet  was  put  into  the  chamber,  supplied  with 
a strong  current  of  air.  At  the  end  of  five  minutes,  after  the  bird 
had  become  quiet,  the  respirations  were  50  per  minute.  The  air 
was  then  ozonised.  In  thirty  seconds,  the  eyes  were  closed ; in  one 
minute,  the  respirations  were  reduced  to  30  per  minute;  four  minutes 
thereafter,  the  respiration  was  slow  and  gasping,  and  the  number 
of  movements  15  per  minute ; and  in  ten  minutes,  that  is,  fifteen 
and  a half  minutes  after  the  introduction  of  ozonised  air,  the  bird 
was  dead.  On  opening  the  body,  there  was  venous  congestion  of  all 
the  viscera.  The  lungs  were  of  a dark  purple  colour,  and  showed 
a mottled  appearance.  The  heart  was  still  pulsating  feebly.  It 
was  full  of  venous  blood.  The  brain  was  pale.  The  blood  cor- 
puscles, when  examined  microscopically,  were  normal. 

Mammals. — Several  experiments  were  made  on  white  mice  and 
rabbits.  With  regard  to  mice,  the  general  effects  will  be  under- 
stood by  detailing  one  experiment.  A full-grown  and  apparently 
healthy  white  mouse  was  introduced  into  a vessel  through  which  a 
stream  of  air  was  passing  at  the  rate  of  8 cubic  inches  per  minute. 
Five  minutes  thereafter,  the  animal  was  evidently  at  ease,  and  the 
respirations  were  136  per  minute.  The  air  was  then  ozonised. 
One  minute  after,  the  respirations  were  somewhat  slower,  but  could 
not  be  readily  counted,  owing  to  the  animal  moving  uneasily  about 
and  rubbing  its  nose  with  its  fore  paws.  In  four  minutes  from  the 
time  of  introduction  of  the  ozone,  the  respirations  were  32  in  a 
minute.  The  mouse  now  rested  quietly,  occasionally  yawned,  and 
when  touched  by  a wire,  moved,  but  always  in  such  a direction  as 
to  place  its  head  away  as  far  as  possible  from  the  stream  of  ozonised 
air.  At  the  end  of  fifteen  minutes,  the  animal  became  excited,  ran 
rapidly  backwards  and  forwards,  and  then  had  a convulsive  attack. 
It  died,  much  convulsed,  nineteen  minutes  after  the  introduction  of 
the  ozone.  The  body  was  colder  than  natural.  There  was  venous 
congestion  of  all  the  abdominal  viscera.  The  heart  was  still  feebly 
pulsating,  and  the  right  auricle  and  ventricle  were  full  of  venous 
blood.  The  left  side  of  the  heart  contained  a small  quantity  of 
venous  blood.  The  sinuses  of  the  brain  were  full  of  dark  blood, 
and  the  surface  and  base  of  the  brain  was  traversed  by  vessels  con- 
taining dark-coloured  blood. 

Two  experiments  were  also  made  upon  mice,  in  which,  instead 

VOL.  VIII.  2 E 


216  Proceedings  of  the  Royal  Society 

of  being  supplied  with  ozonised  air,  they  received  ozonised  oxygen. 
When  a mouse  breathed  an  atmosphere  of  pure  oxygen,  it  became 
exceedingly  active  in  its  movements.  It  ran  about  examining 
every  part  of  its  prison,  and  breathed  with  such  rapidity  as  to 
make  it  impossible  to  count  the  number  of  respirations  taken  during 
a minute.  When  the  oxygen  was  ozonised,  the  mouse  quickly 
showed  the  usual  phenomena  of  the  closed  eyes  and  the  reduction 
of  the  number  of  respirations,  but  it  lived  for  a much  longer  period 
than  in  ozonised  air.  Instead  of  dying  at  the  end  of  fifteen  or 
twenty  minutes  after  the  introduction  of  the  ozonised  atmosphere, 
it  lived  for  thirty-five  or  forty  minutes.  The  number  of  respirations 
per  minute  became  smaller,  and  the  animal  died  in  severe  general 
convulsions.  The  blood,  when  examined  quickly  after  death,  has 
been  found  venous  in  all  parts  of  the  body.  In  both  experiments, 
the  temperature  of  the  body  was  found  to  be  much  reduced. 

As  the  reduced  temperature  of  the  body  in  these  experiments 
might  have  been  owing  to  the  current  of  gas  passing  quickly 
over  the  bodies  of  the  animals,  two  experiments  were  made,  in 
which  the  glass  air-chamber  was  immersed  in  a water-bath  kept  at 
a temperature  of  SO0  C.  The  animals  were  supplied  with  atmo- 
sphere at  the  rate  of  13  cubic  inches  per  minute.  The  general 
results  were  the  same  as  in  the  experiments  made  without  the 
water-bath,  but  the  temperature  of  the  body  on  death  was  still 
below  the  normal. 

Various  experiments  were  also  made  on  rabbits,  with  the  same 
general  results  as  in  the  case  of  mice.  There  was  evident  irrita- 
tion of  the  eyes,  causing  closure  of  the  lids,  and  the  exudation 
from  between  their  margins  of  a whitish  fluid,  probably  lachrymal 
secretion.  The  respirations  were  reduced  in  number  from  100  or 
110  to  from  36  to  30  per  minute.  In  one  experiment,  only  the 
head  of  the  rabbit  was  introduced  into  a glass  vessel,  into  which 
the  stream  of  ozonised  oxygen  was  transmitted  so  as  to  allow  the 
experimenter  to  count  by  touch  the  number  per  minute  of  the  pul- 
sations of  the  heart.  The  result  was,  that  immediately  on  the  in- 
troduction of  ozone  the  number  of  pulsations  was  much  diminished, 
and  the  force  of  the  contractions  of  the  heart  was  so  enfeebled  that 
it  could  not  be  felt  through  the  wall  of  the  thorax.  Still,  in  the 
bodies  of  rabbits  killed  in  an  atmosphere  of  ozonised  air,  or  of 


217 


of  Edinburgh,  Session  1873-74. 

ozonised  oxygen,  the  heart  was  found  pulsating,  and,  as  in  the  other 
cases,  engorged  with  venous  blood. 

On  breathing  an  atmosphere  of  ozonised  oxygen  ourselves,  the 
chief  effects  observed  were  a suffocating  feeling  in  the  chest,  a ten- 
dency to  breathe  slowly,  an  irritation  of  the  back  of  the  throat  and 
of  the  glottis,  and  a tingling  sensation,  referred  to  the  skin  of  the 
face  and  the  conjunctivas.  The  pulse  became  feebler.  After  breath- 
ing it  as  long  as  it  was  judicious  to  do,  say  for  five  or  eight  minutes, 
the  suffocating  feeling  became  stronger,  and  we  were  obliged  to 
desist.  The  experiment  was  followed  by  violent  irritating  cough 
and  sneezing,  and  for  five  or  six  hours  thereafter  by  a sensation  of 
rawness  in  the  throat  and  air-passages. 

The  action  of  ozone  on  several  of  the  chief  physiological  systems, 
and  on  various  tissues,  was  also  examined. 

1.  On  the  Circulation. — By  a suitable  apparatus,  a frog  was  im- 
prisoned in  a chamber  through  which  a stream  of  ozonised  air,  or 
of  ozonised  oxygen,  passed,  while  at  the  same  time  the  web  was  so 
placed  under  a microscope  that  the  circulation  in  the  smaller  ves- 
sels and  capillaries  could  be  readily  observed.  The  result  was  nega- 
tive, inasmuch  as  no  appreciable  acceleration  or  retardation  of  the 
current  of  the  circulation  was  seen. 

2.  On  the  Reflex  Action  of  the  Spinal  Cord. — This  function  was  not 
affected  to  any  appreciable  degree. 

3.  On  Muscular  Contractility. — By  means  of  a myographion,  the 
work  done  by  the  gastrocnemii  of  frogs,  subjected  to  the  action 
of  ozone,  was  noted.  The  muscles  were  stimulated  by  a single 
opening  or  closing  induction  shock  produced  by  Du  Bois  Reymond’s 
apparatus  and  a Daniell’s  cell.  The  result  was  that  the  contractility 
and  work-power  of  the  muscle  were  found  unaffected,  as  far  as  could 
be  appreciated. 

4.  On  the  Blood. — When  a thin  layer  of  human  blood  on  a slide 
is  exposed  to  the  action  of  ozone,  the  coloured  corpuscles  become 
paler,  lose  their  definite  outline,  and  if  exposed  for  a period  of  five 
or  ten  minutes  to  the  action  of  the  current,  they  are  dissolved,  and 
a mass  of  molecular  material  is  seen.  The  coloured  corpuscles  of 
the  frog  show,  after  the  action  of  ozone,  the  formation  of  a nucleus. 
By  prolonged  exposure  many  of  the  nuclei  apparently  pass  out  of 
the  substance  of  the  corpuscle,  numerous  free  nuclei  are  seen,  and 


218  Proceedings  of  the  Royal  Society 

some  in  the  act  of  separating  from  the  corpuscle  have  been  ob- 
served. The  colourless  corpuscles  are  contracted  into  globular 
masses  after  the  action  of  ozone.  The  general  effects  resemble 
those  produced  by  a weak  acid,  sucb  as  very  dilute  acetic  acid  or  a 
stream  of  carbonic  acid. 

5.  On  Ciliary  Motion. — When  the  cilia  of  the  common  mussel 
(Mytilus  edulis ) were  exposed  to  the  action  of  ozone,  while  bathed 
in  the  fluid  contained  in  the  shell  (sea- water),  no  effect  was  observed. 
This  is  owing  to  the  protection  to  the  cilia  afforded  by  the  water. 
If  a very  small  amount  of  water  covered  the  cilia,  their  action  was 
at  once  arrested. 

From  the  preceding  experiments  the  following  general  facts 
m ay  be  stated  : — 

1.  The  inhalation  of  an  atmosphere  highly  charged  with  ozone 
diminishes  the  number  of  respirations  per  minute. 

2.  The  pulsations  of  the  heart  are  reduced  in  strength,  and  this 
organ  is  found  beating  feebly  after  the  death  of  the  animal. 

3.  The  blood  is  always  found  in  a venous  condition  in  all  parts 
of  the  body,  both  in  cases  of  death  in  an  atmosphere  of  ozonised 
air  and  of  ozonised  oxygen. 

4.  Ozone  exercises  a destructive  action  on  the  living  animal  tis- 
sues if  brought  into  immediate  contact  with  them ; but  it  does  not 
affect  them  so  readily  if  they  are  covered  by  a layer  of  fluid. 

5.  Ozone  acts  as  an  irritant  to  the  mucous  membrane  of  the 
nostrils  and  air-passages,  as  all  observers  have  previously  remarked. 

At  the  present  state  of  this  inquiry,  it  would  be  premature  to 
generalise  regarding  the  relation  between  physiological  action  and 
the  chemical  properties  of  ozone ; but  we  can  hardly  avoid  pointing 
out  that  oxygen  in  this  altered  condition  (03  = 24)  is  slightly  denser 
than  carbonic  acid  (C02=  22),  and  that,  although  the  chemical  acti- 
vity of  the  substance  is  much  increased,  yet  when  inhaled  into  the 
lungs,  it  must  retard  greatly  the  rate  of  diffusion  of  carbonic  acid 
from  the  blood,  which  accounts  for  the  venous  character  of  that 
fluid  after  death.  If,  however,  the  physiological  effect  of  ozone  on 
respiration  were  merely  due  to  its  greater  density,  then  we  would 
expect  its  behaviour  to  be  analogous  to  that  of  an  atmosphere 
highly  charged  with  carbonic  acid.  This  has  been  found  to  be 
the  case,  more  especially  as  regards  the  diminished  number  of  re- 
spirations per  minute,  and  the  appearance  of  the  blood  after  death. 


219 


of  Edinburgh,  Session  1873-74. 

If,  however,  this  analogy  were  perfect,  we  would  anticipate  that  the 
action  of  oxygen,  partially  ozonised,  would  not  have  produced 
death,  as  the  amount  of  ozone  in  these  experiments  certainly  did 
not  exceed  10  per  cent.  As  it  was,  all  we  have  observed  is  that  the 
animal  only  lives  a somewhat  longer  time  in  ozonised  oxygen  than 
in  ozonised  air.  We  are  thus  induced  to  regard  ozone  as  having 
some  specific  action  on  the  blood,  or  in  the  reflex  nervous  arrange- 
ments of  respiration,  that  future  experiments  may  elucidate. 

4.  On  a Compound  formed  by  the  addition  of  Bromacetic 
Acid  to  Sulphide  of  Methyl,  and  on  some  of  its  Deriva- 
tives. By  Professor  Crum  Brown  and  Dr  E.  A.  Letts. 

(. Abstract .) 

The  sulphine  compounds  discovered  by  v.  Oefele,  indicate  that, 
notwithstanding  the  difference  of  atomicity,  there  exists  an  analogy 
between  sulphur  and  nitrogen,  these  compounds  corresponding  to 
the  salts  of  the  ammonium  bases,  not  only  in  chemical  properties 
but  also  in  physiological  action.* 

The  research,  the  results  of  which  are  communicated  in  this 
paper,  was  undertaken  with  the  view  of  examining  this  analogy 
in  some  other  directions. 

It  seemed  reasonable  to  suppose  that,  as  the  nitrile  bases,  such  as 
trimethylamine  and  strychnia  unite  with  chloracetic  acid  to  form 
compounds  such  as  hydrochlorate  of  betaine  and  of  glycolyl- 
strychnia,  the  sulphides  of  the  alcohol  radicals  should  act  in  a 
similar  way.  Experiments  show  that  this  is  the  case — bromacetic 
acid  acting  readily  on  sulphide  of  methyl  to  form  a beautifully 
crystallised  compound  to  which  the  authors  give  the  name  of 
hydrobromate  of  methyl-thetine.  Analyses  proved  this  substance 
to  have  the  composition  corresponding  to  the  formula  C4H9SBr02 
which  is  that  of  the  sulphur  analogue  of  the  hydrobromate  of 
betaine. 

(CH3)2  (CH3)3 

II  III 

Br - S — CH2 - COOH  ; Br- N -CHa- COOH 

hydrobromate  of  methylthetine.  hydrobromate  of  betaine. 

This  view  of  its  constitution  is  confirmed  by  its  reactions. 

* Brown  and  Fraser,  “ Proc.  Royal  Soc.  Edin.,”  March  4th,  1872. 


220 


Proceedings  of  the  Royal  Society 

In  addition  to  this  substance,  which  served  as  a starting-point 
for  the  research,  the  nitrate,  the  chloroplatinate,  the  chloraurate, 
the  bromaurate,  and  compounds  formed  by  the  action  of  the  hydro- 
bromate  on  the  oxides  of  mercury,  copper,  and  lead,  on  ammonia 
and  on  ethylate  of  sodium  were  examined. 

Corresponding  addition  products  of  sulphide  of  ethyl  were  also 
prepared,  but  owing  to  the  extremely  deliquescent  character  of 
the  hydrobromate  of  ethyl-thetine,  attention  was  chiefly  devoted 
to  the  derivatives  of  the  methyl  compound. 

Iodacetic  ether  does  not  form  an  addition  product  with  sulphide 
of  methyl.  The  reaction  here  takes  a different  direction,  free 
iodine  and  iodide  of  trimethylsulphine  being  produced.  The 
authors  are  engaged  in  the  investigation  of  this  reaction,  and  also 
of  the  products  of  the  oxidation  of  the  thetine  compounds. 

5.  Note  on  the  Various  Possible  Expressions  for  the  Force 
Exerted  by  an  Element  of  one  Linear  Conductor  on  an 
Element  of  another.  By  Professor  Tait. 

In  the  Quarterly  Mathematical  Journal  for  1860,  I gave  a 
quaternion  process  for  obtaining  in  a very  simple  manner,  from 
Ampere’s  experimental  data,  his  well-known  expression  for  the 
mutual  action  between  two  elements  of  currents.  As  one  of  the 
data  the  assumption  was  made,  after  Ampere,  that  the  action  is  a 
force  whose  direction  is  that  of  the  line  joining  the  middle  points 
of  the  elements,  i.e .,  it  was  assumed  that  the  necessary  equality  of 
action  and  reaction  holds,  not  merely  for  two  closed  circuits  but,  for 
each  pair  of  elements  of  these  circuits.  I promised  in  that  paper  to 
publish  a more  general  investigation,  in  which  no  such  assumption 
should  be  made ; but  I was  prevented  from  doing  this  by  having 
seen  a reference  to  a memoir  by  Cellerier,  in  which  it  was  stated 
that  such  an  investigation  had  been  given.  I did  not,  till  very  re- 
cently, succeed  in  getting  any  information  about  that  memoir,  none 
of  which  seems  indeed  to  have  been  printed  except  a very  brief 
extract  in  the  Gomptes  Rendus  for  1850,  vol.  xxx.,  giving  no 
details:  but  the  subject  was  recalled  to  my  memory  by  Clerk- 
Maxwell’s  Treatise  on  Electricity , &c .,  in  which  there  is  an  investi- 


221 


of  Edinburgh,  Session  1873-74. 

gation  of  the  possible  expressions  for  the  forces  which  satisfy 
Ampere’s  data  without  necessarily  satisfying  his  assumption.  Both 
of  these  authors  make  the  undetermined  part  of  the  expression 
depend  upon  a single  arbitrary  function.  My  investigation  leads 
to  two.  The  question  is  one  of  comparatively  little  physical 
importance,  but  I give  this  investigation  for  its  extreme  sim- 
plicity. 

The  following  is,  as  nearly  as  I can  recollect,  my  original  pro- 
cess, which  has,  at  least  at  first  sight,  nothing  in  common  with 
that  of  Clerk-Maxwell. 

1.  Ampere’s  data  for  closed  currents  are  briefly  as  follows : — 

1.  Reversal  of  either  current  reverses  the  mutual  effect. 

II.  The  effect  of  a sinuous  or  zig-zag  current  is  the  same  as  that 
of  a straight  or  continuously  curved  one,  from  which  it  nowhere 
deviates  much. 

III.  No  closed  current  can  set  in  motion  a portion  of  a circular 
conductor  movable  about  an  axis  through  its  centre,  and  perpen- 
dicular to  its  plane. 

IY.  In  similar  systems,  traversed  by  equal  currents,  the  forces 
are  equal. 

2.  First,  let  us  investigate  the  expression  for  the  force  exerted 
by  one  element  on  another. 

Let  a be  the  vector  joining  the  elements  a19  a of  two  circuits  ; 
then,  by  I.,  II.,  the  action  of  aL  on  a'  is  linear  in  each  of  a15  a', 
and  may,  therefore,  be  expressed  as 

K, 

where  p is  a linear  and  vector  function,  into  each  of  whose  con- 
stituents cq  enters  linearly. 

The  resolved  part  of  this  along  a is 

S . T5a!tpa  , 

and,  by  III.,  this  must  be  a complete  differential  as  regards  the 
circuit  of  which  al  is  an  element.  Hence, 

(pa'  = - (S  . af7)if/a'  + Va'xoq  , 

where  if/  and  x are  linear  and  vector  functions  whose  constituents 


222 


Proceedings  of  the  Royal  Society 

involve  a only.  That  this  is  the  case  follows  from  the  fact  that 
pa'  is  homogeneous  and  linear  in  each  of  av  a'.  It  farther  follows, 
from  IV.,  that  the  part  of  pa'  which  does  not  disappear  after 
integration  round  each  of  the  closed  circuits  is  of  no  dimensions 
in  Ta,  Ta,  Tax.  Hence  ^ is  of  - 2 dimensions  in  Ta,  and  thus 

_ paSaa,  qa}  rYaax 

X 1 Ta4  Ta2  + Ta3 


where  p,  q,  r are  numbers. 
Hence  we  have 


_ / q/  ^7\  » / . pVaa'Saa.  qYa'a. 
pa'  = - S(a1V)'K  + Ta4— t + 


rY.a'Y  aax 
+ Ta? 


Change  the  sign  of  a in  this,  and  interchange  a'  and  ax,  and  we 
get  the  action  of  a on  ax.  This,  with  a and  ax  again  interchanged, 
and  the  sign  of  the  whole  changed,  should  reproduce  the  original 
expression — since  the  effect  depends  on  the  relative,  not  the  abso- 
lute, positions  of  a,  a1?  a.  This  gives  at  once, 


and 


P = o , q = 0, 

rY.a'Y  aa. 


pa'  = — S(a1V)i^a/  + • 


Ta3 


with  the  condition  that  the  first  term  changes  its  sign  with  a,  and 
thus  that 

pa'  = aSaa'F(Ta)  4-  a'F(Ta), 
which,  by  change  of  F,  may  be  written 

= aS(a'V)/(Ta)  + a'F(Ta)  , 


where  / and  F are  any  scalar  functions  whatever. 
Hence 

pa'  = - S(a1V)[aS(a'V)/(Ta)  + a'F(Ta)]  + 


rY.a'Yaax 

Ta3 


which  is  the  general  expression  required. 

3.  The  simplest  possible  form  for  the  action  of  one  current- 
element  on  another  is,  therefore, 


pa 


rY.a'Yaax 

TW3 


of  Edinburgh,  Session  1873-74.  223 

Here  it  is  to  be  observed  that  Ampere’s  directrice  for  the  circuit 
cq  is 


the  integral  extending  round  the  circuit;  so  that,  finally, 

<pa  — - rSoqVVa'0  . 

4.  We  may  obtain  from  the  general  expression  above  the  abso- 
lutely symmetrical  form, 

rV.  a/acq 
TW*  ’ 

if  we  assume 

/( Ta)  = const , F (Ta)  = ~ . 

Here  the  action  of  a'  on  ax  is  parallel  and  equal  to  that  of  cq  on  a'. 
The  forces,  in  fact,  form  a couple,  for  a is  to  be  taken  negatively 
for  the  second — and  their  common  direction  is  the  vector  drawn  to 
the  corner  a of  a spherical  triangle  a be,  whose  sides  ab,  be,  ca  in  order 
are  bisected  by  the  extremities  of  the  vectors  Ua',  Ua,  Ucq.  Com- 
pare Hamilton’s  Lectures  on  Quaternions , §§  223-227. 

5.  To  obtain  Ampere’s  form  for  the  effect  of  one  element  on 
another  write,  in  the  general  formula  above, 

/(Ta)  = ^ , F(Ta)  = 0 , 

and  we  have 

1 . , o « F aSaa'~l  V.a'Vaa, 

avJT— ’ 

_ _ c^Saa'  aSctja'  SaSaa/Sacq  ( V.a'Vaa, 

~Ta?  TV~  ~ Ta5  + ’ 

==  + ~ Saa'Saa^  , 

= — ,YaaYaax  -f  ^ Saa'Saa^  , 

which  are  the  usual  forms. 

6.  The  remainder  of  the  expression,  containing  the  arbitrary 
terms,  is  of  course  still  of  the  form 

- S(aiV)  [aS(a'V)/(Ta)  + a'F(Ta)]  . 

2 f 


VOL.  VIII. 


224 


Proceedings  of  the  Royal  Society 


In  the  ordinary  notation  this  expresses  a force  whose  components 
are  proportional  to 


(1.)  Along  a 


(Note  that,  in  this  expression,  r is  the  distance  between  the  ele- 
ments.) 

(2.)  Parallel  to  a' 

dsx 

(3.)  Parallel  to  o,  -df,. 


If  we  assume  f = F = - Q,  we  obtain  the  result  given  by  Clerk- 
Maxwell  ( Electricity  and  Magnetism , § 525),  which  differs  from 
the  above  only  because  he  assumes  that  the  force  exerted  by  one 
element  on  another  when  the  first  is  parallel  and  the  second  per- 
pendicular to  the  line  joining  them  is  equal  to  that  exerted  when 
the  first  is  perpendicular  and  the  second  parallel  to  that  line. 

7.  What  precedes  is,  of  course,  only  a particular  case  of  the 
following  interesting  problem  : — 

Required  the  most  general  expression  for  the  mutual  action  of  two 
rectilinear  elements , each  of  which  has  dipolar  symmetry  in  the  direc- 
tion of  its  length , and  which  may  be  resolved  and  compounded  accord- 
ing to  the  usual  kinematical  law. 

The  data  involved  in  this  statement  are  equivalent  to  I.  and  II. 
of  Ampere’s  data  above  quoted.  Hence,  keeping  the  same  nota- 
tion as  in  § 2 above,  the  force  exerted  by  cq  on  a must  be  ex- 
pressible as 

<pd 


where  <p  is  a linear  and  vector  function,  whose  constituents  are 
linear  and  homogeneous  in  cq ; and,  besides,  involve  only  a. 

By  interchanging  cq  and  a,  and  changing  the  sign  of  a,  we  get 
the  force  exerted  by  a on  cq.  If  in  this  we  again  interchange  cq 
and  a , and  change  the  sign  of  the  whole,  we  must  obviously  repro- 
duce (pa'.  Hence  we  must  have  pa'  changing  its  sign  with  a,  or 

p>a  — PaScqa/  + QaSacqSaa  + RcqSaa/  + Ra'Sacq 
where  P,  Q,  R,  R are  functions  of  Ta  only. 


of  Edinburgh,  Session  1873-74.  225 

8.  The  vector  couple  exerted  by  aL  on  a!  must  obviously  be  ex- 
pressible in  the  form 

V.a Va,  , 

where  w is  a new  linear  and  vector  function  depending  on  a alone. 
Hence  its  most  general  form  is 

-nax  — Poq  + QaSacq , 

where  P and  Q are  functions  of  Ta  only.  The  form  of  these  func- 
tions, whether  in  the  expression  for  the  force  or  for  the  couple, 
depends  on  the  special  data  for  each  particular  case.  Symmetry 
shows  that  there  is  no  term  such  as 
RVaoq . 

9.  As  an  example,  let  cq  and  a be  elements  of  solenoids  or  of 
uniformly  and  linearly  magnetised  wires,  it  is  obvious  that,  as  a 
closed  solenoid  or  ring-magnet  exerts  no  external  action, 

(pa  = — ScqV.  \f/a' . 

Thus  we  have  introduced  a different  datum  in  place  of  Ampere’s 
No.  III.  But  in  the  case  of  solenoids  the  Third  Law  of  Newton 
holds — hence 

<pa'  = Sc^VSaV.^a , 

where  x is  a linear  and  vector  function,  and  can  therefore  be  of  no 
other  form  than 

af  (To). 

Now  two  solenoids,  each  extended  to  infinity  in  one  direction,  act 
on  one  another  like  two  magnetic  poles,  so  that  (this  being  our 
equivalent  for  Ampere’s  datum  No.  IV.) 


Hence  the  vector  force  exerted  by  one  small  magnet  on  another  is 

pS^VSa'V^. 

10.  For  the  couple  exerted  by  one  element  of  a solenoid,  or  of 
a uniformly  and  longitudinally  magnetised  wire,  on  another,  we  have 
of  course  the  expression 

V.  a' zzrax , 

where  w is  some  linear  and  vector  function. 


226  Proceedings  of  the  Royal  Society 

Here,  in  the  first  place,  it  is  obvious  that 

- - SaxV.  =^5 
F(Ta) 

for  the  couple  vanishes  for  a closed  circuit  of  which  ax  is  an  ele- 
ment, and  the  integral  of  wax  must  be  a linear  and  vector  function 
of  a alone.  It  is  easy  to  see  that  in  this  case 

F(Ta)  a (Ta)3  . 

11.  If,  again,  be  an  element  of  a solenoid,  and  a'  an  element  of 
current,  the  force  is 

pa  = — Sc^V.  \(/a' , 

where 

\pa'  = Pa'  + QaSaa'  -I-  RVaa' . 

But  no  portion  of  a solenoid  can  produce  a force  on  an  element  of 
current  in  the  direction  of  the  element,  so  that 

(pa  = Y.a'x<hi 

P '=  0,  Q = 0, 

pa  = — SajV^Vaa') . 

This  must  be  of  - 1 linear  dimensions  when  we  integrate  for  the 
effect  of  one  pole  of  a solenoid,  so  that 

T?  = M 
K Ta3  * 

If  the  current  be  straight  and  infinite  each  way,  its  equation  being 
a = /3  + xy , 

where 

Ty  = 1 and  S/?y  = 0 , 

we  have,  for  the  whole  force  exerted  on  it  by  the  pole  of  a solenoid, 
the  expression 


so  that 
and  we  have 


ppy 

J C. 


+ GO 


dx 


- 2pP~'y, 


which  agrees  with  known  facts. 

12.  Similarly,  for  the  couple  produced  by  an  element  of  a solenoid 
on  an  element  of  a current  we  have 
YaW,  , 


where 


of  Edinburgh,  Session  1873-74.  227 

zrcL^  = — SaxV.  \f/a  , 
and  it  is  easily  seen  that 

, ra 
^=5V- 

13.  In  the  case  first  treated,  the  couple  exerted  by  one  current- 
element  on  another  is  (§  8 above) 

V.  a/srC^  , 

where,  of  course,  ± wax  are  the  vector  forces  applied  at  either  end 
of  a.  Hence  the  work  done  when  a changes  its  direction  is 
— S.SaVc^  , 

with  the  condition 

S.a'Sa'  = 0 . 

So  far,  therefore,  as  change  of  direction  of  a alone  is  concerned, 
the  mutual  potential  energy  of  the  two  elements  is  of  the  form 

S.a^Oj . 

This  gives,  by  the  expression  for  w in  § 8,  the  following  value 
PSa'c^  + QSaa/SaaL . 

Hence,  integrating  round  the  circuit  of  which  ax  is  an  element,  we 
have  ( On  Green's  and  other  Allied  Theorems , § 11,  Trans.  H.S.E., 
1869-70) 

y^PSactj  -f-  QSaa'Sac^)  = ff isfi . U V (P a -f-  QaSaa')  , 

=//d,ls.Vv1  - «-oq)  , 

= ffds1$.TJv1Vaa<&  , 

where 

*=Ta+Q- 

Integrating  this  round  the  other  circuit  we  have  for  the  mutual 
potential  energy  of  the  two,  so  far  as  it  depends  on  the  expression 
above,  the  value 

ffdsfi.UvJYaa'Q 
= - ffdsfi.VvJfds'V.YiVv'vy® 

= ffdsJfd»'  •[  S.UnW(2$  + Tatf)  + SaWSaUv,  ?L  J . 


228 


Proceedings  of  the  Royal  Society 


But,  by  Ampere’s  result,  that  two  closed  circuits  act  on  one  another 
as  two  magnetic  shells,  it  should  be 

ff is-JfdsS . U V S . Ui/ V 

= ffdsiffds'(  S.UVJV  + 3 SaUv'SaUi/,  -j-g)  . 


Comparing,  we  have 


giving 


Taa 


=s  Ta<£' 


. 1^3 

® = — — , <p  — . 

Ta3  ’ Ta4  ’ 

which  are  consistent  with  one  another,  and  which  lead  to 


V ,Q  = _ J_ 

Ta  + ^ Ta3 


Hence,  if  we  put 
we  get 


Q = 

P 


1 - n 
2wTa3 1 

1 -\-n 
' 2^Ta’ 


and  the  mutual  potential  of  two  elements  is  of  the  form 


which  is  the  expression  employed  by  Helmholtz  in  his  recent 
paper.  (Ueber  die  Bewegungsgleichungen  der  Rlectricitdt,  Crelle, 
1870,  p.  76.) 


of  Edinburgh,  Session  1873-74. 


229 


Monday,  22 d December  1873. 

Sir  W.  THOMSON,  President,  in  the  Chair. 

Professor  Andrews,  Hon.  F.R.S.E.,  Vice-President  of 
Queen's  College,  Belfast,  gave  an  Address  on  Ozone. 

Monday,  5th  January  1874. 

Professor  Sir  WILLIAM  THOMSON,  President, 
in  the  Chair. 

The  following  Communications  were  read  ■ 

1.  A new  Method  of  Determining  the  Material  and  Thermal 

Diffusivities  of  Fluids.  By  Sir  William  Thomson. 

2.  Continuants — A New  Special  Class  of  Determinants. 
By  Thomas  Muir,  M.A.,  Assistant  to  the  Professor  of 
Mathematics  in  the  University  of  Glasgow. 

1.  A determinant  which  has  the  elements  lying  outside  the 
principal  diagonal  and  the  two  bordering  minor  diagonals  each 
equal  to  zero,  and  which  has  the  elements  of  one  of  these  minor 
diagonals  each  equal  to  negative  unity,  may  be  called  a Continuant. 
Thus 

al  bl  0 0 

- 1 a2  b.2  0 

0-1  as  b a 

0 0-1  a. 

is  a continuant  of  the  fourth  order. 

2.  A continuant  is  evidently  a function  of  the  elements  of  the 
principal  diagonal  and  the  variable  minor  diagonal,  and  of  these 
alone.  Let  this  function  be  denoted  by  K.  The  above  continuant, 
for  example,  may  then  be  written 


230 


Proceedings  of  the  Royal  Society 


3.  By  the  cyclical  transposition  of  rows  and  thereafter  of 
columns,  we  establish  a first  law  of  continuants,  viz. : — 

k(  b‘ b — 1 )Ak(  J”-1 . (I.) 

\ax  a2  . . . . an_1  aj  \an  an_1  . ...  a2  aj  v ' 

4.  By  expansion  of  the  continuant  in  terms  of  its  principal 
minors  we  have 


K 


fb' J— 1 ) = a^(  b* 6-'  ) + bfi(  l* ' ' ■ b ) (II.) 

• • • <WV  1 W* a • • • <WV  1 V«3  • • • v 7 


5.  From  this  we  see  how  to  evaluate  a continuant  for  special 
values  of  its  elements,  and  also  to  change  a continuant  into  the 
ordinary  notation,  i.e.>  to  free  it  of  determinant  forms.  Thus, 

K/  4 6 S 9 7 \ 

K \7  2 3 1 4 5J 

would  be  evaluated  by  first  evaluating  K ^ > thence  K ^ , 


thence  K 


/ W)  7 \ 
\3  1 4 5/ 


and  so  on. 


6.  By  means  of  Laplace’s  expansion-theorem  we  can  establish  a 
result  which  includes  (II.)  viz., 


K 


('  h ®*-i  ^ = kY  ^ “ ^-1  ^ K ( ^+1  * * * ^ 

\aLa2  ...ap...  an_xaj  \aLa2 ap  ) \ap+1 an  ) 


+ IJl(  bl  br+f-bn-i 

Vh. ap-\J  vh>+2 an) 

(in.); 

and,  using  instead  the  present  author’s  extension  of  Laplace’s 
theorem,  we  arrive  at  a still  more  general  proposition,  viz., 

kY  • * * ^-1  \k(  ‘ ‘ V-1  \ 

W*a W V 

= kY  ^eY  ^ 

V«i <v  w °v 

(iv.), 


of  Edinburgh,  Session  1873-74.  231 


where  of  course  h<p<n.  An  important  particular  case  is  that 
for  which  p = n-l  and  h = 2. 

7.  Another  result  which  is  easily  proved  by  induction  is 


:(  1 1 )={-iyK(  b*-')  . (Y.) 

\-«l,  -«./  ' V«l«-  • • ' ' 


8.  In  any  continuant 


K f • • • . K-i  \ 
a„  j 


we  may  call  an_x an  the  ' main  diagonal , and  bfi.2 .....  bn_x 

the  minor  diagonal ; ay , a2 , , blt  &2, . . . . being  known  as 

elements.  When  each  element  of  the  minor  diagonal  is  unity,  the 
continuant  may  be  called  simple , and  in  writing  such  continuants 
we  may  agree  to  omit  the  minor  diagonal,  putting,  for  example, 


K («1a2a3 ....  for  K 


'11.. 

A «a  «3- 


9.  If  the  elements  of  the  first  column  of  the  determinant 
K(1  axal . . . an)  be  subtracted  from  the  corresponding  elements  of 
the  second  column,  it  will  be  seen  that 

K (1,  ax , a2 , . . . an)  = K (aL  + 1 , a2 , . . . aH)  . (VI.) 


10.  From  (II.)  it  is  clear  that 


K (0  , a2 , a3 , . . . a J = K (a3 . . . aH)  , 
thence,  with  the  help  of  (III.),  we  can  show  that 
K (. . . a,  b,  c,  0,  e j,  g, , . . ) = K ( . . . a,  b,  c + e,f,  g, . . . ) (VII.), 
and  from  this  that 

K ( . . . a,  b,  c,  0,  0,  0,  e,/, . ..)  = K(.  . . a,  b,  c + e,/, . . .) 

and  so,  generally,  when  the  number  of  consecutive  zero  elements  is 
odd. 

11.  Similarly,  from  (II.) 

K (0,  0,  a.6,  a4,  . . . an ) - K (a.i9  a49  . . . an)  , 

2 o 


VOL.  VIII. 


232  Proceedings  of  the  Royal  Society 

and  from  this,  with  the  help  of  (III.),  we  can  prove  that 

K (...  a,  &,0,0,e, /,...)  = K(...a,  b,e,f ,...)  . (VIII.), 

and  so,  generally,  when  the  number  of  consecutive  zero  elements  is 
even. 

12.  Using  the  ordinary  process  of  finding  the  greatest  common 
measure  of  two  numbers,  we  may  establish  another  special 
property  of  simple  continuants,  viz.,  that,  whatever  alt  aa,  . . . 
may  be, 

K On  •••«*-!>  O 

is  prime  to 

K (a„  <J2,  . K(oa,  a.),  K (a,  - 1,  a„  . . . a,),  and 

K(°i>  »«>  ••  •“»-!)« 

13.  When  both  diagonals  of  a continuant  are  the  same  when 
read  backwards  as  when  read  forwards,  it  may  be  called  symme- 
trical. 

In  connection  with  simple  symmetrical  continuants,  the  follow- 
ing identities  may  be  mentioned  : — 

K (aL,  a2 , . .. oM_1}  an , an_x ,...oa,a1)  = K(a1,as,... an_i) { K (ax , as aw_2) 
+ K (alt  a2J...an)}  (IX.) 

K (a1}  a2,  ...  tfn,  an, a2,  aA)  = K (a1?  a2, . . . an_i)2 

+ K (a1?  a2,  . .• . aw)2  (X.) 

«w-1v..fta,a1)=K(aJ,oa..^l()2 

. - K Ol,«2J  •■•«n-2)2  (XI.) 

K(aA,  a2,...an_15  2on,  aj=  2K(a1,  K (alf  a2,...an) 

(XII.) 

Connection  between  Continuants  and  Continued 
Fractions. 

14.  The  value  of  the  special  study  of  this  class  of  determinants 
lies  in  the  fact  that  by  means  of  them  the  convergents  of  a con- 


of  Edinburgh,  Session  1873-74.  233 

tinued  fraction  are  expressible  in  an  unexpectedly  simple  and 
elegant  manner.  Thus — 


and  thus  by  induction  we  prove  that — 


a2  + a3  + 

15.  In  virtue  of  this  connection  continuants  will  be  found  of  the 
utmost  aid  in  investigating  the  properties  of  continued  fractions. 
The  following  are  a few  instances  of  this  relating  to  those  con- 
tinued fractions  which  are  expressible  in  the  form  of  quadratic 
surds. 

16.  Consider  the  periodic  continued  fraction — 


K-i 


* • • 4"  «»_  1 + 


( h \ \ 

' \a, .a.-i,  aj 
k(  h 2 h"~l  ) 

\a,,a3.  ..  o._, , aj 


(XIII.) 


a + : 


«i  + (l2  + d3  -f 


+ a2  + ax  + 2A  + , 


where  the  asterisks  are  used  like  the  superposed  dots  in  the  nota- 
tion of  decimal  fractions  to  indicate  the  recurring  portion  or 
period. 


234 


Proceedings  of  the  Royal  Society 


Denoting  it  by  x,  we  have 

a , b,  b,  A b,  b 

ax  + a2  4-  . . . + «2  + «i  4-  2A  + x - A 

^2  ^1  \ 

_ \A,  , a2 . . . . a2 , cq,‘  A 4-  xj 

~ “K/  &2 &2  b y’ 

W ^ «2>  «d  A + a;/ 

whence  it  can  be  shown  that 

^2 ) = k(  K ^ ^3“  * 

\«15  «2 a2»  V W ®1,  a2  * 

and  thus  we  have  the  theorem— 

&,  K bA  b. 


\ \ \ 
, «i»  A/ 


A 4- 


4"  tt2  "b  C%  + • • • + + «!  + 2A  + 

* * 

/x(  »■  \) 

/ \A,  «l,  «2 «2,  «1,  A/ 

./  xf5- j=  y 

N/  \alt  . . . . a2,  aj 


(XIV.) 


17.  From  (XIV.)  it  is  easy  to  deduce  a series  of  identities  ex- 
in continuants,  viz., 


/ 6,  h \ ll  \ X(  Jl  ^ ^ A J2  hl  \ 

" \A , «, , a3...ffl2, «[ , A/  A)  „ 

K/  A- *2  V V Kf  *• :*.  *•  6.  M ’ &°-  ( V / 

\aD  ^2***®2)  %/  v^n  ^2,,,®2»(*i)  2A,  aLJ  a2..,a2J  ai) 


18.  With  the  help  of  (XIV.)  we  can  also  establish  an  important 
proposition  in  reference  to  the  well-known  subject  of  the  expres- 
sion of  the  square  root  of  an  integer  as  a continued  fraction  with 
unit-numerators.  The  proposition  is : — The  general  expression 
for  every  integer  whose  square  root  when  expressed  as  a continued 
fraction  with  unit  numerators  has  q2,  . . . q2,  q1  for  the  symmetric 
portion  of  its  cycle  of  partial  denominators  is 

(<Zi  j Vi  ? • • • 9.2  > fZi)  m ~~  ( ~ l)1  k G?i » 9.2  > • • • 9.2)  ( 9.2  • • • 9.2)  } 2 

+ K (<?,...&)  m - ( - 1)'  K (q2 . . . qxy  . (XVI.), 

I being  the  number  of  elements  in  the  cycle. 


of  Edinburgh , Session  1873-74. 


235 


This  is  established  by  taking  the  general  expression  for  every 
such  number,  fractional  as  well  as  integral,  viz., 


and  proceeding  to  determine  what  form  for  A is  necessary  and 
sufficient  to  make  this  expression  integral.  The  form  found  is 


and  substituting  this  for  A in  (a),  we  arrive  at  the  expression 
(XVI.)  after  some  reduction. 

19.  Further,  no  integer  can  be  found  whose  square  root  when 
expressed  as  a continued  fraction  with  unit-numerators  has 
!2i>  9.2  • • • 9A  2i  f°r  the  symmetric  portion  of  it's  cycle  of  partial 
denominators,  unless  either  K(^1 . . . ^2)  or  K(g2  . . . g2)  be  even. 
This  is  deducible  from  the  preceding. 

20.  Many  interesting  results  may  also  be  arrived  at  in  reference 
to  the  possibility  of  expressing  in  more  ways  than  one  by  a con- 
tinued fraction  the  square  root  of  any  number. 

All  that  is  requisite  in  order  to  find  as  an  equivalent  for  any 
quadratic  surd,  J18  say,  a periodic  continued  fraction  with  a 
period  of  any  given  number  of  elements,  say  5,  is  the  solution  in 
integers  of  an  indeterminate  equation  of  the  form 


21.  This  leads  to  the  consideration  of  the  various  identical 
forms  of  periodic  continued  fractions,  and  on  this  subject  much 
may  be  learned.  As  an  instance,  we  may  show  how  a continued 
fraction  with  unit-numerators,  such  as  is  found  in  the  usual  way 
as  the  equivalent  of  a quadratic  surd,  may  always  be  reduced  to  a 
periodic  continued  fraction  with  only  three  elements  in  its  period. 
The  identity  is 


K(A>  2.;2a---2a;2l.A) 
K (?,,  2 a • • • 2a;  2i) 


2 K (2;  • • • 2j)“-(-  1)!  2 K(?l  • • • 2a)  K (2a  • • • 2a); 


A + 1,1, 


ci- I-  6 -f-  b ci-\-  2 A -f- . . . 

* * 


.cl)  (-iy-1  K (bc,..cb) 

. c 6)  + K (a  & . . . c 6)  + 2A  + . . . 


236  Proceedings  of  the  Royal  Society 

where  l is  the  number  of  elements  in  the  period  of  the  first  fraction. 
This  we  may  prove  by  deducing  from  the  expression  which  is 
given  by  (XIV.)  for  the  square  of  the  right  hand  member,  the 
expression  also  given  by  (XIV.)  for  the  square  of  the  left  hand 
member. 

Similarly,  we  may  show  that 

A+1  1 1 1 1 ± 

cl b c 5 4~  a 4~  2 A.  -f- . . . 

* * 

_ ^ be  + 2 1 1 be  + 2 

(ibe  -)-  2 n 4-  c 4~  b 4-  nbc  -l-  2d  4*  c 4-  2 A.  4- . . . 

* * 

and  many  other  such  identities. 

22.  Lastly,  it  is  easily  demonstrated  that  the  condition  that  any 
periodic  continued  fraction 

. a.2  an_x  an 

bx  4-  by  4-  • . . 4-  bn_x  + bn+ . . . 

* * 

may  represent  a quadratic  surd  is 


and  that  this  can  be  satisfied  in  other  ways  than  by  choosing  the 
elements  so  that  the  diagonals  of  the  one  continuant  when  read 
forward  may  be  the  same  as  those  of  the  other  when  read  backward. 

3.  Remarks  upon  the  Footprints  of  the  Dinornis  in  the  Sand 
Rock  at  Poverty  Bay,  Hew  Zealand,  and  upon  its  recent 
extinction.  By  T.  H.  Cockburn-Hood,  F.G-.S. 

Impressions  of  the  tracks  of  large  birds  from  this  locality  have 
lately  been  objects  of  attraction  to  visitors  to  the  museum  at 
Wellington,  New  Zealand.  To  these  Dr  Hector,  F.R.S.,  has  affixed 
a label,  stating  that  they  are  from  the  “ Sea  shore  sand  ” at  Poverty 
bay,  a harbour  on  the  east  coast  of  the  north  island.  “ Sand  rock  ” 
would  have  been  a preferable  term,  as  to  most  observers  the  descrip- 
tion is  calculated  to  convey  the  idea  that  these  footprints  are  but 
of  yesterday’s  date.  Indeed,  were  it  not  probable  that  the  moa  was 


of  Edinburgh,  Session  1873-74.  237 

extinct  in  the  northern  island  for  a considerable  time  before  it  was 
exterminated  on  the  opposite  side  of  Cook’s  Straits  (which  is  a matter 
still  quite  open  to  doubt),  they  might  be  merely  the  tracks  of  indi- 
viduals, contemporary  with  that,  the  egg  of  which  was  found  in  the 
grave  of  the  Hurunui  chieftain,  placed  there  to  serve  him  as  pro- 
vision on  his  way  to  happier  hunting  grounds,  and  would  thus  lose 
much  of  the  interest  which  appertains  to  them  as  very  ancient 
memorials. 

The  present  specimens  were  obtained  by  the  writer  on  a late 
visit  to  the  district  of  Poverty  Pay. 

The  slabs  were  cut  out  of  a bed  of  rock,  crossing  a small  affluent 
which  falls  into  the  Turanganui  river,  near  its  mouth,  and  the  foot- 
prints, first  observed  by  the  ferryman,  and  pointed  out  to  Arch- 
deacon Williams,  are  now  washed  by  every  tide.  The  deposit  can 
be  traced  across  the  estuary  to  a point  under  the  high  land,  on  the 
northern  shore  of  the  bay,  where  similar  impressions  are  to  be  seen. 

It  has  been  suggested  that  this  bed  is  but  a portion  left  of  the 
ancient  plateau  composed  of  strata  known  to  local  geologists  as  the 
Hawke’s  Bay  series,  but  no  such  antiquity  can  be  assigned  to  it, 
having  been  formed  from  the  detritus  of  the  cliffs  (which  rival  in 
whiteness  the  chalk  walls  of  the  English  channel)  swept  into  this 
spot  by  a current  which  eddied  round  under  the  precipitous  coast, 
at  a time  when  the  shallow  bay  extended  further  inland,  but  when 
otherwise  the  configuration  of  the  land  was  much  the  same  as  it 
is  now. 

From  the  number  of  the  footprints  crossing  and  recrossing  each 
other,  and  the  proximity  of  those  of  individuals,  it  seems  that  these 
birds  were  in  the  habit  of  resorting  to  the  sea-shore  to  feed  upon 
the  small  fish  and  mollusks  left  by  the  receding  tide,  as  the  Kheas 
of  South  America  do  at  the  present  day. 

The  strata  among  which  the  impressions  occur  appear  to  be  the 
result  partly  of  the  accumulation  of  blown  sand,  partly  of  subaqueous 
deposit  during  a period  of  gradual  submergence. 

At  the  mouth  of  the  Hutt  River,  and  along  the  shore  of  Welling- 
ton harbour,  during  the  earthquakes  of  1855,  the  land  rose  nine 
feet,  and  a corresponding  depression  took  place  of  the  valley,  it  is 
stated,  in  which  the  town  of  Blenheim  is  situated  on  the  southern 
shore  of  Cook’s  Straits. 


238  Proceedings  of  the  Roycd  Society 

At  one  time  this  ornithichnite  bed,  now  washed  by  every  tide,  was 
(as  it  is  still  beyond  its  influence)  covered  by  many  feet  of  the 
delta  alluvium.  The  river  Waipaoa,  which  formed  these  extensive 
plains  of  rich  soil,  averaging  twenty  to  twenty-five  feet  in  depth, 
now  very  rarely  overflows  its  banks.  Only  once,  in  the  memory  of  the 
oldest  native,  has  it  done  so  to  any  extent,  and  this  was  since  the 
settlement  of  Europeans,  on  which  occasion  there  was  a deposit  left 
of  half  an  inch,  in  some  few  spots  of  an  inch  of  silt ; although  in 
bygone  times,  under  different  cosmical  influences,  it  probably  dis- 
charged a much  greater  volume  of  water  into  the  bay,  at  a point 
opposite  the  island  on  the  northern  shore,  and  left  after  every  fresh 
a larger  amount  of  soil  than  it  does  now  on  these  rare  occasions,  a 
vast  time  must  have  elapsed  since  it  left  the  first  layer  of  mud  over 
the  sandstone  bed. 

Dr.  Hochstetter,  the  accomplished  naturalist  who  accompanied 
the  Austrian  expedition  of  1859,  remarks,  u These  gigantic  birds 
belong  to  an  era  prior  to  the  human  race,  to  a Post-Tertiary  period ; 
and  it  is  a remarkably  incomprehensible  fact  of  the  creation,  that 
whilst  at  the  very  same  period  in  the  old  world,  elephants, 
rhinoceroses,  hippopotami — in  South  America,  gigantic  sloths  and 
armadillos — in  Australia,  gigantic  kangaroos,  wombats,  and 
dasyures  were  living, — the  colossal  forms  of  life  were  represented 
in  New  Zealand  by  gigantic  birds.”  But  whilst  these  gigantic 
birds  have  a higher  antiquity  than  even  the  megatherium,  the 
diprotodon,  or  zygomaturus,  and  other  strange  quadrupedal  forms 
of  life,  which  have  long  passed  away,  or  left  only  puny  representa- 
tives, like  the  aepiornis  of  Madagascar,  which  maintained  its  ground 
down  to  a late  period  in  that  great  island,  and  against  men,  too, 
singularly,  of  an  allied  race  to  the  Maorie,  the  moa  has  the  credit 
of  having  held  its  own  down  to  the  present  century,  through  all 
the  great  changes  of  scene  and  climate  which  have  taken  place  since 
its  ancestors  stalked  over  the  plains  of  the  southern  portion  of  a 
great  land, — the  backbone  of  which,  and  little  more,  remains, — per- 
haps with  large  lacertians  for  its  companions,  long  after  the  giant 
marsupials,  the  contemporaries  of  its  congener  * on  the  Australian 
savannahs,  had  disappeared. 

* The  interesting  discovery  there  of  a large  fossil  bird  has  lately  been  made 
known  by  the  distinguished  geologist  the  Rev.  W.  B.  Clarke,  who  first  made 


of  Edinburgh , Session  1873-74.  239 

The  evidences  of  the  late  existence  of  the  moa  are  to  he  seen. 
It  is  not  possible  that  the  tender  skull  and  small  bones  could  have 
been  preserved  in  the  situations  in  which  they  have  been  found 
for  any  great  lapse  of  time.  Exposed  to  the  fierce  summer  sun, 
and  the  severe  winter  frosts  on  the  upper  Otago  plains,  the  bones 
of  a bullock  soon  decay,  but  upon  these  downs  nearly  perfect 
skeletons  of  moas  have  been  found  amongst  the  high  fern,  with  a 
heap  of  the  so-called  moa  stones  beside  them,  evidently  undis- 
turbed since  the  birds  died  upon  the  spot.  The  feathers  in  the 
museum  at  Wellington  are  some  of  those  preserved  by  the  chiefs 
in  the  carved  boxes  which  most  persons  of  distinction  possessed 
for  the  purpose  of  keeping  such  prized  ornaments.  These,  and 
the  egg  with  the  well-developed  bones  of  the  embryo  chick,  of 
which  a photograph  is  here  presented, — the  extremely  interesting 
relic,  the  cervical  vertebrae  of  a moa,  to  which  the  skin,  partially 
covered  with  feathers,  is  still  attached  by  the  shrivelled  muscles 
and  integuments,  found  in  a cave  in  Otago  formed  by  an  over- 
hanging cliff  of  mica  schist, — are  amongst  the  objects  in  that  collec- 
tion affording  proofs  almost  incontrovertible,  to  say  nothing  of  the 
traditions  of  the  mode  of  hunting  the  grand  quarry,*  preserved  in 
Maorie  song  and  story. 

The  remains  of  these  gigantic  birds  are  common  throughout 
both  islands.  No  Maorie,  upon  being  shown  any  of  the  principal 
bones,  will  hesitate  in  referring  them  at  once  to  the  moa.  If 
credence  is  denied  to  their  traditions,  we  are  obliged  to  come  to 
the  conclusion  that  the  different  tribes  possessed  persons  endowed 
with  the  acumen  of  a Cuvier  or  an  Owen,  who  explained  from 

public  the  marvellous  auriferous  and  general  mineral  wealth  of  that  continent, 
and  by  his  indefatigable  researches  has  added  so  much  to  our  knowledge  of  its 
strange  denizens  in  the  past,  as  well  as  at  the  present  time.  Professor  Owen 
has  named  this  bird  dromornis,  considering  it  to  have  been  more  allied  to  the 
emeu  than  the  moa  or  apterix  tribe. 

* The  paper  was  accompanied  by  two  photographs.  Of  these,  one  was  that 
of  the  skeleton  of  one  of  the  largest  specimens  hitherto  obtained.  It  is 
placed  in  the  museum  at  Christ  Church,  New  Zealand,  beside  that  of  a tall 
man.  It  was  one  of  a great  number  dug  up  by  Mr  Moore  at  Glenmark  in 
Canterbury  province,  in  a piece  of  swampy  ground,  now  transformed  into  a 
fine  garden,  which  had  been  one  of  those  places  into  which  the  bones  of 
different  individuals  were  washed  from  the  hills  around  during  freshes,  and 
into  which  the  moas  rushed  when  driven  by  the  fires  kindled  by  the  natives 
for  the  purpose  of  driving  their  game,  dray  loads  of  bones  being  here  collected. 

2 H 


VOL.  VIII. 


240  Proceedings  of  the  Royal  Society 

tlieir  knowledge  of  comparative  anatomy  that  these  huge  remains 
appertained  to  birds.  If  the  theory  of  the  extinction  of  the 
dinornis  before  the  arrival  of  the  Maories  be  accepted,  a very 
great  age  must  be  granted  to  these  singularly  well-preserved  bones ; 
for,  from  some  of  the  traditions  of  those  people,  we  are  led  to  the 
conclusion  that  the  date  of  their  forefathers’  landing  in  this 
country  is  much  more  remote  than  generally  supposed. 

It  may  be  that,  as  well  as  possessing  a knowledge  of  comparative 
anatomy,  the  Maorie  fathers  were  also  acute  geologists ; but  it  is 
much  more  probable  that  the  poetical  story  of  the  quarrel  of  the 
three  brother  gods  of  the  volcanos  of  Kua-pehu,  Tonjoriro,  and 
Taranaki,  and  the  flight  of  the  latter  down  to  the  plain  which 
now  bears  his  name,  tearing  up,  as  he  fled,  the  deep  gorge  of  the 
Whanjarioa  river,  the  taking  of  the  remarkable  truncated  cone 
of  Ranjitolo*  from  the  lake  on  the  north  shore  of  Auckland 
harbour,  and  other  similar  stories,  have  reference  to  memories  of 
those  great  disturbances,  when  the  almost  matchless  cone  of  Mount- 
Egmont  was  thrown  up  on  the  Taranaki  shore,  and  the  geyser 
circled  lake  of  Taupo  was  formed,  where  the  third  great  crater  of 
the  group  formerly  stood  upon  u that  huge  flat  cone,” — the  sterile 
pumice-stone  plateau  of  Taupo, — events  which  took  place  at  a 
period  when  the  stepping-stones  from  New  Zealand  to  the  old 
home  of  the  Maorie  were  probably  not  so  far  apart  as  they  are  to- 
day, as  far  back,  it  may  be,  as  the  time  when  the  skeletons  of  men 
of  this  most  ancient  type,  now  from  time  to  time  exhumed  from 
their  graves  deep  in  the  solid  limestone  rock,  covered  with  the 
ashes  and  scoriae  of  long  quiescent  craters,  lay  bleaching  upon  the 
coral  strand  of  Oahu. 

* This  volcano  has  evidently  been  quiet  for  a long  period,  but  its  name, 
“bloody  heavens,”  denotes  that  it  has  not  always  been  so,  since,  the  Maories 
first  sailed  up  Hauraki  Gulf. 


of  Edinburgh,  Session  1873-74. 


241 


Monday,  19  th  January  1874. 

Principal  Sir  ALEX.  GRANT,  Vice-President,  in  the  Chair. 
The  following  Communications  were  read  : — 

1.  Supplementary  Notice  of  the  Fossil  Trees  of  Craigleith 
Quarry.  By  Sir  R.  Christison,  Bart.,  Hon.  Vice-President, 
R.S.E.,  &c. 

This  notice  supplements  that  of  5 th  May  last,  which  has  been  published 
in  the  Abstracts  of  the  Proceedings  of  the  Society. 

Seven  fossils,  all  apparently  belonging  to  the  Pine  tribe,  and 
either  to  the  same  species,  or  to  two  closely  allied  to  one  another, 
have  been  uncovered  since  1826  in  the  sandstone  of  Craigleith 
Quarry.  Six  are  stems  of  great  trees  ; and  one  is  a longitudinally 
split  section  of  a large  branch,  or  possibly  of  another  stem.  Portions 
of  all  seven  have  been  traced  as  still  in  existence,  and  have  been 
subjected  more  or  less  to  examination.  Of  one,  the  greatest  of 
all,  about  36  continuous  feet,  from  12  to  14  feet  in  girth,  have 
been  removed  in  large  fragments  to  the  British  Museum,  and  will 
be  pieced  and  erected  there.  Another,  found  in  1830,  is  now 
partly  in  the  Botanic  Garden,  and  will  be  supplemented  by  other 
portions  at  present  in  the  Museum  of  Science  and  Art,  so  as  to 
make  a nearly  perfect  fossil  stem  30  feet  in  length.  A third, 
nearly  9 feet  in  girth,  has  been  sliced  and  polished,  to  show  its 
structure  on  the  great  scale,  and  will  be  exhibited  in  the  British 
Museum,  the  Edinburgh  Museum,  and  the  Edinburgh  Botanic 
Garden. 

The  composition  of  all  these  great  fossils  is  substantially  the 
same.  The  great  mass  of  each  consists  of  carbonate  of  lime, 
carbonate  of  magnesia,  carbonate  of  protoxide  of  iron,  and  free 
carbon,  *the  proportions  varying  in  different  parts  of  the  same 
fossil.  The  iron-carbonate  and  charcoal  vary  most  in  their  amount. 
The  charcoal,  which  is  left  after  the  action  of  diluted  acids,  some- 
times without  any  other  insoluble  residuum,  seems  to  form  three 
per  cent,  of  the  mass,  unless  when  collected,  as  it  often  is,  in 


242  Proceedings  of  the  Itoyal  Society 

cavities.  This  charcoal  contains  only  about  3^  per  cent,  of  incom- 
bustible ash. 

The  surface  of  the  fossils  is  covered  with  a shining  coat  of 
very  bituminous  caking  coal,  which  on  the  principal  part  of  the 
stem  varied  from  only  a 20th  to  a 10th  in  thickness,  but  at  the 
lower  end  of  that  now  at  the  British  Museum,  increased  to  half 
an  inch,  and  at  last  to  two  inches  and  a half.  This  coaly  covering 
contains  only  4,  3,  2,  and  sometimes  only  1*1  per  cent,  of  mineral 
matter;  which  is  not  the  same  as  the  fossilising  matter  of  the 
included  wood,  but  is  chiefly  siliceous  in  nature,  being  at  least 
insoluble  in  acids.  The  crust  is  not  altered  bark,  for  bark  could  not 
fail  to  undergo,  in  part  at  least,  fossilisation  by  the  material  which 
has  fossilised  the  wood.  Moreover,  the  coaly  crust  is  found  round 
fragments  and  on  broken  points  where  bark  could  never  have  existed. 

The  rock  of  the  quarry  is  a very  pure  quartzy  sandstone,  hard, 
tough,  and  quite  free  from  earthy  carbonates  or  iron.  But  for 
some  feet  around  the  fossils,  and  also  here  and  there  throughout 
the  quarry,  where  there  is  no  fossil  near,  the  rock  has  quite  a 
different  appearance,  has  a higher  density,  is  more  sharp-edged, 
much  tougher,  and  harder  to  pulverise,  and  becomes  yellow  under 
exposure  to  the  air.  These  changes  are  owing  to  the  siliceous 
particles  of  the  sandstone  being  bound  together  by  carbonate  of 
lime,  carbonate  of  magnesia,  and  carbonate  of  protoxide  of  iron, 
forming  together  from  10  to  38  per  cent,  of  the  rock,  and  bearing 
much  the  same  relation  in  proportion  to  each  other  as  in  the 
mineral  material  of  the  fossils, — consequently  derived  from  the 
same  fluid  which  fossilised  them. 

Thus  the  interesting  fact  is  presented  of  these  great  trees  and 
the  rock  in  which  they  are  imbedded  having  been  both  similarly 
mineralised,  so  to  speak,  by  the  same  fossilising  fluid,  while  there 
is  between  them  a thin  uniform  coating  of  bituminous  coal,  which 
has  refused  admission  to  any  of  the  fossilising  agents.  After 
rejecting  various  theories  to  account  for  this  exemption,  the  only 
one  which  stands  the  test  of  facts  is,  that  a part  of  the  process  of 
fossilisation  consists  in  a slow  process,  analogous  in  its  results  to 
the  destructive  distillation  of  wood,  the  result  of  which  is  charcoal 
left  behind,  and  bitumen  gradually  forced  outwards,  and  collected 
on  the  exterior  surface. 


of  Edinburgh,  Session  1873-74.  243 

The  charcoal  which  remains  in  the  stems  renders  their  minute 
internal  structure  singularly  distinct  when  a thin  transparent 
slice  is  placed  before  the  microscope.  Longitudinal  woody 
bundles,  transverse  medullary  rays,  crowded  cells  of  the  longitudinal 
fibres  cut  crosswise,  are  all  seen  most  characteristically ; and  in 
one  specimen  two  inches  in  breadth  the  boundaries  and  whole 
structure  of  five  annual  layers  of  wood  are  displayed  characteristi- 
cally, even  to  the  naked  eye.  On  the  polished  surface  of  one  of 
the  great  stems,  too,  the  eye  can  easily  trace  many  annual  rings  for 
long  distances. 

2.  On  a Method  of  Demonstrating  the  Delations  of  the  Con- 
volutions of  the  Brain  to  the  Surface  of  the  Head.  By 
Professor  Turner. 

The  outer  surface  of  the  skull  does  not  correspond  in  shape  to 
the  outside  of  the  brain.  If  it  had  corresponded  there  would 
have  been  no  difficulty  in  determining  the  form  of  the  brain  from 
an  inspection  of  the  form  of  the  head. 

The  shape  of  the  brain  does  correspond  to  the  wall  of  the  cranial 
cavity.  This  wall  is  formed  by  the  inner  table  of  the  cranial 
bones,  which  table,  though  separated  from  the  brain  itself  by  the 
cerebral  membranes,  is  moulded  upon  the  exterior  of  the  organ. 

The  difference  between  the  form  of  the  inner  table  of  the  skull 
and  that  of  the  outside  of  the  cranium  is  owing  to  the  superaddition 
of  the  diploe  and  of  the  outer  table,  which  superadded  parts  modify 
the  shape  of  the  outer  surface  of  the  skull. 

The  diploe  varies  somewhat  in  thickness  in  different  bones,  or 
in  different  parts  of  the  same  bone,  and  even  at  different  periods 
of  life,  and  these  variations  necessarily  cause  the  outer  table  to 
be  removed  to  a greater  distance  from  the  inner  table  in  some 
parts  of  the  cranial  wall  than  in  others. 

The  outer  table  is  modified  in  shape  by  ridges  and  processes  for 
the  attachment  of  muscles ; e.g.,  temporal  ridge,  curved  lines  of 
occiput,  occipital  protuberance,  mastoid  process;  but  in  certain 
localities,  as  the  superciliary  ridges,  glabella  and  mastoid  processes, 
more  especially  in  the  male  skull,  it  is  still  further  modified  by  the 
hollowing  out  of  the  diploe  into  the  frontal  and  mastoid  air  cells 


244  Proceedings  of  the  Royal  Society 

or  sinuses,  and  the  elevation  of  the  corresponding  part  of  the 
outer  table. 

These  difficulties  in  the  way  of  estimating  the  exact  shape  of 
the  exterior  of  the  brain,  from  an  inspection  of  the  outside  of  the 
head,  were  pointed  out  and  discussed  at  the  time  when  the  phren- 
ological systems  of  Grail  and  Spurzheim  were  advocated  in  this 
city  by  George  Combe  and  his  disciples. 

But  at  that  period  an  additional  and  even  more  important  diffi- 
culty stood  in  the  way  of  determining  the  exact  relations  of  the 
outside  of  the  brain  to  the  outside  of  the  skull,  for  the  external 
configuration  of  the  brain  itself  was  not  properly  understood. 

Spurzheim  had  undoubtedly  recognised  that,  in  general  form 
and  direction,  the  convolutions  of  the  human  brain  are  “ remark- 
ably regular.”  Thus  he  says — “ The  transverse  convolutions  of  the 
superior,  lateral,  and  middle  parts  of  the  hemispheres  are  never 
found  running  in  any  other  direction — never  longitudinally,  for 
example.  Those  that  lie  longitudinally  again,  as  they  do  under 
the  squamous  suture,  behind  the  temporal  bone  and  on  either  side 
of  the  olfactory  nerve,  are  never  met  with  disposed  transversely.”* 
His  contemporaries  Beil,  Rolando,  Foville,  and  Huschke  had  also 
directed  attention  to  the  constancy  of  individual  convolutions.  It 
was  not,  however,  until  the  publication  in  1854  of  Gratiolet’s  great 
work  on  the  cerebral  convolutions-}*  that  the  surface  of  the  cerebrum 
was  so  mapped  out  that  definite  descriptive  names  were  applied, 
not  only  to  the  several  lobes,  but  to  the  individual  convolutions 
composing  them,  and  the  constancy  of  their  position  and  relations 
to  each  other  precisel}7  determined.  The  study  of  Gratiolet’s  work, 
and  the  adoption  by  so  many  anatomists  of  the  greater  number 
of  his  descriptive  terms,  have  tended  materially  to  advance  our 
knowledge  of  the  convolutions,  and  to  make  them  more  definite 
objects  of  physiological  and  pathological  research.  A need  has 
therefore  arisen  for  localising  the  position  of  the  cerebral  lobes  and 
convolutions  on  the  surface  of  the  skull  and  head,  and  a method,  or 
methods,  of  readily  doing  so  is  to  be  desiderated.  In  selecting 
names  for  four  of  the  five  lobes  into  which  he  subdivided  each 
cerebral  hemisphere,  Gratiolet  employed  terms  which  expressed 

* The  Anatomy  of  the  Brain,  translated  by  Willis,  p.  111.  London,  1826. 

f Memoires  sur  les  Plis  Cerebraux.  Paris,  1854. 


of  Edinburgh,  Session  1873-74.  245 

the  relations  he  believed  to  exist  between  these  lobes  and  the 
vault  of  the  skull,  e.g.  frontal,  parietal,  occipital,  and  temporo- 
sphenoidal  lobes.  In  an  essay  published  in  1861,*  M.  Broca  pointed 
out  that  the  frontal  bone  was  not  equal  in  extent  to  the  frontal  lobe, 
but  that  the  fissure  of  Bolando  was  invariably  some  distance  behind 
the  coronal  suture.  In  eleven  males  examined  the  minimum  dis- 
tance of  the  upper  end  of  this  fissure  was  40  mm.,  the  maximum 
63  mm.  from  the  suture.  He  further  stated  that  a constant  rela- 
tion existed  between  the  lambdoidal  suture  and  the  fissure  which 
separates  the  parietal  from  the  occipital  lobe.  He  never  found  the 
suture  more  than  15  mm.  from  the  fissure,  rarely  more  than  5 mm. 
M.  Broca’s  method  of  determining  these  relations  was  by  drilling 
holes  in  the  skull,  inserting  wooden  pegs  into  the  brain,  and  then, 
after  removing  the  skull  cap,  ascertaining  the  part  of  the  surface 
of  the  hemisphere  into  which  the  pegs  had  penetrated.  Almost 
similar  results  were  obtained  by  Professor  Bischoff  by  pursuing  the 
same  mode  of  examination,  f 

This  plan  of  drilling  holes  through  the  skull,  and  inserting  pegs 
through  them  into  the  brain,  is  one  which  may  be  conveniently 
employed  when  the  object  is  merely  to  obtain  an  idea  of  the  extent 
of  the  lobes  of  the  cerebrum  in  relation  to  the  surface  of  the  head, 
as  only  a few  holes  require  to  be  bored  to  effect  this  object.  But 
as  the  operation  of  drilling  a number  of  holes  through  the  cranial 
bones  demands  the  expenditure  of  much  time  and  labour,  it  is  not 
very  convenient  if  it  is  desired  to  fix  the  position  of  the  individual 
convolutions.  It  occurred  to  me,  therefore,  that  some  other  method 
might  be  resorted  to  to  effect  this  object. 

As  a preliminary  measure,  I sub-divided  the  surface  of  the  skull 
into  regions : a prae-coronal  or  frontal,  the  region  of  the  frontal 
bone;  a parietal,  sub-divided  into  antero-  and  postero-parietal  by  a 
vertical  line  drawn  upwards  from  the  squamous  suture  through  the 
parietal  eminence  to  the  sagittal  suture;  a post-lambdoidal  or 
occipital,  between  the  lambdoidal  suture  and  the  superior  curved 
line  of  the  occiput ; a squamosal  and  a sphenoid,  corresponding  to 
the  squamous  temporal  and  to  the  great  wing  of  the  sphenoid. 
The  line  of  the  temporal  ridge  sub-divides  the  antero-  and  postero- 

* Sur  le  Siege  de  la  Faculty  du  Langage  articule.  Paris,  1861. 

t Die  Grosshirnwindungen  des  Menschen.  Munich,  1868. 


246 


Proceedings  of  the  lioyal  Society 

parietal  into  a supero-  and  infero-anterior  and  supero-  and  infero- 
posterior  parietal  regions,  and  marks  off  also  an  in fero- frontal  area 
on  the  frontal  bone.  The  frontal  bone  may  be  still  further  sub- 
divided into  a supero-and  mid-frontal  region  by  a longitudinal  line 
drawn  back  from  the  upper  border  of  the  orbit  through  the  frontal 
eminence  to  the  coronal  suture. 

With  a fine  saw  I then  cut  out,  one  after  another,  the  pieces  of  bone 
along  the  lines  which  constituted  the  boundaries  of  these  different 
regions,  and  examined  with  care  the  particular  convolution,  or  group 
of  convolutions,  which  lay  immediately  subjacent  to  the  portion  of 
bone  removed.  In  this  manner  I was  able  to  localise  in  the  speci- 
mens examined  the  relations  of  the  convolutions  to  the  surface  of 
the  skull  and  head.  As  I have  already  detailed  the  results  of  my 
examinations  in  the  “ Journal  of  Anatomy  and  Physiology,”  Novem- 
ber 1873, 1 need  not  repeat  them  here;  but  it  may  not  be  out  of  place 
to  point  out  that  the  lobes  of  the  brain  by  no  means  precisely  corres- 
pond to  the  areas  of  the  cranial  bones,  after  which  four  of  them  are 
named.  The  frontal  lobe  is  not  only  covered  over  by  the  frontal 
bone,  but  extends  backwards  for  a considerable  distance  under  cover 
of  the  parietal  bone.  If  we  accept,  as  I have  elsewhere  described,* 
the  fissure  of  Eolando  as  the  posterior  limit  of  this  lobe,  then  the 
larger  part  of  the  antero-parietal  region  corresponds  with  the 
frontal  lobe,  for  not  only  does  it  contain  the  origins  of  the  superior, 
middle,  and  inferior  frontal  gyri,  but  also  the  ascending  frontal 
convolution.  But  even  if  we  were  to  regard  the  ascending  frontal 
gyrus,  and  not  the  fissure  of  Rolando,  as  bounding  the  frontal  lobe 
posteriorly,  the  frontal  lobe  would  still  not  be  wholly  localised 
under  cover  of  the  frontal  bone,  for  the  superior,  middle  and 
inferior  frontal  gyri  all  arise  from  the  ascending  frontal  gyrus, 
behind  the  line  of  the  coronal  suture. 

The  occipital  lobe  also  is  not  limited  to  the  region  covered 
by  the  squamous  part  of  the  occipital  bone,  but  slightly  over- 
lapping the  lambdoidal  suture,  extends  forwards  for  a short  dis- 
tance into  the  back  part  of  the  upper  postero-parietal  area,  and 
through  the  superior  annectent  gyrus  reaches  the  parieto-occipital 
fissure. 

* Edinburgh  Medical  Journal,  June  1866,  and  separate  publication,  “The 
Convolutions  of  the  Human  Cerebrum  topographically  considered.” 


247 


of  Edinburgh,  Session  1873-74. 

The  superior  temporo-sphenoidal  gyrus,  though  for  the  most 
part  situated  under  cover  of  the  squamous-temporal  and  great 
wing  of  the  sphenoid,  yet  ascends  into  both  the  lower  antero-  and 
lower  postero-parietal  areas. 

The  area  covered  by  the  parietal  bone,  so  far  then  from  being 
conterminous  with  the  parietal  lobe  of  the  cerebrum,  is  trenched 
on  anteriorly,  posteriorly  and  inferiorly  by  three  of  the  other  lobes 
of  the  brain.  The  convolutions  of  the  parietal  lobe  itself  are 
especially  grouped  round  the  parietal  eminence,  and  in  the  interval 
between  that  structure  and  the  sagittal  suture. 

The  Insula  or  central  lobe  does  not  come  to  the  surface,  but 
lies  deep  in  the  Sylvian  fissure,  and  is  concealed  by  the  convolu- 
tions which  form  the  margin  of  that  fissure  anteriorly.  It  lies 
opposite  the  upper  part  of  the  great  wing  of  the  sphenoid  and  its 
line  of  articulation  with  the  antero-inferior  angle  of  the  parietal 
and  the  squamous  part  of  the  temporal. 

3.  On  some  Peculiarities  in  the  Embryogeny  of  Tropceolum 
speciosum,  Endl.  & Poepp.,  and  T.  peregrinum , L.  By 
Professor  Alexander  Dickson. 

4.  Notes  on  Mr  Sang’s  Communication  of  7th  April  1873 
on  a Singular  Property  possessed  by  the  Fluid  enclosed  in 
Crystal  Cavities  in  Iceland  Spar.  (1.)  By  Professor  Tait ; 
(2.)  By  Professor  Swan. 

(1.)  Professor  Tait. 

The  very  beautiful  experiment  of  Mr  Sang,  communicated  to 
the  Society  on  the  7th  April,  1873,  suggested  to  me,  as  soon  as  I 
heard  him  read  his  description  of  it,  an  explanation  which  was 
confirmed  by  a subsequent  examination  of  his  specimens.  Some 
remarks  made  to  me  by  members  of  the  Council  of  the  Society, 
three  days  afterwards,  led  me  to  write,  and  deposit  (under  seal, 
as  Mr  Sang  had  announced  that  he  was  still  prosecuting  his 
inquiry)  with  the  Secretary  the  following  hastily  written  docu- 

2 i 


VOL.  VIII. 


248 


Proceedings  of  the  Iioyal  Society 

ment,  which  has  been  since  that  time  in  his  possession,  and  is 
now  printed  verbatim  : — 

“ April  10  thy  1873. 

“ Carbonic  Acid — partly  liquid,  partly  gaseous — fills  the  cavity. 

“ Distillation,  when  one  end  is  heated  ever  so  slightly  above  the 
other,  the  circumstances  being  of  almost  unexampled  favourability 
for  such  an  effect.  Hence  the  apparent  motion  of  the  bubble. 
It  is  not  the  same  bubble  as  it  moves. 

“ General  problem  suggested  by  this,  and  easily  solved  by  the 
dynamical  theory  of  heat. 

“ Find  distribution  of  Least  Entropy  of  contents  of  a vessel 
where  the  temperature  is  a given  function  of  the  position  in  space, 
and  the  contents  are  one  or  more  substances  (say,  for  simplicity, 
not  chemically  acting  on  one  another)  in  two  or  more  different 
states  (as  to  latent  heat,  &c.) 

“ This  is  more  (much  more)  than  the  whole  affair. 

P.  G.  Tait.” 

A day  or  two  afterwards  I tried  the  experiment  on  a large  scale, 
with  the  assistance  of  my  laboratory  students,  and  at  once 
succeeded  in  showing  to  them,  and  to  several  of  my  colleagues,  Mr 
Sang’s  results  in  quill  tubes  of  three  or  four  inches  in  length, 
containing  sulphurous  acid  partly  in  the  liquid  and  partly  in  the 
gaseous  state. 

The  present  communication,  like  that  of  Professor  Swan  which 
follows  it,  is  now  made  to  the  Society  at  the  request  of  Mr  Sang 
himself. 

(2.)  Professor  Swan. 

The  following  note  is  a narrative  of  experiments  made  by  me 
nine  months  ago,  on  the  5th  and  6th  May  1873,  on  the  motions 
observed  in  the  cavities  of  Iceland  spar  by  Mr  Sang,  with  an 
explanation  of  the  manner  in  which  I believe  these  singular  move- 
ments to  be  caused  by  heat.  Being  unwilling  to  interfere  with 
Mr  Sang’s  investigations  then  in  progress,  I did  not  at  the  time 
seek  to  publish  my  note,  but  forwarded  it  in  a sealed  envelope  to 
the  secretary  of  the  Society,  in  whose  custody  it  has  since  remained. 
It  is  now  communicated  to  the  Society  in  accordance  with  Mr 
Sang’s  wishes,  and  is  printed  without  alteration  or  addition. 


of  Edinburgh,  Session  1873-74. 


249 


On  Certain  Motions  observed  by  Mr  Sang  in  Cavities  of  Iceland 
Spar.  By  Professor  W.  Swan,  LL.D. 

I have  received  from  my  friend,  Mr  Edward  Sang,  a crystal  of 
Iceland  Spar  with  a letter  dated  1st  May,  in  which  he  W'rites  as 
follows : — 

“ In  the  accompanying  little  bit  of  Iceland  spar  you  will  find 
a number  of  microscopic  cavities  of  various  shapes,  in  which  you 
may  perceive  a small  bubble  of  vapour,  which  serves  to  show  the 
movement  of  the  enclosed  fluid.” 

The  glass  slide  carrying  the  crystal  being  placed  horizontally 
on  the  stage  of  a microscope,  if  “ you  bring  a piece  of  metal,  say  a 
coin,  gradually  until  its  edge  come  almost  into  the  field  of  view,  you 
will  see  all  the  bubbles  take  the  (apparently)  opposite  sides  of  their 
cavities  : that  is  to  say,  the  metal  repels  the  fluid.  On  inclining 
the  microscope  the  bubbles  take  the  tops  ” of  their  cavities,  and 
“ you  will  find  that  the  repulsion  exceeds  gravity  in  intensity.  I 
have  only  found  this  repulsion  with  metals  : oxides  and  sulphurets 
have  no  action,  and  each  metal  has  its  own  specific  repulsion. 
Silver  is  more  active  than  lead,  and,  if  I mistake  not,  also  than 
gold.  Mercury  has  little  or  no  effect.” 

To-day  (5th  May)  I had  no  difficulty  in  verifying  Mr  Sang’s  re- 
sult as  to  the  motion  of  the  vapour  bubbles  when  a coin  touching 
the  Iceland  spar  was  brought  near  the  fluid  cavities,  but  the  ex- 
periments I was  thereafter  induced  to  make  lead  to  conclusions  in 
some  respects  differing  from  those  which  he  has  obtained. 

Having  placed  his  specimen  of  Iceland  spar  on  the  stage  of  an 
excellent  Boss’s  microscope  belonging  to  the  United  College,  and 
using  a one-inch  object  glass,  I saw  distinctly  the  motion  of  the 
vapour  bubbles,  when  a florin  piece  taken  out  of  my  pocket  was 
brought  up,  touching  the  surface  of  the  spar  so  to  come  into  the  field 
of  view,  and  nearly  to  cover  the  fluid  cavity  observed.  The  apparent 
effect  was  the  attraction  of  the  vapour  bubble,  which  always  ran  to 
the  side  of  the  cavity  nearest  to  the  edge  of  the  coin.  I could  dis- 
tinctly mark  the  tendency  which  the  bubble  exhibited  to  run  in 
a direction  normal  to  the  edge  of  the  piece  of  metal. 

Before  having  tried  any  experiments,  and  while  meditating  on 
Mr  Sang’s  letter,  I could  not  help  concluding  that  most  probably 


250  Proceedings  of  the  Royal  Society 

heat  would  prove  to  be  the  agent  which  caused  the  curious  motions 
which  he  had  observed.  I therefore  placed  the  coin  outside  the 
window  to  be  cooled  in  the  east  wind,  and  the  rain  which  was 
falling  plentifully.  I found  that  the  cold  coin  caused  no  sensible 
motion  of  the  bubbles.  I next  heated  the  coin  in  a spirit  lamp 
flame  as  hot  as  I could  conveniently  handle  it.  Its  energy  in 
moving  the  bubbles  was  now  so  greatly  increased,  that  in  some 
trials  rapid  motions  were  observed  while  the  coin  was  still  out  of  the 
field  of  view. 

Seeing  that  the  bubbles  thus  moved  towards  the  heated  side  of 
their  cavities,  I concluded  that  they  ought  to  be  repelled  from  a side 
which  was  cooled:  and  to  try  if  such  were  the  case,  I cooled  a florin 
piece  in  a freezing  mixture  of  nitre,  sal  ammoniac,  and  water,  to  a 
temperature  below  0°  C.  I had  now  the  satisfaction  to  find  that 
the  cold  coin,  resting  on  the  spar  and  brought  up  towards  a cavity, 
sent  the  bubble  away  to  the  remote  side  of  the  cavity,  just  as  the 
hot  coin  had  brought  it  to  the  near  side. 

It  is  clear,  then,  that  the  phenomenon  is  not  due  to  a repulsion  of 
the  liquid  in  the  cavity  by  the  piece  of  metal,  but  is  a consequence 
of  the  passage  of  a heat  current  through  the  liquid,  the  bubble 
always  moving  in  a direction  opposite  to  that  in  which  heat  is 
flowing. 

I found  that  metals  possess  no  specific  property  in  causing  these 
motions.  The  bubbles  moved  on  the  approach  of  a silver  coin  or  a 
copper  wire.  But  similar  motions  were  readity  obtained  when,  in- 
stead of  these,  were  substituted  a heated  rod  of  glass,  a slender  thin 
test  tube  containing  hot  water,  or  a piece  of  shellac  moulded  into  a 
pencil  shape,  and  still  hot  from  the  flame  employed  to  soften  it. 
All  these  substances — glass,  water  in  the  thin  tube,  and  shell-lac — 
when  cooled  in  the  freezing  mixture,  repelled,  or  seemed  to  repel, 
the  bubble,  just  as  when  heated  they  had  attracted,  or  seemed  to 
attract  it.  The  temperatures  in  these  experiments  were  not  accurately 
observed,  but  they  must  have  been  as  follows  : — Coins  taken  from 
my  pocket  would  be  hotter  than  the  air  of  the  room,  which  was 
10°  C.  or  50°  F.  The  coins  being  of  silver,  an  excellent  conductor 
of  heat,  would,  when  held  in  the  hand,  be  hotter  than  the  spar 
lying  on  the  microscope  stage  in  air  at  10°  C.  The  coins  taken 
from  the  flame  were  as  hot  at  first  as  could  well  be  handled,  and 


251 


of  Edinburgh,  Session  1872-73. 

therefore  hotter  than  the  spar.  The  freezing  mixture  at  the  con- 
clusion of  the  experiment  had  still  a temperature  of  — 5°  C.  or  23°  F. 

I found  that  the  direction  of  motion  of  the  hubbies  was  the 
same  whether  a heated  copper  wire  was  held  above  or  below  the 
Iceland  spar,  with  the  slide  resting  horizontally  on  the  stage 
of  the  microscope.  I fully  verified  Mr  Sang’s  statement  re- 
garding the  motion  of  the  bubbles  when  the  microscope  is  inclined. 
Placing  its  tube  horizontally,  so  that  the  face  of  the  stage  and  the 
glass  slide  were  vertical,  the  bubbles,  of  course,  all  rose  to  the  tops 
of  their  cavities.  A hot  copper  wire  or  silver  coin  touching  the 
surface  of  the  spar  at  a point  on  a lower  level  than  that  of  one  of 
the  cavities,  instantly  drew  the  bubble  down  to  the  bottom.  The 
motion  in  a vertical  plane  with  a tolerably  hot  wire  seemed  almost 
as  brisk  as  it  had  been  in  a horizontal  direction,  so  as  to  indicate 
that  the  effect  of  hydrostatic  pressure,  due  to  gravity,  on  the  minute 
bubble  was  trifling  as  compared  with  the  action  set  up  by  the  heat 
current. 

Considering  the  enormous  dilatability  by  heat  of  liquids,  which, 
under  ordinary  conditions  of  temperature  and  pressure,  are  perma- 
nent gases,  I at  first  thought  the  motions  of  the  bubbles  might  be 
due  to  currents  caused  by  unequal  heating  of  the  liquid  on  opposite 
sides  of  the  cavities.  The  heat  flowing  from  a piece  of  metal  brought 
near  a cavity  would  cause  dilatation  of  the  liquid  on  the  nearer  side. 
A current  would  then  evidently  flow  along  the  upper  surface  of  the 
cavity  away  from  the  heated  metal,  and  carry  a bubble  resting  at 
the  top  in  that  direction.  But  this  is  precisely  the  reverse  of  the 
motion  actually  observed  ; so  admitting,  as  we  can  scarcely  doubt, 
the  setting  up  of  a current  due  to  unequal  heating,  there  must  be 
some  other  and  more  energetic  action  at  work,  causing  a real  or 
apparent  motion  against  any  such  current ; and  this  I take  to  be 
rapid  evaporation  and  condensation  of  the  liquid  on  opposite  sides 
of  the  bubble.  Suppose  A B to  be  a bubble  floating  in  a cavity 
through  which  a heat  current  passes  in  the  direction  A B.  A state 
of  equilibrium  of  the  bubble  is  then  evidently  impossible.  Liquid 
will  evaporate  from  the  hotter  side  A of  the  bubble,  and  vapour  will 
condense  into  liquid  on  the  colder  side  B.  The  liquid  surface  A 
will  then,  by  continual  loss,  travel  in  the  direction  B A,  and  the 
surface  B will  by  continual  gain  follow  A in  the  same  direction ; so 


252 


Proceedings  of  the  Royal  Society 

that  there  will  be  an  apparent  motion  of  the  bubble  towards  the 
hotter  end  of  the  cavity, — an  apparent  motion  only,  for  in  reality  it 
is  not  one  and  the  same  mass  of  vapour  which  is  travelling  through 
the  liquid.  Any  such  identical  bubble  has  only  a momentary 
existence.  It  is  continually  being  changed  into  a new  bubble  in  a 


new  position  by  the  accretion  of  vapour  on  the  side  A,  and  by  the 
restoration  of  vapour  to  the  liquid  state  on  the  side  B ; and  the 
change  of  place  of  the  existing  bubble  is  in  the  direction  from  B to 
A,  or  in  a direction  opposite  to  that  of  the  heat  current.  Such  a 
motion,  it  is  scarcely  necessary  to  remark,  agrees  with  that  which 
is  actually  observed. 

The  action  thus  set  up  in  a vapour  bubble  is  precisely  that  which 
takes  place  in  Wollaston's  cryophorus,  where  vapour,  rapidly 
generated  at  the  hotter,  is  recondensed  into  liquid  and  frozen  at  the 
colder  end  of  the  apparatus.  Suppose  a cryophorus  to  consist 
simply  of  a cylindrical  tube  placed  vertically  and  cooled  by  a freez- 
ing mixture  at  its  upper  end.  The  cavity  occupied  by  vapour  will 
then  suffer  a continual  displacement  downwards ; for  the  surface 
of  the  water,  which  is  its  lower  boundary,  is  being  depressed  through 
loss  by  evaporation,  while  the  glass  at  the  top,  which  was  at  first 
its  upper  boundary,  is  becoming  coated  with  ice  of  constantly  in- 
creasing thickness.  The  downward  displacement  of  the  cavity  of 
such  a cryophorus  may  serve  to  illustrate  that  of  a bubble  in  a 
liquid  heated  from  below.  But  it  may  seem  that  any  movement 
thus  produced  would  be  far  too  slow  to  displace  a bubble  downwards, 
which  was  rising  freely  through  a liquid.  In  considering  such  an 
objection  to  the  proposed  explanation  of  the  motions  of  bubbles  in 
the  cavities  of  crystals,  when  these  motions  take  place  vertically, 
or  otherwise  than  in  a horizontal  direction,  it  is  to  be  borne  in  mind, 


of  Edinburgh,  Session  1878-74.  258 

— first,  that  the  upward  motion  through  a liquid  of  a microscopic 
bubble  must  necessarily  be  very  slow,  even  although  under  a high 
magnifying  power  it  may  seem  otherwise ; and  next,  that  in  space 
containing  only  vapour  of  a liquid  in  contact  with  the  liquid  itself, 
evaporation  and  recondensation  may  proceed  with  excessive  rapidity. 
The  action  of  Wollaston’s  cryophorus,  to  which  reference  has  just 
been  made,  and  Dalton’s  experiments  on  vapours,  made  by  passing 
liquids  up  into  a Torricellian  vacuum,  alike  exhibit  the  facility 
with  which  vapours  form  and  recondense  in  spaces  void  of  gases 
which  are  permanent  at  the  existing  temperature.  Add  to  these 
considerations  the  information  derived  from  the  experiments  of 
Cagniard  de  la  Tour,  Faraday,  and  Andrews,  as  to  the  enormous 
celerity  with  which  substances  pass  from  the  liquid  to  the  gaseous,  or 
from  the  gaseous  to  the  liquid  condition,  when  near  their  critical  tem- 
peratures, which  for  different  substances  range  probably  between  the 
very  remote  limits  773°  and  - 166°  Fahrenheit,  and  the  explanation 
which  I have  ventured  to  propose  of  the  motion  of  a vapour  bubble 
in  a liquid  conveying  a heat  current  becomes  sufficiently  feasible. 

I have  to-day  IHen  at  some  pains  to  verify  the  result  obtained 
yesterday,  namely,  that  a piece  of  metal  at  the  same  temperature  as 
the  Iceland  spar  has  no  power  to  move  the  globules  of  vapour  in 
the  fluid  cavities.  Placing  a shilling  on  the  microscope  stage 
beside  the  crystal,  I left  it  for  about  ten  minutes.  Then  holding  it 
in  forceps  to  avoid  heating  it  by  the  hand,  I moved  it  up  into  the 
field  touching  the  spar,  and  so  as  almost  to  cover  a fluid  cavity  from 
view.  No  motion  of  the  bubble  ensued.  But,  on  putting  my  finger 
on  the  top  of  the  shilling,  by-and-by  the  bubble  began  to  move,  and 
slowly  but  steadily  crossed  the  cavity  towards  the  shilling.  The 
same  experiment  was  repeated  with  a bit  of  sheet  lead  about  an 
inch  square  and  008  inch  thick,  with  precisely  the  same  result.  I 
do  not  find  lead  notably  less  active  than  silver ; but  the  experi- 
ments made  were  necessarily  too  hasty  and  imperfect  to  settle  the 
point  as  to  whether  any  difference  exists.  The  relative  thermal 
conductivities  of  silver  and  lead  being  in  air  as  100  to  8'5,  accord- 
ing to  Wiedemann  and  Franz’s  experiments,  we  might  expect, 
when  heat  was  conducted  from  the  hand  into  the  crystal  through  a 
piece  of  metal,  that  silver  would  produce  more  energetic  effects  than 
lead.  May  the  effects  be  due,  in  part  at  least,  to  radiant  heat,  the 


254  Proceedings  of  the  Royal  Society 

liquid  in  the  cavities  being  possibly  less  diathermanous  than  the 
Iceland  spar,  and  absorbing  the  beat  transmitted  to  it  by  radiation 
through  the  crystal  ? 

In  order  to  try  if  the  motion  of  a vapour  bubble  could  be  ex- 
hibited on  a larger  scale,  I made  use  of  a hermetically  sealed  tube 
containing  liquefied  sulphurous  acid  (sulphur  dioxide)  which  I had 
some  time  ago  prepared  to  show  the  high  dilatability  by  heat  of 
that  liquid.  When  the  tube  was  placed  horizontally  the  void  space, 
like  the  bubble  of  a spirit  level,  was  about  15  inches  long ; and  I 
found  that  its  extremity  moved  towards  the  point  where  a piece  of 
heated  brass  was  applied  to  the  tube.  I then  nearly  filled  a tube 
with  ether  made  from  methylated  alcohol ; and  after  heating  the 
top,  so  as  to  vaporise  the  ether  and  expel  the  air,  I hermetically 
sealed  the  tube.  Placing  the  tube  horizontally,  the  vapour  bubble 
is  about  0-3  of  an  inch  long ; and  when  a finger  is  put  on  the  tube 
about  0’25  of  an  inch  from  the  bubble,  in  a little  while  the  bubble 
moves  towards  the  finger  with  a rapidly  accelerated  motion,  and 
places  itself  in  a position  of  stable  equilibrum  under  the  finger, 
about  which  it  slightly  oscillates  even  after  the  finger  is  removed 
from  the  tube.  A piece  of  metal  too  hot  to  be  touched  acts  still 
more  energetically. 

I have  thought  it  proper  to  note  that  the  ether  I used  had  been 
made  from  methylated  alcohol,  because  in  exhibiting  as  a lecture 
experiment  Dalton’s  method  of  measuring  vapour  tensions,  I have 
found  that  ether  made  from  methylated  alcohol  seems  to  show  a 
higher  vapour  tension  than  that  of  ether  as  determined  by  Regnault. 
This  is  probably  due  to  the  presence  of  some  other  substance  more 
volatile  than  common  or  diethyl  ether,  possibly  to  a portion  of 
dimethyl  ether  whose  boiling-point  is  so  low  as  - 21°  C. 

United  College,  St  Andrews, 
nth  Mai f 1873. 


of  Edinburgh,  Session  1873-74. 


255 


5.  Preliminary  Note  on  the  sense  of  Rotation  and  the 

Function  of  the  Semicircular  Canals  of  the  Internal  Ear. 
By  Professor  A.  Crum-Brown. 

As  far  as  I am  aware,  the  sense  of  rotation  has  not  hitherto 
been  recognised  either  by  physiologists  or  by  psychologists  as  a 
distinct  sense,  but  a little  consideration  and  a few  experiments 
seem  to  me  to  be  enough  to  show  that  it  really  is  so.  By  means 
of  this  sense  we  are  able  to  determine' — a , the  axis  about  which 
rotation  of  the  head  takes  place ; b,  the  direction  of  the  rotation  ; 
and  c,  its  rate. 

In  ordinary  circumstances  we  do  not  wholly  depend  upon  this 
sense  for  such  information.  Sight,  hearing,  touch,  and  the  mus- 
cular sense  assist  us  in  determining  the  direction  and  amount 
of  our  motions  of  rotation,  as  well  as  of  those  of  translation ; but 
if  we  purposely  deprive  ourselves  of  such  aids  we  find  that  we 
can  still  determine  with  considerable  accuracy  the  axis,  the  direc- 
tion, and  the  rate  of  rotation.  The  experiments  that  I have  made 
with  the  view  of  determining  this  point  were  conducted  as  follows  : 
a stool  was  placed  on  the  centre  of  a table  capable  of  rotating 
smoothly  about  a vertical  axis ; upon  this  the  experimenter  sat,  his 
eyes  being  closed  and  bandaged;  an  assistant  then  turned  the 
table  as  smoothly  as  possible  through  an  angle  of  the  sense  and 
extent  of  which  the  experimenter  had  not  been  informed.  It 
was  found  that,  with  moderate  speed,  and  when  not  more  than 
two  or  three  complete  turns  were  made  at  once,  the  experimenter 
could  form  a tolerably  accurate  judgment  of  the  angle  through 
which  he  had  been  turned.  By  placing  the  head  in  various  posi- 
tions, it  was  possible  to  make  the  vertical  axis  coincide  with  any 
straight  line  in  the  head.  It  was  found  that  the  accuracy  of  the 
sense  was  not  the  same  for  each  position  of  the  axis  in  the  head, 
and  further,  that  the  minimum  perceptible  angular  rate  of  rotation 
varied  also  with  the  position  of  the  axis. 

The  sense  of  rotation  is,  like  other  senses,  subject  to  illusions, 
rotation  being  perceived  where  none  takes  place.  Vertigo  or 
giddiness  is  a phenomenon  of  this  kind. 

When,  in  the  experiments  just  mentioned,  rotation  at  a uniform 

2 K 


VOL.  VIII. 


256  Proceedings  of  the  Royal  Society 

angular  rate  is  kept  up  for  some  time,  the  rate  appears  to  the 
experimenter  to  be  gradually  diminishing  ; if  the  rotation  be  then 
stopped,  he  experiences  the  sensation  of  rotation  about  the  same 
axis  in  the  opposite  direction.  If  the  position  of  the  head  he 
changed  after  the  prolonged  rotation  has  been  made,  the  position 
of  the  axis  of  the  apparent  rotation  is  changed,  remaining  always 
parallel  to  a line  in  the  head  which  was  parallel  to  the  axis  of 
the  real  rotation.  The  readiness  with  which  this  complementary 
apparent  rotation  is  produced  is  not  the  same  for  each  axis.  In 
such  experiments,  as  long  as  the  eyes  are  shut,  and  the  axis  of 
rotation  kept  vertical,  a sensation  of  giddiness  is  not  experienced. 
That  sensation  appears  to  be  caused  by  the  discordance  between 
the  testimony  of  the  sense  of  sight  and  that  of  the  sense  of  rotation. 

It  is  obvious  that  this  sense  must  have  a peripheral  organ  physi- 
cally constituted  so  as  to  he  affected  by  rotation,  and  that  it  must 
be  such  as  to  receive  different  impressions  when  the  axis,  direc- 
tion, or  rate  of  rotation  is  changed.  These  impressions  must  be 
transferred  to  the  ends  of  afferent  nerves,  and  by  these  nerves 
conducted  to  a central  organ. 

The  semicircular  canals  of  the  internal  ear  are  eminently  fitted 
by  their  form  and  arrangement  to  act  as  the  peripheral  organ  of 
this  sense.  I shall  consider  first  the  action  of  one  semicircular 
canal,  and  for  simplicity  suppose  that  there  is  only  one.  Starting 
from  rest,  let  us  suppose  rotation  of  the  head  to  take  place  about 
an  axis  at  right  angles  to  the  plane  of  the  canal.  The  bony  canal, 
being  part  of  the  skull,  of  course  shares  in  this  rotation,  but 
the  perilymph  lags  behind,  and  thus  the  membranous  canal,  which 
floats  in  the  perilymph,  does  not  immediately  follow  the  motion 
of  the  bony  canal,  but,  as  the  membranous  canal  is  continuous 
at  both  ends  with  the  utricle,  the  relative  motion  of  the  bony 
and  the  membranous  canal  must  produce  a pulling  or  stretching 
of  the  forward  end  of  the  membranous  canal.  If  this  is  the  end 
at  which  the  ampulla  is  situated,  such  stretching  will  necessarily 
move  the  terminal  nervous  organs  in  the  ampulla,  and  may  reason- 
ably be  expected  to  stimulate  the  nerves.  This  stimulus  will  no 
doubt  be  greater  the  stronger  the  pull,  i.e.,  the  more  rapid  the 
rotation.  We  should  thus  with  one  semicircular  canal  have  the 
means  of  perceiving,  and  of  estimating  the  rate  of,  rotation  in 


of  Edinburgh,  Session  1873-74. 


257 


one  direction  about  one  axis.  But  we  have  six  semicircular  canals, 
three  in  one  ear  and  three  in  the  other,  and  these  are  arranged 
in  pairs — the  two  exterior  being  nearly  in  the  same  plane,  and 
the  superior  in  one  ear  being  nearly  parallel  to  the  posterior  in 
the  other.  We  have  thus  a system  of  three  rectangular  axes, 
each  axis  having  two  semicircular  canals  at  right  angles  to  it, — 
one  influenced  by  rotation  in  one  direction  about  the  axis,  the 
other  by  rotation  in  the  opposite  direction.  Any  rotation  what- 
ever of  the  head  can  be  resolved  into  three  rotations,  one  about 
each  of  the  said  three  rectangular  axes,  and  will  thus  in  general 
affect  three  ampullae.  If  the  ampullae  affected  are  known,  and 
the  amount  of  pull  at  each  is  known,  the  axis  about  which  rotation 
takes  place  and  the  rate  of  the  rotation  can  be  deduced.* 

I am  at  present  engaged  in  making  measurements  and  experi- 
ments in  reference  to  this  inquiry,  and  hope  before  long  to  lay 
a more  complete  account  of  the  various  phenomena  before  the 
Society. 

* When  rotation  has  continued  for  some  time,  friction  of  the  periosteum 
of  the  bony  canals  against  the  perilymph,  and  fluid  friction  in  the  perilymph, 
gives  to  the  perilymph,  and,  of  course,  also  to  the  membranous  canal,  the  same 
rotation  as  the  bony  canal  has ; the  perception  of  rotation  will  thus  cease. 
If  we  now  stop  the  rotation  of  the  head  the  bony  canal  stops,  but  the  peri- 
lymph and  the  membranous  canal  move  on,  and  a pull  takes  place  at  the 
opposite  ends  of  the  semicircular  canals,  causing  a perception  of  rotation 
round  the  same  axis  in  the  opposite  direction. 

The  members  of  the  three  pairs  of  semicircular  canals  are  not  always 
accurateiy  parallel  to  each  other,  and  in  some  animals  the  three  axes  are  not 
accurately  at  right  angles,  so  that  in  the  most  general  case  we  have  two 
systems  of  co-ordinates,  not  necessarily  rectangular,  which  we  may  call  z,  y,  z, 
and  £,  77,  C — ©ach  °f  these  six  axes  having  an  organ  capable  of  being  influenced 
by  rotation  about  the  axis  in  one  direction.  But  in  all  cases,  as  far  as  I know, 
these  six  axes  and  the  corresponding  organs  are  so  placed  that  a different 
set  of  impressions  will  be  produced  by  each  form  of  rotation,  that  is,  by  each 
combination  of  axis,  direction,  and  rate. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


yol.  ym.  1873-74.  No.  88. 


Ninety-First  Session. 

Monday,  2 d February  1874. 

Professor  Sir  WILLIAM  THOMSON,  President, 
in  the  Chair. 

The  following  Obituary  Notices  of  Deceased  Fellows  of 
the  Society  were  read : — 

1.  Biographical  Notice  of  J.  S.  Mill.  By  Professor  Fraser. 

John  Stuart  Mill  was  born  in  London  on  the  20th  of  May  1806, 
and  died  at  Avignon  on  the  8th  of  May  1873.  He  was  of  Scotch 
descent.  He  was  connected  with  Edinburgh  not  only  as  having  been 
an  honorary  member  of  this  Society,  but  because  his  father,  James 
Mill,  the  historian  of  British  India,  and  author  of  the  u Analysis  of 
the  Human  Mind,”  received  his  academical  education  here.  His 
grandfather  was  a small  farmer,  at  Northwater  Bridge,  in  the 
county  of  Angus,  of  whom  I find  nothing  more  recorded.  The 
father,  by  his  extraordinary  intellectual  promise  when  a boy,  drew 
the  attention  of  Sir  John  Stuart,  then  member  for  Kincardine- 
shire, by  whom  he  was  sent  to  the  University  of  Edinburgh,  at  the 
expense  of  a fund,  established  by  Lady  J ane  Stuart  and  some  other 
ladies,  for  educating  young  men  for  the  Church  of  Scotland. 
Towards  the  end  of  last  century,  James  Mill  attended  the  classes 
in  Arts  and  Divinity.  He  was  a pupil  of  Dalziel,  the  Professor  of 
G-reek,  whose  prelections  he  attended,  I believe,  for  three  sessions, 
and  his  philosophical  powers  were  called  forth  by  Dugald  Stewart’s 

2 L 


VOL.  vm. 


260  Proceedings  of  the  Royal  Society 

lectures  in  Moral  Philosophy.  I do  not  know  by  what  Presbytery 
he  was  licensed  to  preach,  but  I have  heard  Sir  David  Brewster  say 
that  he  had  listened  to  one  of  his  sermons.  When  a student  at 
the  University  it  seems  that  he  was  given  to  reading  books  of  a 
sceptical  tendency  in  religion.  He  soon  found  the  ministry  uncon- 
genial to  him,  having  satisfied  himself  that  he  could  not  believe  the 
doctrines  of  any  Christian  Church. 

About  the  year  1800  James  Mill  removed  to  London,  where  for 
nearly  twenty  years  he  made  his  living  by  his  pen.  He  was  a man 
of  singular  force  of  character  and  subtlety  of  intellect — a stern 
Scotch  Stoic  or  Cynic,  with  an  Epicurean  creed.  He  married  soon, 
after  he 'settled  in  the  metropolis,  with  only  the  precarious  income 
of  a literary  adventurer.  The  eldest  son  of  his  large  family  was 
John  Stuart  Mill.  He  was  born  about  the  time  the  “History  of 
India”  was  begun.  In  the  twelve  following  years  the  extraordi- 
nary energy  of  the  father  was  chiefly  given  to  this  great  work,  and 
to  the  instruction  of  his  eldest  son. 

That  eldest  son  has  himself  described  in  his  “Autobiography” 
some  of  the  original  influences  by  which  his  own  mind  and  character 
were  formed.  The  stern  paternal  schoolmaster  was  one  of  the  most 
important.  The  story  of  young  Mill’s  early  instruction  is  as  extra- 
ordinary as  any  in  the  records  of  English  training.  Books  in  G-reek, 
Latin,  and  English ; in  history,  logic,  and  analytical  psychology, 
were  among  the  means — the  end  being  the  production  of  as  per- 
fect a reasoning  machine  as  could  be  produced  out  of  the  hoy. 
What  is  commonly  included  in  the  higher  education  began  with 
him  in  childhood.  He  was  introduced  to  G-reek  when  he  was  three 
years  of  age.  Before  he  was  eight  he  had  read  many  Greek  books, 
including  the  Theaetetus  of  Plato.  He  had  also  read  a great  deal 
of  history,  including  Hume  and  Gibbon,  and  had  discussed  what 
he  had  read  with  his  father,  in  their  rural  walks  about  Newington 
Green,  where  the  Mills  were  living  from  1810  to  the  end  of  1813. 
In  the  winter  of  1813  they  moved  into  a house,  rented  from  their 
friend  Jeremy  Bentham,  in  Queen  Square,  Westminster.  About 
the  time  this  change  was  made  young  Mill  began  to  learn  Latin. 
Before  he  was  twelve  he  had  read  most  of  the  Latin  and  Greek 
poets,  historians,  and  orators,  much  of  the  Rhetoric  of  Aristotle, 
and  a great  deal  of  ancient  history.  At  twelve  his  philosophical 


261 


of  Edinburgh,  Session  1873-74 

education  began.  He  studied  logic  in  the  Organon,  in  Latin 
treatises  of  scholastic  logic,  and  in  Hobbes.  His  later  experience 
made  him  set  great  value  on  this  early  familiarity  with  Aristotelian 
logic.  The  first  intellectual  operation  in  which  he  arrived  at 
proficiency  was  dissecting  bad  arguments,  and  finding  in  what 
the  fallacy  lay.  Ricardo  and  a course  of  political  economy  fol- 
lowed ; also  much  study  of  Plato.  The  high  expectations  his  stern 
and  exacting  preceptor  had  of  him  at  this  time  appear  in  a letter 
from  James  Mill  to  Jeremy  Bentham  in  1812. 

In  May  1820  he  was  sent  to  France.  His  father  had  in  the  year 
before  been  appointed  one  of  the  Assistants  of  the  Examiner 
of  Correspondence  in  the  India  House.  Abroad  the  boy  lived 
in  the  family  of  Sir  Samuel  Bentham,  a brother  of  Jeremy. 
He  was  introduced  to  M.  Say,  the  political  economist,  and  other 
French  savans  in  Paris.  This  was  the  beginning  of  the  intimate 
sympathy  with  the  literary  and  political  society  of  France,  which 
was  always  characteristic  of  John  Mill. 

In  July  1821  he  returned  to  England.  He  resumed  his  old 
studies,  with  the  addition  of  some  new  ones.  He  read  Condillac 
“ as  much  for  warning  as  example.”  In  the  winter  of  1821-22,  he 
studied  jurisprudence  under  John  Austin,  and  also  in  the  writings 
of  his  father’s  friend,  Jeremy  Bentham.  His  whole  previous  educa- 
tion had  been  in  a certain  sense  a course  of  Benthamism,  for  he 
had  been  always  taught  to  apply  Bentham’s  standard  of  “ the 
greatest  happiness.”  He  lived  much  in  Bentham’s  society,  and 
often  accompanied  him  and  his  father  in  their  walks  together,  at 
Newington  G-reen  and  afterwards  in  Westminster,  besides  making 
long  summer  visits  to  him  at  Ford  Abbey,  in  Devonshire. 
Before  he  was  fifteen,  his  studies  were  carried  into  analytic  psycho- 
logy, still  under  his  father’s  direction.  He  read  Locke,  Berkeley, 
Helvetius,  Hartley,  Hume,  Beid,  Stewart,  and  Brown  on  “ Cause 
and  Effect.”  The  elder  Mill  about  this  time  began  to  write  his 
“Analysis  of  the  Human  Mind,”  which  was  published  seven  years 
later,  in  1829,  and  the  son  was  allowed  to  read  the  manuscript, 
portion  by  portion,  as  it  advanced. 

This  training,  while  it  produced  an  astonishing  precocity  of 
logical  intelligence,  was  not  equally  favourable  to  physical  vigour, 
and  practical  skill  or  sagacity.  Mr  Mill  tells  us  that  as  he  had 


262  Proceedings  of  the  Royal  Society 

no  boy  companions,  and  the  animal  need  of  physical  action  was 
satisfied  by  walking,  his  amusements,  which  were  mostly  solitary, 
were  in  general  of  a quiet  if  not  bookish  turn,  and  gave  little 
stimulus  to  any  other  kind  of  mental  acting  than  that  which  was 
already  called  forth  by  his  studies.  He  consequently  remained  long, 
and  in  a less  degree  always  remained,  inexpert  in  everything  re- 
quiring manual  dexterity,  and  his  mind  as  well  as  his  hands  did 
its  work  lamely,  when  it  was  applied  to  the  practical  details  which 
are  the  chief  interest  of  life  to  the  majority  of  men.  He  was  con- 
stantly meriting  reproof  by  inattention,  inobservance,  and  general 
slackness  of  mind  in  matters  of  daily  life. 

Beauchamp’s  “ Analysis  of  the  Influence  of  Natural  Religion 
on  the  Temporal  Happiness  of  Mankind  ” (papers  of  Bentham 
edited  by  G-rote)  was  read  by  young  Mill.  This  was  an  examina- 
tion not  of  the  truth,  but  of  the  usefulness  of  religion,  and  suited 
his  mental  condition  well.  His  father  had  educated  him  from  the 
first  without  any  religious  belief.  The  elder  Mill,  “ finding  no 
halting-place  in  Deism,  had  yielded  to  the  conviction  that  nothing 
whatever  can  be  known  concerning  the  origin  of  things.”  He 
impressed  upon  his  son  from  the  first  that  the  manner  in  which  the 
universe  came  into  existence  was  a matter  on  which  nothing  was  or 
could  be  discovered;  that  the  question,  “ Who  made  me  ? ” cannot 
be  answered,  because  we  can  have  no  experience  from  which  to 
answer  it;  and  that  any  answer  only  throws  the  difficulty  a step 
further  back,  since  the  question  immediately  presents  itself,  “Who 
made  G-od  ? ” He  assumed  it  to  be  impossible  that  a world  so  full 
of  evil  could  be  the  production  of  a cause  combining  infinite  power 
with  perfect  goodness.  John  Mill  was  thus,  he  says  himself, 
“ one  of  the  very  few  examples  in  this  country  of  one  who  has 
not  thrown  off  religious  belief,  but  who  has  never  had  any.”  He 
looked  upon  the  modern  exactly  as  he  did  upon  the  ancient  religion, 
as  something  which  in  no  way  concerned  him.  If  a philosopher 
has  to  comprehend  what  exists,  it  was  unfortunate  for  Mr  Mill,  and 
unfavourable  to  the  comprehensiveness  of  his  philosophy,  that  he 
should  have  thus  been  trained  to  overlook  Christianity,  the  greatest 
fact  in  European  life. 

Other  than  home  influences  now  began  to  have  play.  In  May 
1829  his  professional  occupation  was  determined.  He  became  a 


263 


of  Edinburgh,  Session  1873-74. 

subordinate  in  the  India  House  under  his  father,  who  was  resolved 
not  to  leave  him  to  the  uncertainty  of  the  adventurous  literary 
life.  Steady  official  duties  in  Leadenhall  Street  occupied  him  in 
the  thirty-five  following  years,  at  the  end  of  which  the  East  India 
Company  was  extinguished  as  a governing  power.  But  his  duties 
there  always  allowed  him  to  have  time  enough  for  study. 

He  was  now  introduced  gradually  to  a wider  companionship.  In 
the  winter  of  1822-23,  he  had  formed  the  plan  of  a little  society, 
composed  of  young  men  acknowledging  Utility  as  the  standard  in 
ethical  and  political  thought.  At  his  suggestion  it  was  called  the 
Utilitarian  Society.  It  was  the  first  time  that  any  one  had  taken 
the  title  of  Utilitarian ; but  the  term  soon  made  its  way  into  the 
English  language.  John  Austin,  William  Ellis,  John  Arthur 
Boebuck,  G-eorge  Grrote,  and  others,  appear  among  his  friends 
and  associates. 

He  began  about  this  time  to  show  himself  in  print.  His  first 
published  writings  were  two  letters,  which  appeared  in  the  end  of 
1822,  in  the  “ Traveller  ” newspaper,  in  defence  of  some  opinion  of 
Ricardo  and  his  father  in  political  economy.  Early  in  the  following 
year  he  published  some  letters  in  the  “ Morning  Chronicle,”  in 
favour  of  complete  freedom  of  religious  discussion,  in  connection 
with  the  trial  of  Richard  Carlile  for  blasphemy.  During  1823 
several  of  his  writings  appeared  in  the  “Traveller”  and  “Morning 
Chronicle.” 

In  April  1824  the  “ Westminster  Review”  was  started,  under 
the  auspices  of  Jeremy  Bentham,  with  John  Bowring  as  editor. 
From  that  time  till  July  1828  Mr  Mill  was  its  most  frequent  con- 
tributor. He  wrote  thirteen  articles  in  these  years.  One  is  especi- 
ally worthy  of  note, — a review  of  Whately’s  “Logic,”  which  appeared 
in  January  1828,  which  it  is  interesting  to  compare  with  the 
modification  and  extension  of  the  science  proposed  fifteen  years 
afterwards  in  his  own  System.  In  1827,  at  Bentham’s  request,  his 
name  was  given  to  the  world  as  editor  of  that  philosopher’s  greatest 
treatise,  the  “Rationale  of  Evidence,”  the  preface  to  which  was 
written  by  Mr  Mill : his  previous  publications  were  anonymous. 
This  work,  and  the  annotations,  occupied  much  of  his  time  for 
about  a year.  The  connection  of  the  subject  with  the  form  which 
logic  afterwards  took  in  his  own  hands  is  manifest. 


264  Proceedings  of  the  Royal  Society 

In  these  years  various  influences  helped  to  show  that  he  had 
a nature  too  deep  and  human  to  be  satisfied  with  the  hard 
Benthamite  creed  in  which  he  was  trained.  For  some  years  after 
1828  he  wrote  little,  and  nothing  regularly,  for  publication. 
He  congratulates  himself  on  this.  If  he  had  gone  on  writing,  it 
would  have  disturbed,  he  thinks,  an  important  transformation  in 
his  opinions  and  character  which  was  taking  place  about  this  time. 
For  years  his  one  object  in  life  had  been  to  be  a reformer  of 
society.  He  was  now  awakened  from  this  as  from  a dream.  All 
his  happiness  was  to  have  been  found  in  the  steady  pursuit  of 
this  end : the  end,  he  found,  had  ceased  to  charm  him,  and  he 
seemed  to  himself  to  have  nothing  left  to  live  for.  He  was  weighed 
down  by  melancholy.  Part  of  the  explanation  probably  was  that 
his  nerves  were  exhausted  by  an  early  life  too  purely  intellectual. 
His  condition  so  far  reminds  one  of  the  account  which  David  Hume 
gives  of  himself  in  the  very  curious  letter  to  a physician,  written 
at  a corresponding  period  of  life,  and  preserved  among  the  papers 
in  the  possession  of  this  Society,  published  by  Mr  Burton  in  his 
u Life  of  David  Hume.”  It  is  interesting  to  compare  Hume’s  story, 
in  that  letter,  and  Mr  Mill’s  in  his  “Autobiography.”  The  health 
of  both  seems  to  have  been  broken  for  the  time  by  a too  ardent 
application  to  abstract  studies.  The  truth,  however,  was  that  Mill 
had  discovered  in  some  degree  the  narrowness  of  the  theory  of  life 
on  which  his  early  training  had  been  based.  It  had  left  him 
nothing  worth  living  for.  Mill,  like  Hume,  gradually  recovered, 
but  with  a more  marked  change  in  his  mental  tone  and  opinions 
afterwards  than  one  finds  in  Hume.  His  early  Utilitarianism  was 
modified.  While  still  convinced  that  happiness  was  the  chief  end 
of  human  life,  he  now,  with  doubtful  consistency,  thought  that  this 
was  to  be  attained  by  not  making  it  the  direct  end ; and  that  those 
only  are  happy  who  have  their  minds  fixed  on  some  object  other 
than  their  own  happiness — the  philanthropic  improvement  of  man- 
kind, for  instance.  He  found,  too,  that  the  emotions  needed  to  be 
cultivated  as  well  as  the  intellect.  He  began  to  feel  the  import- 
ance of  poetry  and  art,  especially  music,  as  instruments  of  human 
culture.  He  was  always  very  fond  of  music,  and  a scientific  pro- 
ficient. 

The  reading  of  Wordsworth  for  the  first  time,  in  the  autumn  of 


265 


of  Edinburgh,  Session  1873-74. 

1828,  was  an  important  event  in  Mr  Mill’s  life.  Beauty  in  nature 
had  a power  over  him  then  that  was  a foundation  for  his  taking  plea- 
sure in  Wordsworth’s  poetry.  He  became  a Wordsworthian,  and 
contended  on  this  side  against  Koebuck  in  a Debating  Society.  His 
sympathies  were  carrying  him  more  and  more  away  from  Ben- 
thamism, and  towards  a deeper  and  truer  philosophy  of  life. 
He  was  brought  into  friendly  companionship  with  Frederick 
Maurice,  and  John  Sterling,  and  other  admirers  of  Coleridge.  He 
became  one  of  Coleridge’s  occasional  visitors  at  Highgate,  to  whom 
I have  heard  that  he  was  introduced  by  Sir  Henry  Taylor.  After 
1829  he  withdrew  from  the  Debating  Society,  and  pursued  his 
studies  and  meditations  in  private,  endeavouring  thus  to  adjust 
the  relation  of  his  new  ideas  and  sympathies  to  his  old  opinions. 
Indeed,  after  this  he  seems  to  have  lost  his  early  fondness  for 
Societies  for  discussion  : a few  years  ago  he  declined  to  connect 
himself  with  the  lately-founded  Metaphysical  Society  of  London, 
having  the  opinion  that  valuable  results  in  subjects  of  abstract 
philosophy  are  best  attained  in  solitary  dialectic,  or  with  a single 
interlocutor. 

In  the  Society  from  which  he  withdrew,  logical  questions  had 
been  often  discussed.  About  1830  he  began  to  put  on  paper 
thoughts  on  the  theory  of  logic,  and  especially  on  the  relations  of 
induction  to  syllogism.  Thus  his  own  system  of  logic  began  to 
take  shape.  In  political  philosophy,  too,  he  began  to  see  that  the 
truth  was  something  more  complex  and  many-sided  than  his  early 
instruction  had  presupposed.  This  tendency  was  encouraged  by  a 
sympathetic  study  of  the  writings  of  the  St  Simonian  school  in 
France,  and  of  the  early  works  of  Auguste  Comte.  Thomas 
Carlyle,  too,  had  an  effect  upon  him.  He  felt  himself  at  an 
increasing  distance  from  his  father’s  whole  tone  of  thought  and 
feeling. 

The  year  1830,  above  all,  was  the  commencement  of  what  he 
considered  the  most  valuable  friendship  of  his  life — that  of  Mrs 
Taylor,  who,  twenty  years  afterwards,  became  his  wife,  and  whose 
influence  over  him,  for  good  or  evil,  marked  the  whole  remainder 
of  his  course. 

About  1832  and  the  two  or  three  following  years  of  political 
excitement,  he  published  writings  in  the  “Examiner”  and  other 


266  Proceedings  of  the  Royal  Society 

newspapers,  and  in  the  “ Monthly  Repository,”  which  were  more 
according  to  his  matured  judgment  than  his  previous  periodical 
essays. 

His  father  died  in  June  1836.  This  seems  to  have  freed  him 
from  some  restraints  and  reticences.  His  friend  Sir  William 
Molesworth,  a political  and  metaphysical  thinker,  had  proposed 
to  found  a new  Review,  provided  Mr  Mill  would  agree  to  conduct 
it.  In  this  way  he  was  editor  of  the  “London” — latterly  the 
“London  and  Westminster — Review”  in  the  years  between  1835 
and  1840.  This  Review  was  the  organ  which  he  then  used  for 
the  spread  of  his  opinions.  It  enabled  him  to  express  in  print 
the  results  of  his  altered  modes  of  thought,  and  to  separate  him- 
self in  a marked  manner  from  the  narrower  Benthamism  of  his 
early  writings.  He  resigned  the  editorship  in  1840,  after  which 
he  usually  preferred  for  his  essays  the  wider  circulation  of  the 
“ Edinburgh  Review.” 

The  first  use  Mr  Mill  made  of  the  leisure  gained  by  freedom  from 
the  cares  of  a brilliant  editorship  was  to  resume  his  “Logic.”  The 
preparation  of  this  historically  important  treatise  had  occupied  him 
at  intervals  for  twelve  years.  In  1841  it  was  ready  for  the  press, 
but  circumstances  delayed  the  publication  till  the  spring  of  1843. 
He  now  appeared  for  the  first  time  as  the  author  of  a book,  and  of 
his  greatest  book — “A  System  of  Logic,  Ratiocinative  and  In- 
ductive, being  a Connected  View  of  the  Principles  of  Evidence 
and  the  Methods  of  Scientific  Investigation.”  It  is  the  most 
elaborate  treatise  in  the  English  language  on  the  logical  procedure 
in  Induction.  Since  the  publication  of  the  “Novum  Organum”  and 
the  “ Essay  on  Human  Understanding,”  no  such  comprehensive 
attempt  in  logical  theory  and  the  principles  of  the  formation  of 
knowledge. had  been  made  by  an  Englishman.  Mr  Mill  had  not 
forgotten  his  early  studies  in  Aristotelian  logic,  which,  in  his 
correlation  of  induction  and  syllogism,  he  tried  to  assimilate  with 
the  methods  of  modern  science.  If  we  do  not  accept  the  result 
as  satisfactory,  we  may  at  any  rate  allow  that  it  has  usefully  called 
attention  to  the  one-sidedness  of  merely  formal  logic.  If  he  fails 
to  show  that  all  inference  is  ultimately  from  observed  particulars 
to  unobserved  particulars,  without  any  need  for  general  notions, 
he  has  at  least  helped  to  prove  the  fruitlessness  of  merely  verbal 


267 


o f Edin  burgli , Session  1873-74. 

syllogising,  and  to  show  the  part  which  facts  have  in  all  our  actual 
reasonings.  It  is  as  a logician  probably  that  Mr  Mill  will  be 
longest  remembered  in  the  history  of  English  and  European 
thought,  and  as  having  connected  the  revived  logical  studies  of  this 
country  with  the  spirit  and  procedure  of  modern  experimental 
science. 

The  same  decade  which  gave  birth  to  Mr  Mill’s  “ Logic  ” saw 
the  first  publication  of  the  other  great  treatise  of  his  life — next  in 
importance  to  his  “ Logic.”  In  1848  his  “ Principles  of  Political 
Economy,  with  some  of  their  Applications  to  Social  Philosophy,” 
were  given  to  the  world.  Through  this  book  he  became  to  the 
nineteenth  century  in  some  degree  what  Adam  Smith  had  been  to 
the  eighteenth  by  his  “ Wealth  of  Nations.”  It  had  been  heralded 
in  1844  by  “ Five  Essays  on  some  Unsettled  Questions  in  Eco- 
nomic Science.”  The  “Political  Economy  ’’showed  a return  in 
some  particulars  from  his  previous  extreme  of  reaction  against 
his  early  Penthamism,  along  with  a disposition  to  sceptical  criticism 
of  many  of  the  presuppositions  of  the  older  school  of  political  econo- 
mists. His  ideas  of  ultimate  social  improvement  were  becoming 
more  revolutionary.  His  view  of  private  property  was  becoming 
modified,  and  especially  of  the  rights  of  individuals  to  land.  Co- 
operation and  Socialism  began  to  take  the  place  of  Competition 
and  Democracy  in  his  thoughts. 

The  “ System  of  Logic”  and  the  “ Principles  of  Political  Eco- 
nomy ” are  the  two  books  round  one  or  the  other  of  which  almost 
all  that  Mr  Mill  has  ever  written  may  be  said  to  circulate.  The 
one  describes  his  view  of  the  intellectual  means  ; the  other  is 
connected  with  the  aim  or  end  of  the  whole  labour  of  his  manhood. 
The  logical  employment  of  intellect  for  the  improvement  of  society 
was  in  brief  his  life.  Eight  editions  of  the  “ Logic  ” have  now 
been  published;  the  “Political  Economy,”  after  passing  through 
seven  editions,  was  issued  in  a cheap  form  in  1865. 

The  ten  years  which  followed  the  publication  of  the  “ Political 
Economy”  formed  a long  pause  in  Mr  Mill’s  course  as  an  author. 
He  was  married  to  Mrs  Taylor  in  April  1851,  her  former  husband 
having  died  two  years  before.  They  lived  in  extreme  seclusion 
for  some  years,  withdrawn  even  from  the  society  of  his  intimate 
friends,  and  under  influences  which  tended  again  to  confine  his 

2 M 


¥OL.  vm. 


268  Proceedings  of  the  Royal  Society 

sympathies.  The  silence  was  broken  only  by  an  occasional  article 
in  the  “ Edinburgh  Review/5  or  by  replies  to  criticisms  on  one  or 
other  of  his  two  great  books. 

Changes  now  occurred.  In  1856  he  was  made  Examiner  of 
Indian  Correspondence,  and  thus  placed  at  the  head  of  the  office 
in  the  India  House,  in  which  he  had  served  for  thirty-three  years. 
In  the  following  year  the  Government  of  India  was  transferred 
from  the  Company  to  the  Crown  ; after  an  unavailing  remonstrance, 
drafted  by  Mr  Mill,  in  the  name  of  the  Court  of  Directors,  which 
was  pronounced  by  Lord  Grey  the  ablest  State  paper  he  had  ever 
read.  He  afterwards  declined  an  invitation  by  the  present  Lord 
Derby,  then  Indian  Secretary,  to  form  one  of  the  newly-constituted 
Board  of  Indian  Council. 

Mr  Mill  had  arranged  to  spend  the  winter  of  1858-59 — the  first 
after  his  retirement  from  office — in  the  south  of  Europe.  The  death 
of  his  wife  at  Avignon,  on  their  journey,  frustrated  his  plans  and 
hopes.  The  profound  effect  of  this  event  upon  his  feelings  is  ex- 
pressed in  the  most  touching  sentences  he  ever  wrote,  and  to  which 
there  are  few  parallels  in  literature.  It  induced  him  to  settle  as 
near  as  possible  to  the  place  where  she  was  buried.  It  thus 
became  his  habit  to  spend  a great  part  of  each  year  in  his  cottage 
at  Avignon. 

He  soon  reappeared  as  an  author.  His  essay  on  “ Liberty 55  was 
published  in  1859.  It  had  been  planned  and  written  as  a short 
paper  in  1854.  It  was  in  mounting  the  steps  of  the  Capitol  in  the 
following  year  that  the  thought  suggested  itself  of  converting  it 
into  a volume.  The  essay  is  a vindication  of  the  importance  to 
society,  and  for  the  discovery  of  truth,  of  giving  men  full  freedom 
to  expand  themselves  in  opposite  and  even  conflicting  directions, 
limited  only  by  the  prevention  of  injury  to  others.  This  little 
volume  may  be  supposed  to  have  had  no  inconsiderable  effect  in 
promoting  that  toleration  for  the  free  expression  of  opinion, 
even  regarding  beliefs  longest  reverenced,  which,  compared  with 
the  past,  is  a remarkable  characteristic  of  this  generation  in  Great 
Britain. 

In  the  same  year  Mr  Mill  republished,  in  a collected  form,  in 
two  volumes,  under  the  title  of  “ Dissertations  and  Discussions,” 
articles  formerly  contributed  to  the  “ London/5  “ London  and  West- 


269 


of  Edinburgh,  Session  1873-74. 

minster,”  and  “Edinburgh  ” Reviews,  as  well  as  to  other  periodicals  : 
a third  volume  followed  in  1867.  A pamphlet  of  “ Thoughts  on 
Parliamentary  Reform”  was  also  produced  in  1859.  In  1861  he 
published  “ Considerations  on  Representative  Government.” 

In  1862  the  essay  on  “Utilitarianism”  appeared.  It  contains 
his  latest  view  of  ethical  theory,  and  of  the  new  criterion  of  morality 
which  it  was  one  great  endeavour  of  his  life  to  make  known. 

Mr  Mill’s  principal  contribution  to  analytical  psychology  and 
metaphysics  was  made  in  1865.  It  took  the  form  of  an  “ Examin- 
ation of  Sir  William  Hamilton’s  Philosophy;”  a large  and  elaborate 
volume,  equal  in  scope  and  comprehensiveness  to  his  greatest  works. 
The  “ Examination  ” is  a sort  of  philosophical  supplement  to  his 
“Logic,”  in  which  many  of  the  principles  here  argued  had  been 
silently  assumed.  Its  tendency  is  to  promote  an  explanation, 
through  circumstances  and  association,  of  beliefs  and  feelings, 
which  are  apparently  necessary  and  universal ; in  opposition  to 
those  who  treat  them  as  ultimate  elements  of  human  nature,  and 
even  as  absolute  or  ontological  necessities  of  reason.  By  Mr  Mill 
this,  like  other  questions,  was  not  regarded  as  a mere  matter  of 
abstract  speculation.  Like  his  illustrious  predecessor  Locke,  he 
thought  he  saw,  in  a prevailing  tendency  to  consider  some  princi- 
ples to  be  independent  of  the  verification  of  experience,  one  of  the 
most  powerful  obstructions  to  the  efforts  of  the  social  reformer; 
and,  like  his  predecessors  on  the  same  path,  it  may  be  thought  that 
his  theory  makes  science  speculatively  impossible  for  man.  If 
rationality  in  nature  is  the  basis  of  science,  knowledge  must  pre- 
suppose reason  in  nature  as  the  condition  of  its  own  existence ; and 
then  all  ordinary  inductive  verification  proceeds  on  the  assumption 
of  beliefs  which  do  not  admit  themselves  of  being  verified  by  obser- 
vation. 

This  remarkable  essay  in  metaphysics  was  followed  by  an  essay 
in  which  he  offers  his  final  estimate  of  “ Auguste  Comte  and  Posi- 
tivism.” 

After  this  productive  literary  period,  Mr  Mill  was  withdrawn  for 
three  years  from  his  studious  seclusion  at  Avignon.  At  the  general 
election  in  1865  he  was  chosen  member  for  Westminster,  and  he 
appeared  in  the  House  of  Commons  when  Parliament  met  in 
February  1866.  In  that  and  the  two  following  sessions  he  was  an 


270 


Proceedings  of  the  Royal  Society 

active  and  deeply  interested  member  of  the  House  of  Commons — 
sessions  of  Parliament  which  passed  the  second  Reform  Bill.  He 
spoke  occasionally,  and  was  heard  with  respect  and  curiosity,  as 
the  representative  of  large  philosophical  principles  and  a sort  of 
philanthropic  socialism.  The  advocacy  of  women’s  suffrage  is  that 
perhaps  with  which  his  Parliamentary  name  is  most  associated.  In 
these  years  in  England,  he  lived  at  Blackheath. 

One  result  of  the  general  election  in  November  1868  was  to  send 
Mr  Mill  hack  to  his  old  pursuits,  and  to  seclusion  at  Avignon.  The 
Parliamentary  episode  had  not  indeed  entirely  interrupted  his 
studies.  In  1866  he  read  through  Plato,  as  a preparation  for  a 
review  of  G-rote.  A fervid  pamphlet  in  the  same  year,  on  “ England 
and  Ireland,”  urged  a radical  reform  in  the  land  system  of  the  sister 
island.  In  1867  he  delivered  an  elaborate  address  on  the  Higher 
Education  to  the  students  of  the  University  of  St  Andrews,  who 
had  chosen  him  as  their  Rector.  He  was  also  employed  about  a 
new  edition  of  his  father’s  “ Analysis  of  the  Human  Mind,”  in 
conjunction  with  Mr  G-rote,  Professor  Bain,  and  our  townsman  Dr 
Findlater,  which  was  published  in  1869. 

The  years  which  followed  Mr  Mill’s  short  Parliamentary  career 
were  mostly  spent  at  Avignon,  where  he  continued  his  life  of 
literary  labour.  His  essay  on  the  “ Subjection  of  Women”  ap- 
peared in  1869,  and  this,  with  his  efforts  in  Parliament,  helped 
to  make  the  education,  and  the  political  and  social  condition  of  the 
sex  one  of  the  questions  of  the  day.  His  last  published  writing  in 
philosophy  of  which  I am  aware  was  a review,  in  November  1871, 
of  the  Clarendon  Press  edition  of  Berkeley’s  works.  He  had  always 
been  a great  admirer  of  Berkeley.  In  this  essay  he  expresses  the 
opinion  that  “of  all  who  from  the  earliest  times  have  applied  the 
powers  of  their  minds  to  metaphysical  inquiries,  Berkeley  was  the 
one  of  greatest  philosophical  genius;  though  among  these  are 
included  Plato,  Hobbes,  Locke,  Hartley,  and  Hume,  as  well  as 
Des  Cartes,  Spinoza,  Leibnitz,  and  Kant.”  But  it  was  the  negative 
and  analytic  side  of  Berkeley  that  he  admired ; he  had  no  appre- 
ciation of  the  constructive  part  of  his  doctrine,  on  which  Berkeley 
himself  lays  most  stress. 

In  March  of  last  year,  Mr  Mill  visited  London,  and  lived  for 
six  weeks  in  a suite  of  rooms  he  had  taken  in  Victoria  Street, 


of  Edinburgh,  Session  1873-74  271 

Westminster.  He  spoke  at  a meeting  on  the  land  question,  in 
support  of  kis  opinion  with  regard  to  “ the  unearned  increment  in 
the  value  of  land.”  He  had  previously  published  “ Chapters  and 
Speeches  on  the  Irish  Land  Question,”  followed  by  a “Programme 
of  the  Land  Tenure  Reform  Association.”  During  these  weeks  in 
London  he  mixed  much  in  society.  The  writer  of  this  Notice 
spent  part  of  Mr  Mill’s  last  day  in  England  with  him  in  his 
rooms  in  Westminster,  when  he  seemed  full  of  physical  and 
intellectual  vigour,  and  indulged  in  youthful  recollections  of  his 
father  and  of  Bentham.  Next  day,  the  18th  of  April,  he  returned 
to  Avignon.  On  Saturday  the  3d  of  May,  he  made  a long 
botanising  excursion  in  that  neighbourhood.  Botanical  research 
had  been  an  enthusiasm  of  his  life,  and  his  original  collection  of 
herbaria  is,  I believe,  of  great  value.  He  caught  a chill  on  his 
way  home.  It  issued  in  a severe  form  of  erysipelas,  of  which  he 
died  on  the  morning  of  the  following  Thursday.  He  was  buried 
the  day  after  beside  his  wife.  The  Protestant  pastor,  the  physi- 
cian, and  his  domestic  servant,  formed  the  small  company  of 
mourners  who  saw  him  laid  in  his  grave. 

Mr  Mill’s  appearances  in  public  in  his  later  years,  aided  by  the 
art  of  the  photographer,  have  made  his  earnest,  thoughtful  face, 
with  its  sensitive,  nervous  action,  familiar  to  many.  A refined, 
delicate  organism,  and  wiry  form,  suggested  the  moderately  good 
health  which,  notwithstanding  extraordinary  intellectual  labour 
he  enjoyed  through  life.  He  was  fond  of  walking ; allured 
by  his  love  of  botany  and  his  passion  for  rural  nature.  He 
was  a great  reader  of  all  sorts  of  current  and  periodical  litera- 
ture. His  conversation,  like  his  books,  was  remarkable  for  its 
abundance  of  logically  digested  information,  judicially  deliberate, 
distinct,  and  everywhere  vivified  by  the  presence  of  active  intelli- 
gence. He  showed  little  or  no  appreciation  of  humour,  hut  both 
his  spoken  and  written  words  revealed  a subdued  and  grave  emo- 
tional fervour,  especially  for  the  propagation  of  opinions  in  which 
he  believed,  and  the  promotion  of  social  changes  which  be  supposed 
to  be  advantageous. 

Probably  no  contemporary  has  modified  more  than  Mr  Mill  the 
tone  and  manner  of  thinking  of  the  fairly-educated  community  in 
G-reat  Britain.  The  time  is  hardly  come,  however,  for  a satisfac- 


272  Proceedings  of  the  Royal  Society 

tory  estimate  of  what  he  has  done,  what  he  has  failed  to  do,  and 
what  his  influence  in  the  future  is  likely  to  be.  The  habit  of 
thinking  characteristic  of  this  generation  is  too  much  affected  by 
his  logical  methods,  and  pervaded  by  his  spirit,  to  admit  of  a per- 
fectly just  estimate. 

That  he  has  been  in  a great  degree  the  representative  English 
thinker  of  his  generation  will  be  generally  allowed ; for  we  already 
see  enough  to  recognise  in  him  the  leader  in  this  age  of  that 
school  of  British  philosophy,  which,  in  the  seventeenth  century, 
was  represented  by  Hobbes  and  Locke,  and  in  last  century  by 
Hartley  and  Hume.  If  he  wanted  the  rugged  masculine  vigour 
and  originality  of  Hobbes,  he  had  more  ardent  sympathies  and  a 
more  indulgent  candour.  Locke  undoubtedly  far  excelled  him  in 
massive  common  sense  and  in  practical  knowledge  of  human 
nature,  and  was  more  complete  as  a man ; but  he  was  hardly 
superior  as  a subtle  analytical  psychologist,  or  equal  as  a lucid 
expositor.  If  Mr  Mill  wanted  Hume’s  grace,  humour,  gaiety  of 
temper,  and  insight,  in  the  expression  of  a philosophy  of  life  in  a 
large  degree  common  to  them  both,  he  had  a moral  earnestness  and 
intensity  of  sentiment  which  one  does  not  find  in  Hume.  Mill 
was  eminently  a logician  rather  than  a metaphysician  or  a specu- 
lative moralist ; his  conception  of  life  was  limited  in  its  scope 
and  aim.  He  methodised  the  experience  of  an  age  devoted  to  the 
physical  sciences,  and  tending  towards  materialism.  He  was  not 
a speculative  philosopher,  who  sought  to  comprehend  the  universe  : 
he  was  a reformer  who  wanted  to  make  society  better,  by  improving 
its  relations  to  its  circumstances  on  this  planet.  He  accordingly 
explained  to  his  countrymen  their  own  scientific  habits  of  research, 
in  which  inductive  methods  and  presuppositions  are  employed  with 
extraordinary  vigour  and  success,  for  the  improvement  of  circum- 
stances and  of  the  external  arrangements  of  society.  As  a meta- 
physician, he  always  tried  to  keep  speculation  within  the  limits  of 
positive  science,  and  to  dissolve  by  analysis,  as  hurtful  prejudices, 
the  faith  or  thought  which  does  not  admit  of  ordinary  inductive 
verification,— thus,  it  may  be  alleged,  overlooking  in  man,  and  with- 
drawing from  human  life,  some  of  their  best  and  noblest  possessions. 

Yet  in  some  of  their  aspects  Mr  Mill’s  life  and  writings  witness  to 
a broader  and  deeper  philosophy  than  he  professed.  His  heart  and  his 


273 


of  Edinburgh,  Session  1873-74. 

sympathies  outgrew  the  adverse  influences  of  a sunless  childhood. 
And  his  doctrines  in  metaphysics  and  ethics  sometimes,  I think, 
unconsciously  recognise  principles  which  break  the  logical  sym- 
metry of  his  professed  Utilitarianism  and  philosophy  of  Custom 
and  Association,  producing,  as  in  the  case  of  Locke  and  others, 
an  ambiguity  in  the  exposition  of  his  most  important  conclusions. 
As  Sir  James  Mackintosh  suggests  of  David  Hume,  it  would  indeed 
be  a matter  of  wonder  if  his  esteem  for  moral  excellence  should  not 
at  least  have  led  him  to  envy  those  who  are  able  to  contemplate 
the  perfection  of  excellence  in  the  Supreme  Reason  that  is  accepted 
by  them  as  the  support  of  their  lives,  and  the  all-reconciling  unity 
of  existence. 

2.  Obituary  Notes  of  the  Eev.  Dr  Guthrie.  By  the  Rev.  Dr 
Lindsay  Alexander. 

Dr  Thomas  Guthrie  was  a native  of  Brechin,  where  he  was  born 
on  the  12th  of  July  1803.  His  father,  David  Guthrie,  was  one  of 
the  principal  merchants  in  that  ancient  city,  and  long  occupied  an 
influential  position  in  it,  being  versant  in  all  its  affairs,  and  for 
several  years  holding  the  place  of  chief  magistrate.  Thomas  was 
his  sixth  son.  Having  received  a sound  elementary  education 
under  different  teachers  in  Brechin  and  the  vicinity,  Thomas 
was,  at  the  early  age  of  twelve,  entered  as  a student  in  the  Uni- 
versity of  Edinburgh ; and  there,  for  ten  consecutive  sessions,  he 
continued  prosecuting  studies  through  the  prescribed  curriculum 
in  arts  and  divinity,  with  the  addition  of  certain  branches  of  natural 
science,  to  which  he  spontaneously  betook  himself.  In  1825  he 
received  from  the  Presbytery  of  Brechin  license  as  a preacher,  and 
began  forthwith  to  preach  as  occasion  presented  itself.  Shortly 
after  he  was  offered  the  presentation  to  an  important  charge,  but 
as  the  offer  was  clogged  with  conditions  which  appeared  to  him  to 
threaten  his  independence  of  thought  and  action  he  declined  it; 
and  no  other  professional  opening  appearing  he  went  to  Paris, 
where,  for  the  best  part  of  a year,  he  prosecuted  medical  studies  at 
the  Sorbonne,  attending  the  lectures  of  Gay-Lussac,  Thenard,  and 
St  Hilaire,  and  witnessing  surgical  operations  by  Dupuytren  and 
Lisfranc  at  the  hospitals.  On  his  return  home,  being  still  dis- 


274  Proceedings  of  the  Royal  Society 

appointed  in  his  professional  prospects,  he  purposed  spending  a 
year  at  one  of  the  G-erman  universities,  but  from  this  he  was 
turned  aside  in  consequence  of  the  death  of  his  elder  brother,  who 
was  a banker  in  Brechin,  and  who,  dying  somewhat  suddenly,  left 
his  business  in  danger  of  being  transferred  to  other  hands,  unless 
some  one  should  be  found  to  carry  it  on  until  such  time  as  his 
son,  then  a boy,  should  be  able  to  succeed  him.  In  this  emer- 
gency the  only  one  of  the  family  who  was  free  to  come  to  the  help 
of  the  minor  was  his  uncle  Thomas,  and  he  at  once  threw  himself 
into  the  breach,  and  for  two  years  conducted  the  business  of  the 
bank.  On  this  he  looked  back  with  satisfaction  as  affording  not 
the  least  valuable  part  of  his  training  and  education,  as  it  brought 
him  acquainted  with  the  busy  world,  enlarged  his  knowledge  of 
men  and  things,  and  gave  him  an  aptitude  for  the  management  of 
affairs  of  which  he  found  the  advantage  in  after  life.  Whilst 
engaged  in  the  business  of  the  bank  he  did  not  intermit  his  studies 
or  neglect  opportunities  of  preaching  when  these  were  offered  to 
him.  He  thus  let  it  be  known  that  he  had  no  intention  of  aban- 
doning his  proper  profession,  and  was  only  waiting  till  some  suit- 
able sphere  was  opened  for  him  to  enter  upon  the  active  discharge 
of  its  duties.  Such  a sphere  was  at  length  obtained  by  his  being 
presented  to  the  church  and  parish  of  Arbirlot,  in  Forfarshire, 
where  he  was  ordained  minister  on  the  13th  of  May  1830.  Here 
he  continued  to  labour  with  much  assiduity  and  success  for  seven 
years,  caring  not  only  for  the  spiritual  interests  of  his  people,  but 
bringing  all  the  resources  which  previous  culture  and  observation, 
as  well  as  natural  ability  and  good  sense,  had  enabled  him  to 
accumulate,  to  bear  upon  the  promotion  of  their  temporal  welfare. 
Here  he  laid  the  foundation  of  that  eminence  as  a preacher  which 
he  afterwards  attained,  and  here  also  he  entered  on  that  acquaint- 
ance with  the  condition,  habits,  wants,  and  perils  of  the  poor, 
which  in  after  years  he  turned  to  such  excellent  account  in  his 
philanthropic  efforts.  The  fame  of  his  power  in  the  pulpit  as  a 
preacher,  as  well  as  of  his  administrative  ability  in  his  parochial 
cure,  having  reached  the  metropolis,  where  personally  he  was  a 
stranger,  he  was  in  1.837  presented  to  the  church  and  parish  of 
Old  G-reyfriars,  Edinburgh,  as  colleague  with  the  lateKev.  J.  Sym. 
This  charge  he  accepted,  on  the  understanding  that  he  would 


275 


of  Edinburgh,  Session  1873-74. 

exchange  it  for  a single  charge  as  soon  as  arrangements  could  be 
made  for  erecting  a new  parish  in  one  of  the  more  densely  crowded 
and  spiritually  destitute  parts  of  the  city.  This  was  accomplished 
when  the  new  church  was  built  in  what  used  to  be  the  West  Bow, 
but  where  Victoria  Street  now  stands ; and  on  this  Mr  Gluthrie 
entered  as  the  minister  of  the  new  parish  of  St  John’s  in  1840, 
determined,  as  far  as  in  him  lay,  to  work  out  the  theory  of  tho  old 
parochial  system  in  the  centre  of  the  city,  and  among  a population 
many  of  whom  were  sunk  in  vice  and  degradation.  Here  he  con- 
tinued till  the  great  secession  from  the  Church  of  Scotland  in 
1843,  when,  having  cast  in  his  lot  with  the  retiring  party,  of 
whose  principles  he  cordially  approved,  and  in  whose  proceedings 
he  had  taken  an  active  share,  he  resigned  his  parochial  charge 
and  removed  from  the  church  of  St  John’s,  carrying  with  him  his 
congregation.  After  some  time,  during  which  he  preached  in  the 
Methodist  Chapel,  Nicolson  Square,  a new  place  of  worship  was 
erected  not  far  from  that  which  he  had  left,  and  to  this,  which 
came  to  be  called  Free  St  John’s,  he  removed  in  1844.  In  this 
church,  where  subsequently  he  had  for  his  colleague  the  Rev.  Dr 
Hanna,  he  continued  to  preach  from  Sunday  to  Sunday  to  audi- 
ences which  crowded  every  corner,  where  room  to  sit  or  to  stand 
could  be  found,  for  twenty  years.  During  this  period  he  was  un- 
doubtedly the  most  popular  preacher  in  Scotland,  perhaps  in 
Britain.  Persons  of  all  ranks,  and  of  every  variety  of  culture, 
were  found  among  his  regular  auditors;  and  illustrious  strangers, 
statesmen,  economists,  and  men  of  literature  who  visited  the  city, 
were  often  seen  in  the  crowded  pews.  The  care  which  he  bestowed 
on  the  preparation  of  his  discourses,  the  skill  with  which  he 
arranged  his  topics,  the  vigour  and  perspicuity  of  his  style,  and, 
above  all,  the  felicity  of  his  illustrations  and  the  truth  and  vivid- 
ness of  his  descriptions,  with  the  earnestness  of  his  tone  and  the 
ease  and  naturalness  of  his  delivery,  combined  to  secure  him  this 
pre-eminence  among  the  pulpit  orators  of  his  day. 

But  it  was  not  only  in  the  pulpit  that,  at  this  time,  Mr  Guthrie 
distinguished  himself  and  drew  to  him  popular  esteem  and  homage. 
Even  more,  perhaps,  as  a philanthropist  than  as  a preacher  was  his 
fame  spread  through  the  community.  In  him  all  good  causes 
found  an  able  and  willing  advocate ; but  it  is  chiefly  with  efforts 

2 N 


VOL.  VIII. 


276 


Proceedings  of  the  Royal  Society 

for  the  prevention  of  intemperance,  and  the  rescue  of  destitute  and 
degraded  children,  that  his  name  is  associated.  Though  not 
exactly  the  founder  of  ragged  schools,  he  was  the  first  to  take  a 
just  estimate  of  their  importance,  the  first  to  arouse  the  com- 
munity in  their  favour,  and  the  first  to  organise  them  formally  and 
on  an  adequate  scale ; and  to  his  powerful  advocacy  and  persever- 
ing assiduity  and  care  it  is  chiefly  owing  that  these  institutions  are 
now  so  firmly  established  throughout  the  kingdom,  where  they 
have  largely  contributed  to  diminish  pauperism,  prevent  crime, 
and  add  to  the  industrial  strength  of  the  nation.  If  his  efforts  for 
the  suppression  of  intemperance  have  not  met  with  the  same 
success  it  is  not  because  these  were  put  forth  with  less  zeal,  perse- 
verance, and  self-denial  on  his  part,  but  because  tbe  evil  has  grown 
to  such  a gigantic  height  as  to  render  almost  hopeless  all  attempts 
to  remove  or  cure  it.  Nor,  in  referring  to  his  labours  for  the 
benefit  of  others,  should  his  great  effort  to  raise  money  for  the 
erection  of  comfortable  residences  for  his  brethren  in  the  ministry 
be  overlooked  or  mention  of  it  omitted, — an  effort  to  which,  at  a 
great  amount  of  personal  sacrifice,  he  devoted  an  entire  year, 
traversing  the  country  from  end  to  end,  visiting  family  after 
family,  ‘‘from  Cape  Wrath  to  the  Border,  and  from  the  German 
to  the  Atlantic  Ocean,”  and  bringing  into  the  treasury  of  his 
Church,  for  the  purpose  he  had  in  view,  upwards  of  L. 116, 000.  It 
was  when  appearing  on  the  platform,  as  the  advocate  of  such 
schemes  of  benevolence,  that  he  came  out  in  all  his  strength  as 
an  orator.  On  such  occasions  all  his  faculties  had  full  play,  and 
his  mastery  over  his  audience  was  complete — at  one  time  guiding 
their  judgments  by  reasoning  and  strong  good  sense,  at  another, 
bearing  them  along  on  the  stream  of  impassioned  declamation — 
now  melting  them  to  tears  by  some  deep  touch  of  pathos  or  some 
thrilling  tale  of  sorrow  or  of  suffering,  and  anon  convulsing  them 
with  laughter  by  some  rich  stroke  of  humour,  some  amusing 
description,  or  some  ludicrous  anecdote.  The  only  weapon  of  the 
orator  which  he  did  not  use  was  sarcasm,  for  which  his  kindly 
nature  had  no  taste. 

In  recognition  of  his  abilities  and  valuable  public  services,  the 
University  of  Edinburgh  conferred  on  him,  in  1849,  the  degree  of 
D.D.  In  May  1862  he  was  raised  to  the  Moderator’s  chair  in  the 


277 


of  Edinburgh,  Session  1873-74. 

twentieth  General  Assembly  of  the  Free  Church  of  Scotland, — a 
dignity  which,  in  all  probability,  would  have  been  conferred  on  him 
some  years  earlier  had  the  state  of  his  health  permitted  him  to 
undertake  the  duties  of  the  office. 

Gifted  with  a vigorous  constitution,  Dr  Guthrie  had  enjoyed 
good  health,  notwithstanding  the  excitement  and  toil  attendant  on 
the  discharge  of  his  official  functions  and  his  philanthropic  efforts. 
But  the  continuous  over-exertion  to  which  he  was  exposed,  espe- 
pecially  in  connection  with  the  Manse  scheme,  began  at  length 
to  tell  upon  him,  and  alarming  symptoms,  the  prelude  of  that  dis- 
ease which  ultimately  carried  him  off,  became  apparent.  By  the 
advice  of  medical  friends  he  was  induced,  though  reluctantly,  to 
retire  from  the  public  exercise  of  his  ministry,  and  from  all  engage- 
ments that  might  have  an  exciting  effect  upon  the  system.  This 
took  place  in  1864,  when  a valuable  testimonial  was  presented  to 
him,  amounting  to  L.5000,  contributed  by  friends  and  admirers  in 
all  parts  of  the  kingdom.  On  his  retirement  from  the  pulpit,  Dr 
Guthrie  devoted  himself  chiefly  to  literary  pursuits.  He  became 
editor  of  the  “ Sunday  Magazine,”  and  contributed  largely  to  its 
pages.  Whilst  thus  employed  he  found  time  to  make  repeated 
excursions  to  the  continent;  and  of  his  contributions  to  the  “ Sun- 
day Magazine”  not  the  least  striking  and  instructive  is  a series  of 
papers  containing  graphic  sketches  of  what  he  saw  when  abroad, 
with  characteristic  observations  and  reflections  on  the  scenes  and 
incidents  he  describes.  Most  of  his  papers  in  the  magazine  were 
subsequently  collected  and  published  separately.  These,  with  some 
volumes  of  sermons  and  a few  pamphlets,  comprise  Dr  Guthrie’s 
efforts  as  an  author.  His  writings  have  been  widely  circulated 
in  Great  Britain,  the  colonies,  and  the  United  States,  and  have 
afforded  instruction  and  delight  to  thousands  who  never  saw  his 
face  or  heard  his  voice. 

After  his  retirement  from  the  pulpit  Dr  Guthrie  was  enabled  to 
continue  his  literary  labours  in  the  enjoyment  of  a considerable 
measure  of  vigour  till  towards  the  close  of  1872,  when  his  illness 
began  to  assume  a more  virulent  form.  In  the  beginning  of  the 
following  year  he  went  to  St  Leonards-on-the-Sea,  to  obtain  the 
benefit  of  the  milder  climate  of  that  locality ; and  there,  on  the 
24th  of  February,  he  closed  his  mortal  career.  His  remains  were 


278  Proceedings  of  the  Royal  Society 

brought  to  Edinburgh,  and  were  interred  in  the  G-range  Cemetery. 
The  funeral  was  attended  by  a very  large  company,  including  the 
magistrates  and  council  of  the  city,  ministers  of  nearly  every  deno- 
mination, both  in  the  city  and  from  different  parts  of  the  country, 
representatives  of  various  public  bodies,  the  directors  and  children 
of  the  Original  Bagged  School,  as  well  as  the  personal  friends  and 
relations  of  the  deceased.  The  procession  extended  for  about 
three  quarters  of  a mile,  and  moved  through  an  immense  crowd  of 
people  of  all  classes,  assembled  to  show  the  last  mark  of  respect  to 
one  than  whom  no  citizen  of  Edinburgh  was  better  known  or  more 
universally  esteemed,  as  well  for  his  private  virtues  and  noble 
character  as  for  his  unwearied  exertions  for  the  benefit  of  others, 
especially  for  the  relief  of  the  destitute  and  the  recovery  of  the 
fallen. 

3.  Obituary  Notice  of  Mr  E.  W.  Thomson.  By 
Professor  Fleeming  Jenkin. 

Mr  E.  W.  Thomson,  most  widely  known  as  the  inventor  of  the 
road-steamer,  died  on  the  8th  of  March  1873,  in  the  fiftieth  year 
of  his  age.  By  his  death  the  community  has  lost  a distinguished 
engineer,  a remarkable  thinker,  and  a highly  original  inventor. 

Bom  in  1822,  in  Stonehaven,  Mr  Thomson  furnishes  one  more 
example  of  the  many  Scotchmen  who  by  sheer  force  of  character, 
without  any  adventitious  aid,  have  risen  to  be  leaders  in  their 
profession  and  benefactors  to  their  country.  His  father  started 
on  a small  scale  the  only  factory  which  even  now  Stonehaven 
possesses,  and  destined  his  eldest  son  (the  subject  of  our  memoir) 
to  the  pulpit,  but  the  lad  showed  such  dislike  to  classical  studies 
that  he  was  sent  to  Charleston,  U.S.,  at  the  age  of  fourteen,  to 
be  educated  as  a merchant.  Commerce  proved  as  distasteful  as 
the  classics,  and  he  returned  at  the  age  of  sixteen  to  this  country, 
where  he  began  his  self-education,  aided  materially  by  a weaver 
who  chanced  to  be  a mathematician. 

Now,  when  scientific  and  technical  education  is  almost  thrust 
upon  careless  students,  it  is  well  to  remember  how  this  able  and 
successful  engineer  acquired  his  knowledge,  and  to  learn  that 
energy  in  the  pursuit  of  science  is  far  more  important  than  the 


279 


of  Edinburgh , Session  1872-73. 

most  elaborate  machinery  for  its  distribution.  At  this  time  Mr 
Thomson  conceived  the  idea  of  the  ribbon  saw,  afterwards  worked 
out  by  other  hands.  The  elliptic  rotary  steam-engine,  to  which  he 
afterwards  gave  much  time,  was  also  then  first  conceived  by  him. 
He  gained  some  experimental  knowledge  of  chemistry  and  elec- 
tricity, and  his  successful  application  of  these  sciences  in  after 
years  proves  the  rare  judgment  with  which  he  directed  his  studies. 
A short  practical  apprenticeship  in  workshops  at  Aberdeen  and 
Dundee  formed  the  next  step  in  his  education.  He  had  great 
pleasure  in  telling  how  the  foreman  at  the  end  of  the  first  fort- 
night’s work  paid  him  more  than  he  expected  to  receive,  and  when 
the  apparent  error  was  pointed  out,  told  him  that  there  was  no 
mistake,  “ he  was  worth  it.”  He  was  next  employed  by  a cousin, 
Mr  Lyon  (the  builder  of  the  Dean  Bridge),  in  connection  with  the 
blasting  by  which  Dunbar  Castle  was  blown  down,  and  on  this 
occasion  conceived  the  happy  idea  of  firing  mines  by  electricity. 
Having  brought  his  idea  into  a practical  form,  he  went  at  the 
age  of  nineteen  to  London.  Faraday,  to  whom  the  invention 
was  shown,  gave  him  hearty  encouragement ; and  Sir  William 
Cubitt  was  so  much  struck  by  the  idea  that  he  at  once  gave  him 
an  important  charge  in  connection  with  the  blasting  operations 
then  in  progress  near  Dover.  About  this  time  he  was  engaged 
with  a civil  engineer  in  Glasgow,  and  subsequently  passed  into  the 
employment  of  the  Stephensons. 

At  the  time  of  the  railway  mania,  he  was  twenty-two  years 
old,  and  began  business  on  his  own  account,  having  a large  staff, 
at  ten  guineas  per  diem,  engaged  in  making  plans  and  surveys 
for  a line  in  the  Eastern  counties.  He  even  achieved  a triumph 
over  Stephenson  before  a Parliamentary  Committee,  having  refused 
to  withdraw  from  competition  at  the  instance  of  influential  directors. 
The  route  he  had  chosen  was  ultimately  adopted,  although  by  other 
men,  as  the  railway  panic  at  the  time  stopped  the  undertaking. 

Debarred  by  the  result  of  the  panic  from  prosecuting  his  pro- 
fession as  a business,  Mr  Thomson  began  again  to  invent,  and 
devoted  much  time  to  the  introduction  of  india-rubber  tires,  which 
he  patented.  The  patent  was  not  profitable,  for  the  material  was 
scarce  and  dear,  and  its  manufacture  ill  understood ; but  he  was 
fortunately  rewarded  at  a later  date  by  finding  an  important  and 


280  Proceedings  of  the  Royal  Society 

successful  application  for  these  tires  in  connection  with  his  road- 
steamer.  At  this  period  of  comparative  leisure,  he  read  much,  and 
probably  laid  the  foundation  for  that  great  cultivation  and  wide 
range  of  information  which  were  so  remarkable  in  the  later  years 
of  his  life. 

When  railway  business  revived,  he  did  not  seek  to  re-enter  on 
the  practice  of  this  branch  of  his  profession,  which  had  no  attrac- 
tions for  him,  partaking  as  it  does  more  of  the  nature  of  commerce 
than  science.  As  a boy  he  nearly  lost  his  place  in  the  workshop 
by  refusing  to  repeat  some  operation  with  which  he  was  familiar, 
and  as  a man  he  never  cared  for  the  familiar  routine  which  is 
most  profitable.  He  sent  in  a creditable  design  for  the  great 
Exhibition  of  1851,  and  a little  invention  of  his,  “the  fountain 
pen,’’  was  sold  in  the  building.  In  1852  he  went  as  agent  for 
an  engineering  firm  to  Java,  to  erect  some  sugar  machinery,  and 
here  he  found  a new  field  in  which  his  powers  could  be  worthily 
exerted.  Although  without  capital,  he  was  offered  and  he  accepted 
a partnership  in  an  important  house  shortly  after  his  arrival.  He 
then  designed  machinery  for  the  manufacture  of  sugar  so  greatly 
superior  to  anything  previously  in  use  in  the  island,  as  to  give 
a great  impulse  to  the  production  of  that  commodity;  and  up  to 
the  time  of  his  death  he  continued  to  supply  the  best  machinery 
used  in  Java,  where  his  honourable  character  commanded  the 
unbounded  confidence  of  the  Dutch  planters. 

We  owe  perhaps  the  most  universally  useful  of  Mr  Thomson’s 
inventions  to  the  refusal  of  the  Dutch  authorities  to  allow  him 
to  erect  a waterside- crane,  unless  it  could  be  removed  every  night, 
lest  the  natives  should  stumble  over  it.  Mr  Thomson  hereupon 
designed  the  first  portable  steam-crane.  He  did  not  patent  the 
idea,  but  Messrs  Chaplin,  who  made  the  first  small  steam-crane 
for  him,  had,  when  he  next  re-visited  England,  two  large  factories 
engaged  in  the  manufacture  of  these  now  indispensable  appliances. 
The  invention  consisted  mainly  in  employing  the  boiler  as  a 
counterpoise.  In  1860  he  re-visited  Europe,  to  order  a hydraulic 
dock  consisting  of  a few  types  or  classes  of  plates,  each  plate  being- 
interchangeable  with  every  other  plate  of  its  class.  He  by  this 
plan  avoided  the  expense  of  double  erection  in  England  and 
abroad.  The  first  dock  thus  made  sunk  when  erected,  in  Mr 


281 


of  Edinburgh,  Session  1873-74. 

Thomson’s  absence,  owing  to  the  inexperience  of  the  young 
engineer  to  whom  it  was  intrusted.  Fortunately  two  other  docks 
from  Mr  Thomson’s  designs  were  in  course  of  construction, — one 
for  the  French  Government  at  Saigon,  and  the  other  for  a com- 
pany at  Callao.  These  have  been  thoroughly  successful. 

In  1862  Mr  Thomson  retired  from  business  in  Java  and  settled 
in  Edinburgh.  lie  devoted  much  time  and  labour  to  perfecting 
the  elliptic  rotary  engine,  a clear  and  simple  model  of  which  may 
be  seen  in  the  Industrial  Museum.  His  next  invention,  the  Road 
Steamer,  was  the  result  of  a direct  practical  want.  An  efficient 
traction  engine  was  required  for  the  transport  of  sugar-canes  in 
Java,  and  none  could  be  found  capable  of  doing  the  work.  Mr 
Thomson  recurred  to  his  old  idea  of  india-rubber  tires,  and  found 
in  these  a solution  of  the  main  difficulty  in  designing  a traction 
engine.  The  tires  are  not  fastened  to  the  wheel,  but  adhere  to 
it  by  friction.  They  form  a broad  pad  or  elephant’s  foot,  by  which 
the  great  weight  of  the  engine  is  distributed  over  a large  surface. 
The  outer  surface  adapts  itself  to  every  peculiarity  of  the  ground, 
and  the  inner  surface  forms,  as  it  were,  a constant  endless  platform 
on  which  the  comparatively  rigid  engine  works.  The  india-rubber 
does  in  a thoroughly  practical  manner  what  Boydell  attempted  to 
do  by  his  impracticable  endless  railway.  Both  inventors  wished 
to  enable  the  steam-engine  to  work  under  constant  conditions,  but 
Mr  Thomson’s  plan  is  strong,  simple,  and  yielding,  where  Boy- 
dell’s  was  weak,  complex,  and  rigid.  The  perfect  success  of  the 
plan  is  perhaps  best  attested  by  the  numerous  imitations  which 
it  has  called  forth,  the  object  in  most  of  these  being  to  dispense 
with  the  expensive  material  india-rubber.  The  steel-protecting 
grooves  for  the  tires  are  a later  invention,  and  only  a day  or  two 
before  his  death  the  inventor  made  an  important  improvement 
in  their  construction. 

The  zeal  and  energy  of  the  true  inventor  in  conquering  difficul- 
ties and  discouragement  have  often  been  told.  Those  who  had 
the  privilege  of  knowing  Mr  Thomson  have  seen  this  spectacle 
heightened  in  tragic  interest  by  the  grandeur  of  mind  with  which 
he  contended  against  the  terrible  malady  which  has  so  much  too 
soon  closed  his  labours.  If  mental  and  moral  qualities  could  be 
as  simply  described  as  mere  mechanical  inventions,  more  should 


282  Proceedings  of  the  Royal  Society 

be  said  of  the  man,  and  less  of  the  engineer.  No  written  record 
can  express  the  singular  powers  of  Mr  Thomson’s  mind  and  the 
charm  of  his  character.  The  specialist  in  science,  the  professed 
chemist,  the  professed  electrician,  the  professed  geologist,  the 
professed  lawyer,  all  received  suggestions  from  his  fertile  mind. 
The  able  and  original  paper  on  coal,  read  in  this  Society  shortly 
before  his  death,  affords  an  illustration  of  this  sagacity  of  thought 
on  subjects  not  specially  his  own.  In  art  he  had  a cultivated 
taste,  in  narration  and  conversation  he  was  unrivalled.  All  who 
conversed  with  him  felt  that  they  had  never  spoken  so  well  them- 
selves, and  had  seldom  met  with  so  sympathetic  a listener.  He 
had  an  untiring  toleration  for  the  failings  of  mankind,  without 
abating  for  an  instant  in  its  application  to  himself  the  high 
standard  which  he  shrank  from  applying  to  others.  Even  under 
terrible  pain,  his  enjoyment  of  truth,  of  nature,  of  all  that  was 
noble,  seemed  not  to  flag.  He  never  repined,  but  worked  to  the 
last  hour,  not  with  mere  resignation,  but  with  a noble  contentment. 

4.  Obituary  Notice  of  Archibald  Smith.  By 
Sir  William  Thomson. 

[Abridged  (by  direction  of  the  Author)  from  Proc.  R.  £.] 
Archibald  Smith,  only  son  of  James  Smith,  of  Jordanhill, 
Renfrewshire,  was  born  on  the  10th  of  August  1813,  at  G-reenhead, 
Glasgow,  in  the  house  where  his  mother’s  father  lived.  His  father 
had  literary  and  scientific  tastes  with  a strong  practical  turn, 
fostered  no  doubt  by  his  education  in  the  University  of  Glasgow, 
and  his  family  connection  with  some  of  the  chief  founders  of  the 
great  commercial  community  which  has  grown  up  by  its  side. 
In  published  works  on  various  subjects  he  left  enduring  monuments 
of  a long  life  of  actively  employed  leisure.  His  discovery  of 
different  species  of  Arctic  shells,  in  the  course  of  several  years’ 
dredging  from  his  yacht,  and  his  inference  of  a previously  existing 
colder  climate  in  the  part  of  the  world  now  occupied  by  the  British 
Islands,  constituted  a remarkable  and  important  advancement  of 
geological  science.  In  his  “ Voyage  and  Shipwreck  of  St  Paul,” 
a masterly  application  of  the  principles  of  practical  seamanship 
renders  St  Luke’s  narrative  more  thoroughly  intelligible  to  us  now 


283 


of  Edinburgh,  Session  1873-74. 

than  it  can  have  been  to  contemporary  readers  not  aided  by 
nautical  knowledge.  Later  he  published  a “ Dissertation  on  the 
Origin  and  Connection  of  the  Gospels,”  and  he  was  engaged  in 
the  collection  of  further  materials  for  the  elucidation  of  the  same 
subject  up  to  the  time  of  his  death,  at  the  age  of  eighty-five. 
Archibald  Smith’s  mother  was  also  of  a family  distinguished  for 
intellectual  activity.  Her  paternal  grandfather  was  Dr  Andrew 
Wilson,  Professor  of  Astronomy  in  the  University  of  Glasgow, 
whose  speculations  on  the  constitution  of  the  sun  are  now  generally 
accepted,  especially  since  the  discovery  of  spectrum-analysis  and 
its  application  to  solar  physics.  Her  uncle,  Dr  Patrick  Wilson, 
who  succeeded  to  his  father’s  Chair  in  the  University,  was  author 
of  papers  in  the  “ Philosophical  Transactions  ” on  Meteorology  and 
on  Aberration. 

Archibald  Smith’s  earliest  years  were  chiefly  passed  in  the  old 
castle  of  Roseneath.  In  1818  and  1819  he  was  taken  by  his  father 
and  mother  to  travel  on  the  continent  of  Europe.  Much  of  his 
early  education  was  given  him  by  his  father,  who  read  Yirgil  with 
him  when  he  was  about  nine  years  old.  He  also  had  lessons  from 
the  Roseneath  parish  schoolmaster,  Mr  Dodds,  who  was  very  proud 
of  his  young  pupil.  In  Edinburgh,  during  the  winters  1820-22, 
he  went  to  a day  school ; and  after  that,  living  at  home  at  Jordan- 
hill,  he  attended  the  Grammar  School  of  Glasgow  for  three  years. 
As  a boy  he  was  extremely  active,  and  fond  of  everything  that 
demanded  skill,  strength,  and  daring.  At  Roseneath  he  was  con- 
stantly in  boats;  and  his  favourite  reading  was  anything  about  the 
sea,  commencing,  no  doubt,  with  tales  of  adventurers  and  buc- 
caneers, but  going  on  to  narratives  of  voyages  of  discovery,  and  to 
the  best  text-books  of  seamanship  and  navigation  as  he  grew  older. 
He  had,  of  course,  the  ordinary  ardent  desire  to  become  a sailor, 
incidental  to  boys  of  this  island ; but  with  him  the  passion 
remained  through  life,  and  largely  influenced  the  scientific  work 
by  which  he  has  conferred  never-to-be-forgotten  benefits  on  the 
marine  service  of  the  world,  and  made  contributions  to  nautical 
science  which  have  earned  credit  for  England  among  maritime 
nations.  He  was  early  initiated  into  practical  seamanship  under 
his  father’s  instructions  in  yacht  sailing.  He  became  an  expert 
and  bold  pilot,  exploring  and  marking  passages  and  anchorages  for 

2 o 


VOL.  VIII. 


284  Proceedings  of  the  Royal  Society 

himself  among  the  intricate  channels  and  rocks  of  the  West  High- 
lands, when  charts  did  not  supply  the  requisite  information.  His 
most  loved  recreation  from  the  labours  of  Lincoln’s  Inn  was  always 
a cruise  in  the  West  Highlands.  In  the  last  summer  of  his  life,  after 
a naturally  strong  constitution  had  broken  down  under  the  stress  of 
mathematical  work  on  ships’  magnetism  by  night,  following  days 
of  hard  work  in  his  legal  profession,  he  regained  something  of  his 
health  and  strength  in  sailing  about  with  his  hoys  in  his  yacht, 
between  the  beautiful  coasts  of  the  Firth  of  Clyde,  hut  not  enough, 
alas  ! to  carry  him  through  unfavourable  influences  of  the  winter 
that  followed. 

In  1826  he  went  to  a school  at  Eedland,  near  Bristol,  for  two 
years;  and  in  1828  he  entered  the  University  of  Glasgow,  where 
he  not  only  began  to  show  his  remarkable  capacity  for  mathe- 
matical science  in  the  classes  of  Mathematics  and  Natural  Philo- 
sophy, but  also  distinguished  himself  highly  in  classics  and  logic. 
Among  his  fellow-students  were  Norman  Macleod  and  Archibald 
Campbell  Tait,  with  both  of  whom  he  retained  a friendship 
throughout  life.  After  completing  his  fourth  session  in  Glasgow, 
he  joined  in  the  summer  of  1832  a Cambridge  reading  party,  under 
Hopkins,  at  Barmouth  in  North  Wales,  and  in  the  October  follow- 
ing commenced  residence  in  Trinity  College,  Cambridge. 

While  still  an  undergraduate  he  wrote  and  communicated  to  the 
Cambridge  Philosophical  Society  a paper  on  Fresnel’s  wave-surface. 
The  mathematical  tact  and  power  for  which  he  afterwards  became 
celebrated  were  shown  to  a remarkable  degree  in  this  his  first 
published  work. 

In  1836  he  took  his  degree  as  Senior  Wrangler  and  first  Smith’s 
Prizeman,  and  in  the  same  year  he  was  elected  to  a Fellowship  in 
Trinity  College. 

Shortly  after  taking  his  degree,  he  proposed  to  his  friend  Duncan 
Farquliarson  Gregory,  of  the  celebrated  Edinburgh  mathematical 
family,  then  an  undergraduate  of  Trinity  College,  the  establish- 
ment of  an  English  periodical  for  the  publication  of  short  papers 
on  mathematical  subjects.  Gregory  answered  in  a letter  of  date 
December  4th,  1836,  cordially  entering  into  the  scheme,  and 
undertaking  the  office  of  editor.  The  result  was  the  “ Cambridge 
Mathematical  Journal,”  of  which  the  first  number  appeared  in 


285 


of  Edinburgh,  Session  1873-74. 

November  1837.  It  was  carried  on  in  numbers,  appearing  three 
times  a year,  under  the  editorship  of  Gregory,  until  his  death,  and 
has  been  continued  under  various  editors,  and  with  several  changes 
of  name,  till  the  present  time,  when  it  is  represented  by  the 
“ Quarterly  Journal  of  Mathematics”  and  the  “Messenger  of 
Mathematics.”  The  original  “ Cambridge  Mathematical  Journal  ” 
of  Smith  and  Gregory,  containing  as  it  did  many  admirable  papers 
by  Smith  and  Gregory  themselves,  and  by  other  able  contributors, 
early  attracted  to  it,  among  whom  were  Greatheed,  Donkin, 
Walton,  Sylvester,  Ellis,  Cayley,  Boole,  inaugurated  a most  fruitful 
revival  of  mathematics  in  England,  of  which  Herschel,  Peacock, 
Babbage  and  Green,  had  been  the  prophets  and  precursors. 

It  is  much  to  be  regretted  that  neither  Cambridge  nor  the 
university  of  his  native  city  could  offer  a position  to  Smith, 
enabling  him  to  make  the  mathematical  and  physical  science  for 
which  he  felt  so  strong  an  inclination,  and  for  which  he  had  so 
great  capacity,  the  professional  work  of  his  life.  Two  years  after 
taking  his  degree,  he  commenced  reading  law  in  London,  but  his 
inclination  was  still  for  science.  Relinquishing  reluctantly  a 
Trinity  Lectureship  offered  to  him  by  Whewell  in  1838,  and  offered 
again  and  almost  accepted  in  1810,  resisting  a strong  temptation 
to  accompany  Sir  James  Boss  to  the  Antarctic  regions  on  the 
scientific  exploring  expedition  of  the  “ Erebus”  and  “ Terror”  in 
1810-11,  and  regretfully  giving  up  the  idea  of  a Scottish  professor- 
ship, which,  during  his  early  years  of  residence  in  Lincoln’s  Inn, 
had  many  attractions  for  him,  he  finally  made  the  bar  his  pro- 
fession. But  during  all  the  long  years  of  hard  work,  through  which 
he  gradually  attained  to  an  important  and  extensive  practice,  and 
to  a high  reputation  as  a Chancery  barrister,  he  never  lost  his 
interest  in  science,  nor  ceased  to  be  actively  engaged  in  scientific 
pursuits;  and  he  always  showed  a lively  and  generous  sympathy 
with'  others,  to  whom  circumstances  (considered  in  this  respect 
enviable  by  him)  had  allotted  a scientific  profession. 

About  the  year  1811  his  attention  was  drawn  to  the  problem  of 
ships’  magnetism  by  his  friend  Major  Sabine,  who  was  at  that 
time  occupied  with  the  reduction  of  his  own  early  magnetic 
observations  made  at  sea  on  board  the  ships  “Isabella”  and 
“ Alexander,”  on  the  Arctic  Expedition  of  1818,  and  of  corres- 


286  Proceedings  of  the  Royal  Society 

ponding  magnetic  observations  which  had  been  then  recently  made 
on  board  the  “ Erebus”  and  “ Terror”  in  Captain  Ross’s  Antarctic 
Expedition  of  1840-41.  The  systematic  character  of  the  devia- 
tions, unprecedented  in  amount,  experienced  by  the  “Isabella” 
and  “ Alexander  ” in  the  course  of  their  Arctic  voyage,  had  attracted 
the  attention  of  Poisson,  who  published  in  1824,  in  the  “ Memoirs 
of  the  French  Institute,”  three  papers  containing  a mathematical 
theory  of  magnetic  induction  with  application  to  ships’  magnetism. 
The  subsequent  magnetic  survey  of  the  Antarctic  regions,  of  which 
by  far  the  greater  part  had  to  be  executed  by  daily  observations  of 
terrestrial  magnetism  on  ship-board,  brought  into  permanent  view 
the  importance  of  Poisson’s  general  theory  ; but  at  the  same  time 
demonstrated  the  necessity  for  replacing  his  practical  formulae  by 
others,  not  limited  by  certain  restrictions  as  to  symmetry  of  the 
ship,  which  he  had  assumed  for  the  sake  of  simplicity.  This  was 
the  chief  problem  first  put  before  Smith  by  Sabine,  and  his  solution 
of  it  was  the  first  great  service  which  he  rendered  to  the  practical 
correction  of  the  disturbance  of  the  compass  caused  by  the 
magnetism  of  ships. 

In  1850  he  published  separately  an  account  of  his  theoretical 
and  practical  investigations  on  the  correction  of  the  deviations 
of  a ship’s  compass,  which  was  afterwards  given  as  a supplement 
to  the  Admiralty  “ Practical  Rules  ” in  1855.  The  large  devia- 
tions found  in  iron-plated  ships  of  war  “ having  rendered  necessary 
the  use  of  the  exact  instead  of  the  approximate  formulae,”  this 
article  was  rewritten  by  Smith  for  the  Compass  Department  of 
the  Admiralty.  It  now  forms  Part  III.  of  the  “ Admiralty  Manual 
for  the  Deviations  of  the  Compass,”  edited  by  Evans  and  Smith, 
to  which  are  added  appendices  containing  a complete  mathematical 
statement  of  the  general  theory,  proofs  of  the  practical  formulae, 
and  constructions  and  practical  methods  of  a more  mathematical 
character  than  those  given  in  the  body  of  the  work  for  ordinary 
use.  A separate  publication,  of  “ Instructions  for  Correcting  the 
Deviation  of  the  Compass,”  by  Smith,  was  made  by  the  Board 
of  Trade  in  1857. 

It  is  satisfactory  to  find  that  the  British  Admiralty  “ Compass 
Manual,”  embodying  as  it  does  the  result  of  so  vast  an  amount 
of  labour,  guided  by  the  highest  mathematical  ability  and  the 


287 


of  Edinburgh,  Session  1873-74. 

most  consummate  practical  skill,  has  been  appreciated  as  a gift 
to  the  commonwealth  of  nations  by  other  countries  than  our  own. 
It  is  adopted  by  the  United  States  Navy  Department,  and  it  has 
been  translated  into  Russian,  German,  Portuguese,  and  French. 
Smith’s  mathematical  work,  and  particularly  his  beautiful  and 
ingenious  geometrical  constructions,  have  attracted  great  interest, 
and  have  called  forth  fresh  investigation  in  the  same  direction, 
among  the  well-instructed  and  able  mathematicans  of  the  American, 
Russian,  French,  and  German  Navy  Departments. 

The  constancy  to  the  compass  problem,  in  which  Smith  persevered 
with  a rare  extreme  of  disinterestedness,  from  the  time  when 
Sabine  first  asked  him  to  work  out  practical  methods  from  Poisson’s 
mathematical  theory,  until  his  health  broke  down  two  years  before 
his  death,  was  characteristic  of  the  man.  It  was  pervaded  by  that 
“ tenacite  passionee”  which  a generous  French  appreciation  de- 
scribes as  a peculiarity  of  the  English  nation ; but  there  was  in 
it  also  a single-mindedness  and  a purity  of  unselfishness  to  be  found 
in  few  men  of  any  nation,  but  simply  natural  in  Archibald  Smith. 

Honourable  marks  of  appreciation  reached  him  from  various 
quarters,  and  gave  him  the  more  pleasure  from  being  altogether 
unsought  and  unexpected.  The  Admiralty,  in  1862,  gave  him 
a watch.  In  1864  he  received  the  honorary  degree  of  LL.D.  from 
the  University  of  Glasgow.  The  Royal  Society  awarded  to  him  the 
Royal  Medal  in  the  year  1865.  The  Emperor  of  Russia  gave  him, 
in  1866,  a gold  compass,  emblazoned  with  the  Imperial  Arms  and 
set  with  thirty-two  diamonds,  marking  the  thirty-two  points.  Six 
months  before  his  death  Her  Majesty’s  Government  requested  his 
acceptance  of  a gift  of  L.2000,  as  a mark  of  their  appreciation  of 
“ the  long  and  valuable  services  which  he  had  gratuitously  rendered 
to  the  Naval  service  in  connection  with  the  magnetism  of  iron 
ships,  and  the  deviations  of  their  compasses.”  The  official  letter 
intimating  this,  dated  Admiralty,  July  1st,  1872,  contains  the 
following  statement,  communicated  to  Smith  by  command  of  the 
Lords  of  the  Admiralty  : — “ To  the  zeal  and  ability  with  which  for 
many  years  you  have  applied  yourself  to  this  difficult  and  most 
important  subject,  My  Lords  attribute  in  a great  degree  the  accu- 
rate information  they  possess  in  regard  to  the  influence  of  mag- 
netism, which  has  so  far  conduced  to  the  safe  navigation  of  iron 


288 


Proceedings  of  the  Royal  Society 

ships,  not  only  of  the  Royal  and  Mercantile  Navies  of  this  country, 
but  of  all  nations.” 

In  private  life  those  who  knew  Archibald  Smith  best  loved  him 
most ; for  behind  a reserve  which  is  perhaps  incident  to  engrossing 
thought,  especially  when  it  is  concerned  with  scientific  subjects,  he 
kept  ever  a warm  and  true  heart ; and  the  affectionate  regrets  of  his 
friends  testify  to  the  guileless  simplicity  and  sweetness  of  his  dis- 
position, which  nothing  could  spoil  or  affect.  About  the  close  of 
1870  he  was  compelled  by  ill-health  to  give  up  work,  but  two  years 
later  he  had  wonderfully  rallied ; and  though  he  was  not  strong 
enough  to  resume  his  legal  or  scientific  work,  he  was  able  to  take 
his  old  interest  in  his  boys’  mathematical  studies.  A few  weeks 
before  his  death  he  revised  the  instructions  for  compass  observa- 
tions to  be  made  on  board  the  “ Challenger,”  then  about  to  sail 
on  the  great  voyage  of  scientific  investigation  nowin  progress; 
and  he  spoke  several  times  of  the  satisfaction  it  gave  him  to  feel 
able  again  to  do  such  work  without  effort  or  fatigue.  The  attack 
of  illness  which  closed  his  life  was  unexpected  and  of  but  a few 
hours’  duration.  In  1853  he  married  a daughter  of  Vice-Chan- 
cellor Sir  James  Parker,  then  deceased,  and  he  leaves  six  sons 
and  two  daughters.  He  died  on  the  26th  of  December  1872. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

A.  Forbes  Irvine^  Esq. 

Benjamin  Carrington,  M.D.,  Eccles,  Lancashire. 

William  Ferguson,  F.L.S.,  F.G.S., 

T.  B.  Sprague,  M.A.  Cantab. 

Thomas  Muir,  M.A. 

J.  Batty  Tuke,  M.D.,  F.R.C.P.E. 

William  Durham,  Esq. 


of  Edinburgh,  Session  1873-74. 


289 


Monday,  16th  February  1874. 

Sir  W.  THOMSON,  President,  in  the  Chair. 

The  following  Obituary  Notices  of  Deceased  Fellows  of 
the  Society  were  read  : — 

1.  Obituary  Notice  of  the  Very  Rev.  Dean  Ramsay. 

By  the  Rev.  D.  F.  Sandford. 

The  Very  Reverend  Edward  Bannerman  Ramsay,  Dean  of  the 
Diocese  of  Edinburgh,  in  the  Episcopal  Church  of  Scotland,  was 
horn  in  Aberdeen  on  the  31st  day  of  January  1793.  His  father 
was  Sir  Alexander  Ramsay,  Bart.,  of  Balmain  and  Fasque.  Sir 
Alexander  was  the  second  son  of  Sir  Thomas  Burnett,  Bart.,  of 
Leys,  but  had  assumed  the  name  of  Ramsay,  and  been  created 
a Baronet,  on  succeeding  to  the  estates  of  his  maternal  uncle  in 
Forfarshire.  He  was  by  profession  an  advocate  at  the  Scottish 
bar,  and  Sheriff  of  his  native  county  of  Kincardine.  In  that 
county  the  family  of  Burnett  of  Leys  have  held  lands  and  a high 
position  for  many  hundred  years.  Bishop  Burnet  of  Salisbury,  the 
historian  of  his  own  times,  and  a divine  of  enlarged  mind  and 
liberal  views,  belonged  to  it.  The  Bishop’s  picture,  in  his  robes  as 
Chancellor  of  the  Order  of  the  G-arter,  is  among  the  family  portraits 
at  Crathes  Castle,  the  seat  of  the  present  Sir  James  Burnett,  Bart. 

The  Dean’s  mother  was  Elizabeth,  eldest  daughter  and  co- 
heiress of  Sir  Alexander  Bannerman,  Bart.,  of  Elsick,  a lady  of 
considerable  personal  attractions  and  marked  character.  She  and 
her  husband  were  in  Paris  at  the  outbreak  of  the  great  French 
Revolution.  They  escaped  from  France  under  the  protection  of 
a tricolour  cockade  worn  by  the  Sheriff,  which  Dean  Ramsay 
presented  some  years  ago,  as  an  interesting  relic  of  the  time,  to 
the  Antiquarian  Museum  in  Edinburgh.  On  reaching  Scotland 
they  settled  at  Aberdeen,  and  so  Edward  Bannerman,  their  fourth 
son,  who  was  born  soon  after,  first  saw  the  light  in  his  own 
ancestral  country.  This  was  always  a subject  of  deep  gratification 
to  one  whose  whole  heart  and  sympathies  were  so  eminently 
Scottish.  In  early  life  Edward  Ramsay  was  sent  to  reside  with 


290  Proceedings  of  the  Royal  Society 

his  great-uncle,  the  then  Sir  Alexander  Ramsay,  who  placed  him 
at  school  in  a small  village  near  his  own  residence,  Harlsey,  in 
Yorkshire.  The  locality  was  a very  retired  one,  and  old  customs 
lingered  there  which  time  had  changed  or  obliterated  in  other 
parts  of  England.  The  Bible  lay  chained  to  the  desk  in  the 
parish  church,  as  in  the  days  of  Edward  VI.  and  Queen  Elizabeth. 
The  bodies  of  the  deceased  were  carried  to  the  quiet  churchyard 
by  those  of  their  own  sex,  age,  and  condition.  The  village  girls 
bore  their  companions,  the  boys  their  schoolfellows,  the  young 
men  and  women,  the  middle-aged  and  the  old,  their  contemporaries 
and  associates  who  had  been  called  away.  The  parish  curate 
dined  with  the  squire  every  Sunday,  hut  did  not  omit  to  drink 
to  the  health  of  the  old  butler  who  waited  at  table,  as  well  of 
his  host,  and  the  other  guests.  The  village  carpenter,  a strange 
character,  forestalled  Archbishop  Whately’s  historic  doubts  as  to 
the  existence  of  Napoleon  Buonaparte,  and  boldly  declared  that  he 
did  not  believe  there  was  any  such  person.  His  conviction  was  that 
the  name  was  used  to  frighten  children,  and  to  terrify  the  British 
nation  into  keeping  up  the  army  and  navy,  and  paying  the  very 
heavy  taxes  imposed  upon  them.  From  this  primitive  spot,  where 
doubtless  his  powers  of  observation  and  his  interest  in  localpeculiari- 
ties  were  first  awakened  by  the  circumstances  just  mentioned,  which 
he  never  forgot,  Ramsay  was  transferred  to  the  G-rammar  School 
at  Durham.  Here,  as  he  often  stated  with  regret,  he  was  taught 
little  and  learnt  less.  After  leaving  Durham,  he  was  a pupil 
for  a short  time  of  Dr  Joynes,  a clergyman  at  Sandwich  in  Kent, 
and  then  entered  St  John’s  College,  Cambridge,  where  he  took 
his  degree  in  1816.  Although  not  distinguished  in  any  remark- 
able way  as  a scholar  or  mathematician  in  the  University,  Mr 
Ramsay  seems  to  have  felt  satisfied  with  the  result  of  more  than 
one  of  the  College  examinations,  and  he  obtained  during  his 
residence  at  St  John’s  a scholarship  on  that  learned  foundation. 
Within  a very  short  period  after  taking  his  degree,  he  received  a 
title  for  holy  orders  as  curate  of  Rodden  in  Somersetshire  ; and  was 
ordained  by  the  Bishop  of  Bath  and  Wells,  Deacon  in  December 
1816,  and  Priest  in  the  following  year.  When  acting  in  after 
life  as  examiner  of  candidates  for  the  ministry,  he  frequently 
drew  a comparison  between  the  meagre  superficial  examinations, 


291 


of  Edinburgh,  Session  1873-74. 

confined  to  a paper  on  the  Evidences  of  Christianity,  and  a few 
verses  of  the  G-reek  Testament,  to  which  he  was  subjected,  and 
the  more  thorough  and  searching  ordeal  through  which  aspirants 
to  the  clerical  office  are  now  required  to  pass.  He  continued  at 
Rodden  for  seven  years,  perhaps  in  some  respects  the  happiest 
in  his  life.  Although  his  rector  was  non-resident,  he  was  allowed 
to  conjoin  the  care  of  the  neighbouring  parish  of  Buckland  with 
that  of  Rodden,  and  to  discharge  also  for  a time  the  duties  of 
evening  lecturer  in  the  parish  church  of  Frome.  This  afforded 
to  him  another  contrast  in  his  own  remembrance  with  the  present 
requirements  as  to  residence,  experience,  and  work  on  the  part 
of  the  clergy.  While  at  Rodden,  he  employed  his  leisure  time 
and  annual  holiday  in  the  study  of  botany,  making  more  than 
one  expedition  into  Wales  and  elsewhere  with  this  object.  He 
also  gave  some  time  to  the  cultivation  of  music,  for  which  he  had 
considerable  talent.  And  he  seems  also  to  have  turned  his  atten- 
tion to  mathematics  and  astronomy,  incited  thereto  by  his  brother, 
the  late  Admiral  Sir  William  Ramsay,  who  gave  him  a box  of 
instruments  and  a telescope,  which  he  used  in  the  instruction  of 
a class  of  young  friends  and  parishioners. 

After  declining  the  offer  of  an  appointment  to  a chapel  in  his 
native  city,  Aberdeen,  Mr  Ramsay  came  to  Edinburgh,  at  the 
end  of  1823,  as  curate  to  Mr  Shannon,  the  incumbent  of  St 
George’s  Episcopal  Chapel  in  York  Place.  This  change  of  resi- 
dence introduced  him  to  Edinburgh  at  a time  when  not  only  agita- 
tion for  political  and  municipal  reform,  but  also  the  awakening 
of  religious  thought  and  feeling  to  which  the  Clapham  School  had 
given  rise  in  England,  and  which  was  soon  to  merge  in  the  remark- 
able Oxford  movement  of  1833,  were  intermingling  with  its  intel- 
lectual culture  and  social  life.  The  refined,  cultivated,  and  earnest- 
minded  young  clergyman,  possessing  hereditary  claims  to  be 
received  among  the  highest  circle  of  its  inhabitants,  soon  estab- 
lished also  close  and  intimate  relations  with  manjr  of  those  who 
then  made  our  city  so  distinguished.  He  became  popular  in  the 
best  sense  of  the  word.  His  ministrations  and  preaching  were 
highly  appreciated.  His  kindly  pleasing  manners  and  unaffected 
genuine  character  won  for  him  an  influence  which  was  soon  felt 
for  good  in  many  quarters.  After  serving  the  curacy  of  St  George’s 

2 p 


VOL.  VIII. 


292  Proceedings  of  the  Itoyal  Society 

for  two  years,  Mr  Bamsay  was  appointed  incumbent  and  pastor 
of  the  interesting  old  chapel  and  genuine  Scottish  Episcopalian 
congregation  of  St  Paul’s,  Carru'bber’s  Close,  in  the  Old  Town. 
The  chapel  was  largely  attended  during  his  ministry,  and  the 
value  of  the  living  while  he  held  it  was  L 400  per  annum. 

In  1827  he  was  appointed  assistant  minister  of  St  John’s,  and, 
on  the  death  of  the  late  Bishop  Sandford  in  1 830,  was  elected 
to  the  incumbency  of  that  charge,  which  he  continued  to  hold 
until  his  long  and  honoured  life  reached  its  close  on  the  27th 
December  1872.  The  more  strictly  professional  details  and  charac- 
teristics of  Mr  Bamsay’s  career  are  not  subjects  of  comment  or 
notice  in  this  place.  It  will  suffice  to  mention  that  in  the  faithful 
and  assiduous  discharge  of  his  duties  he  secured  to  himself  appre- 
ciation, confidence,  and  esteem,  which,  as  years  rolled  on  and  in 
proportion  as  he  became  better  known,  grew  and  ripened  into 
genuine  and  universal  regard  and  love. 

In  1838  he  proposed  and  carried  through  the  General  Synod  of 
the  Scottish  Episcopal  Church  a canon  for  establishing  a society, 
the  main  object  of  which  was  to  supplement  the  very  inadequate 
stipends  of  the  clergy,  to  provide  teachers  for  the  poor,  and  gene- 
rally to  improve  the  financial  condition  of  the  Communion  to  which 
he  belonged.  He  was  specially  useful  as  a catechist  among  the 
young  of  his  flock,  and  compiled  a manual  of  catechetical  instruction 
for  their  use,  which  has  passed  through  more  than  twelve  editions. 
He  published  a volume  of  Advent  Sermons,  also  pastoral  letters 
addressed  to  his  congregation  on  various  subjects,  occasional  ser- 
mons and  pamphlets  on  matters  connected  with  his  own  com- 
munion, and  a series  of  Lectures  on  Diversities  of  Character,  and 
another  series  on  Faults  in  Christian  Believers,  which  were  subse- 
quently combined  and  expanded  into  a Treatise  on  the  Christian 
Life.  In  1841  Mr  Bamsay  was  appointed  by  Bishop  Terrot,  on 
his  own  elevation  to  the  Episcopate,  Dean  of  the  Diocese  of  Edin- 
burgh. In  1845  he  was  offered  by  Sir  Bobert  Peel,  on  behalf  of 
the  Crown,  the  Bishopric  of  New  Brunswick  in  Nova  Scotia,  and  in 
1848,  and  again  in  1862,  he  was  elected  by  the  clergy  of  two  Scot- 
tish dioceses  to  be  their  Bishop.  But  he  saw  fit  to  decline  on  each 
of  these  occasions  the  offer  of  a mitre,  much  to  the  satisfaction 
of  his  own  congregation,  who  viewed  with  little  favour  these 


293 


of  Edinburgh,  Session  1873-74. 

attempts  to  deprive  them  of  their  tried  and  valued  friend  and  pastor. 
In  1859,  on  the  occasion  of  the  installation  of  his  distinguished 
friend,  Mr  Gladstone,  as  Lord  Bector,  the  University  of  Edinburgh 
conferred  on  the  Dean  the  degree  of  LL.D.  In  1828-1829,  he 
was  one  of  the  secretaries  of  the  ordinary  meetings  of  the  Boyal 
Society.  He  subsequently  became  a member  of  Council,  and  in 
1859  a Vice-President.  In  1861  he  opened  the  winter  session 
with  an  address  from  the  chair,  which  was  published  in  the  Pro- 
ceedings. The  only  paper  contributed  by  him  to  the  Society’s 
General  Transactions  was  a biographical  memoir  of  the  late  Dr 
Chalmers,  with  whom  he  was  on  terms  of  intimate  friendship. 
A few  years  ago  he  inaugurated  a movement  for  erecting  a statue 
of  the  same  eminent  philosopher  and  divine,  which  is  now  approach- 
ing completion  in  the  studio  of  Mr  John  Steele,  and  is  to  be  placed 
at  the  intersection  of  George  Street  and  Castle  Street  in  this  city. 

The  Dean’s  continued  interest  in  botanical  study  was  evinced 
by  his  publishing  a notice  of  the  works  and  discoveries  of  his 
friend  Sir  J.  E.  Smith.  His  taste  for  the  highest  style  of  music, 
and  his  earnest  desire  to  extend  the  knowledge  and  cultivation 
of  it,  led  him  to  choose,  as  the  subject  of  two  lectures  before  the 
Philosophical  Institution  of  Edinburgh,  “ The  Genius  and  Works 
of  Handel,”  They  were  delivered  to  a crowded  audience  in  the 
Music  Hall,  with  the  assistance  of  illustrations  by  a choir,  and 
were  afterwards  published.  The  Dean  delivered  before  the  same 
body  a lecture  on  Pulpit  Oratory  and  Orators,  and  pursued  the 
subject  thus  suggested  in  a printed  letter  to  a young  clergyman 
on  the  art  of  clear  and  articulate  public  speaking,  in  which  he 
was  himself  an  unsurpassed  proficient.  The  work,  however,  with 
which  his  name  is  most  widely  connected  is  his  u Beminiscences 
of  Scottish  Life  and  Character.”  It  has  gone  through  twenty 
editions,  and  more  than  ninety  thousand  copies  of  it  have  been 
sold.  It  is  to  be  found  on  the  library  tables  of  royalty  and  in 
the  cottage  of  the  peasant.  It  is  sold  by  the  newsboys  at  every 
railway  station.  It  is  to  be  seen  in  the  huts  of  new  settlements 
in  Western  America,  and  of  the  cattle  and  sheep  runs  of  New 
Zealand  and  Australia.  It  has  made  the  Dean’s  good  Scottish 
name  a household  word  in  every  land  on  which  the  sun  shines. 
Wherever  the  exiled  Scotchman  goes,  he  carries  with  him  the 


294  Proceedings  of  the  Royal  Society 

“ Reminiscences  ” as  one  of  the  links  which  will  continue  to  bind 
his  heart  to  his  own  country,  and  to  keep  alive  in  his  memory  the 
most  vivid  and  pleasing  recollections  of  her  history  and  people.  The 
object  of  the  book  was  not  to  produce  a mere  momentary  amuse- 
ment, hut  to  contribute  to  an  important  branch  of  historical  science, 
the  neglect  of  which  has  left  us  too  ignorant  of  what  our  fore- 
fathers and  their  times  really  were.  It  was  intended  to  preserve 
the  remembrance  of  old  Scottish  customs,  and  of  national  peculiari- 
ties and  characteristics,  the  traces  of  which,  in  many  respects  to 
our  loss,  are  fast  dying  out.  That  jocular  sayings  and  anecdotes 
should  prove  the  staple  of  the  work  was  an  accident,  or  rather 
I might  say  a necessity,  and  not  an  arbitrary  choice  of  the  author. 
It  may  have  its  literary  faults.  But  many  of  us  were  too  partial 
to  the  man,  too  much  in  sympathy  with  his  purpose  and  with 
the  genuine,  kindly,  patriotic  motives  which  guided  his  pen,  to 
dwell  on  them.  Nay  more,  critics  have  been  slow  to  point  them 
out,  and  the  judgment  of  the  public  has  done  more  than  condone 
them.  It  may  not  be  too  much  to  apply  to  the  “ Beminiscences  ” the 
language  which  the  greatest  Scottish  novelist  has  used  with  regard 
to  his  own  works,  and  to  say  that  the  Dean  was  happy  in  the  know- 
ledge that  the  perusal  of  his  book  has  amused  hours  of  relaxation 
and  relieved  those  of  languor,  pain,  and  anxiety,  and  that  it  has 
contributed  in  no  small  degree  to  the  happiness  and  instruction  of 
his  fellow-countrymen.  It  is  no  little  credit,  the  Dean  felt  it 
to  have  been  a great  privilege,  to  have  followed,  however  humbly, 
in  the  footsteps  of  Sir  Walter  Scott,  and  to  have  added  to  the 
literature  of  his  country  a volume  which  must  always  serve  to 
make  Scotland  better  known,  appreciated,  and  loved,  wherever  it  is 
read. 

We  may  not  intrude  into  the  sacred  domestic  circle  to  find 
material  for  this  biographical  notice ; it  may  suffice  to  say  that 
those  who  knew  Dean  Ramsay  best  loved  him  best.  He  was 
honoured  above  most  men  with  the  friendship  of  the  good  and 
great.  Dignified  ecclesiastics,  eminent  statesmen,  nobles  of  cha- 
racter and  renown  no  less  exalted  than  their  rank,  sought  and 
valued  his  acquaintance,  his  wise  counsels,  his  kindly  sympathy. 
Men  of  distinction  and  repute  from  all  quarters  found  a welcome 
under  his  roof,  and  never  left  it  without  feeling  that  they  had 
added  to  their  circle  of  life-long  friends. 


295 


of  Edinburgh,  Session  1873-74. 

In  every  philanthropic  movement  the  Dean  was  ready  to  assist 
with  his  money  and  influence.  He  gave  largely,  from  no  great 
means,  to  charitable  agencies  and  to  individual  cases  of  need 
and  distress.  He  was  a friend  to  those  of  every  class  with  whom 
he  was  brought  in  contact.  The  cabmen  vied  with  each  other 
as  to  which  of  them  should  take  him  for  his  daily  drive,  and 
they  counted  his  presence  at  more  than  one  of  their  yearly  social 
entertainments  a special  honour.  Every  one  seemed  gratified  at 
any  occasion  for  intercourse  with  him,  even  for  a few  moments. 
He  was  essentially  a gentleman,  dignified,  courteous,  and  kindly. 
The  Dean’s  influence  in  his  own  Communion  was  deservedly  very 
great,  and  if  it  was  exerted  in  every  way  in  his  power  to  advance 
her  usefulness  and  prosperity,  it  was  at  the  same  time  always 
tempered  and  guided  by  a spirit  of  charity  and  good-will,  which 
enabled  him  to  do  more  than  almost  any  man  of  his  day  and 
generation  to  purify  and  sweeten  the  atmosphere  both  of  social 
and  ecclesiastical  life  in  this  city  and  country.  Whatever  estimate 
may  be  formed  of  the  views  he  held,  the  work  he  did,  this  at 
least  must  be  universally  admitted,  and  may  not  unfitly  be  put 
on  record  even  here.  To  Dean  Ramsay,  charity,  freedom  from 
bigotry,  narrowness,  and  ill-will,  were  not  the  accidents  of  tempera- 
ment, or  the  fruits  of  an  easy  disposition,  of  high  breeding,  and 
culture.  They  were  essential  elements  in  the  ideas  he  had  formed 
of  the  Christian  religion  and  of  the  Christian  character.  He 
was  never  tired  of  enforcing  them  in  his  teaching,  as  he  never 
ceased  to  illustrate  and  exemplify  them  in  his  conduct.  And  that 
his  endeavours  to  do  this  by  every  means  he  could,  and  towards 
men  of  every  creed  and  party  known  to  the  religious  and  political 
world,  were  acknowledged  and  appreciated,  the  great  demonstration 
which  took  place  at  his  funeral  amply  testified.  It  was  not  only 
in  numbers  one  of  the  largest  which  ever  took  place  in  this  city, 
but  it  was  attended  by  the  leading  representatives,  both  lay  and 
clerical,  of  every  denomination.  Men  forgot  their  differences  and 
the  causes  of  their  separation  one  from  another,  as  they  gathered 
round  his  grave.  It  was  the  realisation  for  once  of  the  dream 
and  aspiration  of  Dean  Ramsay’s  own  life.  It  was  the  most  strik- 
ing and  worthy  tribute  which  could  possibly  have  been  paid  to 
his  memory. 


296  Proceedings  of  the  Royal  Society 

It  will  be  well  for  religion,  as,  I may  venture  to  add,  it  will 
be  well  also  for  learning,  and  science,  and  truth  in  all  its  forms 
and  aspects,  if  the  same  spirit  which  breathed  and  spoke  in  all 
that  Dean  Bamsay  did  and  said  shall  increase,  and  spread,  and 
deepen  among  us,  in  our  various  spheres  arid  callings.  We  cannot 
but  feel  that  in  every  point  of  view  Dean  Bamsay’s  was  a career 
which,  as  it  was  honoured  while  he  was  spared  to  us,  and  marked 
by  such  distinctions  as  befitted  his  position  in  the  Church  and 
in  society  during  his  life,  so  it  demanded  some  tribute  and  notice 
in  this  place,  now  that  his  name  is  withdrawn  from  the  roll  of 
our  living  Fellows.  If  it  was  not  given  him  to  further  the  cause 
of  science  and  learning,  as  many  belonging  to  the  Boyal  Society 
have  done,  yet  his  teaching  and  example  were  such  as  all  may 
profitably  recall  to  memory  and  strive  to  follow  and  imitate. 

2.  Obituary  Notice  of  Professor  Rankine. 

By  Lewis  D.  B.  Gordon,  C.E. 

William  John  Macquorn  Bankine  was  the  son  of  Lieutenant 
David  Bankine  of  the  Bifle  Brigade,  younger  son  of  Macorne  or 
Macquorn  Bankine,  Esq.,  of  Drumdow  in  Ayrshire,  and  thus  of 
an  ancient  Scottish  family.  His  mother  was  Hie  elder  daughter 
of  Archibald  Grahame,  Esq.,  of  Drumquhassel.  He  was  born  in 
Edinburgh,  5th  July  1820.  Bankine  records  of  himself,  “My 
earliest  distinct  recollection  is  that  of  my  mother  teaching  me 
the  Lord’s  Prayer,  next  my  father  explaining  to  me  the  character 
of  Jesus  Christ;”  and  further  he  records,  “ My  early  instruction 
in  arithmetic  and  elementary  mechanics  and  physics  was  mainly 
obtained  from  my  father.”  The  mutual  dependency  thus  begun 
continued  through  as  beautiful  a life  of  mutual  self-devotion 
between  parents  and  son  as  can  be  pictured ; for  the  three  were 
rarely  far  separate  during  the  fifty  years  the  parents  lived  after 
his  birth. 

Bankine  went  to  the  Ayr  Academy  in  1828,  and  afterwards  to 
the  High  School  of  Glasgow  in  1830,  and  thence  to  Edinburgh, 
where  he  studied  geometry  under  Mr  George  Lees ; but  his  know- 
ledge of  the  higher  mathematics  was  chiefly  obtained  by  private 
study.  He  records  that  in  1834  “ My  uncle  Archibald  Grahame 


of  Edinburgh,  Session  1873-74. 


297 


gave  me  a copy  of  ‘Newton’s  Principia,’  which  I read  carefully; 
this  was  the  foundation  of  my  knowledge  of  the  higher  mathe- 
matics and  dynamics  and  physics.”  He  read  the  Principia  in 
the  original  Latin,  and  in  after  life  recommended  his  pupils  so 
to  read  this  work  of  paramount  authority  and  reputation  ; “ for,” 
said  he,  “ modern  science  has  added  no  new  principle  to  the 
dynamics  of  Newton ; what  it  has  done  is  to  extend  the  applica- 
tion of  dynamical  principles  to  phenomena  to  which  they  had 
not  been  previously  applied ; in  fact,  to  the  correlation  of  the 
physical  sciences — or,  in  other  words,  what  is  denoted  by  the 
convertibility  of  energy.”  Thus,  at  the  early  age  of  fourteen,  had 
Rankine  begun  to  discipline  his  mind  and  train  his  analytical 
powers  on  Newton’s  model  of  unquestionable  definition  and  exhaus- 
tive demonstration,  characteristics  of  the  many  works  on  cognate 
subjects  he  was  himself  in  after  years  to  contribute  for  the  educa- 
tion of  engineers  of  every  class,  and  for  the  advancement  of  physical 
science.  For  two  years,  from  1836  to  1838,  Rankine  was  a student 
in  the  University  of  Edinburgh,  and  took  the  courses  of  Natural 
Philosophy,  Chemistry,  Natural  History,  and  Botany.  He  continued 
for  two  sessions  under  Professor  Forbes;  and  the  first  year  gained  the 
gold  medal  for  “ An  Essay  on  the  Undulatory  Theory  of  Light,”  and 
the  extra  prize  (gold  medal)  for  “ An  Essay  on  Methods  in  Physical 
Investigation.”  At  this  period,  too,  he  read  much  metaphysics, 
chiefly  Aristotle,  Locke,  Hume,  Stewart,  Degerando.  The  whole 
tendency  of  his  mind  was  to  the  digestion  and  assimilation  of 
the  highest  human  knowledge.  But  the  res  angusta  domi  demanded 
that  he  should  take  a profession  ; and  at  this  period  none  was 
more  in  vogue,  or  apparently  more  promising  of  abundant  employ- 
ment, than  that  of  a civil  engineer. 

Rankine  having  for  a short  time  assisted  his  father,  who  was 
superintendent  of  the  Edinburgh  and  Dalkeith  Railway,  in  1838 
became  a pupil  of  Mr  M‘Neil  (afterwards  Sir  John  M‘Neil),  whose 
practice  in  Ireland  was  varied  and  extensive.  Accordingly,  for 
four  years  Rankine  was  actively  employed  as  a pupil  on  various 
surveys  and  schemes  for  river  improvements,  water  works,  and 
harbour  works,  and  on  the  Dublin  and  Drogheda  Railway.  While 
on  tins  work,  he  contrived  and  practised  a method  of  “ setting 
out  curves  ” by  chaining  and  angles  at  the  circumference,  since 


298  Proceedings  of  the  Pioyal  Society 

known  as  Rankine  s method.  He  was  much  loved  and  respected 
by  his  numerous  fellow-pupils,  several  of  whom  have  attained 
high  professional  status.  His  pupilage  ended,  Eankine  returned 
to  Edinburgh,  and  was  occupied  for  some  time  in  the  preparation 
and  publication  of  an  “ Experimental  Inquiry  into  the  Advantages 
attending  the  Use  of  Cylindrical  Wheels  on  Railways.” 

The  theoretical  investigation,  and  the  deductions  from  the 
results  of  the  experiments,  conducted  by  his  father  and  himself, 
are  characterised  by  the  same  completeness  in  every  respect  as 
his  more  important  and  more  famous  writings  of  maturer  years. 
But  cylindrical  wheels  never  came  into  use.  It  was  “ too  late  ” 
to  begin  an  obvious  improvement,  or  there  was  no  time  to  think 
of  it ; and  yet,  taking  everything  into  consideration,  the  wheels 
would  he  better  cylindrical,  so  formed  that  they  should  retain  that 
shape  for  the  longest  time. 

In  1842-43  various  papers  were  sent  to  the  Institution  of  Civil 
Engineers,  and  prizes  were  granted  for  them.  There  is  one  on 
“ The  Fracture  of  Axles,”  in  which  the  importance  of  continuity  of 
form  and  fibre  was  first  shown,  and  the  hypothesis  of  spontaneous 
crystallisation  disproved.  The  conclusions  of  this  paper  were  gene- 
rally accepted  and  acted  upon  in  the  construction  of  axles. 

In  1844-45,  and  afterwards  till  1848,  Rankine  was  employed 
under  Messrs  Locke  and  Errington  on  various  railway  projects 
promoted  by  the  Caledonian  Railway  Company,  of  which  his  father 
had  become  secretary.  But  from  1842  onwards  his  mind  had 
been  much  occupied  in  perfecting  himself  in  the  use  of  the  higher 
analysis  and  in  its  application  to  the  mechanics  of  molecular 
vortices. 

Rankine’s  first  investigation  of  the  principles  of  the  mechanical 
action  of  heat  appeared  in  a paper  received  by  the  Royal  Society 
of  Edinburgh  in  December  1849,  and  published  in  their  Trans- 
actions, vol.  xx.  It  is  based  on  what  he  calls  u the  hypothesis 
of  molecular  vortices  ; ” that  is  to  say,  the  supposition  that  the 
motions  of  which  Davy  showed  thermotic  heat  to  consist  are  of 
the  nature  of  vortices — whirls  or  circulating  streams.  This  is 
the  part  of  the  hypothesis  that  is  specially  connected  with  the 
phenomena  of  the  mechanical  action  of  heat ; but  in  order  to 
connect  these  with  some  other  phenomena,  Rankine  makes  the 


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of  Edinburgh,  Session  1873-74. 

further  suppositions  that  the  whirling  motion  is  diffused  in  the 
form  of  atmospheres  round  nuclei,  which  may  be  either  bodies  of 
a special  kind  or  centres  of  condensation  and  attraction  in  the 
atmospheres  ; and  that  radiance,  whether  of  heat  or  light,  consists 
in  the  transmission  of  a vibratory  motion  of  the  nuclei,  by  means 
of  forces  which  they  exert  on  each  other. 

The  quantity  of  heat  in  a body  is  the  energy  of  its  molecular 
vortices ; the  absolute  temperature  of  the  body  is  the  same  energy 
divided  by  a specific  co- efficient  for  each  particular  substance.  A 
perfect  gas  is  a substance  in  which  the  elastic  pressure  is  sensibly 
that  which  varies  with  the  centrifugal  force  of  the  vortices  only ; 
and  the  intensity  of  the  pressure,  according  to  the  known  principles 
of  mechanics,  must  be  proportioned  directly  to  the  energy  of 
the  vortices,  and  inversely  to  the  space  that  they  occupy.  In 
substances  not  perfectly  gaseous , the  elasticity  is  modified  by 
attractive  or  cohesive  forces.  When  the  deviation  from  the  per- 
fectly gaseous  state  is  small,  the  effects  of  such  forces  may  be 
approximately  represented  by  series,  in  terms  of  the  reciprocal  of 
the  absolute  temperature.  Eankine  had  previously  published  an 
example  of  the  use  of  such  series,  in  a paper  on  the  Elasticity 
of  Vapours  (Edin.  Phil.  Journal,  July  1849),  and  he  also  applied 
them  with  success  to  the  elasticity  of  carbonic  acid  and  some  other 
gases  (Phil.  Mag.  1851).  Sensible  heat  is  the  energy  employed  in 
varying  the  velocity  of  the  whirling  particles  ; latent  heat  the  work 
done  in  varying  the  dimensions  of  their  orbits,  when  the  volumes 
and  figures  of  the  spaces  in  which  they  whirl  are  changed.  The 
force  which  keeps  any  particle  in  its  orbit  is  equal  and  opposite 
to  the  centrifugal  force  of  that  particle;  therefore  the  work  done 
in  varying  the  orbits  of  the  particles  is  proportionate  to  their 
centrifugal  forces,  therefore  to  the  energy  of  the  vortices,  there- 
fore to  the  absolute  temperature.  And  to  compute  that  quantity 
of  work,  or  latent  heat,  when  a body  undergoes  a given  variation 
of  dimensions,  the  absolute  temperature  is  to  be  multiplied  by  the 
corresponding  variation  of  a certain  function  of  the  dimensions 
and  elasticity  of  the  body.  This  function  is  computed  by  taking 
the  rate  of  variation  with  temperature,  of  the  external  work  done 
during  the  kind  of  change  of  dimensions  under  consideration. 

Such  is  an  outline  of  the  method  by  which  Rankine  deduces 

VOL.  VIII.  2 Q 


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the  second  law  of  thermodynamics,  or  general  equation  of  the 
mechanical  action  of  heat,  from  the  hypothesis  of  molecular  vor- 
tices, by  means  of  known  dynamical  principles.  The  quantity 
whose  variation  being  multiplied  by  the  absolute  temperature  gives 
the  latent  heat,  corresponding  to  a given  change  of  dimensions 
at  that  temperature,  is  expressed  in  Rankine’s  earlier  papers  by 
symbols,  but  is  not  designated  by  a special  name. 

In  a paper  read  in  January  1853  (Edin.  Trans,  xxi)  he  proposes 
the  name  Heat  Potential ; and  in  a paper  read  to  the  Royal  Society 
of  London,  January  1854,  he  gives  to  the  same  quantity,  with  a 
certain  additional  term,  depending  on  changes  of  temperature, 
the  name  of “ Thermodynamic  Function,” — a name  which  has  since 
been  adopted  by  various  other  authors. 

In  Rankine’s  paper  of  1849,  the  chief  applications  of  the  general 
equation  of  thermodyamics  are  as  follow  : — The  values  of  apparent 
as  distinguished  from  real  specific  heat,  for  gases  and  vapours  under 
various  circumstances.  The  demonstration  that  the  apparent 
specific  heat  of  a vapour  kept  constantly  at  the  pressure  of  satura- 
tion, while  its  volume  varies,  is  negative  for  most  fluids  at  ordinary 
temperature — in  other  words,  that  steam,  for  example,  tends  to 
become  partially  liquified  when  it  works  expansively,  contrary  to 
what  had  been  previously  believed.  This  fact  was  first  verified 
experimentally  by  M.  Hirn  of  Colmar.  And  the  demonstration  that 
the  total  heat  of  evaporation  of  a perfect  gas  increases  with  tem- 
perature at  a rate  equal  to  the  completed  specific  heat  of  the  gas 
at  constant  pressure. 

In  the  paper  read  December  1850,  he  deduced  from  Joule’s 
Equivalent  the  value  0*24  for  the  specific  heat  of  air,  and  con- 
cluded that  the  previously  received  value  0*2669  must  be  erroneous. 
This  was  exactly  verified  by  Regnault’s  experiments,  but  not  till 
more  than  three  years  afterwards. 

In  a paper  read  April  1851  (Edin.  Trans,  vol.  xx.  205)  he 
deduced  from  the  general  equation  of  thermodynamics,  as  given 
in  his  paper  of  1849,  the  following  law  of  the  efficiency  of  a 
perfect  heat  engine,-— that  the  whole  heat  expended  is  to  the  heat 
which  disappears  in \ doing  mechanical  work,  as  the  absolute  tem- 
perature at  which  heat  is  received  to  the  difference  between  the  tem- 
peratures at  which  it  is  received  and  rejected. 


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of  Edinburgh , Session  1873-74. 

In  Rankine’s  paper  of  1849,  groups  of  circular  vortices  were  sup- 
posed to  be  arranged  in  spherical  layers  round  the  atomic  nuclei, 
in  order  to  simplify  the  investigation.  On  the  18th  December 
1851,  he  read  a paper  (Edin.  Trans,  xx.  p.  425)  in  which  it  was 
shown  that  precisely  the  same  results  as  to  the  relations  between 
heat,  elasticity,  and  mechanical  work,  follow  from  the  supposition 
of  molecular  vortices  of  any  figure  arranged  in  any  way.  In  a 
long  series  of  papers  he  applied  the  principles  of  thermodynamics 
to  various  practical  equations  relating  to  the  steam-engine  and 
other  heat  engines,  and  he  was  the  author  of  the  first  separate 
treatise  in  which  the  science  of  thermodynamics  was  set  forth 
with  a view  to  its  practical  application  (A  Manual  of  the  Steam- 
Engine  and  other  Prime  Movers,  1859).  In  two  papers  read  to 
the  Philosophical  Society  of  Glasgow  in  1853-1 855  respectively, 
he  pointed  out  how  the  laws  of  thermodynamics  and  of  electro- 
dynamics might  be  regarded  as  particular  cases  of  general  laws 
applicable  to  energy  in  the  abstract,  and  especially  to  transforma- 
tion between  the  two  great  classes  of  tl actual  and  potential” 
energy. 

Clausius,  who,  it  is  well  known,  discovered  the  second  law  of 
thermodynamics  consentaneously  with  Rankine,  having  taken  occa- 
sion in  1866  to  lay  great  weight  on  his  having  adopted  no  special 
hypothesis  on  the  molecular  constitution  of  bodies,  hut  to  have 
deduced  the  second  law  from  general  principles,  Rankine,  in  an 
address  to  the  Philosophical  Society  of  Glasgow,  concluded  an 
eloquent  justification  of  the  mechanical  hypothesis  of  molecular 
vortices  in  these  words  : — u I wish  it  to  be  clearly  understood  that 
although  I attach  great  value  and  importance  to  sound  mechani- 
cal hypothesis  as  means  of  advancing  physical  science,  I firmly 
hold  that  they  can  never  attain  the  certainty  of  observed  facts ; 
and  accordingly,  I have  laboured  assiduously  to  show  that  the 
two  laws  of  thermodynamics  are  demonstrated  as  facts  independent 
of  any  hypothesis ; and  in  treating  the  practical  application  of 
those  laws,  I have  avoided  all  reference  to  hypothesis  whatsoever.” 

In  March  1854  he  was  awarded  the  Keith  medal  of  the  Royal 
Society  of  Edinburgh  for  the  researches  above  summarised,  mostly 
in  his  own  words.  His  name  and  fame  had  become  European. 
He  was  elected  Fellow  of  the  Royal  Society  of  London,  and  con- 


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tributed  to  that  Society  many  papers  of  permanent  interest  in  the 
course  of  the  next  sixteen  years. 

From  January  to  20th  April  1855,  Rankine  lectured  for  Pro- 
fessor G-ordon  at  Glasgow  College,  on  “ Applied  Mechanics  ” and 
the  “ Application  of  Thermodynamics  to  the  Theory  of  the  Steam- 
Engine.”  These  lectures  were  of  so  high  a character  of  usefulness, 
and  delivered  in  so  masterly  a manner,  that  steps  were  imme- 
diately taken  to  get  Rankine  appointed  to  the  professorship  on  the 
resignation  of  Mr  Gordon.  The  Queen’s  commission  appointing 
him  Regius  Professor  of  Civil  Engineering  and  Mechanics  was 
dated  November  7,  1855. 

On  the  3rd  of  January  1856  he  delivered  his  introductory  lecture 
11  On  the  Harmony  of  Theory  and  Practice  in  Mechanics,”  an 
essay  full  of  practical  wisdom.  In  November  1856  the  introduc- 
tory lecture  “ On  the  Science  of  the  Engineer,”  was  delivered,  and 
concludes  thus  : — c:  Let  the  young  engineer  then  be  convinced  that 
the  profession  which  he  studies  is  not  a mere  profitable  business, 
but  a liberal  and  a noble  art,  tending  towards  great  and  good  ends, 
and  that  to  strive  to  the  utmost  to  perfect  himself  in  that  art,  and 
in  the  sciences  on  which  it  depends,  is  not  merely  a matter  of 
inclination  or  of  policy,  but  a sacred  duty.” 

Rankine’s  whole  career  as  a professor  exemplified  this  view  of 
the  profession  of  an  engineer.  Ey  efforts,  which  to  ordinary  men 
seem  altogether  impossible,  he  published  in  rapid  succession  four 
manuals  of  a Mechanical  and  Engineering  Science  and  Practice,” 
on  the  best  models  for  arrangement,  but  original  in  the  treatment 
of  many  subjects, — always  lucid  in  definition  and  demonstration, 
and  replete  with  applications  to  examples  of  the  practice  of  experi- 
enced men  in  all  departments. 

The  students  of  engineering  during  the  previous  existence  of  the 
Professorship  had  gradually  awakened  to  the  necessity  of  acquiring 
some  preliminary  scientific  instruction,  and  Rankine’s  style  of 
teaching  at  once  incited  them  to  far  higher  efforts.  It  is  unques- 
tionable that  his  scientific  works  generally,  and  his  manuals  of 
applied  science  especially,  have  done  more  to  break  down  the  long 
persistent  fallacy  of  a discrepancy  between  rational  and  applied 
mechanics,  between  theory  and  practice  in  engineering,  than  any 
previous  publications  whatever,  and  the  influence  of  his  systematic 


303 


of  Edinburgh,  Session  1873-74. 

scientific  teaching  is  spreading  true  principles  of  engineering 
design  in  this  country,  as  the  works  of  Navier,  Poncelet,  Morin, 
and  Weisbacli  had  done  many  years  previously  on  the  engineering 
practice  of  France  and  Germany.  I say  advisedly,  that  in  far 
fewer  cases  now-a-days  do  we  see  the  strength  and  stability  which 
ought  to  he  given  by  the  skilful  arrangement  of  the  parts  of  the 
structure,  supplied  by  means  of  an  imposing  massiveness  involving 
a lavish  expenditure  of  material  and  labour — that  is,  money — 
than  twenty  years  ago  was  usual. 

His  complete  knowledge  of  foreign  languages  enabled  him  to 
correspond  with  such  men  as  Weisbach,  Zeuner,  Yerdet,  and  other 
professors  of  applied  mechanics  on  the  Continent,  to  the  mutual 
interest  and  advantage  of  all.  He  also  corresponded  in  German 
with  Poggendorf,  Clausius,  and  Helmholz.  Each  of  the  manuals 
has  gone  through  many  editions, — that  on  the  “ Steam  Engine,” 
&c.,  nine  ; “ Applied  Mechanics,”  seven,  and  so  on. 

In  1862  he  effectually  called  the  attention  of  the  Senate  of  the 
University  to  the  manner  in  which  the  usefulness  of  the  Chair  of 
Civil  Engineering  and  Mechanics  was  impaired  through  its  being 
isolated  from  other  branches  of  study,  and  induced  the  authorities 
to  establish  a systematic  curriculum  of  study  and  examination  in 
all  the  sciences  bearing  on  engineering,  followed  by  the  granting  of 
certificates  to  the  successful  candidates ; a measure  which  led  to  a 
steady  and  continuous  increase  in  the  number  and  efficiency  of  the 
students  in  the  engineering  department  of  the  University;  and  it 
could,  indeed,  scarcely  be  otherwise,  seeing  that  William  Thomson 
taught  Natural  Philosophy,  and  Eankine  taught  its  applications. 
His  style  of  lecturing  was  attractive ; he  never  failed  or  faltered  in 
an  exposition  or  demonstration ; and  his  power  of  illustration  of 
the  details  of  steam-engine  practice,  for  example,  was  unusually 
lucid  from  his  knowledge  of  the  chemistry  of  the  subject  being  co- 
extensive with  his  mechanical  and  physical  knowledge.  He  at  once 
gained  the  confidence  of  thoughtful  students,  and  during  the  first 
session,  that  in  which  he  lectured  for  Professor  Gordon,  he  contracted 
an  intimacy  with  Mr  J.  R.  Napier,  a shipbuilder  and  engineer,  am- 
bitious to  emancipate  his  business  from  being  that  of  one  of  mere 
empiricism,  and  this  friendship,  as  it  ripened,  proved  of  great  con- 
sequence to  the  whole  science  of  shipbuilding  and  steam  propulsion. 


304  Proceedings  of  the  Royal  Society 

In  1856  he  first  projected  a treatise  on  shipbuilding,  which  he 
ultimately  finished  in  1866,  and  published  in  conjunction  with  J. 
R.  Napier  and  others.  Of  this  treatise  it  may  be  said  it  is  unique 
of  its  kind.  It  has  recently  been  published  in  G-erman. 

In  the  autumn  of  1857  he  contrived  a theory  of  skin  resistance 
of  ships,  based  on  experiments  furnished  by  J.  R.  Napier,  and  in 
the  next  year  applied  it  with  complete  success  to  the  steam-ship 
“Admiral,”  verifying  his  theory. 

The  work  on  shipbuilding  occupied  much  of  his  spare  time.  He 
records  at  several  intervals,  from  1863  to  1866,  brief  notes,  such  as 
“Working  hard  at  Treatise  on  Shipbuiling,”  “Researches  on 
Neoids,”  “ Stream  lines.”  In  1866  the  folio  treatise  was  pub- 
lished. Rankine  wrote  the  greater  portion  of  it,  and  was  the  editor. 
The  preparation  of  this  treatise  led  to  a series  of  researches  on 
fluid  motion,  which  are  acknowledged  to  be  of  the  highest  import- 
ance, and  they  certainly  belong  to  the  most  abstruse  parts  of 
mathematical  science.  Rankine’s  genius  overcame  all  difficulties, 
and  the  “Theory  of  the  Propagation  of  Waves,”  the  “Theory  of 
Waves  near  the  Surface  of  Deep  Water,”  and  his  investigations  on 
plane  water  lines  in  two  dimensions,  i.e.,  of  the  lines  of  motion 
of  water  flowing  past  a ship,  advanced,  in  his  hands,  the  appli- 
cation of  science  to  naval  architecture  as  much  as  his  discovery  of 
the  second  law  of  thermodynamics  did  that  of  the  theory  of  the 
steam-engine  and  other  heat  engines.  For,  the  practical  use  of  his 
theory  of  oogenous  water-lines  reproduces  known  good  forms  of 
water-line,  and  even  reproduces  their  numerous  varieties , which 
differ  very  much  from  each  other.  In  fact,  there  is  no  form  of 
water-line  that  has  been  found  to  answer  in  practice  which  cannot 
be  imitated  by  means  of  oogenous  neoids — that  is,  ship-shape 
curves  generated  from  an  oval. 

Besides  Mr  J.  R.  Napier,  the  late  John  Elder  was  the  intimate 
friend  of  Rankine,  and  the  bold  improvements  introduced  by 
that  distinguished  engineer  in  marine  steam  machinery  were  con- 
stantly discussed  with  Rankine,  whose  scientific  aid  in  insuring 
success  was  gracefully  and  munificently  acknowledged  by  Elder’s 
widow,  by  the  gift  of  a large  endowment  to  increase  the  emolu- 
ments of  the  chair  of  Civil  Engineering  and  Mechanics. 

Rankine’s  professional  business  was  that  of  a consulting  engi- 


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of  Edinburgh,  Session  1873-74. 

neer,  and  in  this  capacity  he  made  several  reports  to  his  clients  of 
permanent  value.  One,  “On  Canal  Haulage,”  is  of  great  interest, 
and  another  “ On  the  Explosion  of  the  Tradeston  Elour-Mills.” 

He  was  consulting  engineer  of  the  Highland  Society  of  Scotland. 
This  sketch  of  the  leading  incidents  of  the  scientific  works  which 
have  made  Rankine’s  name  and  fame  represents,  though  very 
feebly,  the  more  permanent  portion  of  his  usefulness  to  his  profes- 
sion and  to  his  generation.  But  besides  these  great  works,  he 
contributed  about  150  papers  of  greater  or  less  importance  to 
philosophical  journals,  mechanics’  magazines,  and  to  “ The  Engi- 
neer ” in  particular;  generally  expositions  of  such  questions  as  the 
day  or  week  suggested  connected  with  engineering  and  mechanics; 
and  it  has  been  truly  said — “ With  him  thought  was  never  divorced 
from  work,  both  were  good  of  their  kind ; the  thought  profound 
and  thorough — the  work  a workmanlike  expression  of  the  thought.” 
“ Few,  if  any,  practical  engineers  have  contributed  so  much  to 
abstract  science,  and  in  no  case  has  scientific  study  been  applied 
with  more  effect  to  practical  engineering.” 

Rankine  was  a steady  attendant  at  the  meetings  of  the  British 
Association,  and  took  an  active  part  as  President  of  Section  Gr,  or 
Secretary  of  Section  A,  or  otherwise  in  these  meetings,  where  he 
had  a universal  acquaintance,  and  was  universally  respected  and 
esteemed.  He  was  a member  of  the  “ Red  Lion’s  ” Club. 

In  1857  he  took  the  most  active  part  in  founding  the  “Institu- 
tion of  Engineers  in  Scotland.”  He  was  the  first  President.  It 
has  proved  a successful  and  eminently  useful  institution. 

The  outward  lustre  of  Rankine’s  career  is  of  course  derived  from 
his  scientific  work,  but  there  was  an  inner  halo  surrounding  him, 
which  to  his  friends  shone  even  brighter  than  the  outward  lustre. 
He  was  a true  gentleman,  gentle,  chivalrous,  self-forgetting,  and 
scrupulously  truthful,  a patient  listener,  a quiet  expounder.  He  sup- 
ported applause  without  feeling  the  weakness  of  vanity.  He  had 
not  a vestige  of  the  spirit  of  rivalry,  being  of  a thoroughly  genial 
temperament.  In  his  judgment  of  other  men  he  obeyed  the  pious 
injunction  of  Thomas  a Kempis,  “Ad  hanc  estiam  pertinet,  non 
quibuslibet  hominum  verbis  credere,  nec  audita  vel  credita  mox 
ad  aliorum  aures  effundere.” 

His  health  for  several  years  in  his  early  youth  was  feeble,  and  he 


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Proceedings  of  the  Royal  Society 

occupied  himself  much  with  the  theory  of  music,  and  practised 
the  piano  and  violoncello.  Though  too  much  occupied  in  after  life 
to  allow  of  his  attaining  much  proficiency,  he  could  always  interest 
and  amuse  his  friends  by  singing  his  own  songs  to  his  own  music, 
always  gay  and  cheery.  “ The  Coachman  of  the  Skylark  ” in  1854, 
“ The  Engine-driver’s  Address  to  his  Engine  ” in  1858,  and  “ The 
Mathematician  in  Love,”  and  “ The  Three-foot  Rule,”  somewhat 
later,  had  a grotesque  gracefulness  of  humour  which  were  irresist- 
ible. His  appearance  was  highly  prepossessing,  as  the  Fellows  of 
the  Royal  Society  of  Edinburgh  well  know.  His  social  qualities 
were  the  admiration  of  his  acquaintances  and  the  delight  of  his 
friends.  Full  of  anecdote  and  information,  he  was  an  ornament  to 
society,  of  which  he  was  always  the  least  obtrusive  member,  but 
often  the  centre  of  attraction.  Everything  he  did  he  did  well. 
Singing,  croquet,  or  bezique,  he  used  to  join  in  them  cordially,  and 
intent  on  the  moment’s  amusement. 

His  first  great  grief  was  the  death  of  his  father  in  May  1870. 
Rankine’s  affectionate  and  devoted  nature  was  deeply  moved,  and 
he  himself  began  soon  after  to  experience  symptoms  of  decay  of 
his  hitherto  vigorous  health.  When,  in  April  1871,  his  excellent 
mother  died,  he  was  for  a time  quite  absorbed  by  his  grief  for  her 
loss.  His  own  health  became  more  and  more  unsatisfactory. 
Especially  his  eyesight  became  very  weak,  and  during  1872  he 
had  to  employ  an  amanuensis  and  an  assistant  in  his  class  work, 
one  of  his  pupils,  M.  Bamber. 

He  visited  his  more  intimate  friends  much  during  the  summer 
of  this  year,  where  he  could  enjoy  rest,  and  quiet,  and  amusement. 
But  his  health  gradually  gave  way,  and  towards  the  end  of  Novem- 
ber his  medical  friends  perceived  that  the  great  mind  of  Rankine 
was  giving  way. 

On  the  24th  December  he  died,  leaving  a noble  record  of  genius 
to  future  generations,  and  a sweet  memory  to  those  of  his  contem- 
poraries who  knew  him  personally. 


if  Edinburgh,  Session  1873-74. 


307 


3.  Obituary  Notice  of  Justus  Liebig.  By  Professor 
Orum  Brown. 

Justus  Liebig  was  born  on  the  12th  May  1803,  at  Darmstadt, 
where  his  father  carried  on  business  as  a grocer  and  colour  mer- 
chant. He  early  showed  a strong  inclination  to  the  study  of 
experimental  chemistry,  reading  all  the  chemical  books  he  could 
procure  from  the  Darmstadt  Library,  and  repeating  every  experi- 
ment he  read  of,  as  far  as  he  could  obtain  from  his  father’s  ware- 
house necessary  materials.  His  father  acceded  to  his  wish  that 
he  should  be  a chemist,  and  as  the  only  way  in  which  this  could 
be  carried  out,  sent  him  at  the  age  of  fifteen  to  an  apothecary’s 
shop  to  learn  chemistry.  There  he  remained  only  ten  months, 
and  he  returned  to  Darmstadt  satisfied  that  he  must  seek  some 
other  mode  of  obtaining  his  object.  He  remained  at  home  for 
some  months  preparing  for  a University  course,  upon  which  he 
entered  in  1819  at  Bonn.  He  soon  left  Bonn  for  Erlangen,  where 
he  studied  chemistry  under  Kastner.  When  at  Erlangen  he 
attended  Schelling’s  lectures,  and  long  after  used  to  speak  of 
the  interest  he  had  taken  in  them,  and  of  the  injurious  effect  they 
had  exercised  upon  his  success  as  a practical  investigator.  Both 
at  Bonn  and  at  Erlangen  he  founded  a students’  society  of 
chemistry  and  physics,  in  which  the  members  communicated  and 
discussed  novelties  of  science.  Liebig  left  Erlangen  in  1822, 
having  already  published  a paper  on  the  preparation  of  Schwein- 
furth  green. 

Assisted  by  the  liberality  of  the  Grand  Duke  Louis  of  Hesse, 
he  proceeded  to  Paris,  where  he  attended  the  lectures  of  Gay-Lussac, 
Thenard,  and  Dulong,  and  obtained  from  Gay-Lussac  permission 
to  work  in  his  private  laboratory.  He  there  carried  on  his  investi- 
gation into  the  composition  and  properties  of  the  fulminates,  the 
results  of  which  he  communicated  to  the  Academy.  He  at  once 
attracted  the  notice  of  Humboldt,  who  was  then  resident  in  Paris, 
and  through  his  influence  was  appointed,  in  1824,  Extraordinary 
Professor  of  Chemistry  in  the  University  of  Giessen.  In  1826 
he  was  raised  to  the  ordinary  professorship.  In  1845  the  Grand 
Duke  of  Hesse  conferred  upon  him  the  title  of  Baron  von  Liebig. 
In  1852  he  accepted  an  invitation  by  the  Bavarian  Government 
VOL.  VIII.  2 R 


308  Proceedings  of  the  Royal  Society 

to  the  ordinary  Professorship  of  Chemistry,  and  the  Directorship 
of  the  Chemical  Laboratory  in  the  University  of  Munich.  He 
died  18th  April  1873,  at  Munich. 

The  time  had  not  yet  come  for  a calm  and  judicial  estimate 
of  Liebig’s  influence  on  the  progress  of  chemistry.  It  must  be 
left  for  future  generations  of  chemists,  removed  from  the  direct 
influence  of  his  work,  and  unbiassed  by  personal  recollection,  to 
assign  him  his  proper  place  among  the  great  leaders  of  chemical 
thought  and  investigation.  It  is,  however,  possible  for  us  to 
give  a general  sketch  of  his  career,  and  to  point  out  some  of 
the  more  prominent  effects  of  his  work  as  seen  in  the  present 
state  of  the  science. 

We  may  consider  him  as  a teacher  of  chemistry,  as  an  inventor 
of  new  means  of  investigation,  as  a discoverer  of  new  facts  and 
a creator  of  new  ideas  in  pure  chemistry,  and  as  an  expounder  of 
the  relations  of  chemistry  to  common  life  and  to  the  arts.  As 
a teacher,  he  introduced  into  Gfermany  systematic  practical  train- 
ing in  laboratory  work,  and  induced  the  Darmstadt  Government 
to  build  at  Giessen  a students’  laboratory,  which  has  served  as 
the  type  of  those  magnificent  scientific  laboratories  which  have 
recently  been  erected  in  connection  with  all  the  great  German 
universities.  His  stinging  attacks  upon  the  great  German  Govern- 
ments for  their  neglect  of  practical  scientific  education,  his  own 
success  as  a teacher,  and  the  zeal  for  the  good  cause  which  he 
imparted  to  his  pupils,  have  had  for  their  effect  the  establishment 
throughout  Germany  of  numerous  well-equipped  and  usefully 
active  schools  of  practical  science.  It  is  not  too  much  to  say 
that  there  is  no  school  of  chemistry  in  the  world  which  does  not 
owe  a great  part  of  its  usefulness  to  the  example  of  the  Giessen 
laboratory. 

It  is  unnecessary  here  to  catalogue  the  improvements  in  chemical 
apparatus  which  we  owe  to  Liebig,  but  there  is  one  invention 
which  must  at  once  occur  to  every  chemist  as  of  vital  importance 
in  the  history  of  the  science.  Organic  analyses  were  made  with 
great  accuracy  before  1831,  but  they  could  be  made  only  by  highly 
skilled  chemists,  and  involved  great  labour  and  trouble.  The 
publication  by  Liebig,  in  that  year,  of  his  method  of  organic 
analyses — the  method  which  (with  important  but  secondary  improve- 


309 


of  Edinburgh , Session  1873-74. 

ments)  we  still  employ,  made  it  easy  for  any  advanced  student  to 
make  an  accurate  analysis  of  an  organic  body.  It  may  be  truly 
said  that  the  astonishingly  rapid  development  of  organic  chemistry, 
which  dates  from  that  time,  was  only  rendered  possible  by  the 
simplification  of  the  method  of  organic  analysis  entirely  due  to 
Liebig. 

Of  Liebig’s  discoveries  and  speculations  it  is  possible  to  give, 
in  such  a notice  as  this,  only  an  outline.  The  whole  progress  of 
chemistry  for  the  last  fifty  years  is  so  intimately  connected  with 
what  he  did,  that  a life  of  Liebig  would  necessarily  include  the 
history  of  chemistry  for  that  period. 

His  investigations  extend  to  nearly  every  branch  of  chemistry, 
but  it  was  to  organic  chemistry  that  he  specially  devoted  himself ; 
and  it  is  through  his  work,  in  this  direction  chiefly,  that  he  has 
influenced  other  departments  of  chemistry  and  the  science  gene- 
rally. His  first  research,  that  on  fulminic  acid,  published  in 
Paris  in  1823,  led  to  the  recognition  of  the  isomerism  of  ful- 
minic acid  and  the  cyanic  acid  discovered  in  1822  by  Wohler, 
and  was  followed  by  a long  series  of  investigations  on  the  com- 
pounds related  to  cyanogen,  in  which  he  opened  out  and  to  a 
great  extent  explored  this  intricate  and  interesting  path  of  inquiry. 
Another  group  of  researches  was  directed  to  the  determination 
of  the  composition  and  constitution  of  organic  acids.  In  a com- 
prehensive memoir  published  in  1838,  he  pointed  out  the  analogies 
between  many  organic  acids  and  phosphoric  acid,  and  introduced 
the  idea  of  polybasic  acid  into  organic  chemistry,  enumerating  the 
criteria  for  the  determination  of  the  basicity  of  an  acid  with  extra- 
ordinary precision  and  accuracy. 

He  made  numerous  analyses  of  the  vegetable  alkaloids,  and 
greatly  increased  our  knowledge  of  their  properties,  of  their  equi- 
valents, and  of  the  relation  of  equivalent  to  composition. 

His  investigations  into  the  derivatives  of  alcohol,  particularly 
those  formed  by  oxidation  and  by  the  action  of  chlorine,  including 
the  discovery  of  aldehyde  and  chloral,  poured  a flood  of  light  upon 
the  whole  question  of  the  constitution  of  organic  compounds. 
Liebig  was  the  first  to  regard  ether  as  an  oxide,  of  which  alcohol  is 
the  hydrate,  and  the  compound  ethers  salts.  By  doing  so  he  chal- 
lenged the  defenders  of  the  “etherine”  theory,  who  looked  upon 


310  Proceedings  of  the  Royal  Society 

ether  as  a hydrate  of  olefiant  gas.  The  result  was  one  of  those 
controversies  which  have  proved  of  immense  value  in  the  progress 
of  chemistry.  In  the  course  of  this  controversy  the  relations  of 
alcohol  and  ether  to  other  substances  were  investigated  and  dis- 
cussed with  great  minuteness,  and  the  result  was  the  general  adop- 
tion of  Liebig’s  ethyl  theory.  The  subject  of  decay,  putrefaction, 
and  fermentation  early  engaged  Liebig’s  attention.  Entirely 
opposed  to  the  vital  theory  of  fermentation,  he  attacked  it  with 
both  argument  and  ridicule,  and  proposed  a purely  chemical 
theory,  which  he  defended  with  great  ingenuity. 

A very  important  part  of  Liebig’s  work  in  pure  organic  chemistry 
was  carried  on  along  with  Wohler.  As  might  be  expected,  the 
joint  efforis  of  two  men  of  such  genius  and  industry  produced 
results  unexampled  in  number  and  importance.  One  of  the  first 
objects  of  their  research  (in  1830)  was  cyanic  acid,  a substance 
discovered  by  Wohler,  and  in  which  Liebig  had  a special  interest 
from  its  isomerism  with  his  fulminic  acid.  But  the  investigations 
undertaken  by  them,  which  exercised  the  greatest  influence  on 
the  science  of  chemistry  were  those  on  the  benzoic  compounds  and 
on  uric  acid.  These  are  models  of  what  such  work  ought  to  be, 
not  only  enriching  the  science  with  new  facts,  but  compacting  it 
by  the  discovery  of  new  relations.  The  theoretical  views  brought 
forward  in  the  papers  on  benzoic  acid  and  bitter  almond  oil  were 
the  commencement  of  the  development  of  the  new  theory  of  com- 
pound radicals  which  soon  took  the  place  of  that  of  Berzelius. 

The  most  widely  known  part  of  Liebig’s  work  consists  in  his 
applications  of  chemistry  to  physiology  and  agriculture.  The  facts 
he  discovered  in  reference  to  the  chemistry  of  animal  and  vege- 
table nutrition,  and  the  explanations  he  gave  of  the  chemical  pro- 
cesses involved  in  the  life  of  organisms,  have  had  an  incalculable 
effect  upon  physiological  chemistry.  In  his  application  of  the 
principles  of  chemistry  to  agriculture,  he  proceeded  in  a thoroughly 
scientific  manner;  and  although  he  in  some  cases  generalised  too 
fast,  and  was  thus  led  into  practical  error,  his  work  forms  the  foun- 
dation of  a true  science  of  agriculture. 

By  far  the  greater  part  of  Liebig’s  scientific  work  was  done  at 
Gfiessen.  After  his  removal  to  Munich,  the  claims  of  society  and 
the  court  life  of  a capital  upon  his  time  made  the  devotion  to 


311 


of  Edinburgh,  Session  1873-74. 

laboratory  work  which  distinguished  the  earlier  part  of  his  career 
impossible.  His  work  in  Munich  consisted  chiefly  in  elaborations 
of  his  previous  ideas,  and  in  researches,  the  results  of  which  are  of 
comparatively  little  general  scientific  interest,  although  in  some 
cases  of  considerable  practical  value.  Among  these  may  be  men- 
tioned the  discovery  of  the  mode  of  preparing  the  extract  of  meat, 
and  that  of  a method  of  depositing  a uniform  coherent  layer  of 
silver  of  any  thickness  upon  smooth  surfaces. 

Liebig  was  a most  voluminous  author.  His  papers  were  pub- 
lished in  many  journals,  but  chiefly  in  Poggendorff’s  “ Annalen,” 
and  in  the  “Annalen  der  Pharmacie”  (now  “Justus  Liebig’s 
Annalen  der  Chemie  und  Pharmacie  ”),  of  which  he  became  one  of 
the  editors  in  1831.  Of  separately  published  books,  the  most 
important  are  “ Introduction  to  the  Analysis  of  Organic  Bodies,” 
1837 ; “ Chemistry  in  its  Application  to  Agriculture  and  Physio- 
logy,” 1840;  “Animal  Chemistry,”  1842  ; “ Handbook  of  Organic 
Chemistry”  (as  second  volume  of  a revised  edition  of  Geiger’s 
“ Pharmacy  ”),  1843  ; “ Chemical  Letters,”  1844  ; “ On  the 
Chemistry  of  Food,”  1847 ; “ On  Some  Causes  of  the  Motions  of 
the  Juices  in  the  Animal  Body,”  1848;  “Principles  of  Agricul- 
tural Chemistry,  with  special  Eeference  to  the  late  Researches  made 
in  England,”  1855.  Of  most  of  these  works  many  editions  were 
published  in  German  and  in  almost  every  European  language. 
From  1831  till  bis  death  he  was  one  of  the  editors  of  the  chemical 
journal  now  known  as  “Justus  Liebig’s  Annalen  der  Cbemie  und 
Pharmacie.”  Along  with  Kopp  he  edited,  from  1847  to  1856,  the 
“ Jahresbericht  fiber  die  Fortschritte  der  Chemie  ;”  and  along  with 
Poggendorff  and  Wohler,  the  “ Handworterbuch  der  Chemie.” 

His  personal  character  was  simple  and  easily  characterised. 
Open,  amiable,  and  generous,  vehement  in  carrying  out  his  convic- 
tions, utterly  intolerant  of  pretence  and  dishonesty,  he  was  either 
a warm  friend  or  a declared  enemy.  In  controversy  he  was  often 
violent,  sometimes  ferocious,  but  he  never  struck  an  unfair  blow. 

By  his  death  many  chemists  have  lost  a friend,  and  all  feel  one 
more  link  attaching  them  to  the  last  generation  broken. 


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Proceedings  of  the  Royal  Society 


4.  Obituary  Notice  of  Gustav  Rose.  By  Professor 
Crum  Brown. 

Gustave  Rose  was  born  in  Berlin  on  the  18th  of  March  1798. 
He  was  the  youngest  son  of  the  pharmaceutical  chemist,  Valentin 
Rose,  and  the  brother  of  Heinrich  Rose,  the  eminent  analytical 
chemist.  He  intended  to  devote  himself  to  mining  engineering, 
and  began  his  practical  studies  in  Silesia;  but  in  consequence  of 
illness  gave  up  this  profession,  and  occupied  himself  with  scientific 
chemistry  and  mineralogy.  He  studied  mineralogy  under  Weiss, 
in  the  University  of  Berlin,  and  made  a large  number  of  careful 
measurements  of  crystals.  His  first  published  work  was  his  gradu- 
ation thesis,  “De  Sphenis  atque  Titanitae  systemate  Crystallino,” 
1820. 

Like  many  young  chemists  of  his  time,  he  was  attracted  to 
Stockholm,  where  he  studied  under  the  guidance  of  Berzelius,  the 
greatest  and  most,  accurate  chemist  of  that  age,  and  by  frequent 
excursions  in  Sweden  made  himself  thoroughly  acquainted  with 
the  varied  mineralogy  of  that  country.  In  Stockholm  he  met 
Mitscherlich,  with  whom  he  maintained  a life-long  friendship. 
Late  in  life  he  felt  it  necessery  for  him  to  explain,  which  he  did 
in  a friendly  and  modest  way,  the  share  he  had  in  the  work  which 
led  to  Mitscherlich ’s  discovery  of  isomorphism.  In  1823  he  be- 
came lecturer  on  mineralogy  in  the  University  of  Berlin;  in  1826 
he  received  the  title  of  extraordinary  Professor ; and  in  1849  was 
appointed  ordinary  Professor  of  Mineralogy  and  Director  of  the 
Mineralogical  Collections. 

Rose  travelled  much  in  search  of  mineralogical  knowledge.  He 
visited  England,  Scotland,  Scandinavia,  Italy,  and  France,  studying 
rocks,  mines,  and  museums;  and  in  1829  was  selected  by  Humboldt 
as  one  of  his  companions  in  his  examination  of  the  Ural  and  Altai 
Mountains.  There  Rose  discovered  many  new  minerals,  and  in  a 
special  work,  “ Reise  nach  dem  Ural,”  1837  and  1842,  made  known 
the  remarkable  mineral  wealth  of  that  part  of  the  Russian  empire. 
His  holidays  were  usually  occupied  by  excursions  in  Silesia  or  in  the 
Harz,  where  he  collected  the  materials  for  some  of  his  most  valu- 
able investigations.  During  one  of  his  walks  in  Silesia  he  sustained 
an  injury  of  the  knee,  from  which  he  suffered  much,  but  continued 


313 


of  Edinburgh , Session  1873-74. 

his  lectures  till  the  11th  July  1873,  when  he  was  attacked  with 
inflammation  of  the  lungs,  from  the  effects  of  which  he  died  on  the 
15th  of  July. 

His  most  important  works  were  an  elaborate  memoir  on  fel- 
spar (1823) ; numerous  investigations  on  quartz,  on  granite,  on 
the  metals  which  crystallise  in  rhombohedra;  on  the  conditions 
under  which  carbonate  of  lime  crystallises  in  the  form  of  calcspar, 
or  in  that  of  arragonite,  on  meteorites,  and  on  the  mineralogical 
constituents  of  trap-rocks.  Besides  these  purely  mineralogical 
researches,  special  interest  attaches  to  his  study  of  the  relation 
between  the  crystalline  form  and  the  physical  properties  of 
minerals.  He  pointed  out  that  in  tourmaline  and  in  electric 
calamine  the  pyro-electiic  polarity  is  connected  in  a constant 
manner  with  the  crystalline  polarity,  and  described  with  great 
minuteness  the  forms  of  these  minerals. 

In  1857  Marbach  showed  that  the  crystals  of  iron  pyrites  and 
also  those  of  cobaltine,  both  minerals  crystallising  in  forms  belong- 
ing to  the  regular  system,  could  be  divided  into  two  sets,  differing 
extremely  in  thermo-electric  character,  the  one  set  more  positive 
than  antimony,  the  other  more  negative  than  bismuth.  Kose  saw 
at  once  that  this  difference  must  be  related  to  their  crystalline 
form,  and  that  these  two  sets  must  possess  crystalline  characters 
of  a right  and  left  handed  kind,  and  at  last  succeeded  in  detecting 
the  difference  between  them. 

Most  of  his  researches  were  published  in  “Poggendorff ’s  Anna- 
len,”  in  the  Transactions  of  Berlin  Royal  Academy  of  Sciences,  and 
in  the  Journal  of  the  German  Geological  Society.  Besides  the 
“Reise  nach  dem  Ural,”  already  mentioned,  he  published  a short 
work  on  the  “ Elements  of  Mineralogy,”  distinguished  by  beauti- 
fully drawn  figures,  and  one  on  a crystallo-chemical  system  of 
classification  of  minerals. 

Professor  Rammelsberg,  from  whose  notice  of  Rose’s  life  most  of 
the  foregoing  sketch  has  been  taken,  testifies  to  the  remarkable 
kindliness  and  geniality  of  his  character,  to  the  pleasure  which  he 
felt  in  the  success  of  his  young  scientific  friends,  and  to  his  hatred 
of  polemical  discussion. 


314  Proceedings  of  the  Royal  Society 

5.  Obituary  Notice  of  the  Eev.  Professor  Stevenson,  D.IX 
By  John  Small,  M.A.,  Librarian  to  the  University  of 

Edinburgh. 

Professor  William  Stevenson  was  born  at  Barfod,  in  the  parish 
of  Lochwinnoch,  on  the  26th  October  1805.  His  father  was  the 
proprietor  of  a small  estate  called  Broadfield,  and  William  was 
his  second  son.  He  entered  the  University  of  Glasgow  in  1821, 
and  pursued  his  studies  at  that  University  during  the  usual 
curriculum  in  the  Faculty  of  Arts,  with  the  exception  of  one 
session  (1824-25)  which  he  spent  at  St  Andrews,  attracted  by  the 
popularity  of  Dr  Chalmers,  who  was  at  that  time  Professor  of 
Moral  Philosophy  there.  While  at  the  University  of  Glasgow 
he  attended  diligently  to  his  studies,  and  worked  particularly 
for  the  classes  of  mathematics  and  natural  philosophy.  During 
the  summer  months  he  acted  as  tutor  in  the  family  of  the  late 
Mr  Cochran  of  Ladyland,  and  thus  began  a friendship  which  lasted 
uninterruptedly  till  the  time  of  his  death.  It  was  the  arranging 
and  cataloguing  the  old  library  at  Ladyland  that  developed  the 
love  of  books  for  which  he  was  afterwards  so  remarkable,  and  the 
catalogue  he  then  made  is  still  carefully  preserved.  He  pursued 
his  theological  studies  at  the  University  of  Glasgow,  but  was  in 
session  1828-29  at  the  University  of  Edinburgh.  In  theology  he 
was  a distinguished  student,  in  some  sessions  carrying  off  the 
highest  honours.  After  finishing  his  university  course,  he  was 
licensed  by  the  Presbytery  of  Paisley  on  the  5th  of  May  1831. 

He  officiated  for  six  months  in  the  Presbyterian  Church  in 
Limerick  in  1832,  and  in  July  1833  was  appointed  by  the  Crown 
assistant  and  successor  to  the  Eev.  George  Gleig,  minister  of 
Arbroath,  on  whose  death  two  years  afterwards  he  succeeded  to  the 
charge. 

While  at  Arbroath  Mr  Stevenson  enjoyed  the  friendship  of  the 
Eev.  Dr  Thomas  Guthrie,  then  minister  of  Arbirlot,  and  an  amusing 
account  is  given  in  the  autobiography  of  that  eminent  divine,  of  a 
public  discussion  with  the  Eev.  Dr  Eitchie,  “ the  Goliath  of 
Voluntaryism,”  held  at  Arbroath,  in  which  Mr  Stevenson  took  a 
prominent  part  (vol.  i.  p.  167).  The  account  of  the  discussion 
on  this  occasion  was  published  in  the  form  of  a pamphlet,  with  the 


315 


of  Edinburgh,  Session  1873-74. 

following  title : “ Account  of  a Meeting  held  at  Arbroath  on  the 
16th  April  1834,  in  Defence  of  Church  Establishments,  with  a full 
Report  of  the  Speeches  delivered  on  that  occasion  by  the  Rev. 
Messrs  Stevenson,  Meek,  Whitson,  Lee,  Guthrie,  and  Muir.” 
This  publication  attracted  considerable  attention,  and  brought  the 
speakers  prominently  before  the  public ; one  of  them  was  the  Rev. 
Dr  Robert  Lee,  afterwards  Professor  of  Biblical  Criticism,  then 
minister  of  a Chapel-of-Ease  at  Inverhrothock.  In  1839  Mr 
Stevenson’s  health  gave  way,  and  he  suffered  so  much  from  chronic 
bronchitis  that  he  had  to  spend  the  winter  of  that  and  the  follow- 
ing year  at  Torquay. 

On  the  re-establishment  of  his  health,  Mr  Stevenson  was  in  1844 
presented  by  the  Crown  to  the  first  charge  of  the  parish  of  South 
Leith.  This  valuable  preferment  enabled  him  to  gratify  his  in- 
tense love  of  reading,  and  he  collected  rare  and  valuable  books,  not 
only  on  theology,  but  on  every  subject  illustrating  the  history  and 
antiquities  of  Scotland.  In  1848  he  was  elected  a Fellow  of  the 
Society  of  Antiquaries  of  Scotland,  and  in  1849  he  received  the 
degree  of  D.D.  from  the  University  of  Edinburgh. 

Whilst  minister  of  South  Leith  Dr  Stevenson  took  much  interest 
in  his  parochial  duties,  and  in  1851  published  a small  volume, 
entitled  “ Christianity  and  Drunkenness.”  He  was  also  a con- 
tributor to  Macphail’s  “ Edinburgh  Magazine,”  and  the  topics  he 
handled  were  “The  Buchanites,”  “ Pusey  and  the  Confessional,” 
and  matters  relating  to  the  great  Gorham  controversy  in  the 
Church  of  England.  He  took  part  in  the  proceedings  of  the 
General  Assembly,  and  was  appointed  Convener  of  the  Colonial 
Committee  in  1859. 

In  1858  he  was  elected  a Fellow  of  the  Royal  Society  of  Edin- 
burgh. 

In  1861  he  was  appointed  to  the  Chair  of  Divinity  and  Eccle- 
siastical History  in  the  University,  on  the  death  of  the  Rev.  Dr 
Robertson.  As  Professor,  his  method  of  conducting  the  class  was 
somewhat  peculiar.  In  place  of  giving  in  each  session  a simple 
outline  of  his  very  extensive  subject,  he  chose  rather  to  take  a 
limited  period  in  the  Church’s  history,  and  illustrate  this  in  the 
most  minute  manner.  Every  heresy  or  controversy  that  had 
cropped  up  in  the  period  selected  received  due  attention,  and  was 

2 s 


VOL.  VIII. 


316 


Proceedings  of  the  lioyal  Society 

illustrated  by  extracts  from  rare  works  which  he  had  collected  f6r 
the  purpose.  In  his  first  session  (1861-62),  the  period  embraced 
in  his  lectures  was  only  from  a.d.  30  to  100. 

Although  the  Government,  when  he  was  appointed  Professor  of 
Church  History,  dissociated  from  the  Chair  the  valuable  appoint- 
ment of  Secretary  to  the  Bible  Board  for  Scotland,  still  Dr 
Stevenson,  from  his  private  resources,  was  enabled  to  gratify  to  the 
utmost  his  passion  for  adding  to  his  library.  He  was  a member  of 
the  Bannatyne  Club  and  other  literary  societies  originated  for 
printing  valuable  historical  manuscripts,  ancient  poetry,  &c.,  &c., 
and  the  recondite  works  he  thus  received  were  not  in  his  case  put 
hastily  on  his  shelves,  but  were  carefully  read  and  criticised. 

He  was  Vice-President  of  the  Society  of  Antiquaries  for  several 
years,  and,  as  his  colleague,  Sir  James  Simpson,  had  given  a great 
impetus  to  archseological  matters  in  Scotland,  Dr  Stevenson  went 
with  him  hand  in  hand.  His  reminiscences  of  excursions  (“  howking 
expeditions”  as  they  were  called)  planned  by  Sir  James  to  places 
of  antiquarian  interest  in  the  neighbourhood  of  Edinburgh,  were 
very  amusing.* 

As  Dr  Stevenson,  from  his  excellent  scholarship,  desired  extreme 
minuteness  and  accuracy  in  every  literary  work,  this  may  account 
for  his  published  writings  being  fewer  than  his  abilities  led  his 
friends  to  expect.  But,  while  it  was  supposed  that  his  appoint- 

* One  of  these,  arranged  in  honour  of  Dr  Reeves,  of  Trinity  College,  Dubliu , 
was  to  inspect  the  curious  buildings  still  existing  at  Culross,  and  Sir  James 
had  chartered  a steamer  to  take  a large  party  from  Leith  to  visit  that  ancient 
Burgh.  So  much  time,  however,  had  been  lost  in  visiting  Inch  Garvie  and 
other  islets  in  the  Firth,  that  on  reaching  Culross,  from  the  shallowness  of 
the  water,  the  steamer  had  to  anchor  a long  way  from  the  shore.  Nothing 
daunted.  Sir  James,  with  a dozen  of  followers,  got  into  a small  boat,  but  it  at 
last  ran  aground.  The  rest  of  the  party  getting  into  another  boat,  and  avoid- 
ing the  error  the  first  had  committed,  reached  the  pier  by  a circuitous  route, 
and  lent  their  aid  to  bring  the  party  which  had  first  left  the  steamer  ashore. 
They  were  at  last  carried  through  the  shallow  water  and  mud  on  the  shoulders 
of  the  Culross  boatmen,  and  the  appearance  of  Sir  James  himself  as  he  was 
supported  on  the  backs  of  two  sailors,  with  other  two  lending  their  assistance, 
created  great  merriment  This  was  often  referred  to  by  Dr  Stevenson  as  one 
of  his  happiest  excursions.  Although  differing  in  Church  politics,  a great 
friendship  existed  between  Sir  James  and  Dr  Stevenson,  and  on  the  death  of 
the  former  Dr  Stevenson  was  much  affected.  He  expressed  his  feelings  in  a 
poem,  a portion  of  which  was  inserted  in  the  Life  of  Sir  James  by  the  Rev. 
Dr  Duns. 


317 


of  Edinburgh,  Session  1873-74. 

ment  to  the  Chair  of  Church  History  might  have  allowed  him 
leisure  to  publish  some  results  of  his  extensive  reading  and  matured 
thought,  the  plan  he  had  laid  down  for  teaching  the  history  of 
the  Church  (as  before  observed)  necessitated  the  writing  of  new 
lectures  for  each  year.  In  this  way  he  sometimes  wrote  seventy 
new  lectures  in  one  session.  In  any  intervals  of  leisure,  however, 
he  enjoyed  miscellaneous  reading,  and  sometimes  indulged  in 
poetical  effusions.  He  translated  into  verse  the  Latin  rhymes  in 
the  well-known  Aberdeen  Breviary,  which  he  printed,  but  did  not 
then  complete. 

As  ancient  Scottish  literature,  especially  poetry,  had  always  been 
a favourite  subject  with  him,  Dr  Stevenson  was  often  consulted 
about  the  publication  of  manuscript  remains  of  our  early  Doric 
vernacular,  and  several  works  of  this  kind,  when  they  appeared, 
were  dedicated  to  him.  In  1870  he  took  much  interest  in  an 
edition  of  the  works  of  Gavin  Douglas,  the  poetical  Bishop  of 
Dunkeld,  then  projected.  He  read  over  the  proof  sheets,  and 
aided  in  expiscating  some  circumstances  attendant  on  the  double 
consecration  of  that  ancient  Scottish  Prelate.  About  the  same 
time  he  resolved  to  complete  the  legends  from  the  Aberdeen 
Breviary,  by  appending  historical  notes,  and  they  at  length  ap- 
peared in  an  octavo  volume  about  the  end  of  1872.  The  title  of 
the  work  is  as  follows  : — “ The  Legends  and  Commemorative  Cele- 
brations of  StKentigern,  his  Friends  and  Disciples,  translated  from 
the  Aberdeen  Breviary  and  the  Arbuthnot  Missal,  with  an  illustra- 
tive Appendix.  Printed  for  private  circulation,  1872.” 

In  the  preface,  he  states  that  at  one  time  he  had  in  view  u to 
prepare  a complete  calendar  of  the  Scottish  Saints,  and,  taking  the 
national  legends  of  the  Aberdeen  Breviary  for  a basis,  he  proposed 
to  intercalate  all  that  he  might  be  able  to  ascertain  regarding 
those  DU  minores  of  our  country’s  earlier  faith,  who,  although  not 
enrolled  in  that  dignified  service  book,  are  mentioned  in  other 
literary  monuments  now  less  recondite  than  they  were  then,  or 
have  left  some  dim  memories  of  themselves  in  the  names  of  the 
towns,  villages,  fairs,  and  wells  of  our  country,  sometimes  in 
remote  and  lonely  districts,  or  spots  where  there  had  once  been 
chapels,  cells,  or  hermitages.” 

The  want  of  leisure  prevented  his  carrying  out  so  extensive  a 


318  Proceedings  of  the  Royal  Society 

plan,  but  we  are  indebted  to  him  for  some  interesting  information 
regarding  the  group  of  saints  more  immediately  connected  with 
the  Lothians  and  Fife,  viz.,  St  Kentigern,  and  his  mother  St 
Thenew  (daughter  of  Loth,  King  of  the  Lothians),  St  Servanus  or 
St  Serf,  St  Columba,  St  Asaph,  St  Baldred  of  the  Bass,  St  Con- 
wall,  and  St  Palladius. 

From  his  family  connection  with  Clackmannanshire  he  was 
much  attached  to  that  district,  and  for  several  summers  he  occupied 
a villa  in  the  neighbourhood  of  Muckart.  In  this  retirement  he 
was  always  happy,  surrounded  by  his  family,  and  supplied  with  the 
newest  literature.  One  season  was  distinguished  by  some  rural 
festivities,  which  he  commemorated  in  verse  in  a tiny  volume 
printed  in  1872  (“  The  Yetts  o’  Muckart;  or  the  Famous  Pic-nic 
and  the  brilliant  Barn-Ball.  In  hairst  auchteen  bunder  an’ 
seventy -one.”) 

Finding  his  health  failing,  Dr  Stevenson,  with  much  reluctance, 
resigned  his  Chair  in  November  1872. 

This  step  was  much  regretted  by  his  colleagues,  and  his  retire- 
ment was  gracefully  referred  to  by  Principal  Sir  Alexander  G-rant, 
in  his  opening  address  of  the  College,  session  1872-73,  and  in  the 
introductory  lectures  of  his  colleagues  in  the  Faculty  of  Theology, 
who  all  expressed  the  hope  that  he  would  enjoy  the  rest  to  which 
he  was  so  well  entitled.* 

The  good  wishes  of  the  learned  Principal  and  the  Professors 
were  not  realised,  and  the  last  year  of  Dr  Stevenson’s  life  was 
spent  in  much  annoyance  from  the  effects  of  an  accident  he  had 


* The  allusion  by  Sir  Alexander  Grant  to  Dr  Stevenson  was  in  the  follow- 
ing terms : — “ I regret  now  to  have  to  announce  the  retirement,  owing  to 
impaired  health,  of  Dr  Stevenson,  who  for  eleven  years  has  occupied  the  im- 
portant Chair  of  Divinity  and  Ecclesiastical  History.  During  that  time 
Professor  Stevenson  has  shown  himself  to  be  a man  of  real  learning;  he  has 
exhibited  that  quality  which  the  philosopher  Coleridge  used  to  value  highly, 
and  which  he  called  ‘ book-mindedness.’  In  an  age  distracted  by  a number 
of  ephemeral  interests,  and,  at  the  same  time  vaunting  itself  on  a Baconian 
adhesion  to  things  rather  than  to  words,  this  quality  of  * book-mindedness,’ 
the  characteristic  of  the  scholar  of  the  olden  times,  has  a tendency  to  become 
rare.  But,  for  the  interests  of  humanity,  it  is  necessary  that  there  should  be 
not  only  men  who  study  nature,  but  also  men  whose  life  is  spent  in  books — 
whose  minds  are  more  taken  up  with  the  past  than  the  present ; to  whom 
everything  suggests  an  association  with  some  great  writer,  and  who  thus 


319 


of  Edinburgh,  Session  1873-74. 

the  misfortune  to  receive  some  years  previously ; but,  enfeebled  as 
he  was,  he  spent  any  intervals  from  suffering  in  preparing  addi- 
tional notes  to  his  work  on  St  Kentigern  (which  had  been  very 
favourably  noticed),  in  the  event  of  an  edition  being  published 
after  his  demise.  [It  is  believed  that  this  edition  is  nearly  ready 
for  publication.] 

Till  within  a few  days  of  his  death  he  was  able  to  see  his  friends, 
and  at  last  died  peaceably  on  the  14th  of  June  1873,  in  the  68th 
year  of  his  age. 

Dr  Stevenson  was  twice  married,  and  left  issue  by  both  mar- 
riages. 

6.  Obituary  Notice  of  Auguste  De  la  Rive.  By  Professor 
George  Forbes. 

Auguste  De  la  Rive,  one  of  our  foreign  Honorary  Fellows,  was 
born  in  the  year  1801.  He  resided  principally  at  Geneva,  where 
for  a long  time  he  held  a professorial  chair.  He  made  journeys  in 
various  European  countries,  and  spent  a considerable  time  in  Eng- 
land and  Scotland.  After  a long  and  active  life,  he  was  struck 
down  by  paralysis.  A severe  attack  of  gout  added  to  his  infirmity. 
The  death  of  numbers  of  his  friends  and  relatives  deeply  affected 
him.  His  state  of  health  rendered  it  desirable  that  he  should 
winter  in  the  south  of  France  in  1873.  He  died  at  Marseilles  on 
the  27th  November  1873,  at  the  age  of  72  years.  His  faculties 
were  not  impaired  by  infirmities,  and  up  to  the  year  of  his 
death  he  continued  to  communicate  memoirs  to  the  Physical 
Society  of  Geneva. 

M.  De  la  Rive  was  chiefly  interested  in  the  study  of  electricity. 
In  the  Royal  Society  catalogue  we  find  106  articles,  chiefly  on  this 

serve  as  the  living  interpreters  of  libraries,  and  as  links  to  maintain  the 
hereditary  succession  of  thought.  Such  a man  as  this  is  our  friend  Professor 
Stevenson,  and  such  a character  as  his  is  the  appropriate  ornament  of  Univer- 
sities. He  has  ever  manifested  not  only  the  learning,  but  also  the  urbanity, 
of  the  true  scholar ; and  in  quitting  the  labours  of  the  class-room  and  the 
Senate-hall  to  seek  that  repose  which  has  now  become  necessary  to  him,  he 
will  not  leave  a single  enemy  behind.  He  will  take  with  him  into  privacy 
the  regrets  of  his  colleagues,  and  their  sincere  wishes  that  he  may  yet  enjoy 
many  years  of  happiness  and  peace.” 


320  Proceedings  of  the  Royal  Society 

subject,  written  by  himself,  besides  10  in  company  with  others. 
Since  the  date  of  that  catalogue  he  added  to  the  number.  The 
first  paper  of  importance  written  by  him  was  published  in  the  year 
1822,  and  contained  many  ingenious  and  important  experiments 
illustrative  of  the  discoveries  of  Oersted  and  Ampere.  His  interest 
in  chemistry  led  him  to  espouse  the  chemical  theory  of  the 
voltaic  current.  On  seven  different  occasions  he  supported  this 
view  in  various  scientific  journals.  His  researches  on  electro- 
chemical decomposition  were  in  part  the  basis  of  the  modern  art  of 
electro-plating.  He  made  several  experimental  inquiries  into  the 
heat  generated  by  the  passage  of  electricity  through  conductors; 
some  of  his  most  celebrated  and  original  experiments  had  reference 
to  the  action  of  magnetism  upon  the  electric  discharge.  These 
experiments  led  him  to  form  a theory  of  the  aurora,  on  which  sub- 
ject he  published  a series  of  articles  from  the  year  1848  to  the 
year  1862.  In  1862  he  illustrated  the  theory  by  a number  of 
beautiful  experiments  publicly  exhibited  at  Geneva.  At  various 
epochs  he  discussed  historically  the  progress  of  electrical  science. 

But  the  work  of  M.  De  la  Bive  was  not  confined  to  electricity. 
In  the  years  1838-39  he  discussed  the  phenomenon  of  sunset,  usually 
called  the  second  coloration  of  Mont  Blanc ; and  his  explanation 
is  now  generally  adopted.  He  made  experiments  on  specific  heats; 
and  his  communications  on  the  variations  of  terrestrial  magnetism, 
as  depending  upon  elevation  above  and  depression  below  the  sur- 
face of  the  soil,  are  of  considerable  value.  Some  of  his  latest 
researches  had  reference  to  Faraday’s  discovery  of  the  magneto- 
rotary effect  of  bodies  upon  plane-polarised  light.  He  was  a great 
friend  of  Faraday’s,  of  whose  life  he  wrote  an  interesting  review, 
published  in  the  “ Bibliotheque  Universelle.” 

Auguste  He  la  Bive  exerted  himself  to  spread  an  interest  in 
science  among  those  with  whom  he  came  in  contact.  His  genial 
manner  and  his  open  hospitality  gathered  round  him  a large  circle 
of  friends.  He  always  extended  a helping  hand  to  the  young  man 
of  science.  Many  could  bear  witness  to  this  trait  in  his  character ; 
and  it  was  well  illustrated  by  the  manner  in  which  he  welcomed 
Faraday,  and  discovered  his  talent,  at  a time  when  the  coldness  of 
Sir  Humphrey  Davy  would  have  led  many  to  neglect  him. 

Most  of  the  scientific  societies  of  Europe  bestowed  upon  M.  He 


321 


of  Edinburgh,  Session  1873-74.  . 

la  Rive  the  title  of  Honorary  Member.  The  Royal  Society  of 
London  elected  him  a Foreign  Member.  He  was  also  a Correspond- 
ing Member  of  the  Academy  of  Sciences  at  Paris. 


7.  Obituary  Notice  of  Dr  J.  Lindsay  Stewart.  By  Dr 
Cleghorn,  Stravithy. 

Dr  Stewart  was  a native  of  Kincardineshire,  and  obtained  his 
medical  education  in  Glasgow.  After  graduating  he  proceeded  in 
1856  to  the  Presidency  of  Bengal  as  assistant-surgeon ; he  was 
present  at  the  siege  of  Delhi  in  1857,  and  in  1858  he  joined  the 
expedition  to  the  Yuzufzai  country.  In  1860-61  he  officiated  for 
Dr  W.  Jameson  as  superintendent  of  the  Botanic  Garden,  Saharun- 
pore.  His  position  gave  him  an  excellent  opportunity  of  becoming 
acquainted  with  the  vegetation  of  the  Terai  and  North-West 
Himalaya,  and  afterwards  at  Bijnour  he  studied  the  Flora  of 
Rohilkund,  and  of  the  valleys  between  the  Ganges  and  Sardah. 
As  Conservator  of  the  Forests  of  the  Punjab  (1864),  his  duties 
took  him  to  all  parts  of  that  province,  and  also  to  Sindh,  Kashmir, 
and  the  inner  Himalayan  tracts  on  the  Upper  Indus,  Chenab,  and 
Sutlej  rivers,  which  adjoin  Turkistan  and  Tibet.  During  his  journeys, 
under  the  most  difficult  circumstances,  he  maintained  his  habit  of 
taking  copious  notes,  and  accumulated  an  immense  store  of  infor- 
mation regarding  the  plants  of  North-West  India.  The  results  of 
these  researches  are  embodied  in  numerous  papers  published  in  the 
Journals  of  the  Royal  Geographical  Society,  the  Asiatic  Society  of 
Bengal,  the  Agri-Horticultural  Society  of  India,  and  the  Transac- 
tions of  the  Botanical  Society  of  Edinburgh.  A most  interesting 
account  of  the  vegetation  of  the  extreme  north-west  corner  of  the 
Punjab  and  the  hills  beyond  it,  which  he  studied  during  the  Yuzufzai 
campaign,  is  contained  in  his  “Memoranda  on  the  Peshawur  Valley, 
chiefly  regarding  its  Flora”  (Journ.  As.  Soc.,  1863),  and  in  his 
“ Notes  on  the  Flora  of  Waziristan”  (Journ.  Boy.  Geo.  Soc.,  1863). 
In  the  “Journal  of  the  Agri-Horticultural  Society  of  India”  ap- 
peared “The  Sub-Sevalik  Tract,  with  special  reference  to  the  Bijnour 
Forest  and  its  Trees”  (vol.  xiii.  1865);  “Journal  of  a Botanising 
Tour  in  Hazara  and  Khagan”  (vol.  xiv.  1866);  and  “A  Tour  on 
the  Punjab  Salt  Range”  (vol.  i.  new  series,  1867).  His  last 


322 


Proceedings  of  the  Royal  Society 

communication,  “ Notes  of  a Botanical  Tour  in  Ladak  or  Western 
Tibet,”  appeared  in  the  “ Transactions  of  the  Botanical  Society  of 
Edinburgh”  (vol.  x.  1869).  In  1869,  after  twelve  years  of  un- 
remitting labour,  mental  and  bodily,  Dr  Stewart  returned  to 
England,  and  the  G-overnment  of  India  entrusted  him  with  the 
preparation  at  Kew  of  a Forest  Flora  of  Northern  and  Central 
India.  To  this  great  work  Dr  Stewart  devoted  a large  part  of  his 
furlough,  and  he  would  doubtless  have  completed  it  in  a satisfactory 
manner  if  his  health  had  not  given  way.  That  this  was  the  cause 
became  apparent  on  his  return  to  India,  when,  after  a few  months  of 
office  work,  sickness  obliged  him  to  move  from  Lahore  to  the  Hill 
Sanitarium  at  Dalhousie,  where  he  died  on  5th  July  1873,  aged 
forty-one. 


8.  Obituary  Notice  of  John  Hunter.  By  J.  T.  Bottomly, 
Esq.,  The  University,  Glasgow. 

Mr  John  Hunter  was  born  in  Belfast  on  the  23d  of  March  1843. 
He  was  the  only  son  of  the  late  Dr  Hunter  of  Belfast,  a gentleman 
who,  though  he  was  for  many  years  before  his  death  unable  to 
move,  was  highly  esteemed  as  a consulting  physician.  Mr  Hunter, 
till  he  entered  Queen’s  College,  Belfast,  received  his  education 
chiefly  at  home.  During  his  undergraduate  course  he  was  distin- 
guished in  nearly  every  branch  of  science  ; and  in  1863  he  obtained 
the  degree  of  B.A.  in  the  Queen’s  University,  with  first-class 
honours  in  Chemistry  and  Experimental  Physics.  With  similar 
distinction  he  took  the  degree  of  M.A.  the  following  year.  In  the 
interval  he  held  the  Senior  Scholarship  in  Chemistry  in  Belfast,  a 
scholarship  which  is  competed  for  annually  by  Bachelors  in  Arts 
of  the  Queen’s  University ; and  it  was  during  this  year  that  he 
published  his  first  paper  on  the  “ Absorption  of  Gases  by  Charcoal.” 
In  1865  he  became  assistant  to  Dr  Andrews,  the  Professor  of 
Chemistry  in  Queen’s  College,  Belfast,  an  office  which  he  held  till 
1870,  when  he  was  elected  Professor  of  Mathematics  and  Natural 
Philosophy  in  King’s  College,  Windsor,  Nova  Scotia.  At  Windsor 
his  health  suffered  severely  from  the  climate ; and,  feeling  unable 
to  encounter  a second  winter,  h$  resigned  his  professorship,  and 
returned  home  in  the  autumn  of  1871. 


323 


of  Edinburgh,  Session  1873-74. 

During  tbe  winter  of  that  year  lie  took  up  his  residence  at 
Enniscrone,  county  Mayo,  being  under  medical  advice  to  give  up 
active  work  for  some  months  at  least ; but  with  a strong  desire  to 
carry  on  bis  chemical  researches,  be  fitted  up  for  himself  a temporary 
laboratory  there ; and  be  was  actively  engaged  in  prosecuting  them 
at  the  time  of  bis  sudden  death,  on  the  13th  of  September  1872. 
His  death  was  occasioned  by  an  acute  disease  of  the  brain,  of  which 
he  seems  to  have  had  a slight  warning  some  months  previously; 
but  his  last  illness  wras  not  more  than  a few  hours  of  intense  pain. 

He  was  married  in  1869.  His  wife  survives  him  ; hut  he  left  no 
children. 

Mr  Hunter’s  researches  were  chiefly  concerned  with  tlfe  absorp- 
tion of  gases  by  charcoal.  He  examined  a large  number  of  char- 
coals, and  came  to  the  conclusion  that  the  greatest  absorptive 
power  is  possessed  by  the  dense  charcoal  of  the  shell  of  the 
cocoa-nut.  With  this  material  he  proceeded  to  examine  the  absorp- 
tion of  a very  large  number  of  gases  and  vapours  ; and  he  extended 
his  researches  to  the  absorption  of  mixed  vapours.  He  also  inves- 
tigated the  relation  between  absorption  and  temperature  in  the 
cases  of  ammonia  and  cyanogen,  and  showed  that,  while  raising 
the  temperature  at  which  the  charcoal  is  exposed  to,  the  gas 
decreases  the  absorption  in  both  cases;  the  rate  of  decrease  is  much 
greater  in  the  case  of  ammonia  than  in  the  case  of  cyanogen, 
between  0°  C.  and  55°  C. ; but  at  55°  C.  the  rate  of  decrease  in 
the  case  of  ammonia  suddenly  diminishes,  and  up  to  80°  0.  it  is 
not  very  much  greater  than  the  rate  of  decrease  for  cyanogen.  At  a 
point  a little  higher  than  55°  the  volumes  absorbed  are  the  same  for 
the  two  gases.  Above  this  point  more  of  cyanogen  gas  is  absorbed 
by  a given  weight  of  charcoal  than  of  ammonia;  but  below  that 
point  ammonia  is  enormously  more  absorbed  than  cyanogen.  Mr 
Hunter  was  extending  his  observations  to  the  effect  of  pressure  on 
absorption.  He  had  already  published  two  papers  on  the  subject. 
The  last  of  these  was  communicated  to  the  Chemical  Society  of 
London  only  a few  weeks  before  his  death ; and  it  is  in  fact 
scarcely  complete,  through  wanting  his  final  corrections  in  type 
on  it. 

Mr  Hunter  accompanied  the  Deep  Sea  Dredging  Expedition  in 
H.M.S.  “Porcupine”  in  the  autumn  of  1869,  and  published  two 

2 T 


VOL.  VIII. 


324  Proceedings  of  the  Royal  Society 

important  papers  “On  tlie  composition  of  Sea- water  collected  at  dif- 
ferent depths  of  the  Atlantic,  from  a few  feet  below  the  surface  up 
to  2090  fathoms,”  and  “ On  the  Composition  of  the  Atlantic  Ooze.” 
These  analyses  included  also  analysis  of  the  absorbed  gases  of  the 
water.  His  papers  are  all  published  in  the  “Journal  of  the 
Chemical  Society.” 

He  was  genial,  warm-hearted,  affectionate,  a universal  favourite 
with  those  who  knew  him,  enthusiastically  devoted  to  science, 
and  withal  highly  cultivated  in  literature  and  the  arts.  His  pre- 
mature death,  at  a time  when  a life  of  usefulness  seemed  to  have 
just  commenced,  is  deeply  regretted. 


The  following  statement  respecting  the  Fellows  of  the 
Society  was  submitted  : — 

I.  Honorary  Fellows — 


Royal  Personage,  .....  1 

British  Subjects, 17 

Foreign, 32 


Total  Honorary  Fellows,  . . 50 

II.  Non-resident  Member  under  the  Old  Laws,  . . 1 

III.  Ordinary  Fellows — 

Ordinary  Fellows  at  November  1872,  . . . 343 

New  Fellows — William  Boyd,  Esq. ; Donald  Craw- 
ford, Esq. ; Dr  John  Gr.  M‘Kendrick ; M.  M. 

Pattison  Muir,  Esq.;  Dr  J.  Bell  Pettigrew; 

Andrew  Pritchard,  Esq. ; Walter  Stewart, 

Esq. ; Robert  Tennent,  Esq. ; Robert  Walker, 

Esq.;  Dr  Morrison  Watson ; Robert  Wilson, 

Esq. ; Major  Welsh, 12 

W.  Dittmar,  Esq.,  reinstated,  ....  1 

356 


Carried  forward, 


356 


o f Edinburgh , Session  1873-74.  325 

Brought  forward,  356 

Deduct  Deceased — Rev.  Dr  Guthrie;  Prof.  John 
Hunter;  Very  Rev.  Dean  Ramsay;  Prof. 
Macquorn  Rankine  ; Arch.  Smith,  Esq.  ; 

Rev.  Prof.  Stevenson  ; Dr  J.  L.  Stewart ; R. 


W.  Thomson,  Esq.,  .....  8 

Resigned — J.  E.  M’Lennan,  Esq. ; Dr  Alex.  Wood,  2 

Cancelled — Dr  Richardson,  Dr  Foulerton,  . . 2 

12 

Total  number  of  Ordinary  Fellows  at  Nov.  1873,  . 344 


The  following  Communications  were  read 

9.  The  Kinetic  Theory  of  the  Dissipation  of  Energy.  By 
Sir  William  Thomson. 

In  abstract  dynamics  the  instantaneous  reversal  of  the  motion 
of  every  moving  particle  of  a system  causes  the  system  to  move 
backwards,  each  particle  of  it  along  its  old  path,  and  at  the  same 
speed  as  before,  when  again  in  the  same  position.  That  is  to  say, 
in  mathematical  language,  any  solution  remains  a solution  when 
t is  changed  into  - 1.  In  physical  dynamics  this  simple  and  perfect 
reversibility  fails,  on  account  of  forces  depending  on  friction  of 
solids  ; imperfect  fluidity  of  fluids ; imperfect  elasticity  of  solids  ; 
inequalities  of  temperature,  and  consequent  conduction  of  heat 
produced  by  stresses  in  solids  and  fluids;  imperfect  magnetic 
retentiveness;  residual  electric  polarisation  of  dielectrics;  genera- 
tion of  heat  by  electric  currents  induced  by  motion ; diffusion  of 
fluids,  solution  of  solids  in  fluids,  and  other  chemical  changes ; 
and  absorption  of  radiant  heat  and  light.  Consideration  of  these 
agencies  in  connection  with  the  all-pervading  law  of  the  conserva- 
tion of  energy  proved  for  them  by  Joule,  led  me  twenty-three  years 
ago  to  the  theory  of  the  dissipation  of  energy,  which  I communi- 
cated first  to  the  Royal  Society  of  Edinburgh  in  1852,  in  a paper 
entitled  “On  a Universal  Tendency  in  Nature  to  the  Dissipation 
of  Mechanical  Energy.” 

The  essence  of  Joule’s  discovery  is  the  subjection  of  physical 
phenomena  to  dynamical  law.  If,  then,  the  motion  of  every  par- 


326  Proceedings  of  the  Poyal  Society 

tide  of  matter  in  tlie  universe  were  precisely  reversed  at  any 
instant,  the  course  of  nature  would  be  simply  reversed  for  ever 
after.  The  bursting  bubble  of  foam  at  the  foot  of  a waterfall 
would  reunite  and  descend  into  the  water ; the  thermal  motions 
would  reconcentrate  their  energy,  and  throw  the  mass  up  the  fall 
in  drops  re-forming  into  a close  column  of  ascending  water.  Heat 
which  had  been  generated  by  the  friction  of  solids  and  dissipated  by 
conduction,  and  radiation  with  absorption,  would  come  again  to  the 
place  of  contact,  and  throw  the  moving  body  back  against  the  force  to 
which  it  had  previously  yielded.  Boulders  would  recover  from  the 
mud  the  materials  required  to  rebuild  them  into  their  previous 
jagged  forms,  and  would  become  reunited  to  the  mountain  peak 
from  which  they  had  formerly  broken  away.  And  if  also  the 
materialistic  hypothesis  of  life  were  true,  living  creatures  would 
grow  backwards,  with  conscious  knowledge  of  the  future,  but  no 
memory  of  the  past,  and  would  become  again  unborn.  But  the 
real  phenomena  of  life  infinitely  transcend  human  science,  and 
speculation  regarding  consequences  of  their  imagined  reversal  is 
utterly  unprofitable.  Far  otherwise,  however,  is  it  in  respect  to 
the  reversal  of  the  motions  of  matter  uninfluenced  by  life,  a very 
elementary  consideration  of  which  leads  to  the  full  explanation  of 
the  theory  of  dissipation  of  energy. 

To  take  one  of  the  simplest  cases  of  the  dissipation  of  energy, 
the  conduction  of  heat  through  a solid- — consider  a bar  of  metal 
warmer  at  one  end  than  the  other,  and  left  to  itself.  To  avoid  all 
needless  complication,  of  taking  loss  or  gain  of  heat  into  account, 
imagine  the  bar  to  be  varnished  with  a substance  impermeable  to 
heat.  For  the  sake  of  definiteness,  imagine  the  bar  to  be  first 
given  with  one-half  of  it  at  one  uniform  temperature,  and  the  other 
half  of  it  at  another  uniform  temperature.  Instantly  a diffusing 
of  heat  commences,  and  the  distribution  of  temperature  becomes 
continuously  less  and  less  unequal,  tending  to  perfect  uniformity, 
but  never  in  any  finite  time  attaining  perfectly  to  this  ultimate 
condition.  This  process  of  diffusion  could  be  perfectly  prevented 
by  an  army  of  Maxwell’s  “ intelligent  demons,”  * stationed  at  the 

* The  definition  of  a demon,  according  to  the  use  of  this  word  by 
Maxwell,  is  an  intelligent  being  endowed  with  free-will  and  fine  enough 
tactile  and  perceptive  organisation  to  give  him. the  faculty  of  observing  and 
influencing  individual  molecules  of  matter. 


327 


of  Edinburgh,  Session  1873-74. 

surface,  or  interface  as  we  may  call  it  with  Professor  James 
Thomson,  separating  the  hot  from  the  cold  part  of  the  bar.  To 
see  precisely  how  this  is  to  he  done,  consider  rather  a gas  than  a 
solid,  because  we  have  much  knowledge  regarding  the  molecular 
motions  of  a gas,  and  little  or  no  knowledge  of  the  molecular 
motions  of  a solid.  Take  a jar  with  the  lower  half  occupied  by 
cold  air  or  gas,  and  the  upper  half  occupied  with  air  or  gas  of  the 
same  kind,  but  at  a higher  temperature,  and  let  the  mouth  of  the 
jar  be  closed  by  an  air-tight  lid.  If  the  containing  vessel  were 
perfectly  impermeable  to  heat,  the  diffusion  of  heat  would  follow  the 
same  law  in  the  gas  as  in  the  solid,  though  in  the  gas  the  diffusion 
of  heat  takes  place  chiefly  by  the  diffusion  of  molecules,  each 
taking  its  energy  with  it,  and  only  to  a small  proportion  of  its 
whole  amount,  by  the  interchange  of  energy  between  molecule  and 
molecule;  whereas  in  the  solid  there  is  little  or  no  diffusion  of 
substance,  and  the  diffusion  of  heat  takes  place  entirely,  or  almost 
entirely,  through  the  communication  of  energy  from  one  molecule 
to  another.  Fourier’s  exquisite  mathematical  analysis  expresses 
perfectly  the  statistics  of  the  process  of  diffusion  in  each  case, 
whether  it  be  “conduction  of  heat,”  as  Fourier  and  his  followers 
have  called  it,  or  the  diffusion  of  substance  in  fluid  masses  (gaseous 
or  liquid),  which  Fick  showed  to  be  subject  to  Fourier’s  for- 
mulas. Now,  suppose  the  weapon  of  the  ideal  army  to  be  a club, 
or,  as  it  were,  a molecular  cricket  bat;  and  suppose,  for  convenience, 
the  mass  of  each  demon  with  his  weapon  to  be  several  times 
greater  than  that  of  a molecule.  Every  time  he  strikes  a molecule 
he  is  to  send  it  away  with  the  same  energy  as  it  had  immediately 
before.  Each  demon  is  to  keep  as  nearly  as  possible  to  a certain 
station,  making  only  such  excursions  from  it  as  the  execution  of 
his  orders  requires.  He  is  to  experience  no  forces  except  such  as 
result  from  collisions  with  molecules,  and  mutual  forces  between 
parts  of  his  own  mass,  including  his  weapon.  Thus  his  voluntary 
movements  cannot  influence  the  position  of  his  centre  of  gravity, 
otherwise  than  by  producing  collision  with  molecules. 

The  whole  interface  between  hot  and  cold  is  to  be  divided  into 
small  areas,  each  allotted  to  a single  demon.  The  duty  of  each 
demon  is  to  guard  his  allotment,  turning  molecules  back,  or  allow- 
ing them  to  pass  through  from  either  side,  according  to  certain 


328  Proceedings  of  the  Royal  Society 

definite  orders.  First,  let  the  orders  be  to  allow  no  molecules  to 
pass  from  either  side.  The  effect  will  be  the  same  as  if  the  inter- 
face were  stopped  by  a barrier  impermeable  to  matter  and  to  heat. 
The  pressure  of  the  gas  being,  by  hypothesis,  equal  in  the  hot  and 
cold  parts,  the  resultant  momentum  taken  by  each  demon  from  any 
considerable  number  of  molecules  will  be  zero ; and  therefore  he 
may  so  time  his  strokes  that  he  shall  never  move  to  any  consider- 
able distance  from  his  station.  Now,  instead  of  stopping  and  turn- 
ing all  the  molecules  from  crossing  his  allotted  area,  let  each  demon 
permit  a hundred  molecules  chosen  arbitrarily  to  cross  it  from  the 
hot  side;  and  the  same  number  of  molecules,  chosen  so  as  to  have 
the  same  entire  amount  of  energy  and  the  same  resultant  momen- 
tum, to  cross  the  other  way  from  the  cold  side.  Let  this  be  done 
over  and  over  again  within  certain  small  equal  consecutive  inter- 
vals of  time,  with  care  that  if  the  specified  balance  of  energy  and 
momentum  is  not  exactly  fulfilled  in  respect  to  each  successive 
hundred  molecules  crossing  each  way,  the  error  will  be  carried 
forward,  and  as  nearly  as  may  be  corrected,  in  respect  to  the  next 
hundred.  Thus,  a certain  perfectly  regular  diffusion  of  the  gas 
both  ways  across  the  interface  goes  on,  while  the  original  different 
temperatures  on  the  two  sides  of  the  interface  are  maintained  with- 
out change. 

Suppose,  now,  that  in  the  original  condition  the  temperature  and 
pressure  of  the  gas  are  each  equal  throughout  the  vessel,  and  let  it 
be  required  to  disequalise  the  temperature,  but  to  leave  the  pressure 
the  same  in  any  two  portions  A and  B of  the  whole  space.  Station 
the  army  on  the  interface  as  previously  described.  Let  the  orders 
now  be  that  each  demon  is  to  stop  all  molecules  from  crossing  his 
area  in  either  direction  except  100  coming  from  A,  arbitrarily 
chosen  to  be  let  pass  into  B,  and  a greater  number,  having  among 
them  less  energy  but  equal  momentum,  to  cross  from  B to  A.  Let 
this  be  repeated  over  and  over  again.  The  temperature  in  A will 
be  continually  diminished  and  the  number  of  molecules  in  it  con- 
tinually increased,  until  there  are  not  in  B enough  of  molecules 
with  small  enough  velocities  to  fulfil  the  condition  with  reference 
to  permission  to  pass  from  B to  A.  If  after  that  no  molecule  be 
allowed  to  pass  the  interface  in  either  direction,  the  final  con- 
dition will  be  very  great  condensation  and  very  low  temperature  in 


329 


of  Edinburgh,  Session  1873-74. 

A ; rarefaction  and  very  high  temperature  in  B ; and  equal  tem- 
perature in  A and  B.  The  process  of  disequalisation  of  tempera- 
ture and  density  might  be  stopped  at  any  time  by  changing  the 
orders  to  those  previously  specified  (2),  and  so  permitting  a certain 
degree  of  diffusion  each  way  across  the  interface  while  maintaining 
a certain  uniform  difference  of  temperatures  with  equality  of  pres- 
sure on  the  two  sides. 

If  no  selective  influence,  such  as  that  of  the  ideal  “ demon,” 
guides  individual  molecules,  the  average  result  of  their  free 
motions  and  collisions  must  be  to  equalise  the  distribution  of 
energy  among  them  in  the  gross;  and  after  a sufficiently  long 
time,  from  the  supposed  initial  arrangement,  the  difference  of 
energy  in  any  two  equal  volumes,  each  containing  a very  great 
number  of  molecules,  must  bear  a very  small  proportion  to  the 
whole  amount  in  either;  or,  more  strictly  speaking,  the  probability 
of  the  difference  of  energy  exceeding  any  stated  finite  pro- 
portion of  the  whole  energy  in  either  is  very  small.  Suppose 
now  the  temperature  to  have  become  thus  very  approximately 
equalised  at  a certain  time  from  the  beginning,  and  let  the  motion 
of  every  particle  become  instantaneously  reversed.  Each  molecule 
will  retrace  its  former  path,  and  at  the  end  of  a second  interval  of 
time,  equal  to  the  former,  every  molecule  will  be  in  the  same 
position,  and  moving  with  the  same  velocity,  as  at  the  beginning ; 
so  that  the  given  initial  unequal  distribution  of  temperature  will 
again  be  found,  with  only  the  difference  that  each  particle  is 
moving  in  the  direction  reverse  to  that  of  its  initial  motion.  This 
difference  will  not  prevent  an  instantaneous  subsequent  commence- 
ment of  equalisation,  which,  with  entirely  different  paths  for  the 
individual  molecules,  will  go  on  in  the  average  according  to  the 
same  law  as  that  which  took  place  immediately  after  the  system 
was  first  left  to  itself. 

By  merely  looking  on  crowds  of  molecules,  and  reckoning  their 
energy  in  the  gross,  we  could  not  discover  that  in  the  very  special 
case  we  have  just  considered  the  progress  was  towards  a succession 
of  states,  in  which  the  distribution  of  energy  deviates  more  and 
more  from  uniformity  up  to  a certain  time.  The  number  of  mole- 
cules being  finite,  it  is  clear  that  small  finite  deviations  from 
absolute  precision  in  the  reversal  we  have  supposed  would  not 


330 


Proceedings  of  the  Royal  Society 

obviate  the  resulting  disequalisation  of  the  distribution  of  energy. 
But  the  greater  the  number  of  molecules,  the  shorter  will  be  the 
time  during  which  the  disequalising  will  continue ; and  it  is  only 
when  we  regard  the  number  of  molecules  as  practically  infinite 
that  we  can  regard  spontaneous  disequalisation  as  practically  im- 
possible. And,  in  point  of  fact,  if  any  finite  number  of  perfectly 
elastic  molecules,  however  great,  be  given  in  motion  in  the  interior 
of  a perfectly  rigid  vessel,  and  be  left  for  a sufficiently  long  time 
undisturbed  except  by  mutual  impact  and  collisions  against  the 
sides  of  the  containing  vessel,  it  must  happen  over  and  over  again 
that  (for  example)  something  more  than  x9xths  of  the  whole  energy 
shall  be  in  one-half  of  the  vessel,  and  less  than  xVth  of  the  whole 
energy  in  the  other  half.  But  if  the  number  of  molecules  be  very 
great,  this  will  happen  enormously  less  frequently  than  that  some- 
thing more  than  x6oths  shall  be  in  one-half,  and  something  less 
than  x4xths  in  the  other.  Taking  as  unit  of  time  -the  average 
interval  of  free  motion  between  consecutive  collisions,  it  is  easily 
seen  that  the  probability  of  there  being  something  more  than  any 
stated  percentage  of  excess  above  the  half  of  the  energy  in 
one-half  of  the  vessel  during  the  unit  of  time,  from  a stated 
instant,  is  smaller  the  greater  the  dimensions  of  the  vessel  and 
the  greater  the  stated  percentage.  It  is  a strange  but  never- 
theless a true  conception  of  the  old  well-known  law  of  the  con- 
duction of  heat,  to  say  that  it  is  very  improbable  that  in  the  course 
of  1000  years  one-half  of  the  bar  of  iron  shall  of  itself  become 
warmer  by  a degree  than  the  other  half;  and  that  the  probability 
of  this  happening  before  1,000,000  years  pass  is  1000  times  as 
great  as  that  it  will  happen  in  the  course  of  1000  years,  and  that 
it  certainly  will  happen  in  the  course  of  some  very  long  time. 
But  let  it  be  remembered  that  we  have  supposed  the  bar  to  be 
covered  with  an  impermeable  varnish.  Do  away  with  this  impos- 
sible ideal,  and  believe  the  number  of  molecules  in  the  universe 
to  be  infinite;  then  we  may  say  one-half  of  the  bar  will  never 
become  warmer  than  the  other,  except  by  the  agency  of  external 
sources  of  heat  or  cold.  This  one  instance  suffices  to  explain  the 
philosophy  of  the  foundation  on  which  the  theory  of  the  dissipa- 
tion of  energy  rests. 

Take  however  another  case,  in  which  the  probability  may  be 


331 


of  Edinburgh,  Session  1873-74. 

readily  calculated.  Let  a hermetically  sealed  glass  jar  of  air  con- 
tain 2,000,000,000,000  molecules  of  oxygen,  and  8,000,000,000,000 
molecules  of  nitrogen.  If  examined  any  time  in  the  infinitely 
distant  future,  what  is  the  number  of  chances  against  one  that 
all  the  molecules  of  oxygen  and  none  of  nitrogen  shall  be  found 
in  one  stated  part  of  the  vessel  equal  in  volume  to  |th  of  the 
whole?  The  number  expressing  the  answer  in  the  Arabic  notation 
has  about  2,173,220,000,000  of  places  of  whole  numbers.  On  the 
other  hand,  the  chance  against  their  being  exactly  -^ths  of  the 
whole  number  of  particles  of  nitrogen,  and  at  the  same  time 
exactly  T%ths  of  the  whole  number  of  particles  of  oxygen  in  the 
first  specified  part  of  the  vessel,  is  only  4021  x 109  to  1. 


APPENDIX. 

Calculation  of  'probability  respecting  Diffusion  of  Oases. 

For  simplicity,  I suppose  the  sphere  of  action  of  each  molecule 
to  be  infinitely  small  in  comparison  with  its  average  distance  from 
its  nearest  neighbour ; thus,  the  sum  of  the  volumes  of  the  spheres 
of  action  of  all  the  molecules  will  be  infinitely  small  in  proportion 
to  the  whole  volume  of  the  containing  vessel.  For  brevity,  space 
external  to  the  sphere  of  action  of  every  molecule  will  be  called 
free  space : and  a molecule  will  be  said  to  be  in  free  space  at 
any  time  when  its  sphere  of  action  is  wholly  in  free  space ; 
that  is  to  say,  when  its  sphere  of  action  does  not  overlap  the 
sphere  of  action  of  any  other  molecule.  Let  A,  B,  denote  any 
two  particular  portions  of  the  whole  containing  vessel,  and  let 
a , b , be  the  volumes  of  those  portions.  The  chance  that  at 
any  instant  one  individual  molecule  of  whichever  gas  shall  be 

in  A is  — qLj , however  many  or  few  other  molecules  there  may  be 

in  A at  the  same  time;  because  its  chances  of  being  in  any  speci- 
fied portions  of  free  space  are  proportional  to  their  volumes ; and, 
according  to  our  supposition,  even  if  all  the  other  molecules  were 
in  A,  the  volume  of  free  space  in  it  would  not  be  sensibly  diminished 
by  their  presence.  The  chance  that  of  n molecules  in  the  whole 

2 u 


VOL.  VIII. 


332 


Proceedings  of  the  Royal  Society 

space  there  shall  be  i stated  individuals  in  A,  and  that  the  other 
n — i molecules  shall  be  at  the  same  time  in  B,  is 

/ a V / b V“ i aibn~'i 
\a  + b)  \a  + b)  ’ ° (a  + b)n  ' 

Hence  the  probability  of  the  number  of  molecules  in  A being 
exactly  i,  and  in  B exactly  n-i,  irrespectively  of  individuals,  is  a 
fraction  having  for  denominator  (a  + by,  and  for  numerator  the  term 
involving  a1  bn~{  in  the  expansion  of  this  binomial ; that  is  to  say, 
it  is — 

n(ii- 1)  . . . . {n-i  + 1)  / a V / b \n_i 
1.2  ....  i -f-  b)  \<x  -f - b) 

If  we  call  this  , we  have 


T 


i + l 


71  — 'Id  m 

i+l  b ■ 


Hence  is  the  greatest  term  if  i is  the  smallest  integer,  which 
makes 

n-i  b 
i + 1 < a ’ 

this  is  to  say,  if  i is  the  smallest  integer  which  exceeds 

a b 

n . 

a+b  a+b 

Hence  if  a and  b are  commensurable,  the  greatest  term  is  that  for 
which 


n 


a 

a + b 


To  apply  these  results  to  the  cases  considered  in  the  preceding 
article,  put  in  the  first  place 

n = 2 x 1012, 

this  being  the  number  of  particles  of  oxygen ; and  let  i — n. 
Thus,  for  the  probability  that  all  the  particles  of  oxygen  shall  be 
in  A,  we  find 

/ a \8xl0» 


+ b, 


333 


of  Edinburgh,  Session  1873-74. 

Similarly,  for  the  probability  that  all  the  particles  of  nitrogen  are 
in  the  space  JB,  we  find 

/ 6 \2x  1012 

UTb) 

Hence  the  probability  that  all  the  oxygen  is  in  A and  all  the 
nitrogen  in  B is 

/ a \2  x 1012  / b \8  x 1012 

\a  + b)  \a  + b) 


Now  by  hypothesis 


and  therefore 


a 2 

cTT~b = 10’ 

= . 
a + b 10  ’ 


hence  the  required  probability  is 

026  x 1012 


10 


iou 


Call  this  — , and  let  log  denote  common  logarithm. 


We  have 


log  N = 1013  - 26  x 1012  x log  2 = (10 -26  log  2)  x 1012=  2173220 
x 106.  This  is  equivalent  to  the  result  stated  in  the  text  above. 
The  logarithm  of  so  great  a number,  unless  given  to  more  than 
thirteen  significant  places,  cannot  indicate  more  than  the  number  of 
places  of  whole  numbers  in  answer  to  the  proposed  question,  ex- 
pressed according  to  the  Arabic  notation. 

The  calculation  of  T4 , when  i and  n-i  are  very  large  numbers, 
is  practicable  by  Stirling’s  theorem,  according  to  wThioh  we  have 
approximately 


1.2.  • 


‘A, 


and  therefore 


n(n  — 1)  . . . . bn  — % + 1)  nn  + i 

1.2  ....  i J27rii+*(n-i)n~i  + lt 


334 


Proceedings  of  the  Royal  Society 


Hence  for  the  case 


i — n 


a 

V 


which,  according  to  the  preceding  formulas,  gives  T,  its  greatest 
value,  we  have 

T.=—  1 . ; 

sJZirnef 


where 


e 


a 

a + b 


and  / = 


b 

a -j-  b 


Thus,  for  example,  let  n = 2 x 1012 ; 


e=  '2,  / = -8, 

we  have 

T = 1 _ 1 

1 800000  Jtt  1418000  * 

This  expresses  the  chance  of  there  being  4 x 1011  molecules  of 
oxygen  in  A,  and  16  x 1011  in  B.  Just  half  this  fraction  expresses 
the  probability  that  the  molecules  of  nitrogen  are  distributed  in 
exactly  the  same  proportion  between  A and  B,  because  the  number 
of  molecules  of  nitrogen  is  four  times  greater  than  of  oxygen. 

If  n denote  the  molecules  of  one  gas,  and  n that  of  the  mole- 
cules of  another,  the  probability  that  each  shall  he  distributed 
between  A and  B in  the  exact  proportion  of  the  volume,  is 

_\_1 

2 rref  Jnn 

The  value  for  the  supposed  case  of  oxygen  and  nitrogen  is 

1 _ 1 
27rx*16x  -4xl012  4021  X l0®  ’ 


which  is  the  result  stated  at  the  conclusion  of  the  text  above. 


of  Edinburgh,  Session  1873-74. 


335 


10.  On  the  Stresses  due  to  Compound  Strains.  By  Prof.  C. 
Niven.  Communicated  by  Prof.  Tait. 

{Abstract) 

In  the  treatment  of  questions  which  relate  to  the  equilibrium 
vibrations  of  elastic  solids,  it  is  usual  to  suppose  the  substance  to 
start  from  a state  without  strain,  and  in  general  to  consider  only 
the  case  of  small  distortions,  for  which  squares  and  products  of  the 
space-variations  of  displacement  may  be  neglected.  The  mathe- 
matical solution  depends,  in  the  first  instance,  on  the  expression 
of  the  work  done  in  distorting  an  element.  This,  as  was  first  done 
by  Green,  is  expressed  in  terms  of  six  functions  of  the  distortions, 
termed  strains.  The  part  of  the  potential  function  which  is  of  the 
second  degree  contains  21  coefficients,  reducible  to  18  by  a proper 
choice  of  axes.  But  in  the  present  state  of  our  knowledge  of  the 
constitution  of  seolotropic  substances,  it  is  in  general  impossible  to 
effect  a further  reduction,  and  it  is  probable  that  the  function  will 
have  different  forms  according  to  the  previous  history  of  the 
substance. 

The  case  in  which  the  eeolotropy  has  been  produced  by  the  action 
of  considerable  stress  has  formed  the  subject  of  investigations  by 
Cauchy,  St  Yenant,  and  others.  Cauchy’s  results  were  based 
directly  on  the  consideration  of  molecular  attractions;  and  though 
the  other  authors  have  employed  Green’s  theory  of  the  potential 
energy,  they  have  still  made  use  of  molecules  to  find  its  form. 

In  the  present  paper  the  author  has  sought  to  base  the  treatment 
of  the  subject  on  the  law  of  superposition  of  one  set  of  strains  on 
another.  If  these  states  of  strain  be  called  respectively  primary 
and  secondary,  it  is  shown  that  the  total  strains  differ  from  the 
primary  by  linear  functions  of  the  secondary,  and  this  whether  the 
latter  be  small  or  large.  The  true  form  of  the  potential  in  terms 
of  the  secondary  strains  is  thereafter  readily  found.  It  agrees  so 
far  with  the  result  of  M.  Boussinesq,  and  furnishes  expressions  for 
the  stresses  agreeing  to  a certain  extent  with  those  originally  given 
by  Cauchy. 

There  is  one  part  of  the  potential  energy  due  to  the  secondary 
strains  which  has  not  hitherto  been  discussed.  It  consists  of  terms 


336  Proceedings  of  the  Royal  Society 

due  to  parts  in  the  primary  potential,  which  are  respectively  of  the 
degrees  2,  3,  4 . . . in  the  strains.  The  first  of  these  has  been 
completely  investigated  in  the  present  paper,  and  the  potential  is 
shown  to  depend  on  two  invariants  which  are  functions  of  the 
secondary  strains,  and  of  six  quantities  called  the  primary  quasi- 
strains. In  fact,  borrowing  a term  from  the  theory  of  reciprocal 
surfaces,  we  may  say  shortly  that  the  part  of  the  potential  energy 

under  consideration  is  + n J2^  , where  is  the  invariant 

of  the  first  order  of  the  secondary  strains  and  primary  quasi-strains, 
and  - J2  is  the  corresponding  invariant  for  the  reciprocals  of  these 
systems. 

It  is  also  shown  in  the  present  paper  that  these  quasi-strains 
play  an  important  part  in  the  elasticity  of  isotropic  solids ; for 
besides  the  above  result,  it  appears  that,  with  the  limitation  of  the 
potential  already  mentioned,  the  products  of  the  stresses  into  the 
strained  element-volume  are  directly  expressible  in  terms  of  them, 
and  that  the  principal  axes  of  stress  coincide  with  those  of  quasi- 
strains. The  present  paper  also  contains  the  equations  which 
express  the  small  motions  of  a strained  solid,  with  the  view  of 
testing  whether  they  present  any  analogy  with  the  luminous 
waves.  The  results  are  negative,  as  was  to  be  expected,  there 
being  in  glass  three  real  waves  for  every  direction  of  the  wave- 
front,  and  the  wave  surface  being  of  the  sixth  class.  In  the  case 
where  the  primary  stress  is  symmetrical  round  an  axis,  an  ellipsoid 
of  revolution  detaches  itself  from  the  general  surface. 

Among  other  subsidiary  results  of  this  paper  may  be  mentioned 
the  derivation  (from  the  law  of  superposition  of  strains)  of  the 
symbolical  expressions  for  the  stresses  in  terms  of  the  strain- 
variations  of  the  potential  energy  (already  found  in  another  shape 
by  M.  Boussinesq),  and  the  symbolized  solution  of  the  converse 
problem. 

The  law  of  resolution  of  strains  and  quasi-strains  has  been  shown 
to  be  identical  with  that  of  stresses  and  with  various  other  mathe- 
matical magnitudes,  among  which  may  be  mentioned  the  system 
consisting  of  the  moments  and  negative  products  of  inertia  of  a 
solid  body.  A general  view  of  this  law  of  resolution  of  stresses  is 
given  and  coupled  with  a parallel  view  of  forces,  along  with  a 


of  Edinburgh,  Session  1873-74.  337 

general  method  of  deducing  the  corresponding  invariants  and  the 
derived  stress-  and  force-functions.  It  enables  us  to  see  at  a glance 
the  meaning  of  the  form  found  for  the  potential  energy  in  the 
secondary  strain.  The  author  may  he  allowed  to  add,  that  these 
methods  have  been  since  developed  with  the  view  of  applying  them 
to  the  problem  of  the  elasticity  of  crystals,  and  that  the  results 
obtained,  though  dual  in  form,  exhibit  a striking  coincidence  with 
these  now  given. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  viii.  1873-74.  No.  89. 


Ninety-First  Session. 

Monday,  2d  March  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Communications  were  read : — 

1.  On  the  Parallel  Roads  of  Glen  Roy.  By  the 
Rev.  Thomas  Brown,  F.R.S.E. 

( Abstract .) 

After  describing  the  general  appearance  of  these  terraces,  the 
author  referred  to  the  discussions  which  had  taken  place  as  to 
their  formation.  More  than  fifty  years  ago  it  was  conclusively 
proved  by  Dr  Macculloch*  and  Sir  Thomas  Dick  Lauder, f that 
these  parallel  roads  are  the  margins  of  ancient  lakes,  and  since 
then  the  question  has  been  whether  these  were  freshwater  or  sea 
lochs.  Mr  Darwin,  Dr  Robert  Chambers,  Professor  Nichol,  and 
others,  have  contended  that  they  were  marine ; while  Agassiz,  Dr 
Milne  Home,  Mr  Jamieson,  and  others,  have  maintained  that  they 
were  freshwater. 

As  the  problem  is  confessedly  one  of  some  difficulty,  it  seemed 
desirable  to  obtain,  if  possible,  the  evidence  of  fossils.  It  has  been 
ascertained,  indeed,  that  the  deposits  contain  no  shells  nor  similar 
remains,  and  Mr  Darwin  has  suggested  that  they  may  have  been 
destroyed  by  the  carbonic  acid  gas  absorbed  by  the  rain-water  which 
for  ages  has  percolated  through  the  beds.  This,  however,  could  not 
have  taken  place  with  the  valves  of  diatoms,  which  are  siliceous,  and 

* Geol.  Trans  , ser.  1,  vol.  iv.  f -Edin.  Roy.  Soc.  Trans.,  vol.  ix. 

2 X 


VOL.  VIII. 


340 


Proceedings  of  the  Royal  Society 


on  which,  therefore,  carbonic  acid  could  produce  no  effect.  They 
have  this  further  advantage,  that  the  marine  and  freshwater  species 
each  keep  to  their  own  distinct  localities,  and  if  any  such  fossils, 
therefore,  could  be  found  in  the  parallel  roads,  they  might  give 
important  assistance  in  deciding  between  the  marine  and  fresh- 
water theories. 

Accordingly,  in  the  autumn  of  1872,  and  again  in  1873,  an 
attempt  was  made  to  obtain  fossil  diatoms  from  these  deposits.  It 
was  found  that  in  Grlen  Roy  there  were  a good  many  points  where 
the  parallel  roads  were  cut  through  and  laid  open.  Four  of  these 


8 in.  to  1 foot. 

2 to  3 feet. 

3 in.  to  8 in. 

about  20  feet  going 
down  to  the  rock. 

sections  were  examined  with  some  care,  and  one  was  especially 
fixed  on  lying  high  and  dry  on  the  hill  side,  where  the  internal 
structure  of  the  lowest  terrace  was  distinctly  shown.  The  object 
was  to  obtain  specimens  of  diatoms  which  may  have  been  alive 
when  the  terraces  were  formed,  and  which  were  then  included  in 
the  deposits;  but  to  secure  this,  various  precautions  were  necessary. 
The  nature  of  the  different  beds  composing  these  terraces  will  be 

* It  may  be  a question  whether  this  bed  d really  belongs  to  the  time  of 
the  lowest  shelf,  or  whether  it  is  not  some  anterior  formation — the  sloping 
bottom  of  the  lake,  perhaps,  at  some  earlier  time. 


a,  Humus — peaty, 

b,  Stones  with  clay, 

c,  Finely  stratified  sand  and  clay, 

d , Clay  with  boulders  indistinctly 

stratified,  with  thin  irregular 
courses  of  sand,*  . 


of  Edinburgh,  Session  1873-74.  341 

understood  from  the  preceding  diagram  representing  the  section 
just  referred  to. 

In  searching  for  diatoms,  it  was  necessary  to  avoid  the  bed  a, 
which  has  been  formed  since  the  time  of  the  parallel  roads.  It 
was  thought  safer  also  to  throw  out  of  view  the  bed  5,  the  upper 
surface  of  which  is  in  contact  with  a.  Attention  was  therefore  con- 
fined to  the  beds  c and  d.  The  outside  weathered  portion  of  the 
bed  was  in  each  case  removed,  and  part  of  the  internal  contents  of 
the  bed  cut  cleanly  out — that  from  d being  about  10  feet  below  the 
surface.  The  material  thus  obtained  was  washed  in  distilled  water 
and  microscopically  examined.  It  was  found  that  the  search  re- 
quired much  patience.  Diatoms  were  ascertained  to  be  present 
scattered  very  rarely  through  the  material,  but  at  last  a series  of 
specimens  were  got.  These  were  sent  to  Professor  Dickie,  of 
Aberdeen,  one  of  our  highest  authorities  in  this  department  of 
natural  history,  and  the  following  species  were  determined  by 
him  : — 

Pinnularia  viridis.  Diatoma  vulgare. 

Himantidium  undulatum.  Surirella  panduriformis  ? 

Of  these  the  first  three  were  got  from  bed  c,  and  the  first  two  and 
the  last  from  bed  d. 

Now  these  are  all  freshwater  species,  and  their  evidence  is 
strengthened  by  the  fact  that  there  is  the  entire  absence  of  any 
marine  diatom  or  other  organism.  This  would  indicate  that  it  was 
an  old  freshwater  lake  which  had  these  parallel  roads  for  its  margins. 
Freshwater  diatoms  might,  indeed,  have  been  brought  down  into  it 
even  if  it  had  been  a sea  loch,  but  the  important  fact  is,  that  while 
freshwater  species  are  found,  it  has  been  impossible  to  detect  a 
single  trace  of  anything  marine. 

It  is  indeed  true  that  it  is  only  a single  locality  which  has  been 
searched  in  this  way,  and  it  would  be  going  too  far  to  hold  the 
results  as  at  once  conclusive.  Enough,  however,  has  been  done  to 
show  that  this  method  of  approaching  the  solution  of  the  problem 
deserves  to  be  followed  out.  Search  should  be  made  at  other 
points  along  these  parallel  roads  where  they  are  laid  open.  They 
have  been  a kind  of  battle-field  fought  over  by  rival  theorists  for 
the  last  fifty  years,  and  it  will  be  strange  if  all  the  time  multitudes 


342 


Proceedings  of  the  Royal  Society 

of  witnesses  have  been  lying  shut  up  in  the  deposits,  only  waiting 
to  be  called  into  court  to  give  decisive  evidence.  So  far  as  the 
investigation  has  gone,  it  is  in  favour  of  the  Freshwater  Theory. 

2.  Note  on  the  Perception  of  Musical  Sounds. 

By  John  G.  M‘Kendrick,  M.D. 

Certain  individuals  appear  to  be  incapable  of  appreciating  musi- 
cal sounds.  They  cannot  distinguish  one  melody  from  another; 
and  if  by  many  repetitions  of  the  melody  in  their  hearing,  they  at 
last  appear  to  know  it,  the  addition  of  one  or  more  of  the  parts  of 
the  harmony  again  renders  the  music  unrecognisable  to  them.  The 
question  naturally  arises,  Is  this  defect  owing  to  any  peculiarity  in 
the  structure  of  the  internal  ear  of  persons  so  constituted  which  pre- 
vents them  hearing  certain  sounds,  or  is  it  to  be  referred  to  the 
condition  of  the  brain  ? On  the  other  hand,  many  have  what  is 
termed  a “fine  ear,”  by  which  we  understand  the  faculty  of  appre- 
ciating, remembering,  and,  in  some  cases,  of  successfully  imitating 
musical  sounds.  Have  those  individuals  the  organ  of  hearing  more 
delicately  developed  ? 

This  physiological  problem  does  not,  in  the  present  state  of  our 
knowledge  of  the  minute  structure  of  the  organ  of  hearing  in  man, 
permit  of  being  examined  histologically.  We  would  not  probably 
find  any  appreciable  histological  difference  between  the  internal 
structure  of  the  ear  of  a genius  in  music  and  that  of  a person  who 
could  not  distinguish  one  melody  from  another.  So  far  as  this 
method  of  inquiry  is  concerned,  differences  may  exist,  but  the 
minute  size  of  the  ultimate  recipients  of  sound-waves,  and  the 
vagueness  of  our  present  knowledge  of  the  number  of  these  in  the 
depths  of  the  cochlea,  would  prevent  any  one  from  noticing  those 
differences. 

It,  therefore,  occurred  to  me  to  examine  this  question  by  testing 
experimentally  whether  those  individuals  who  profess  to  be  unable 
to  know  music  were  incapable  of  hearing  certain  musical  sounds, 
limited  as  regards  pitch,  within  the  extreme  keys  on  the  key-board 
of  a piano.  I have  examined  ten  cases  of  this  kind. 

In  a musical  sound  three  elements  have  to  be  considered, — ls£, 
loudness  or  intensity,  which  depends  on  the  extent  of  vibration  ; 


343 


of  Edinburgh,  Session  1873-74. 

2 d,  pitch,  determined  by  rate  of  vibration;  and,  3d,  quality,  which 
depends  on  the  orders,  numbers,  and  relative  intensities  of  the 
simple  tones  into  which  it  can  be  resolved. 

Up  to  the  present  point  of  this  inquiry  I have  devoted  attention 
chiefly  to  the  element  of  quality.  The  apparatus  I have  employed 
was  made  by  G-eorg  Appunn  of  Hanau.  It  is  a long  wooden  box 
inclosing  a row  of  vibrating  tongues  or  free  reeds,  which  can  be 
thrown  into  action  by  propelling  air  into  the  box  by  means  of  a 
bellows.  The  note  produced  by  the  longest  reed,  No.  1,  is  that 
obtained  by  a vibrating  cord,  of  a certain  length,  thickness,  and 
tension,  as  in  a monochord,  and  corresponds  to  C2,  having  32 
vibrations  per  second.  On  dividing  the  cord  into  2,  3,  4,  5,  6, 
&c.  equal  segments,  each  segment,  when  caused  to  vibrate,  will 
produce  a note  composed  of  2,  3,  4,  5,  or  6 times  the  number  of 
vibrations  in  No.  1.  This  apparatus  is  capable  of  producing  64 
tones,  a larger  number  than  are  included  within  the  key-board  of 
a piano.  The  names  and  number  of  vibrations  per  second  of  these 
tones  in  this  apparatus  is  as  follows  :■ — 


No, 

No. 

1. 

C2 

32,  Fundamental  tone. 

21. 

f2 

672 

2. 

C1 

64,  Octave. 

22. 

F2  + 

704 

3. 

G1 

96,  Fifth  above  No.  2. 

23. 

Fis2 

736 

4. 

C° 

128,  Fourth  above  No.  3. 

24. 

G2 

768 

5. 

e° 

160,  Major  third  above 

25. 

gis2~ 

800 

No.  4. 

26. 

a2~ 

832 

6. 

G° 

192,  Minor  third  above 

27. 

a2 

864 

No.  5. 

28. 

b2 

896 

7. 

C° 

224 

29. 

Ais2 

928 

8. 

C1 

256 

30. 

h2 

960 

9. 

D1 

288 

31. 

H2 

992 

10. 

e1 

320 

32. 

C3 

1024 

11. 

pi+ 

352 

33. 

C3+ 

1056 

12. 

G1 

384 

34. 

Des3+ 

1088 

13. 

a1- 

416 

35. 

d3- 

1120 

14. 

b1 

448 

36. 

D3 

1152 

15. 

h1 

480 

37. 

D3+ 

1184 

16. 

C2 

512 

38. 

Es3~ 

1216 

17. 

Des2 

544 

39. 

e3— 

1248 

18. 

D2 

579 

40. 

e3 

1280 

19. 

Es2" 

608 

41. 

E3+ 

1312 

20. 

e2 

640 

42. 

f3 

1344 

Proceedings  of  the  Royal  Society 

No. 

No. 

43. 

f3+ 

1376 

54.  A3 

1728 

44. 

]73+ 

1408 

55.  A3+ 

1760 

45. 

Fis3 

1440 

56.  b3 

1792 

46. 

Fis3+ 

1472 

57.  B3 

1824 

47. 

g3 

1504 

58.  Ais3 

1856 

48. 

G3 

1536 

59.  Ais3+ 

1888 

49. 

As3- 

1568 

60.  h3 

1920 

50. 

Gis3~ 

1600 

61.  H3+ 

1952 

51. 

As3 

1632 

62.  H3++ 

1984 

52. 

a3- 

1664 

63.  c4~ 

2016 

53. 

a3 

1696 

64.  C4 

2038 

I have  also  a series  of  64  resonators,  tuned  to  these  64  tones,  and 
having  corresponding  numbers.  When  tone  No.  12  on  the  over- 
tone apparatus  is  sounded,  and  the  narrow  end  of  resonator  No.  12 
is  placed  in  the  ear,  the  instrument  sings  into  the  ear  of  the 
observer  with  great  intensity.  I have  thus  in  the  group  of  resona- 
tors an  apparatus  for  analysing  any  compound  musical  note  into  its 
constituent  tones ; and,  in  the  overtone  apparatus,  I have  a means 
of  checking  the  sensation  of  the  listener  by  sounding,  with  much 
greater  intensity,  the  tone  corresponding  to  the  resonator  by  which 
he  heard  any  particular  tone  in  a compound  note.  The  method  I 
adopted  was,- — ls£,  to  strike  a note  on  the  piano,  which,  of  course, 
consisted  of  a fundamental  tone,  and  of  certain  overtones;  2d,  to 
allow  the  person  whose  ear  was  being  examined  to  listen  with  the 
various  resonators  until  he  selected  one  by  which  he  heard  a tone 
(one  existing  in  the  note,  and  strengthened  in  intensity  by  the 
resonator);  3 d,  after  the  listener  had  satisfied  himself  that  he 
clearly  heard  the  overtone  ringing  in  his  ear,  the  note  on  the  piano 
was  arrested,  the  stop  of  the  overtone  apparatus  corresponding  to 
the  overtone  was  withdrawn,  so  as  to  sound  the  overtone,  and  the 
listener  had  to  decide  whether  or  not  this  was  the  same  sound  as 
the  one  he  heard  when  listening  to  the  musical  note.  The  result 
in  the  ten  cases  I examined  was  as  follows  : — In  .nine  of  the  cases 
the  overtone  was  readily  perceived ; and  in  the  tenth,  the  lower 
overtones  of  the  series  were  observed  directly,  whereas  the  higher 
overtones  were  not  noticed  by  means  of  the  resonator,  but  were 
clearly  observed  when  those  overtones  were  sounded  on  the  over- 
tone apparatus.  This  individual  asserted  he  had  often  noticed  he 


of  Edinburgh,  Session  1873-74.  345 

was  deaf  to  very  highly-pitched  sounds  which  other  people  said 
they  heard. 

These  results  indicate  that,  so  far  as  the  structure  of  the  ear  is 
concerned,  those  individuals  who  are  said  not  to  know  one  note 
from  another,  are  equally  capable,  by  the  use  of  resonators,  of  ana- 
lysing a compound  musical  note — that  is,  of  hearing  the  various 
tones  of  which  it  is-  composed — with  those  who  have  a good  ear. 
Physiologically,  they  seem  to  be  capable  of  splitting  up,  uncon- 
sciously, the  compound  vibration  into  the  simple  vibrations,  the 
rates  of  which  are  once,  twice,  or  thrice  that  of  the  fundamental 
note. 

The  next  point  which  I examined  was  regarding  the  percep- 
tion by  persons  having  no  musical  ear  of  difference  and  summation 
tones,  which,  as  is  well  known,  play  an  important  part  in  the  theory 
of  concord  and  discord. 

If,  on  the  overtone  apparatus,  two  tones  of  different  pitch  are 
sounded,  a third  and  deeper  tone  may  be  frequently  observed. 
These  tones  were  first  discovered  by  a German  organist,  Andreas 
Sorge,  in  1740.  For  example,  if  2 : 3,  or  3 : 4,  or  6 : 7,  or  7 : 8,  &c., 
are  sounded,  a third  and  deeper  tone  may  be  perceived  by  the  use 
of  a proper  resonator,  which  will  be  always  found  to  beC2=l; 
that  is,  this  combination  tone  is  produced  by  32  vibrations  per 
second,  the  difference  between  the  respective  vibration  numbers  of 
the  tones  2 : 3,  or  3 : 4,  or  6 : 7,  &c.  I have  found  that  the  differ- 
ence tone  heard  with  greatest  distinctness  corresponds  to  one  pro- 
duced by  128  vibrations  per  second.  For  example,  on  sounding 
16  : 20,  or  24  or  28,  or  32  and  36,  with  resonator  No.  4,  I can  dis- 
tinctly hear  the  tone  corresponding  to  No.  4 = 128  vibrations  per 
second  in  each  case.  I have  found  no  marked  difference  between 
non-musical  and  musical  individuals  in  the  perception  of  difference 
tones,  except  as  regards  intensity.  I had  the  opportunity  of  ex- 
amining two  persons  of  marked  musical  ability,  who  could  distin- 
guish, by  great  attention,  without  the  aid  of  resonators,  difference 
tones  to  the  6th  of  the  series,  and  who  could  observe  difference 
tones,  2,  3,  and  4,  with  comparative  ease.  Non-musical  persons  did 
not  observe  these  difference  tones  without  the  use  of  resonators  to 
add  to  their  intensity ; and,  in  one  case,  the  person  could  not  hear 
them  at  all.  In  addition  to  these  primary  difference  tones,  I have 


346 


Proceedings  of  the  Royal  Society 

met  with  only  one  individual  who  could  hear  what  are  termed 
secondary  and  tertiary  difference  tones,  and  he  could  not  hear  these 
without  apparently  a strong  effort  of  attention.  They  were  as  fol- 
lows: — On  sounding  16,  C2=512  vibrations  per  second,  and  20, 
e2  = 640,  he  heard  C°  = 128,  that  is,  20  - 16  = 4.  By  using  resona- 
tor No.  12,  he  heard  12  = 384,  that  is  16-4  = 12;  and  on  using- 
resonator  No.  8,  he  heard  very  feebly  8,  that  is  12  - 4 = 8.  When 
C2  and  e2,  that  is  tones  corresponding  to  512  and  640  vibrations  per 
second,  were  sounded  in  this  person’s  ears,  he  heard  other  three 
tones  with  the  use  of  resonators,  namely,  those  produced  by  128, 
256,  and  384  vibrations  per  second. 

But  when  two  tones  are  sounded,  in  addition  to  a tone  produced 
by  a vibration  number  equal  to  the  difference  between  the  vibration 
number  of  the  two,  another  tone  is  produced,  the  vibration  number 
of  which  is  equal  to  the  sum  of  the  vibration  numbers  of  the  two 
primaries.  This  tone  is  called  a summation  tone.  For  example,  on 
sounding  4 = 128  and  6 = 192  vibrations  per  second,  by  using  resona- 
tor No.  10  = a tone  having  320  vibrations  per  second  may  be  dis- 
tinctly heard.  Thus,  2 : 3,  and  3 : 4,  and  5 : 9,  will  produce  sounds 
heard  by  resonators  Nos.  5,  7,  and  14,  respectively.  I have  found 
that  non-musical  people  can  hear  these  summation  tones  with  great 
distinctness  if  increased  by  resonators.  They  can  hear  the  lower 
order  of  summation  tones  much  more  easily  than  the  higher  order. 
For  example,  all  could  hear  the  summation  tone  2 (64)  : 3 (96)  = 5 
(160)-  , or  4 (128)  : 6 (192)=  10  (320)  ; but  only  four  out  of  the 
ten  could  hear  7 (221)  + 8 (256)  = 15  (480),  and  8 (256)  + 9 (288) 
= 17  (544).  Only  one  out  of  the  ten  could  hear  30  (960) + 28  (896) 
= 58  (1856),  and  none  could  hear  32  (1024) + 30  (960)  = 62  (1984). 
I observed  also  that  they  could  hear  the  higher  summation  tones 
only  when  the  intensity  was  increased  to  as  great  an  extent  as 
possible.  The  two  musical  persons  examined  were  able  to  hear  all 
these  sounds  with  ease,  with  even  diminished  intensity. 

According  to  Helmholtz,  there  are  secondary  and  tertiary  sum- 
mation tones,  which  spring  from  combinations  of  the  primary  sum- 
mation tones  with  its  elements.  Thus,  3 (96)  : 5 (160),  with  the 
overtone  apparatus,  give  8 (256);  3 (96)  and  8 (256)  give  11  (352); 
5 (160)  and  8 (256)  and  give  13  (416).  Therefore,  when  3 (96)  and 
5 (160)  are  sounded,  according  to  this  statement,  the  listener  with 


347 


of  Edinburgh,  Session  1873-74. 

resonators  may  hear  3 (96),  5 (160),  8 (256),  11  (352),  and  14 
(448).  I have  examined  this  and  various  other  combinations.  I 
can  with  my  own  ears  hear,  by  using  the  appropriate  resonator,  the 
primary  combination  series  quite  distinctly,  but  no  farther.  The 
secondary  tones  I have  never  heard.  Eight  out  of  the  ten  non- 
musical  people  I have  examined  have  heard  the  primary  series ; 
the  other  two  said  they  thought  they  could  hear  the  second.  The 
two  musical  persons  asserted  they  could  hear  the  tones  distinctly. 

If  then  “the  presence  of  overtones  confers  on  music  its  most 
characteristic  charms,”  as  stated  by  Sedley  Taylor,*  it  appears  to 
me  that  non-musical  persons,  when  aided  by  resonators,  are  as 
capable  as  musical  persons  of  recognising  the  existence  of  certain  of 
these  overtones.  The  difference  between  the  two  classes  of  listeners 
is  either — (1),  that  the  intensity  of  the  overtone  requires  to  be 
greater  to  be  appreciated  by  a non- musical  than  by  a musical  per- 
son ; or  (2),  that  musical  persons,  by  previous  education  of  the 
sense,  are  better  able  to  appreciate  distinctions  of  sound.  Non- 
musical persons  seem  to  be  incapable  of  noticing  the  existence  of 
the  higher  overtones,  which  are,  of  course,  much  less  intense  than 
the  lower  overtones.  They  are  incapable  of  observing  the  differ- 
ence and  summation  tones  having  high  vibration  numbers.  Thus,  so 
far  as  the  mere  perception  of  musical  sounds,  and  of  those  secondary 
vibrations,  which  produce  overtones,  and  give  quality  to  the  funda- 
mental tone,  or  duad,  or  triad,  &c.,  is  concerned,  non-musical  persons 
are  affected  by  the  vibrations  just  as  musical  persons  are  affected. 
The  only  difference  I Lave  noticed  between  the  two  is  that  of  in- 
tensity. A musical  person  hears  tones  of  low  intensity,  such  as  the 
higher  overtones,  quickly,  and  apparently  without  difficulty;  where- 
as, a person  who  is  non-musical  hears  the  lower  overtones,  but  he 
cannot  hear  the  upper  at  all,  even  with  the  aid  of  a resonator.  The 
question  of  intensity  of  tones  and  overtones  I have  still  under  expe- 
rimental inquiry.  These  researches  indicate  that  in  the  sense  of 
hearing  there  is  no  state  analogous  to  that  of  colour-blindness  in 
the  eye. 

* Sound  and  Music : A Non-Mathematical  Treatise  on  the  Physical  Consti- 
tution of  Musical  Sounds  and  Harmony,  &c.  By  Sedley  Taylor,  M.A.,  &c. 
London,  1873. 

2 Y 


vol.  vrn. 


348 


Proceeding  s of  the  Boy  at  Society 


3.  On  the  Establishment  of  the  Elementary  Principles  of 
Quaternions  on  an  Analytical  Basis.  T>y  G.  Plarr,  Esq. 
Communicated  by  Professor  Tait. 


4.  Preliminary  Note  “On  a New  Method  of  obtaining  very 
perfect  Vacua.”  By  Professor  P.  G.  Tait  and  Mr  James 
Dewar. 

Professor  Andrews,  in  the  “ Philosophical  Magazine”  for  1852, 
recalled  the  attention  of  physicists  to  the  method  originally  devised 
by  Davy  of  making  a vacuum  so  perfect,  that  the  residual  gas 
exercised  no  appreciable  pressure  as  registered  by  the  depression 
of  a barometric  column.  This  he  effected  by  filling  the  vessel  to 
be  exhausted  with  carbonic  acid  gas,  having  previously  inserted  a 
cup  containing  a concentrated  solution  of  caustic  potash.  On 
rapidly  exhausting  with  an  air-pump,  and  leaving  time  for  the 
absorption  of  the  residual  carbonic  acid  by  the  caustic  potash,  he 
obtained  a vacuum  as  perfect  as  a Torricellian.  Andrews’  method 
was  afterwards  employed  by  Gassiot  in  his  well-known  investiga- 
tions on  the  passage  of  electricity  through  attenuated  media.  By 
the  use  of  stick  potash  in  carbonic  acid  vacuum  tubes,  he  succeeded 
in  rendering  the  tubes  so  free  from  any  traces  of  gas,  that  the 
electric  discharge  will  not  pass.  Caustic  potash  for  this  purpose 
is  unsatisfactory,  from  the  fact  of  its  requiring  to  be  fused  before 
rapid-  absorption  takes  place,  and  also  from  the  fact  that  aqueous 
vapour  is  apt  to  be  left.  This  plan  is  besides  entirely  confined 
to  carbonic  acid  tubes,  although  other  chemical  agents  might  be 
procured  to  effect  absorption  of  traces  of  other  gases.  The  method 
we  have  devised  to  absorb  traces  of  gases  is  based  on  the  remarkable 
power  of  absorption  of  cocoa-nut  charcoal  for  gaseous  bodies  gene- 
rally. By  placing  a piece  of  this  charcoal  in  a glass  tube,  having  two 
platinum  terminals  for  the  purpose  of  passing  an  electric  discharge 
and  exhausting  with  a Sprengel  pump,  heating  the  charcoal  to  a low 
red  heat  during  the  exhaustion,  when  the  tube  is  sealed  the  vacuum 
is  so  perfect  that  no  spark  will  pass  with  a coil  giving  quarter  of 
an  inch  sparks  in  air.  On  now  heating  the  charcoal  with  a spirit 
lamp,  sufficient  gas  is  given  out  to  allow  the  spark  to  pass;  on  cooE 


349 


of  Edinburgh,  Session  1873-74. 

ing,  rapid  reabsorption  takes  place,  and  the  tube  is  rendered  again 
impervious  to  tbe  discharge.  This  operation  may  apparently  be 
repeated  ad  infinitum  with  the  same  results. 

Many  important  determinations  may  be  effected  through  tbe  em- 
ployment of  carbon  vacua,  such  as  the  temperature  at  which 
dissociation  takes  place  between  the  carbon  and  the  dissolved  gas, 
tbe  time  required  for  reabsorption,  and  the  effect  of  different  gases 
in  influencing  tbe  action  of  the  carbon.  We  need  hardly  say  that 
this  easy  means  of  obtaining  vacua  will  be  of  importance  in  spec- 
troscopic observations,  and  we  intend  shortly  to  communicate 
observations  in  this  direction. 

5.  Laboratory  Notes.  By  Professor  Tait. 

1.  On  Atmospheric  Electricity. 

For  some  days  past  I have  been  in  tbe  habit  of  observing  atmo- 
spheric electricity  about  one  o’clock,  with  the  view  of  ascertaining 
whether  the  concussion  produced  by  the  time-gun  has,  as  I 
suspected  from  an  experiment  of  ten  years  ago,  an  effect  on  the 
amount  collected  by  the  water  dropper.  For  several  successive 
days  the  atmospheric  charge  was  small  and  only  slowly  variable, 
and  uniformly  on  these  occasions  I found  a sudden  slight  increase 
of  the  deflection  of  tbe  electrometer  (whether  it  was  originally 
positive  or  negative)  to  occur  simultaneously  with  tbe  sound, 
precisely  the  result  obtained  in  the  single  experiment  of  date  21st 
May  1864.  It  appears  to  be  most  probably  due  to  mere  shaking 
of  the  instruments. 

On  Thursday  last,  the  26th,  during  the  great  storm,  the  amount  of 
electricity  collected  was  so  large,  as  in  general  to  be  beyond  the  range 
of  my  divided  ring  electrometer  after  a fraction  of  a second.  I there- 
fore connected  the  water  dropper  with  a gold  leaf  electroscope,  whose 
leaves  were  thick,  and  about  five  inches  long  by  one  broad.  These 
leaves  are  made  to  diverge  so  as  to  touch  the  tinfoil  coating  of 
the  case  in  periods  often  less  than  a quarter  of  a minute,  indicating 
a potential  of,  roughly  speaking,  many  thousand  G-rove’s  cells. 
The  most  curious  phenomenon,  however,  was  this,  that  at  intervals, 
often  not  exceeding  a minute,  and  while  rain  and  hail  were 
alternating,  the  charge  of  tbe  electroscope,  even  on  this  large 


350  Proceedings  of  the  Royal  Society 

scale,  changed  from  + to  - and  back  again.  It  seemed,  in  fact, 
as  if  there  were  alternate  changes  of  atmospheric  potential  from 
high  + to  high  - , and  not,  as  is  usual  in  such  weather,  changes 
merely  from  higher  to  lower  - . The  water  dropper  projected  2J- 
feet  from  the  wall  of  the  College  at  an  elevation  of  44J  feet  from 
the  ground  below,  and  discharged  at  an  average  about  2’5  cubic 
inches  of  water  per  minute. 

2.  On  the  Thermo-Electric  Position  of  Sodium. 

I owe  to  Mr  Dewar’s  skill  in  manipulation  the  means  of  deter- 
mining the  line  of  sodium  in  the  thermo-electric  diagram.  He 
constructed  for  me  a long  quill  tube  of  Gferman  glass,  with  platinum 
wires  inserted  near  the  ends;  exhausted  it  by  means  of  a Sprengel 
pump,  and  drew  in  melted  sodium  from  a bath  of  paraffin.  Exact 
determinations  will  require  considerable  time,  even  with  this 
excellent  apparatus ; but  in  the  meantime  I may  state  (as  a first 
approximation)  that  the  line  of  sodium  is  nearly  parallel  to  that  of 
palladium,  and  somewhat  above  it  in  the  diagram. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

John  Anderson,  M.D. 

James  Napier,  Esq.,  Glasgow. 

Alexander  Hunter,  M.D.,  F.R.C.S.E. 

The  following  Gentlemen  were  elected  Honorary  Fellows, 
to  supply  the  vacancies  caused  by  the  deaths  of  Sir  John 
Herschel,  Sir  Boderick  Murchison,  John  Stuart  Mill,  Hugo 
Yon  Mohl,  Wilhelm  Karl  Haidinger,  Baron  Justus  von 
Liebig,  and  Gustav  Bose  : — 

1.  British  Honorary. 

James  Joseph  Sylvester,  LL.D.,  Loudon. 

William  Hallowes  Miller,  LL.D.,  Professor  of  Mineralogy,  Cambridge. 

John  Anthony  Froude,  London. 

2.  Foreign  Honorary. 

Adolphe  Theodore  Brongniart,  Professor  of  Botany,  Paris. 

Louis  Pasteur,  Paris. 

Wilhelm  Eduard  Weber,  Gottingen. 

Otto  Torell,  Professor  of  Zoology  and  Geology,  Lund,  and  Director 
Geological  Survey  of  Sweden. 


RESISTANCES  IN  TERMS  OF  VELOCITIES 


RESISTANCES  IN  TERMS  OF  SINES  OF  INCLINATIONS 


O JOO^o”  ZOO  a”  300 n”  400  a'1 

RESISTANCES  IN  TERMS  OF  AREAS 


of  Edinburgh,  Session  1873-74. 


351 


Monday,  16  th  March  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Commnnications  were  read : — 


1.  On  the  Resistance  of  the  Air  to  the  Motion  of  Fans.  Ry 
James  C.  Fair  weather.  Esq.  Communicated  by  George 
Forbes,  Esq.  (With  two  Plates.) 

The  design  of  this  paper  is  to  describe  the  results  of  some  experi- 
ments on  “the  Resistance  of  the  Air,”  which  I made  under  the 
superintendence  of  Professor  Forbes,  in  the  physical  laboratory  of 
the  Andersonian  University,  Glasgow.  The  apparatus  employed 
resembles  somewhat  that  used  by  M.  le  Chevalier  de  Borda,  whose 
experiments  on  “the  Resistance  of  Fluids”  are  recorded  in  the 
“Memoires  de  l’Academie  Royale  des  Sciences.”  It  consists 
essentially  of  a wooden  frame,  which  was  firmly  secured  to  the 
floor,  and  supporting  a horizontal  axis,  at  one  extremity  of  which 
is  fixed  a wooden  arm,  on  to  which  were  bolted  the  vanes  of  different 
forms  and  sizes,  the  resistance  of  which  it  was  desired  to  ascertain. 
A cylinder  or  barrel,  about  3 inches  in  diameter,  is  fastened  to  the 
axis,  whereon  was  wound  a cord,  which,  being  acted  on  by  weights, 
gave  a circular  motion  to  the  axis,  and  consequently  to  the  arm, 
thereby  carrying  the  vanes  in  the  circumference  of  a circle  of  3 
feet  diameter,  and  causing  them  to  impinge  upon  the  air  with 
velocities  due  to  the  force  applied.  The  moving  force  consisted  of 
weights  of  from  J lb.  to  20  lbs.,  suspended  at  the  end  of  the  cord, 
which  passed  over  a guide-pulley,  made  fast  in  such  a position  that 
a drop  of  35  feet  was  obtained.  For  each  experiment  the  cord  was 
wound  on  to  the  cylinder  by  hand,  and  afterwards  abandoned  to 
the  action  of  the  weight  at  a beat  of  a second’s  pendulum ; and  the 
vanes  thereby  allowed  to  make  a definite  number  of  revolutions, 
ascertained  by  a distinct  mark  on  the  cord ; the  times  of  which 
were  recorded  for  each  observation.  After  a few  trials  the  pendulum 


352 


Proceedings  of  the  lloyal  Society 

was  replaced  by  an  ordinary  metronome,  adjusted  so  as  to  make  a 
vibration  every  half  second.  This  instrument,  from  the  distinct- 
ness of  its  beats,  was  found  much  better  adapted  to  our  purpose. 
The  time,  by  this  means,  could  be  registered  with  perfect  accuracy 
to  one-fourth  of  a second  of  time. 

The  mean  result  of  three  observations  was  always  taken  with 
each  different  weight;  and  when  there  appeared  to  be  any  dis- 
crepancy, additional  observations  were  made,  in  order  to  get  a more 
exact  average  for  the  result.  But  except  when  the  smaller  weights 
were  used  this  was  quite  unnecessary,  as  the  results  of  the  different 
observations  agreed  very  well. 

The  mean  result  with  each  weight  was  registered,  forming 
Table  I.,  where,  in  a line  with  each  weight,  is  to  be  found  the  time 
in  seconds  required  for  the  vanes  to  make  forty-seven  revolutions. 


Table  I. 


Weight 
on  cord 
in  lbs. 

54-85  rr 

Square. 

Ri 

41-15  O' 

Round. 

S2_ 

1G6--3Q" 

Square. 

r2 

125-8  □" 
Round. 

S3 

345-2  □" 
Square. 

r3 

264-8  O' 
Round. 

1 

82 

73 

145 

140 

61 

55 

110 

94 

2 

50 

46 

89 

77i 

138 

114 

3 

40 

361 

70 

59i 

106 

91 

4 

34 

31 

58 

51 

92 

76 

6 

27 

25 

47 

41J 

74 

61 

8 

23| 

211 

401 

36 

64 

53 

10 

21 

19£ 

37 

32 

56 

47^ 

1 2 

19 

17* 

34 

29 

52 

44 

14 

18 

161 

311 

27 

481 

41 

16 

16f 

151 

29ir 

25h 

45 

381 

18 

16 

14j 

28 

24“ 

43 

36^ 

20 

15 

13f 

261 

22 

41 

341 

To  ascertain  the  absolute  resistance  of  the  surfaces,  curves 
similar  to  those  on  Plate  I.  were  laid  down,  where  the  ordinates 
represented  pressure  in  pounds,  and  the  abscissas  velocities;  the 
vanes  now  moving  perpendicularly  to  their  planes.  In  the  same 
manner  curves  were  laid  down  from  Table  II.,  which  shows  the 
weights  required  to  give  different  velocities  when  the  vanes  moved 
in  their  own  planes.  The  difference  between  the  ordinates  of  a 
pair  of  curves  belonging  to  the  same  vanes,  the  velocity  being  the 


353 


of  Edinburgh,  Session  1873-74. 

same  in  both,  gives  the  weight  which,  with  that  velocity,  was 
required  to  overcome  the  resistance  of  the  air.  (The  skin  resist- 
ance is  neglected  as  insensible).  By  this  means  the  effects  of 
inertia  and  friction  in  the  apparatus  are  completely  eliminated. 

The  equation  of  the  curve  of  absolute  resistances  may  be  put  in 
the  form — 

B = Av  + Bv2  + Cv3  + &c. 

When  B is  the  resistance,  v the  velocity,  A B and  0 constants. 
Here  A and  C are  small,  but  if  we  include  A in  the  expression  we 
must  have  C also,  for  A is  negative.  The  crosses  marked  on 
Plate  I.  are  the  calculated  results  A and  B alone  being  taken  ; in 
which  case  the  formula  of  course  fails  for  small  values  of  v. 


Table  II. 


Weight 
on  cord 

Si 

Ri 

s2 

R2 

S3 

r3 

in  lbs. 

1 

46 

41 

47 

60 

61 

56 

2 

3 

284 

22j 

264 

2H 

304 

24 

324 

25 

35 

284 

334 

26| 

as} 

4 

19j 

184 

214 

204 

244 

5 

1 n 

164 

21| 

204 

6 

15f 

154 

17 

17 

19| 

184 

8 

15 

14f 

10 

134 

13 

12 

12 

12 

In  the  case  of  the  smaller  surfaces,  with  high  velocities,  the 
resistance  would  appear  to  increase  in  a somewhat  greater  ratio. 
Comparing  this  with  the  results  of  Dr  Hutton  (who  gives  a volu- 
minous description  of  his  experiments  in  the  third  volume  of  his 
“ Mathematical  Tracts”)  we  find  them  to  agree.  He  found  that  u the 
resistance  to  the  same  surface  with  different  velocities,  is  in  the 
case  of  slow  motions,  nearly  as  the  square  of  the  velocity ; but, 
gradually  increasing  more  and  more  above  that  proportion  as  the 
velocity  increases.”  This  is  rendered  obvious  by  calculating  the 
index  of  the  power  after  his  manner,  and  tabulating  the  results  as 
annexed. 


354 


Proceedings  of  the  Royal  Society 


V elocity. 

Resistance. 

Index. 

*01 

10-5 

*015 

24-5 

2-089 

•02 

43  5 

2-050 

*025 

70-0 

2-070 

*03 

101-0 

2-121 

•035 

150-0 

2-122 

•04 

195-0 

2-107 

Mean,  2*093 

The  index  of  the  power  of  the  velocity  is  set  down  in  the  third 
column  for  the  resistance  due  to  the  curve  S2.  By  comparing  the 
first  velocity  with  each  of  the  following  ones,  it  will  be  seen  that 
the  numbers  in  the  index  column  slowly  and  gradually  increase, 
and  would  doubtless  continue  to  do  so  to  a very  great  extent. 
The  mean  of  these  is  2 093;  whence  it  would  appear  that  with 
these  velocities,  the  resistance  to  the  same  surface  is  nearly  as'  the 
2-093  power  of  the  velocity. 

The  curves  marked  Rx , R2,  and  R3  are  derived  from  circular 
plane  surfaces  of  4T15,  125-8,  and  264-8  square  inches  respectively. 
Those  marked  S1?  S2 , and  S3  are  from  square  plane  surfaces  of  54*85, 
116-3,  and  345*2  square  inches  respectively.  The  lines  Cx  and  C2 
are  from  circular  concave  surfaces  of  199  and  192-5  square  inches, 
and  their  radii  of  curvature  are  24,//375  and  12-25  inches  respectively. 

All  these  curves  were  obtained  by  means  of  vanes  having  their 
plane  surfaces  at  right  angles  to  their  plane  of  rotation.  The 
curves  Ix , I2 , and  I3  were  derived  from  a plane  square  surface  of 
166*3  square  inches,  inclined  at  angles  of  30°,  45°,  and  60°  to  the 
plane  of  rotation. 

The  curves  on  the  lower  part  of  Plate  II.  are  intended  to  exhibit 
the  manner  in  which  the  resistance  increases  with  the  surface. 
The  abscissae  of  these  curves  represent  the  areas  of  the  surfaces  in 
square  inches,  and  the  ordinates  resistances ; the  velocity  remain- 
ing constant.  It  is  at  once  seen  from  these  curves,  that  the  resist- 
ance does  not  vary  directly  as  the  surface ; but  increases  in  a some- 
what greater  ratio.  Within  the  limits  of  these  experiments, the  com- 
pound ratio  of  the  resistance  to  the  surface  rises  from  1 to  1*7. 

The  curves  in  the  upper  part  of  the  same  plate  are  intended  to 


of  Edinburgh,  Session  1873-74  355 

show  the  manner  in  which  the  resistance  varies  with  the  inclina- 
tion of  the  vanes  to  the  plane  of  rotation.  In  these  the  abscissa 
denote  the  sines  of  the  angles  of  incidence  (the  angle  of  incidence 
being  the  angle  which  the  vanes  make  with  the  plane  of  rotation), 
and  the  ordinates  resistances. 

The  equation  which  satisfies  these  curves,  is — 

Sin3^  = R x 0 

where  i,  the  angle  of  incidence,  R,  the  resistance,  and  0,  a constant. 

This  being  shown  by  a dotted  line,  found  by  calculation  from 
this  formula,  and  which  almost  coincides  with  the  curve  found 
from  the  experiments.  This  clearly  proves  that  the  resistance 
varies  as  the  cube  of  the  sine  of  the  angle  of  incidence. 

The  curves  Cx  and  02  and  the  points  0X , C2  on  the  curves  of  areas 
represent  the  effects  due  to  concavity  of  the  vanes ; from  which  we 
conclude,  that  a certain  amount  of  concavity  offers  a greater  resist- 
ance than  the  same  area,  and  configuration  of  a plane  surface. 
But,  on  comparing  the  greater  with  the  less  concave  surface,  there 
appears  to  be  little  or  no  difference  within  the  limits  of  these  ex- 
periments. This  appears  to  be  due  to  the  manner  in  which  the 
particles  act  upon  the  surface.  First,  in  comparing  the  concave 
surface  with  a plane  surface  of  the  same  area,  we  find  that  the 
concave  vane  offers  most  resistance.  This  may  be  accounted  for,  by 
imagining  a certain  quantity  of  the  particles  to  be  caught  in,  as  it 
were,  in  front  of  the  vanes,  and  consequently  forming  a denser  me- 
dium ; this  extra  dense  medium  being  continually  kept  up  in  front, 
while  the  vanes  are  in  motion.  This  overcrowding  of  space  has  a 
tendency  to  prevent  the  particles  from  moving  past  the  perimeter  of 
the  vanes  with  the  same  ease,  and  consequently  retards  the  apparatus. 

Again,  by  comparing  the  less  with  the  more  concave,  we  would 
at  first  sight  conclude  that  this  was  simply  an  amplified  case  of 
the  foregoing ; but  here  we  have  something  to  balance  the  extra 
dense  medium  in  front,  viz.,  the  action  of  the  particles  of  the  con- 
vex surface  behind.  Their  action  may  be  said  to  be  analogous  to 
the  action  of  the  water  closing  in  at  a ship’s  stern  ; and,  therefore, 
tends  to  impel  the  surface  forward,  and  in  that  way  diminish  the 
effects  of  any  resistance  due  to  the  extra  concavity  in  front.  So 
that,  looking  at  the  matter  in  this  light,  we  should  conclude  that 

2 z 


VOL.  VIII. 


356  Proceedings  of  the  Royal  Society 

there  would  be  a maximum  resistance  with  a certain  degree  of 
curvature  This,  however,  cannot  be  proved  by  the  small  number 
of  observations  made  curved  surfaces,  but  would  be  very  interesting 
to  ascertain  experimentally. 

2.  On  the  Curve  of  Second  Sines  and  its  Variations. 

By  Edward  Sang,  Esq. 

The  idea  of  this  class  of  curves  arose  during  an  attempt  to 
resolve  an  important  problem  in  the  doctrine  of  wheel- work  ; a 
statement  of  the  conditions  of  that  problem  is  thus  the  natural 
introduction  to  the  subject. 

When  the  shape  of  the  tooth  of  one  wheel  A has  been  assumed, 
the  shape  of  the  tooth  of  another  wheel  B,  to  work  along  with  it, 
may  he  deduced  by  a very  simple  graphic  process  ; and  when  these 
two  wheels  are  made  to  turn  together,  the  points  of  contact  describe 
a certain  line  or  path.  In  my  “ New  G-eneral  Theory  of  the  Teeth 
of  Wheels”  it  is  shown  that  this  path,  and  the  manner  of  motion  in 
it,  are  independent  of  the  size  of  the  second  wheel  B,  and  result 
entirely  from  the  arbitrarily  assumed  form  of  A ; that  is  to  say,  if 
we  delineate  the  form  of  a new  wheel  B,  to  work  along  with  A,  the 
path  and  the  motion  of  the  contact  point  along  it  are  the  same  as 
before ; the  originally  assumed  form  A thus  gives  rise  to  a system  of 
conjugate  forms  B.  Not  only  so,  but  if  we  use  any  one  of  the 
wheels  B as  an  originator,  we  shall  obtain  from  it  a system  of  con- 
jugates A,  of  which  our  first  wheel  A is  a member.  Thus  the 
assumption  of  one  wheel  gives  rise  to  two  conjugate  systems,  A and 
B,  so  related  that  any  wheel  of  the  one  works  with  any  wheel  of  the 
other,  the  contact  path  remaining  the  same  for  every  couple.  It 
does  not,  however,  follow  that  two  wheels  of  the  same  set  can  work 
together;  in  the  arrangement  of  wheel- work  it  is  important  that 
the  two  systems  he  identic.  Now,  when  the  wheel  is  indefinitely 
enlarged,  its  boundary  merges  into  a straight  rack,  and  the  rack  A 
is  necessarily  a copy  of  the  rack  B ; hence  we  come  to  the  most 
important  theorem  in  the  doctrine  of  engrainage,  that  “ if  we 
assume  for  the  outline  of  a straight  rack  any  curve  consisting  of 
equal  undulations,  symmetrically  arranged  on  either  side  of  its 
pitch-line,  all  the  wheels  determined  by  it  work  with  each  other, 


357 


of  Edinburgh , Session  1873-74. 

and  are  reversible  face  to  face.”  This  theorem  is  general  so  far 
as  geometry  is  concerned,  but  is  restricted  in  its  mechanical  appli- 
cation by  the  condition  of  material  continuitj7-,  and  hence  there 
arise  some  difficult  and  interesting  problems. 

Each  assumed  form  of  undulation  has  its  peculiar  path  for  the 
point  of  contact ; this  path  is  obtained  by  drawing  normals  PX, 
meeting  the  line  of  abscissae  in  X,  as  in  figs.  1 and  9,  and  then 
through  some  fixed  point  Q,  technically  called  the  pitch-point , 
drawing  QP'  equal  and  parallel  to  NP. 

If  we  suppose  the  point  P,  in  fig.  1,  to  move  steadily  along  the 
curve  EXTYY,  accompanied  by  the  normal,  the  point  N will  move 
continuously,  though  not  uniformly,  from  E to  Y ; and  from  no 
point  in  the  axis  ESTUV  can  more  than  one  normal  be  drawn  to 
the  curve.  Such  a rack  would  give  rise  to  a system  of  wheels 
having  only  one  point  of  contact,  and  so  useless  in  machinery. 
On  augmenting  the  ordinates  HP  in  some  fixed  ratio,  we  obtain  a 
curve  with  deeper  undulations,  and  augment  the  subnormals  HX 
in  the  duplicate  ratio ; in  this  way  we  may  cause  the  point  X to 
pass  beyond  S before  P has  arrived  at  X.  In  such  case  N must 
become  stationary,  and  then  return  to  S,  when  P shall  reach  X ; 
passing  back  towards  E,  N must  again  become  stationary,  and 
thereafter  progressive,  reaching  T just  when  P does  so.  In  this 
way  the  motion  of  N along  EY  will  resemble  the  direct  and  retro- 
grade movements  in  longitude  of  the  superior  planets.  Parts  of 
the  line  of  abscissae  will  thus  be  traversed  thrice,  once  forward, 
once  backward,  and  once  forward  again  ; and  from  each  point  of 
these  parts  three  normals  may  be  drawn  to  the  curve.  Ey  properly 
adapting  the  ratio  of  enlargement  we  may  cause  the  first  stationary 
position  of  N to  be  at  T,  and  then  every  part  of  the  pitch-line  is 
traversed  thrice, — that  is  to  say,  wheels  deduced  from  such  a rack 
must  always  touch  in  three  points.  If  we  augment  the  ordinates 
in  such  a ratio  as  to  bring  the  first  stationary  position  of  X onwards 
to  U,  every  part  of  the  pitch-line  will  be  traversed  five  times,  and 
the  corresponding  wheels  will  always  touch  at  five  places.  In  this 
way,  when  the  general  character  or  equation  of  the  curve  is  deter- 
mined on,  we  can  discover  the  exact  depth  of  tooth  giving  any 
specified  odd  number  of  contacts. 

In  machinery  we  should  have  at  least  two  teeth  completely  engaged, 


358 


Proceedings  of  the  Royal  Society 

for  which  there  must  be  seven  contacts,  and  the  first  stationary  posi- 
tion of  N must  be  brought  forward  to  V,  as  is  the  case  in  fig.  8. 

The  most  convenient  process  for  tracing  the  shapes  of  wheel- 
teeth  from  such  a rack  is  to  determine  the  positions  of  the  contact 
points  corresponding  to  equidifferent  positions  of  the  wheels,  and 
to  combine  the  motion  along  the  path  with  the  proper  angular 
motion  of  a blank  disc.  In  this  way  we  obtain  very  readily  the 
outline  of  the  wheel ; this  outline,  however,  though  always  giving 
the  proper  number  of  contacts  geometrically,  is  not  always  mechani- 
cally possible ; for  low-numbered  wheels  it  is  exceedingly  convo- 
luted, as  is  seen  in  fig.  9,  which  is  that  of  a wheel  of  one  tooth, 
belonging  to  the  system  of  fig.  8.  As  the  number  of  teeth  is 
augmented,  the  convolutions  become  less,  and  at  a certain  limit, 
the  limit  of  mechanical  possibility,  they  disappear. 

Hence  arises  an  exceedingly  important  and  most  difficult  problem, 
“ To  discover  that  form  of  rack  which,  giving  a determinate  number 
of  contacts,  shall  admit  of  the  lowest  numbered  wheels.”  The  idea 
of  the  curve  of  second  sines  occurred  in  the  attempt  to  resolve  this 
problem. 

Here  the  condition  of  optimism  cannot  be  put  in  the  form  of 
maximum  or  minimum,  so  that  the  known  methods  of  analysis  are 
inapplicable,  and  we  must  have  recourse  to  successive  trials  with 
known  or  with  invented  lines,  and  after  all  we  can  only  conclude  that 
such  or  such  a curve  is  preferable  to  any  other  that  has  been  tried. 

The  simplest  line,  consisting  of  an  endless  series  of  equal  and 
symmetric  undulations,  is  the  well-known  curve  of  sines ; this 
curve,  when  used  as  the  form  for  a rack,  gives  convolutions  on  the 
outlines  of  wheels  of  considerable  size,  and  it  becomes  desirable  to 
obtain  a better  shape ; for  this  we  are  naturally  led  to  try  modifi- 
cations of  the  curve  of  sines. 

If  we  write  u for  the  absciss,  y for  the  ordinate,  and  v for  some 
variable  arc,  the  equations 

u - v + <£  sin  2 v ; y - A . 0 sin  v , 

in  which  </>  and  0 represent  two  unknown  functions,  will  give  equi- 
distant and  symmetric  undulations,  it  being  essential,  however, 
for  our  purpose  that  0 = 0 ; #0  = 0 ; <£(  — 2)  = - <p(  + 2)  and 
0(_  2)  = ~0(  + 2).  We  have  thus  an  endless  variety  of  modifi- 
cations among  which  to  make  our  trials. 


of  Edinburgh,  Session  1873-74. 


359 


On  omitting  the  term  cj>  sin  2v,  and  putting  0sin  v = sin  sin?;,  we 
obtain  the  equation 

y - A . sin  2u  , 

that  of  the  curve  of  second  sines.  The  transition  from  the  ordi- 
nary wave-line  to  this  curve  is  abrupt,  and  symbolically  of  the  same 
nature  as  the  transition  from  the  straight  line  to  the  curve  of  sines 
itself,  as  is  seen  on  comparing  the  three  equations 

y = A . u ; y = A . sin  u;  y = A . sin  sin  u ; 

but  for  the  elucidation  of  the  theory  of  wheel-teeth  we  require  a 
gradual  transition  from  the  one  kind  of  curve  to  the  other ; that  is 
to  say,  we  must  obtain  some  comprehensive  genesis  which  shall 
include  both  species  of  curve,  and  permit  of  an  imperceptible 
change  from  the  one  to  the  other. 

If  a body  vibrate  along  the  straight  line  AOB,  in  virtue  of  some 
elastic  arrangement  whereof  the 

redressing  tendency  is  propor-  ? $ 5 A 

tional  to  the  distance  from  the 

mean  point  0,  and  if,  while  it  is  1‘ 

so  vibrating,  a sheet  of  paper  be  carried  over  it  with  a uniform 

velocity  in  a direction  perpendicular  to  AOB,  the  trace  made  on 

that  sheet  is  a curve  of  sines. 

Instead  of  the  rectilineal  oscillation,  let  us  use  the  motion  of  the 
balance-wheel  of  a watch — that  is  to  say,  let  the  vibration  be  in 
the  circular  arc  AOB  ; and  while  the  abscissae,  measured  along  the 
line  BST,  are  made  proportional  to  the  times,  let  the  ordinates  be 
made  equal  to  the  sines  pp  of  the  arcs,  instead  of  to  the  arcs  Op 
themselves,  and  we  shall  have  a variety  of  the  curve  of  second  sines. 

If  the  extent  of  the  arc  be  small,  its  sinepp  hardly  differs  from 
itself,  and  the  curve  merges 
into  the  ordinary  curve  of  sines. 

When  the  length  of  the  half- 
arc OA  is  just  equal  to  the 
radius  CO  of  the  circle,  we 
obtain  the  curve  of  second 
sines  proper,  which  is  repre- 
sented in  figure  1,  the  base 
RV  being  equal  to  the  circum- 
ference of  the  circle,  whose  radius  is  CO.  As  the  extent  of 


360  Proceedings  of  the  Royal  Society 

the  oscillation  is  augmented,  the  curve  shows  its  tendency  to  flatten 
at  the  vertex  X,  and  when  the  oscillation  extends  over  the  semi- 
cumference  BAO,  the  curve,  as  shown  in  fig.  2,  becomes  quite  flat 
at  X,  the  radius  of  curvature  there  being  infinite. 

Where  OA  extends  beyond  the  quadrant,  the  ordinate  rises  to 
be  equal  to  the  radius  00,  and  then  decreases  to  reach  a minimum 
value  at  X,  after  which  it  again  rises,  and  so  produces  the  saddle 
form  seen  in  fig.  3 ; and  when  the  oscillation  extends  over  a com- 


plete turn,  the  vertex  X of  the  curve  comes  down  to  S,  as  shown 
in  fig.  4.  If  the  oscillation  extend  over  more  than  the  whole 
circumference,  the  vertex  X passes  to  the  other  side  of  the  axis,  as 
seen  in  fig.  5 ; and  when  the  extent  is  one  turn  and  a half,  the 
curve  is  again  flattened  on  the  opposite  limit,  preparatory  as  it 
were,  to  the  return  towards  S,  when  the  oscillation  is  still  farther 
extended.  Thus  this  genesis  produces  a great  variety  of  phases, 
beginning  with  the  curve  of  sines,  passing  to  the  curve  of  second 
sines,  and  continuing  in  an  endless  series  of  variations  beyond. 

As  soon  as  we  pass  beyond  the  flattened  vertex,  these  curves  lose 
all  interest  to  the  practical  mechanician,  who  can  hardly  contemplate 
the  use  of  wheel-teeth  with  hollowed  tops;  yet  to  the  speculative 
engineer  they  offer  the  attraction  of  peculiar  phases  in  the  con- 
figuration of  the  relative  contact-path,  and  in  the  convolutions  of 
the  tooth  outlines;  but  their  real  interest  is  centred  in  this,  that 
amongst  them  we  find  the  best  known  form  for  the  rack. 

When  the  arc  OA  is  three-fourth  parts  of  a quadrant,  and  when 


361 


of  Edinburgh,  Session  1873-74. 

the  curve  is  raised  to  such  a height  as  to  have  always  seven  normals 
from  a point  in  the  axis,  wheels  of  14  teeth,  developed  by  its  help, 
have  their  outlines  mechanically  complete. 

Putting  r for  the  length  of  OA,  the  half-arc  of  oscillation,  the 
equation  of  the  curve  is 

y - A . sin  (r  sin  u ), 

and  the  length  of  the  HN  subnormal  is  given  by  the  formula 

x — i A2 . cos  u . sin  (2 r sin  u),  . . (1), 

A 

which  gives,  at  the  same  time,  the  form  of  the  contact  path. 
Hence  we  have  EN,  the  length  of  the  pitch-line,  corresponding  to 
the  contact  at  P, 

EN  = a - u -f  -i  rA2 . cos  u . sin  ( 2r  sin  u),  . (2). 

2 


Hence  if  we  denote  by  U that  value  of  u which  corresponds  to 
the  extreme  position  of  the  point  N,  we  must  have 

= sin  U . sin  (2 r sin  U)  - 2r  . cos  U2 . cos  (2 r sin  U),  (3), 


and  when  the  number  of  contacts  is  to  be  n,  we  must  have  the 
corresponding  value  of  EN  equal  to  ; wherefore 


tan  (2rsinIJ) 

tanU  , tan(2rsinU)  - 2 r . cosU 


+ U = 


> + l 


(4) 


by  help  of  which  equation  we  can  determine  the  values  of  U and  A, 
corresponding  to  any  assumed  value  of  r,  and  to  any  desired  number 


of  contacts. 


For  seven  contacts,  and  when  r = 


3 


we  obtain 


A = 3*469167  and  the  maximum  value  of  y , 3-205089  ; by  help  of 
which  dimensions  fig.  8 has  been  drawn. 

If  the  point  P be  carried  along  the  saddle-shaped  curve  EX  of 
fig.  3,  the  subnormal  HN  lies  first  on  the  one  and  then  on  the 
other  side  of  the  ordinate  PH,  so  that  we  may  have  two  stationary 
positions  of  N as  Nx  and  Na,  and  these  may  be  placed  so  that  the 
part  N2  Nx  is  traversed  thrice,  as  actually  happens  in  the  figure. 
By  lessening  the  ordinates  the  whole  curve  may  be  flattened,  and 


362 


Proceedings  of  the  Royal  Society 

the  problem  arises,  “What  must  be  the  degree  of  flattening  in  order 
that  the  points  Nx  and  N2  may  coincide?”  in  which  case  no  more 
than  one  normal  can  be  drawn  to  the  curve  from  any  point  in  its 
axis. 

Again,  by  augmenting  the  ordinates,  as  in  figure  7,  the  extent 
of  the  overlap  N2  Nx  may  be  increased,  and  the  limiting  station  for 
one  quadrant  may  touch  that  for  another  quadrant  of  the  curve, 
and  thus  we  may  determine  the  character  and  height  needed  to 
ensure  that  some  specified  odd  number  of  normals,  neither  more  nor 
less,  may  be  drawn  from  any  point  assumed  in  the  axis. 

In  the  solution  of  such  a problem  we  have  to  consider  the  two 

roots  of  equation  3 below  u = ~ 7r,  and  recurring  in  each  succes- 

n 

sive  quadrant  of  the  curve.  When  r exceeds  7 r,  and  is  less  than 
3 

— 7r , there  are  three  such  roots,  as  in  fig.  5,  and  the  discussion  of 
2 

the  number  of  normals  becomes  exceedingly  involved.  The  con- 
sideration of  the  wheel  systems  deduced  from  such  curves  belongs 
to  purely  speculative  geometry. 


3.  Laboratory  Note.  By  Professor  Tait. 

On  the  Thermo-electric  Positions  of  Sodium  and  Potassium. 

Farther  experiments  with  the  apparatus  described  in  the  “Proceed- 
ings” of  2d  March  1874,  and  with  a similar  one  containing  potas- 
sium, have  led  to  the  following  values  of  the  tangent  of  the  inclina- 
tion of  the  corresponding  lines  in  the  thermo-electric  diagram.  I 
have  added  its  value  in  palladium  for  comparison — 

Na  - *00212 
K - *00066 
Pd  - *00182 

To  reduce  these  to  the  corresponding  numerical  values  of  the 
specific  heat  of  electricity,  the  factor  required  is  4xl0“8of  a 
Grove’s  cell. 

The  line  of  Na  in  the  diagram  intersects  that  of  Pb  at  about 
- 20°  C,  and  the  line  of  K intersects  that  of  Arg  about  the  same 
temperature.  By  the  help  of  these  data  they  may  easily  be  inserted 
in  my  diagram  in  vol.  xxvii.  part  i.  of  the  Transactions  R.  S.  E. 


of  Edinburgh,  Session  1873-74 


363 


4.  On  a New  Form  of  Mariner's  Compass. 
By  Sir  William  Thomson. 


Monday , 6th  April  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  following  Communications  were  read : — 

I.  Further  Note  on  Spectra  under  exceedingly  Small 
Pressures.  By  Professor  Tait  and  James  Dewar,  Esq. 

2.  On  the  After-glow  of  Cooling  Iron  at  a Dull-Red 
Heat.  By  George  Forbes,  Esq. 

The  facts  to  be  explained  were  observed  by  Messrs  Gore  and 
Barrett,  and  were  described  by  the  latter  gentleman  in  the  “ Philo- 
sophical Magazine  ” for  1873. 

The  experiments  are  performed  on  an  iron  or  steel  wire  of  no 
great  thickness.  When  this  is  heated  to  an  intense  white  heat 
and  allowed  to  cool,  the  following  facts  appear  at  the  instant  it 
has  cooled  down  to  a dull-red  heat : — 

1.  The  wire  expands  for  an  instant,  and  then  continues  its 
normal  contraction. 

2.  The  glow  from  the  wire  is  at  the  same  instant  seen  to  increase. 

3.  The  temperature  of  the  air  round  the  wire  is  at  the  same 
instant  increased. 

4.  The  same  facts  are  seen  when  the  wire  is  in  an  atmosphere 
of  hydrogen. 

5.  If  the  wire  be  very  thin  the  cooling  is  so  rapid  that  the 
effects  are  not  observed. 

6.  If  the  iron  be  massive  the  effects  are  not  observed, 

7.  If  the  wire  be  not  originally  heated  up  to  an  intense  white 
heat  the  effects  are  not  observed. 

That  iron  should  increase  its  temperature  at  a dull- red  heat 


VOL.  VIII. 


364  Proceedings  of  the  Boyal  Society 

while  it  is  cooling  from  an  intense  white  heat,  and  that  it  should 
not  do  so  when  cooling  from  a temperature  a little  over  a dull- 
red  heat,  is  a hypothesis  so  inconsistent  with  all  known  facts  as 
to  make  it  desirable  to  find  some  explanation  more  in  accordance 
with  known  principles.  Iron  is  a very  bad  conductor,  and  Professor 
Tait  has  shown  (R.  S.  E.  Proceedings,  1873)  that  the  conductivity 
is  much  worse  above  than  below  a dull-red  heat.  Now,  the  cool- 
ing of  such  an  iron  wire  as  that  used  is  effected  so  rapidly  that 
the  temperature  falls  through  an  enormous  range  of  temperature  in 
a few  seconds.  This  is  effected  by  convection  and  radiation  from 
the  surface.  It  is  quite  possible  that  the  internal  heat  cannot 
be  conducted  outwards  with  sufficient  rapidity  to  compensate 
this  outer  loss.  Thus  the  temperature  of  the  interior  of  the  wire 
is  greater  than  that  of  the  exterior.  At  very  high  temperatures 
the  rapidity  of  cooling  is  enormous.  But  as  the  cooling  proceeds, 
the  deviation  from  the  Newtonian  law  of  cooling  is  much  less. 
Hence  the  cooling  by  radiation  becomes  less,  and  the  heat  which 
has  been  stored  up  in  the  interior  of  the  wire  has  a tendency 
to  show  itself  on  the  surface.  At  a dull-red  heat  the  wire  becomes 
a better  conductor,  and  this  tendency  is  assisted,  so  that  about 
this  stage  the  temperature  throughout  the  wire  is  nearly  equalised. 
The  second  experimental  fact  is  explained  by  this  raising  of  the 
external  temperature.  The  third  fact  is  explained  in  the  same 
way.  And  it  must  be  noticed,  that  a difference  in  temperature 
between  the  interior  and  exterior  is  the  only  means  of  explaining 
the  rise  in  temperature  of  the  external  air,  unless  we  suppose  that, 
while  cooling,  the  wire  increases  in  temperature.  And  even  then 
it  would  he  difficult  to  understand  why  the  effect  is  not  produced 
by  cooling  from  a temperature  a little  above  a dull-red  heat.  If 
the  wire  be  massive,  or  if  a poker  be  used,  the  cooling  is  not  rapid 
enough  to  produce  the  effects ; apparently,  because  the  convection 
currents  are  not  nearly  so  strong  in  proportion  to  the  surface 
which  has  to  be  cooled.  Other  causes  come  into  play  in  this  case, 
all  tending  to  prevent  the  effect  from  being  apparent.  The 
explanation  I have  given  shows  why  the  effect  is  observed  only 
when  the  wire  has  been  originally  heated  to  an  intense  white 
heat ; for  it  is  only  then  that  a great  difference  of  temperature  can 
exist  between  the  interior  and  exterior. 


365 


of  Edinburgh,  Session  1873-74. 

It  only  remains  now  to  explain  the  first  experimental  fact,  i.e., 
the  expansion  of  the  wire  at  the  critical  instant.  This  follows 
from  what  has  already  been  said,  when  we  consider  certain  experi- 
ments made  by  Colonel  Clarke,  communicated  to  the  Royal  Society 
of  London  in  1863,  and  the  explanation  of  them  which  was  given  by 
Professor  Stokes.  A hollow  cylinder  of  iron  was  heated  in  a 
furnace,  and  plunged  into  water,  so  that  half  of  it  was  buried  in 
the  water,  the  axis  of  the  cylinder  being  vertical.  After  cooling, 
the  cylinder  was  found  to  be  permanently  indented  at  the  water- 
level,  so  that  its  diameter  was  there  diminished.  The  explanation 
is  as  follows  : — When  plunged  in  water  the  lower  part  immediately 
contracts  and  cools.  The  upper  part  remains  expanded.  At  this 
instant  there  is  at  the  water-line  a conflict  between  the  upper, 
hot,  expanded  portion  and  the  lower,  cool,  contracted  portion. 
Now  iron  is  much  stronger  when  cool  than  when  hot.  Hence  the 
cool  iron  has  the  advantage,  and  at  the  water-line  the  iron  is  at  first 
forcibly  shrank,  and  afterwards  cooled,  and  hence  at  that  line 
the  cylinder  is  contracted. 

Now,  exactly  the  same  thing  may  happen  in  the  cooling  wire. 
Before  cooling  down  to  the  dull-red  heat,  the  hot  inner  part  is 
expanded,  and  the  cooler  outer  part  contracted,  and  owing  to  the 
greater  strength  of  the  cooler  iron,  the  wire  is  on  the  whole  unduly 
contracted.  But  at  the  moment  of  after-glow  the  internal  heat 
is  driven  out,  and  the  contraction  is  no  longer  maintained.  Hence 
the  expansion  at  that  temperature. 

The  hypothesis  I have  now  given  explains  all  the  facts  observed ; 
but  it  cannot  be  stated  to  be  proved.  An  alternative,  and  only 
one  remains,  which  is  to  consider  that  when  iron  is  heated  to  an 
intense  white  heat  it  becomes  different  in  its  nature  from  cold  iron , 
and  that  the  iron  in  the  hot  state  has  a certain  amount  of  latent  heat , 
which  is  given  out  when , by  cooling , the  iron  changes  its  nature . 

In  the  absence  of  any  data  for  determining  between  these  two, 
I prefer  the  former  hypothesis,  as  it  does  not  involve  a new  pro- 
perty of  iron  quite  unlike  that  of  any  other  substance  yet  examined. 
The  apparently  opposite  phenomena  observed  when  the  iron  is 
massive  can  be  explained  equally  well  on  either  hypothesis.  But 
the  second  hypothesis  is  favoured  by  certain  experiments  made  by 
Professor  Barrett  while  heating  the  iron. 


366 


Proceedings  of  the  Royal  Society 


3.  On  a Form  of  Eadiation  Diagram. 

By  George  Forbes,  Esq. 

The  following  facts  appear  to  have  been  conclusively  established 
by  universal  experience  : — 

1.  Nearly  all,  if  not  all,  solid  substances  become  self-luminous  at 
the  same  temperature. 

2.  The  red  rays  are  the  first  to  become  visible,  and,  on  increasing 
the  temperature,  colours  of  less  wave-lengths  are  successively  added 
in  the  order  of  their  wave-lengths. 

3.  While  colours  of  shorter  wave-lengths  are  being  added,  those 
which  were  previously  visible  become  more  intense. 

It  appears,  then,  that  the  intensity  of  radiation  (i)  of  any  parti- 
cular colour  is  connected  with  the  temperature  0 , and  the  wave- 
length A,  by  some  equation 


» =/(*,*•)• 


No  data  at  present  exist  by  means  of  which  the  form  of  this  func- 
tion can  be  determined.  Theoretically,  however,  its  determination 
is  of  great  importance,  and  it  also  leads  to  some  practical  applica- 
tions. For  this  reason  it  is  worth  while  making  an  attempt  to 
approximate  roughly  to  a radiation  diagram,  on  which  shall  be 
drawn  curves  that  are  isothermals,  the  ordinate  of  any  point  indi- 
cating the  intensity  of  the  radiation  of  a wave-length  indicated  by 
the  abscissa,  at  the  temperature  of  the  particular  isothermal  con- 
sidered. 

The  experimental  data  for  an  exceedingly  rough  approximation 
to  such  a curve  exist.  But  difficulties  of  several  kinds  are  met 
with. 

1.  If  we  judge  the  intensity  of  radiation  by  the  eye,  as  Frauen- 
hofer  did,  we  can  only  see  a limited  portion  of  the  spectrum;  and 
if  we  use  a thermo-pile,  with  the  face  covered  with  lamp-black,  we 
have  no  proof  that  all  the  invisible  rays  are  as  thoroughly  absorbed 
as  we  know  the  visible  rays  to  be.  A thermo-pile  covered  with 
chalk  would  not  absorb  the  luminous  rays  so  intensely  as  one  coated 
with  lamp-black.  But  we  cannot  say  that  lamp-black  does  not 


of  Edinburgh,  Session  1873-74.  367 

behave  like  chalk,  in  this  respect,  to  some  of  the  invisible  rays.  In 
fact,  Melloni’s  experiments  show  that  this  is  the  case. 

2.  The  second  difficulty  is,  that  in  employing  the  eye,  a source 
of  error  is  introduced  by  the  fact  that  a certain  intensity  of  radia- 
tion is  necessary  before  a light  becomes  visible  to  the  eye.  This 
intensity  ( i ')  is  evidently  dependent  upon  the  wrave-length  (A)  of 
the  light  considered.  Hence 

i'=p(A). 

The  difference  between  i and  i\  or 

/(*,  *)“*>(*) 

gives  a third  curve, 

I = if/  (<9,  A) , 

which  shows  the  apparent  intensity  of  any  colour  in  terms  of  the 
temperature. 

In  this  paper  I wish  to  pay  attention  to  the  luminous  portion  of 
the  spectrum,  with  the  object  of  determining  the  nature  of  the 
function  <p  (A)  as  much  as  that  of  / ( 6 , A). 

I shall  enumerate  the  different  experimental  facts  which  throw 
some  light  on  the  forms  of  these  two  curves. 

1.  Mossotti  has  shown*  from  the  experiments  of  Frauenhofer 
that  the  curve  of  apparent  intensities  ( i.e .,  the  curve  if/  (0,  A)  ) is,  in 
the  case  of  sun-light,  a sinuous  line,  symmetrical  about  the  mean 
wave-length. 

2.  Draper f has  shown  that  the  radiation  from  the  parts  on  either 
side  of  the  mean  wave-length  are,  with  visible  radiations  equal. 

Thus  we  are  led  to  conclude  that  i and  i - i'  are  both  symmetrical 
about  the  wave-length  of  mean  visibility;  and  hence  i—f  or  <p  (A) 
is  also  symmetrical  about  that  line. 

3.  Dewar  J has  shown  that  several  methods  combine  to  prove  that 
the  temperature  of  the  sun  is  about  16,000°  C. 

Hence  the  isothermal  on  our  diagram,  corresponding  to  16,000° 
C.,  has  a maximum  value  of  i for  the  mean  visible  wave-length. 

* Atti  Scienz.  Ital.,  1843. 
t Pliil.  Mag.,  1872. 

f Proceedings  of  the  Royal  Society  of  Edinburgh,  1871-72. 


368  Proceedings  of  the  Royal  Society 

(Here  we  are  only  speaking  of  luminous  radiations.  But  it  is  not 
improbable  that  in  the  scale  of  wave-lengths  this  is  true  in  other 
parts.  For  refraction  by  prisms  accumulates  rays  of  different 
wave-lengths  so  much  in  the  ultra-red  part  of  the  spectrum  that 
no  experiments  exist  which  can  settle  this  point.) 

4.  At  lower  temperatures  the  apparent  maximum  is  nearer  to  the 
red,  i.e .,  the  maximum  of  the  curve  i - i'  is  nearer  to  the  red. 

But  the  curve  % is  always  a minimum  at  the  yellow.  Hence,  at 
lower  temperatures,  the  maximum  of  the  curve  i= /(0,  A)  passes  to 
the  region  of  greater  wave-lengths.  (It  has  just  been  stated  that 
the  curve  i=  <p  (A)  has  a minimum  at  the  centre  of  the  diffraction 
spectrum.  This  is  nearly  certain,  because  we  have  seen  that  the 
curve  is,  at  any  rate,  nearly  symmetrical  about  this  point,  and  it 
certainly  increases  enormously  at  the  two  limits  of  visibility  of  the 
spectrum.) 

The  only  other  remark  I have  to  make  on  the  curves  f (0,  A)  is, 
that  we  cannot  estimate  the  nature  of  the  curve  in  the  ultra- red  at 
present.  For  all  we  know,  there  may  be  radiations  of  much  greater 
wave-length  than  any  which  lamp-black,  or  any  other  substance  we 
know  of,  could  absorb. 

As  to  the  curve  of  limiting  visibility,  it  appears,  from  what  has 
already  been  said,  that  it  has  a minimum  in  the  yellow;  and  although 
fromMossotti’s  interpretation  of  Frauenhofer’s  observations,  it  would 
seem  to  be  a sinuous  line,  I do  not  think  that  the  small  variations 
there  indicated  could  be  detected  accurately  in  judging  of  the  rela- 
tive brightness  of  different  colours. 

We  can  scarcely  see  those  parts  of  the  spectrum  that  lie  be- 
yond the  lines  A and  H respectively.  The  question  arises  as  to 
whether  they  are  always  invisible.  If  this  were  so,  the  curve  of 
limiting  visibility,  which  we  have  called  <p  (A)  would,  at  those  two 
points,  be  an  ordinate  of  the  curve. 

But  I do  not  think  this  is  the  case.  So  far  as  I can  see,  the  limit 
of  the  spectrum  depends  upon  the  intensity  of  the  light.  Thus,  Mr 
Glaisher,  in  his  report  to  the  British  Association  in  1863  on  his 
balloon  ascents,  stated  that,  at  great  heights  in  the  solar  spectrum, 
he  could  “ see  H,  and  far  beyond,”  when  on  the  ground  the  line 
“ H was  quite  the  limit.” 

Again,  I remember  (although  I cannot  find  a reference),  that  Sir 


369 


of  Edinburgh,  Session  1873-74. 

David  Brewster  increased  the  limits  of  the  visible  spectrum  by 
dilating  his  pupil  with  Belladonna,  so  as  to  increase  the  amount  of 
light. 

From  all  these  considerations,  I believe  that  the  diagram  here 
given*  is  not  a bad  approximation  to  such  a radiation  diagram  as  I 
have  described,  data  for  its  accurate  determination  being  at  present 
unobtainable.  The  principal  Frauenhofer  lines  are  marked  below, 
and  the  numbers  along  the  axis  of  abscissae  represent  thirteenth- 
metres .f 

I have  drawn  particular  attention  to  what  I have  called  the  curve 
of  limiting  visibility,  because  a consideration  of  it  affords  an  explan- 
ation of  some  curious  facts  which  have,  from  time  to  time,  been 
brought  before  the  Royal  Astronomical  Society. 

Many  fellows  of  that  Society  were  puzzled  by  the  varying  colours 
of  stars,  and  of  Jupiter  particularly,  when  observed  with  different 
telescopes.  Mr  Huggins  suggested  that  the  amount  of  light,  as 
depending  upon  the  magnifying  power  and  aperture  of  the  object 
glass,  might  be  the  explanation  of  it.  Mr  Browning  tested  this, 
and  found  that  it  afforded  a complete  explanation.  Colonel  Strange 
corroborated  these  views  by  an  independent  observation. 

I have  tried,  in  a variety  of  ways,  to  produce  this  result  experi- 
mentally, and  believe  that  I have  at  length  succeeded  by  employing 
gas  light,  and  viewing  it  through  a number  of  plates  of  the  com- 
mon blue  glass  coloured  with  cobalt.  This  thickness  of  the  glass 
allows  only  blue  and  red  rays  to  pass;  the  boundaries  of  these  bright 
bands  in  the  spectrum  being  sharply  defined.  When  a piece  of 
white  paper,  illuminated  by  the  gas-flame,  is  examined  with  this 
glass,  it  appears  to  be  blue,  but  the  gas-flame  itself  appears  to  be 
red.  This  is  due  to  no  effect  of  fluorescence.  Now,  let  Ir  be  the 
intensity  of  the  red  rays  of  the  flame  as  seen  through  the  glass,  and 
I6  the  intensity  of  the  blue  rays.  Also  letLr  be  the  limiting  inten- 
sity for  visibility  in  the  red  rays,  and  L6  in  the  blue  rays.  Then, 


I,-L- (1) 

and 

I* -I* (2) 


* The  diagram  here  referred  to  is  not  reproduced.  It  will  probably  appear 
in  a text-book  on  Physics  now  in  preparation. — G.  F.,  1874,  April  20. 

+ A thirteenth-metre  = 10 — 13  x 1 metre. 


370  Proceedings  of  the  Royal  Society 

are  the  apparent  intensities  of  the  red  and  bine  parts.  But,  if  ^th 

only  of  the  light  from  the  flame  is  scattered  from  white  paper;  the 
intensities  of  the  red  and  blue  rays,  when  the  paper  is  examined, 
are 


H-L 

71 

....  (3) 

. . . . 

71 

....  (4). 

Now,  it  is  quite  possible  that  while  (1)  is  greater  than  (2),  (4) 
should  be  greater  than  (3).  Hence  the  light  seen  from  the  gas- 
flame  has,  on  the  whole,  a red  tinge,  while  that  of  the  paper  has  a 
blue  tinge,  exactly  as  is  seen  to  be  the  case. 

I hope  that  this  attempt  at  approximating  to  a better  knowledge 
of  some  theoretically  important  facts  will  be  of  some  interest  to  the 
Society,  and  that  the  meagre  nature  of  our  data  will  be  sufficient 
apology  for  the  small  advance  I have  been  able  to  make. 

4.  On  the  Semicircular  Canals  of  the  Internal  Ear. 

By  Professor  Crum  Brown. 

( Abstract .) 

The  author  had  laid  before  the  Society,  on  the  19th  January,  a 
preliminary  note  containing  an  outline  of  a theory  of  the  function 
of  the  semicircular  canals  of  the  internal  ear.  In  that  note  it  was 
stated  that  the  six  semicircular  canals  form  three  pairs — the  mem- 
bers of  each  pair  being  parallel,  and  having  their  ampullae  at 
opposite  ends.  In  this  paper  the  author  communicates  the  results 
of  measurements  of  the  position  of  the  bony  canals  in  a large 
number  of  animals. 

The  only  manner  in  which,  assuming  bilateral  symmetry,  the 
canals  can  be  arranged  in  parallel  pairs,  with  the  ampullae  at  the 
opposite  ends,  is  as  follows: — In  each  ear,  one  canal  at  right  angles 
to  the  mesial  plane,  and  the  two  others  making  equal  angles  with  the 
mesial  plane.  Calling  the  canals  of  the  one  ear  a , b , c,  and  those  of 
the  other  ear  a',  b',  c' ; a and  a',  b and  c',  c and  b'  are  the  three  pairs  ; 
a and  a'  are  coplanar,  b is  parallel  to  c'  and  c to  V . The  measure- 


371 


of  Edinburgh,  Session  1873-74. 

ments  show  that  this  is  approximately  the  case — deviations  of  10° 
from  parallelism  being  rare,  even  when,  as  is  often  the  case,  the 
three  canals  of  one  ear  are  not  at  right  angles  to  one  another. 

The  methods  employed  in  making  these  measurements  were 
explained  and  illustrated. 

[ Note  by  the  Author. — Since  presenting  to  the  Society,  on  January 
19th,  the  Preliminary  Note  on  the  Sense  of  Rotation  and  the 
Function  of  the  Semicircular  Canals  of  the  Internal  Ear,  I have  seen 
abstracts  of  papers  on  the  same  subject  by  Professor  Mach  and  by 
Dr  Breuer.  As  far  as  I can  judge  from  these  abstracts,  while  Pro- 
fessor Mach  and  Dr  Breuer  refer  the  action  of  rotation  upon  the 
ampullary  nerves  to  the  inertia  of  the  contents  of  the  canals,  they 
do  not  seem  to  have  noticed  the  parallelism  of  the  plane  of  the 
superior  canal  of  the  one  ear  to  that  of  the  posterior  canal  of  the 
other,  nor  to  have  observed  that  approximate  parallelism  of  these 
planes  is  essential,  if  the  semicircular  canals  are  the  peripheral 
organs  of  the  sense  of  rotation.] 

The  following  Gentlemen  were  admitted  Fellows  of  the 
Society : — 

R.  H.  Traquair,  M.D.,  Mus.  Science  and  Art. 

Francis  Jones,  Esq.,  Lecturer  on  Chemistry,  Manchester. 

W.  F.  Barrett,  F.O.S.,  R.  College  of  Science,  Dublin. 


Monday,  20 th  April  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  following  Commnnications  were  read : — 

1.  On  Last-Place  Errors  in  Vlacq’s  Table  of  Logarithms. 

By  Edward  Sang,  Esq. 

Now  fifty  years  ago,  while  engaged  with  some  heavy  calculations 
connected  with  engineering  work,  I became  impressed  with  the 
advantage  of  having  logarithmic  tables  much  more  extensive  than 
those  in  use.  The  trouble  of  the  interpolations  at  the  early  part 
of  the  table,  contrasted  with  the  convenience  of  the  small  addi- 

3 B 


VOL.  VIII. 


372  Proceedings  of  the  Royal  Society 

tional  part  from  100,000  to  108,000  printed  in  Hutton,  gave  rise 
to  the  idea  of  carrying  the  table  onwards  even  so  far  as  to  one 
million.  Although  the  bulk  of  such  a table  appears  to  be  an 
objection,  and  the  turning  of  so  many  leaves  a toil,  the  ease  to  the 
habitual  computer  of  finding  at  once  the  number  of  which  he  is  in 
search  is  so  great  as  far  to  outweigh  the  opposite  considerations. 
Thus,  though  working  only  to  five  places,  we  prefer  to  use  the 
extensive  seven-place  tables  rather  than  to  take  up  Lalande’s 
small  volume;  and  so,  while  working  to  seven  places,  we  should 
gladly  avail  ourselves  of  a nine-place  million  table,  the  construction 
of  which  I proposed  to  myself,  notwithstanding  the  vast  amount  of 
the  labour. 

The  first  idea  was  to  interpolate  from  tables  already  published, 
but  this  was  opposed  by  the  feeling  of  dependency  on  the  accuracy 
of  the  previous  calculations.  On  examining  the  sources  of  our 
information  on  denary  logarithms,  it  became  apparent  that  the 
original  work  of  Henry  Briggs  (1620),  carried  on  in  the  laborious 
way  indicated  to  him  by  John  Nepair  in  his  u Constructio,”  is  the 
only  foundation ; and  that  the  completion  of  the  canon  by  Adrian 
Ylacq  (1628)  was  the  last  of  the  original  labour  that  has  been 
bestowed  on  this  matter  so  essential  to  the  progress  of  exact 
knowledge. 

The  more  convenient  methods  of  calculation  developed  by  the 
progress  of  logistics  have  come,  as  it  were,  too  late  to  be  of  service. 
It  is  indeed  surprising  that,  after  the  lapse  of  two  hundred  and  fifty 
years,  we  are  still  relying  on  the  unchecked  calculations  of  Briggs 
and  Ylacq;  that  among  so  many  generations  of  scientific  men 
there  has  not  been  zeal  enough  to  effect  a revision  of  the  canon. 

Even  on  the  supposition  that  Vlacq’s  logarithms  are  true  in  the 
last  place,  the  attempt  to  interpolate  between  them  would  lead  to 
frequent  uncertainty  in  the  seventh  place.  In  order  to  form  an 
extensive  table  of  seven-place  logarithms  true  in  the  last  figure,  we 
should  have  to  carry  our  original  computations  at  least  five  steps 
farther. 

Thus  I came  to  perceive  the  necessity  of  making  the  whole 
computation  anew.  From  time  to  time  I took  up  the  work  to  lay 
it  down  in  alarm  at  its  magnitude,  for  years  of  labour  only  seemed 
to  make  a beginning ; but  about  1849  I happened  to  obtain  a copy 


373 


of  Edinburgh,  Session  1873-74. 

of  the  great  “ Table  des  Diviseurs,”  by  Burckhardt.  The  facility 
afforded  by  this  admirable  work  for  finding  convenient  formulas  of 
approximation,  determined  me  to  persevere  in  the  construction  of 
the  large  table  ; and,  putting  aside  all  my  previous  calculations,  I 
arranged  a comprehensive  scheme  for  recording  each  step  of  the 
process,  so  that  it  might  serve  as  occasion  might  arise  to  facilitate 
subsequent  steps,  and  so  that  any  suspected  error  might  be  traced 
to  its  source.  By  this  means  the  progress  of  the  work  was  effec- 
tually secured,  because  each  little  addition  took  its  proper  place,  at 
however  long  an  interval  of  time  it  might  happen  to  be  made. 

Without  going  into  the  details  of  the  procedure,  it  is  enough  to 
mention  here  that  the  logarithms  of  prime  numbers  up  to  3600, 
and  of  many  others  occurring  incidentally,  have  been  computed  to 
twenty-eight  places  with  the  view  of  being  exact  to  twenty-five, 
and  that  the  logarithms  of  all  their  products  under  10,000  have 
been  tabulated  ; and,  by  help  of  these,  tables  have  been  made  to 
fifteen  places  of  the  logarithms  of  all  numbers  from  300,000  to 
320,000,  with  their  first  and  second  differences.  These,  filling  in 
all  twenty-four  quarto  volumes,  are  laid  on  the  Society’s  table. 

Henry  Briggs  computed  to  fourteen  places  the  logarithms  of  all 
numbers  up  to  20,000,  and  of  numbers  from  90,000  to  100,000 ; so 
that  Ylacq,  in  shortening  them  to  ten  places,  was  safe  from  error 
excepting  in  one  or  two  rare  cases.  But  when  Ylacq  set  himself 
to  fill  in  the  intermediate  70,000,  he  sought  to  lessen  the  labour 
by  using  only  twelve  places,  thus  making  his  last  figure  insecure 
in  many  more  cases ; and,  moreover,  the  process  followed  by  him 
wanted  the  quality  of  self-verification.  On  these  accounts  I sus- 
pected the  occurrence  of  last-place  errors  in  Ylacq’s  part  of  the 
table.  Seeing  that  each  tenth  logarithm  of  my  own  computation 
from  200,000  to  300,000,  should  agree  with  Vlacq’s  from  20,000 
to  30,000,  the  comparison  was  made,  and  the  result  was  the  dis- 
covery of  forty-two  errors  in  this  single  myriad — an  exceedingly 
small  number  when  the  nature  of  the  process  is  considered,  but  a 
very  large  number  to  have  escaped  detection  for  two  centuries  and 
a half.  At  the  same  rate  for  each  of  the  remaining  six  myriads, 
we  may  expect  a total  of  nearly  three  hundred  errors. 

In  1658,  that  is  thirty  years  after  Ylacq,  John  Newton  published 
a translation  of  Gellibrand’s  “ Trigonometria  Britannica,”  in  which 


374 


Proceedings  of  the  Royal  Society 

he  gives  an  eight-place  table  of  logarithms  arranged  in  the  compact 
manner  now  usually  adopted.  In  the  address  to  the  reader,  he 
speaks  contemptuously  of  Adrian  as  “ Ylaq  the  Dutchman,”  11  from 
whose  corrupt  and  imperfect  copy,”  &c. ; and  in  the  introduction  he 
describes  a mode  of  computing  logarithms  which  the  innocent 
reader  may  believe  to  have  been  followed  by  the  author  of  the 
book,  but  a collation  shows  that  Ylacq’s  misprints  have  been 
slavishly  copied  by  the  indignant  Newton. 

It  was  not  until  1794  that  anything  claiming  to  be  a revision  of 
the  original  table  appeared  ; this  was  the  ten-place  table  given  by 
G-eorg  Yega  in  his  “ Thesaurus  Logarithmorum,”  the  arrangement 
being  after  the  compact  manner  introduced  by  Newton.  Yega 
gives  a long  list  of  corrections  on  Ylacq’s  table,  which  by  that 
time  had  become  scarce,  and  it  was  generally  understood  that  he 
had  at  least  taken  the  precaution  of  adding  up  Ylacq’s  differences 
in  order  to  eliminate  the  misprints.  But  on  collating  the  list  of 
errors  which  I have  just  discovered  in  Ylacq,  with  Yega’s  table, 
we  are  forced,  however  reluctantly,  to  the  conclusion  that  Ylacq’s 
identical  table  had  been  used  by  the  compositor  of  Yega’s  pages. 
A review  of  the  character  of  the  errors  will  make  this  clear ; a list 
of  them  is  subjoined,  showing  the  logarithms  true  to  fifteen  places 
(the  first  five  being  omitted),  the  last  group  as  it  should  have  been 
in  Ylacq,  Ylacq’s  corresponding  five,  and  Yega’s  last  group  of  three. 

Of  the  forty-two  errors  shown  in  Ylacq,  forty  are  last-place 
errors,  such  as  we  are  considering;  and  two,  marked  with  asterisks, 
are  misprints,  as  is  known  by  the  circumstance  that  the  adjoining 
differences  are  correct.  As  was  to  have  been  expected,  all  the 
final  errors  are  copied  by  Yega,  who  never  pretended  to  have  made 
a new  computation ; of  the  misprints  one,  a 9 for  a 6,  is 
corrected;  but  the  other,  646  instead  of  626,  is  retained.  Not 
only  so,  among  the  final  errors  there  are  six  belonging  to  numbers 
ending  in  0 ; now  these  logarithms  occur  in  the  preceding  part  of 
the  table,  where  they  are  correctly  given,  and  yet  these  also,  of 
easy  detection,  are  retained  by  Yega.  Thus,  again,  Yega  is  only 
Ylacq  in  a new  and  much  more  convenient  form. 

The  only  work  claiming  to  be  an  original  computation  of 
logarithms  is  that  done  in  the  Bureau  du  Cadastre,  at  the  instance 
of  the  French  Government.  This  unpublished  work  contains  to 


375 


of  Edinburgh,  Session  1873-74. 

nineteen  places  the  logarithms  of  numbers  from  1 to  10,000,  and  to 
fourteen  places  of  those  from  10,000  to  200,000.  In  the  year  1819 
the  House  of  Commons,  on  the  motion  of  Mr  Davies  Gilbert,  pre- 
sented an  address  to  the  Prince  Eegent,  recommending  that  our 
Government  should  join  with  that  of  France  in  the  expense  of  pub- 
lishing these  and  the  accompanying  Trigonometrical  Tables ; but 
the  negotiations  fell  through,  for  reasons  that  have  not  been  made 
public.  I have  not  learned  that  these  computations  have  been  used 
for  the  verification  of  those  already  printed,  or  that  they  have  served 
for  the  production  of  any  seven-place  table ; and  thus,  up  to  the 
present  moment,  we  have  no  verification  of  Vlacq’s  great  work. 

The  eminent  astronomer  Lalande,  in  publishing  his  little  five- 
place  table,  was  able  confidently  to  assert  that  it  does  not  contain 
a single  error,  and  although  many  thousands  of  copies  have  been  in 
use  now  for  seventy  years  no  fault  has  been  detected.  Thus  the 
production  of  a faultless  table  is  quite  within  the  range  of  pos- 
sibility ; it  is  a matter  of  time,  of  care,  of  expense ; and  with  our 
modern  appliances  the  endless  reproduction  of  the  plates  is  easy ; 
so  that  computers  ought  to  be  in  possession  of  tables  trustworthy 
throughout,  especially  of  such  tables  as  are  of  universal  application. 

Though  not  needed  for  the  every-day  work  of  the  computer, 
tables  of  excessive  precision  are  not  the  less  needed  in  special  de- 
partments, and  in  the  preparation  of  other  tables  for  ordinary  use. 
Their  extent  and  the  expense  of  preparing  them,  coupled  with  the 
smallness  of  the  number  of  those  by  whom  they  are  desired,  pre- 
cludes their  preparation  by  private  parties,  and  relegates  the 
matter  to  the  care  of  public  authorities. 

In  the  same  way  that  the  “ Nautical  Almanac,”  which  is  far 
beyond  the  reach  of  private  enterprise,  and  yet  is  needed  for  the 
advancement  of  navigation  and  astronomy,  is  undertaken  by  the 
Government,  it  would  be  right  to  carry  out  the  idea  of  Davies 
Gilbert,  and  to  confer,  by  the  publication  of  exact  tables,  a similar 
boon  upon  the  other  branches  of  science. 

It  would  be  fitting  that  this  should  be  done  by  the  British 
Government,  seeing  that  the  invention  and  completion  of  the 
logarithmic  method  belong  to  the  Island  ; and  it  would  be  not  less 
fitting  that  the  first  public  body  to  move  in  the  matter  should  be 
the  Koyal  Society  of  Edinburgh,  from  whose  place  of  meeting 


376  Proceedings  of  the  Royal  Society 

we  could  almost  have  seen  the  roof  under  which  John  Nepair 
elaborated  his  invention,  and  could  fancy  to  have  heard  the  creak- 
ing of  the  screw  with  which  Andrew  Hart  imprinted  the  “ Canon 
Mirificus 


Number. 

Log.  to  15  Places. 

To  10. 

Ylacq. 

Vega. 

20071 

90109  36054 

90109 

90110 

110 

20280 

79506  61298 

79507 

79506 

506 

20375 

76174  12014 

76174 

76175 

175 

20645 

48872  10721 

48872 

48873 

873 

20822 

24421  41256 

24421 

24422 

422 

20866 

92030  46050 

92030 

92031 

031 

21245 

67354  25533 

67354 

67355 

355 

21749 

92932  69231 

92933 

92932 

932 

21795 

68733  53703 

68734 

68735 

735 

21904 

34307  89915 

34308 

34309 

309 

22016 

84165  55417 

84166 

84167 

167 

22200 

29744  50639 

29745 

29744 

744 

22312 

85012  57993 

85013 

85012 

012 

22877 

90721  80887 

90722 

90721 

721 

22996 

22999  73937 

23000 

22999 

999 

23274 

10299  83700 

10300 

10299 

299 

23492 

99921  70919 

99922 

99923 

923 

23820 

17571  46759 

17571 

17572 

572 

24156 

50209  36279 

50209 

50210 

210 

24580 

18785  50435 

18786 

18785 

785 

25173 

49758  10852 

49758 

49759 

759 

25524 

87359  50354 

87360  ' 

87359 

359 

25586 

23955  50655 

23956 

23955 

955 

25707 

13975  50452 

13976 

13975 

975 

26004 

01573  67443 

01574 

01573 

573 

26407 

90654  45820 

90654 

90655 

655 

26517 

43886  18717 

43886 

43889* 

886 

26642 

68239  65258 

68240 

68239 

239 

26699 

49953  49034 

49953 

49954 

954 

26717 

76904  57995 

76905 

76904 

904 

26728 

64626  30075 

64626 

64646* 

646 

27291 

94494  30434 

94494 

94495 

495 

27560 

92132  35588 

92132 

92133 

133 

27586 

87318  72159 

87319 

87318 

318 

27861 

67002  67696 

67003 

67002 

002 

27921 

09686  32521 

09686 

09687 

687 

28486 

14699  52392 

14700 

14699 

699 

28680 

91469  95763 

91470 

91469 

469 

29226 

93799  55414 

93800 

93799 

799 

29446 

63077  50861 

63078 

63077 

077’ 

29639 

35467  49658 

35467 

35468 

468 

29703 

03152  31285 

03152 

03153 

153 

of  Edinburgh,  Session  1873-74. 


377 


2.  Note  on  the  Submerged  Fossil  Trees  of  Granton  Quarry. 
By  Sir  R.  Christison,  Bart.,  Hon.  Y.P.,  R.S.E. 

It  may  interest  those  who  are  acquainted  with  the  history, 
structure,  and  composition  of  the  Craigleith  fossil  trees,  described 
in  the  two  papers  recently  read  to  this  Society,  to  learn  that  an 
opportunity  has  occurred  for  examining  comparatively  specimens 
from  the  submerged  fossil  trees  of  Granton  Quarry.  The  speci- 
mens were  preserved  by  Mr  Hawkins,  engineer  of  the  Granton  har- 
bour, and  have  been,  through  his  kindness,  not  only  subjected  to 
examination,  but  also  presented  for  preservation  to  the  Botanic 
Garden  collection. 

It  turns  out  that  the  microscopic  structure  and  chemical  com- 
position of  the  greater  of  the  two  Granton  fossils  are  precisely 
the  same  with  the  structure  and  composition  of  the  fossils  of 
Craigleith,  two  miles  distant.  The  embedding  rock  is  also  the 
same  in  composition,  whether  in  its  pure  state,  or  where  altered  by 
percolating  water.  That  is,  the  microscopic  structure  of  the 
Granton  fossils  appears  to  be  that  of  the  pine  tribe;  and  the 
fossilising  material  consists  of  the  carbonates  of  lime,  magnesia, 
and  iron,  all  in  notable  proportion;  and  while  the  fundamental  rock 
of  the  quarry  is  a very  pure  quartzy  sandstone,  without  any  binding 
calcareous  carbonate,  many  masses  may  be  seen  among  the  blocks 
raised  many  years  ago  from  the  quarry,  but  not  made  use  of,  which 
like  similar  altered  specimens  from  Craigleith,  have  their  fracture, 
colour,  and  toughness  changed  by  the  same  material  which  has 
fossilised  the  trees.  In  the  fossils,  too,  there  is  the  same  three 
or  four  per  cent,  of  charcoal  left  after  the  solvent  action  of  acids 
on  the  fossils  of  Granton  as  on  those  of  Craigleith. 

That  part  of  Mr  Witham’s  fossil  of  1830  which  lay  in  front 
of  the  Museum  of  Science  and  Art,  has  now  been  removed  to  the 
Botanic  Garden,  to  be  added  to  the  lower  part  of  the  trunk  of 
which  it  is  the  continuation.  In  separating  two  of  the  segments, 
a cavity  was  found  which  contained  a matter  like  charcoal,  some 
fragments  of  which  even  presented  the  fibrous  appearance  of 
charcoal  to  the  naked  eye;  and  Mr  Sadler,  of  the  Botanic  Garden, 
has  ascertained  that  some  of  these  fragments  show  before  the 


378  Proceedings  of  the  Royal  Society 

microscope  the  characteristic  punctated  structure  of  the  vertical 
section  of  the  pine  family.  This,  I believe,  is  the  first  time 
that  this  particular  part  of  the  pinaceous  structure  has  been 
observed  in  any  of  these  fossils. 

It  may  be  farther  noticed  that  there  are  now  in  the  Botanic 
Garden  Museum  two  great  polished  slabs,  nearly  three  feet  in 
diameter,  from  the  Craigleith  fossil  last  discovered, — one  of  which 
shows  in  many  places  to  the  naked  eye  the  annual  layers  of  wood 
concentrically  ; and  that  in  breaking  up  a large  mass  of  the  same 
fossil,  in  the  hope  of  discovering  a deposit  of  charcoal  in  a cavity, 
several  fine  fractures  were  obtained,  showing  distinctly  to  the 
naked  eye  large  surfaces  of  the  ribbon-like  structure  of  the 
transverse  medullary  rays,  and  one  surface  presenting  to  the  naked 
eye  not  only  these  markings,  but  likewise  the  annual  layers  cut 
vertically. 


3.  Mote  on  G-rouse  Disease.  By  Professor  Maclagan. 

The  result  of  the  author’s  examination  of  diseased  birds  has 
been  to  confirm  the  statements  of  Drs  Cobbold  and  Crisp,  lately 
published  in  the  “British  Medical  Journal,”  that  diseased  grouse, 
or  at  least  the  emaciated  birds  commonly  known  as  “ piners,” 
owe  their  depraved  condition  to  a small  thread-like  worm  ( Strongylus 
pergracilis , Cobbold)  which  infests  the  caeca.  The  author  concurs 
in  the  opinion  entertained  by  most  of  those  who  have  written  on 
the  subject,  that  the  tape-worm  ( Tcenia  calva ),  which  is  well  known 
to  infest  the  grouse,  is  not  the  cause  of  the  disease.  The  Tcenia 
is  undoubtedly  often  present  along  with  the  Strongylus  in  diseased 
birds,  but  is  often  found  by  itself  in  plump  healthy  grouse.  The 
worst  cases  seem  to  be  those  in  which  both  are  present  in  quantity, 
as  in  one  examined  by  the  author,  whose  ca3ca  was  crowded  with 
Strongyli,  whilst  the  intestine  contained  ten  tape-worms,  the  whole 
weight  of  the  bird,  a full-grown  cock,  being  only  15J  ounces. 
It  is  not  possible  accurately  to  determine  the  number  of  Strongyli 
in  any  one  case,  but,  so  far  as  it  could  be  determined,  it  appeared 
that  the  more  numerous  were  the  Strongyli  in  any  one  bird,  the 
greater  was  its  emaciation.  By  a rough  but  moderate  calculation 


of  Edinburgh,  Session  1873-74.  379 

the  author  was  led  to  estimate  the  number  of  these  worms  in  one 
of  his  birds  as  at  least  4800. 

There  is,  however,  no  definite  line  between  birds  with  and  those 
without  this  disease,  for  almost  every  grouse  is  the  “ host  ” of 
fewer  or  more  of  the  parasites.  Of  eleven  birds  carefully  examined 
by  the  author,  with  the  aid  of  Mr  Stirling  of  the  University 
Anatomical  Museum,  in  one  only,  a fine  Irish  cock  weighing 
one  pound  eleven  ounces,  were  none  detected.  The  other  birds 
examined  were  from  various  localities  : those  containing  the  fewest 
worms,  and  of  the  heaviest  weight,  were  from  Ireland  and  Orkney ; 
those  from  Lanarkshire,  East  Perthshire,  and  Sutherland  were  the 
most  affected  by  the  worm  and  most  emaciated. 

So  far  the  author  concurs  with  the  writers  named  above,  that  one 
form  of  grouse  disease  is  this  helminthiasis,  due  to  the  Strongylus , 
which  destroys  the  birds  by  ultimately  annulling  the  functions 
of  the  caeca,  in  which  the  real  digestion  of  the  birds’  food  goes 
on.  The  mucous  membrane  is  not  inflamed,  but  irritated,  throw- 
ing off  great  quantities  of  large  columnar  epithelium,  and  instead 
of  true  feeculent  matter,  or  remains  of  food,  the  intestines  and 
caeca  usually  contain  only  a pinkish  grey  mucus.  The  caeca, 
however,  seem  occasionally  to  be  softer  and  more  easily  torn  than 
is  natural.  In  none  of  these  birds  was  any  other  morbid  appear- 
ance found  capable  of  accounting  for  their  morbid  state. 

It  is  not  yet  clear  to  the  author,  however,  that  this  helminthiasis 
is  the  disease  which  has  so  often  swept  the  moors  of  Scotland 
and  England.  It  is  quite  possible  it  may  be  so,  and  there  is 
nothing  in  its  rapid  spread  on  particular  moors  in  certain  seasons 
to  prevent  its  being  due  to  parasites;  but  the  author  thinks  that 
further  inquiry  is  desirable,  and,  speaking  as  a sportsman,  would 
suggest  to  the  proprietors  and  tenants  of  moors,  which  are  now 
so  valuable  as  to  be  a subject  of  national  importance,  to  raise 
by  subscription  a sufficient  fund  to  enable  them  to  commission 
some  competent  naturalist  to  work  out  the  subject.  The  genesis 
of  the  worms,  both  Strongyli  and  Taeniae , in  a scientific  point  of 
view,  irrespective  of  the  hope  of  some  practical  conclusion,  appears 
to  be  worth  the  expenditure  of  some  money. 


3 c 


VOL.  VIII. 


380 


Proceedings  of  the  Royal  Society 


4.  Latent  Heat  of  Mercury  Vapour. 
By  James  Dewar,  Esq. 


5.  Notes  by  James  Dewar,  Esq.  (1.)  Problems  of  Dissoci- 
ation; (2.)  Formation  of  Allotropie  Sulphur;  (3.)  Heat 
of  Fermentation. 

6.  Further  Note  on  Continuants.  By  Thomas  Muir,  M.A., 
F.R.S.E.,  Assistant  to  the  Professor  of  Mathematics  in 
Glasgow  University. 


In  my  paper  on  Continuants,  recently  communicated  to  the  Royal 
Society,  it  was  shown  that  the  order  of  a continuant  may  he  de- 
pressed if  the  first  element  of  the  main  diagonal  be  unity,  viz., 
thus 


/ b,  b2  b3  \ / 

Kll  aj  a2  a.A  . . . j = K l ax  + bx 

and  from  the  definition  it  is  evident  that 


K 


(mbl  b3  \ / 

max  a.2  aA  . . . ) = m K ( ax  < 


by  b2 
a , a .. 


Hence  we  have 

( + »,)&,  (b2  + a2)b3  \ 

K \1  ax  a%  a3 J 

f + {b2  + a2)b3  \ 

'=  K \bx  + a,  a2  «3 J 

( t>3  (b2  + a2)b3  \ 

7 (Pi  + «i)K\l  az  .... ) 

= (bl  4-  aA)  (Z>2  + «2)  (&a  + a8) 


) 


From  this  it  is  clear  that,  in  virtue  of  the  relation  which  has 
given  rise  to  the  name  “ continuant,”  continued  fractions  of  a 
certain  class  may  he  transformed  into  simple  fractions,  with  con- 
tinued products  for  numerator  and  denominator. 


of  Edinburgh , Session  1873-74. 


381 


A general  theorem  on  this  transformation  is  given  by  Stern  in 
u Crelle’s  Journal,”  vol.  x.  (1833),  p.  267  ; and  by  a quite  similar 
method  several  allied  identities  have  been  reproduced  in  a paper 
recently  read  before  the  Mathematical  Society  of  London.  All  of 
them,  however,  may  be  established  much  more  easily  by  means  of 
the  above  results.  Thus — 


1 + 


dl 


(d.2  ~ e8)  dxex 
dft^  — e4e2  — 


(di  ~ ex)  (d,6  - e3)  d,2  ea 


df  , ~ e,2e6 


(d.2  - ea)  (d4  — e4)  dzeit 
d.d,  - e e, — ,, 


/ dl  — ey  — ( d2  — &^)dy&y  — (dy  — ey)  ( d3  — e3)  d2e2 

K \1  dyd.2  e-yG,.2  d.2dz  e263 


- {d2  — 62)  d\Cy 


— (^1  (^8  ^3)  ^2^2 


K (e*  dyd^  - cxe2  cZ2e3  - e2e3 

_ . d2  {d1  - et)  . ^ (d2  - e2)  . . . . . 

. e2  (c?!  - ei)  . e3  (rf8  - e.2) 

_ dyd2ds  .... 

eie2e3  • • • • 


which  is  the  general  result  obtained  by  Stern,  and  which  probably 
includes  all  the  others. 

I am  indebted  to  Professor  Cayley  for  the  remark  that  any  con- 
tinuant may  be  expressed  by  means  of  a simple  continuant.  Thus 
dividing  the  second  column  by  the  first  constituent  of  it  which  is 
not  zero,  and  then  multiplying  the  third  row  by  the  same,  and  so 
on  through  the  remaining  columns  and  rows  in  succession,  we  have 


ox  by  0 0 0 

- 1 a2  h.2  0 0 

0-1  a3  b3  0 
0 0-1  a4  b4 

0 0 0 - 1 ab 


oj  1 0 0 0 

-1  4*  0 0 

0 -1  a ir  1 0 

0 0-1  ad)ydi *  1 


x bjbA 


0 0 0 -1 


bybz 

'Jzb2bi 


382 


Proceedings  of  the  Royal  Society 


And  so  generally 

( \ \ \ 

K \eq  a2  a6. . . . anJ 


= K 


/ 1 bx  _&2_ 

\^1  » a2^  5 «3&2  5 <liblb3  > ai 


Ms 

5M 


...X-ibn^ 


• ■•K-X 


To  this  may  be  added  the  following  as  being  derived  in  similar 
fashion  : — 


K l a2x  1,  a.x  , a3x  , ajc  ....  anx ^ ^ / = K (eq  , a2 , a3  ...  an) 

if  n be  even,  and 

= K (eq , a2 , a3  ...  a^)x  ~ i 

if  n be  odd. 

The  simple  continuant  I have  found  to  be  identical  with  Euler’s 
11  Novus  Algorithmus .”  An  examination  of  his  paper  with  this 
title  will  at  once  make  evident  the  advantages  of  the  new  mode  of 
considering  the  function. 


Monday,  4 th  May  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Communications  were  read : — 

1.  On  the  Formation  of  Allotropic  Sulphur. 

By  James  Dewar,  Esq. 

2.  On  Some  Compounds  of  Dimethyl-Thetine.  By  Professor 
Crum  Brown  and  Dr  E.  A.  Letts. 

( Abstract .) 

In  this  paper  the  authors  describe  in  detail  compounds  of 
dimethyl-thetine,  some  of  which  were  enumerated  in  an  earlier 
communication.  Hydrobromate  of  dimethyl-thetine  is  readily 
obtained  as  a colourless  crystalline  body  by  the  action  of  sulphide 
of  methyl  on  bromacetic  acid  at  ordinary  temperatures.  Its  analysis 
shows  that  it  contains  quantities  of  the  different  elements  agree- 


383 


of  Edinburgh,  Session  1873-74. 

ing  with  the  formula  C^IhSCXj,  and  its  mode  of  formation  and 
reaction  lead  to  the  constitutional  formula  — 


(CII3)2 


Br— S— CH  — C00I1  . 


The  result  of  its  analysis  are  as  follows  : — 


Calculated. 


Obtained. 


C4 

= 48  ... 

....  23-9 

23-7  ... 

...  231 

H9 

=--  9 ... 

....  45 

4-5  ... 

...  4-8 

0a 

= 32  .. 

....  15*9 

— ... 

...  — 

s 

32  .. 

....  15-9 

— ... 

...  16-1 

B4 

80  .. 

....  39-8 

40-0  ... 

...  39-7 

201 

100-0 

It  is  a very  deliquescent  body,  and  has  a powerful  acid  reaction. 

Dimethyl-thetine. — The  base,  of  which  the  body  just  described  is 
the  hydrobromate,  is  obtained  from  the  latter  by  the  action  of  oxide 
of  silver.  It  may  also  be  prepared  from  the  sulphate  of  dimethyl- 
thetine  by  treatment  with  carbonate  of  baryta.  It  is  a very  deli- 
quescent crystalline  body,  containing  one  molecule  of  water  of 
crystallisation,  which  it  loses  if  exposed  for  several  days  over  sul- 
phuric acid  in  vacuo. 

The  numbers  calculated  for  the  formula 


c4h8so2Jh.2o  = 


(CH3)2 

II 

S— CH  — CO , H20 


agree  with  those  obtained  by  experiment,  thus — 


Calculated  in  100. 

Obtained. 

c 

N 

.34-7 

34-0  33-9 

H 

. 7*2 

7*3  7-3 

h2o 

. 13*0 

18-0  — 

Hydrochlorate  of  dimethyl-thetine. — This  body  may  be  obtained 
either  by  saturating  a solution  of  the  base  with  hydrochloric  acid, 
or  by  means  of  double  decomposition  between  the  sulphate  of 


384 


Proceedings  of  the  Royal  Society 

dimethyl-thetine  and  chloride  of  barium.  It  is  a crystalline  sub- 
stance of  strong  acid  reaction. 

The  formula 

(CH3)2 

C4H9C1S02  = II 

01— S— CH— COOH 

was  verified  by  a chlorine  determination. 

Calculated  in  100.  Obtained. 

"~cT 22*7  23-4 

Chloroplatinate  of  dimetliyl-thetine  is  obtained  in  beautiful  light 
orange-coloured  crystals  when  solutions  of  the  bydrocblorate  and 
chloride  of  platinum  are  mixed.  This  salt  contains  two  molecules 
of  water  of  crystallisation,  and  has  the  formula 

2(C4H9ClS0a),PtCl4,2HJJ0. 

The  salt  was  analysed  by  determination  of  water  and  platinum — 
Calculated  in  100.  Obtained  in  100. 

Pt  = 28-6  ' '28-5  28-r 

H20  = 5-2  5-4  — 

Bromaurate  of  dimethyl-thetine  was  obtained  by  mixing  alcoholic 
solutions  of  hydrobromate  of  methyl-thetine  and  bromide  of  gold. 
The  analysis  shows  too  small  a quantity  of  gold  for  the  normal 
bromaurate,  but  agrees  with  the  amount  required  for  a salt  crystal- 
lising with  three  molecules  of  alcohol.  This  compound  has  not  been 
more  particularly  examined. 

Sulphate  of  dimethyl-thetine  was  prepared  by  the  action  of  sul- 
phate of  silver  on  hydrobromate  of  dimethyl-thetine.  It  can  be 
obtained  in  large  crystals,  which  are  not  deliquescent.  It  was 
analysed  by  a sulphuric  acid  determination. 

(CHa)2 

.S— CH—  COOH 

S04<^  requires  28  4 per  cent.  SO, 

XS — CH2 — COOH 

II 

(CH3)2 

whereas  28-2  per  cent,  and  28’0  per  cent,  were  obtained  by  experi- 
ment. 


385 


of  Edinburgh,  Session  1873-74. 


Nitrate  of  dimethyl-thetine , prepared  by  treating  the  hydro- 
bromate  with  nitrate  of  silver,  is  a transparent  crystalline  sub- 
stance. 

The  formula 


C4H9(N03)S02= 


(CH3)2 

N 03— S— CHa— COOH 


was  verified  by  an  organic  analysis — 


Calculated. 


C 26‘2 

H 4-9 


Obtained. 

26-4 

4*9 


Double  Salt  of  dimetliyl-tlietine  and  bromide  of  lead. — A boil- 
ing solution  of  hydrobromate  of  dimethyl-thetine  dissolves  car- 
bonate of  lead  with  evolution  of  carbonic  acid,  and  on  cooling 
deposits  beautiful  silvery  scales. 

The  formula  of  this  body  is 

C4H8S02 , 2PbBr2 

Calculated.  Obtained. 


0 

...  5-6 

5-7  ... 

...  5-7 

H ... 

...  *9 

•9  ... 

...  -9 

Br  ... 

...  37-0 

37-0  ... 

...  37 *5 

Pb  ... 

...  48-4 

48-4  ... 

...  48*5 

. In  addition  to  these  compounds,  a very  beautiful  salt  was 
obtained  by  the  action  of  hydriodic  acid  on  the  base,  or  by  double 
decomposition  between  iodide  of  barium  and  sulphate  of  dimethyl- 
thetine.  In  appearance  it  resembles  permanganate  of  potash,  and  is 
a poly-iodide;  but  its  examination  is  not  as  yet  completed. 

Hydrobromate  of  diethyl-thetine  was  prepared  in  a similar  manner 
to  the  corresponding  dimethyl  compound,  which  it  resembles ; 
it  is  so  deliquescent,  however,  as  to  render  its  analysis  almost 
impossible.  It  gives  beautiful  orange-coloured  salts  with  bichloride 
of  platinum. 


386 


Proceedings  of  the  Royal  Society 

In  the  course  of  these  experiments  the  action  of  iodacetic  ether 
upon  sulphide  of  methyl  was  studied.  The  reaction  here  takes  a 
different  course,  iodide  of  trimethyl-sulphine  being  produced  in 
large  quantity. 


3.  On  a New  Example  of  the  Opheliidse  (Linotrypane 
apogon )*  from  Shetland.  By  W.  C.  M£Intosh. 

This  peculiar  iridescent  pinkish  Annelid  was  dredged  in  1871 
in  Bressay  Sound,  in  four  or  five  fathoms,  on  a bottom  of  coarse 
sand  and  gravel,  which  abounded  with  finely-branched  Melobesia 
calcarea,  Ell.  and  Soland. 

The  form  resembled  an  active  nematoid  worm,  being  elongated, 
nearly  cylindrical  throughout  the  greater  part  of  its  length,  and 
devoid  of  bristles  or  lateral  projections.  It  progressed  in  the  most 
vigorous  and  spasmodic  manner,  by  twisting  or  thrusting  itself 
through  the  sand,  after  the  mode  of  Ammotrypane,  or  a most  rapid 
eel-like  fish.  Moreover,  the  slightest  interference  caused  it  to 
break  in  pieces,  so  that  not  a single  specimen  out  of  the  whole 
series  remains  entire,  though  every  precaution  was  taken  to  im- 
merse the  animals  in  spirit  on  removal  from  the  dredge.  The 
activity  and  purpose  displayed  by  the  species  are  diagnostic  when 
compared  even  with  the  most  nimble  of  the  nematoid  group,  so 
that  no  difficulty  is  experienced  in  distinguishing  it. 

The  Annelid  reaches  the  length  of  three  or  four  inches,  and  is 
only  about  a millimetre  (^th  inch)  in  diameter.  The  body  is 
rounded,  slightly  tapered  in  front,  where  the  pinkish  colour  is  best 
marked,  and  richly  iridescent,  even  to  a greater  degree  than  either 
Ammotrypane  or  Ophelia.  The  head  terminates  in  a rounded  ante- 
rior border,  from  which  two  short  clavate  processes  project.  The 
latter  have  a very  thin  investment  of  the  hyaline  cuticle,  with  a thick 
layer  of  granular  cells  (hypoderm) beneath.  Some  longitudinal  fibres 
occur  at  the  base,  but  the  contractility  of  the  organs  is  limited. 
Two  eyes,  consisting  of  encapsulated  masses  of  black  pigment,  are 
situated  near  the  dorsal  surface  of  the  tissues  of  the  snout. 


* Xivev,  a thread,  and  r^vrdvyi ; the  specific  name  from  u-Truyuv,  beardless 


387 


of  Edinburgh , Session  1873-74. 

Body-wall. — The  external  investment  is  a translucent,  perfectly 
smooth,  glistening  cuticle,  very  thin  on  the  snout,  cephalic  pro- 
cesses and  the  anterior  region,  but  of  considerable  thickness  and 
great  tenacity  throughout  the  rest  of  the  body.  It  is  this  layer 
which  enables  such  forms  to  bear  much  strain  in  a longitudinal 
direction,  and,  by  its  great  elasticity,  to  dispense  with  a special 
circular  layer  of  muscular  fibres.  In  some  of  the  Nemerteans,  for 
instance,  where  the  cutaneous  tissues  are  soft  and  easily  injured,  a 
very  perfect  circular  muscular  coat  occurs  next  the  basement- 
membrane  of  the  latter,  and  exterior  to  the  longitudinal  layer. 
When  a single  layer  of  this  hyaline  cuticle  is  examined,  after 
mounting  in  chloride  of  calcium,  a number  of  puncta,  arranged  with 
greater  or  less  regularity,  and  apparently  passing  quite  through  it, 
are  found.  By  tearing  with  needles,  or  examination  in  simple 
water,  it  is  further  seen  to  be  composed  of  a closely  interwoven 
series  of  very  fine  fibres,  many  of  which  have  a crossed-spiral,  or 
oblique  direction.  This  is  a common  arrangement  in  such  irides- 
cent forms.  The  cuticle  readily  separates  from  the  subjacent 
layers  in  the  preparations,  a feature  less  evident  in  Ammotrypane 
and  Ophelia.  Beneath  the  foregoing  is  a cellulo-granular  layer 
(hypoderm),  which  in  transverse  sections  preserves  a nearly  uniform 
thickness,  except  inferiorly,  where  the  nerve-cords  occur.  The  cells 
vary  in  size,  are  filled  with  granules,  and  embedded  in  a hyaline 
intercellular  substance.  Many  granules  also  exist  amongst  the 
cells.  In  the  cephalic  region  a considerable  thickening  of  the 
coat  takes  place,  especially  inferiorly,  and  this  enlargement  coin- 
cides with  the  diminution  of  the  hyaline  cuticular  layer  formerly 
mentioned.  A boundary  or  basement-layer  occurs  on  the  inner 
surface. 

Within  is  a great  longitudinal  muscular  coat,  which  (besides 
the  passage  of  the  oblique  muscular  fibres)  is  interrupted  at  two 
points  in  its  circumference,  viz.,  at  the  median  line  of  the  dorsum, 
and  the  opposite  point  inferiorly.  The  former  is  but  a faint  sepa- 
ration, caused  by  the  suspensory  fibres  of  the  alimentary  region ; 
the  latter  is  a boldly-marked  hiatus — the  inferior  fibres  of  the 
alimentary  canal,  the  oblique  muscular  bands  of  the  body-wall,  and 
the  ventral  blood-vessel  meeting  at  this  point.  In  ordinary  trans- 
verse sections  this  coat  presents  a somewhat  wavy,  radiated  appear- 

3 n 


VOL.  VIII. 


388  Proceedings  of  the  Royal  Society 

ance,  from  the.  arrangement  of  the  fasciculi.  In  stating  that  the 
direction  of  the  muscular  fibres  in  such  sections  is  radiated,  some 
explanation  is  perhaps  necessary,  for,  while  the  fasciculi  of  the 
dorsal  and  lateral  regions  point  more  or  less  in  this  way,  the  arrange- 
ment at  the  raphe  is  different,  since  the  oblique  bands,  passing 
down  at  an  acute  angle,  direct,  in  the  contracted  state,  the  fasci- 
culi upwards  and  outwards.  They  gradually  become  vertical,  and 
then  slant  in  the  opposite  direction,  before  leaving  what  may  be 
termed  the  ventral  region.  A firm  band,  apparently  of  the  limit- 
ing membrane  of  the  hypoderm,  proceeds  from  angle  to  angle  at 
the  raphe. 

From  this  coat,  at  somewhat  regular  intervals,  pass  a series  of 
muscular  bridles,  each  forming  a kind  of  diaphragm  (dissepiment). 
Most  of  the  fibres  have  a vertical  direction.  The  same  arrange- 
ment is  observed  in  the  Nemerteans  and  in  most  of  the  Annelida. 
Such  bundles,  of  course,  are  altogether  independent  of  the  charac- 
teristic oblique  bands  of  muscular  fibres  which  pass  from  the 
lateral  dorsal  region  on  each  side  to  the  raphe  at  the  ventral  edge. 
Anteriorly  the  latter  bands  form,  in  contraction,  a curve  on  each 
side,  with  the  convexity  directed  inwards,  and  they  enclose  a some- 
what elliptical  portion  of  the  great  longitudinal  layer,  writh  a few 
cells  and  granules.  The  oblique  bands  spring  from  the  basement- 
membrane,  and  thus  pass  through  the  longitudinal  layer, — an 
arrangement  very  well  seen  in  front,  where  the  bands  are  of  great 
thickness.  Posteriorly  the  comparative  slenderness  of  the  oblique 
muscles  makes  this  subdivision  of  the  longitudinal  layer  indistinct, 
but  it  is  nevertheless  present.  In  this  region,  also,  the  distance 
between  the  middle  of  the  oblique  band  and  the  longitudinal  coat 
is  considerable,  the  space  being  filled  with  cellular  tissue  and  a 
few  fibres. 

It  will  thus  be  observed  that  the  animal  has  a very  complete 
muscular  system,  relatively  of  great  power,  for  the  execution  of  its 
remarkable  boring  propensities  in  sand  and  gravel. 

Digestive  System. — The  mouth  opens  in  the  preparations  on  the 
ventral  surface,  a short  distance  behind  the  tip  of  the  snout,  and 
has  prominent  lips.  It  leads  into  a richly  ciliated  digestive 
chamber,  which  runs  to  the  posterior  end  of  the  body.  No  dental 
organs  of  any  kind  exist,  the  food  apparently  consisting  of  sand 


of  Edinburgh,  Session  1873-74. 


389 


or  sandy  mud,  requiring  nothing  more  than  simple  engulfment. 
Anteriorly,  what  may  he  termed  the  oesophageal  division  of  the 
canal  has  internally  a well-defined  margin,  covered  with  closely-set 
cilia,  the  wall  consisting  of  the  usual  granular  gland-cells,  em- 
bedded in  a hyaline  stroma,  with  muscular  fibres.  Posteriorly,  it 
is  more  opaque  and  granular,  and  appears  to  end  in  an  anus  without 
processes.  All  the  specimens,  however,  were  imperfect.  The 
organ  is  thrown  into  innumerable  rugae  internally  ; while  externally 
it  is  kept  in  position  by  the  dorsal  and  ventral  fibres  formerly 
noted,  as  well  as  by  the  dissepiments.  The  broad  inferior  fibres 
pass  to  the  transverse  band  at  the  raphe,  and  a few  even  extend  in 
some  sections  to  the  exterior  border  of  the  cellular  coat  in  this 
region,  at  the  nerve-cords. 

Nervous  System. — It  is  somewhat  difficult  to  make  out  the 
arrangement  of  the  cephalic  ganglia  in  the  specimens ; but  they 
are  situated  in  the  snout,  near  the  eyes,  and  form  two  slightly  tinted 
masses,  terminating  on  each  side  in  a buccal  cord,  which  passes 
downwards  to  the  ventral  surface,  and  extends  along  the  body 
beneath  the  transverse  band  of  the  raphe.  The  cords  are  larger  in 
front,  and  somewhat  farther  apart,  but  throughout  the  rest  of  the 
body  are  closely  approximated.  The  usual  granular  sheath  sur- 
rounds them,  and  they  are  also  protected  by  part  of  the  cellular 
coat  inferiorly. 

In  comparing  the  foregoing  form  with  the  representatives  of  the 
Opheliidce  at  present  described,  it  is  at  once  distinguished  by  the 
absence  of  bristles.  In  Ammotrypane  the  united  nerve-cords  are 
situated  at  the  ventral  edge  of  the  T-shaped  prolongation  of  the 
body-wall  inferiorly,  and  have  a muscular  column  between  them 
and  the  perivisceral  cavity.  In  Ophelia  the  nerve-cord  lies  within 
the  great  longitudinal  muscular  cord,  at  the  junction  of  the  ventral 
prolongations  (in  transverse  sections).  The  body-wall  differs  in 
the  relative  thickness  of  the  several  layers,  and  especially  in  the 
great  bulk  of  the  cellular  coat  in  the  new  form.  One  of  its  nearest 
allies  seems  to  be  a new  Ammotrypane  dredged  in  Valentia  harbour 
by  Dr  Gwyn  Jeffreys,  which  shows  a very  minute  trace  of  bristles, 
though  the  form  of  the  body  closely  agrees  with  the  Ammotrypane 
aulogaster  of  H.  Bathke.  In  the  Irish  species,  however,  the  united 
nerve-cords  lie  between  the  ventral  ends  of  the  powerfully- 


390  Proceedings  of  the  Royal  Society 

developed  oblique  muscular  bands  which  separate  the  longitudinal 
coat  in  the  median  line  inferiorly. 

The  occurrence  of  an  Annelid  proper  devoid  of  bristles  is  an 
interesting  fact ; for,  though  such  organs  are  feebly  developed  in 
Tomopteris , they  have  been  considered  on  the  whole  so  universal, 
that,  for  example,  the  two  great  divisions  Polychseta  and  Oligo- 
cheeta  rest  thereon.  The  new  form  likewise  shows  no  trace 
of  segmentation  externally,  in  this  respect  agreeing  with  the 
Nemerteans,  yet  in  structure  it  is  truly  an  Annelid  proper.  It  is 
difficult  to  assign  its  exact  position  at  present,  and  the  association 
with  the  Opheliidm  may  be  regarded  as  provisional. 


4.  The  following  concluding  Kemarks  were  made  by  Mr 
D.  Milne  Home,  who  occupied  the  Chair  in  room  of  the 
President : — 

I.  I have  been  requested  by  our  Secretary  to  announce  formally 
from  the  Council,  that  this  is  the  last  meeting  for  the  Winter 
Session. 

You  will  have  seen  from  the  billet,  that  our  President,  Sir 
William  Thomson,  was  to  have  been  in  the  chair  to-night,  and 
to  have  closed  the  session  with  some  remarks  suitable  to  the  occa- 
sion. 

The  Council  are  much  disappointed,  and  no  doubt  you  also  are; 
but  I am  more  distressed  than  any  one  at  Sir  William  Thomson’s 
absence.  There  is  a letter  from  him  to  the  Secretary,  dated  on 
Friday  last,  mentioning  that  he  could  not  attend  this  evening,  as 
he  expected  to  be  in  his  yacht  to-day  in  the  Bay  of  Biscay. 

The  Council,  therefore,  had  no  alternative  but  to  appoint  me,  as 
the  only  Vice-President  at  hand,  to  occupy  the  chair  to-night.  The 
occupation  of  the  chair  is  unaccompanied  by  any  difficulty,— but  the 
other  duty,  of  offering  concluding  remarks  worthy  of  your  accept- 
ance, I find  it  simply  impossible  to  perform.  I am  sure  you  will 
neither  expect  it,  nor  wish  me  to  attempt  it. 

Such  remarks,  therefore,  as  I shall  offer,  will  be  matter  of  mere 
form,  and  will  not  contain  thoughts  or  suggestions,  or  information 
of  any  scientific  value. 


of  Edinburgh,  Session  1873-74.  391 

II.  I must,  however,  detain  you  for  a few  moments  in  adverting 
to  our  proceedings  during  the  past  winter. 

1.  I think  from  my  recollection  of  the  papers  which  have  come 
before  our  meetings,  that  we  have  attended  to  most  of  the  objects 
for  which  our  Society  was  established. 

We  have  had  papers  on  the  various  physical  sciences — Che- 
mistry, Natural  Philosophy,  Geology,  Botany,  Mathematics,  Ana- 
tomy, and  Zoology.  But  besides  science,  our  Society  was  intended 
for  the  encouragement  of  Literature ; and  I regret  to  say,  that  I do 
not  remember  any  paper  read  this  winter  of  a literary  character. 

At  our  last  meeting,  one  of  the  papers  was  by  Mr  Sang  on  Loga- 
rithms, and  he  produced  on  our  table  no  less  than  20  MS.  volumes 
of  logarithms  to  15  places  of  decimals!  the  publication  of  which, 
he  pointed  out,  would  be  of  great  advantage  to  astronomers  and 
others  who  require  the  aid  of  logarithms  in  their  calculations,  and 
accompnaied  by  minute  accuracy.  That  opinion  was  publicly  con- 
firmed by  other  members  of  the  Society  very  competent  to  judge ; 
and  I may  now  announce,  that  our  Council  have,  in  accordance  with 
that  opinion,  come  to  the  resolution  of  ascertaining  whether  Govern- 
ment will  undertake  the  publication  of  Mr  Sang’s  valuable  tables, 
— for  the  cost  would  go  far  beyond  our  own  resources  as  a Society. 

2.  I cannot  conclude  what  I have  to  say  of  our  Society,  without 
adverting  to  the  losses  we  have  sustained  by  the  death  of  several 
distinguished  Honorary  Associates,  viz.,  Louis  Agassiz,  Lambert 
Adolphe  Jacques  Quetelet,  Auguste  de  la  Bive,  and  John  Stuart 
Mill.  Obituary  notices  of  some  of  these  distinguished  men  have 
already  appeared  in  our  Proceedings.  The  others  will  be  noticed 
by  our  President  in  his  Address,  when  the  next  session  commences. 

The  Council  have  filled  up  these  vacancies  by  selecting  other 
eminent  men  as  Honorary  Associates ; and  these  nominations  have 
been  confirmed  by  the  Society.  • 

Whilst  referring  to  the  list  of  our  Honorary  Fellows,  I cannot 
avoid  mentioning  a name,  which  I see  standing  on  the  same  page, 
and  standing  by  itself,  viz.,  Sir  Richard  Griffiths. 

Sir  Richard  is,  I believe,  the  oldest  member  of  our  Society.  He 
will,  in  September  next,  have  completed  his  ninetieth  year.  He 
was  in  my  house  two  months  ago,  in  good  health,  on  hi?  way  to 
Ireland,  where  he  is  at  present  residing.  It  so  happens  that  this 


392 


Proceedings  of  the  Royal  Society 

forenoon  I bad  the  pleasure  of  receiving  a letter  from  him,  accom- 
panied by  a short  biographical  memoir  of  his  many  scientific 
researches  as  a geologist,  and  of  his  great  public  services  as  a high 
officer  of  the  Irish  Government. 

This  memoir  I have  brought  with  me  this  evening,  that  you  may 
see  in  it  an  excellent  photograph  of  my  venerable  friend,  and  our 
oldest  colleague. 

III.  Having  said  all  that  occurs  to  me  of  ourselves  and  our  own 
doings  as  a Society,  perhaps  you  will  permit  me,  before  closing,  to 
allude  to  what  is  doing  generally  in  the  country  for  the  advance- 
ment of  science. 

There  are  two  aspects  in  which  science  may  be  viewed  : — First , 
The  teaching  of  what  is  known ; and,  second , The  investigation  of 
what  is  not  known. 

1.  As  regards  the  teaching  of  what  is  known, — 

(1.)  I must  advert  to  the  great  additional  impulse  lately  given 
in  Scotland,  England, and  Ireland,  by  the  Kensington  Department 
of  Science  and  Art. 

The  efforts  of  that  department  are  confined  chiefly  to  schools — 
Middle-Class  Schools — though  they  do  not  object  to  assist  science 
classes,  even  in  elementary  schools. 

In  Scotland,  ten  years  ago,  there  were  only  4 schools  in  connec- 
tion with  the  department,  now  there  are  118.  I observe  a list  of 
42  of  these  Scotch  schools  to  which  payments  were  made  last  year, 
amounting  to  L.1746,  as  perquisites  to  the  teachers,  which  is  no 
small  pecuniary  encouragement. 

(2.)  Another  measure — not  yet  adopted,  but  which,  if  adopted, 
will  probably  conduce  to  the  advancement  of  science  teaching — is 
one  about  to  be  proposed  to  Parliament  by  a distinguished  Fellow  of 
the  Society,  Mr  Lyon  Playfair.  He  intends  to  ask  the  House  of 
Commons  to  pass  a resolution,  recommending  the  Government  to 
create  a department  for  Education,  Science,  and  Art,  with  a respon- 
sible minister  at  the  head  of  that  department. 

I feel  very  sure  that  Mr  Playfair  wall  be  able  to  make  out  a good 
case  for  such  an  appointment. 

There  is  no  country  in  the  world  whose  various  industries  are 
more  benefited  than  ours,  by  the  help  of  science,  and  by  that  offi- 


of  Edinburgh , Session  1873-74.  393 

cial  encouragement  of  science  which  is  at  present  almost  entirely 
awanting. 

2.  The  other  aspect  of  science  to  which  I referred,  is  aiding  in 
the  investigation  of  truths  not  yet  known. 

In  Germany  there  exist  colleges  of  research,  in  which  persons 
can  get  the  use  of  instruments,  and  a laboratory  for  conducting 
experiments  in  any  department  of  science  to  which  they  devote 
themselves. 

Every  one  in  the  least  acquainted  with  science  must  appreciate 
the  importance  of  such  institutions.  In  this  country  there  are 
none,  at  least  none  except  on  a very  small  scale,  and  belonging  to 
individual  professors.  But  I am  happy  to  say  that  there  seems  every 
prospect  of  this  great  desideratum  being  likely  to  be  soon  supplied. 

The  need  of  these  institutions  has  been  for  some  years  pointed 
out  by  various  scientific  bodies,  ourselves  among  the  number ; and 
the  fruits  of  these  expositions  are  now  appearing. 

(1.)  Thus,  I read  in  the  “ Scotsman”  newspaper  of  Saturday  last, 
that  in  Glasgow  University  such  an  institution  is  about  to  be  formed. 
Principal  Caird  announces  it  in  these  terms, — terms  which,  whilst 
gratifying  to  Glasgow  University,  you  will  see  that  we  as  a Society 
also  have  reason  to  be  proud  of. 

“ A valuable  gift  has  been  made  to  the  University  by  one  of  its 
most  distinguished  professors,  Sir  William  Thomson,  in  conjunc- 
tion with  the  representatives  of  Dr  Neil  Arnott.  To  a donation  of 
L.1000  by  Dr  Arnott’s  widow,  Sir  William  has  added  a sum  of 
L.2000  for  the  endowment  of  the  new  office  of  Demonstrator  in 
Experimental  Physics,  in  connection  with  the  chair  of  Natural 
Philosophy.  By  that’  endowment  Sir  William  has  conferred  new 
obligations  on  the  University,  on  which  his  great  name  reflects  so 
much  honour.” — Scotsman  Newspaper,  2d  May  1874. 

\ (2.)  Another  example  I find  from  the  April  number  of  “ Nature,” 
in  the  following  terms  : — 

“ The  magnificent  sum  of  L.  10, 000  has  .been  made  over  by  the 
late  Mr  E.  K.  Langworthy  to  the  Owens  College,  Manchester,  for  the 
purpose  of  developing  the  chair  of  Experimental  Physics.  The 
terms  in  which  the  bequest  is  made  are  so  forcible  and  clear,  that 
they  deserve  to  be  quoted  : — 1 1 bequeath  to  the  trustees  of  Owens 
College  ten  thousand  pounds.  It  is  my  desire  that  students  may 


39  I Proceedings  of  the  Royal  Society 

be  instructed  in  the  method  of  Experiment  and  Research,  and  that 
science  may  he  advanced  by  original  investigation.  I also  desire 
that  the  professor  appointed  may  be  selected  on  account  of  his 
knowledge  having  been  especially  obtained  by  original  investiga- 
tion; and  that  his  appointment  shall  be  contingent  upon  the  con- 
tihuance  of  such  investigation.’  ” 

(3.)  The  third  example  I give  is  from  the  March  number  of  the 
same  newspaper. 

“ Thu  Cavendish  Laboratory. — This  laboratory,  in  which  every 
facility  is  furnished  for  the  prosecution  of  physical  research,  is  the 
munificent  gift  of  William  Cavendish,  Duke  of  Devonshire,  K.Gf., 
Chancellor  of  the  University  of  Cambridge,  who  has  intimated  his 
intention  of  presenting  it  complete  to  the  University. 

“ The  building,  which  is  now  finished,  was  erected  at  an  expense 
of  about  L. 10, 000. 

“ The  laboratory  is  open  daily  from  10  a.m.  till  6 p.m.,  under  the 
superintendence  of  the  professor  of  Experimental  Physics,  for  the 
use  of  any  member  of  the  University  who  may  desire  to  acquire  a 
knowledge  of  experimental  methods,  or  to  take  part  in  physical 
researches.” 

3.  These  measures  are  all  intended  to  give  greater  facilities  for 
original  research.  They  indicate  the  strong  belief  existing  in  all 
thoughtful  minds,  of  the  importance  of  giving  such  facilities. 

It  is  to  be  wished  that  this  opinion  may  have  impressed  itself 
on  the  minds  of  the  Royal  Commissioners,  who  are  about  to  issue 
their  report  on  the  aid  which  should  be  given  in  this  country  by  the 
State  to  science. 

It  is  a hopeful  circumstance  towards  that  view,  that  His  Grace  the 
Duke  of  Devonshire,  to  whom  I have  just  alluded,  is  at  the  head 
of  that  Royal  Commission.  His  munificent  gift  to  Cambridge 
University  shows  how  well  His  Grace  knows  what  is  necessary  for 
the  advancement  of  science  in  this  country. 

IY.  With  these  remarks,  gentlemen,  I now  declare  the  Winter 
Session  of  our  Royal  Society  closed ; and  I only  farther  express  a 
hope  that  all  of  us  here  may  be  spared,  and  many  more  of  our  col- 
leagues also,  to  meet  again  at  the  commencement  of  our  next 
Winter  Session. 


of  Edinburgh,  Session  1873-74.  395 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

John  Chiene,  M.D.,  F.R.C.S.E. 

Joseph  Bell,  M.D.,  F.R.C.S.E. 

E.  A.  Letts,  Ph.D.,  Assistant  to  the  Professor  of  Chemistry  in  the 
University  of  Edinburgh. 

Baden  Powell,  Esq.,  Conservator  of  Forests  in  the  Punjab. 


VOL.  VlII. 


3 E 


396 


Proceedings  of  the  Royal  Society 


Donations  to  the  Royal  Society  Library  during  Session 

1873-74 : — 

I.  Authors. 

Archer  (William  Henry).  Abstracts  of  English  and  Colonial 
Patent  Specifications  relating  to  the  Preservation  of  Food. 
Melbourne,  1870.  8vo. — From  the  Author. 

Arrest  (Dr  H.  d’).  Indbydelsesskrift  til  Kjbenhavn  Universitets 
Aarsfest  til  brindring  om  Kirkens  Reformation.  4to.  1872. 
— From  the  Author. 

Beetz  (W.).  Der  Arnheil  der  K.  bayerischen  Akademie  der 
Wissenschaften  an  der  Entwickelung  der  Electricitatslehre. 
Munich,  1873.  4to. — From  the  Author. 

Benson  (Lawrence  S.).  Notes  on  the  First  Book  of  Benson’s 
Geometry.  1873.  8vo. — From  the  Author. 

Bow  (Robert  H.),  C.E.  Economics  of  Construction  in  Relation  to 
Framed  Structures.  1873.  8vo. — From  the  Author. 

Brunton  (T.  Lauder),  M.D.,  and  J.  Fayrer,  M.D.  On  the  Nature  and 
Physiological  Action  of  the  Poison  of  Naja  tripudians  and  other 
Indian  venomous  Snakes.  Part  II.  8vo. — From  the  Authors. 

Clarke  (Hyde).  On  the  Influence  of  Geological  Reasoning  on 
the  other  Branches  of  Knowledge.  8vo. — From  the  Author. 
Clarke  (Lieut.  Col.  A.  R.).  Comparisons  of  Standards  and  Lengths 
of  Cubits.  4to. — From  the  Author. 

Coxe  (Eckley  B.).  A New  Method  of  Sinking  Shafts,  as  applied 
at  the  New  Deep  Shafts  of  the  Philadelphia  and  Reading  Coal 
and  Iron  Company,  1873.  8vo. — From  Sir  Charles  Hartley. 
Dollinger  [(J.  von).  Rede  in  der  Offentlichen  Sitzung  der  K. 
Akademie  der  Wissenschaften  am  25  Juli  1873.  Munich, 

1873.  4to. — From  the  Author. 

Edland  (E.).  Theorie  des  Phenomenes  Electriques.  Stockholm, 

1874.  4to. — From  the  Author. 

Ellis  (Alexander  J.).  Algebra  Identified  with  Geometry.  1874. 
8 vo. — From  the  Author. 

Erdmann  (Edouard).  Description  de  la  Formation  Carbonifere  de 
la  Scanie.  Stockholm,  1873.  4to. — From  the  Author. 


397 


of  Edinburgh,  Session  1873-74. 

Erdmann  (Edouard).  Jakttagelser  ofver  Meranbildningar  och 
der  afBetackta  Skiktade  Jordlager  i Skane.  Stockholm,  1872. 
8 vo. — From  the  Author. 

Froud  (William).  Eeport  to  the  Lords  Commissioners  of  the 
Admiralty  on  Experiments  for  the  Determination  of  the 
Besistance  of  a Full-Sized  Ship  at  various  Speeds.  1874. 
8 vo. — From  the  Author. 

G-runer  (M.  L.).  Studies  of  Blast  Furnace  Phenomena.  1873. 
8vo. — From  the  Author. 

Handyside  (P.  D.),  M.D.  The  Medico-Chirurgical  Society 
Jubilee  Chronicon.  1874.  8vo. — From  the  Author. 

Hornstein  (0.).  Magnetische  und  Meteorologisclie  an  der  K.  K. 
Stern warte  zu  Prag  im  Jahre  1872.  4to. — From  the  Author. 

Karoly  (Than).  A.  M.  Kir  Egyetem  Yegytani  Intezetenek, 
Leirasa.  Pesth,  1872.  4to. — From  the  Author. 

Klein  (E.),  M.D.  The  Anatomy  of  the  Sympathetic  System 
1873.  8vo. — From  the  Author. 

Lindsay  (W.  Lauder),  M.D.  Memoirs  on  the  Spermogones  and 
Pycnides  of  Lichens.  4to. — From  the  Author. 

Luvini  (Giovanni).  Di  un  Nuovo  Stromento  Meteorologico 
Geodetico-Astronomico  il  Dieteroscopio.  1874.  4to. — From 
the  Author. 

Mapother  (E.  D.),  M.D.  Lessons  from  the  Lives  of  Irish  Sur- 
geons. Dublin,  1873.  8vo. — From  the  Author. 

Meldrum  (C.).  Notes  on  the  Form  of  Cyclones  in  the  Southern 
Indian  Ocean,  and  on  some  of  the  Kules  given  for  avoiding 
their  Centres.  1873.  8vo. — From  the  Author. 

Milne  (James  Mitchell).  On  some  of  the  Derivatives  of  Benzyl- 
toluol.  Glasgow,  1872.  8vo. — From  the  Author. 

Naumann  (Alexander).  Jahresbericht  liber  die  Fortschritte  der 
Chemie,  &c.,  fur  1871.  Heft  1-23.  Giessen.  8vo. — From 
the  Editor. 

Perry  (John).  An  Elementary  Treatise  on  Steam.  1874.  12mo. 

— From  the  Author. 

Pillischer’s  Illustrated  Catalogue  of  Achromatic  Microscopes, 
Telescopes,  Opera,  Pace,  and  Field  Glasses,  and  other  Op- 
tical, Philosophical,  Mathematical,  Surveying,  and  Standard 
Meteorological  Instruments.  1873.  8vo. — From  the  Author. 


398 


Proceedings  of  the  Royal  Society 

Roebling  (W.  A.),  Pneumatic  Tower  Foundations  of  the  East  River 
Suspension  Bridge.  1873.  8vo. — From  Sir  Charles  Hartley. 

Scliromke  (T.).  Description  of  the  New  York  Croton  Aqueduct, 
in  English,  German,  and  French.  1855.  4to. — From  Sir 
Charles  Hartley. 

Sercomhe  (Edwin).  Inaugural  Address  upon  the  occasion  of  the 
Opening  of  the  New  Premises  of  the  Dental  Hospital  of 
London.  1 874.  8vo. — From  the  Author. 

Settimanni  (C.).  Supplement  a la  nouvelle  Theorie  des  principaux 
Elements  de  la  Lune  et  du  Soleil.  Florence,  1871.  4to. — 
From  the  Author. 

Smith  (Dr  John  Alexander).  Notes  on  the  Ancient  Cattle  of 
Scotland.  8vo. — From  the  Author. 

Stevenson  (David).  On  the  Reclamation  and  Protection  of  Agri- 
cultural Land.  1874.  8vo. — From  the  Author. 

Trinchera  (Francesco).  Storia  Critica  della  economia  Pubblica 
dai  tempi  Antichi  sino  ai  Giorni  Nostri.  Yol.  I.  Naples, 
1873.  8vo. — From  the  Author. 

II.  Transactions  and  Proceedings  of  Learned  Societies, 
Academies,  and  Universities. 

Albany. — Annual  Report  of  the  Auditor  of  the  Canal  Department 
on  the  Tolls,  Trade,  and  Tonnage  of  the  Canals  of  the 
State  of  New  York,  for  the  years  1867,  1868,  1869, 
1871,  1872,  1873.  8vo. — From  Sir  Charles  Hartley. 

Annual  Reports  of  the  State  Engineer  and  Surveyor  of  the 
State  of  New  York,  1869,  1870,  1871,  1872.  8vo. — 

From  Sir  Charles  Hartley. 

Amsterdam. — Flora  Batava,  afheelding  en  beschrigving  van  Neder- 
landsche  Gewassen  Aangevangen,  door  Wij'len  Ian  Kops 
Hoogleeraar  te  Utrecht  Yoortgezet  door  F.  W.  van  Eeden 
te  Haarlem.  Nos.  222-224.  4to. — From  the  King  of 
Holland. 

Processen-verbaal  van  de  Gewone  Vergaderingen  der 
Koninklijke  Akademie  van  Wetenschappen.  1872, 
1873.  8 vo. — From  the  Academy. 

Verhandelingen  der  Koninklijke  Akademie  van  Wetens- 
chappen. Deel  XIII.  4to. — From  the  Academy. 


399 


of  Edinburgh , Session  1873-74. 

A msterdam. — Yerslagen  en  Mededeelingen  der  Koninklijke  Akade- 
mie van  Wetenschappen  Afdeeling  Natuurkunde.  Deel 
YII.  Letterkunde,  Deel  III.  8vo. — From  the  Academy. 

Basel.— Yerhandlungen  der  Naturforschenden  Gi-esellsciiaft.  Theil 
YI.  Heft  1.  8 vo. — From  the  Society. 

Berlin. — Abhandlungen  der  Koniglichen  Akademie  der  Wissens- 
chaften  zu  Berlin.  1872.  4to. — From  the  Academy. 

Die  Fortschritte  du  Pliysik  im  Jalire  1869.  Dargestellt 
von  der  Physikalischen  G-esellscliaft  zu  Berlin.  XXY. 
Jahrgang,  1 und  2 Abtheilung.  8vo.  — From  the 
Society. 

Jahresberichtder  Commission  zur  Wissenschaftlichen  Unter- 
suchung  der  Deutscben  Meere  in  Kiel  fiir  das  Jalir  1871. 
Fol. — From  the  Commission. 

Inhaltsverzeichniss  der  Abhandlungen  der  Konigl.  Aka- 
demie der  Wissensckaften.  1873.  8vo. — From  the 
Academy. 

Monatsbericht  der  Koniglich  Preussiscben  Akademie  der 
Wissenscliaften  zu  Berlin.  1873,  Mai  (1,  2),  Jnni,  Juli, 
August,  Septembre,  Octobre,  Novembre,  Decembre. 
1874,  Januar,  Februar,  Marz.  8vo. — From  the  Academy. 

Berne. — Beitrage  zur  Geologischen  Ivarte  der  Scliweiz  herausge- 
geben  von  der  Geologischen  Commission  der  Schweiz. 
Naturforsch  Gesellschaft  auf  kosten  der  Eidgenossen- 
schaft.  1873,  1874.  4to. — From  the  Commission. 

Materiaux  pour  la  Carte  Geologique  de  la  Suisse  publies 
par  la  Commission  de  la  Societe  Helvetique  des  Sciences 
Naturelles,  aux  frais  de  la  Confederation,  Livraison  Y. 
4to. — From  the  Commission. 

Bologna. — Memorie  del  Accademia  dell  Scienze  dell  Istituto 
di  Bologna.  Serie  III.  Tomo  II.  Fasc.  2-4.  Tomo  III. 
Fasc.  1,  2.  4to. — From  the  Academy. 

Rendiconto  delle  Sessioni  delle  Accademia  delle  Scienze  dell 
Istituto  di  Bologna  Anno  Accademico  1873-74.  8vo. 
— From  the  Academy. 

Bunn. — Yerhandlungen  des  Naturliistorischen  Yereines  der  Preuss- 
ischen  Rheinlande  und  Westphalens  Jahrgang  XXIX 
Halfte  2 ; XXX.  Halfte  1.  8vo. — From  the  Society. 


400 


Proceedings  of  the  Royal  Society 

Bordeaux. — Memoires  de  la  Societe  des  Sciences  Physiques  et 
Naturelles  de  Bordeaux.  Tome  IX.  No.  2;  X.  No.  1. 
8 vo. — From  the  Society. 

Boston. —Memoirs  of  the  Society  of  Natural  History.  Vol.  II. 
Part  2,  Nos.  2,  3.  4to. — From  the  Society. 

Proceedings  of  the  Society  of  Natural  History.  Vol.  XIV.; 

Vol.  XV.  Parts  1,  2.  8vo. — From  the  Society. 
Thirty-Sixth  Annual  .Report  of  the  Board  of  Education. 
1873.  8vo. — From  the  Board. 

Brooklyn. — Keports  of  the  Executive  Committee,  General  Superin- 
tendent, and  Treasurer  of  the  New  York  Bridge  Com- 
pany. 1873.  8vo. — From  Sir  Charles  Hartley. 

Brussels. — Bulletin  de  l’Academie  Royale  des  Sciences,  des  Lettres 
et  des  Beaux- Arts  de  Belgique.  Tome  XXXVI.  Nos.  7- 
10,  12.  ; Tome  XXXVII.  Nos.  1-5.  8vo .—From  the 
Academy. 

Funerailles  de  Lambert-  Adolphe- Jacques  Quetelet  secretaire 
perpetuel  de  l’Academie  Eoyale  de  Belgique.  1874. 
8vo. — From  the  Academy. 

Calcutta. — Journal  of  the  Asiatic  Society  of  Bengal.  Part  I. 

No.  23  ; Part  II.  No.  2.  Proceedings  of  1873,  Nos. 
7-10.  8vo. — From  the  Society. 

Journal  of  the  Asiatic  Society  of  Bengal,  Vol.  XLII.  No. 

187.  (New  Series).  8vo. — From  the  Society. 

Memoirs  of  the  Geological  Survey  of  India.  Vol.  X. 

Part  1.  8 vo. — From  the  Survey. 

Memoirs  of  the  Survey  of  India.  Palmontologia.  Vol. 
IV.  Nos.  3,  4;  Ser.  VIII.  Vol.  I.  No.  1;  Ser.  IX. 
4to. — From  the  Survey. 

Papers  regarding  the  Village  and  Rural  Indigenous  Agency 
employed  in  taking  the  Bengal  Census  of  1872.  8vo. — 
From  the  Bengal  Government. 

Proceedings  of  the  Asiatic  Society  of  Bengal.  No.  1.  1874. 
8vo. — From  the  Society. 

Records  of  the  Geological  Survey  of  India.  Vol.  VI.  Parts 
1-4.  8vo. — From  the  Survey. 

California. — Proceedings  of  the  Academy  of  Sciences.  Vol.  I.  ; 
Vol.  V.  Part  II.  8vo. — From  the  Academy. 


401 


of  Edinburgh,  Session  1873-74. 

Cambridge  ( U.S ). — Illustrated  Catalogue  of  the  Museum  of  Com- 
parative Zoology  at  Harvard  College.  No.  YIl.  Part  3. 
4to. — From  the  University. 

The  Harvard  University  Catalogue,  1872-1873.  8vo. — 
From  the  University. 

Forty-Seventh  Annual  Report  of  the  President  of  Har- 
vard College.  1871-72.  8vo. — From  the  University. 

The  Complete  Works  of  Count  Rumford,  published  by  the 
American  Academy  of  Arts  and  Science.  Yol.  II.  1873. 
8 vo. — From  the  Academy. 

Memoirs  of  the  American  Academy  of  Arts  and  Sciences, 
New  Series.  Yol.  IX.  Part  2.  4to.  Proceedings, 
1872.  8 vo. — From  the  American  Academy. 

Proceedings  of  the  American  Academy  of  Arts  and  Sciences. 
Yol.  VIII.  8vo. — From  the  Academy. 

Proceedings  of  the  American  Association  for  the  Advance- 
ment of  Science.  1872.  8vo. — From  the  Associa- 

tion. 

Canada. — Geological  Survey.  Report  of  Fossil  Plants  of  the 
Lower  Carboniferous  and  Millstone  Grit  Formations  of 
Canada.  1873.  8vo. — From  the  Director. 

Geological  Survey.  Report  of  Progress  for  1872-73.  8vo. 
— From  the  Director. 

Catania. — Atti  dell  Accademia  Gioenia  de  Scienze  Naturali.  Serie 
terza.  Tomo  VII.  VIII.  Carta  Geologica,  Fol.  8vo 
— From  the  Academy. 

Cherbourg. — Catalogue  de  la  Bibliotheque  de  la  Societe  National 
des  Sciences  Naturelles  de  Cherbourg.  Part  I.  8vo. 
— From  the  Society. 

Memoires  de  la  Societe  Nationale  des  Sciences  Naturelles  de 
Cherbourg.  Tome  YI I.  8vo. — From  the  Society. 

Christiania. — Det  Kongelige  Norste  Frederiks-Universitets  Aares- 
beretning  for  1872.  8vo. — From  the  University. 

Fordhandlingar  i Videnskabs-Selskabet,  Aar  1872-1873. 
Heft  1.  8vo. — From  the  Society . 

Norsk  Meteorologiske,  Aarbog  1872.  4to. — From  the 

Meteorological  Institute. 


402 


Proceedings  of  the  Royal  Society 


Christiania. — Nyt  Magazin  for  Naturvidenskaberne.  Bind  XIX. 

Hefte  3,  4 ; XX.  Hefte  1,  2.  8vo. — From  the  Royal  Uni- 
versity of  Norway. 

Connecticut. — Transactions  of  the  Connecticut  Academy  of  Arts 
and  Sciences-  Yol.  II.  Part  2.  8vo. — From  the 

Academy. 

Copenhagen. — Memoires  de  l’Academie  Royale  de  Copenhagen. 
Yol.  X.  Nos.  3-6.  4to. — From  the  Academy. 

Oversigt  over  det  Kongelige  Danske  Yidenskabernes  Sels- 
kabs  Forhandlinger  ogdets  Medlemmers  Arbeider  i,  Aaret 
1873.  Nos.  1,  2.  8 vo. — From  the  Society. 

Delira  Boon. — General  Report  on  the  Operations  of  the  Great 
Trigonometrical  Survey  of  India,  during  1872-73.  Fob 
— From  the  Survey. 

Dublin. — Journal  of  the  Royal  Geological  Society  of  Ireland. 
Yol.  III.  Part  3.  8vo. — From  the  Society. 

Proceedings  of  the  Royal  Irish  Academy.  Vol.  X.  Part 
4;  Yol.  I.  Ser.  II.  Nos.  2-6.  8vo. — From  the  Academy. 

Transactions  of  the  Royal  Irish  Academy  (Science).  Vol. 
XXIY.  Parts  16,  17;  XX Y.  (Science)  Parts  1-3.  4to. 
From  the  Academy. 

Edinburgh. — Journal  of  the  Scottish  Meteorological  Society.  Nos. 
40-42.  8 vo. — From  the  Society. 

Quarterly  Returns  of  Births,  Deaths,  and  Marriages, 
registered  in  the  Divisions,  Counties,  and  Districts  of 
Scotland;  also  Monthly  Returns  of  Births,  Deaths,  and 
Marriages  in  the  eight  Principal  Towns  of  Scotland, 
from  June  1873  to  July  1874.  8vo. — From  the  Registrar- 
General. 

Forty-Sixth  Annual  Report  of  the  Council  of  the  Royal 
Scottish  Academy  of  Painting,  Sculpture,  and  Architec- 
ture. 1873.  8vo. — From  the  Academy. 

Transactions  and  Proceedings  of  the  Botanical  Society. 
Yol.  XI.  Part  3.  8vo. — From  the  Society. 

Erlangen. — Sitzungsberichte  der  Physicalisch-Medicinischen  So- 
cietat  zu  Erlangen.  Heft  4,  5.  8vo. — From  the 
Society. 


403 


of  Edinburgh,  Session  1873-74. 

Erlangen. — Verhandlungen  der  Physicalisch-Medicinischen  Socie- 
tal zu  Erlangen.  1865-67.  Heft  2,  1867-1870.  8vo. — 
From  the  Society. 

Frankfort. — Abhandlungen  lierausgegeben  von  der  Sencken- 
bergischen  Naturforschenden  Gesellschaft.  Band  IX. 
Heft  1,  2.  4to. — From  the  Society. 

Bericbt  fiber  die  Senckenbergisclie  Naturforschenden  Gesell- 
sebaft.  1872-1873.  8vo. — From  the  Society. 

Geneva. — Memoires  de  la  Societe  de  Physique  et  d’Histoire 
Naturelle  de  Geneve.  Tome  XXIII.  Part  1.  4to. — 
From  the  Society. 

Glasgow. — Transactions  of  the  Geological  Society.  Part  1.  4to. 
— From  the  Society 

Gottingen. — Abhandlungen  der  Koniglichen  Gesellschaft  der  Wis- 
senchaften  zu  Gottingen.  Band  XVIII.  4to .—From 
the  Society. 

Nachrichten  von  der  K.  Gesellschaft  der  Wissenschaften 
und  der  Georg-Augusts-Universitat,  aus  dem  Jahre  1873. 
12mo. — From  the  University. 

Greenwich. — Astronomical  and  Magnetical  Observations  made  at 
the  Royal  Observatory  in  the  year  1871.  4to. — From  the 
Observatory . 

History  and  Description  of  the  Water  Telescope  of  the 
Royal  Observatory.  4to. — From  the  Observatory. 

Haarlem. — Archives  Neerl  an  daises  des  Sciences  Exactes  et  Na- 
turelles  publiees  par  la  Societe  Hollandaise  a Haarlem. 
Tome  VIII.  Liv.  3,  4.  8vo. — From  the  Society. 

Archives  du  Musee  Teyler.  Vol.  III.  Fasc.  3.  8vo. — 
From  the  Museum. 

Bibliotheca  Ichthyologica  et  Piscatoria.  1873.  8vo. — 
From  D.  Mulder  Bosgoed. 

Innsbruck.  — Berichte  des  Naturwissenschaftlich-Medizinischen 
Vereines  in  Innsbruck.  Jahrgang  III.  Heft  2,  3.  8vo. 
— From  the  Society. 

Jena. — Jenaische  Zeitschrift  fur  Medicin  und  Naturwissenschaft 
lierausgegeben  von  der  Medicinisch  Naturwissenscbaft- 
lichen  Gesellschaft  zu  Jena.  Band  VII.  Heft  1-4  ; 
VIII.  Heft  1.  8 vo. — From  the  Society. 

VOL.  VIII.  3 F 


404  Proceed hujs  of  the  Royal  Society 

Kasan. — Reports  of  the  University  of  Kasan.  1872,  1873.  Nos. 
2-6.  8vo. — From  the  University . 

Kiel. — Scliriften  der  Universitat.  1872.  Band  XIX.,  XX.  4to. — 
From  the  University . 

Konigsberg. — Astronomische  Beobachtungen  auf  der  Konigliclien 
Universitats-Sternwarte.  1870.  Fol. — From  the  Uni- 

versity. 

Leeds. — The  Fifty-Third  Report  of  the  Council  of  the  Leeds 
Philosophical  and  Literary  Society.  1872-73.  8vo. — 
From  the  Society. 

Leipzig.  — Berichte  iiber  die  Verhandlungen  der  Koniglich 
Sachsischen  G-esellschaft  der  Wissenschaften  zu  Leip- 
zig; Math.-Phys.  Classe.  1872,  Nos.  3,  4;  1873,  Nos. 
1,  2.  8 vo. — From  the  Royal  Saxon  Academy. 

Der  homerische  G-ebrauch  der  Partikel  ei  von  Ludwig 
Lange.  Band  YI.  No.  5.  8vo. — From  the  Royal  Saxon 
Academy. 

Die  Melanesischen  Sprachen  nacli  ihrem  G-rammatischen 
bau  und  ihrer  Yerwandtschaft  unter  sicli  und  mit  den 
Malaiisch-Polynesischen  Sprachen  untersucht,  von  H.  K. 
von  der  G-abelentz.  Band  YII.  No.  1.  8vo. — From  the 
Royal  Saxon  Academy. 

Elemente  des  Ersten  Cometen  vom  Jahre  1830.  Yon  Dr  L. 
R.  Schulze.  8 vo. — From  the  Royal  Saxon  Academy. 

Preisschriften  gekront  und  herausgegeben  von  der  furst- 
lich  Jablonowskischen  G-esellschaft  zu  Leipzig.  XYII. 
8vo. — From  the  Royal  Saxon  Academy. 

Uber  du  den  Kraften  Elektrodynamischen  Ursprungs 
zuzuschreiben  den  Elementargesetze  Carl  Neumann. 
Band  X.  No.  6.  8vo. — From  the  Royal  Saxon  Academy. 

Lisbon. — Historia  e Memorias  da  Academia  Real  das  Sciencias  de 
Lisboa,  Classe  de  Sciencias,  Moraes,  Politicas,  e Bellas- 
Lettras.  Nova  Serie.  Tomo  IV.  Parte  1.  4to. — From 
the  Academy. 

Journal  de  Sciencias  Mathematicas  Physicas  e Naturaes 
publicado  sob  os  auspicias  da  Academia  Real  das 
Sciencias  de  Lisboa.  Tome  I.,  II.,  III.  8vo. — From 
the  Society. 


405 


of  Edinburgh,  Session  1873-74. 

Liverpool. — Index  to  the  First  and  Second  Series  of  the  Transac- 
tions of  the  Historic  Society  of  Lancashire  and  Cheshire. 
8 vo.  1874. — From  the  Society. 

Proceedings  of  the  Literary  and  Philosophical  Society, 
No.  27.  8 vo. — From  the  Society. 

London. — Annual  Report  of  the  Geologist's  Association  for  1873. 
8vo. — From  the  Association. 

Contributions  to  our  Knowledge  of  the  Meteorology  of  the 
Antarctic  Regions.  4to. — From  the  Meteorological  Com- 
mittee of  the  Royal  Society. 

Journal  of  the  Chemical  Society.  1873,  October,  Novem- 
ber, December;  1874,  January,  February,  March,  April, 
May,  June.  Index.  List  of  the  Fellows.  8vo. — From 
the  Society. 

Journal  of  the  East  India  Association.  Yol.  VII.  Nos. 
2,  3;  Yol.  VIII.  Part  1.  8vo. — From  the  Associa- 

tion. 

Journal  of  the  Linnean  Society.  Yol.  XIY.  (Botany), 
Nos.  73-75;  Yol.  XII.  (Zoology),  No.  57.  8vo. — From 
the  Society. 

Journal  of  the  Royal  Asiatic  Society  of  Great  Britain  and 
Ireland.  Yol.  VII.  (New  Series),  Part  1.  8vo. — From 
the  Society. 

Journal  of  the  Royal  Geographical  Society.  Yols.  XLII., 
XLIII.  8vo. — From  the  Society . 

Journal  of  the  Royal  Horticultural  Society.  Yol.  IY.  Parts 
13,  14.  8vo. — From  the  Society. 

Journal  of  the  Society  of  Arts  for  1873-74.  8vo. — From 
the  Society. 

Journal  of  the  Statistical  Society.  Yol.  XXXYI.  Part  3, 
4;  Yol.  XXXVII.  Part  1.  8vo. — From  the  Society . 

Monthly  Notices  of  the  Royal  Astronomical  Society  for 
1873-74.  8vo. — From  the  Society. 

Proceedings  of  the  Geologists’  Association.  Address  at  the 
Opening  of  the  Session  1873-74.  8vo. — From  the 

Society. 

Proceedings  of  the  Geologists’  Association.  Yol.  III.  Nos. 

1-5.  8vo. — From  the  Society. 


406 


Proceedings  of  the  Boyal  Society 

London. — Proceedings  of  the  Institution  of  Civil  Engineers.  Yols 
XXXV.,  XXXYI.  8 vo. — From  the  Society. 

Proceedings  of  the  Linnean  Society.  Session  1873-74. 
8 vo. — From  the  Society. 

Proceedings  of  the  London  Mathematical  Society.  Nos. 

64,  65.  8vo. — From  the  Society. 

Proceedings  of  the  Eoyal  G-eograpliical  Society.  Yol.  XYII. 
Nos.  3,  4,  5 ; Yol.  NYIII.  Nos.  1,  2,  3.  8vo. — From  the 

Society. 

Proceedings  of  the  Royal  Institution  of  Great  Britain. 

Yol.  YII.  Parts  1,  2.  8vo. — From  the  Society. 
Proceedings  of  the  Royal  Medical  and  Chirurgical  Society. 

Yol.  YII.  Nos.  5,  6.  8vo. — From  the  Society. 

Proceedings  of  the  Royal  Society.  Nos.  147,  148,  149,  150, 
151,  152.  8vo. — From  the  Society. 

Proceedings  of  the  Society  of  Antiquaries.  Yol.  Y.  No.  8. 
8vo. — From  the  Society. 

Proceedings  of  the  Zoological  Society.  1873.  Parts  1,  2. 
8vo. — From  the  Society. 

Quarterly  Journal  of  the  Geological  Society.  Yol.  XXIX. 

Part  4;  Yol.  XXX.  Part  1.  8vo. — From  the  Society. 
Quarterly  Journal  of  the  Meteorological  Society.  Yol.  I. 

No.  8.  8vo. — From  the  Society. 

Quarterly  Weather  Report  of  the  Meteorological  Office. 
Part  4,  1872 ; Parts  1 and  2,  1873.  4to. — From  the 

Meteorological  Committee  of  the  Royal  Society. 

H.  M.  S.  “Challenger.” — Reports  of  Captain  G.  S.  Nares, 
R-'N.-j  with  Abstracts  of  Soundings  and  Diagrams  of 
Ocean  Temperatures  in  North  and  South  Atlantic  Oceans. 
1873.  4to. — From  the  Lords  Commissioners  of  the  Ad- 
miralty. 

Statistical  Report  on  the  Health  of  the  Navy  for  the  year 
1871.  8vo. — From  the  Admiralty. 

Transactions  of  the  Clinical  Society.  Yol.  YI.  1873. 
8vo. — From  the  Society. 

Transactions  of  the  Linnean  Society.  Yol.  XXYI1I. 
Part  4.  Yol.  XXX.  Part  1.  4to. — From  the  Society. 


of  Edinburgh,  Session  1873-74.  407 

London. — Transactions  of  the  Pathological  Society.  Vols.  XXIII., 
XXIV.  8vo. — From  the  Society. 

Transactions  of  the  Eoyal  Medical  and  Chirurgical  Society. 

Yol.  LYI.  8 vo. — From  the  Society. 

Transactions  of  the  Eoyal  Society.  Vol.  CLXIII.  Parts 
1,  2.  List  of  Fellows,  1873.  4to. — From  the  Society. 
Transactions  of  the  Society  of  Antiquaries.  Yol.  XLIII. 

Part  2;  XLIY.  Part  1.  4to. — From  the  Society. 
Transactions  of  the  Eoyal  Society  of  Literature.  Yol.  X. 

Part  3.  8vo. — From.the  Society. 

Transactions  of  the  Zoological  Society.  Yol.  VIII.  Part 
6.  4to. — From  the  Society. 

Madras. — Census  of  the  Town  of  Madras,  1871.  Fol. — From  the 
Census  Office. 

Manchester. — Memoirs  of  the  Literary  and  Philosophical  Society. 
Yol.  IY.  (Third  Series).  8vo. — From  the  Society. 
Proceedings  of  the  Literary  and  Philosophical  Society. 

Yols.  VIII.,  IX.,  X.  8vo.— From  the  Society. 
Transactions  of  the  Manchester  Geological  Society.  Yol. 
XIII.  Part  4.  8vo. — From  the  Society. 

Massachusetts. — Nineteenth  and  Twentieth  Annual  Eeports  of  the 
Board  of  Agriculture.  1871-73.  8vo.  — From  the 
Board. 

Ninth  Annual  Eeport  of  the  Board  of  State  Charities. 
1873.  8vo. — From  the  Board. 

Melbourne. — Abstracts  of  Specifications  of  Patents  Applied  for 
from  1854  to  1866.  4to. — From  the  Registrar -General  of 
Victoria. 

Official  Eeport  on  the  London  International  Exhibition  of 
1873.  8vo. — From  the  Commissioners. 

Patents  and  Patentees.  Yols.  I .-VI.  4to. — From  the 

Registrar- General  of  Victoria. 

Statistical  Tables  relating  to  the  Colony  of  Victoria.  Fol. 
— From  the  Registrar-General  of  Victoria. 

Mexico. — Boleten  de  la  Sociedad  de  Geografia-y-Estadistica  de  la 
Eepublica  Mexicana.  Tomo  I.  Nos.  1-7.  8vo. — From 
the  Society. 


408  Proceedings  of  the  Royal  Society 

Milan . — Atti  della  Societa  Italiana  di  Scienze  Naturali.  Yol.  XY. 

Ease.  3 ; Yol.  XYL  Fasc.  1,  2 ; Yol.  XY.  Fasc.  4,  5. 
8 vo. — From  the  Society. 

Moscow. — Bulletin  de  la  Societe  Imperiale  des  Naturalistes.  1873. 
Nos.  2,  3.  8 vo. — From  the  Society. 

Munich. — Abhandlungen  der  koniglich.  bayerischen  Akademie  der 
Wissenschaften.  Historischen  Classe.  Band  XLIII. 
— Mathematiscli  - Physikalischen  Classe.  Band  XL. — 
Philosopkisch-Philologischen  Classe.  Band  XLYI.  4to* 
— From  the  Academy. 

Sitzungsberichte  der  konigl.  bayer.  Akademie  der  Wissen- 
scbaften.— Philologischen  und  Historischen  Classe.  1872. 
Hefts  4,  5 ; 1873,  1-5. — Mathematisch-Physikalischen 
Classe.  1872,  Heft  3.;  1873,  Hefts  1,2.  8vo. — From 
the  Academy. 

Catalogus  Codicum  Latinorum  Bibliothecae  Regiee.  Tom. 
I.  Pars.  3 ; Tom.  II.  Pars  1.  8vo. — From  the  Com- 

pilers. 

Naples. — Atti  dell’  Accademia  delle  Scienze  Fisiche  e Matematiche 
Yol.  Y.  4to. — From  the  Academy. 

Bendiconto  dell’  Accademia  delle  Scienze  Fisiche  e Mate- 
matiche, Anno  IX.,  X.,  XI.  4to. — From  the  Academy. 

Neuchatel. — Bulletin  de  la  Societe  des  Sciences  Naturelles  de 
Neuchatel.  Tome  IX.  Part  3.  8vo.  — From  the 
Society. 

New  Haven  ( U.S. ). — Journal  ( American J of  Science  and  Art,  con- 
ducted by  Benjamin  Silliman.  Yol.  YI.  Nos.  31-36; 

Yol.  YII.  Nos.  37-41.  8vo. — From  the  Editor. 

New  York. — Catalogue  of  the  New  York  State  Library,  1872.  Sub- 
ject-Index. 8vo. — From  the  University. 

Fifty-Fourth  and  Fifty-Fifth  Annual  Report  of  the  Trustees 
of  the  New  York  State  Library.  8vo.- — From  the 

Library. 

Results  of  a Series  of  Meteorological  Observations  made 
under  Instructions  from  the  Regents  of  the  University 
at  sundry  Stations  in  the  State  of  New  York,  from  185 
to  1863  inclusive.  4to. — - From  the  University. 


409 


of  Edinburgh,  Session  1872-73. 

New  York. — Eiglity-Fonrth  and  Eighty-Fifth  Annual  Report  of  the 
Regents  of  the  University  of  the  State  of  New  York. 
8vo. — From  the  University. 

New  Zealand. — Catalogue  of  the  Land  Mollusca,  with  descriptions 
of  the  Species.  1873.  8vo. — From  the  Colonial  Museum 
and  Geological  Survey  Department , N.  Z. 

Ottawa. — General  Report  of  the  Minister  of  Public  Works  for 
1867-1872.  8vo. — From  Sir  Charles  Hartley. 

Paris. — Annales  des  Mines.  Tome  IV.  Liv.  4e5rae;  Tome.  V. 
Liv.  le  8vo. — From  the  Fcole  des  Mines. 

Annales  Ilydrographiques.  Nos.  1,  2.  1873.  8vo. — From 

the  Depot  de  la  Marine. 

Bulletin  de  la  Societe  G<iographique.  1873,  Aout,  Septemhre, 
Octobre,  Novembre,  Decembre;  1874,  Janvier,  Fevrier, 
Mars,  Avril.  8vo. — From  the  Society. 

Comptes-Rendus  Hebdomadaires  des  Seances  de  l’Academie 
des  Sciences.  1873-74.  4to. — From  the  Academy. 
Nouveiles  Archives  du  Museum  d’Histoire  naturelle  de 
Paris.  Tom  VIII.  IX.  4to. — From  the  Museum. 
Publications  of  the  Depot  de  la  Marine,  with  Charts,  Nos. 
516,  518,  519.  8 vo. — From  the  Depot. 

Pest. — A Magyar  Tudomanyos  Akademia  Ertesitoje  A.  M.  T.  Aka- 
de  mia  Rendeletebol.  1871,  Szam.  1-17 ; 1872,  1-8, 
13-18.  Pest.  8vo.— From  the  Academy. 

Ertekezesek  a Termeszettudomanyok  Korebol  Kiadja  A. 
Magyar  Tudomanyos  Akademia,  A.  III.  Osztaly  Rende- 
letebol. 1870,  Szam  3-8;  1871,  7 15;  1872,  1-3.  8vo. 
— From  the  Academy. 

Magyar  Tudom  Akademiai  Almanach,  1871-1872.  8vo. — 
From  the  Academy. 

Philadelphia. — Proceedings  of  the  Academy  of  Natural  Sciences, 
1872.  Parts  1-3.  8vo. — From  the  Academy. 
Proceedings  of  the  American  Philosophical  Society.  Vol. 

XIII.  Nos.  90,  91.  8 vo. — From  the  Society. 

Transactions  of  the  American  Philosophical  Society.  Vol. 
XV.  New  Series.  Part  1.  4to. — From  the  Society. 
Quebec. — Transactions  of  the  Literary  and  Historical  Society. 
Part  10,  Session  1872-3.  8vo. — From  the  Society. 


410  Proceedings  of  the  Royal  Society 

Salem  ( U.S. ). — Bulletin  of  the  Essex  Institute.  Yol.  IY.  Nos. 
1-12.  8 vo. — From  the  Institute. 

Fifth  Annual  Report  of  the  Trustees  of  the  Peabody 
Academy  of  Science  for  the  year  1872.  8vo. — From  the 
Peabody  Academy  of  Science. 

The  American  Naturalist.  Yol.  YII.  Yol.  YIII.  No.  1. 
8vo. — From  the  Peabody  Academy  of  Science. 

San  Francisco. — Proceedings  of  the  California  Academy  of  Sciences. 

Vol.  Y.  Part  1.  8vo. — From  the  Academy. 

Shanghai. — Catalogue  of  the  Library  of  the  North  China  Branch 
of  the  Royal  Asiatic  Society.  8vo. — From  the  Society. 
Journal  of  the  North  China  Branch  of  the  Royal  Asiatic 
Society  for  1871  and  1872.  No.  7.  8vo. — From  the 

Society. 

St  Petersburg. — Annalen  des  Physikisclien  Centralobservatoriums. 
1872.  4to. — From  the  Russian  Government. 

Bulletin  de  l’Academie  Imperiale  des  Sciences  de  St  Peters- 
bourg.  Tome  XYIII.  Nos.  3-5 ; XIX.  Nos.  1-3.  4to. 
— From  the  Academy. 

Jahresbericht  des  Physikalischen  Central-observatoriums, 
fur  1871  und  1872.  4to. — From  the  Academy. 
Jahresbericht  fur  1871-72,  1872-73.  8vo. — From  the  Ob- 
servatory. 

Observations  de  Poulkova.  Yols.  IY.,  Y.  4to. — From  the 
Observatory. 

Memoires  de  l’Academie  Imperiale  des  Sciences  de  St 
Petersbourg.  Tome  XIX.  Nos.  8-10;  XX.,  XXI.  Nos. 
1-5.  4to. — From  the  Academy. 

Repertorium  fur  Meteorologie.  Band  III.  4to. — From  the 
Royal  Academy. 

Stockholm.—  Sveriges  G-eologiska  Undersokning ; with  Charts. 

8 vo. — From  the  Bureau  de  la  Recherche  Geologique  de 
la  Suede. 

Toronto. — The  Canadian  Journal  of  Science,  Literature,  and 
History.  Yol.  XIY.  Nos.  1,  2.  8vo. — From  the  Cana- 
dian Institute. 

Turin. — Atti  della  Reale  Accademia  delle  Scienze  de  Torino. 
Yol.  YIII.  Despensa  1-6.  8vo. — From  the  Academy. 


of  Edinburgh,  Session  1873-74. 


411 


Turin. — Bolletino  Meteorologico  ed  Astronomico  del  Begio  Osser- 
vatorio  dell’  Universita.  4to. — From  the  University. 
Memorie  della  Beale  Accademia  delle  Scienze  di  Torino 
Serie  Seconda.  Tomo  XXVII  4to. — From  the  Academy . 
Upsala. — Bulletin  Meteorologtque  Mensuel  de  l’Observatoire  de 
l’Universite.  Yol.  IV.  Nos.  1-12  ; Y.  1-6.  4to. — From 
the  University. 

Nova  Acta  Begiae  Societatis  Scientiarum  Upsaliensis.  Yol. 
YIII.  Fasc.  2.  4to. — From  the  Society. 

Victoria  ( Australia ). — Census  of  Victoria  for  1871.  Occupations 
of  the  People.  Part  9.  Fol. — From  the  Australian 

Government. 

Progress  Beports  and  Final  Beport  of  the  Exploration 
Committee  of  the  Boyal  Society.  1872.  Fol. — From 
the  Society. 

Beports  of  the  Mining  Surveyors  and  Begistrars  for  Quarter 
ended  31st  December  1873.  Fol. — From  the  Registrar- 
General. 

Statistics  of  the  Colony,  1871-72.  Accumulation.  Fol. 
— From  the  Registrar-General. 

Statistics  of  the  Colony,  1872.  Blue  Book.  Part  1.  Fol. 

—From  the  Registrar-General. 

Statistics  of  the  Colony,  1872.  Finance,  &c.  Part  2.  Fol. 
— From  the  Registrar-General. 

Statistics  of  the  Colony,  1872.  Law,  Crime,  &c.  Part  5. 

Fob- — From  the  Registrar-General. 

Statistics  of  the  Colony,  1872.  Population.  Part  3.  Fol. 

— From  the  Registrar- General. 

Statistics  of  the  Colony,  1872.  Production.  Part  6.  Fol. 
— From  the  Registrar-General. 

Vienna. — Das  G-ebirge  um  Hallstatt  eine  G-eologisch-Palaontolo- 
gische  Studie  aus  den  Alpen  von  Edmund  Mojsisvocs,  v. 
Mojsvar.  Theil  I.  Heft  1.  4to. — From  the  Society. 
Denkschriften  der  kaiserlichen  Akademie  der  Wissen- 
schaften.  Phil.-Hist.  Classe.  Band  XXII.  4to. — From 
the  Academy. 

Die  Fauna  der  Schichten  mit  Aspidoceras  Acanthicum,  von 
De  M.  Neumayr.  Band  Y.  No.  6.  4to. — From  the  Society 

3 G 


YOL.  VIII. 


412 


Proceedings  of  the  Royal  Society 

Vienna. — Jahrbucli  der  kaiserlich-koniglichen  geologischen  Reich  - 
sanstalt.  Band  XXIII.  Nos.  2,  3,  4;  Band  XXIY.  No. 
1.  8 vo. — From  the  Society. 

Sitzungsberichte  der  kaiserlichen  Akademie  der  Wissen- 
schaften.  Phil.  Hist.  Classe.  Band  LXXII.,  LXXIII., 
LXXIY.  Heft  1-3.— Math.  Nat.  Classe.  Band  LXYI., 
LXYII.  Heft  1-5;  LXYIII.  Heft  1,  2.— Phys.-Anat. 
Band  LXYI.,  LXYII.  Heft  1-5. — Min.  Bot.  Zool.  Geo. 
Pal.  Band  LXYI.,  LXYII.,  LXYIII.  Heft  1,  2.  8vo.— 
From  the  Academy. 

Yerhandlungen  der  kaiserlich-koniglichen  geologischen 
Reichsanstalt.  1873,  Nos.  7-18.  8vo. — From  the  Society. 

Yerhandlungen  der  kaiserlich-koniglichen  zoologisch-botan- 
ischen  Gesellschaft  in  Wien.  Band  XXIII.  8vo. — From 
the  Society. 

Almanach  der  kaiserlichen  Akademie  der  Wissenschaften. 
8vo. — From  the  Academy. 

Washington. — Acrididse  of  North  America,  by  Cyrus  Thomas, 
Ph.I).  4to. — From  the  U.S.  Geological  Survey. 

Annual  Report  of  the  Board  of  Regents  of  the  Smith- 
sonian Institution  for  1871.  8vo. — From  the  Institu- 
tion * 

Annual  Report  of  the  Chief  Signal  Officer  to  the  Secretary 
of  War  for  the  year  1872.  8vo. — From  the  Secretary  of 
War. 

Astronomical  and  Meteorological  Observations  made  during 
the  year  1871.  4to. — From  the  U.S.  Naval  Observa- 
tory. 

Contributions  to  the  Extinct  Yertebrate  Fauna  of  the 
Western  Territories,  by  Joseph  Leidy.  4to. — From  the 
U.S.  Geological  Survey. 

Daily  Bulletin  of  Weather  Reports,  1872.  4to. — From  the 
War  Department. 

First,  Second,  and  Third  Annual  Reports  of  the  United 
States  Geological  Survey  of  the  Territories  for  the  years 
1867,  1868,  and  1869.  8vo.— From  the  U.S.  Geological 

Survey. 


413 


of  Edinburgh,  Session  1873-74. 

Washington . — Lists  of  Elevations  in  that  portion  of  the  United 
States  west  of  the  Mississippi  Eiver.  1873.  4to. — From 
the  U.S.  Geological  Survey. 

Meteorological  Observations  during  the  year  1872  in  Utah, 
Idaho,  and  Montana.  8vo. — From  the  U.S . Geological 
Survey. 

Reports  of  Explorations  and  Surveys  to  ascertain  the 
Practicability  of  a Ship  Canal  between  the  Atlantic  and 
Pacific  Oceans  by  the  way  of  Tehuantepec.  1872.  4to. 
— From  Sir  Charles  Hartley. 

Report  on  the  North  Sea  Canal  of  Holland,  and  on  the 
Improvement  of  Navigation  from  Rotterdam  to  the  Sea. 
1872.  4to. — From  Sir  Charles  Hartley. 

Report  of  the  United  States  Geological  Survey  of  the 
Territories.  Yols.  I.,  Y.  4to. — From  the  United  States 
Survey. 

Sixth  Annual  Report  of  the  United  States  Geological 
Survey  of  the  Territories,  embracing  Portions  of  Montana, 
Idaho,  Wyoming,  and  Utah,  for  the  year  1872.  8vo. — 
From  the  U.S.  Geological  Survey. 

Smithsonian  Miscellaneous  Collections.  Yob  N.  8vo. 
— From  the  Institution . 

Wellington , N.  Z. — Catalogue  of  the  Marine  Mollusca  of  New  Zea- 
land, with  Diagnoses  of  the  Species.  1873.  8vo. — From 
the  Colonial  Museum  and  Geological  Survey. 

Catalogue  of  the  Tertiary  Mollusca  and  Echinodermata  of 
New  Zealand.  1873.  8vo. — From  the  Colonial  Museum 
and  Geological  Survey. 

Critical  List  of  the  Mollusca  of  New  Zealand  contained  in 
European  Collections.  1873.  8vo. — From  the  Colonial 
Museum  and  Geological  Survey. 

Statistics  of  New  Zealand.  1872.  Eol. — From  the  Neiv 
Zealand  Government. 

Whitby. — The  Fifty-First  Report  of  the  Whitby  Literary  and 
Philosophical  Society.  1873.  8vo. — From  the  Society. 

Wisconsin. — Transactions  of  the  Academy  of  Sciences,  Arts,  and 
Letters.  1870—72.  8vo. — From  the  Society. 


414  Proceedings  of  the  Royal  Society , 1873-74. 

Wisconsin. — Transactions  of  the  Wisconsin  State  Agricultural 
Society.  Yol.  X.  1871;  XI.  1872-73.  8vo. — From  the 
Society. 

Zurich. — Neue  Denkschriften  der  allgemeinen  schweizerischen 
G-essellschaft  fur  die  gesammten  Naturwissenschaften — 
(Nouveaux  Memoires  de  la  Societe  Helvetique  des 
Sciences  Naturelles).  Band  XXY.  mit  23  Tafeln.  4to. 
— From  the  Society. 

Yierteljahrsschrift  der  Naturforschenden  G-esellschaft  in 
Zurich,  Jahrgang  I.  -XYIII.  8vo. — From  the  Society. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


VOL.  VIII. 


1874-75. 


No.  90. 


Ninety-Second  Session. 

Monday , 23  d November  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Council  were  elected 
President. 

Sir  WILLIAM  THOMSON,  Knt.,  LL.D. 

Honorary  Vice-Presidents. 

His  Grace  the  DUKE  of  ARGYLL. 

Sir  ROBERT  CHRISTISON,  Bart.,  M.D. 

Vice-Presidents. 

Sir  W.  Stirling-Maxwell,  Bart.  [ Rev.  W.  Lindsay  Alexander,  D.D. 
David  Milne  Home,  LL.D.  David  Stevenson,  Esq.,  C.E. 

Professor  Kelland.  | The  Hon.  Lord  Neaves. 

G-eneral  Secretary — Dr  John  Hutton  Balfour. 

Secretaries  to  Ordinary  Meetings. 

Professor  Tait. 

Professor  Turner. 


Treasurer — David  Smith,  Esq. 

Curator  of  Library  and  Museum — Dr  Maclagan. 


Councillors. 


Professor  Lister. 

George  Robertson,  Esq.,  C.E. 

The  Right  Rev.  Bishop  Cotterill. 
Professor  A.  Crum  Brown. 

Dr  Arthur  Mitchell. 

George  Forbes,  Esq. 

VOL.  VIII. 


Principal  Sir  Alex.  Grant,  Bart. 
Professor  Geikie. 

Dr  Andrew  Fleming,  H.M.I.S. 
Dr  Charles  Morehead. 
Alexander  Buchan,  A.M. 
Robert  Wyld,  Esq. 

3 ii 


416 


Proceedings  of  the  Royal  Society 


Monday,  7th  December  1874. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  Keith  Prize  for  the  Biennial  Period  (1871-73)  having 
been  awarded  by  the  Council  to  Professor  Tait  for  his  Paper, 
entitled  “ First  Approximation  to  a Thermo-Electric  Diagram,” 
which  has  been  published  in  the  Transactions,  the  Medal  was 
delivered  to  him  by  the  President  at  the  commencement  of  the 
meeting. 

The  President  said — I have  now  the  pleasing  duty  of  awarding 
the  Keith  Medal,  for  1871-73,  to  Professor  Tait,  for  a paper 
entitled  “First  Approximation  to  aThermo-ElectricDiagram.”  This 
paper  is  published  in  the  number  of  the  Transactions  which  I hold 
in  my  hand,  being  Part  1.  of  Volume  XXVII.,  for  Session  1872-73. 
The  Society,  considering  the  remarkable  interest  which  attaches  to 
the  subject  of  this  paper,  and  the  very  important  discovery  which 
it  contains,  will,  I am  sure,  pardon  me  if  I take  up  a little  of  their 
time  by  referring  to  some  of  the  antecedents  of  Professor  Tait’s 
investigation.  In  the  first  place,  there  was  the  great  discovery  by 
Seebeck,  about  the  year  1821,  of  thermo-electric  currents.  Accord- 
ing to  this  discovery,  if  a circuit  be  formed  of  two  different  metals, 
and  if  the  two  junctions  be  kept  at  different  temperatures,  an 
electric  current  will  be  found  to  go  round  the  circuit : — that  is 
Seebeck’s  great  discovery.  Quickly  following  upon  it  was  the 
very  remarkable  discovery  made  by  Cumming,  the  late  professor 
of  chemistry  in  the  University  of  Cambridge,  that  there  is  in 
certain  pairs  of  metals  an  inversion  of  the  thermo-electric  cur- 
rent of  a very  remarkable  kind.  A few  words  are  necessary  to 
make  it  intelligible.  Take  a circuit  of,  let  us  say,  bismuth  and 
antimony.  Let  one  of  the  junctions  be  kept  at  an  ordinary  tem- 
perature. Let  the  other  junction  be  gradually  raised  in  tempera- 
ture. With  a proper  instrument  for  measuring  the  strength  of  the 
current  flowing  through  the  circuit,  it  will  be  found  that  the 
strength  of  the  current  gradually  increases  as  the  hot  junction  is 
made  hotter  and  hotter.  That  was  part  of  Seebeck’s  discovery. 


417 


of  Edinburgh,  Session  1874-75. 

Cumming  experimented  on  many  other  pairs  of  metals,  and, 
amongst  them,  copper  and  iron.  In  experimenting  upon  copper 
and  iron,  he  found  that  as  the  hot  junction  is  made  hotter  and 
hotter,  the  current  increases,  but  only  up  to  a certain  limit. 
When  the  hot  junction  is  made  still  hotter  than  a certain  critical 
temperature,  the  current  begins  to  diminish  in  strength,  till  it 
becomes  zero.  When  the  hot  junction  is  made  hotter  still,  the 
current  becomes  reversed.  This  was  a very  great  discovery 
indeed  in  thermo-electricity.  I could  be  tempted  to  go  into 
some  more  details,  but  I should  perhaps  tax  the  patience  of  the 
Society  were  I to  do  so.  But  I cannot  refrain  from  mentioning 
the  thermo-dynamic  relations  of  this  discovery  and  the  collateral 
discovery  by  Peltier,  that  there  is  a thermal  effect  produced  at  a 
junction  of  two  different  metals  when  by  any  means  an  electric 
current  is  caused  to  cross  from  one  metal  to  another.  I call 
that  a collateral  discovery, — collateral  with  Seebeck’s,  because  it 
might  have  been  made  quite  independently  of  Seebeck’s.  That 
might  be  one  discovery  and  Seebeck’s  another,  thoroughly  dis- 
connected, had  we  not  light  from  theory  to  put  them  into  relation 
with  one  another.  The  first  ray  of  light  thrown  on  the  subject  is 
to  be  found  in  an  almost  casual  remark  made  by  Joule  in  the 
course  of  some  not  casual — but  thoroughly  worked-out — observa- 
tions upon  the  relations  between  the  generation  of  heat  on  the  one 
hand  and  the  development  of  work  from  heat  on  the  other.  He 
remarked  that  the  absorption  of  heat  or  the  production  of  cold, 
manifested  under  certain  circumstances  by  electric  currents  cross- 
ing a junction  of  dissimilar  metals  in  Peltier’s  discovery,  was  to  be 
looked  to  as  a source  of  the  power  to  be  developed  from  a current 
of  electricity  produced  by  a thermo-electric  action.  The  thorough 
working  out  of  this  remark  of  Joule’s  required  the  application  of 
Carnot’s  theory.  The  relation  between  heat  absorbed  in  one  junc- 
tion of  the  thermo-electric  circuit,  heat  evolved  in  the  other,  and 
work  done  by  the  current  in  any  instrument  driven  by  the  current 
put  into  the  circuit — let  us  say,  a mechanical  engine  raising 
weights,  driven  by  the  current — the  relation,  I say  between  heat 
absorbed  in  the  one  junction,  heat  developed  in  the  other,  and 
mechanical  work  performed,  was  fully  worked  out  by  the  applica- 
tion of  Carnot’s  theory.  The  introduction  of  Cumming’s  inver- 


418 


Proceedings  of  the  Royal  Society 

sion  led  to  a very  novel  idea  regarding  the  properties  of  matter, 
and,  I may  say,  a novel  discovery  of  action  in  connection  with 
heat  and  electricity.  To  this  action  the  name  of  the  electric 
convection  of  heat  has  been  given.  When  this  is  taken  into 
account  in  connection  with  the  discoveries  of  Peltier,  Gumming, 
and  Seebeck,  it  appears  that  the  heat  supply  by  which  an  engine 
driven  by  the  thermo-electric  current  gets  its  energy  may  be  not 
in  a junction  between  two  dissimilar  metals,  but  by  the  peculiar 
absorption  of  heat,  or  generation  of  heat,  which  the  discovery  I 
have  last  mentioned  points  at  when  a current  passes  from  hot  to 
cold  or  cold  to  hot  in  the  same  metal.  I am  afraid  the  subject 
is  somewhat  involved ; but  I can  only  say  that  if  the  Fellows  of 
the  Royal  Society  diligently  read  their  own  Transactions,  it  would 
not  be  necessary  for  me  to  speak  about  it,  because  it  was  very 
minutely  unfolded  in  a paper  published  a good  many  years  ago. 
I chanced  to  be  the  author  of  that  paper  myself,  and  I speak  just 
now,  I must  confess,  with  a considerable  pride  of  the  position 
it  bears  in  relation  to  Professor  Tait’s  discovery.  This  dis- 
covery is,  that  there  are  in  many  cases  no  doubt,  but  notably  in 
cases  in  which  iron  is  one  of  the  metals,  not  merely  one  neutral 
point,  as  discovered  by  Cumming,  but  several  neutral  points. 
Tait  finds  that  when  a circuit,  composed  of  iron  and  (let  us 
suppose)  platinum,  has  the  temperature  of  one  junction  gra- 
dually elevated,  while  that  of  the  other  is  maintained  constant, 
the  current  first  increases,  then  diminishes,  then  increases,  then 
diminishes, — or,  it  may  be,  first  increases,  then  diminishes  to 
nothing,  and  goes  in  the  contrary  direction,  attains  a maximum  in 
that  contrary  direction,  then  diminishes  from  that  maximum  to 
zero,  and  increases  in  the  first  direction  to  a maximum,  and  so  on 
with  every  alternation.  “ Multiple  neutral  points”  is  the  shortest 
name  I can  give  in  words  to  the  great  discovery  in  Professor  Tait’s 
paper.  But  I would  do  Professor  Tait  great  injustice,  and  give  you 
a very  imperfect  idea  of  the  substantial  character  of  the  investiga- 
tion for  which  the  award  has  been  made,  were  I to  lead  you  to 
suppose  that  it  was  merely  a discovery  which  some  of  you  might 
for  a moment  imagine  could  be  hit  off  by  chance,  and  by  an  ex- 
perimenter who  had  not  his  eyes  absolutely  closed.  This  discovery 
was  made  in  the  course  of  an  elaborate  investigation,  of  which 


of  Edinburgh,  Session  1874-75. 


419 


results  have  been  published  from  year  to  year,  and  generally  within 
the  two  years  for  which  the  award  has  been  given,  in  the  Pro- 
ceedings of  this  Royal  Society.  From  year  to  year  Professor  Tait 
had  accurate  measurements  of  thermo-electric  currents  executed  in 
his  laboratory.  The  results  he  tabulated  and  represented  graphi- 
cally ; and  even  before  making  this  discovery,  he  had  made  some 
exceedingly  important  contributions  towards  the  laws  of  thermo- 
electric force  in  various  combinations  of  metals.  It  was  in  pursu- 
ing this  elaborate  investigation  that  he  came  upon  the  very 
astounding  discovery — I call  it  really  astounding — that  there  are 
several  consecutive  neutral  points  between  one  and  another  of 
certain  pairs  of  metals — iron,  platinum,  iridio-platinum.  It  is  not 
my  object  to  give  you  imperfectly  a small  part  of  the  information 
contained  in  this  paper  of  Tait’s.  I desire  rather  to  call  your 
attention  to  a thing  of  much  value  which  you  have  in  your 
Transactions.  But  I may  be  allowed  the  pleasure  of  referring  to 
the  relation  which  my  own  previous  investigation  bears  to  this 
discovery  of  Tait’s.  I did  succeed  in  doing  away  with  the  Peltier 
effect  at  one  junction  ; I showed  a thermo-electric  current  without 
the  Peltier  effect  at  one  junction  but  with  Peltier  effect  at  the 
other  junction,  and  the  counter  effect,  absorption  or  evolution  as  it 
might  be,  made  by  my  own  thermo-electric  convection  in  the 
homogeneous  parts  of  the  circuit.  Now,  Tait  gives  us  a circuit  in 
which  there  is  no  Peltier  effect  at  all,  and  in  which  the  whole 
origin  of  the  power  is  to  be  found  in  absorption  on  the  one  hand 
and  evolution  on  the  other  through  electric  convection  of  heat.  I 
am  afraid  I have  taxed  your  patience  too  long,  because  these 
matters  have  been  reported  in  the  Proceedings  of  the  Society,  and 
we  have  now  a combined  statement  of  the  results  in  this  paper. 
Before  concluding,  I wish  to  call  your  attention  to  the  title 
of  the  paper,  “ A Thermo-electric  Diagram,”  and  the  admirable 
manner  in  which  Professor  Tait  has  represented  those  results 
graphically  to  the  eye,  and  the  good  use  he  has  made  of  that 
graphical  representation  in  aiding  him  to  wrork  out  rigorously  the 
laws  of  the  phenomenon.  I am  sure  the  Society  will  feel  very 
great  satisfaction  in  the  award  which  has  been  made  on  the  pre- 
sent occasion.  (To  Professor  Tait)  I have  now  much  pleasure 
in  presenting  you  with  the  Keith  Medal.  If  it  were  necessary 


420 


Proceedings  of  the  Royal  Society 

that  there  should  be  an  inducement  to  you  to  continue  your 
labours, — I cannot  say  with  increased  zeal, — hut  with  zeal  equal  to 
that  with  which  you  have  carried  them  on  for  the  last  few  years, 
let  me  hope  that  the  presentation  of  this  medal  may  form  a small 
part  at  least  in  such  a motive. 

The  President  opened  the  Session  with  an  Address  on 
Stability  of  Steady  Motion. 

The  following  statement  respecting  the  Members  of  the 


Society  was  read  by  the  President : — 

I.  Honorary  Fellows — 

Eoyal  Personage,  ......  1 

British  Subjects,  ......  20 

Foreign, 30 

Total  Honorary  Fellows,  . , 51 


Foreign  Honorary  Fellows  Deceased  since  Session 
1872-73:  — Agassiz,  Elie  de  Beaumont, 

Gluizot,  Hansteen,  Quetelet,  and  De  la 

Kive, 6 

II.  Non-resident  Member  under  the  Old  Laws,  . . 1 

III.  Ordinary  Fellows — 

Ordinary  Fellows  at  November  1873,  . . . 346 

New  Fellows,  1873-74. — Dr  John  Anderson;  W. 

F.  Barrett,  Esq.;  Dr  Joseph  Bell;  Thomas 
Muir,  M.A.;  Dr  Benjamin  Carrington;  Dr 
John  Chiene;  William  Durham,  Esq.;  William 
Ferguson,  Esq. ; Dr  Alexander  Hunter;  A. 

Forbes  Irvine,  Esq. ; Francis  Jones,  Esq. ; 

Dr  E.  A.  Letts;  James  Napier,  Esq.;  T.  B. 

Sprague,  M.A.  Cantab.;  Dr  R.  H.  Traquair; 

Dr  J.  Batty  Tuke, 16 

362 


Carry  forward,  362 


of  Edinburgh,  Session  1874-75.  421 

Brought  forward,  352 

Deduct  Deceased — Professor  Thomas  Anderson  ; 

George  Berry,  Esq. ; Adam  Black,  Esq. ; 

Sheriff  Cleghorn;  The  Bight  Hon.  Lord 
Golonsay ; Francis  Deas,  Esq. ; Henry 
Dircks,  Esq.;  William  Euing,  Esq.;  Dr  Bobert 
Grant;  Professor  John  Hunter;  Professor 
Cosmo  Innes;  Charles  Lawson,  sen.,  Esq.; 


and  Henry  Stephens,  Esq.,  . . . .13 

Resigned — Dr  W.  M.  Buchanan,  Dr  Alex.  Wood,  . 2 

Cancelled — Alfred  B.  Catton,  Bev.  Dr  Hodson,  . 2 

17 

Total  number  of  Ordinary  Fellows  at  Nov.  1873,  . 345 

Add  Honorary  and  Non-Besident  Fellows,  . . 52 

Total  to  1874,  397 


Monday,  21  st  December  1874. 

Professor  KELLAND,  Vice-President,  in  the  Chair. 

The  following  Communications  were  read : — 

1.  Remarks  on  the  Great  Logarithmic  and  Trigonometrical 
Tables  computed  in  the  Bureau  du  Cadastre  under  the 
direction  of  M.  Prony.  By  Edward  Sang. 

The  volume  marked  “ Logarithms  0,”  now'  placed  on  the  Society’s 
table  contains,  to  28  places,  the  Logarithms  of  all  numbers  up  to 
Ten  Thousand.  In  preparing  it,  care  was  taken  that  each  prime 
should  be  placed  in  connection  with  two  distinct  sets  of  other  prime 
numbers,  in  order  that  all  likelihood  of  mistake  should  he  avoided. 
This  amounts  to  the  computation  of  each  logarithm  by  two  inde- 
pendent processes.  Opposite  each  prime,  reference  is  made  to  the 
page  of  the  record  of  calculations  ; and  the  accompanying  volumes 
marked  “Construction,  I.,  II.,”  contain  minutes  of  each  articulate 


422  Proceedings  of  the  Royal  Society 

step,  so  that  the  genesis  of  any  logarithm  may  readily  be  traced 
and  examined. 

The  logarithms  of  the  composite  numbers  have  been  found 
addition ; the  greater  part  of  these  have  been  twice  computed,  but 
the  whole  await  a revision  in  the  manner  about  to  be  described. 

Though  very  unlikely,  it  is  yet  possible  that  the  same  error  may 
happen  in  each  of  the  two  calculations ; thus  in  computing  the 
logarithm  of  8447,  two  distinct  formulas  were  used,  namely — 

2 • 3769  • 10s  + 1 = 3 • 37  • 251  • 3203  • 8447 
643  • 107  - 1 = 3 • 89  • 2851  • 8447 

and  the  agreement  of  the  two  results  would  show  conclusively  both 
to  be  right,  were  it  not  for  the  possibility  of  a coincidence  of  error 
in  some  of  the  other  logarithms,  or  of  an  error  in  the  logarithm  of 
3 which  is  common  to  both. 

In  order  to  remove  this  exceedingly  slight  doubt,  I prepared  an 
index  on  movable  cards,  to  show  the  page  on  which  each  formulae 
is  found;  and  another  index,  laid  on  the  table,  to  show  the  formulae 
into  which  each  prime  enters ; this  list,  however,  being  limited  to 
the  first  five  occurrences.  The  above  prime  is  there  found  in  two 
more  combinations : — 

2017- 10 ; + 1 = 73-3271-8447 
8447 -101  + 1 = 3-7-  11  - 37  * 9883, 

which  also  consist  with  previous  determinations.  Such  coincidence 
removes  all  doubt  as  to  the  accuracy  of  the  logarithm  of  8447, 
excepting,  indeed,  the  last-place  uncertainty  incident  to  all  com- 
putations of  incommensurable  quantities. 

To  put  the  last  touch  to  the  trustworthiness  of  this  table,  I had 
begun  to  supply,  from  the  larger  primes  downwards,  a third  formula 
to  each  prime  having  only  two  marked  against  it ; that  is,  to  place 
each  prime  in  at  least  three  distinct  combinations,  with  the  inten- 
tion, when  this  revision  shall  have  been  completed,  to  cause  the 
whole  of  the  logarithms  of  the  primes  to  be  re-extracted  from  the 
minutes,  and  the  summations  to  be  redone  by  another  hand;  when 
my  attention  was  drawn  to  a note  in  the  scientific  periodical 
“Nature,”  in  reference  to  the  proposed  publication  of  the  Million 


423 


of  Edinburgh , Session  1874-75. 

Table  for  which  this  Yol.  0,  though  then  incomplete,  had  served 
as  the  foundation.  This  note  I recite  in  full : — 

Note  from  u Nature  f 8th  October  1874. 

“ The  President  and  Council  of  the  Eoyal  Society  of  Edinburgh, 
impressed  with  the  conviction  that  the  progress  of  the  sciences 
demands,  and  has  long  demanded,  fuller  and  more  exact  tables  of 
logarithms  than  any  which  at  present  exist,  have  memorialised  Sir 
Stafford  Northcote  with  the  view  of  inducing  the  G-overnment  to 
print  a nine-figure  table  of  logarithms  from  unity  to  a million,  part 
of  which  has  already  been  calculated  by  Mr  Sang,  who  has  carried 
a fifteen-figure  table  up  to  300,000.  The  subject  of  undertaking 
the  publication  of  logarithm  tables — so  long  as  the  number  of 
figures  does  not  exceed  ten,  the  limit  of  utility — is  one  well  worthy 
the  attention  of  the  G-overnment;  but  in  the  present  case  there  are 
several  reasons  why,  if  the  application  is  refused,  the  loss  to  science 
will  not  be  so  great  as  some  might  think.  In  the  first  place,  a table 
of  1800  large  pages,  whether  in  one,  two,  or  three  volumes,  will  be 
so  unwieldy  that,  notwithstanding  the  ease  of  the  interpolations,  it 
would  probably  be  very  seldom  used  by  computers  ; and  secondly, 
because  all  who  require  more  than  seven  figures  will,  no  doubt, 
prefer  to  use  ten,  and  consult  the  existing  works.  In  fact,  nearly 
all  computors  would,  we  believe,  employ  Vlacq  or  Yega  in  prefer- 
ence to  the  proposed  table.  Mr  Sang,  in  the  pamphlet  which 
accompanies  the  memorial,  makes  a remarkable  error  when  he 
intimates  that  the  great  French  tables  have  not  been  used  to  verify 
any  seven-figure  table,  so  that,  ‘up  to  the  present  moment  we  have 
no  verification  of  Ylacq’s  great  work.’  In  point  of  fact,  the  whole 
of  Vlacq  was  read  with  the  copy  of  the  French  tables,  at  the  Paris 
Observatory,  by  M.  Lefort,  and  the  results  are  published  in  Yol. 
IV.  of  the  ‘ Annales  de  l’Observatoire  de  Paris.’  Almost  all  the 
errors  found  by  Mr  Sang,  by  means  of  this  table  are  among  those 
there  given  by  Lefort,  and  any  one  who  choses  ean,  without  much 
expenditure  of  trouble,  render  his  copy  of  Ylacq  all  but  free  from 
error — much  more  accurate  than  any  new  table  could  possibly  be.” 

In  my  paper  on  last-place  errors  in  Ylacq,  read  here  on  the  20th 
April,  I say,  speaking  of  the  Tables  du  Cadastre , “I  have  not 
learned  that  these  computations  have  been  used  for  the  verification 

3 i 


VOL.  VIII. 


424  Proceedings  of  the  Royal  Society 

of  those  already  printed,  . . . . ” and  I have  now  to  thank,  very 
cordially,  the  author  of  the  note  for  having  mentioned  the  labours 
of  M.  Lefort,  and  so  put  me  in  the  way  of  obtaining  very  startling 
and  very  important  information  in  regard  to  Prony’s  Tables. 

Concerning  the  errors  in  Ylacq,  the  author  of  the  note  says, 
“Almost  all  the  errors,  found  by  Mr  Sang  by  means  of  this  table 
are  among  those  there  given  by  Lefort,”  and  deduces  from  this  fact, 
in  accordance  with  the  well-established  axiom  that  the  part  is 
greater  than  the  whole — the  futility  of  this  or  of  any  other  new 
table.  Not  having  yet  mastered  the  first  principles  of  this  system 
of  logic,  I shall  not  venture  to  discuss  any  of  the  opinions  of  its 
inventor,  and  shall  only  look  at  the  wisdom  of  his  conclusion. 

The  studious  investigator  living  in  Iceland,  in  Terra  del  Fuego, 
or  even  here  in  Edinburgh,  where  logarithms  had  their  birth, 
needing  an  extensive  table  of  logarithms,  must  apply  to  his  book- 
seller for  Ylacq ; the  book  has  been  “ out  of  print  ” for  two  hun- 
dred years;  if  found  at  all,  its  price  is  antiquaries’  price.  Having 
succeeded,  his  next  business  is  to  procure  a copy  of  the  volume  of 
the  “ Annales  de  l’Observatoire.”  I myself  have  tried  the  libraries 
here  in  vain,  so  that  “without  much  expenditure  of  trouble,”  I 
have  not  made  my  copy  of  Ylacq  “ all  but  free  from  error, — much 
more  accurate  than  any  new  table  could  possibly  be.”  Even  after 
I shall  have  effected  the  correction  by  help  of  Lefort’s  list,  there 
will  remain  a great  uncertainty,  arising  from  the  fact  that  two 
copies  of  Vlacq  may  not  be  in  accordance  with  each  other.  To 
understand  this,  we  may  turn  to  the  Errata  printed  on  page  64  of 
Taylor’s  Tables.  There  we  find,  among  others,  the  following 
remarks : — 

“In  about  100  copies;  in  about  120  copies;  doubtful  whether 
a few  copies  are  erroneous  or  not ; in  about  half  the  impression ; 
only  in  one  copy  ; and  so  on.” 

The  movable  types  had  been  drawn  out  by  the  inking  dabber, 
and  erroneously  replaced  by  the  pressman.  But  in  this  case  there 
is  another  uncertainty.  Complaints  were  made  of  pirated  editions, 
fac  simile  of  the  original  Ylacq. 

The  search  for  the  list  of  errors  mentioned  in  the  above  note, 
led  me  to  find  two  papers  by  M.  F.  Lefort.  The  first  of  these, 
coutained  in  the  “ Comptes  Rendus,”  tome  xliv.  page  1097,  was 


of  Edinburgh , Session  1874-75.  425 

read  to  the  Academy  on  the  25th  May  1857,  and  entitled  “ Note 
snr  les  erreurs  que  contient  une  des  Tables  de  Logarithmes  de 
Callet,  par  M.  F.  Lefort,”  shows  its  author  to  possess  every  claim 
to  our  confidence  and  respect  as  a computer.  The  indication  of 
wholesale  errors  in  Callet’s  twenty-place  table  (copied  also  into 
Hutton’s)  is  invaluable,  as  preventing  farther  mistake,  and  as 
showing  the  absolute  need  for  a revision  of  our  most  trusted  tables. 

The  second  paper  is  in  vol.  xlvi.,  and  was  occasioned  by  remarks 
on  the  presentation  to  the  Library  of  the  Institute  of  a manuscript 
copy  of  the  great  tables  which  had  been  in  the  possession  of  Prony 
himself.  It  was  presented  by  Prony’s  heirs,  at  the  meeting  of  the 
Academy,  on  Monday  the  17th  May  1858. 

In  the  course  of  remarks  after  the  presentation,  M.  Elie  de 
Beaumont  expressed  his  opinion  that  the  best  means  of  preserving 
the  work  would  be  to  print  it ; and  M.  Leverrier,  drawing  attention 
to  M.  Lefort’s  labours,  spoke  as  if  a doubt  exist  even  as  to  the 
whereabouts  of  the  veritable  original  calculations. 

At  the  next  meeting,  that  of  the  24th  May  1858,  the  note  above  men- 
tioned was  read,  entitled,  ‘‘Note  sur  les  deux  exemplaires  manuscrits 
des  G-randes  Tables  logarithmiques  et  trigonometriques,  calculees  au 
Bureau  du  Cadastre,  sous  la  direction  de  Prony ; par  M.  F.  Lefort.” 

I regret  that  the  length  of  this  most  remarkable  and  most 
valuable  memoir  precludes  its  reproduction  here.  As,  however, 
the  “ Comptes  Rendu s”  are  very  widely  distributed,  a verification 
of  my  remarks  upon  it  is  within  the  reach  of  many.  The  note 
refers  almost  exclusively  to  the  logarithmic  part  of  the  tables. 

It  tells  us  that  the  great  work  was  accomplished  by  a staff  of 
computors,  divided  into  three  sections ; the  first  section  consist- 
ing of  four  or  five  geometers,  whose  business  was  to  do  the  purely 
analytical  part,  and  to  calculate  certain  fundamental  numbers ; the 
second  section  was  formed  of  seven  or  eight  calculators  acquainted 
with  analysis  : they  made  calculations  directly  from  the  formulae 
arranged  by  the  first  section.  The  third  section  contained  seventy 
to  eighty  persons  having  a very  slight  acquaintance  with  mathe- 
matics, whose  business  was  to  perform  the  additions  and  subtrac- 
tions prescribed  by  the  second  section. 

We  have  here  a little  army,  with  its  generals  and  lieutenants, 
M.  Prony  himself  being  commander-in-chief.  Lefort  does  not 


426  Proceedings  of  the  Royal  Society 

acquaint  us  with  the  duties  undertaken  by  the  director,  neither 
does  he  indicate  the  nature  of  the  logarithmic  formulae  which 
needed  the  concurrence  of  four  or  five  geometers  for  their  estab- 
lishment. The  actual  business  described  by  him  begins  with  the 
doings  of  the  second  section,  composed  of  “ sept  on  huit  calcula- 
teurs,  possedant  l’analyse  et  ayant  une  grande  pratique  de  la 
traduction  des  formules  en  nombres.” 

These  calculated  1°,  the  ten  thousand  first  logarithms  to  nine- 
teen decimals. 

In  regard  to  this  part  of  the  work,  M.  Lefort  supplies  us,  some- 
what indirectly  however,  with  some  very  distinct  information. 
He  says  (page  996)  that  Prony  had  borrowed  a copy  of  Briggs’ 
Arithmetica  Logarithmica , which  he  returned  enriched  with  an 
u errata preceded  by  a note  to  the  following  effect; — 

“ This  ‘ errata’  is  composed  1°  of  that  which  is  at  the  top  of  the 
Latin  introduction  (of  Briggs);  2°  of  the  faults  found  by  the 
citizens  Leteilier  and  G-uyetant,  calculators  in  the  Bureau  du 
Cadastre,  on  collating  Briggs’  table  with  the  great  tables  of  the 
Cadastre.  These  latter  faults  are  marked  by  (a  particular  sign) 
the  sign 

Lefort  goes  on  to  say  that  this  collation  brought  out  thirty-two 
new  faults,  of  which,  however,  he  finds  that  four  belong  to  the 
Cadastre  table,  leaving  twenty-eight  only  to  Briggs.  Farther  on 
he  tells  us  that  all  the  corrections  for  numbers  above  10,000  refer 
to  figures  within  eleven  decimal  places,  leaving  the  twelfth, 
thirteenth,  and  fourteenth  places  of  Briggs  unchecked.  From 
this  I understand,  although  it  be  not  explicitly  so  stated,  that 
within  the  ten  thousand,  even  these  figures  in  Briggs  had  been 
examined. 

Now,  here  I shall  take  the  liberty  of  making  an  interjection  of 
my  own. 

In  March,  while  comparing  my  fifteen-place  table  with  Vlacq, 
I thought  it  desirable  to  examine  also  the  last  places  of  Briggs; 
so  the  final  groups  of  four  figures  in  the  Arithmetica  Logarithmica 
were  read  with  the  corresponding  figures  in  the  volume  now  on 
the  table,  up  to  3000.  The  readers  found  the  labour  of  recording 
the  discrepancies  so  great  that  they  had  to  content  themselves 
with  a pencil  mark  when  the  difference  was  only  unit,  and  with 


427 


of  Edinburgh,  Session  1874-75. 

a double  mark  when  the  divergence  was  more.  Moreover,  since 
perusing  M.  Lefort’s  note,  I have  caused  the  same  readers  to 
examine  the  tenth  thousand,  and  1 exhibit  the  book  itself  with 
their  pencil  marks.  On  counting  these,  it  is  found  that  consider- 
ably over  forty  per  cent,  of  Briggs’  final  figures  are  in  error. 

When  we  consider  that  Briggs  used  only  fifteen  decimals  in  his 
“ Tabula  inventioni  Logarithmorum  inserviens,”  we  can  hardly 
expect  a smaller  proportion  of  errors  than  this  among  his  final 
figures;  and  the  examination  exhibits  in  a very  strong  light  the 
scrupulous  care  bestowed  by  him  upon  the  work.  But  M.  Prony’s 
coadjutors  of  the  second  section  carried  their  operations  to  nine- 
teen decimals — that  is,  to  one  hundred  thousand  times  the  exacti- 
tude aimed  at  by  Briggs,  and  not  one  of  his  errors  should  have 
escaped  detection.  It  becomes,  then,  quite  a mystery  how  MM. 
Letellier  et  Gfuyetant  should  have  allowed  upwards  of  four  thousand 
errors  to  escape  their  notice. 

To  resume.  Having  accomplished  this  first  part  of  their  labour, 
the  members  of  the  second  section  computed  2°  “ the  logarithms 
from  10,000  to  200,000  by  intervals  of  200  to  14  decimals,  and 
with  four,  five,  and  even  six  orders  of  differences.  The  number  of 
decimals  was  successively  augmented  by  two  for  each  order;  so 
that,  for  example,  the  sixth  difference  was  written  with  26 
decimals;”  and  this  seems  to  have  concluded  their  labours  so  far 
as  the  logarithmic  table  is  concerned.  The  results  were  handed 
over  to  the  third  section. 

Again,  leaving  for  a while  the  course  of  M.  Lefort’s  details  con- 
cerning the  preparation  of  the  ruled  sheets,  I shall  begin  in 
earnest  the  computation  of  the  final  table.  The  logarithm  of 
10,000,  and  the  differences  of  the  successive  orders,  are  inscribed 
on  the  upper  horizontal  line  of  a sheet,  as  in  the  annexed  example. 
Our  business  is  to  add  the  first  difference  to  the  accompanying 
logarithm  ; to  take  the  second  difference  from  the  first  p^the  third 
from  the  second,  and  so  on  ; and  this  has  to  be  repeated  255  times, 
until  we  reach  the  number  10,200,  whose  logarithm,  with  its  differ- 
ences,  ought  to  agree  with  what  has  been  prepared  for  the  second 
sheet.  There  are  then  to  be  performed  two  hundred  additions  and 
one  thousand  subtractions  of  large  numbers  before  the  calculator 
of  the  third  section  arrive  at  a check  on,  or  can  know  anything  of, 


428 


Proceedings  of  the  Royal  Society 


the  accuracy  of  his  work.  Also,  an  error  in  the  determination  of 
the  first  difference  of  the  sixth  order  is  augmented  82,472,326,300 
times  in  the  final  logarithm.  Perhaps  it  is  on  this  account  that 
the  differences  are  carried  two  places  further  at  each  step. 

I do  not  understand  in  what  way  the  two  additional  figures 
belonging  to  one  order  of  difference  are  disposed  of  when  sub- 
tracted from  the  difference  of  the  next  lower  order,  and  M.  Lefort 
gives  us  no  information  on  this  most  perplexing  subject.  Putting 
the  embarrassment  therewith  connected  out  of  view,  the  perform- 
ance of  these  twelve  hundred  operations,  subject  at  every  step  to  the 
prodigious  accumulation  of  early  error,  is  a task  which,  I venture 
to  affirm,  was  never  successfully  accomplished  by  any  computer. 

This,  however,  is  but  a small  part  of  the  difficulty.  In  order  to 
make  the  matter  clear,  I have  placed  in  the  accompanying  scheme 
the  logarithims  of  the  first  ten  numbers,  with  their  differences 
arranged  in  the  manner  described,  as  they  ought  to  be  found  on  the 
first  sheet,  each  of  them  true  to  the  last  figure. 


N. 

Log. 

1st  Diff. 

2d  Diff. 

3d  Diff. 

4th. 

5th. 

6th. 

10000 

•00000  00000  0000 

4 34272  76862  7 

43  42076  382 

868  19823 

26036  83 

10  4100 

520  2 

01 

04  34272  7686 

4 34229  34786  3 

43  41208  184 

867  93786 

26026  42 

10  4048 

519  9 

02 

08  68502  1165 

4 34185  93578  1 

43  40340  246 

867  67760 

26016  02 

10  3996 

519  6 

03 

13  02688  0523 

4 34142  53237  9 

43  39472  568 

867  41744 

26005  62 

10  3945 

519  2 

04 

17  36830  5846 

4 34099  13765  3 

43  38605  151 

867  15738 

25995  23 

10  3893 

519  0 

10005 

06 

07 

08 
09 

10010 

21  70929  7223 
26  04985  4739 
30  38997  8481 
34  72966  8536 
39  06892  4991 

43  40774  7932 

4 34055  75160  1 
4 34012  37422  1 
4 33969  00551  0 
4 33925  64546  6 
4 33882  29408  5 

43  37737  994 
43  36871  096 
43  36004  459 
43  35138  081 

866  89743 
866  63758 
866  37783 

25984  84 
25974  45 

10  3841 

There  we  find  that  the  sixth  difference  is  rapidly  becoming  less ; 
at  the  top  of  the  page  it  is  5202,  and  at  the  end  of  the  200  opera- 
tions it  should  shrink  to  4619.  Now  the  third  class  computer,  to 
whom  the  ruled  sheet  with  only  the  first  line  inscribed  on  it  was 
delivered,  must  necessarily  have  carried  the  same  sixth  difference 
all  the  way  down,  and  therefore,  even  on  the  most  favourable  suppo- 
sition that  all  the  differences  had  been  carried  out  to  the  twenty- 
sixth  place,  the  result  must  have  been  egregiously  erroneous. 

Again,  we  come  inevitably  to  the  number  10010.  Now  the 


429 


of  Edinburgh,  Session  1874-75. 

essential  character  of  the  denary  system  of  logarithms,  that  from 
which  it  derives  all  its  advantages,  is  this, — that  the  mantissa  of 
the  logarithm  of  such  a number  as  10010  is  an  exact  copy  of  that 
for  1001 ; but  this  number  1001  has  had  its  logarithm  already 
computed  to  nineteen  places,  so  that  we  have  only  to  collate  the 
two  in  order  to  verify  this  much  of  the  work.  That  is  to  say,  this 
great  unwieldy  gap  of  200  intervals  had  already  been  divided  into 
twenty  smaller  gaps,  and  the  labour  of  the  interpolation  has  been 
uselessly  augmented  at  least  one  hundred  times. 

And  yet  further,  in  the  accompanying  second  scheme  I have 
put  the  logarithms  of  the  first  ten  numbers  on  the  first  sheet  of 
the  Cadastre  manuscript,  true  all  to  the  fourteenth  place,  with 
their  differences  of  the  first,  second,  and  third  orders.  Differences 
of  the  fourth  order  only  make  their  appearance  in  the  sixteenth 
decimal  place,  and  are  here  awanting.  Fourteen  place  logarithms, 
then,  for  numbers  above  10,000  can  have  no  differences  of  the 
fourth,  fifth,  and  sixth  orders;  and  all  this  display  of  high  orders 
of  differences  and  of  additional  places  of  decimals  has  been  a matter 
of  pure  supererogation. 


N. 

Log. 

1st  Diff. 

2d. 

3d. 

10000. 

•00000  00000  0000 

4 34272  7686 

43  4207 

86 

01 

04  34272  7686 

4 34229  3479 

43  4121 

86 

02 

08  68502  1165 

4 34185  9358 

43  4035 

89 

03 

13  02688  0523 

4 34142  5323 

43  3946 

85 

04 

17  36830  5846 

4 34099  1377 

43  3861 

87 

10005 

21  70929  7223 

4 34055  7516 

43  3774 

87 

06 

26  04985  4739 

4' 34012  3742 

43  3687 

87 

07 

30  38997  8481 

4 33969  0055 

43  3600 

86 

08 

34  72966  8536 

4 33925  6455 

43  3514 

87 

09 

39  06892  4991 

4 33882  2941 

43  3427 

86 

10010 

11 

12 

43  40774  7932 
47  74613  7446 
52  0S409  3619 

4 33838  9514 
4 33795  6173 

43  3341 

Here  the  third  differences  are,- as  it  were,  constant;  the  irregu- 
larities shown  by  them  are,  as  every  calculator  knows,  due  to  the 
neglect  of  the  farther  decimal  parts.  The  third  differences,  if 
absolutely  true,  should  show  a slight  steady  diminution,  and  thus 
we  may  expect,  without  any  calculation,  that  the  two  succeeding 
third  differences  should  be  from  88  to  85.  Now  the  logarithm 


430  Proceedings  of  the  Royal  Society 

of  5006  had  been  computed  to  nineteen  places,  and  if  we  write 
the  logarithm  of  2 on  the  edge  of  a piece  of  paper,  and  then 
appose  it  to  that  of  5006,  we  shall  obtain  at  a glance  the  logarithm 
of  10012.  However,  we  shall  not  even  take  the  trouble  of  this 
addition,  but  shall  content  ourselves  with  the  fourteenth  figure, 
which  we  find  to  be  9.  Let  us  write  this  9 in  its  proper  place, 
which  -is  two  lines  below.  All  that  remains  for  us  is  to  discover 
what  two  digits  must  be  written  in  the  last  place  of  the  third 
difference  in  order  to  produce  this  digit  9,  knowing  also  that  these 
digits  should  be  about  6. 

The  strict  investigation  is  simplicity  itself.  Let  us  put  a , b,  c,  cZ, 
for  the  last  numbers  in  the  successive  columns  alt  biy  r15  du  for 
those  which  are  to  succeed  a2,  b..y  c2,  d.2,  for  the  next  again,  and 
we  find 

a2  — a - 2b  + 3c  = 3 d1  + d2 . 

In  resolving  this  equation  we  need  attend  only  to  the  last  figures, 
so  that,  applying  it  to  the  example  before  us, 

• • • 9 — 2 — 2 + 2 = 3dy  + d.2%  or 
7 = Sd±  + d%- 

Recollecting  that  dx  and  d.2  must  be  absolutely  or  nearly  alike, 
we  may  put  for  trial 

7=4  dlt 

whence  d1  is  nearly  7,  and  we  have  actually  dx  = 7,  d.2  = 6;  so  that 
the  succeeding  pair  of  differences  must  be  87,  86.  Writing  these 
in  their  places,  we  readily  compute  the  next  pair  of  logarithms  as 
shown  by  the  slender  figures. 

By  a computation  performed  mentally  in  a few  seconds,  without 
putting  pen  to  paper,  we  thus  compute  the  third  differences  for  the 
next  pair  of  logarithms,  with  the  certainty  that  the  alternate  one 
is  absolutely  true  in  the  last  place,  and  with  a very  slight  uncer- 
tainty as  to  the  intermediate.  The  whole  magnificent  array  of 
fourth,  fifth,  and  sixth  differences,  with  decimals  to  the  twenty- 
sixth  place,  disappears. 

This  amounts  to  the  recognition  of  the  fact  that  the  large  gap 
of  200  intervals  had  already  been  supplied  with  100  stepping- 
stones,  a fact  of  which  neither  Prony  nor  any  one  of  his  regiment 


431 


o f Edinburgh,  Session  1874-75. 

of  geometers  seems  to  have  been  aware.  The  method  followed 
in  the  calculation  of  the  Cadastre  table  of  logarithms  was  an 
egregious  blunder.  The  result  was  in  accordance  with  the 
method. 

After  having  told  us  that,  for  numbers  above  10,000,  the  errors 
in  Brigg’s  last  three  figures  are  not  given,  M.  Lefort  goes  on  to 
say  (page  997): — “For  all  that  there  do  exist  numerous  diver- 
gencies in  the  thirteenth  and  fourteenth  places.  We  must  thence 
conclude  that  the  calculators  did  not  suppose  the  Cadastre  tables 
to  have  enough  of  precision  for  correcting  Brigg’s  last  places.  In 
that  they  were  perfectly  right.  The  bases  of  the  calculation  had 
been  chosen  so  as  to  make  sure  of  twelve  places,  and  the  precautions 
taken  were  only  applicable  to  the  research  of  these  twelve  places, 
which  are  all  that  are  fit  for  publication.” 

In  order,  after  the  method,  but  not  behind  it  in  importance, 
comes  the  conscientiousness  with  which  the  work  is  performed. 

The  careful  computer  who  may  have  to  revise  his  own  work  puts 
the  first  performance  aside,  even  leaves  it  for  a considerable  time, 
lest  the  sight  of  the  figures,  or  the  remembrance  of  them,  should 
lead  to  the  repetition  of  an  error : better  still,  he  arranges  the 
operation  in  another  way,  so  that  the  same  additions  and  subtrac- 
tions may  not  recur.  But  when  he  has  to  do  with  hired  assistants 
he  must  contrive  safeguards  against  carelessness,  even  against 
simulation.  Against  the  former  it  is  possible,  though  difficult,  to 
protect  one’s  self,  but  against  the  latter  there  is  no  protection 
other  than  in  repeating  the  work,  which  comes,  in  effect,  to  the 
dismissal  of  the  delinquent.  The  most  obvious  safeguard  is  to 
have  the  work  done  by  two  or  more  computers  who  have  no  oppor- 
tunity of  intercommunication. 

Now  the  above  described  fundamental  arrangement  of  the  work 
excluded  the  possibility  of  such  isolation.  The  computer^ra  very 
ordinary  computer,  knowing  little  of  mathematics — ^s  desired 
to  make  a chain  of  calculations  involving  about  13,000  figures ; 
and  the  test,  to  him,  of  the  accuracy  of  his  performance  was  to  be 
found  at  its  conclusion.  By  the  time  that  the  twentieth  part  of 
this  task  was  done,  the  calculator  must  have  felt  the  danger  of 
error;  perhaps  he  revised  thus  far  on  loose  paper,  found  errors, 
and  corrected  them.  Another  division  of  the  task  was  done  in 

3 K 


VOL.  VIII. 


432  Proceedings  of  the  Royal  Society 

the  same  way,  and,  with  trembling,  the  conscientious  worker 
having  toiled  for  several  days,  arrived  at  the  end,  to  find,  in  spite 
of  all  his  care,  some  lamentable  errors.  The  search  for  the  source 
of  these,  and  their  correction,  might  occupy  more  time  and  be 
more  irksome  than  the  actual  work.  But  his  collaborator  had 
experienced  the  same  troubles.  In  order  to  lessen  these,  and 
really  to  improve  the  performance,  the  two  came  to  exchange  their 
loose  sheets;  and  the  habit  of  working  on  separate  papers  from 
which  copies  were  made  upon  the  official  sheets  came  to  be  firmly 
established.  This  was  inevitable,  and  might  easily  have  been 
foreseen. 

On  page  998,  M.  Lefort  details  circumstances  which  seem  to  him 
to  prove  that  the  majority,  if  not  the  totality,  of  the  calculators  of 
the  third  section  made  their  additions  and  subtractions  on  loose 
leaves,  which  they  could  dispose  of  freely;  afterwards  writing  the 
results  on  the  ruled  official  paper.  He  remarks,  ‘‘  This  was  incon- 
testably a fault.”  It  was,  in  my  opinion,  a complete  relinquish- 
ment of  the  safe-guard  afforded  by  duplicate  manipulation.  Now 
this  gross  and  habitual  infraction  of  the  official  rules  could  not  have 
remained  hid  from  the  superintendents.  It  must  have  been  winked 
at;  nay,  it  must  have  been  controlled  by  them.  The  existence  of 
many  local  and  restricted  “surcharges,”  or  corrections,  proves  that 
the  loose  paper  of  the  one  had  been  collated  with  that  of  the  other 
computer;  and  thus  the  whole  operation  was  conducted  with  a 
laxity  of  discipline  which  detracts  enormously  from  its  value. 

But  M.  Lefort  tells  us,  on  page  996,  that  Prony  was  so  jealous 
of  the  errors  induced  by  transcription,  that,  when  pressed  by  the 
Grovernment  to  extract  seven-place  trigonometric  tables  from  his 
extended  ones,  he  preferred  to  proceed  to  their  direct  construction, 
rather  than  to  incur  the  risk  of  the  errors  of  copying.  To  me  this 
appears  an  unintelligible  motive ; because,  whether  computed 
directly  or  not,  the  table  must  be  copied  in  type,  while  the  pro- 
bability of  exactitude  is  immensely  in  favour  of  the  extended 
calculation.  Lefort  proceeds  to  say,  “On  no  occasion  did  Prony  or 
his  collaborators  say  or  give  reason  to  think  that  there  had  been 
copying  on  the  ruled  sheets.” 

It  is  to  be  remarked,  that  Lefort  does  not  advert  at  all  to  that 
very  circumstance  which  gave  occasion  for  his  paper,  namely,  the 


of  Edinburgh,  Session  1874-75. 


433 


presentation  to  the  Library  of  the  Institute  of  a third  copy  of  the 
great  tables:  yet  he  says,  on  page  995,  that  the  collection  of  the 
leaves  filled  by  interpolation  was  to  form  a double  original ; that 
such  was  the  object,  the  only  object  of  the  operation,  “ Tel  etait  le 
but,  le  but  unique  de  l’operation.”  On  what  hypothesis,  then,  shall 
we  explain  the  existence  of  this  third  copy  a qui  avait  ete  laisse  a 
Prony  a titre  de  Minute/’  M.  Prony  could  not  have  possessed  it 
and  been  ignorant  of  the  fact  that  at  least  one  of  the  three  was  the 
result  of  transcription.  Yet  for  these  three  quarters  of  a century 
the  whole  mathematical  world  has  been  led  to  believe,  has  believed, 
has  acted,  and  has  spoken  in  the  belief  that  these  “Grandes  Tables” 
were  constructed  with  every,  the  most  scrupulous,  attention  to  the 
requirements  of  exactitude. 

Having  made  a most  careful  examination  of  the  logarithmic  part 
of  the  work — having  performed  the  duty  of  a most  conscientious 
witness  in  stating  the  facts  as  they  appeared  to  him — M.  Lefort  has 
not  ventured  to  sum  up  the  evidence ; but,  speaking  of  the  tables, 
concludes  his  paper  with  the  words,  “ Je  n’ai  voulu  aujourd’hui 
qu’en  constater  la  valeur,”  leaving  to  others  to  form  their  own 
opinions  of  the  exact  value  determined  by  his  revelations. 

He  does,  indeed,  express  a qualified  commendation,  for,  at  the 
foot  of  page  998,  he  says: — “ The  Cadastre  Tables,  like  all  human 
works,  are  then  not  perfect ; they  are  so  neither  in  their  execution 
nor,  perhaps,  in  the  details  of  their  conception nevertheless,  they 
much  surpass,  not  only  in  extent,  but  also  and  above  all  in  correct- 
ness, all  the  tables-  that  have  preceded  them,  and  the  more  modern 
tables  which  have  not  been  compared  with  them  before  publication.” 

Here  M.  Lefort  has  omitted  to  observe  that  he  had  been  collating 
a manuscript  calculation,  in  which  there  should  have  been  no  error, 
with  printed  books  subject  to  all  the  chances  of  mistakes  in  reading 
and  accidents  in  printing;  he  has  surely  also  forgotten  that  these 
manuscript  tables  were  so  imperfect,  and  were  known  to  their  com- 
puters to  be  so  imperfect  as  to  be  unfit  for  the  verification  of  the 
last  three  places  in  the  “ Arithmetica  Logarithmica,”  the  very  first 
work  on  denary  logarithms,  a work  undertaken  and  completed  by  a 
private  person,  amid  all  the  difficulties  and  round-aboutness  of 
infant  algebra.  As  to  the  details  of  the  conception,  he  has  told 
us  that  the  orders  of  differences  were  extended  to  the  .sixth,  that 


434 


Proceedings  of  the  Royal  Society 

the  decimal  places  went  to  the  twenty-sixth,  with  the  admirable 
result  of  an  exactitude  not  reaching  beyond  the  twelfth  place, 
where  differences  of  even  the  third  order  barely  appear.  And  above 
all,  he  has  failed  to  perceive  that  what  confidence  we  can  now  have 
in  these  prodigious  piles  of  figures  is  derived  from  the  labours  of  a 
single  individual,  whose  zeal  and  perseverance  led  him  to  collate 
with  the  Cadastre  table,  the  only  two  tables  which  preceded  them, 
and  to  examine  the  divergences  by  help  of  calculations  more  trust- 
worthy than  either;  that,  in  fact,  the  portion  of  the  “Grande 
Tables  ” entitled  to  claim  our  confidence  rests  that  claim  on  the 
joint  labours  of  Adrian  Ylacq  and  M.  F.  Lefort.  The  further  dic- 
tum, that  these  tables  are  more  exact  than  later  ones  which  have 
not  been  compared  with  them,  is  supported  by  no  evidence  or  argu- 
ment, besides  implying  an  obvious  absurdity. 

Concerning  the  rest  of  the  Logarithmic  Table,  that  belonging  to 
numbers  from  100,000  to  200,000  we  have  no  information,  because 
there  existed  no  table  for  comparison,  and  our  confidence  must  be 
founded  exclusively  on  what  we  know  of  the  principles  of  the 
method  followed,  of  the  fidelity  of  the  execution,  and  of  the  candour 
of  the  statements.  On  these  three  heads,  M.  Lefort  has  placed 
before  us  information  which  it  is  not  necessary  for  me  to  reca- 
pitulate. 

The  advantages  of  a uniform  scale  of  numeration  have  been 
recognised  in  all  ages.  The  ancient  geometers  adopted  the  basis 
60,  and  their  system  has  come  down  even  to  the  present  day.  If  the 
circumference  of  the  earth  be  divided  into  60  parts,  each  of  these 
again  into  60,  and,  once  more,  each  of  these  subdivisions  into  60 
parts,  we  come  almost  exactly  to  the  stadium;  according  to  the 
same  plan,  the  hour  and  the  degree  are  each  divided  in  sixtieths. 
It  is  the  uniformity,  the  self-consistency  of  this  system,  which  has 
so  long  preserved  it.  Twenty  centuries  ago,  the  sage  of  Syracuse 
placed  before  ‘King  G-elo  the  powers  of  the  more  convenient  denary 
system ; he  showed  how  a few  steps  of  a progression  by  myriads 
enabled  him  to  express  the  number  of  grains  of  sand,  not  in  the 
bay  of  Syracuse,  not  on  the  whole  shores  of  Sicily,  but  that  would 
be  contained  in  a sphere  having  the  moon’s  distance  for  its  radius. 
The  denary  system  has  gradually  gained  supremacy  in  the  languages 


of  Edinburgh,  Session  1874-75. 


435 


of  all  civilised  nations,  to  the  obliteration,  in  most  of  them,  of  every 
trace  of  any  other  system ; 260  years  ago,  it  was  crowned  by  the 
invention  of  logarithms,  which  invention  has  rendered  its  exclusive 
use  in  every  department  of  science  only  a question  of  time.  Briggs 
computed  a trigonometric  table  to  each  hundredth  part  of  the 
degree  ; and  near  the  end  of  the  last  century  the  still  further  im- 
provement was  proposed  of  dividing  the  quadrant  itself  into  one 
hundred  degrees,  and  each  degree  centesimally.  Borda,  about  1793, 
computed,  to  each  minute  of  this  division,  a table,  which  was  given 
in  a compressed  and  inconvenient  form  by  Callet,  in  his  “ Tables  Por- 
tatives but  an  extension  of  this,  at  least  so  far  as  to  each  tenth 
second,  was  absolutely  needed  before  the  centesimal  division  could 
be  used  in  the  higher  departments  of  geodesy  and  astronomy. 

The  French  government,  with  a most  enlightened  regard  for  the 
interests  of  science,  that  is,  for  the  interests  of  humanity,  ordered 
the  computation  to  be  proceeded  with,  and  entrusted  the  execution 
thereof  to  M.  Prony.  In  confident  expectation  of  the  speedy 
appearance  of  this  table,  M.  de  La  Place  gave  in  his  great  treatise 
on  Astronomy,  the  “ Mecanique  Celeste,”  the  data  and  formulae, 
according  to  the  new  division  of  the  circle.  The  calculations  have 
been  finished,  but  have  remained  in  the  libraries  of  the  Institute, 
and  of  the  Observatory,  inaccessible  and  useless  to  the  general 
scientific  public. 

It  would  be  difficult  indeed  to  over-estimate  the  injury  done  to 
the  progress  of  exact  science  by  this  calculation  and  this  occlusion, 
accompanied,  as  they  have  been,  by  the  pretence  of  exhaustive 
accuracy  and  unrivalled  extent.  There  was  enough  of  enterprise, 
enough  of  zeal,  to  have  long  ago  completed  the  necessary  work  to 
seven  places.  Michael  Taylor,  in  1792,  had  finished  a far  more 
extensive  work,  the  compilation  of  a seven-place  table  to  each  single 
second  of  the  old  division.  But  these  existent  and  unpublished 
tables  barred  the  way ; for  no  private  person  would  think  of  under- 
taking of  new  a work  which  had  been  already  so  well  accomplished. 
Thus  the  most  excellent  and  most  laudable  design  of  the  French 
Government  has  been  frustrated, — has  been  turned  from  a benefit 
to  an  injury. 

Though  sorely  needed  and  urgently  demanded,  the  new  tables 
did  not  appear ; and  when  expectation  had  been  stretched  to  the 


436 


Proceedings  of  the  lloyal  Society 

utmost,  tlie  English  G-overnment,  in  1819,  at  the  instance  of  Mr 
Davies  G-ilbert,  proposed  to  defray  one-half  of  the  expense.  The 
negociations  led  to  no  result.  M.  Lefort  gives  an  extract  from  a 
note  addressed  by  the  celebrated  astronomer  Delambre  to  the 
English  commissioner,  apparently  the  farewell  note.  I transcribe 
the  extract  from  page  999. 

“ Ces  tables,  non  plus  que  celles  de  Briggs,  ne  serviront  pas  dans 
les  cas  usuels,  mais  seulement  dans  des  cas  extraordinaires.  Comme 
celles  de  Briggs*  elles  seront  la  source  ou  viendrous  puiser  tous  ceux 
qui  impriment  les  tables  usuelles  avec  plus  ou  moin  d’etendue.  Elles 
serviront  de  point  de  comparaison  pour  tout  ce  qui  a ete  fait  ou  se 
fera.” 

Whether  shall  we  accept  this  magniloquent  praise  or  the  refusal 
to  print  the  tables  as  the  measure  of  their  value  ? Even  had  these 
tables  been  all  which  they  should  have  been, — all  that  was  pretended 
for  them, — the  concluding  sentence  is  preposterous.  Is  every  calcu- 
lation in  all  futurity  to  be  tested  by  comparison  with  Prony  ? No  ! 
Even  away  from  the  revelations  of  M.  Lefort,  the  independent 
original  computer  would  not  seek  to  dip  his  pitcher  in  the  well  at 
the  Bureau  de  Cadastre,  he  only  cares  to  fill  his  cup  at  the  small 
overflowing  spring  of  conscientious  performance. 

The  tables  of  Prony  cannot  be  printed  without  entire  revision ; 
in  such  a case  to  revise  is  to  supersede,  and  therefore  I call  upon 
the  whole  body  of  cultivators  of  exact  science  to  shake  off  this 
incubus,  to  hold  these  tables  as  non-existent,  and  to  face  manfully 
the  problem  of  computing  decimal  Trigonometrical  Tables  of  extent 
and  precision  sufficient  for  their  pioneers,  and  therefore  capable  of 
supplying  all  the  shorter  and  less  precise  tables  needed  for  their 
more  ordinary  pursuits. 


2.  On  the  Elimination  of  a,  (3,  y,  from  the  conditions  of 
integrability  of  S.  uaBp,  S.  u/38p,  S.  uySp.  By  M.  G-.  Plarr. 
Communicated  by  Professor  Tait. 


of  Edinburgh,  Session  1874-75. 


437 


3.  The  Development  of  the  Ova,  and  the  Structure  of  the 
Ovary,  in  Man  and  other  Mammals.  By  James  Foulis, 
M.D.  (Edin.)  Communicated  by  Prof.  Turner. 

After  an  historical  introduction,  in  the  course  of  which  the  author 
gave  an  abstract  of  the  important  observations  of  Pfliiger  and  Wal- 
deyer,  he  proceeded  to  state  his  own  observations  on  the  develop- 
ment of  the  ova  and  structure  of  the  ovary  in  calves,  kittens,  and 
the  human  female.  The  following  general  conclusions  have  been 
arrived  at  by  the  author  in  the  course  of  his  investigations : — 

The  corpuscles  of  the  germ  epithelium  are  derived  by  direct  pro- 
liferation from  those  columnar  corpuscles  which  invest  the  median 
side  or  surface  of  the  Wolffian  body,  and  which  are  continuous  with 
the  layer  of  columnar  corpuscles  that  lines  the  pleuro -peritoneal 
cavity  of  the  embryo  in  the  early  stages  of  development.  The 
stroma  of  the  ovary  in  the  early  stages  of  development  is  pro- 
duced by  a direct  growth  out  from  the  interstitial  tissue  of  the 
Wolffian  body  immediately  beneath  the  germ  epithelium  on  the 
median  side  of  the  Wolffian  body. 

The  germ  epithelial  corpuscles  proliferate  by  fission.  In  the 
human  foetal  ovary  of  7J  months  they  measure  2"§V v ^ oVo  °f  an 
inch  in  their  longest  diameter,  and  about  °f  an  inch  in  their 
shortest  diameter.  Each  germ  epithelial  corpuscle  is  a nucleus 
surrounded  by  a thin  film  or  investment  of  clear  protoplasm.  The 
nucleus  of  each  germ  epithelial  corpuscle  becomes  the  germinal 
vesicle  of  the  mature  ovum ; and  every  germ  epithelial  corpuscle  is 
potentially  an  ovum.  In  the  act  of  becoming  primordial  ova,  the 
nucleus  of  each  germ  epithelial  corpuscle  swells  up  into  a spherical 
corpuscle  with  dark  granular  contents,  within  which  is  generally 
seen  a nucleolus,  and  around  which  is  produced  clear  homogenous 
protoplasm  which  subsequently  forms  the  yelk  of  the  ovum.  Germ 
epithelial  corpuscles  are  seen  in  all  stages  of  development  into 
primordial  ova.  In  each  primordial  ovum  the  spherical  germinal 
vesicle  presents  a sharply  defined  limiting  membranous  wall. 
Within  the  germinal  vesicle  is  the  nucleolus  or  germinal  spot.  All 
the  ova  in  the  ovary  are  derived  from  germ  epithelial  corpuscles. 

In  all  parts  of  the  ovary  processes  of  vascular  connective  tissue 
stroma  grow  in,  between  and  around  certain  of  the  germ  epithelial 


438 


Proceedings  of  the  Royal  Society 

corpuscles,  whereby  the  latter  become  more  and  more  embedded  in 
the  stroma  of  the  ovary.  G-erm  epithelial  corpuscles  are  being 
constantly  produced  on  the  surface  of  the  ovary,  to  take  the  place 
of  those  already  embedded  in  the  stroma.  The  embedded  cor- 
puscles increase  in  number  by  division,  and  the  nucleus  of  each 
swells  up  into  a spherical  germinal  vesicle,  around  which  is  gradu- 
ally produced  the  yelk  of  the  ovum.  In  all  parts  of  the  young 
ovary  under  the  germ  epithelium,  groups  of  germ  epithelial  cor- 
puscles become  embedded  in  meshes  of  the  stroma.  As  each  indi- 
vidual in  the  group  swells  up  the  nucleus  or  germinal  vesicle  of 
each  becomes  very  distinct  as  a round  or  spherical  body.  From 
the  swelling  out  of  each  germ  epithelial  corpuscle  in  the  group,  the 
whole  group  expands  and  becomes  more  or  less  spherical.  Such 
groups  of  developing  corpuscles  are  called  egg  clusters.  Each  egg 
cluster  is  enclosed  in  a mesh  or  capsule  of  vascular  stroma  of  the 
ovary. 

The  stroma  of  the  young  ovary  consists  for  the  most  part  of 
fusiform  connective  tissue  corpuscles  and  blood-vessels.  The  walls 
of  the  young  blood-vessels  in  the  young  stroma  consist  of  connec- 
tive tissue  corpuscles.  These  connective  tissue  corpuscles  are  direct 
offshoots  from  the  ovarian  stroma,  and  are  found  in  contact  with 
the  yelk  or  protoplasm  of  each  primordial  ovum  situated  among 
the  germ  epithelial  corpuscles  on  the  surface  of  the  ovary.  Wher- 
ever we  find  primordial  ova  we  see  connective  tissue  corpuscles 
in  contact  with  the  yelk  of  each.  In  all  parts  of  the  ovary  we 
find  the  nuclei  of  connective  tissue  corpuscles  dividing.  Some- 
times these  corpuscles  are  swollen  out  into  round  bodies  containing 
three  to  four  nuclei.  In  each  egg  cluster  several  of  the  included 
germ  epithelial  corpuscles  are  in  a much  farther  advanced  stage  of 
development  than  their  fellow's.  From  the  walls  of  the  meshes  en- 
closing the  egg  clusters,  delicate  processes  of  vascular  connective 
tissue  grow  in,  between,  and  around  individual  corpuscles  in  the 
egg  clusters,  and  by  a continued  intergrowth  of  the  young  stroma  in 
this  manner  each  individual  of  the  group  becomes  at  last  enclosed 
in  a separate  mesh  or  capsule.  These  last  formed  meshes  are  the 
G-raafian  follicles. 

As  a rule,  each  G-raafian  follicle  is  occupied  by  one  young  ovum. 
The  protoplasm  or  yelk  of  each  ovum  is  in  close  contact  with  the 


439 


of  Edinburgh,  Session  1874-75. 

wall  of  each  Graafian  follicle.  In  contact  with  the  yelk  of  each 
young  ovum,  and  indenting  it,  are  connective  tissue  corpuscles, 
which  form  part  of  the  wall  of  each  Graafian  follicle.  In  the 
formation  of  the  membrana  granulosa,  these  connective  tissue 
corpuscles  in  the  wall  of  the  Graafian  follicle,  and  in  contact  with 
the  yelk  of  the  contained  ovum,  increase  in  number  by  division, 
their  nuclei  swell  out  into  little  vesicles,  and  at  last  a perfect 
capsule  of  such  corpuscles  is  produced  round  the  ovum.  This 
capsule  is  the  membrana  granulosa  or  follicular  epithelium  of  the 
follicle.  At  first  the  membrana  granulosa  consists  of  a simple 
layer  of  cells  lining  the  follicle.  The  individual  corpuscles  of  the 
membrana  granulosa  measure  about  3^3-  inch.  As  the  ovum 
becomes  mature,  the  corpuscles  of  the  membrana  granulosa  pro- 
liferate, and  then  many  layers  of  small  corpuscles  are  produced 
between  the  ovum  and  the  follicular  wall.  The  cells  of  the 
membrana  granulosa  are  thus  derived  from  the  corpuscles  of  the 
connective  tissue  stroma,  and  not,  as  Waldeyer  states,  from  the 
germ  epithelial  corpuscles.  The  follicular  space  is  formed  by  a 
breaking  down  and  probable  solution  of  certain  of  the  corpuscles  of 
the  thickened  follicular  epithelium  in  the  middle  parts  of  the  same. 
The  discus  proligerus  consists  of  follicular  epithelial  corpuscles, 
which  are  in  contact  with  the  zona  pellucida  of  the  ovum.  The 
zona  pellucida  or  vitelline  membrane  is  formed  by  a hardening  of 
the  outer  part  of  the  yelk  or  protoplasm  of  the  ovum,  and  is  not,  as 
Eeichert,  Pfluger,  and  Waldeyer  stated,  a product  of  the  follicular 
epithelium.  At  birth  the  human  ovary  contains  not  less  than 
30,000  ova,  few  of  which  reach  maturity. 

In  the  human  ovary  at  birth  the  germinal  vesicles  measure 
Troo- ” T2V0  °f  an  inch.  Most  of  them  are  about  the  same  size, 
and  also  present  a sharply-defined  membranous  wall.  In  some 
germinal  vesicles  two  or  three  germinal  spots  are  seen.  The 
tunica  albujinea  is  the  thickened  stroma  growing  round  the  ovary. 
At  the  age  of  2J  years  all  formation  of  ova  from  the  germ  epi- 
thelium has  ceased. 

Graafian  follicles  are  not  formed  from  tubular  structures  in  the 
manner  described  by  Pfluger,  Spiegelberg,  and  Waldeyer.  The 
appearances  of  tubular  structures  passing  into  the  stroma  of  the 
ovary  are  produced  by  sections  through  furrows  and  depressions 

3 L 


VOL.  VIII. 


440 


Proceedings  of  the  Royal  Society 


between  irregular  prominences  on  the  surface  of  the  foetal  ovary. 
The  irregularities  of  the  surface  of  the  foetal  ovary  are  produced 
by  the  expansion  of  egg  clusters  upwards  under  the  germ  epithelium. 
When  the  walls  of  furrows  and  depressions  come  in  contact,  egg 
clusters  are  formed  by  the  embedding  of  germ  epithelial  corpuscles  in 
that  situation,  just  as  in  other  situations.  Egg  clusters  are  formed 
in  connection  with  the  germ  epithelium  lining  the  furrows  and 
depressions.  Among  the  germ  epithelium  corpuscles  lining  the 
furrows,  &c.,  we  find  large  primordial  ova,  and  corpuscles  in  all 
stages  of  development  into  the  same,  just  as  in  other  situations 
among  the  ordinary  germ  epithelial  corpuscles. 

At  the  age  of  six  years  the  epithelium  on  the  human  ovary  con- 
sists of  very  small  flat  hexagonal-shaped  corpuscles,  measuring 
- 3"2lo~o  of  an  inch.  The  corpuscles  are  seen  dividing.  This 
layer  can  be  stripped  off  without  difficulty.  At  the  age  of  twelve 
Ihe  epithelium  has  little  difference  in  appearance  from  the  above, 
the  small  size  of  the  epithelial  corpuscles  being  remarkable. 
The  epithelium  is  beautifully  seen  in  old  cats,  and  must  be 
regarded  as  homologous  with  the  peritoneal  epithelium.  In  old 
cats  the  epithelium  on  the  surface  of  the  ovary  consists  of  very 
small  distinct  cells,  measuring  from  ygVoth  to  g-J^th  inch,  with 
granular  oval  nuclei. 

4.  Mathematical  Notes.  By  Professor  Tait. 

{Abstract.) 

(1.)  On  a singular  Theorem  given  by  Abel. 

The  theorem  in  question,  in  its  simplest  form,  is 


Abel’s  proof  of  it  involves  the  properties  of  the  gamma-function, 
and  requires  that  f'(f)  should  be  capable  of  development  in  powers 
of  £.  ( (Euvres , I.  27.) 

Independently  of  the  interesting  kinetic  application  for  which  it 


of  Edinburgh,  Session  1874-75. 


441 


was  originally  designed,  this  result  is  very  curious,  as  suggesting  a 
form  of  the  square  root  of  the  operation  of  simple  integration.  In 
fact  it  gives 


( )=4  rui  j 

o %Jx~y 


Seeking  to  obtain  an  elementary  proof  of  Abel’s  result,  which 
should  at  the  same  time  be  applicable  to  any  function,  whether 
developable  or  not,  I hit  upon  the  simple  expedient  of  inverting 
the  order  of  the  two  integrations.  We  thus  get  the  proof  im- 
mediately in  the  form 


dy/XQdi  = r‘  r‘ 

Jx-yJy-t  A A Jx-yJy-t 


Now  it  is  known  (and  a simple  geometrical  proof  is  easily  given) 
that 


dy ' 

x-y  Jy-£ 


7 r . 


Hence  the  integral  becomes  at  once 


»[/(«) -/(°)]  • 


Numerous  extensions  and  applications  of  the  theorem  are  given. 
As  one  example  of  these  extensions  the  following,  which  assigns 


an  expression  for 


in 


, may  here  be  given- 


r*  aa  doc  ^ p x2  dx  3 

Jo  (x2  - X.f^rT 


■s. 


•«.  f(.m 

n — 

(Xn  - 


= E1E2 E,_,  [/(*,)-/((>)]. 


442  Proceedings  of  the  Royal  Society 

and  therefore 


rGW^)  W!)y 

r(2)  rQ  r(i)  | \TUJ) 


Hence 


(l)~U  ) = r(n 


: ( )dy 

n — ] 
( x-y)~T 


Tbe  theorem  given  by  Abel  is  easily  seen  to  be  the  particular 
case  of  this  when  n = 2,  for  then 


Another  form  of  the  above  multiple  integral  is  easily  seen  to  be 


r1  ^ » dex  r de2  P\ 

J ~ jEz!  J 7 ’ ' ' ' J 


lf\ep2  • • • • enxx)den 


0 (1  — ejn  0 (1  — e2)  n 


n — 1 

(1  - en)  n 


and  curious  expressions  for  (jj~j  (when  n is  even)  may  be  ob- 
tained by  evaluating  the  integral 


dx» 


dx~ 


/x\  M,U/2  r»x 

Y(n  — 1)  J 2(m  — l)(n— T) 

u (pcx-x.2)  mn  j 0 (a?2-a?3) 


/ 


■J 


/'©<** 


2(»  — 1)  / 2(m  — 1)  (w  — 1) 

0 (a?w_i-a3ra)  (#»-£)" 


where  m is  any  real  quantity  whatever. 

Other  instances  of  the  use  of  this  process  were  adduced,  but  those 
just  given  are  sufficient  for  an  abstract  like  the  present. 


of  Edinburgh,  Session  1874-75. 


443 


(2.)  On  the  Equipotential  Surfaces  for  a Straight  Wire. 


Some  results  given  in  Yol.  I.  of  Thomson  and  Tait's  Natural 
Philosophy  may  be  much  more  simply  obtained  by  calculating  the 
potential  of  a wire  rather  than  its  attraction.  That  potential  is 
easily  found  as 


p los- 


ri  + r3  + c 
rx  + r2  - c ’ 


where  c is  the  length  of  the  wire,  p its  line  density,  rx  and  r2  the 
distances  of  its  ends  from  the  point  at  which  the  potential  is  to  be 
found. 

In  this  form  we  see  at  a glance  that  the  equipotential  surfaces 
are  prolate  ellipsoids  of  revolution  with  common  foci  at  the  ends 
of  the  wire. 

The  method  is  extended  to  polygons  plane  or  gauche,  closed  or 
unclosed. 

(3.)  On  a Fundamental  Principle  in  Statics. 

The  principle  that,  while  additional  constraints  cannot  disturb 
equilibrium,  unnecessary  constraints  may  be  removed  without  dis- 
turbing equilibrium,  is  of  very  great  use  in  the  statics  of  fluids 
and  of  elastic  and  flexible  bodies.  But  it  seems  not  to  have  been 
made  use  of  to  the  extent  its  importance  deserves. 

My  attention  was  recalled  to  it  when  attempting  to  compare  the 
shares  taken  by  gravity  and  cohesion  in  resisting  the  tendency  of 
the  so-called  centrifugal  force  to  split  a planet.  The  problem 
which  first  proposed  itself  was  to  determine  the  gravitation  attrac- 
tion of  one- half  of  a uniform  sphere  upon  the  other. 

The  sextuple  integral  which  a direct  solution  of  this  problem 
would  require  may  be  entirely  dispensed  with,  and  its  place  sup- 
plied by  a simple  single  integral,  if  we  imagine  a thin  film  of  the 
solid  on  each  side  of  a diametral  plane  to  be  converted  (without 
change  of  bulk  or  density)  into  an  incompressible  liquid. 

Or  we  may  commence  with  a sphere  of  homogeneous  incom 
pressible  liquid.  If  a be  its  radius,  p its  density,  it  is  easily  shown 
that  the  whole  pressure  normal  to  any  diametral  plane — which  is 
of  course  the  attraction  of  the  hemispheres  on  one  another — is 


444 


Proceedings  of  the  Royal  Society 

If  each  hemisphere  were  collected  at  its  centre  of  inertia  the  attrac- 
tion would  he  times  as  great.  The  centrifugal  force  tending 

to  split  the  planet  across  a diametral  plane  through  the  axis  (it  is 
easily  shown  to  be  greater  per  unit  of  area  on  a diametral  than  on 
any  other  plane)  is 


where  <o  is  the  angular  velocity  of  rotation.  The  ratio  of  these  is 
4 

CIO)2 


or  the  ratio  of  gravity  to  centrifugal  force  at  any  point  on  the 
equator.  Hence,  so  far  as  gravity  is  concerned,  the  earth  would 
split  across  a meridian  if  it  were  to  revolve  more  than  seventeen 
times  faster  than  it  does. 

It  is  known  that,  if  the  earth  revolved  seventeen  times  faster 
than  it  does,  centrifugal  force  would  just  balance  gravity  at  the 
equator.  The  relation  of  this  fact  to  the  above  statement  depends 
upon  the  geometrical  proposition  that  the  volume  of  a very  small 
slice  from  the  surface  of  a sphere  is  half  the  product  of  its  thick- 
ness by  the  area  of  its  base. 

And  cohesion  would  not  sensibly  alter  this  state  of  things ; for, 
assuming  the  earth’s  diameter  to  be  8000  miles,  its  mean  density 
5*5,  and  the  weight  of  a cubic  foot  of  water  at  the  surface  63  lbs., 
while  the  average  tensile  strength  of  its  materials  is  taken  as  500 
lbs.  weight  per  square  inch,  the  cohesion  between  two  hemispheres 


is  shown  to  be  only 


1 

25,410 


th  part  of  their  gravitation  attraction. 


Even  if  we  made  the  extreme  assumption  that  the  tensile 
strength  is  (throughout)  that  of  steel,  cohesion  would  in  the  case 

of  the  earth  be  only  about  -i_th  of  gravitation  attraction,  between 

hemispheres. 


445 


of  Edinburgh,  Session  1874-75. 

As  a consequence,  a planet  of  the  earth’s  mean  density  and 
the  above  assumed  tensile  strength  is  held  together  as  much  by 

cohesion  as  by  gravitation  if  its  radius  is  ^25  415^  ^ie 

earth,  or  about  25  miles.  If  of  steel’s  tenacity  it  would  have  a 
radius  of  about  409  miles. 


Monday , 4 th  January  1875. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  President  exhibited  and  described  his  Tide  Calculat- 
ing Machine,  also  his  Improved  Tide-Gauge;  he  also  de- 
scribed certain  Capillary  Phenomena,  with  Experiments. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

C.  H.  Millar,  Esq. 

John  Milroy,  Esq. 

Professor  Daniel  Wilson,  Toronto. 

Anderson  Kirkwood,  LL.D. 

Dr  Ludwik  Bernstein. 

Daniel  G.  Elliot,  Esq.,  New  York. 

Robert  Gray,  Esq. 

William  Craig,  M.D.,  F.R  C.S.E. 


Monday,  18  th  January  1875. 

The  Hon.  Lord  NEAVES,  Vice-President,  in  the  Chair. 

The  following  Obituary  Notices  of  Deceased  Fellows  of 
the  Society  were  read  : — 

1.  Biographical  Notice  of  Lord  Colonsay.  By  the  Hon. 

Lord  Neaves. 

By  the  death  of  Lord  Colonsay,  this  Society  has  lost  a member 
of  great  distinction,  and  well  worthy  of  being  held  in  respectful 
remembrance.  He  was  a man  of  great  vigour  of  mind,  and  with 
powers  and  qualities  which  would  have  earned  for  him  a high  place 


446  Proceedings  of  the  Royal  Society 

in  science  or  in  literature  if  they  had  been  turned  in  either  of  these 
directions ; hut  it  was  his  lot  and  his  choice  to  follow  a professional 
career,  in  which,  as  will  afterwards  be  seen,  he  came  to  attain  all 
the  varied  honours  which  the  practice  of  the  law  is  able  to  confer. 

Duncan  McNeill  was  the  second  son  of  John  McNeill,  proprietor 
of  the  islands  of  Colonsay  and  Oronsay,  and  of  the  estate  of  Ard- 
lussa  in  Jura,  and  was  born  in  Oronsay  on  the  20th  of  August 
1793.  He  was  not  educated  at  any  school,  but  received  private 
tuition  at  home  along  with  his  brothers,  until  he  repaired  to  the 
University  of  St  Andrews,  along  with  his  immediately  younger 
brother,  now  Sir  John  M‘Neill. 

He  used  in  after  life  to  tell  of  an  incident  that  occurred  to  the 
party  when  his  father  and  the  two  boys  passed  a night  in  Glasgow  on 
their  way  from  the  Highlands  to  Sfc  Andrews,  and  it  was  certainly 
one  well  calculated  to  make  a permanent  impression  on  a vigorous 
and  appreciative  mind.  While  he  was  walking  in  the  morning, 
near  the  post-office,  a mail-coach  arrived,  from  the  roof  of  which 
the  guard  announced  to  an  assembled  multitude  the  news  of  the 
victory  of  Trafalgar,  which  occurred  on  21st  October  1805.  The 
intelligence,  of  course,  was'  received  with  tumultuous  cheering, 
after  which,  one  of  the  crowd  proposed  three  cheers  for  Nelson,  but 
when  the  guard  in  a loud  and  sad  whisper  said  “ that  Nelson  was 
killed,”  they  all  instantly  dispersed  in  solemn  silence,  and  left  the 
streets  empty. 

Duncan  McNeill  was  twelve  years  old  when  he  went  to  St  Andrews, 
which  was  not  at  that  time  an  unusual  age  for  college  intrants.  He 
and  his  brother  were  hoarded  with  Dr  James  Hunter,  professor  of 
Logic,  for  whom  and  for  his  family  M‘Neill  always  entertained  a 
strong  feeling  of  attachment  and  regard.  He  became  a diligent 
student  and  a good  classical  scholar,  but  was  still  more  distinguished 
in  mathematics,  for  which  he  had  a remarkable  aptitude. 

After  three  years  spent  at  St  Andrews  he  came  to  Edinburgh, 
and  attended  college  here  for  some  sessions.  As  usual  with  young 
men  of  intellectual  power,  he  applied  himself  diligently  to  Logic 
and  Metaphysics,  for  the  latter  of  which,  undoubtedly,  Dr  Thomas 
Brown,  whom  he  attended,  was  calculated  to  inspire  a strong  taste, 
though  Brown  himself  was  not  a profound  or  perhaps  even  a sound 
metaphysician.  His  lectures,  however,  were  pleasing  and  attrac- 


447 


of  Edinburgh,  Session  1874-75. 

tive,  and  had  often  the  effect  of  leading  his  hearers  to  larger  and 
deeper  views  than  their  teacher  entertained. 

It  has  been  stated  in  a very  able  and  kindly  notice  of  Lord 
Colonsay,  ascribed  to  Mr  Campbell  Smith,  that  about  this  period, 
or  shortly  afterwards,  M‘Neill  formed  the  intention  of  publishing 
the  philosophical  works  of  David  Hume,  of  which  at  that  time  no 
good  collective  edition  existed.  I am  not  able  to  confirm  this 
statement  by  my  own  testimony,  but  I know  well  that  he  was 
always  a great  admirer  of  our  greatest  Scottish  philosopher.  He 
was  not  likely  to  be  led  away  into  those  sceptical  speculations  which 
Hume  propounded  from  his  attempting  to  introduce  metaphysics 
into  a region  which  lies  above  their  reach,  nor  was  he  likely  to 
follow  Hume  in  the  perverse  preference  which  he  seemed  to  feel 
for  French  literature  over  English,  and  which  may  be  traced  partly 
to  the  influence  of  prejudice,  and  partly  to  a feeling  that  he  was  less 
appreciated  in  England  than  on  the  other  side  of  the  channel.  But 
in  other  respects  the  mind  and  style  of  Hume  were  well  calculated 
to  please  and  influence  M‘Neill  in  matters  of  reasoning  and  of 
philosophy.  The  simplicity  and  brevity  with  which  he  wrote,  the 
caution  and  moderation  with  which  he  stated  his  opinions,  and  the 
calmness  with  which  he  dealt  with  his  adversaries,  were  all  con- 
genial to  the  tastes  and  feelings  with  which  McNeill  was  wont  to 
approach  questions  of  evidence  and  reasoning.  It  is  not  to  be  sup- 
posed that  he  was  destitute  of  feelings  and  energies  to  which  Hume 
was  a stranger.  His  Highland  or  Island  blood  was  more  fervid 
than  any  that  circulated  in  Hume’s  veins,  and  his  early  life  and 
athletic  frame  were  a strong  contrast  to  the  indolent  and  somewhat 
obese  form  of  the  philosopher  of  the  Merse. 

With  a view  to  a professional  life,  M‘Neill  entered  on  an  appren- 
ticeship in  the  chambers  of  Mr  Michael  Linning,  W.S.,  and  dis- 
charged with  regularity  and  diligence  the  duties  that  there  devolved 
upon  him. 

I am  not  sure  whether  it  was  originally  intended  by  his  friends 
that  M‘Neill  should  come  to  the  bar,  or  whether  the  remarkable 
talents  which  he  soon  displayed  led  to  his  adopting  that  profession 
instead  of  that  of  a writer  to  the  Signet,  to  which  his  initiation 
at  Mr  Linning’s  would  naturally  have  led.  But  it  cannot  be 
doubted  that  the  time  passed  and  the  instruction  received  by  him 

3 M 


VOL.  VIII. 


448 


Proceedings  of  the  Iioyal  Society 

in  a writer’s  chambers,  as  well  as  the  friendships  which  he  there 
formed,  were  eminently  useful  to  him  at  the  bar. 

Lord  Colonsay  passed  advocate  in  1816,  and  amidst  a great 
number  of  eminent  contemporaries  and  rivals  he  soon  became  dis- 
tinguished in  his  profession.  He  devoted  himself  with  special  dili- 
gence to  the  study  of  criminal  law,  which  he  thoroughly  mastered, 
and  made  himself  so  formidable  as  an  opponent  in  defending 
prisoners  that  the  Crown  authorities  saw  the  advantage  of  securing 
his  services  on  their  side,  and  in  1820  he  was  made  an  Advocate- 
depute  by  Lord  Meadowbank,  then  Lord  Advocate. 

In  1822  he  was  appointed  Sheriff  of  Perth,  in  room  of  Lord 
Medwyn,  promoted  to  the  Bench.  He  continued  in  that  office  with 
great  efficiency  and  usefulness  down  to  1834,  when  he  became 
Solicitor-G-eneral  under  Sir  Bobert  Peel’s  administration.  That 
ministry  retained  office  for  only  a few  months ; but  when  they 
returned  to  power  in  1841,  he  was  again  made  Solicitor  General. 
In  October  1842  Sir  William  Rae,  then  Lord-Advocate,  died,  and 
M‘Neill  succeeded  him  in  that  office.  In  1843  he  was  elected  Dean 
of  the  Faculty  of  Advocates,  and  became  Member  of  Parliament  for 
Argyllshire,  holding  that  position  from  1843  to  1851,  when  he  was 
promoted  to  the  Bench  by  the  Whig  Ministry  at  the  same  time 
with  Lord  Rutherfurd.  In  1852  he  was  made  Lord  Justice- 
General  and  President  of  the  Court  of  Session.  After  serving  in 
that  high  position  for  fifteen  years  he  was  created  Baron  Colonsay 
in  1867,  when  he  retired  from  the  bench. 

Thus  it  is  that  Lord  Colonsay  passed  through  all  the  grades  and 
honours  of  his  profession,  from  that  of  a simple  advocate  to  the 
Presidency  of  the  Court.  We  do  not  know  if  this  is  unprecedented, 
but  it  certainly  has  rarely  happened  that  a member  of  the  bar  has 
become  successively,  as  Lord  Colonsay  did,  a Depute-Advoeate,  a 
Sheriff,  Solicitor- General,  Lord  Advocate,  Dean  of  Faculty,  an 
ordinary  Judge,  and  finally  Lord  Justice-General  and  Lord  Pre- 
sident. The  varied  functions  and  wide  experience  which  these 
successive  positions  involved,  could  not  fail  to  qualify  him  in  the 
highest  degree  for  the  discharge  of  all  his  duties,  and  above  all,  of 
those  which  ultimately  devolved  upon  him  when  placed  at  the  head 
of  legal  administration  of  Scotland.  Every  professional  man 
knows  that  the  inferior  grades  of  legal  preferment  are  eminently 


of  Edinburgh,  Session  1874-75. 


449 


conducive  to  furnish  the  necessary  knowledge  and  practice  required 
for  higher  positions.  It  cannot  be  doubted  that  great  experience 
as  an  advocate  at  the  bar  is  of  the  highest  use  in  discharging  the 
functions  of  the  bench.  Under  some  national  systems,  Judges  have 
been  chosen  who  had  not  practised  as  advocates,  but  they  would 
certainly  not  possess  in  that  way  the  intelligence  and  penetration 
which  an  experienced  barrister  acquires,  and  which  must  enable 
him  when  on  the  bench  to  weigh  the  evidence,  to  detect  the  truth, 
and  to  see  quickly  through  the  fallacies  and  disguises  to  which 
litigants  are  apt  to  resort.  In  another  way  the  exercise  of  the 
inferior  jurisdiction  of  Sheriff  brings  the  holder  of  office  into  closer 
contact  with  country  matters,  and  with  local  and  customary  consi- 
derations, which  will  serve  him  in  good  stead  when  as  a Judge  he 
comes  to  sit  in  review  upon  County-Court  procedure. 

Lord  Colonsay  was  every  way  qualified  for  the  profession  which 
he  adopted,  and  for  the  offices  which  he  held.  His  talents,  which 
were  great,  were  eminently  of  a forensic  and  still  more  of  a judicial 
character.  His  logical  acumen  was  severe  and  unerring.  He 
possessed  also,  though  he  never  exercised  it  unnecessarily,  a power 
of  vivid  and  impressive  eloquence,  in  which  he  was  equalled  by 
few  and  surpassed  by  none.  He  was  a most  able  criminal  advo- 
cate, and  indisputably  the  greatest  criminal  lawyer  of  his  day. 
His  natural  powers  were  aided  and  improved  by  patient  and  labori- 
ous study  as  a young  man,  and  by  the  most  conscientious  and 
careful  discharge  of  duty  in  all  matters  that  came  before  him, 
whether  at  the  bar  or  on  the  bench.  Those  who  had  the  advan- 
tage of  meeting  him  in  consultation  as  an  advocate,  will  bear  testi- 
mony to  the  thorough  mastery  which  he  always  attained  of  his 
client’s  case,  and  to  the  sagacious  and  skilful  perception  which  he 
also  acquired  of  the  probable  case  of  his  opponent.  In  consulta- 
tion he  was  entirely  free  from  the  petty  selfishness  that  has  some- 
times been  laid  to  the  charge  of  seniors  in  bottling  up  their  best 
views  for  their  own  use.  Whatever  point  he  thought  advantage- 
ous to  the  case  was  always  fully  communicated  and  explained  to 
his  juniors. 

In  the  practice  of  his  profession  as  an  advocate  Lord  Colonsay 
had  some  advantages  not  equally  enjoyed  by  some  of  his  brethren. 
The  subjects  with  which  an  advocate  has  to  deal  are  so  various, 


450 


Proceedings  of  the  Royal  Society 

and  often  so  special  and  technical,  that  it  is  impossible  for  any 
man  to  have  a thorough  and  independent  knowledge  of  all.  The 
advocate  has  what  may  be  called  a nisi  prius  faculty  of  learning, 
on  short  notice,  what  he  knew  nothing  of  before,  and  then  for- 
getting it  when  the  occasion  is  over,  in  order  to  make  room  for 
new  acquisitions  equally  temporary  and  transient.  His  great  art 
consists  in  knowing  where  information  is  to  be  found,  and  making 
the  appropriate  use  of  it  for  his  immediate  purpose.  In  an  ex- 
tensive practice  an  advocate  is  thus  brought  in  contact  with  ques- 
tions of  the  most  dissimilar  kind — commerce,  agriculture,  engi- 
neering, chemistry,  and  many  others,  arising  out  of  multifarious 
patents  or  contracts  that  become  the  subject  of  litigation.  I once 
was  able  to  illustrate  this  somewhat  oddly  to  a man  who  knew 
many  subjects  and  wrote  many  books.  The  late  Mr  MacCulloch, 
the  political  economist,  once  asked  me  in  company  whether  his 
“ Commercial  Dictionary,”  which  is  a very  useful  book,  was  ever 
founded  on  or  quoted  in  our  courts  of  law  ? I answered  rather 
abruptly,  “Never;  the  name  of  it  is  never  heard.”  He  appeared 
disappointed  at  this,  and  I then  added,  “ But  very  often  a case 
comes  in  to  us  at  night  to  prepare  for  next  day,  on  a subject  we 
know  nothing  about — general  or  particular  average,  foreign  ex- 
changes, or  the  like — upon  which  we  go  to  our  shelves  and  take 
down  a Commercial  dictionary,  which  enables  us  to  appear  at  the 
bar  when  wanted  next  day  with  an  amount  of  information  that 
astonishes  even  our  own  clients.  But  we  never  mention  the  book 
from  which  the  information  is  got.”  This  statement  seemed  com- 
pletely to  re-establish  the  self-complacency  of  the  sensitive  author. 

I would  say  here  that  Lord  Colonsay,  from  his  scientific  tastes 
and  tendencies,  was  more  fully  and  accurately  grounded  in  many 
of  these  questions  than  the  most  of  his  brethren.  And  this  could 
not  fail  both  to  lighten  his  labours  and  to  give  confidence  to  his 
views. 

As  a judge,  his  judgments  were  models  of  clearness  and  brevity, 
and  were  always  remarkable  for  an  anxiety  to  maintain  the  great 
landmarks  of  legal  principle.  If  he  had  a fault,  it  was  one  which, 
I think,  in  judicial  business,  “leans  to  virtue’s  side.”  When 
he  felt  that  he  could  not  be  bold  he  was  apt  to  be  very  cautious, 
and  certainly  was  ever  anxious  not  to  decide  any  case  but  the  one 


451 


of  Edinburgh,  Session  1874-75. 

that  was  immediately  before  the  Court,  leaving  other  cases  to  be 
determined  at  tbeir  own  time,  and  after  fully  hearing  the  argu- 
ments that  were  specially  directed  to  discuss  them ; and  I am 
much  inclined  to  think  that  it  is  better  always  to  decide  nothing 
but  the  actual  question  raised,  or  necessary  to  be  decided,  as  no 
collateral  point  can  in  general  receive  the  mature  treatment  and 
consideration  that  it  deserves.  His  perfect  command  of  temper,  his 
great  patience  in  listening,  and  his  uniform  courtesy  on  the  bench 
earned  for  him  the  respect  and  gratitude  of  the  whole  bar,  and 
added  greatly  to  the  weight  and  authority  of  his  judgments. 

We  should  not  fully  do  justice  to  Lord  Colonsay’s  merits  if  we 
did  not  notice  and  acknowledge  the  important  benefits  which  the 
country  has  derived  from  his  legislative  exertions.  At  an  early 
period,  T believe,  we  may  say  that  the  great  improvements  made 
on  criminal  procedure  in  Scotland,  by  an  Act  in  the  ninth  year  of 
George  IV.,  emanated  from  Lord  Colonsay,  though  Sir  William 
Eae  was  at  that  time  Lord  Advocate.  The  older  forms  of  criminal 
process  in  Scotland,  whatever  may  have  been  said  to  the  contrary, 
were  highly,  and  perhaps  unduly,  favourable  to  accused  persons — 
in  this  respect,  at  least,  that  many  formal  objections  to  the  designa- 
tion and  citation  of  witnesses  and  otherwise  could  be  kept  back  till 
after  a jury  was  empanelled,  and  could  then  be  brought  forward  so 
as  to  frustrate  the  proceedings,  while  at  the  same  time  the  accused 
could  not  be  tried  again  in  consequence  of  having  “ tholed  an 
assize.”  This  state  of  things,  of  which  no  one  could  make  a 
better  use  than  Lord  Colonsay  when  defending  prisoners,  was 
abolished;  so  that  all  formal  objections  must  now  be  brought  for- 
ward at  once  before  empanelling  a jury,  and  thus,  even  if  they 
prove  fatal,  the  accused  can  be  tried  again  on  a new  indictment. 

When  in  Parliament  as  Lord  Advocate,  Lord  Colonsay  passed, 
or  assisted  in  passing,  many  useful  measures;  but  perhaps  the 
most  conspicuous  of  these  is  the  Poor  Law  Amendment  Act — a 
wise  and  beneficent  measure,  which  has  gone  far  to  solve  the 
great  social  difficulty  of  relieving  pauperism  without  paralysing 
industry  or  oppressing  ratepayers,  many  of  whom  must  always  be 
nearly  as  poor  as  the  objects  who  obtain  relief. 

In  all  matters  of  legal  reform,  Lord  Colonsay’s  services  have 
always  been  at  the  command  of  bis  country,  and  though  unosten- 


452  Proceedings  of  the  Royal  Society 

tatiously  performed,  have  been  thoroughly  appreciated  by  those 
who  had  the  means  of  knowing  and  the  power  of  judging. 

Of  the  debt  which  we  owed  to  Lord  Colonsay  after  he  took  his 
seat  in  the  House  of  Lords,  it  is  unnecessary  to  speak. 

I may  here  advert  to  a part  of  Lord  Colonsay’s  life  which  pos- 
sesses much  interest,  and  is  calculated  to  throw  a strong  light  upon 
his  character.  Some  time  after  the  death  of  his  father  he  became 
by  a family  arrangement  the  proprietor  of  Colonsay  and  Oronsay, 
which  he  retained  till  a comparatively  recent  period.  In  con- 
sequence of  the  advanced  age  of  his  father,  these  estates  had  not 
latterly  been  administered  with  as  much  energy  and  enterprise  as 
the  times  demanded.  They  were  all  in  the  hands  of  the  proprietor, 
except  some  small  possessions  held  by  a number  of  crofters  and 
cotters.  When  Lord  Colonsay  acquired  the  property,  he  applied 
himself  vigorously  to  putting  it  into  perfect  order.  Besides  visit- 
ing it  during  the  vacations  of  the  Court,  he  personally  directed 
the  whole  improvements  which  were  made  upon  it,  and  for  that 
purpose  transmitted,  in  the  midst  of  the  labours  of  his  profession, 
minute  directions  weekly  to  his  managers  on  the  spot,  and  received 
their  detailed  reports  of  everything  that  was  doing.  In  a few 
years  he  had  the  islands  put  into  a most  satisfactory  state  for 
being  let  out  in  separate  farms  of  suitable  size.  The  stock  on  the 
farms  was  every  way  improved.  He  encouraged  and  liberally  aided 
emigration,  and  did  so  with  singular  delicacy,  so  as  to  spare  the 
feelings  and  not  impair  the  means  of  the  emigrants.  Excellent 
farm  houses  and  offices  were  built,  roads  formed,  and  harbours 
improved  at  a very  great  expense,  and  at  last  he  succeeded  in 
lightening  his  own  labours  and  establishing  in  the  islands  respect- 
able tenants  whose  occupations  gradually  increased  in  value.  He 
also  succeeded  in  getting  Colonsay  detached  from  Jura  and  made 
a separate  parish;  and  having  improved  the  church  that  had  been 
there  in  use,  and  built  a comfortable  manse  and  good  school,  he 
settled  a liberal  endowment  on  the  minister,  and  thus  gave  the 
people  on  the  island  the  advantages  of  a.  regular  and  efficient 
ministry,  and  two  good  parish  schools.  It  may  gladden  our  friend 
Professor  Blackie’s  heart  to  hear  that  he  retained  his  Gaelic  in 
perfection  to  the  last,  and  was  thus  enabled  to  exercise  an  influence 
that  might  otherwise  have  been  lost. 


453 


of  Edinburgh,  Session  1874-75. 

I shall  add  only  a few  more  words  as  to  his  personal  life.  He 
was  never  married,  but  his  younger  brother  Archibald,  with  his 
wife  and  family,  were  for  many  years  domesticated  with  him,  and 
when  his  brother  died,  the  widow  and  surviving  children  remained 
with  him  as  before,  and  ultimately  shared  in  a large  portion  of  his 
means.  He  was  a most  affectionate  relative,  and  a very  firm 
friend.  He  never  forgot  a kindness  received,  and  had  particular 
pleasure  in  repaying,  when  it  came  to  be  in  his  power,  any  proofs 
of  friendship  which  he  had  received  in  the  earlier  period  of  his 
career,  when  encouragement  and  assistance  were  calculated  to  be  of 
such  value.  He  was  a man  of  great  goodness  of  temper,  and  of 
inflexible  justice  in  all  his  dealings.  His  estate  of  Colonsay  he 
had  disposed  of  before  his  death  to  his  brother  Sir  John  M‘Neill, 
under  a family  arrangement. 

For  a considerable  part  of  his  life  Lord  Colonsay  laboured  under 
some  weakness  in  the  chest  and  breathing  tubes,  and  latterly  a 
tendency  to  bronchitis  was  perceptible.  We  believe  it  was  to 
this  malady  that  he  fell  a victim.  He  was  only  ill  for  a short 
time,  and  at  the  age  of  eighty  it  was  not  wonderful  that  he  was 
unable  to  resist  the  influence  of  a disease  so  dangerous  in  general 
to  those  advanced  in  life. 

2.  Biographical  Notice  of  Cosmo  Innes.  By  the  Hon. 
Lord  Neaves. 

We  have  lost  another  eminent  member  of  our  Society  in  Mr 
Cosmo  Innes,  of  whom  I shall  venture  to  give  a short  account.  I 
do  not  think  it  necessary  to  make  it  long,  and  this  for  various 
reasons.  Mr  Innes’s  labours  were  more  nearly  akin  to  the  studies 
of  another  Society  which  meets  under  the  same  roof  with  ourselves, 
and  within  that  body,  I believe,  tributes  have  been  paid  to  his 
memory  far  more  intelligent  and  more  worthy  of  his  reputation 
than  any  I could  venture  to  offer.  The  general  features  of  his 
career,  also,  are  so  well  and  widely  known,  and  have  been  recalled  to 
our  recollection  of  late  in  such  various  ways,  that  any  detailed  narra- 
tive would  be  superfluous.  My  endeavour  now,  therefore,  will  mainly 
be  not  to  pay  homage  to  his  antiquarian  attainments,  which  are 


454 


Proceedings  of  the  Royal  Society 

indisputable,  nor  to  the  works  of  interest  and  utility  which  have 
proceeded  from  his  industry,  and  which  are  never  likely  to  be 
forgotten  or  to  remain  unappreciated,  but  to  bear  my  testimony  to 
his  general  accomplishments,  and  to  his  high  personal  character. 
Of  these  I claim  a right  to  speak,  from  an  unbroken  friendship  of 
upwards  of  sixty  years,  varied  by  much  vicissitude  of  events,  much 
community  of  favourite  studies,  constant  professional  or  official 
intercourse,  and  domestic  familiarity  of  the  warmest  and  most 
pleasing  kind. 

Mr  Innes  was  born  on  9th  September  1798.  He  was  educated 
at  the  High  School  of  Edinburgh,  and  at  the  University  of  Glasgow, 
from  which  last  he  proceeded  on  a Snell  exhibition  to  Balliol 
College,  Oxford. 

It  is  well  known,  and  necessary  to  be  remembered,  that  the 
position  of  Mr  Innes’s  family  while  he  was  yet  a young  man,  came 
to  be  greatly  affected  by  a misfortune  that  befell  his  father.  Mr 
Innes,  senior,  who  was  a Writer  to  the  Signet,  was  induced  to  give 
up  business,  and  take  a long  lease  of  the  estate  of  Durris,  in  Kin- 
cardineshire, upon  which  he  expended  great  sums  of  money  in 
improvements.  But  when  the  time  approached  for  reaping  the 
benefits  of  these,  the  lease  was  set  aside,  and  the  estate  carried  off 
by  an  heir  of  entail,  leaving  Mr  Innes,  senior,  with  a very  slender 
equivalent  for  all  the  time  and  money  he  had  thus  expended. 

One  good  thing  resulted  from  this  calamity.  It  brought  out 
the  native  courage  and  vigour  of  Mr  Cosmo  Innes’s  character,  and 
forced  him  to  grapple  manfully  with  his  difficulties.  His  motto  in 
such  circumstances  might  well  have  been  Tu  ne  cede  malis ; sed 
contra  audentior  ito.  He  never  sat  down  with  a listless  look  or  a 
desponding  heart,  but  turned  to  the  first  opening  he  could  find  that 
promised  an  escape  from  trouble.  And  here,  as  she  generally  does, 
Fortune  favoured  the  brave,  and  gave  our  friend  both  a stimulus 
and  an  opportunity  for  exertion  that  might  not  otherwise  have 
existed. 

Another  advantage  that  arose  from  the  strong  interest  felt  by  all 
who  saw  his  position,  was  that  it  excited  the  sympathy  and  atten- 
tion of  many  friends  of  great  influence  and  value.  Much  the  most 
important  of  these,  and  one  who  greatly  moulded  and  affected  his 
future  career,  was  Mr  Thomas  Thomson,  whose  acquaintance  he 


455 


of  Edinburgh,  Session  1874-75. 

formed  in  the  year  1824,  and  with  whose  labours  he  became,  for  a 
long  period,  substantially  identified. 

Thomas  Thomson  was  one  of  the  most  able  and  learned  antiquaries 
and  “ .Record  Lawyers”  that  Scotland  has  produced,  and  he  would 
probably  have  been  recognised  as  the  greatest  among  them,  if  his 
efficiency  had  not  been  marred  or  impaired  by  some  defects  of 
character  and  peculiarities  of  taste  which  interfered  greatly  with 
his  practical  powers.  His  fastidiousness,  his  aversion  to  hasty  or 
ill  considered  opinions,  and  his  general  tendency  to  procrastination, 
led  him  to  allow  duties  to  stand  over  that  should  have  been  in- 
stantly and  resolutely  performed.  As  a member  of  the  “ Record 
Commission”  he  became  busily  occupied  in  the  arrangement  of 
the  Ancient  Records  and  Muniments  of  Scotland,  and  the  publica- 
tion of  the  old  Acts  of  Parliament  of  the  country  came  to  rank  as 
the  “magnum  opus”  of  his  life.  At  the  time  when  Mr  Innes  be- 
came acquainted  with  him,  he  was  completing,  or  had  completed, 
the  eleventh  volume  of  that  collection,  but  the  first  volume  of  it 
had  not  been  begun,  being  the  portion  of  the  work  attended  with 
the  greatest  difficulty,  involved  in  the  deepest  obscurity,  and  for 
which  new  materials  were  daily  coming  to  light  from  sources  hitherto 
undiscovered. 

The  character  of  Mr  Thomson,  and  his  eventful  history,  full  of 
varied  incidents,  some  of  a most  pleasing,  and  some  of  a most 
painful  kind,  are  exhibited  in  the  interesting  Memoir  of  him 
written  after  his  death  by  Mr  Innes,  at  the  request  of  Mr  James 
Craig.  The  latter  years  of  Mr  Thomson’s  life  were  obscured  by  no 
ordinary  gloom  of  misfortune.  In  his  administration  as  a “ Record 
Commissioner,”  and  as  “ Depute  Clerk-Register,”  his  accounts  were 
allowed  to  run  into  great  arrear  and  confusion,  and  attention  came 
at  last  to  be  called  to  them  by  the  officials  connected  with  the 
financial  departments  of  the  Government.  There  had,  undoubtedly, 
been  great  neglect,  and  considerable  disregard  of  the  proper  limits 
of  expenditure,  which  it  was  found  wholly  impossible  to  justify,  but 
which,  I am  satisfied,  would  all  have  been  put  right  by  Mr  Thomson 
and  his  many  friends,  if  time  had  been  allowed.  But  some  of  the 
officials  concerned,  particularly  the  men  of  mere  routine,  were  too 
peremptory,  and  too  punctilious,  to  look  to  anything  but  purely 
arithmetical  considerations,  and  that,  perhaps,  took  place  which  is 

3 N 


VOL.  VIII. 


456  Proceedings  of  the  Royal  Society 

not  unfrequently  observed,  that  injustice  is  done  to  a man  by  bis 
political  friends  for  fear  of  their  being  supposed  to  show  him  undue 
favour  by  protecting  him  from  attack.  However  this  may  be,  a 
step  was  taken  which,  in  the  opinion  of  many,  was  greatly  to  be 
deprecated. 

A criminal  charge  was  preferred  against  Mr  Thomson  for  defal- 
cation in  his  accounts,  and  it  became  necessary  for  him  to  appear 
for  examination  before  the  sheriff  under  that  charge.  At  this  time 
a change  of  government  took  place,  and  it  happened  that,  as  an 
official  under  the  new  crown  authorities,  I was  entrusted  with  the 
duty  of  conducting  Mr  Thomson’s  examination.  It  was  carried 
out  with  every  degree  of  fulness  and  particularity,  and  I had  much 
satisfaction  in  being  able  to  report  to  my  constituents  that  there 
were  no  grounds  for  a criminal  charge.  Mr  Thomson  had  been 
guilty  of  laxity  and  carelessness,  he  had  sometimes  mistaken 
and  exceeded  his  powers  of  expenditure,  and  he  had  ventured 
upon  disbursements  for  what  he  considered  to  be  important  objects 
not  authorised  by  the  strict  letter  of  his  instructions.  But  there 
was  no  trace  of  anything  corrupt  or  fraudulent,  and  the  applica- 
tion of  the  criminal  law  to  his  case  appeared  to  mea  harsh  and 
inappropriate  proceeding.  These  views  were  adopted  by  the  crown 
counsel  of  the  day,  and  Mr  Thomson  was  liberated  from  any 
responsibility  beyond  the  civil  consequences  of  his  pecuniary  errors. 
It  was  impossible,  however,  that  such  occurrences,  overtaking  a man 
of  Mr  Thomson’s  high  position,  unblemished  character,  proud  feel- 
ings, and  eminent  public  services,  should  not  be  overwhelming, 
particularly  at  the  advanced  period  of  life  which  he  had  reached. 
The  whole  colour  of  his  existence  was  thus  changed ; he  had  lost 
his  office  of  “Clerk  Register,”  and  although  he  retained  that  of 
“ Clerk  of  Session,”  the  salary  attached  to  it  was  appropriated  to 
the  discharge  of  his  debts.  “ It  was  intimated  to  him  at  this  time 
that  another  person  was  to  be  employed  to  complete  the  first  volume 
of  the  Acts  of  Parliament.”  This  is  the  language  in  which  the 
occurrence  is  mentioned  in  the  Memoir  of  his  life.  Mr  Innes  was 
the  person  so  employed,  and  nothing  could  well  be  conceived  more 
painfully  interesting  on  both  sides  than  the  relation  that  came  thus 
to  exist  between  the  pupil  and  his  old  master.  Mr  Thomson  must 


of  Edinburgh,  Session  1874-75. 


457 


have  felt  deeply  the  blow  that  thus  deprived  him  of  the  opportunity 
of  completing  the  crowning  act  of  his  long  labours. 

“ He  never  again  entered  the  Eegister  House and  Mr  Innes 
adds,  “that  although  he  was  generously  communicative  on  every 
other  point,  where  his  assistance  or  advice  was  desired,  he  told  me 
soon  after  I had  been  employed  to  complete  the  first  volume  of  his 
great  work,  that  it  must  be  a forbidden  subject  between  us” 

In  1844  Mr  Innes  finished  the  first  volume  thus  handed  over  to 
him,  and  did  so  in  a manner  which  gained,  I believe,  universal 
approbation.  I do  not  say  that  it  was  done  as  well  as  Mr  Thomson 
at  one  time  could  have  done  it,  but  I am  sure  that  it  was  done  as 
well  as  Mr  Thomson  could  then  have  done  it,  or  rather,  that  the 
difference  lay  between  its  being  done  well  by  Mr  Innes  and  its  not 
being  done  at  all. 

The  extinction  that  was  thus  given  to  Mr  Thomson’s  efficiency 
in  his  peculiar  department,  for  such  was  truly  the  result  of  these 
events,  left  Mr  Innes  as  almost  the  only  man  in  the  field  to  whom 
either  the  public  or  individuals  could  resort  for  advice  and  assistance 
in  matters  of  this  kind,  and  he  thus  became  one  of  our  highest 
authorities  on  the  subject  of  general  or  family  antiquities. 

It  cannot  be  said,  I think,  that  Mr  Innes  was  ever  successful  as 
an  advocate.  He  did  not  possess  in  a sufficient  degree  either  what 
has  been  scornfully  called  the  power  “ to  make  the  worse  appear  the 
better  reason,”  or  which,  I think,  is  its  more  correct  description,  the 
peculiar  faculty  on  a properl  deebateable  question,  to  bring  forward 
the  fair  and  legitimate  considerations  that  are  to  be  weighed  on 
either  side.  But  he  held  successively  important  official  appoint- 
ments, that  of  Advocate-Depute,  Sheriff,  and  principal  Clerk  of 
Session,  the  duties  of  which  he  discharged  with  adequate  diligence. 
He  was  latterly  appointed  to  the  chair  of  Universal  History  in  the 
University  of  Edinburgh,  which  was  highly  congenial  to  his  general 
pursuits,  and  in  which,  I believe,  he  endeared  himself  to  his  students 
by  his  uniform  accessibility  and  kindness,  and  by  the  valuable  aid 
which  he  afforded  them  in  their  studies. 

I have  disclaimed  any  intention  here  of  attempting  to  enumerate 
or  estimate  the  different  works  of  an  historical  or  antiquarian  kind 
which  Mr  Innes  produced.  I shall  merely  advert  to  his  “ Scotland 
in  the  Middle  Ages,”  published  in  1863,  and  his  “ Sketches  of  early 


458  Proceedings  of  the  Royal  Society 

Scottish  History,”  published  in  1861,  both  of  which  are  well  known 
and  are  peculiar.  Besides  these,  I may  add  in  the  words  of  Mr 
David  Laing,  which  I am  allowed  to  borrow,  that  “ his  labours  in 
editing  numerous  volumes  of  ancient  chartularies  for  the  Bannatyne, 
Maitland,  and  Spalding  Clubs,  more  especially  those  of  Melrose, 
Moray,  Holyrood,  Dunfermline,  Glasgow,  and  Kelso,  as  well  as  works 
connected  with  the  public  records  of  Scotland,  will  always  be  grate- 
fully remembered.”  One  of  the  works  undertaken  by  him  was  the 
“ Origines  Parochiales  of  Scotland,”  which,  if  it  could  have  been 
finished  as  it  was  begun,  would  have  been  a great  and  valuable 
work ; but  the  difficulties  in  its  execution  proved  to  be  far  greater 
than  had  been  calculated,  and  it  remained  at  last  in  an  unfinished 
state,  which  necessarily  diminished  its  utility  and  importance. 

I have  always  understood  that  the  manner  in  which  Mr  Innes 
prepared  the  official  works  which  he  was  able  personally  to  accom- 
plish, was  much  admired  and  approved  of  by  the  best  judges  both 
in  this  country  and  abroad,  and  in  particular  I have  heard  that  M. 
Guizot,  no  mean  critic,  to  whom  he  was  personally  known,  always 
spoke  highly  of  their  merits.  Partly  on  business  exigencies,  and 
partly  as  a form  of  relaxation,  Mr  Innes  was  latterly  in  the  habit 
of  visiting  Paris  in  time  of  vacation,  and  greatly  enjoyed  the  ad- 
vantages of  good  Parisian  society,  as  well  as  the  opportunity  thus 
afforded  him  of  access  to  the  French  archives  and  other  objects  con- 
nected with  mediaeval  history  and  antiquities.  I may  here  observe 
that  Mr  Innes,  among  other  accomplishments,  had  a very  decided 
talent  for  letter  writing,  and  that  when  he  was  abroad  the  accounts 
thus  conveyed  to  confidential  friends  of  what  he  had  seen  and  felt 
on  his  travels,  were  a source  of  great  interest  and  delight. 

In  Mr  Innes’s  character — let  me  rather  say  within  his  bodily 
frame — two  very  different  aspects  of  human  power  were  to  be  seen. 
In  the  one  we  had  a strong  and  athletic  man,  passionately  fond  of 
the  country  and  country  scenes, particularly  those  of  this  “ Land  of 
the  Mountain  and  the  Flood,”  the  “ Land  of  our  Sires,”  excelling  in 
all  country  sports,  fishing,  shooting,  riding,  coursing,  and  enjoying 
a pleasing  though  always  a temperate  repose  from  these  exertions 
in  some  friendly  or  social  meeting;  while,  in  the  other,  we  saw  a 
man  turned  into  a monk,  busy  among  libraries  and  state  records  all 
day,  and  poring  with  double  magnifiers  and  strong  lamps  till  long 


459 


of  Edinburgh,  Session  1874-75. 

after  midnight,  deciphering  old  and  almost  illegible  manuscripts, 
and  trying  at  once  to  master  their  character  and  make  sense  of 
their  contents.  These  very  different  capacities  and  functions 
existed  harmoniously  together  in  the  same  individual,  and  instead 
of  interfering  with  each  other,  communicated,  perhaps,  a mutual 
zest,  and  enabled  the  change  to  he  pleasantly  or  at  least  contentedly 
acquiesced  in.  The  versatility  thus  existing  and  kept  up  fitted  him 
for  a very  varied  and  interesting  range  of  social  acquaintances,  and 
of  these  he  was  always  glad  to  avail  himself  in  moderation.  Nor 
was  any  one  a more  agreeable  companion.  His  perfect  good  humour 
and  good  temper,  his  strong  affection  for  his  family  and  for  his  old 
friends,  his  never-failing  courtesy,  which  arose  from  and  indicated 
the  chivalrous  feeling  that  was  at  the  foundation  of  his  character, 
his  utter  absence  of  envy,  jealousy,  presumption,  or  self-conceit ; 
and  his  sympathy  with  all  innocent  and  gentlemanly  relaxation 
and  even  merriment,  endeared  him  to  a very  extensive  and  attached 
circle,  and  made  his  home  the  centre  of  much  attraction  and  the 
scene  of  much  social  enjoyment.  To  these  enjoyments  his  surviving 
friends  still  look  back  with  un mixed  pleasure  and  tender  regard. 

His  literary  productions,  apart  from  those  which  appeared  in  an 
official  form,  show  the  same  diversity  of  character  to  which  we  have 
already  alluded.  As  specimens  of  these  I may  mention  two  excel- 
lent but  very  different  papers,  which  a careless  reader  would  scarcely 
conceive  to  have  proceeded  from  the  same  mind : the  one  of  these, 
a contribution  to  the  “ Quarterly  Review”  in  1843,  upon  the  Eccle- 
siastical Antiquities  of  Scotland,  and  the  other  a paper  inserted  in 
the  “North  British  Review”  in  1864,  on  the  Country  Life  of  England. 
Each  of  these  is  well  deserving  of  perusal,  and  the  last  mentioned 
is  particularly  interesting,  as  having  first  introduced  into  notice  the 
achievements  and  writings  of  Charles  St  John,  the  well-known 
lover  of  sport,  with  whose  tastes  and  habits  those  of  Mr  Innes  were 
in  full  accordance,  so  far  as  circumstances  would  permit  of  their 
free  indulgence. 

Mr  Innes’s  love  for  literature  was  strong  and  diversified.  He  was 
a fair  Greek  and  Latin  scholar.  I hesitate  to  call  him  a good  Greek 
scholar,  as  my  old  friend  Archdeacon  Williams  denied  that  title 
to  any  one  who  did  not  know  every  good  Greek  author  from  Homer 
to  Agathias.  He  was  sufficiently  at  home  in  French  and  Italian 


460  Proceedings  of  the  Royal  Society 

to  serve  all  the  purposes  which  he  had  in  view.  But  I think  the 
books  that  he  most  loved  were  those  that  gratified  best  that  chival- 
rous feeling  that  lay  so  deep  in  his  heart.  I remember  as  if  it 
were  yesterday  hearing  him  read,  fifty  years  ago,  in  an  Italian  society 
to  which  we  belonged,  the  concluding  character  of  Sir  Lancelot, 
given  in  Malory’s  translation  of  the  Morte  d’  Arthur,  which  runs 
in  these  striking  terms  “ And  now,  I dare  say,  that,  Sir  Lancelot, 
there  thou  lyest;  thou  wert  never  matched  of  none  earthly  knight’s 
hands.  Add  thou  wert  the  curteist  knight  that  ever  bare  shielde. 
And  thou  wert  the  truest  friende  to  thy  lover  that  ever  bestrode 
horse.  And  thou  wert  the  truest  lover  of  a sinful  man  that  ever 
loved  woman.  And  thou  wert  the  kindest  man  that  ever  stroke 
with  swerde.  And  thou  wert  the  goodliest  person  that  ever  came 
amonge  prece  (press)  of  knights.  And  thou  were  the  meekest  man 
and  the  gentillest  that  ever  eate  in  hal  among  ladies.  And  thou 
were  the  sternest  knight  to  thy  mortale  foe  that  ever  put  spere  in 
the  rest !” 

Mr  Innes  read  these  words  with  the  greatest  effect,  but  in  that 
peculiar  tone  for  which  I think  his  reading  was  remarkable.  He 
never  read  rhetorically,  or  in  a declamatory  style,  but  with  rather 
a cold  and  dry  manner,  which,  however,  had  the  strange  effect  of 
leaving  on  his  hearers  a deep  impression  of  his  earnestness,  and  a 
thorough  belief  in  wfflat  he  said.  It  was  impossible  so  to  hear  him 
without  feeling  convinced,  as  I then  and  ever  wras,  that  his  own 
character  involved  in  it  many  of  those  noble  traits  that  the  romancer 
described  as  forming  the  bright  side  of  his  hero. 

Mr  Innes’s  death  was  sudden,  and  took  place  at  a distance  from 
home,  but  it  was  calm  and  painless,  and  he^was  attended  at  the 
time  by  his  wife  and  his  only  unmarried  daughter.  It  is  right  to 
mention  that  in  the  later  years  of  his  life  he  enjoyed  the  advantage 
of  a considerable  accession  of  fortune,  which  came  to  Mrs  Innes, 
and  which  placed  them  in  comparative  affluence.  At  the  time  he 
was  taken  away,  his  daughter  was  engaged  under  very  happy 
auspices  to  the  gentleman  who  has  since  become  her  husband,  so 
that  his  departure  took  place  amid  circumstances  that  brought 
many  consolations,  and  left  little  more  in  life  to  be  desired. 


of  Edinburgh,  Session  1874-75. 


461 


3.  Biographical  Notice  of  Francis  Deas.  By  the  Hon, 
Lord  Neaves. 

Another  loss  to  our  Society  which  we  have  to  record  and  to 
deplore  at  this  time,  arises  by  the  death  of  Mr  Fkanois  Deas.  This 
loss  forms  a striking  contrast  to  that  of  either  of  the  members  of 
whom  I have  already  spoken.  They  retired  from  the  scene  not 
prematurely,  but  full  of  years  and  well-deserved  honours,  having 
attained  or  approached  the  longer  limit  to  which  human  life  in 
normal  circumstances  is  considered  to  extend ; they  had  played  out 
their  parts,  and,  as  having  done  so,  were  entitled  to  their  dismissal 
amidst  the  plaudits  of  those  who  had  witnessed  and  benefited  by 
their  labours.  Mr  Deas,  on  the  other  hand,  was  cut  off,  first  by 
failing  health,  and  ultimately  by  death,  before  he  had  attained  the 
meridian  of  life,  or  could  carry  out  into  execution  the  capacities 
which,  under  a more  favourable  fate,  would  assuredly  have  earned 
him  high  distinction. 

Francis  Deas,  the  eldest  son  of  the  Hon.  Lord  Deas,  was  born  at 
Edinburgh  on  the  1st  July  1839.  He  went  through  the  usual 
curriculum  of  the  Edinburgh  Academy,  which  he  quitted  in  July 
1856,  having  held  a good  place  in  all  his  classes,  and  having  gained 
in  1855  the  Ferguson  medal,  and  in  1856  the  Mitchell  medal,  both 
of  them  for  proficiency  in  mathematics.  He  then  went  through 
the  usual  course  of  study  at  the  Edinburgh  University,  taking 
prizes  in  almost  all  his  classes — mathematics,  logic  and  metaphysics, 
civil  law,  Scots  law,  rhetoric,  and  belles  lettres,  and  natural  philo- 
sophy; but  he  did  not  confine  his  studies  to  the  usual  routine.  He 

was  a zealous  student  with  Professor  Balfour  for  two  or  more 

♦ 

sessions  in  botany,  and  accompanied  him  in  his  pedestrian  excur- 
sions. He  attended  Dr  Stevenson  Macadam  for  practical  chemistry, 
Professor  Allman  for  natural  history,  and  Dr  Maclagan  for  medical 
jurisprudence.  He  continued  in  after  life  to  keep  up  an  intimacy 
with  many  of  the  Professors  whose  instructions  he  had  thus 
received. 

In  1859,  before  he  was  twenty,  he  went  to  Berlin,  principally  in 
order  to  perfect  himself  in  speaking  G-erman,  with  which  he  was 
otherwise  well  acquainted,  as  well  as -with  French  and  Italian.  He 
attended  law  and  other  classes  at  Berlin  University  in  summer  1859. 


462  Proceedings  of  the  Royal  Society 

In  1860  he  became  acquainted  with  Sir  David  Brewster,  having 
met  him  at  his  daughter-in-law  Mrs  Macpherson’s  house  in  Lass- 
wade,  and  an  intimacy  and  friendship  sprung  up  between  them, 
remarkable  in  several  respects,  and  particularly  in  this,  that  young 
Deas  was  then  barely  one-and-twenty,  while  Sir  David  was  in  his 
eightieth  year.  The  friendship  thus  formed  subsisted  during  their 
joint  lives,  and  was,  I believe,  a source  of  great  pleasure  and  satis- 
faction to  both,  and  certainly  of  great  benefit  to  the  younger  of  the 
two,  though  I venture  to  think  that  the  benefit  was  mutual,  as  no 
one,  and  not  certainly  a man  of  Sir  David’s  years  and  peculiar 
character,  could  fail  to  derive  advantage  from  the  simple  and  sincere 
affection  of  a youth  so  amiable  and  intelligent  as  Mr  Deas. 
Sir  David  said  of  him  from  the  first,  that  he  had  a more  thorough 
and  a more  comprehensive  hold  of  scientific  principles  than  any 
man  of  his  acquaintance  not  professionally  scientific,  and  that  he 
had  so  rare  a combination  of  the  faculties  necessary  for  scientific 
research,  that  he  (Sir  David)  deeply  regretted  “ he  was  crippled  by 
a profession  so  jealous  as  the  law.”  Of  the  intimacy  that  thus 
arose  very  pleasing  traces  are  to  be  found  in  the  interesting  volume 
of  Sir  David’s  Home  life,  by  his  daughter.  In  1866  Sir  David 
was  seized  when  at  Belleville  with  an  unseasonable  attack  of  hoop- 
ing cough,  and  his  illness  was  so  severe  as  to  excite  the  greatest 
alarm  in  Lady  Brewster  and  his  friends,  although  his  mind  re- 
mained bright,  clear,  and  active.  “ A favourite  young  scientific 
friend,”  Mrs  Gordon  states,  “ Mr  Francis  Deas,  was  staying  in  the 
house  at  the  time,  and  after  hours  of  fatigue  and  suffering  it  was 
positive  enjoyment  to  the  invalid  to  make  the  little  preparations  for 
his  visit,  which  was  quite  the  event  of  the  day.  Believing  himself 
a fast  dying  man,  he  left  many  instructions  with  Mr  Deas  as  to 
the  arrangement  of  his  scientific  instruments,  &c.,  and  two  years 
afterwards,  when  the  call  really  came,  it  was  to  this  gentleman 
that  he  confided  the  finishing  and  reading  of  a paper  for  the  Royal 
Society,  which  weakness  prevented  him  from  completing.  It  was 
on  the  Motion,  Equilibrium,  and  Forms  of  Liquid  Films.” 

Mrs  Gordon  gives  us  at  the  same  time  an  interesting  letter, 
written  by  Mr  Deas  to  Mrs  Macpherson  after  Sir  David’s  death, 
sending  his  reminiscences  of  the  three  weeks  spent  by  them  to- 
gether  at  Belleville  on  the  occasion  above  referred  to,  and  in  a letter 


of  Edinburgh,  Session  1874-75. 


463 


written  by  Sir  David  on  his  death-bed,  he  refers  to  Mr  Deas  as  the 
friend  to  whom  he  bad  entrusted  the  final  preparation  of  the  paper 
on  Films  already  mentioned. 

I may  add,  that  there  was  found  in  Mr  Deas’s  repositories,  after 
his  death,  a letter  to  him  from  Mrs  Macpherson,  Sir  David’s 
daughter  in-law,  giving  an  account  of  his  last  moments,  and  refer- 
ring to  the  scientific  subject  in  question,  on  which,  I believe,  Mr 
Deas  read  a paper  in  this  Society  as  requested.  That  letter  will  be 
found  in  an  appendix  to  the  notice  I am  now  reading. 

Mr  Deas  was  admitted  a member  of  the  Royal  Society  in  1867. 

He  had  previously  passed  advocate  in  May  1862.  At  a later 
period,  he  was  the  first  to  receive  the  new  degree  of  LL.B. 
(instituted  in  1862.)  Upon  that  occasion  he  was  presented  for 
graduation  by  Professor  Loriraer,  with  a well-merited  tribute  to 
his  diligence  and  proficiency  in  law.  He  had  thoroughly  studied 
his  profession,  and  continued  to  do  so,  extending  his  attention  at 
the  same  time  to  various  kindred  branches  of  study,  sueh  as  medical 
jurisprudence  and  anatomy. 

He  began  now  to  contemplate  the  publication  of  some  legal  work 
that  should  be  useful  to  him,  and  prior  to  1870  was  engaged  in 
preparing  a second  edition  of  Mr  Fraser’s  work  on  “ Master  and 
Servant,”  which  appeared  in  January  1872.  His  laborious  appli- 
cation however  to  that  task,  carried  on  in  conjunction  with  the 
practice  which  he  was  obtaining  at  the  bar,  seems  to  have  injuri- 
ously affected  his  health,  and  to  have  made  the  first  encroach^ 
ment  that  appeared  upon  his  constitution,  and  in  the  summer  of  1870 
premonitory  symptoms  were  observed  of  that  tenderness  of  chest 
which  ultimately  proved  fatal.  By  advice  of  his  medical  attendants 
he  went  abroad,  in  order  to  make  what  is  called  the  Nile  journey. 
He  had  twice  before  been  abroad,  and  was  thus  not  an  inex- 
perienced traveller.  He  much  enjoyed  the  voyage  up  the  Nile  to 
the  Second  Cataract,  and  tobk  an  interest  in  all  that  he  saw, 
visiting  all  the  objects  of  celebrity  within  his  reach.  The  atmo- 
spheric varieties  of  the  country,  and  in  particular  the  pure  and 
inspiriting  air  ef  the  Desert,  seem  to  have  done  him  good,  as  well 
as  to  have  afforded  him  pleasure.  His  journal  consisting  of  memo- 
randa during  this  voyage,  of  which  I have  seen  a copy,  is  very 
interesting,  particularly  to  those  who  knew  him,  and  shows  how  his 

3 o 


VOL.  VIII. 


464  Proceedings  of  tne  Royal  Society 

scientific  tastes  and  feelings  of  curiosity  were  elicited  at  every  step. 
It  seems  to  be  uncertain  whether  his  health  truly  profited  by  this 
experiment.  He  appears  to  have  doubted  it  himself ; yet  on  arriving 
in  London  in  June  1871,  he  wrote  that  there  had  been  a marked 
change  for  the  better  ever  since  he  recrossed  the  Alps,  and  that  he 
was  now  so  well  that  he  wished  to  resume  business.  He  returned  to 
Edinburgh  accordingly,  and  did  resume  business,  but  without 
attending  the  Parliament  House.  Upon  putting  out  of  hand  his 
book  on  u Master  and  Servant, ” Mr  Deas  bad  commenced  another 
work  of  a still  more  arduous  kind,  on  the  “ Law  of  Railways, ” and 
to  this  he  now  applied  himself  as  a professional  task. 

In  February  1872  he  again,  by  advice,  went  abroad,  spending 
his  time  partly  at  Florence,  but  chiefly  at  Rome,  still  attending  to 
all  objects  of  interest,  but  at  the  same  time  continuing  even  there 
the  progress  of  his  book  on  Railways.  He  returned  home  in  June 
of  that  year,  perseveringly  completed  his  book,  and  published  it  in 
January  1873.  He  very  fittingly  dedicated  the  work  to  his  father, 
Lord  Deas,  “ alike  as  a token  of  filial  regard,  and  as  a tribute  to 
his  acknowledged  eminence  as  a lawyer.”  The  book  was  received 
with  great  approbation,  it  evinces  a wonderful  degree  of  industry 
and  energy,  and  cannot  fail  to  be  eminently  useful  to  the  profes- 
sion, as  many  competent  judges  have  gladly  acknowledged. 

In  the  narrative  given  above  I have  not  said  much  of  Mr 
Deas’s  scientific  tendencies;  but  these,  from  the  first,  were  very 
strong  and  decided.  I have  mentioned,  the  opinion  of  Sir  David 
Brewster  as  to  the  combination  of  qualities,  which  seemed  pecu- 
liarly to  fit  him  for  scientific  research,  and  his  application  to 
scientific  subjects  was  constantly  kept  up.  His  reading  was  exten- 
sive in  all  the  best  books  on  science,  and  he  contributed  papers 
which  were  considered  valuable  to  the  best  scientific  periodicals  of 
the  day.  He  devoted  a good  deal  of  time  to  the  study  of  optics, 
and  had  considerable  practice  in  the  use  of  the  telescope ; but  was 
still  more  interested  in  microscopic  investigations,  in  connection 
with  which  he  amassed  an  extensive  collection  of  objects  for  that 
instrument,  nearly  all  prepared  by  himself,  and  accumulated  during 
many  years,  wherever  he  travelled  or  happened  to  be. 

It  is  to  me  a pleasant  thing  to  record,  and  it  must  have  been  to 
his  friends  a great  consolation  to  know,  that  in  the  midst  of  these 


of  Edinburgh,  Session  1874-75. 


465 


scientific  investigations,  which  were  fearlessly  and  searchingly  con- 
ducted, he  never  lost  sight  of  those  great  principles  that  connect 
the  works  of  the  Deity  with  His  personal  existence  and  moral  per- 
fections. Many  entries  in  his  private  memoranda  show  his  fidelity 
to  these  feelings,  and  prove  that  he  shared  with  his  friend  Brewster 
the  reverence  for  a Supreme  Power  which  that  distinguished  man 
always  evinced  in  the  prosecution  of  his  varied  inquiries.  Mr 
Deas’s  reading  on  sacred  subjects  seems  to  have  been  much  in  the 
Book  of  Psalms,  a book  which  has  proved  a treasure  and  a favourite 
study  with  all  the  devout  admirers  of  nature ; and  he  often 
expresses  in  his  memoranda  how  much  the  admiration  felt  by  the 
authors  of  that  book  for  the  works  of  the  Creator  would  have  been 
exalted  and  enhanced,  instead  of  being  deadened  or  destroyed,  by 
the  new  wonders  revealed  through  the  aid  of  scientific  instruments. 

It  was  not  only  to  professional  and  scientific  subjects  that  he 
directed  his  attention.  He  had,  I think,  a genius  for  music,  and 
performed  on  the  pianoforte  with  perfect  taste  and  with  a degree  of 
skill  that  was  scarcely  to  be  expected  from  an  amateur  who  had 
so  many  other  avocations  and  pursuits  of  a more  urgent  and  en- 
grossing nature.  He  was  also  fond  of  sculpture  and  painting,  and 
his  friend,  Sir  Noel  Paton,  seemed  to  have  pleasure  in  sending  him 
his  paintings  before  they  were  despatched  to  London,  at  a time 
when  Mr  Deas  was,  from  illness,  unable  to  leave  the  house. 

After  what  I have  said,  I think  I may  confidently  claim  your 
sympathy  with  me  in  this  tribute  to  the  memory  of  a young  man 
for  whom,  when  he  was  in  life,  I felt  a strong  esteem  and  regard, 
in  whose  sad  fate  I saw  a great  private  and  public  loss,  and  whose 
memory,  I think,  is  entitled  to  our  affectionate  remembrance. 
Looking  to  his  natural  talents  and  tastes,  to  the  assiduous  cultiva- 
tion that  he  bestowed  upon  them,  to  the  variety  of  subjects  to 
which  his  studies  extended,  and  to  the  high  and  sound  principles 
with  which  his  mind  was  imbued,  I venture  to  say,  that  I know  of 
no  young  man  who,  if  he  had  lived  and  had  preserved  a sufficient 
measure  of  health,  was  more  likely  to  extend  the  range  and 
maintain  the  dignity  of  science,  as  well  as  of  mental  culture 
generally,  while  at  the  same  time  I cannot  help  adding,  and 
there  is  a satisfaction  even  in  this  feeling,  that  I know  of  no  one 
who,  from  the  innocence  of  his  character  and  from  the  purity  of 


466  Proceedings  of  the  Royal  Society 

his  feelings,  as  well  as  from  the  religious  emotions  which  lie  carried 
into  scientific  investigations,  was  better  prepared  to  be  early 
removed  from  this  temporary  scene,  seeing  that  such  was  the  lot 
appointed  for  him.  The  loss  of  such  a youth,  who  was  doing  so 
well,  and  promising  so  much  more  to  be  still  done,  must  be  a 
great  affliction  to  all  who  knew  him,  and  a very  grievous  one  to 
those  most  nearly  connected  with  him ; but  of  such  characters  it 
is  the  privilege  of  survivors  to  speak,  as  good  men  have  often  done, 
that  the  memory  of  the  departed  is  a treasure  that  cannot  be  out- 
weighed even  by  present  blessings. 

APPENDIX. 

Letter  referred  to  on  page  463,  from  Mrs  Brewster  Macpherson, 
found  in  Mr  Deas’s  repositories,  dated  Allerley,  Monday,  February 
10th,  1868. 

“ You  will.  I know,  be  intensely  anxious  to  hear  of  dear,  dear 
papa.  Sir  James  Simpson  says  he  cannot  live  over  the  night.  We 
got  a train  straight  on  to  Melrose  on  Saturday,  so-  I gave  my 
note  to  a porter  to  post  for  me.  I hope  you  got  it.  We  found  Sir 
David  much  stronger  and  better  than  I had  expected,  so  much  so 
that  I could  not  believe  he  was  dying  He  slept  all  that  night, 
and  up  to  twelve  on  Sunday.  I could  not  believe  he  was  dying, 
then  he  sank  very  rapidly.  His  perfect  trust  in  the  love  of  G-od, 
and  in  the  finished  righteousness  of  the  Saviour,  is  wonderful.  He 
has  no  wish  to  live — no  fear  of  death — absolutely  none.  His  faith 
is  pure  and  childlike.  His  mind  is  perfectly  clear.  He  expressed 
a wish  twice  to  me  that  you  should  finish  a paper  which  he  had 
begun  on  Soap-bubbles,  and  read  it  for  him  at  the  Royal  Society. 
He  expressed  the  same  wish  to  Sir  James  Simpson  last  night,  and 
he  has  left  a paper  for  you  with  instructions  about  it.  Lady 
Brewster  wrote  at  his  request  on  Friday.  He  has  spoken  of  you 
repeatedly  to  me  with  such  kindness.  Oh  ! Frank,  it  was  awfully 
solemn  all  yesterday,  and  how  much  more  so  to-day — one  of  the 
great  lights  of  the  world  going  out.” 


of  Edinburgh,  Session  1874-75. 


467 


4.  Biographical  Notice  of  Adam  Black.  By  the  Rev. 

Dr  Lindsay  Alexander. 

Adam  Black  was  a native  of  Edinburgh,  where  he  was  born 
on  the  20th  of  February  1784.  He  received  his  education  at  the 
High  School  of  the  city,  and  afterwards  attended  for  two  sessions  the 
classes  at  the  University.  Having  selected  bookselling  as  his  profes- 
sion, he  became  apprentice  to  Mr  Fairbairn,  an  Edinburgh  bookseller, 
and  at  the  close  of  his  apprenticeship  spent  two  years  in  the  house 
of  Lackington,  Allen,  & Co.,  London.  In  1815  he  commenced 
business  for  himself  in  Edinburgh  as  a bookseller;  and  entered 
upon  that  career  of  wise  and  vigorous  enterprise  which  he  pursued 
to  the  end  of  his  life,  and  in  which,  both  as  a man  of  business  and 
as  a public  man,  he  earned  for  himself  a wide-spread  reputation. 
When  the  first  Town  Council  under  the  New  Municipal  Act  was 
elected,  he  was  returned  as  one  of  the  councillors;  shortly  after 
he  became  treasurer  of  the  city  funds,  and  laid  the  foundation 
of  that  scheme  by  means  of  which  the  pecuniary  affairs  of  the  city 
were  at  length  brought  into  order,  and  the  city  relieved  of  the 
pressure  of  debt;  and  in  1843  he  was  raised  to  the  office  of  Lord 
Provost,  an  office  which  he  held  by  re-election  for  six  years.  On 
his  retirement  from  this  office  he  was  offered  a knighthood  by 
the  Government,  but  this  he  declined,  alleging  that  as  he  was  still 
in  business  as  a retail  bookseller  and  stationer,  it  would  be  incon- 
gruous for  him  to  be  standing  behind  his  counter  to  be  addressed 
there  as  “ Sir  Adam  ” by  some  boy  sent  up  from  the  market  u for 
a hard  pen  and  a pennyworth  of  ink.”  In  1856  he  was  returned  to 
Parliament  as  one  of  the  members  for  the  city,  and  to  this  dignified 
post  he  was  repeatedly  re-elected,  and  represented  the  city  for  nearly 
ten  years.  On  his  retirement  from  Parliament  he  still  continued 
to  take  an  interest  in  public  affairs,  as  well  as  in  the  conduct  of  his 
business.  For  some  years  he  had  been  withdrawing  from  book- 
selling and  confining  his  energies  and  resources  to  publishing.  By 
a happy  union  of  boldness  with  prudence  he  raised  his  house  to  a 
foremost  place  among  the  great  publishing  firms  of  the  country. 
Two  large  editions  of  “ Encyclopaedia  Britannica,”  each  of  which 
was  nearly  all  written  anew,  and  numerous  editions  of  the  “ Wavex- 
ley  Novels,”  and  other  writings  of  Sir  Walter  Scott, in  various  sizes 


468  Proceedings  of  the  Royal  Society 

and  at  prices  that  brought  these  matchless  productions  within  the 
reach  of  all  classes  of  the  community,  attest  the  vigour  and  skill 
with  which  he  carried  on  his  enterprise  as  a publisher.  To  him  also 
is  due  the  honour  of  being  the  first  to  summon  the  learning  of  the 
churches  to  the  preparation  of  a “ Cyclopaedia  of  Biblical  Litera- 
ture,” such  as  should  present  in  a condensed  form  the  results  of 
the  most  advanced  investigation  into  the  history,  literature,  and 
archaeology  of  the  sacred  writings.  These  are  but  a very  few 
of  the  works  he  published,  but  they  are  the  most  important;  of 
the  rest  it  may  be  said  generally,  that  they  all  possess  some 
quality  of  excellence  such  as  makes  them  valuable  contributions  to 
the  literary  or  scientific  products  of  the  day. 

Mr  Black  died  on  the  24th  of  January  1874,  having  nearly  com- 
pleted his  90th  year.  Not  only  for  the  services  he  rendered  in 
various  ways  to  the  city,  not  only  for  his  abilities  and  his  success 
in  business,  not  only  for  his  enterprise  and  wisdom  as  a publisher, 
but  still  more  for  his  moral  qualities,  his  perfect  integrity,  his 
transparent  honesty,  his  steadfast  consistency,  his  unaffected 
piety,  and  his  unswerving  loyalty  to  truth  and  equity,  will  his 
name  be  handed  down  to  posterity  by  the  people  of  this  city  as 
that  of  one  of  the  noblest  and  worthiest  of  her  citizens. 


5.  Biographical  Notice  of  Sheriff  Cleghorn.  By 
David  Maclagan,  Esq.,  C.A. 

Thomas  Cleghorn  was  born  in  Edinburgh  3d  March  1818,  and 
died  there  13th  June  1874.  His  father,  Alexander  Cleghorn, 
Collector  of  Customs,  was  an  esteemed  citizen  of  Edinburgh;  his 
uncle,  David  Cleghorn,  was  long  Crown  Agent;  and  a second  uncle, 
the  Bev.  Thomas  Cleghorn,  was  parish  minister  of  Smailholm,  of 
which  his  great-grandfather,  Dr  Duncan,  had  also  been  pastor. 

Mr  Cleghorn  was  educated  at  the  Edinburgh  Academy  and  at 
the  University,  in  both  of  which  he  was  distinguished  by  earnest 
application  and  by  high  character.  His  favourite  study  was  that 
of  natural  philosophy,  and  in  the  distinguished  occupant  of  that 
chair,  James  David  Forbes,  he  found  a life-long  friend  and  corre- 
spondent. Mr  Cleghorn  wrote  a cordial  and  discriminating  notice 


469 


of  Edinburgh,  Session  1874-75. 

of  Forbes  after  his  death,  in  one  of  the  magazines  of  the  day.  Like 
most  of  the  foremost  students  of  the  University  he  was  a member 
of  the  Speculative  Society,  and  in  later  years,  along  with  his  friend 
Mr  Eobert  Balfour,  now  deceased,  wrote  its  history,  a work  of  great 
research  and  interest. 

Mr  Cleghorn  was  called  to  the  Scottish  bar  in  1839,  and  held 
successively  the  offices  of  Advocate-Depute,  Eegistrar  of  Friendly 
Societies,  and  Sheriff  of  Argyle,  which  latest  appointment  he  con- 
tinued to  hold  until  his  death.  He  was  unanimously  elected  in 
1871  Legal  Adviser  of  the  Free  Church  of  Scotland,  of  which  he  was 
an  attached  member  and  office-bearer.  Mr  Cleghorn’s  connection 
by  marriage  with  the  family  of  the  late  Lord  Cockburn  introduced 
him  to  a highly  cultivated  literary  circle,  in  which  he  was  well 
fitted,  by  his  classical  and  scientific  knowledge  and  wide  range  of 
literary  study,  to  occupy  a place.  For  very  many  years  Mr  Cleg- 
horn  devoted  much  time  to  the  advancement  of  educational,  bene- 
volent, and  religious  objects,  to  all  of  which  he  was  a most  liberal 
contributor.  The  welfare  of  schools  and  colleges  generally  was 
always  a source  of  interest  to  him,  while  the  Edinburgh  Academy, 
of  which  he  was  for  many  years  a Director,  and  the  University  of 
his  native  city,  were  specially  dear  to  him. 

Wellington  School,  an  institution  for  the  reformation  of  young 
criminals,  was  founded  by  him,  and  to  its  support  he  largely  con- 
tributed both  means  and  personal  labour. 

Mr  Cleghorn  has  left  a name  greatly  esteemed,  and  will  be  re- 
membered as  a man  of  much  culture  and  many  acquirements,  as 
well  as  a citizen  of  proved  worth  and  of  large  hearted  public  spirit. 


6.  Biographical  Notice  of  Henry  Stephens.  By 
Professor  Maclagan. 

Mr  Henry  Stephens  was  in  the  Eoyal  Society  essentially  the  re- 
presentative of  the  important  science  of  agriculture,  and  has  left 
behind  him  a reputation  as  an  agriculturist  not  confined  to 
Britain,  for  his  works  on  agriculture  have  been  translated  into 
every  European  tongue,  and  are  thoroughly  appreciated  abroad. 
He  was  born  in  July  1796,  in  Forfarshire,  where  he  inherited  the 


470  Proceedings  of  the  Boyal  Society 

estate  of  Balmadies.  He  seems,  from  his  earliest  youth,  to  have 
had  an  enthusiastic  love  for  agriculture,  and  to  have  from  the  first 
regarded  it  not  as  a business  to  he  conducted  by  empirical  or 
routine  rules,  hut  as  an  art  to  be  practised  under  the  guidance  of 
scientific  principles.  He  intended  that  he  should  be  a practical 
farmer,  but  he  resolved  that  to  fit  himself  for  this  he  should  make 
himself  a well-educated  gentleman.  His  motto  seems  all  along  to 
have  been  u thorough, ” and  his  guiding  rules  diligence  and  method. 
Nothing  can  illustrate  this  better  than  a manuscript  volume  which 
he  left  behind  him,  hearing  on  its  title  page,  “ A Course  of  Educa- 
tion, comprising  Mathematics,  Natural  Philosophy,  Natural  History, 
Chemistry,  and  Agriculture.  Dundee,  1815.”  The  volume,  which 
looks  almost  as  if  he  intended  it  to  be  printed  as  a text-book  for 
young  agriculturists,  was  begun  by  him  when  he  was  19.  It  is 
not  original  work,  but  consists  of  notes  taken  by  him  during  his 
attendance  on  courses  of  instruction,  of  which  he  gives  the  follow- 
ing account  in  a formal  preface  to  his  manuscript  volume : — 

“ The  notes  on  mathematics,  natural  philosophy,  and  the  outlines 
of  chemistry,  were  taken  at  the  lectures  of  Mr  Duncan  in  the 
Dundee  Academy,  from  1st  October  1809  to  1st  August  1810,  and 
from  1st  October  1810  to  1st  August  1811,  which  completed  the 
session  at  the  academy. 

“ The  notes  on  chemistry  were  taken  when  attending  the  lectures 
of  Dr  Charles  Hope  in  the  University  of  Edinburgh,  from  6th 
November  1812  to  the  26th  April  1813.  Those  on  natural  history, 
when  attending  the  class  of  Mr  Kobert  Jameson,  in  the  same  place 
and  during  the  same  period.  In  the  same  place  the  lectures  on 
agriculture  by  Dr  Andrew  Coventry,  commenced  5th  January  1813 
to  28th  April  of  the  same  year;  but  during  that  period  [I]  attended 
his  class  twice  a day,  at  8 o’clock  in  the  morning  and  at  3 o’clock 
in  the  afternoon.” 

This  preface  is  a true  index  of  the  character  of  the  man,  even  as 
he  was  known  in  his  old  age — complete  methodicity,  unsparing 
energy,  and  perfect  precision  in  everything. 

Stephens  had,  by  theoretical  preparation,  made  ready  for  culti- 
vating his  own  estate,  but  he  felt  the  necessity  for  practical  study 
also,  and  therefore  he  placed  himself,  with  a view  to  learning  his 
work  practically,  with  one  of  the  largest  and  most  skilful  agricul- 


471 


of  Edinburgh,  Session  1874-75. 

turists  in  the  county  of  Berwick,  which  had  then  the  repute  of 
being  the  best  farmed  district  of  Scotland.  On  this  farm — Whit- 
some  Hill — he  remained  for  three  years,  engaging,  as  he  himself 
records,  “in  every  sphere  of  work  which  the  ploughman,  the 
shepherd,  and  the  field-worker  must  perform  in  the  field,  or  the 
steward  or  cattleman  at  the  steading;”  even  in  the  dairy  and 
poultry-house  part  of  his  time  was  spent;  and  all  this  he  undertook 
“not  of  necessity,  but  voluntarily,  and  with  cheerfulness,  in  the 
determination  of  acquiring  a thorough  practical  knowledge  of  his 
profession.” 

Thus  armed,  he  was  prepared  to  encounter  the  work  of  cultivat- 
ing a part  of  his  own  estate,  and  he  soon  saw  that  to  do  this 
satisfactorily  a considerable  expenditure  of  money  was  called  for ; 
and  this  was  done,  to  the  effect  of  raising  the  value  of  the  farm 
which  he  personally  worked,  from  L.150  to  L.400  a year.  But  evil 
days  were  in  store  for  him.  By  the  failure  of  an  Indian  house  in 
which  his  money  was  invested,  and  just  at  the  time  when  he  had 
spent  much  on  improving  his  property,  he  was  straitened  in  his 
means,  and  he  had  to  bethink  himself  of  other  ways  of  carrying 
out  his  life’s  object  of  being  an  agriculturist.  It  was  at  this  time, 
when  he  was  under  the  cloud  of  misfortune,  that  an  accident 
occurred  which  laid  the  foundation  for  his  reputation  as  an  agri- 
cultural author.  He  was  travelling  in  the  coach  from  Dundee  to 
Edinburgh  when  he  encountered,  as  travelling  companion,  the 
eminent  founder  of  the  great  publishing-house  of  William  Black- 
wood and  Sons.  The  sagacious  William  Blackwood  was  too  acute 
not  to  perceive  that  in  his  young  travelling  companion  he  had 
found  a man  thoroughly  versed  in  the  science  of  agriculture.  He 
shortly  after  called  Stephens  to  his  aid  in  conducting  the  Journal 
of  Agriculture,  and  thereby  was  commenced  a literary  connection 
with  the  Blackwoods,  which  has  extended  even  to  a third  genera- 
tion. It  was  through  them  that  he  gave  to  the  agricultural  world 
his  “Book  of  the  Farm,”  the  first  edition  of  which  was  pub- 
lished in  1842,  and  a second  edition  in  1871 — the  manuscript  of 
which, — almost  a complete  re-writing  of  the  original  edition, — was 
worked  up  with  the  same  precision,  attention  to  detail,  and  neat- 
ness of  penmanship,  which  characterised  the  “Course  of  Education” 
of  1815,  His  other  works  were — in  conjunction  with  Mr  Gr.  II. 

3 p 


VOL.  VIII. 


472  Proceedings  of  the  Royal  Society 

Slight,  “ The  Book  of  Farm  Implements  and  Machines;”  in  con- 
junction with  Mr  R.  Scott  Brown,  the  “Book  of  Farm  Buildings;” 
in  conjunction  with  Dr  Seller,  “Physiology  at  the  Farm;”  the 
“Manual  of  Practical  Draining;”  the  “Yester  Deep  Land  Cul- 
ture;” and  the  “ Catechism  of  Practical  Agriculture.” 

He  was  an  original  and  active  member  of  the  Meteorological 
Society  of  Scotland,  and,  although  not  writing  much  on  the  subject, 
he  was  in  constant  communication  with  the  Secretary  of  the  Society, 
especially  in  giving  advice  and  assistance  in  all  questions  of  mete- 
orological science  which  had  a special  bearing  on  agriculture. 

Mr  Stephens,  for  many  years  previous  to  his  death,  was  in  the 
habit  of  repairing  annually  for  the  recruitment  of  his  health  to 
Homburg,  and,  in  the  course  of  his  various  visits  to  Germany, 
visited  all  the  more  celebrated  vine  growing  districts  on  the  Rhine. 
He  carried  his  agricultural  spirit  with  him  in  all  these  trips,  noting 
all  the  processes  of  vine  cultivation,  even  to  its  minutest  details, 
and  bringing  back  with  him  an  ever  increasing  appreciation  of  all 
the  best  vintages  of  the  Rhine,  of  which  he  always  possessed  a 
modest  but  select  store,  with  which  he  delighted  to  refresh  any 
friend  visiting  him  at  Redbraes,  whom  he  thought  capable  of  fully 
estimating  his  favourite  wines.  He  had,  however,  even  better 
entertainment  for  his  visitors  in  his  conversation,  which  was  to  the 
last  full  of  good  nature,  with  a large  spice  of  “ pawky  ” humour, 
sometimes  in  his  later  years  a little  prolix,  but  always  yielding 
something  in  the  way  of  anecdote  or  scientific — especially  agricul- 
tural— observation  worth  listening  to.  For  many  years  he  had 
been  made  aware  that  he  had  a certain  amount  of  organic  change  of 
structure  in  the  aortic  orifice  of  the  heart;  but  this  made  no  progress, 
and,  so  far  as  it  was  concerned,  he  might  have  prolonged  his  days. 
His  death,  however,  was  ultimately  due  to  accident.  It  is  remark- 
able that  he  was  three  times  the  subject  of  poisoning.  He  was  one 
of  the  first  of  several  instances  which  have  occurred  of  poisoning 
by  the  flesh  of  American  partridges,  and  his  case  was  graphically 
narrated  by  his  then  medical  attendant  and  friend,  the  late  Dr 
Burt.  He,  on  another  occasion,  suffered  a good  deal  by  the 
inhalation  of  coal  gas  which  had  escaped  in  his  bedroom  during 
the  night,  but  from  this  he  soon  got  well.  It  was,  however,  a 
repetition  of  this  accident  which  ultimately  led  to  his  death.  On 


of  Edinburgh,  Session  1874-75. 


473 


the  night  or  early  morning  of  21st  June  1874  he  had,  as  he  thought, 
extinguished  the  gas  in  his  small  bachelor  bedroom,  but  unfor- 
tunately had  left  the  stop-cock  open,  and  it  was  his  not  making 
any  movement  in  the  morning  that  attracted  the  notice  of  the 
servants ; one  of  them  entering  his  room  found  him  insensible,  in 
an  atmosphere  strongly  charged  with  gas,  and,  seeing  at  once  what 
had  happened,  sagaciously  opened  the  window,  and  got  him  to 
swallow  some  stimulant.  His  medical  attendants  succeeded  in 
rousing  him  from  his  comatose  state,  and  he  seemed  in  the  fair  way 
of  recovery,  but  a low  congestive  inflammation  of  the  lungs  super- 
vened, and  proved  fatal  on  the  4th  of  July. 

7.  Biographical  Notice  of  Christopher  Hansteen.  By 
Alexander  Buchan,  Esq. 

Christopher  Hansteen  was  bom  at  Christiania  on  the  26th  of 
September  1784.  In  1802  he  entered  the  University  of  Copen- 
hagen as  a student  of  law,  which,  however,  he  soon  abandoned  for 
what  was  to  him  the  more  congenial  study  of  mathematics.  He 
became  mathematical  tutor  in  the  Gymnasium  of  Fredericksburg, 
in  the  Island  of  Zealand,  in  1806,  and  about  the  same  time  he 
gained  the  prize  which  had  been  offered  by  the  Boyal  Society  of 
Sciences  of  Copenhagen  for  the  best  essay  on  terrestrial  magnetism. 
Shortly  thereafter,  viz.,  in  1814,  he  was  appointed  to  the  chair  of 
astronomy  in  the  University  of  Christiania,  which  had  recently  been 
founded  by  Frederick  VI.  of  Norway. 

He  continued  to  prosecute  his  researches  into  terrestrial  magnet- 
ism with  ardour  and  success,  the  results  of  which  appeared  in 
his  great  work,  entitled  “ Untersuchungen  fiber  den  Magnetismus 
der  Erde,”  which  was  published  in  1819  by  the  liberality  of  the 
King  of  Norway.  The  work  was  illustrated  with  an  atlas  of  maps, 
and  besides  containing  the  fullest  and  best  collection  of  observa- 
tions on  terrestrial  magnetism  which  had  then  appeared,  if  was 
remarkable  for  great  breadth  of  treatment  and  sound  philosophical 
generalisations. 

In  continuing  the  prosecution  of  his  physical  researches,  he 
made  a journey  into  Siberia,  accompanied  by  Ermann  and  Due,  the 
expenses  of  the  expedition  being  defrayed  by  the  Norwegian 


474  Proceedings  of  the  Royal  Society 

Government.  One  of  the  most  important  results  of  this  expedition 
was  the  establishment,  on  Humboldt’s  recommendation,  of  the  ten 
magnetical  and  meteorological  observatories  by  the  Emperor  of 
Russia,  at  which  hourly  observations  were  recorded  for  many  years, 
and  annually  published  in  extenso  by  the  Russian  Government,  the 
whole  forming  the  completest  record  of  these  phenomena  we  yet 
possess. 

Shortly  after  his  return  from  Siberia  the  Norwegian  Government 
voted  the  funds  for  building  an  astronomical  and  meteorological 
observatory  at  Christiania,  which  was  erected  under  Hansteen’s 
direction.  He  also  superintended  the  trigonometrical  and  topogra- 
phical survey  of  Norway,  which  was  begun  in  1837. 

The  completion  of  his  fifty  years’  public  services  was  commemo- 
rated in  1856,  shortly  after  which  he  ceased  to  lecture,  and  in  1861 
retired  altogether  from  public  duty.  He  died  on  the  11th  April 
1873,  at  the  advanced  age  of  88. 

8.  Biographical  Notice  of  Jacques-Adolphe-Lambert 
Quetelet.  By  Alexander  Buchan.  Esq. 

Jacques-Adolphe-Lambert  Quetelet.— On  17th  Eehruary  1874 
Quetelet  died  at  Brussels,  in  the  seventy-eighth  year  of  his  age, 
having  been  born  at  Ghent  on  22d  February  1796.  At  the  age 
of  18  he  was  appointed  Professor  of  Mathematics  in  the  College  at 
Ghent;  and  in  July  1819,  the  degree  of  Doctor  of  Science  was 
conferred  on  him  by  the  University  of  the  same  town,  which  had 
just  been  founded  by  King  William.  His  dissertation  on  the 
occasion  was  so  well  received  that  he  was  shortly  thereafter  appointed 
to  the  Chair  of  Mathematics  in  the  Royal  Athenaeum  of  Brussels. 
In  February  following  he  was  elected  a member  of  the  Academy  of 
Sciences  and  Belles-Lettres. 

The  earliest  of  Quetelet’s  published  memoirs,  which  began  to  be 
issued  in  1820,  were  on  geometrical  subjects.  He  soon,  however, 
directed  his  attention  more  exclusively  to  physics  and  astronomy, 
and  lectured  publicly  on  these  subjects  with  great  success. 

In  1823  he  was  sent  to  Paris  to  report  on  the  observatory  of  that 
city,  for  the  guidance  of  the  Belgian  Government  in  founding  a 
similar  observatory  at  Brussels.  After  some  delay  the  observatory 


475 


of  Edmburgh,  Session  1874-75. 

was  founded,  with  Quetelet  as  director;  and  in  1833  were  begun 
the  valuable  series  of  astronomical,  meteorological,  and  other  phy- 
sical observations  for  which  this  observatory  is  so  favourably  known. 
Of  the  work  done  by  this  observatory,  special  mention  may  be  made 
of  the  catalogue,  begun  in  1857,  of  stars  which  seem  to  have  ap- 
preciable motion  ; and  the  systematic  observation  and  publication, 
from  1836,  of  the  occurrence  of  meteors  and  shooting-stars, — records 
which  proved  to  be  of  so  great  value  thirty  years  later  when  the 
true  character  of  these  bodies  was  satisfactorily  established.  The 
meteorological  observations  have  been  particularly  full  and  valuable, 
and  they  have  been  exhaustively  discussed  by  Quetelet  in  his  “ La 
meteorologie  de  la  Belgique  comparee  a celle  du  globe,”  published  in 
1867, — a treatise  which  must  yet  be  regarded  as  the  fullest  and  best 
account  of  the  meteorology  of  any  single  locality  on  the  globe. 
Stations  at  Liege,  Ghent,  and  other  places  in  Belgium,  were  also 
established  by  him  in  1835. 

He  was  elected  Perpetual  Secretary  of  the  Academy  of  Sciences 
and  Belles-Lettres  in  1834,  and  to  bis  influence  was  chiefly  due 
the  section  on  the  Fine  Arts  which  was  added  to  the  Academy  in 
1845.  To  this  section  Quetelet  made  extensive  and  original  con- 
tributions, particularly  in  his  researches  regarding  the  proportions 
of  the  human  body,  the  results  of  which  are  published  in  his 
“ Athropometrie.”  In  matters  referring  to  the  higher  education  of 
the  people,  the  census,  and  several  other  national  questions,  the 
Belgian  Government  availed  itself  repeatedly  of  his  great  knowledge 
and  experience. 

He  was  made  President  of  the  Central  Commission  of  Statistics 
at  its  establishment  in  1841,  and  continued  President  till  his  death. 
His  first  paper  on  Statistics  was  published  in  1826;  in  1835  ap- 
peared his  “ Physique  Sociale,”  and  ten  years  later  his  “ Lettres  sur 
la  theorie  des  Probability  appliquees  aux  sciences,  morales,  et  poli- 
tiques.”  He  originated  the  idea  of  convening  an  International 
Congress  of  Statistics,  and  the  first  Congress  was  held  at  Brussels 
in  1853. 

The  many-sidedness  and  fertility  of  Quetelet's  genius  may  be 
seen  from  the  list  of  his  scientific  memoirs,  enumerated  in  the 
Royal  Society’s  Catalogue,  amounting  at  the  close  of  1863  to  220. 
It  is  in  the  field  of  statistics  that  Quetelet  appears  as  a great  d is- 


476  Proceedings  of  the  Royal  Society 

coverer,  and  his  success  in  this  department  is  to  be  attributed  to 
the  clearness  with  which  he  saw  that  statistics  occupy  the  same 
place  in  the  development  of  the  social  and  political  sciences  that 
observational  data  do  in  the  development  of  such  sciences  as  astro- 
nomy and  meteorology;  to  the  patient  industry  with  which,  through 
long  years,  he  gathered  together  his  facts ; and  to  the  mathematical 
skill  he  brought  to  bear  on  their  discussion.  He  was  truly,  as 
stated  by  the  Academy  of  Berlin  in  their  congratulatory  letter  on 
the  occasion  of  the  centenary  of  the  Belgium  Academy,  “ the 
founder  of  a new  science,  which  proceeds  from  the  firm  basis  of 
observation  and  calculation,  to  discover  and  unfold  those  im- 
mutable laws  which  govern  the  phenomena,  apparently  the  most 
accidental,  of  the  life  of  man,  down  even  to  his  most  trivial  actions.” 


9.  Biographical  Notice  of  George  Berry. 

By  George  Barclay,  Esq. 

Mr  George  Berry  was  born  in  Edinburgh  (where  his  father,  of 
a Quaker  family  in  Somersetshire,  had  settled  as  a merchant),  on 
the  12th  of  January  1795.  Bred  to  business  himself,  partly  at 
home  and  partly  in  France,  Mr  Berry  succeeded  his  father  in  Edin- 
burgh, but  about  1834  removed  to  Leith,  whence,  after  a successful 
mercantile  career  of  twenty  years,  he  retired,  and  died  at  Portobello 
on  the  1st  of  May  last. 

While  in  Leith  Mr  Berry  took  an  active  part  in  public  affairs ; 
he  was  one  of  the  founders  of  the  Chamber  of  Commerce,  and 
having  early  become  an  enthusiastic  “Free  trader,”  he  continued, 
during  the  years  of  struggle  which  preceded  the  national  adoption 
of  that  policy,  perhaps  the  most  prominent  representative  of  free 
trade  doctrines  in  Leith. 

But  though  greatly  occupied  with  business,  Mr  Berry  was  through 
all  his  life  also  somewhat  of  a student.  A great  reader,  and  gifted 
with  a retentive  memory,  he  was  well  versed  in  English  literature 
and  in  science.  He  had  been  a pretty  good  chemist  of  his  own  day, 
but  specially  a devoted  and  accomplished  mineralogist  and  geologist 
of  the  school  of  Jameson.  In  pursuit  of  these  studies  he  spent  for 
years  as  a young  man  his  spare  hours  at  home,  and  his  holidays  in 


of  Edinburgh . Session  1874-75. 


477 


wanderings  after  “ specimens,”  in  the  then  little  travelled  Western 
Highlands,  of  which  he  had  many  curious  anecdotes  to  tell;  fol- 
lowing his  master,  he  became  a keen  “Wernerian”  in  those  days 
of  hot  geological  controversy.  He  was  admitted  to  the  membership 
of  the  Koval  Society  in  1861. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  vru.  1874-75.  No.  91. 


Ninety-Second  Session. 

Monday,  1st  February  1875. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  following  Communications  were  read: — 

1.  On  the  Complete  Theory  of  the  Stone  Arch.  By 
Edward  Sang,  Esq. 

In  the  investigations  usually  given  of  the  equilibrium  of  the  stone 
bridge,  it  is  assumed  that  the  strains  follow  the  same  law  as  in  the 
suspension  bridge,  the  one  being  a case  of  stable,  the  other  a case 
of  instable,  equilibrium ; and,  resulting  from  this  hypothesis,  for- 
mulas are  given  whereby  to  determine  the  extrados  suitable  to  a 
prescribed  intrados. 

The  load  of  the  chain  bridge  is  suspended  by  rods,  and  therefore 
acts  only  in  the  direction  of  gravity ; it  cannot  influence  the  hori- 
zontal strain  which  must  be  transmitted  unaltered  from  link  to  link. 
But  the  weight  is  imposed  on  the  stone  arch  in  a different  manner. 
The  stone  which  rests  on  the  voussoir  is  not  jointed  as  the  suspend- 
ing rod  is,  and  may  transmit  an  oblique  as  readily  as  a downward 
strain  : hence  the  fundamental  conditions  of  the  two  structures 
are  essentially  different,  and  require  different  modes  of  treatment. 

The  mason  trusts  greatly  to  the  cohesion  of  the  cement,  which 
easily  makes  up  for  small  inaccuracies  of  arrangement;  but  the 
maximum  stability  of  a stone  structure  is  attained  by  so  adjusting 
its  parts  that  each  would  be  in  equilibrium  even  although  the  sur- 

3 Q 


VOL.  VIII. 


480  Proceedings  of  the  Royal  Society 

faces  had  no  cohesion  and  no  friction.  For  this  we  require  that 
the  thrusts  to  which  each  stone  is  subjected  should  be  in  directions 
normal  to  its  several  surfaces,  and  should  balance  each  other. 

Now  each  arch-stone  is  subjected  to  three  pressures, — one  on 
each  of  its  sides  in  directions  tangent  to  the  curve  of  the  arch,  and 
a third,  the  pressure  of  the  superincumbent  mass  upon  the  inner 
end  of  the  stone. 

To  put  the  structure  in  accordance  with  the  usual  supposition, 
we  must  cause  the  inner  ends  of  these  stones  to  be  dressed  with 
horizontal  surfaces,  in  order  that  the  pressures  exerted  thereon  be 
downwards.  This  being  done,  the  usual  investigations  would  hold 
good,  and  the  intrados  for  a rectilinear  extrados  would  he  a modi- 
fication of  the  catenary.  But  the  inner  ends  of  the  arch-stones 
are  never  dressed  in  this  way;  they  are  rough-hewn,  and  made 
parallel  to  the  curve  of  the  arch,  and  thus  the  deductions  from  the 
usual  hypothesis  are  quite  inapplicable. 

If  we  suppose  the  inner  ends  to  be  made  parallel  to  the  arch  and 
to  be  frictionless,  the  load  resting  upon  them  would  tend  to  slide 
down  the  slope,  and  this  tendency  must  he  counteracted  by  a hori- 
zontal resistance  from  the  adjoining  masonry ; this,  combined  with 
the  gravitation  of  the  load,  produces  a resultant  normal  to  the  arch. 
In  this  way  the  compression  of  the  arch  stones  is  transmitted  un- 
changed along  the  whole  curve,  instead  of  being,  as  in  the  former 
case,  augmented  in  proportion  to  the  secant  of  the  inclination ; and 
at  the  same  time  the  horizontal  thrust,  instead  of  being  conveyed 
unchanged  to  the  ultimate  abutment  course  and  there  resisted,  is 
distributed  through  the  whole  depth  of  the  mason  work.  On  in- 
vestigating that  form  of  the  intrados  which,  on  this  supposition, 
must  suit  a horizontal  roadway,  we  obtain  a differential  equation 
which  can  only  be  integrated  in  somewhat  complex  series.  This 
curve  lies  inside  of  the  circle  which  osculates  the  arch  at  the  vertex, 
while  the  catenarian  curve,  resulting  from  the  former  hypothesis, 
lies  entirely  without  that  circle.  Between  these  two  curves,  there- 
fore, we  may  have  a variety  of  intermediates,  each  of  which  may 
be  brought  strictly  into  accordance  with  the  laws  of  equilibrium  by 
giving  to  the  inner  ends  of  the  arch  stones  an  appropriate  degree  of 
inclination. 

In  this  way  we  are  at  liberty  to  assume,  within  reasonable  limits, 


481 


of  Edinburgh,  Session  1874-75. 

the  forms  of  both  intrados  and  extrados,  and  at  the  same  time  are 
able  to  satisfy  punctiliously  the  conditions  of  equilibrium  by  pro- 
perly adjusting  the  slope  of  the  inner  surface  of  the  arch  stone. 
The  computation  needed  for  this  adjustment  is  simple  and  obvious. 

The  builder,  however,  would  scarcely  think  it  worth  his  while  to 
cut  the  stones  truly  to  the  shape  so  found;  he  would  often  prefer 
the  usual  rough-hewn  surface  and  the  great  cohesion  which  that 
roughness  gives ; and  will  probably  rest  contented  with  a test  for 
safety,  which  test  may  be  found  in  the  very  simple  law,  that  the 
difference  between  the  logarithms  of  the  tangents  of  the  inclina- 
tions at  the  two  proximate  points  of  the  arch  should  always  differ 
by  more  than  the  logarithms  of  the  loads  imposed  between  those 
points  and  the  vertex  of  the  structure. 

2.  On  the  Application  of  Angstrom’s  Method  to  the  Conduc- 
tivity of  Wood.  By  C.  G.  Knott  and  A.  Macfarlane. 
Communicated  by  Professor  Tait. 

This  was  an  account  of  a series  of  experiments  made  in  the 
Natural  Philosophy  Laboratory  of  the  University,  to  test  the  appli- 
cability of  Angstrom’s  method  of  periodic  variations  of  temperature 
to  the  determination  of  low  conductivity.  The  wood  was  cut  into 
discs  of  a standard  thickness,  and  these  were  very  tightly  secured 
together,  after  the  interposition  of  copper-iron  thermo-electric  junc- 
tions (of  very  fine  wire).  One  series  of  discs  was  cut  parallel,  the 
other  perpendicular,  to  the  fibre.  The  results  were  obtained  very 
easily,  and  accorded  satisfactorily  with  those  obtained  by  more 
laborious  methods. 


3.  Notice  of  Striated  Kock  Surfaces  on  North  Berwick  Law. 

By  David  Stevenson,  V.P.R.S.E.,  Civil  Engineer. 

The  well  marked  “crag  and  tail”  formation  of  North  Berwick 
Law  has  long  been  appealed  to  by  geologists  as  a striking  example 
of  the  effects  of  those  mysterious  glacial  currents,  which  at  some 
time  have  wrought  such  changes  on  the  surface  of  the  globe.  The 
Law  presents,  as  is  well  known,  a comparatively  bold  face,  or  crag 


482  Proceedings  of  the  Royal  Society 

to  the  west,  against  which  the  glacial  current  is  supposed  to  have 
impinged,  while,  against  its  eastern  face,  there  is  a gently  sloping 
mass  of  gravel,  clay,  and  stones  supposed  to  have  been  thrown  up 
by  this  current  under  “lee”  of  the  Law,  and  now  forming  what 
is  called  the  “tail.”  It  had  often  occurred  to  me  as  remarkable, 
that  so  great  a mass  of  debris  should  have  been  left  by  the  passing 
current,  whatever  that  may  have  been,  on  the  eastern  extremity  of 
the  hill,  while  it  had  apparently  left  no  impression  on  the  north 
and  south  sides,  along  which  it  must  have  passed.  These  north 
and  south  sides,  in  their  present  condition,  and  to  a casual  observer, 
have  the  ordinary  appearance  of  rough,  angular  weather-beaten 
rocky  faces,  without  a trace  of  glacial  action.  However,  when 
making  an  engineering  examination  of  the  country  around  North 
Berwick  in  September  last,  in  search  of  an  available  water-supply 
for  the  town,  I found  ceitain  very  distinct  traces  of  glacial  action 
on  the  northern  side  of  the  Law,  which,  in  connection  with  the 
“ crag  and  tail”  feature  to  which  I have  referred,  must,  I think, 
be  interesting  to  the  geologist,  while  they  may  possess  additional 
interest  from  their  being  on  a steeply  inclined  open  hill  face,  and 
not  in  a ravine,  or  on  nearly  horizontal  or  slightly  inclined  strata. 

They  extend  vertically  over  a space  of  about  30  feet,  indicating 
the  action  of  a moving  mass  of  at  least  that  depth.  They  can  be 
traced  horizontally  over  a space  of  about  200  feet,  and  they  range 
from  160  to  190  feet  above  the  sea-level.  They  present  the  usual 
two-fold  glacial  aspect  of  smoothly-ground  undulating  surfaces, 
indented  by  occasional  deep  striae  or  scorings.  These  two  kinds  of 
marking  may  have  been  made  at  the  same,  or  at  different  periods, 
but  the  same  abrading  agent  could  not  have  produced  both  of 
them.  The  grinding  or  dressing,  as  it  has  been  termed,  of  the  sur- 
face is  very  distinctly  marked,  and  must  have  been  done  by  the 
passage  of  some  dense,  but  yielding  body,  which  could  be  moulded 
to  the  different  irregularities,  both  vertical  and  horizontal,  in  the 
surface  of  the  hill,  which  must  obviously  have  been  subjected  to 
the  grinding  action  for  a considerable  period  before  the  observed 
effect  could  have  been  produced.  The  striae  again,  must  have  been 
made  by  the  passage  of  sharp-pointed  bodies,  harder  than  the 
felspar  porphyry  of  the  Law,  and  carried  in  a mass  of  material 
of  sufficient  density  firmly  to  retain  the  sharp,  rocky  protuber- 


483 


of  Edinburgh,  Session  1874-75. 

ances  embedded  in  it,  and  to  press  them  against  the  hillside  with 
enormous  force,  so  as  to  groove  the  rock  face  in  passing.  As 
viewed  from  a little  distance,  the  scorings  appear  to  he  nearly 
paralled  and  horizontal.  But  on  examining  such  as  can  be 
reached,  I found,  on  using  the  clinometer,  that  this  is  by  no  means 
the  case.  On  one  patch  of  rock  I found  two  striae  within  18 
inches  of  each  other,  the  upper  of  which  had  a dip  of  4°  and  the 
lower  a dip  of  20°,  and  both  markings  were  dipping  towards  the 
west,  being  the  direction  from  whence  the  movement  -came,  as 
indicated  by  the  “ tail”  on  the  eastern  side  of  the  Law.  But  the 
rise  in  the  direction  of  motion  indicated  by  these  two  striae  may 
have  been  caused  by  local  pressure,  due  to  the  obstructions  offered 
to  the  passage  of  the  mass  by  the  Law.  The  effect  of  this  would 
be  to  elevate  the  mass ; and  this  I think  points  to  ice  carrying 
imbedded  stones  as  probably  the  agent  which  has  so  distinctly 
chronicled  its  passage  over  or  round  the  hill,  while  the  rise  on  these 
lines  indicate  that  the  moving  mass  must  have  been  under 
enormous  pressure ; and  this  again  is  perhaps  sufficient  to  account 
for  the  cutting  of  the  deep  grooves  left  in  the  rocky  face.  In 
short,  the  appearances  I have  noticed  seem  to  be  such  as  might 
naturally  result  from  such  glacial  action  as  Forbes  has  recorded, 
when  he  says,  “ when  the  ice  of  the  glacier  abuts  against  the  foot 
of  Mont  Chetif  it  is  violently  forced  forward,  as  if  it  would  make 
its  way  up  the  face  of  the  hill.”  * 

The  markings  I have  described  have,  till  a comparatively  recent 
period,  been  covered  by  debris,  which  has  fallen  from  the  upper 
portion  of  the  Law,  and  formed  a glacis  at  its  base.  The  removal  of  a 
portion  of  this  debris,  extending  to  about  200  feet,  as  a quarry  for 
road  metal,  has  disclosed  the  original  surface  of  the  rock,  and 
revealed  the  features  I have  described.  A similar  mass  of  debris 
extends  along  the  whole  northern  and  southern  faces  of  the  hill, 
and  if  it  were  removed,  I have  no  doubt  similar  markings  would 
be  found  to  extend  along  both  sides.  I believe  some  traces  of 
glacial  action  have  been  found  at  a high  level  on  the  western  face 
of  the  Law ; but  I carefully  examined  the  north  and  south  faces 
of  the  hill,  and  could  not,  in  their  present  buried  up  state,  find 


Travels  in  the  Alps,  page  205. 


484 


Proceedings  of  the  Royal  Society 

traces  of  markings,  except  at  the  place  I have  described,  from 
which  the  debris  has  been  removed.  Neither  could  I detect 
markings  on  the  rock  faces  immediately  above  the  striated  sur- 
faces, but  these  upper  faces  having  been  exposed  to  the  weather, 
and  never  covered  by  debris,  might,  though  at  one  time  scored, 
gradually  lose  the  markings,  while  those  in  the  lower  portion  of  the 
hill  remained  protected  by  the  debris. 

The  existence  of  these  markings  seems  to  supply  another  link  in 
connecting  the  “ crag  and  tail”  formation  with  glacial  action,  at 
least  in  the  case  of  North  Berwick  Law.  From  the  appearances 
which  the  removal  of  this  debris  have  disclosed,  we  are  warranted 
in  concluding,  that  after  the  passage  of  the  ice-sheet  or  glacial 
current,  the  rocky  face  of  the  Law,  perhaps  to  its  whole  height, 
depending  on  the  depth  of  the  abrading  agent,  was  similarly  rough- 
polished  and  scored,  that  these  markings  on  places  exposed  to 
atmospheric  action  have  been  gradually  destroyed,  while  similar 
markings  on  the  base  have  been  preserved  by  the  covering  of 
debris,  and  may  now  be  seen  almost  in  their  original  state,  if  not  of 
freshness,  as  least  distinctness  of  marking. 

If  this  view  be  correct,  it  is  likely  that  by  removing  similar 
deposits  from  the  base  of  Stirling  Castle,  Craigforth,  and  other 
similar  rocks,  interesting  traces  of  glacial  action  in  connection  with 
the  “tails,”  which  exist  at  these  places  would  be  disclosed. 


4.  Laboratory  Notes.  By  Professor  Tait. 

a.  Photographic  Records  of  the  Sparks  from  a Holtz  Machine. 

To  determine  the  cause  of  the  ordinary  zig-zag  form  of  electric 
sparks,  the  author  requested  Mr  Matheson,  one  of  his  laboratory 
students  well  skilled  in  photographic  processes,  to  take  instantaneous 
photographs  of  the  sparks  of  the  Holtz  Machine,  by  means  of  a 
quartz  lens,  in  hot  and  cold  air  alternately.  Several  of  these 
photographs  were  exhibited,  and  showed  much  greater  smoothness 
of  the  track  of  the  spark  in  heated  than  in  cold  air.  The  zig-zag 
appearance  seems  to  depend  upon  the  presence  of  combustible 
organic  particles  in  ordinary  air,  but  the  experiments  are  still  in 
process. 


of  Edinburgh,  Session  1874-75. 


485 


b.  Determination  of  the  Surface-Tension  of  Liquids  by  the  Ripples 


A slight  modification  of  a formula  given  by  Sir  W.  Thomson 
(Phil.  Mag.  ii.  1871),  shows  that  the  period  ( t ) of  oscillation  of  a 
particle  in  a deep  mass  of  liquid  agitated  by  simple  waves  or 
ripples  is 


where  A is  the  wave-length,  T the  surface-tension,  and  p the 
density  of  the  liquid.  By  producing,  with  the  aid  of  a massive 
tuning-fork,  steady  ripples  in  various  liquids  all  subjected  to  the 
same  conditions,  and  measuring  micrometrically  the  length  of  these 
ripples,  the  quantity  T is  determined  with  considerable  accuracy 
from  the  above  formula. 

c.  Capillary  Phenomena  at  the  Surface  of  Separation  of  two 


The  only  difficulty  in  this  investigation  is  the  selection  of  two 
liquids,  neither  of  which  will  line  the  interior  of  the  capillary  tube 
so  as  to  disturb  the  behaviour  of  the  other.  This  was  effected 
in  various  ways,  most  simply  by  employing  water  and  sulphuric 
ether ; for  when  these  liquids  are  shaken  together  and  allowed  to 
come  to  rest,  the  result  is  the  production  of  a very  sharply  defined 
bounding  surface  between  a weak  solution  of  water  in  ether  (above) 
and  a weak  solution  of  ether  in  water  (below).  The  observations 
and  measurements  were  made  with  contiguous  portions  of  the  same 
capillary  tube, — one  dipping  into  the  upper,  the  other  into  the 
lower,  layer. 

The  following  Gentlemen  were  duly  elected  Fellows  of 
the  Society : — 


produced  by  a Tuning-Fork. 


A 


Liquids. 


Kobert  Clark,  Esq. 

The  Hon.  James  Bain,  Lord  Provost  of  Glasgow. 

Dr  T.  S.  Clouston,  F.R.O.P.E. 

Thomas  Fairley,  Esq.,  Lecturer  on  Chemistry,  Leeds. 


486 


Proceedings  of  the  Royal  Society 


Monday,  1 5th  February  1875. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Communications  were  read : — 

1.  Obituary  Notice  of  Dr  Kobert  Edward  Grant,  late  Pro- 
fessor of  Comparative  Anatomy  in  University  College 
London.  By  Dr  W.  Sharpey. 

Dr  Bobert  Edmond  Grant  was  the  seventh  son  of  Alexander 
Grant,  Esquire,  Writer  to  the  Signet.  He  was  born  in  his  father’s 
house  in  Argyle  Square,  Edinburgh,  on  the  11th  of  November  1793. 
His  mother’s  maiden  name  was  Jane  Edmond.  It  appears  from  a 
memorandum  in  Dr  Grant’s  handwriting,  that  he  was  sent  from 
home  to  be  nursed,  and  saw  little  of  either  of  his  parents  during 
his  infancy  and  childhood.  He  had  eight  brothers  and  three 
sisters,  all  of  whom  died  before  him,  and  as  none  of  them  left  any 
children,  Dr  Grant  was  the  last  survivor  of  his  family. 

When  about  ten  years  old  he  was  placed  at  the  High  School  of 
Edinburgh,  where  he  continued  for  five  years,  under  the  tuition, 
successively  of  Mr  Christison,  afterwards  Professor  in  the  Univer- 
sity, Dr  Carson,  and  Dr  Adam,  the  Bector,  author  of  the  well- 
known  work  on  Boman  Antiquities.  In  1808  his  father  died,  and 
in  November  of  that  year,  Dr  Grant  became  a student  in  the 
University  of  Edinburgh,  attending  the  junior  classes  of  Latin  and 
Greek.  In  the  following  November  he  entered  on  his  curriculum 
of  medical  study,  and  during  its  course  attended  the  several  classes 
in  the  Faculty  of  Medicine  under  the  professors  of  that  day.  He 
also  studied  Natural  History  under  Professor  Jameson,  and  attended 
the  lectures  of  some  of  the  extra-academical  teachers.  After  com- 
pleting his  course  of  medical  study,  he,  in  1814,  took  his  degree  of 
Doctor  of  Medicine,  and  published  his  inaugural  dissertation,  under 
the  title  “ De  Circuitu  Sanguinis.” 

In  the  meantime  he  had  obtained  (in  May  1814)  the  diploma 
of  the  College  of  Surgeons.  In  November  of  the  same  year,  he 
was  elected  one  of  the  presidents  of  the  Medical  Society  of  Edin- 


487 


of  Edinburgh,  Session  1874-75. 

burgh,  a place  justly  regarded  as  an  honourable  object  of  ambition 
among  the  young  aspirant^  in  the  Medical  School. 

Eather  more  than  a year  after  taking  his  degree,  Dr  G-rant  went 
to  the  Continent,  where  he  spent  upwards  of  four  years.  During 
this  time  he  visited  various  places  of  interest  in  France,  Italy,  and 
Germany,  and  made  ^ pedestrian  tour  in  Hungary;  but  his  prin- 
cipal stay  was  in  Paris,  Eome,  Leipsic,  Dresden,  Vienna,  and 
Munich,  on  account,  no  doubt,  of  the  varied  opportunities  for 
scientific  study  and  general  culture  afforded  by  these  foreign  seats 
of  science,  art,  and  learning.  He  returned  to  Edinburgh  in  the 
summer  of  1820,  and  took  up  his  residence  in  his  native  city.  At 
a later  time  he  became  a Fellow  of  the  Edinburgh  College  of 
Physicians,  but  he  seems  not  to  have  engaged  in  medical  practice; 
his  career  had  taken  another  direction.  He  had  early  imbibed  a 
taste  for  comparative  anatomy  and  zoology,  and  now  devoted  him- 
self assiduously  to  the  prosecution  of  these  branches  of  science, 
both  by  continued  systematic  study  and  by  original  research.  The 
study  of  the  invertebrate  animals  was  peculiarly  attractive,  and 
at  this  time  Dr  Grant  published  various  interesting  anatomical 
and  physiological  observations  on  mollusks  and  zoophytes ; and  his 
name  will  always  be  associated  with  the  advances  of  our  knowledge 
concerning  the  structure  and  economy  of  sponges,  to  the  investi- 
gation of  which  Dr  Grant  at  this  time  enthusiastically  applied 
himself.  The  pools  left  by  the  retiring  tides  on  the  shores  of  the 
Firth  of  Forth  afforded  favourable  opportunities  for  observation, 
and  he  would  spend  hours  patiently  watching  the  phenomena  exhi- 
bited by  these  humble  organisms  in  their  native  element. 

Dr  Grant  remained  at  Edinburgh  till  1827,  and  in  the  mean- 
time communicated  the  results  of  his  various  scientific  inquiries  to 
the  Edinburgh  Philosophical  Journal  and  to  the  Memoirs  of  the  Wer- 
nerian Society,  of  which  he  became  an  active  member.  He  was  also 
in  1824  elected  a Fellow  of  the  Eoyal  Society  of  Edinburgh. 

In  June  1827  Dr  Grant  was  elected  Professor  of  Comparative 
Anatomy  and  Zoology  in  the  newly  founded  Dniversity  of  Lon- 
don, afterwards  University  College.  He  was  not  altogether  new  to 
the  work  of  teaching.  He  had  some  early,  though  brief,  experience 
in  Edinburgh  in  1824,  when  Dr  Barclay,  who  for  some  years  had 
delivered  iectures  on  Comparative  Anatomy  during  the  summer 

3 it 


VOL.  VIII, 


Proceedings  of  the  Royal  Society 


session,  entrusted  him  with  the  part  of  the  course  which  related  to 
the  anatomy  of  invertebrate  animals.  He  entered  on  his  duties 
in  London  in  1828,  and  in  October  of  that  year  delivered  his 
Inaugural  Lecture,  which  was  published  at  the  time,  and  went 
through  two  editions.  In  this  office  he  continued  up  to  the  time 
of  his  death,  during  which  long  period  of  forty-six  academical 
years  he  never  omitted  a single  lecture.  This  was  a point  on 
which  he  justly  prided  himself.  Up  to  the  last  session  (1873-74) 
he  continued  to  give  five  lectures  a week,  but,  sensible  of  failing 
strength,  he  proposed  to  reduce  the  number  to  three  in  the  next 
session,  which  he  was  not  destined  to  see.  The  number  of  students 
who  entered  to  his  class  fluctuated  a good  deal,  but  was  never  large, 
attendance  not  being  compulsory  in  the  medical  curriculum  pre- 
scribed by  the  licensing  corporations.  In  one  session  (1836-37)  the 
number  was  fifty- six,  but  usually  it  was  between  thirty  and  forty,  and 
sometimes  much  less. 

After  he  had  thus  laboured  for  more  than  twenty  years,  the 
Council  of  the  College  added  to  the  small  return  he  received  for 
his  services  an  anual  stipend  of  one  hundred  pounds,  which  was 
continued  during  the  rest  of  his  incumbency.  About  the  same 
time  a number  of  his  friends,  in  presenting  him  with  a microscope, 
in  testimony  of  their  esteem,  purchased  for  him  a G-overnment 
annuity  of  fifty  pounds.  Afterwards  he  succeeded  to  some  pro- 
perty left  by  his  brother  Francis,  an  officer  in  the  Madras  army, 
who  died  in  1852,  so  that  in  his  later  years  he  found  himself  in 
easy  circumstances. 

His  leading  pupils  were  much  attached  to  him,  and  he  was 
sincerely  esteemed  and  respected  by  all.  His  style  of  lecturing 
was  clear  and  impressive,  with  a ready  and  copious  flow  of  language. 
Without  meaning  to  speak  of  his  mode  of  treating  his  subjects,  we 
may  nevertheless  remark,  that  on  one  great  biological  question — 
the  origin  of  species — he  was  from  the  first  an  evolutionist,  and  on 
the  promulgation  of  the  Darwinian  hypothesis  of  natural  selection 
he  became  one  of  its  warmest  adherents. 

Between  1838  and  1840,  Dr  Grant  was  frequently  engaged  to 
deliver  lectures  at  the  Literary  and  Scientific  Institutions  of  various 
large  provincial  towns,  where  his  services  were  in  great  request  and 
high  esteem.  In  1833  he  gave  a gratuitous  course  of  40  lectures, 


489 


of  Edinburgh,  Session  1874-75. 

on  the  structure  and  classification  of  animals,  to  the  members  of 
the  Zoological  Society.  In  1837  he  was  appointed  Fullerian 
Professor  of  Physiology  in  the  Royal  Institution,  which  he  held  for 
the  usual  period  of  three  years.  At  a later  period  he  was 
appointed  by  the  Trustees  of  the  British  Museum  to  the  Swiney 
Lectureship  on  Geology,  the  tenure  of  which  is  limited  to  five 
years.  In  1841  he  delivered  the  annual  oration  before  the  British 
Medical  Association.  In  1836  he  was  elected  a Fellow  of  the 
Royal  Society  of  London.  He  was  also  a Fellow  of  the  Linnean, 
Zoological,  and  Geological  Societies. 

Dr  Grant’s  vacations  were  spent  sometimes  in  Scotland,  but 
chiefly  abroad,  in  France,  Germany,  Belgium,  and  Holland.  On 
more  than  one  of  these  occasions  he  was  accompanied  by  an 
intelligent  and  favourite  Hindoo  pupil,  Dr  Chuckerbutty,  who  after- 
wards became  a Professor  in  the  Government  Medical  College  of 
Calcutta.  Dr  Grant  seems  to  have  had  a special  liking  for  Hol- 
land, which  he  visited  and  revisited  several  times,  partly  no  doubt 
on  account  of  its  scientific  institutions  and  zoological  museums, 
but  largely  also  for  the  sake  of  acquiring  the  Dutch  language.  In 
like  manner  he  afterwards  spent  a vacation  in  Copenhagen,  and 
worked  hard  at  Danish.  Indeed,  it  is  to  be  noted  that  he  had  a 
great  taste  for  the  study  of  languages,  both  practical  and.  philo- 
logical, and  spoke  the  principal  European  tongues  fluently. 

Dr  Grant’s  lectures  were  reported  in  the  early  numbers  of  the 
Lancet,”  and  he  afterwards  published  a treatise  on  Comparative 
Anatomy,  which  embodied  the  substance  of  them.  The  work  came 
out  in  parts,  but  was  not  completed.  He  was  also  author  of  the 
article,  “Animal  Kingdom,”  in  Todd’s  Cyclopaedia  of  Anatomy. 
The  titles  and  dates  of  his  communications  to  periodical  works  are 
given  in  the  Royal  Society’s  Catalogue  of  Scientific  Papers ; they 
are  thirty-five  in  number,  and  extend  from  1825  to  1839. 

Dr  Grant  was  a devoted  lover  of  music,  and  attendance  at  operas 
and  concerts  was  one  of  his  chief  enjoyments  in  his  latter  years. 

In  August  1874  Dr  Grant  suffered  from  a dysenteric  attack,  for 
which  at  first  he  would  have  no  medical  advice,  and  although 
subsequently,  by  appropriate  treatment,  the  virulence  of  the  disease 
was  subdued,  his  strength  was  exhausted,  and  he  died  on  the  23d 
of  that  month,  at  his  house  close  by  Euston  Square.  He  was 


490  Proceedings  of  the  Iioyal  Society 

buried  in  Highgate  Cemetery,  attended  to  the  grave  by  a few  old 
friends  and  attached  pupils,  among  whom  was  his  friend  and 
former  companion  in  travel,  Dr  Chuckerbutty,  who  was  then  in 
England,  and  two  months  later  was  destined  to  follow  his  venerated 
master. 

Dr  G-rant  was  never  married ; he  knew  of  no  surviving  relative. 
Three  of  his  brothers,  whose  deaths  he  had  recorded,  were  military 
officers.  Of  these,  James,  a lieutenant  in  the  German  Legionr  fell 
at  the  siege  of  Badajoz  in  1811;  Alexander,  captain  in  the 
Madras  Engineers,  died  in  the  Burmese  War  in  1825 ; and  Francis, 
captain  in  the  Madras  army,  as  already  mentioned,  died  at  Edin- 
burgh in  1852. 

By  his  will  Dr  Grant  bequeathed  the  whole  of  his  property, 
including  his  collections  and. library,  to  University  College,  in  the 
service  of  which  he  had  spent  the  greater  part  of  his  life,  and  to 
the  principles  of  which  he  was  sincerely  attached. 

2.  An  Illustration  of  the  relative  Rates  of  Diffusion  of 
Salts  in  Solution.  By  Professor  Crum  Brown. 

3.  On  the  Oscillation  of  a System  of  Bodies  with  rotating 
Portions.  By  Sir  William  Thomson. 

4.  Laboratory  Notes.  By  Prof.  Tait. 

a.  On  the  Application  of  Sir  W.  Thomson’s  Dead-Beat  Arrange- 
ment to  Chemical  Balances. 

A considerable  amount  of  time  is  lost  in  making  an  accurate 
weighing  on  account  of  the  slowness  of  oscillation  of  the  balance 
when  the  loads  are  nearly  equal ; and  this  loss  of  time  is  nearly 
proportional  to  the  delicacy  or  sensitiveness  of  the  balance.  Hence 
it  becomes  a matter  of  importance  to  endeavour  to  bring  the  balance 
speedily  to  rest  without,  if  possible,  impairing  its  sensitiveness ; as 
thus  much  time  and  labour  would  be  saved  in  weighing.  Several 
methods  of  applying  gaseous  friction  for  this  purpose  have  been 
tried  by  me  of  late.  By  far  the  most  successful  consists  in  sus- 
pending from  the  beam,  either  within  or  beyond  the  scale-pans, 


of  Edinburgh,  Session  1874-75.  491 

two  very  light  closed  cylinders  which  fit  very  closely  (but  without 
touching)  into  two  fixed  cylinders  open  at  the  top.  Applied  to  a 
long  and  massive  beam  with  considerable  loads  in  the  scale-pans, 
and  which  vibrated  for  some  minutes  when  disturbed,  this  trial 
apparatus  brought  it  to  rest  after,  at  most,  three  half  vibrations.  It 
is  now  evident  that  with  a properly-constructed  damper  on  this 
plan,  there  is  practically  no  limit  (so  far  as  rapidity  of  weighing 
alone  is  concerned)  to  the  length  which  may  be  given  to  a balance- 
beam  ; and,  of  course,  no  limit  to  the  consequent  sensibility  of  the 
instrument. 

A very  instructive  hydrodynamical  result  was  observed  with  this 
arrangement.  The  closed  cylinder,  exactly  balanced  inside  the 
cylinder  open  at  the  top,  is  made  to  ascend  briskly  by  a current 
of  air  blown  even  vertically  downwards  on  the  centre  of  its  upper 
end. 

b.  Photographs  of  Electric  Sparks  taken  in  Cold  and  in  Heated 
Air. 

( Ordered  by  the  Council  to  be  'printed  in  the  Transactions. ) 

c.  On  the  Electric  Resistance  of  Iron  at  High  Temperatures. 

This  note  details  various  experiments  made  for  me  by  Messrs 
C.  M.  Smith  and  A.  Macfarlane  in  the  Physical  Laboratory  of  the 
University,  and  has  been  drawn  up  by  these  gentlemen.  The  only 
part  I have  taken  in  the  work  has  been  the  suggestion  of  the  line 
of  investigation  and  the  forms  of  apparatus  employed.  I mention 
this  not  alone  injustice  to  them;  but  also  as  giving  independent 
corroboration  of  results  formerly  arrived  at  by  myself.  [ This  paper 
will  be  inserted  later , when  the  necessary  diagram  is  ready.] 

Monday , 1st  March  1875. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 

The  following  Communications  were  read : — 

1.  Biographical  Notice  of  William  Euing,  Esq.,  F.R.S.E. 

By  Professor  William  P.  Dickson. 

William  Euing  was  born  on  20th  May  1788,  at  Partick,  where 


492  Proceedings  of  the  Boyal  Society 

his  father  had  a printfield  on  the  hanks  of  the  Kelvin.  His  family 
originally  belonged  to  Strathendrick,  which  was,  along  with  the 
Lennox,  the  chief  seat  of  their  name.  Mr  Euing  conceived  the 
latter  (which  he  traced  back  to  Domesday  Book)  to  be  connected 
with  Eugenius,  and  was  somewhat  particular  as  to  its  being  correctly 
spelt  with  a u.  His  grandfather  settled  in  Glasgow  about  1740, 
and  was  a magistrate  of  the  city  in  1767.  His  father  went  to  the 
West  Indies  in  1799,  and  died  there;  whereupon  Mr  Euing,  who 
was  an  only  child,  was  left  to  the  charge  of  his  mother,  and  of  his 
uncle,  Archibald  Smith  of  Jordanhill.  This  relationship  laid  the 
foundation  of  the  close  friendship  that  subsisted  between  Mr  Euing 
and  his  cousins,  Mr  James  Smith  of  Jordanhill,  F.R.S.L.  & E., 
and  Mr  William  Smith  of  Carbeth-Guthrie  (Lord  Provost  of  Glas- 
gow in  1823),  during  the  prolonged  lives  of  all  the  three.  After 
receiving  his  elementary  education  at  two  private  schools,  Mr 
Euing  was  sent  to  the  Grammar  School,  where  he  had  as  his  class- 
fellows  the  late  William  Lockhart  of  Milton-Lockhart,  M.P.,  his 
own  cousin  Mr  Robertson  Reid  of  Gallo  wflat,  and  other  subsequently 
well  known  citizens  of  Glasgow,  all  of  whom  he  survived.  He 
entered  the  University  in  1800  at  the  age  of  twelve,  and  attended 
the  classes  of  Professors  Richardson,  Young,  Jardine,  and  Millar. 
Although  an  earnest  student,  he  did  not  complete  the  regular 
curriculum,  but  early  entered  on  business  in  the  calendering  firm 
of  Inglis,  Euing,  & Co.,  of  which  he  soon  became  a partner.  In 
1815,  in  consequence  of  the  work  being  too  great  for  his  delicate 
health  (for  at  this  period  and  down  to  1845  he  suffered  much  from 
illness)  he  retired,  and,  after  acting  for  some  years  as  a commission 
merchant,  he  began  in  1819  the  business  of  an  underwriter  and 
insurance  broker,  in  which  he  continued  at  the  head  of  the  well- 
known  firm  of  William  Euing  & Co.  till  the  close  of  his  life, 
visiting  daily  almost  to  the  last  his  office  in  the  Exchange. 

As  a merchant,  Mr  Euing  was  held  in  the  highest  esteem  by  all 
who  came  into  contact  with  him  for  his  intelligence,  his  soundness 
of  judgment,  his  probity,  and  stainless  honour.  He  was  a large 
shareholder  in  the  unfortunate  Western  Bank,  and  its  failure  in 
1857  brought  into  play  at  once  his  excellent  habits  of  business 
and  his  cheerfulness  of  temper.  He  carefully  and  promptly  arranged 
his  own  private  affairs  with  a view  to  the  worst,  and  then,  as  direct- 


493 


of  Edinburgh,  Session  1874-75. 

ing  the  proceedings  of  the  Shareholders’  Committee,  applied  all 
his  energies  to  unravel  the  complicated  affairs  of  the  Bank,  and 
to  retrieve  as  far  as  possible  the  ruined  fortunes  of  the  shareholders 
• — a task  in  which  he  was  acknowledged  to  be  beyond  expectation 
successful.  He  was  very  methodical  in  his  habits,  one  of  which 
was  early  rising;  and,  long  after  he  had  reached  eighty  years,  his 
elastic  step  might  have  been  seen  almost  daily  in  the  West  End 
Park — a mile  from  his  house — at  an  hour  when  hut  few  w'ere  awake. 

Mr  Euing  was  in  early  life  somewhat  shy  and  reserved,  having 
in  his  characteristic  modesty  formed  a more  humble  estimate  of 
his  own  abilities,  and  of  his  fitness  to  take  part  in  society,  than 
was  entertained  by  those  who  had  the  privilege  of  knowing  him 
in  after  years,  of  profiting  by  his  varied  information  and  refined 
taste,  and  of  observing  his  deep  and  lively  interest  in  literary  and 
social  questions.  He  early  set  himself  to  the  task  of  self-improve- 
ment; his  thirst  for  fresh  knowledge  never  abated;  and  he  found 
a constant  pleasure  in  its  gratification.  His  letters  written  from 
the  Continent,  during  his  last  tour  a few  years  ago,  show,  I am  told, 
the  same  desire  to  learn  everything,  as  do  his  letters  written  in 
1816,  when  he  made  his  first  visit  to  France ; and  many  of  his 
hooks,  even  of  those  lately  acquired,  contain  memoranda  indicating 
their  perusal  and  evincing  a marked  interest  in  their  contents. 
In  politics  he  took  little  part.  Though  earnest  in  his  religious 
opinions,  which  were  formed  with  conscientious  independence  and 
held  with  firmness,  he  was  very  tolerant  in  spirit;  and,  catholic  in 
his  sympathy  with  all  forms  of  Christian  work  that  approved  them- 
selves to  his  judgment  by  their  fruits,  he  had  but  little  relish  for 
controversy.  Simple  and  unostentatious  in  his  personal  habits,  he 
yet  found  pleasure  in  the  frequent  exercise  of  a genial  hospitality, 
to  which  his  unfailing  cheerfulness  lent  a special  zest. 

Mr  Euing  was  eminently  successful  in  business,  and  at  full 
liberty — so  far  as  family  ties  were  concerned — to  follow  the  bent 
of  his  own  wishes  and  tastes  in  the  application  of  his  wealth.  He 
had  a singularly  warm  and  generous  heart,  and  was  early  drawn 
by  it  into  those  walks  of  practical  philanthropy,  with  which  his 
name  is  specially  associated  in  the  minds  of  his  fellow-citizens, 
and  in  which  he  found  growing  pleasure  as  years  went  on.  "With 
rare  self-denial  he  made  it  a rule— to  which  he  systematically 


494  Proceedings  of  the  Royal  Society 

adhered — to  set  apart  a large  proportion  of  his  income  to  purposes 
of  benevolence.  Upwards  of  forty  years  ago  he  began  to  investi- 
gate the  hardships  connected  with  imprisonment  for  debt,  and  he 
took  a zealous  and  important  part  in  procuring  their  mitigation. 
Subsequently  his  sympathies  were  warmly  enlisted  on  behalf  of 
Sailors’  Homes,  and  the  thriving  Home  in  G-lasgow,  which  was  to 
a very  large  extent  erected  by  his  liberality,  was  the  object  of  his 
constant  care  and  unwearied  bounty  down  to  the  close  of  his  life. 
He  bequeathed  to  it  a legacy  of  L.2000 ; and  a bust,  from  the  chisel 
of  Mr  Gr.  H.  Ewing,  has  just  been  placed  by  the  Directors  in  the 
hall  of  the  institution  as  a fitting  memorial  of  its  patron.  Almost 
all  the  public  charities  of  Glasgow  received,  in  addition  to  his 
regular  contributions,  special  proofs  from  time  to  time  of  his 
liberality ; and  equally  cordial  was  his  interest  in  the  Bible  Society, 
the  City  Mission,  and  other  schemes  to  promote  the  good  of  the 
community. 

Not  less  remarkable  was  his  interest  in  education,  science,  and 
art.  Not  to  speak  of  his  services  and  benefactions  to  the  Buchanan 
Institution,  the  Mechanics’  Institute,  the  School  of  Art,  Stirling’s 
Library,  the  Botanic  G-arden  (to  which  he  left  L.3000),  and  other 
agencies  for  helping  the  education  and  elevating  the  tastes  of  the 
people,  he  manifested  a specially  warm  and  constant  zeal  for  the 
prosperity  of  Anderson’s  University,  of  which  he  was  long  the 
most  valued  counsellor  and,  along  with  his  friend  Mr  Young  of 
Kelly,  the  most  conspicuous  and  munificent  patron.  He  devoted 
much  of  his  time  to  its  service,  cherished  a lively  interest  in  its 
work  and  in  its  teachers,  repeatedly  made  large  donations  to  its 
funds,  and,  besides  founding  and  endowing  in  it  a Lectureship  on 
Music,  left  to  it  a legacy  of  L.6000.  He  was  an  early  subscriber 
of  L.1000  to  the  new  buildings  of  the  University  of  Glasgow;  and, 
besides  various  donations  during  his  life,  he  has  destined  the  sum 
of  L.6000  to  the  endowment  of  fellowships  bearing  his  name,  the 
holders  of  which  are  to  conduct  tutorial  classes  of  limited  numbers, 
more  especially  during  the  vacation,  and  thereby  “ to  confer  on  the 
University  some  of  the  benefits  derived  from  tutorial  instruction 
at  the  English  Universities.”  Mr  Euing  was  also  a liberal  patron 
of  art,  and  had  formed  a considerable  collection  of  pictures,  thirty- 
six  of  which  he  presented  during  his  life  to  the  Corporation  of 


of  Edinburgh,  Session  1874-75. 


495 


Glasgow.  He  has  now  bequeathed  to  them  the  remainder,  giving 
powers  of  sale  or  exchange,  but  directing  the  retention  of  at  least 
fifty  of  his  pictures  in  their  gallery.  His  refined  taste  was  visible 
also  in  a collection  of  old  silver  plate  and  china.  Mr  Euing  was 
a Fellow  of  the  Scotch  Antiquarian  Society,  and  President  of  the 
Glasgow  Archaeological  Society.  He  was  long  an  active  member, 
and  one  of  the  last  surviving  councillors,  of  the  Maitland  Club, 
to  which  he  presented  a volume  prepared  by  the  Rev.  Mr  Muir  of 
Dysart,  containing  extracts  from  the  records  of  that  burgh.  He 
was  ever  ready  to  countenance  and  encourage  any  apparently 
meritorious  enterprise  of  antiquarian  authorship.  He  had  formed 
a very  remarkable  and  highly  interesting  collection  of  autographs, 
which,  as  his  will  does  not  indicate  any  special  destination  for  it, 
will  probably  fall  to  be  dispersed. 

But,  of  all  the  noble  forms  which  the  gratification  of  his  personal 
tastes  assumed,  that  on  which  he  bestowed  most  attention,  and 
which  he  valued  most — cherishing  in  it  a peculiar  modest  pride — 
was  his  library.  It  consisted  of  three  distinct  divisions.  The 
first  contained  a very  large  and — so  far  as  Scotland  at  least  is 
concerned — unrivalled  collection  of  music  and  of  works  on  music, 
amounting  to  several  thousand  volumes.  Mr  Euing  was  an 
enthusiast  in  music,  and  was  conversant  alike  with  its  theory  and 
practice ; indeed  his  love  for  it  was  so  intense,  that  in  early  life 
he  was  in  the  habit  of  meeting  with  some  friends  of  similar  tastes 
as  a Saint  Cecilia  Society  at,  I think,  five  o’clock  in  the  morning. 
This  musical  library  is  bequeathed  to  Anderson’s  University  in  con- 
nection with  the  Euing  Lectureship  in  Music,  along  with  L.1000 
towards  providing  a fireproof  apartment  for  its  reception,  and  L.200 
for  the  compiling  and  printing  of  a catalogue.  The  second  division 
consisted  of  a still  larger  and  invaluable  collection  of  editions  of 
the  Bible  and  its  parts,  chiefly  of  the  various  English  versions 
(which  are  very  largely  represented),  but  including  also  a very 
considerable  number  of  Polyglott,  Greek,  Latin,  French,  German, 
and  Dutch  Bibles,  and  not  a few  in  other  languages,  along  with 
numerous  Psalters,  and  Books  of  Prayers  and  Hymns,  amounting 
to  nearly  3000  volumes.  This  has  been  left  to  the  University 
Library,  to  be  retained  as  a special  collection.  The  third  division 
was  his  general  library,  amounting  to  nearly  20,000  volumes,  which 

3 s 


VOL.  VIII. 


496  Proceedings  of  the  Royal  Society 

is  also  bequeathed,  with  a few  exceptions,  to  the  University  Library. 
This  miscellaneous  collection  possesses  many  features  of  interest. 
It  embraces  about  150  volumes  printed  before  a.d.  1500,  special 
collections  of  works  printed  by  the  Aldine,  Stephanie,  and  Elzevirian 
presses,  of  books  printed  at  Edinburgh,  Glasgow,  Aberdeen,  &c.,  in 
the  17th  century,  as  well  as  of  Baskerville,  Barbou,  Bodoni,  Didot, 
Urie,  and  Foulis  classics  (those  of  the  Bodoni  and  Foulis  presses 
being  especially  numerous),  the  first  and  second  folios  of  Shake- 
speare and  many  rare  first  editions  of  English  classics;  a large 
number  of  privately  printed  works  (including  a great  many  of  the 
reprints  issued  in  very  limited  number  by  his  friend  Mr  Halliwell- 
Phillips)  numerous  books  on  bibliography,  archaeology,  and  the 
fine  arts,  an  extensive  series  of  English  minor  poems,  ballads, 
and  songs;  a very  curious  and  unique  collection  of  Broadsides,  and 
a few  MSS.,  including  a Hebrew  Boll  of  Genesis  of  great  beauty. 
The  books  have  been  selected  by  Mr  Euing  with  much  care  and 
judgment ; many  of  them  are  large  paper  copies,  or  present  other 
specialities  of  bibliographic  interest ; and  most  of  them  are  taste- 
fully bound.  The  value  of  this  gift  to  the  University  cannot 
be  estimated  at  less  than  L.10,000.  Mr  Euing  has  judiciously 
empowered  the  Senate  to  sell  duplicates  to  the  extent  of  half  his 
general  collection ; and  has  directed  the  proceeds  to  be  applied 
towards  the  maintenance  and  binding  of  the  collection,  or  the 
purchase  of  other  books  to  be  added  to  it. 

Mr  Euing  died  on  the  16th  May  1874,  closing,  in  the  words  of 
a relative,  “ gently  and  without  suffering  a long  and  useful  life, 
and  not  leaving  a single  enemy.”  He  was  a Glasgow  merchant 
of  the  noblest  type.  Others  may  have  equalled  him  in  the  shrewd- 
ness and  worth,  or  in  the  generous  heart  and  open  hand,  which 
happily  are  no  uncommon  characteristics  of  the  order  to  which  he 
belonged ; and  some,  of  ampler  resources,  may  even  have  surpassed 
him  in  the  success  with  which  they  have  made  their  wealth  minister 
to  the  gratification  of  some  particular  taste  ; but  in  the  combination 
of  the  highest  standing  as  a merchant  with  the  zeal  of  a philan- 
thropist and  the  refinement  of  a connoisseur,  in  the  many-sided 
excellencies  of  his  character  and  the  variety  of  his  literary  and 
artistic  taste,  and  in  the  wise  destination  of  his  resources  alike 
during  life  and  at  death,  Mr  Euing  may  well  be  regarded  as  unique. 


of  Edinburgh,  Session  1874-75.,  497 

2.  On  a Faulty  Construction  common  in  Skewed  Arches. 
By  Edward  Sang,  Esq. 

In  the  course  of  engineering  works,  bridges  have  to  be  thrown 
obliquely  over  rivers  or  over  roads,  and  thus  the  construction  of 
oblique  or  skewed  arches  is  forced  upon  us.  The  skewed  stone 
arch  has  not  grown  in  favour,  partly  from  the  greater  skill  required 
in  delineating  and  executing  the  forms,  partly  from  the  fact  that 
such  skewed  arches  have  given  signs  of  weakness.  Hence  an  im- 
pression has  gained  ground  that  there  is  something  defective  in  the 
principle. 

The  defect,  however,  of  those  skewed  arches  which  I have  seen 
lies  entirely  in  an  erroneous  mode  of  construction,  which,  but  for 
the  cohesion  of  the  lime,  would  result  in  an  immediate  downfall. 
The  pervading  principle  of  all  good  mason  work  is  this  : that  the 
surfaces  of  each  stone  should  be  dressed  square  to  the  pressures 
transmitted  by  them.  Now,  along  the  ridge  or  centre-line  of  the 
skew  this  principle  is  attended  to ; the  beds  of  the  arch-stones  are 
placed  square  to  the  line  of  the  roadway,  that  is  to  the  line  of 
pressure  there.  In  consequence  the  line  of  the  course  begins  to 
descend  on  the  surface  of  the  vault;  and,  in  continuing  tbe  descent, 
the  architect  lays  off  equal  distances  on  the  curves  to  correspond 
with  equal  distances  along  the  crown.  Hence  all  the  courses 
present  equal  breadths  measured  along  the  lines  of  pressure. 

The  inevitable  consequence  of  this  arrangement  is,  that  the  bed 
of  the  stone  becomes  more  and  more  oblique  to  the  pressure  as  we 
come  down  on  the  haunch  of  the  arch ; the  mechanical  effect  being 
just  the  same  as  if  a mason,  in  building  a wall,  were  to  place  the 
stones  off  the  level.  The  ends  of  tbe  stones,  as  seen  on  the  plane 
of  the  parapet,  present,  in  this  case,  equal  graduations,  and  when- 
ever we  see  the  ends  of  the  arch-stones  equally  placed,  we  may  be 
sure  that  this  fault  pervades  the  whole  structure.  The  fault  is 
clearly  seen  on  one  side  of  the  model  of  a skewed  centering  ex- 
hibited to  tbe  Society. 

Beginning  at  the  crown  of  the  arch,  and  descending  in  this  way, 
the  course  becomes  inclined  to  the  line  of  pressure ; it  is  necessary 
to  bend  it  gradually  upwards  from  the  course  just  described,  and 


498  Proceedings  of  the  Royal  Society 

the  problem  becomes  this, — “ To  draw  upon  the  surface  of  the 
vault  a curve  which  shall  cross  all  the  lines  of  pressure  squarely/’ 
This  belongs  to  a well-known  class  of  problems  in  what  is  called 
the  calculus  of  variations. 

The  nature  of  this  curve  must  depend  on  the  character  of  the 
arch ; yet  it  has  certain  general  features  independent  of  that  char- 
acter. The  chief  of  these  may  be  explained  in  this  way.  If  we 
take  two  closely  contiguous  curves,  inclosing  between  them,  as  it 
were,  a course  of  arch-stones,  the  breadth  of  that  course,  at  any 
place,  is  proportional  to  the  cosine  of  the  inclination  of  the  line  of 
pressure.  Hence,  in  every  skewed  arch  the  breadths  of  the  stones 
as  seen  on  the  parapet  plane,  must  diminish  from  the  crown  down- 
wards, becoming  at  60°  from  the  crown  just  half  as  broad  as  at 
the  top. 

In  the  case  of  the  circular  arch,  the  projection  of  the  curve  upon 
the  plane  of  the  parapet  is  the  well-known  tractory,  which  is 
asymptotical  to  the  horizontal  line  passing  through  the  centre. 
Hence  we  cannot  have  a semicylindric  skewed  arch,  because  the 
curve  of  the  course-joint  cannot  reach  to  the  vertical  part  of  the 
surface. 

The  nature  of  the  true  arrangement  is  shown  on  the  other  side 
of  the  model. 

A glance  at  the  ends  of  the  arch-stones  of  any  skewed  bridge  is 
enough  to  apprise  us  of  whether  or  not  the  structure  have  been 
properly  arranged. 

3.  On  the  mode  of  Growth  and  Increase  amongst  the  Corals 
of  the  Palaeozoic  Period.  By  H.  Alleyne  Nicholson,  M.D., 
D.Sc.,  Professor  of  Biology  in  the  Durham  University 
College  of  Physical  Science. 

In  the  first  portion  of  this  communication,  the  author  discussed 
the  general  phenomena  exhibited  by  the  Palaeozoic  corals  as 
regards  their  mode  of  growth  and  increase.  Five  chief  modes  of 
growth  were  distinguished  : — 


499 


of  Edinburgh,  Session  1874-75. 

a.  Simple  calicular  gemmation , in  which  the  corallum  sends  up 
from  its  calicine  disc  a single  bud,  which  usually  repeats  the  pro- 
cess, until  there  is  produced  a succession  of  corallites  vertically 
superimposed  upon  one  another.  The  peculiarity  of  this  process 
consists  in  the  fact  that  the  same  calice  never  produces  more  than 
one  bud. 

b.  Compound  calicular  gemmation , in  which  the  primitive  coral- 
lite  throws  up  two  or  more  buds  from  its  oral  disc,  these  in  turn 
usually  repeating  the  process,  till  the  corallum  comes  to  form  an 
inverted  pyramidal  mass,  composed  of  numerous  corallites  diverging 
from  the  base. 

c.  Basal  or  marginal  gemmation , in  which  new  corallites  are  pro- 
duced at  the  circumference  of  the  colony  or  along  certain  definite 
lines  proceeding  from  the  base. 

d.  Parietal  or  lateral  gemmation , in  which  the  increase  of  the 
corallum  is  by  the  production  of  buds  at  gome  point  in  the  walls  of 
the  parent  corallite  between  the  lip  of  the  calice  and  the  base. 

e.  Fission , in  which  the  growth  of  the  corallum  is  effected  by 
the  cleavage  of  the  calice  of  the  original  corallite  or  corallites. 

Numerous  examples  were  adduced  of  the  occurrence  of  the 
above  modes  of  growth,  singly  or  in  combination,  amongst  the 
Palseozoic  corals,  and  various  modifications  of  these  processes  were 
discussed. 

The  author  next  discussed  the  value  of  the  mode  of  growth  of 
the  corallum  as  applied  to  the  classification  of  the  Paleeozic  corals, 
and  arrived  at  the  conclusion  that  much  stress  could  not  be  laid 
upon  this  point  unless  accompanied  by  other  distinctive  characters 
as  well.  The  chief  grounds  upon  which  this  conclusion  was  based 
were,  that  allied  forms  in  the  same  genus,  and  sometimes  even 
different  individuals  in  the  same  species,  show  entirely  different 
modes  of  growth ; that  forms  belonging  to  the  most  remotely  allied 
groups  often  increase  in  the  same  way;  and  finally,  that  the  diffi- 
culty in  determining  the  precise  mode  of  growth  amongst  some  of 
the  fossil  corals  is  so  great  as  often  to  render  this  test  practically 
inapplicable. 

In  conclusion,  the  author  discussed  the  relations  between  the 
growth  of  the  different  parts  which  may  comprise  a compound 
corallum,  as  regulating  its  final  form  and  structure. 


500 


Proceedings  of  the  lioyal  Society 

4.  The  President  exhibited  Diagrams  in  illustration  of  the 
Capillary  Surfaces  of  Devolution. 

The  following  Gentlemen  were  duly  elected  Fellows  of 
Society : — 

Charles  Wilson  Vincent,  Esq.,  London. 

Ralph  Richardson,  Esq. 

John  Ramsay  L’Amy,  Esq. 

E.  W.  Prevost,  PLl.D. 

James  Syme,  Esq. 

Sir  John  Hawkshaw,  F.R.S. 

The  following  Gentlemen  were  duly  elected  Foreign 
Honorary  Fellows : — 

Heinrich  Wilhelm  Dove,  Berlin. 

August  Kekule,  Bonn. 

Herman  Kolbe,  Leipzig. 

Ernst  Eduard  Kummer,  Berlin. 

Joseph  Liouville,  Paris. 

John  Lothrop  Motley,  U.S. 

Monday,  1 5th  March  1875. 

DAVID  MILNE  HOME,  Esq.,  LL.D,  Vice-President, 
in  the  Chair. 

The  Council  having  awarded  the  Makdougall  Brisbane 
Prize  for  the  Biennial  Period,  1872-74,  to  Professor  Lister, 
for  his  paper  “ On  the  Germ  Theory  of  Putrefaction  and 
other  Fermentative  Changes,”  Dr  Crum  Brown,  in  request- 
ing the  Chairman  to  present  the  medal,  addressed  the  Chair- 
man as  follows : — 

Mr  Chairman, — I have  been  requested  by  the  Council,  and  I feel 
it  a very  great  honour  that  I have  been  so  requested,  on  the  occa- 
sion of  the  presentation  of  the  Makdougall  Brisbane  prize  to  Pro- 
fessor Lister,  to  state  shortly  the  grounds  upon  which  the  Council 
have  made  the  award. 

Every  Fellow  of  the  Society  who  had  the  privilege  of  hearing 
Professor  Lister’s  paper  read,  must  have  a vivid  recollection  of  the 
interesting  and  admirably  clear  manner  in  which  he  explained 
an  intricate  series  of  experiments;  of  his  hereditary  ingenuity 


of  Edinburgh.  Session  1874-75.  501 

in  devising  and  skill  in  carrying  out  delicate  mechanical  con- 
trivances, and  of  the  eloquent  as  well  as  cogent  logic  with  which 
he  enforced  his  conclusions.  I wish  it  had  fallen  to  one  more  fit 
to  do  justice  to  the  subject,  to  lay  before  the  Society  an  abstract  or 
summary  of  this  very  remarkable  paper. 

Professor  Lister’s  work  may  he  considered  from  several  different 
points  of  view. 

I.  As  a contribution  to  microscopic  botany,  and  as  such  it  takes 
a very  high  place.  A great  obstacle  in  the  way  of  the  study 
of  microscopic  plants  is  the  difficulty  of  the  determination  of  species. 
Each  species  is  liable  to  great  variation  in  form,  and  there  is  a great 
general  resemblance  between  forms  assumed  by  different  species. 
To  get  over  this  difficulty,  the  method  of  “ cultivation”  has  been 
made  use  of — the  doubtful  specimen  is  kept  and  grown  to  see  what 
it  will  become.  Professor  Lister  in  this  paper  describes  his  novel 
method  of  cultivation,  in  which  the  fungi  are  made  to  grow  in 
various  kinds  of  soil.  Thus,  two  fungi  growing  in  Pasteur’s  solution 
may  resemble  one  another  very  closely;  but  if  transplanted  into 
milk,  and  allowed  to  grow  there,  a very  marked  difference  may  be 
produced.  Or  two  fungi  may  present  in  one  solution  forms  indis- 
tinguishable from  one  another,  but  one  may  grow  luxuriantly  and 
the  other  not  at  all,  when  transferred  to  a different  solution.  Such 
cultivation  experiments  are  apt  to  fail  from  a character  which  they 
have  in  common  with  cultivation  experiments  on  a larger  scale. 
The  miniature  garden,  like  other  gardens,  is  liable  to  be  infected 
with  weeds,  and  it  sometimes  happens  that  such  a weed,  or  unwel- 
come intruder,  is  mistaken  for  the  produce  of  the  seed  sown  or  the 
plant  planted.  These  weeds  grow  either  from  seeds  contained  in 
the  soil,  or  introduced  from  without,  and  it  is  essential  to  a success- 
ful experiment  that  the  first  be  killed  or  removed,  and  the  second 
excluded.  Professor  Lister  secures  the  necessary  condition  of 
purity  of  the  soil,  perfect  freedom  of  his  solutions  from  all  trace 
of  life  except  those  fungi  or  germs  purposely  introduced,  and  per- 
fect security  against  accidental  or  unintentional  entrance  of  any 
living  thing,  without  interfering  with  the  readiness  of  access  to 
each  experiment  during  its  progress.  This  is  accomplished  by 
means  of  devices,  of  which  it  is  difficult  to  say  whether  the  com- 
plete success  or  the  wonderful  simplicity  is  more  striking.  Th% 


502  Proceedings  of  the  Royal  Society 

results  obtained  need  not  disappoint  the  most  sanguine  investigator. 
Professor  Lister  has  obtained  proof  that  Bacteria  are,  at  all  events 
in  some  cases,  directly  derived  from  fungi,  of  which  they  are  merely 
a special  development.  He  has  been  able  to  determine,  within  not 
very  wide  limits,  the  number  of  individual  germs  contained  in  a 
drop  of  water,  and  to  show  that  this  number  is  greater  in  warm 
than  in  cold  weather,  and  has  proved  that  the  number  of  distinct 
species  of  microscopic  fungi  is  great  beyond  all  previous  imagina- 
tion. There  is  one  special  result  to  which  I cannot  omit  a reference. 
It  is,  that  there  are  certain  fungi  which,  although  rare,  and,  we  may 
therefore  conclude,  not,  under  ordinary  conditions,  hardy,  still 
flourish  luxuriantly  and  increase  rapidly  under  certain  special  con- 
ditions. Thus  the  fungus  which  causes  the  lactic  fermentation  of 
sugar,  is  scarcely  to  be  found  anywhere  but  in  dairies.  Boiled  milk 
or  perfectly  pure  milk,  may  be  exposed  to  air  anywhere  else  with- 
out undergoing  the  lactic  fermentation;  other  fungi,  producing 
different  effects,  will  grow  in  it;  but  if  milk  be  exposed  in  a dairy, 
this  particular  fungus  overcomes  all  others,  and  the  lactic  fermen- 
tation alone  takes  place.  Milk  is  the  soil  specially  suited  for  its 
growth,  but  it  does  not  appear  there  of  itself — it  must  be  introduced 
from  without. 

II.  Another  matter  of  great  interest  connected  with  Mr  Lister’s 
work,  is  the  means  which  it  will  no  doubt  put  into  our  hands  of 
preparing  many  chemical  substances.  Although  he  has  not  fully 
investigated  the  various  chemical  changes  which  accompany  the 
growth  of  microscopic  fungi,  he  has  shown  that  each  species  pro- 
duces its  own  effect;  and  as  he  has  taught  us  how  to  obtain  speci- 
mens of  each  species  without  mixture  of  any  other,  he  has  put  it 
in  our  power  to  produce  specific  fermentations,  and  study  them  un- 
disturbed by  the  presence  of  other  kinds  of  fermentation. 

III.  But  more  general  interest  attaches  to  Mr  Lister’s  paper  as  a 
very  important  step  in  the  settlement  of  the  question : Does  life 
ever  arise  from  lifeless  matter,  or  is  the  origin  of  life  not  as  great 
a mystery  and  as  far  removed  from  the  grasp  of  our  scientific 
methods  as  the  origin  of  matter  itself?  If  living  things  never 
develope  out  of  dead  nature  in  the  ordinary  processes  of  nature, 
we  are  forced  to  the  conclusion  that  they  either  have  existed 
always,  or  have  been  miraculously  created.  It  has  been  sup- 


503 


of  Edinburgh , Session  1874-75. 

posed  that  there  is  a logical  difficulty  in  the  way  of  proving  that 
life  does  not  grow  out  of  dead  matter — that  to  attempt  to  prove 
this  is  to  attempt  to  prove  a negative.  But  every  man  of  science 
believes  that  the  quantity  of  matter  is  constant,  and  that  the 
quantity  of  energy  is  constant,  although  these  propositions  equally 
involve  the  negatives,  that  matter  and  energy  never  appear  or  dis- 
appear, but  merely  undergo  transformations.  But  although  there 
is  no  absurdity,  there  is  a great  difficulty  in  the  way  of  proving 
that  living  beings  are  always  produced  from  pre-existing  living 
beings.  It  is  difficult  to  make  our  experiments  under  precisely 
the  conditions  under  which  nature  works,  and  at  the  same  time  to 
exclude  the  possibility  of  the  presence  of  living  beings.  If  we 
boil  our  liquid  in  order  to  kill  its  living  contents,  it  may  be  said 
that  we  change  its  chemical  character,  and  deprive  it  of  the  power 
of  producing  life ; if  we  shut  it  up  in  a hermetically  closed  vessel, 
we  prevent  that  access  of  air  which  may  be  essential  to  the  produc- 
tion of  life  from  lifeless  matter.  Mr  Lister  has  shown  us  how  we 
may  obtain  milk,  urine,  and  blood  quite  free  from  living  beings,  and 
keep  them  liquid  for  any  length  of  time  freely  exposed  to  air  with- 
out any  risk  of  the  entrance  of  living  things,  and  he  has  shown  us 
that  if  this  be  done  no  living  things  ever  appear  in  the  liquid.  In 
his  experiments  we  see  two  samples  of  the  same  substance  treated, 
with  one  exception,  in  exactly  the  same  way;  in  the  one  sample 
life  is  abundantly  developed,  in  the  other  not  at  all.  Can  any 
reasonable  man  doubt  that  this  striking  difference  of  result  is  due 
to  the  one  only  difference  of  treatment;  and  this  difference  of 
treatment  is  merely  that  in  the  one  case  living  things  have  had 
access  to  the  substances,  in  the  other  they  have  been  excluded? 
In  all  other  respects  the  two  samples  have  been  exposed  to  pre- 
cisely the  same  influences.  With  all  respect  for  those  experi- 
menters who,  not  having  taken  Mr  Lister’s  precautions,  have 
arrived  at  different  results,  I express  my  conviction  that  it  has 
been  definitely  proved  that  life  is  continuous,  that  living  matter 
cannot  be  produced  by  a chemical  process,  and  that  every  living 
thing  is  descended  from  some  previously  existing  living  parent. 

IV.  Another  aspect  of  this  paper  is  of  less  general  scientific 
interest,  but  of  much  greater  practical  importance.  Mr  Lister’s 
investigation  forms  the  scientific  basis  of  the  system  of  antiseptic 
surgery,  with  which  his  name  will  always  be  associated.  The 

3 T 


VOL.  VIII. 


504  Proceedings  of  the  Royal  Society 

microscopic  fungi,  in  the  consideration  of  which  we  have  been 
engaged,  perform  a very  important  function  in  nature.  They  form 
a brigade  in  nature’s  army  of  scavengers.  They  transform  the 
dead  matter  which  once  formed  part  of  organised  living  beings 
into  raw  materials  out  of  which  new  organisms  construct  their 
bodies;  they  break  down  the  complex  substances,  when  the  com- 
plexity has  become  useless,  into  simpler  compounds  which  can  he 
used  again.  They  demolish  the  old  ruins,  and  render  their  stones 
fit  to  be  employed  as  building  materials.  But  they  not  only  attack 
the  dead,  they  kill  the  weak  and  the  dying;  and  while  this  action 
may  be  considered  useful  on  the  whole,  as  leaving  room  for  the 
development  of  the  strong,  it  is  precisely  the  duty  of  the  medical 
man  to  combat  this  tendency  of  nature,  to  support  the  weak  that  it 
may  have  an  opportunity  to  become  strong,  to  ward  off  nature’s 
blows  that  the  dying  may  recover.  This  is  not  the  place  to  speak  of 
the  extraordinary  results  obtained  by  Mr  Lister’s  mode  of  treatment, 
of  the  certainty  of  cure  in  cases  which  ten  years  ago  would  have 
been  considered  absolutely  hopeless;  my  object  is  rather,  assuming 
these  results,  to  show  how  intimately  they  are  connected  with  the 
scientific  truths  which  form  the  basis  of  this  mode  of  treatment. 

It  has  been  suggested,  and  I confess  that  I at  one  time  thought 
the  suggestion  a good  one,  that  instead  of  trying  to  convince 
surgeons  of  the  truth  of  the  scientific  basis,  Mr  Lister  should  draw 
up  a code  of  practical  rules  which  a surgeon  might  follow  without 
thinking  of  germs  or  bacteria  or  fungi.  A little  consideration  will 
show  the  absurdity  of  this  idea.  A surgeon  impressed  with  the 
truth  of  the  scientific  basis  needs  no  code  of  rules — he  sees  at  once 
what  he  must  do,  and  what  he  must  avoid.  A code  of  rules  drawn 
up  for  one  ignorant  of  the  scientific  basis  would  be  intolerably 
complicated,  and  certain  to  be  violated.  In  this,  as  in  other  and 
higher  and  more  general  motives,  faith  is  essential  to  practice; 
if  we  know  the  why,  we  can,  as  a rule,  find  out  the  how;  and 
antiseptic  surgery  will  be  successful  then,  and  then  only,  when 
the  reasons  for  its  methods  are  understood  and  believed  in. 

I have  endeavoured,  Sir,  to  lay  before  the  Society  some  of  the 
reasons  which  have  led  the  Council  to  award  the  Makdougall  Bris- 
bane prize  to  Mr  Lister,  and  I hope  I have  in  some  measure 
succeeded.  I cannot  express  the  satisfaction  we  all  feel  in  having 
a paper  so  eminently  worthy  of  the  award. 


of  Edinburgh,  Session  1874-75. 


505 


The  following  Communications  were  read : — 

1.  On  the  Diurnal  Oscillations  of  the  Barometer. 

By  Alexander  Buchan,  M.A. 

2.  The  Phenomena  of  Single  and  Double  Vision,  as  shown 
in  the  Stereoscope.  By  R.  S.  Wyld,  Esq. 

When  we  direct  the  axes  of  the  two  eyes  to  any  definite  object,  its 
different  parts  affect  corresponding  parts  of  each  retina,  and  the 
object  appears  single.  When  we  squint,  or  do  not  look  direct  at  the 
object,  its  images  affect  non-corresponding  parts  of  the  two  retinae, 
and  the  object  appears  double.  The  more  widely  the  axes  of  the 
eyes  are  deflected  from  the  object,  the  further  asunder  the  double 
objects  seem ; and  the  less  the  axes  are  deflected  the  less  distant 
from  each  other  the  double  objects  appear.  Thus,  when  we  hold  the 
finger  in  front  of  the  eyes  while  we  look  at  a distant  candle  or  gas  jet, 
the  flame  appears  single  and  the  finger  double.  When  we  turn  the 
eyes  to  the  finger  it  appears  single  and  the  flame  appears  double. 

The  paper  read  to  the  Society  in  February  1871  was  an  attempt 
to  prove  that  all  the  phenomena  connected  with  single  and  double 
vision  were  explanable  on  the  supposition  that  the  nerve  fibres  of 
each  retina  decussate  in  a common  cerebral  sensorium,  as  for 
instance  in  the  corpus  guadrigeminum , which  the  optic  nerves  are 
known  to  enter ; and  that  as,  owing  to  the  fineness  of  the  texture, 
anatomists  had  hitherto  been  unable  to  determine  the  ultimate 
arrangement  of  the  fibres  in  the  brain,  we  were  justified  in  making 
this  suggestion. 

Such  a crossing  of  nerve  fibres  has  in  it  nothing  improbable,  for 
there  are  many  instances  of  such  crossings,  as  for  instance  in  the 
great  and  in  the  lesser  commissures  of  the  brain.  There  is  also  a 
similar  crossing  in  the  medulla  oblongata  of  the  motor  nerves  from 
the  brain,  before  they  descend  the  spinal  cord ; and  there  is  a similar 
crossing  of  the  sensory  nerves  where  they  enter  the  spinal  cord. 
The  supposition  then  of  a decussation  of  the  fibres  of  the  optic 
nerve  within  the  brain  is  in  analogy  with  what  we  know  to  be  of 
frequent  occurrence  in  the  body. 

The  facts  which  Mr  Wyld  now  brings  before  the  Society  are  these — 


506  Proceedings  of  the  Royal  Society 

Is?,  When  we  enter  two  slips  of  white  card-board,  one  at  each  side 
of  the  stereoscope,  they  affect  non-corresponding  parts  of  the  retinae, 
as  shown  in  the  diagram  exhibited,  and  they  appear  as  two  objects . 

2c?,  When  we  push  the  slips  forward  till  they  appear  to  overlap, 
the  overlapping  ends  appear  as  one  object,  because  they  affect  the 
corresponding  central  points  of  the  two  retinae.  If  we  make  a mark 
similar  in  form  and  size  on  each  slip,  but  do  not  approach  the  slips 
sufficiently  near  for  the  marks  at  once  to  coalesce,  such  marks  are 
nevertheless  frequently  observed  to  glide  closer  and  coalesce. 
This  is  owing  to  the  natural  tendency  we  have  to  direct  the  axes 
of  the  eyes  to  the  objects  examined.  This  causes  the  marks  to 
affect  corresponding  points  of  the  retinae,  and  the  marks  conse- 
quently coalesce  visually  and  appear  as  one  object. 

3 d.  When  the  slips  seem  to  overlap,  the  overlapping  portion 
appears  so  greatly  increased  in  brightness  that  the  other  parts  have 
a tendency  either  to  disappear  altogether,  or  they  appear  and  dis- 
appear at  brief  intervals,  so  long  as  we  continue  to  look  at  the 
central  bright  portion.  These  dim  or  invisable  outlying  parts  may, 
however,  at  any  time  be  made  to  reappear  by  simply  moving  the 
card-board  once  or  twice  up  and  down,  and  thereby  exciting  the 
attention  and  the  retina.  They  may  also  be  made  to  appear  by 
winking,  by  moving  the  eyes  from  side  to  side,  or  doing  anything 
to  stimulate  the  retinae. 

4:th,  With  regard,  again,  to  the  overlapping  parts,  it  is  to  be 
observed,  that  though  they  appear  at  first  sight  to  form,  as  it  were, 
one  single  object,  yet  it  is  easy  to  see  that  this  bright  part  is  in 
reality  a double  picture  containing  the  impression  received  from 
each  eye;  and  so  far  as  these  impressions  are  not  incompatible,  but 
may  be  blended  the  one  with  the  other,  they  go  to  form  as  it  were 
a composite  picture,  as  we  know  is  the  case  with  the  figures  on  the 
usual  stereoscopic  slides,  and  as  we  may  prove  to  be  the  case  by 
making  any  distinctive  marks  on  the  slips  of  card-board,  when  these 
marks  will  appear  distinctly  visible,  as  if  integral  parts  of  the  over- 
lapping portion,  though  seen  by  the  different  eyes. 

5th , Another  important  circumstance  is  this.  When  the  slips 
are  of  different  colours,  as  for  instance  one  slip  red  and  the  other 
blue,  or  one  blue  and  the  other  yellow,  these  colours,  when  caused 
to  overlap  in  the  stereoscope,  do  not  produce  the  intermediate 


507 


of  Edinburgh,  Session  1874-75. 

colours  of  purple  or  green ; on  the  contrary,  as  was  stated  in  the 
paper  alluded  to,  at  one  time  the  coloured  slips  appear  alternately 
visible,  at  another  time  one  half  of  each  may  be  visible,  and  occa- 
sionally, spots,  or  it  may  be  only  minute  specks,  smaller  even  than 
the  fifth  part  the  diameter  of  a small  pin  head  of  the  one  colour, 
will  be  seen  shining  on  the  ground  colour  of  the  other  card-board. 
These  particular  changes  seem  to  depend  greatly  on  the  excited  or 
the  fatigued  condition  of  the  retinae  at  the  time;  for  if  we  direct 
our  attention  to  any  conventional  mark  made  on  either  of  the  slips 
presented,  the.  excitement  of  the  retina  of  the  eye,  caused  by  the 
act  of  observing  the  mark,  immediately  causes  the  slip  on  which  the 
mark  is  made  to  become  visible,  and  the  mark  appears  surrounded 
with  a patch  of  the  colour  of  the  slip  on  which  it  is  placed. 

Two  circumstances  then  may  be  mentioned  as  certain  : that  in 
no  instance  do  the  two  colours  blend  into  an  intermediate  colour ; 
and  second,  that  we  never  observe  the  same  portion  of  the  bright  over- 
lapping portion  to  have  at  one  and  the  same  moment  two  different 
colours;  parts  or  spots  or  minute  specks  may,  as  we  have  said, 
appear  of  the  one  colour,  and  other  parts  may  appear  of  the  other 
colour,  but  though  the  one  coloured  slip  visually  overlaps  the  other 
differently  coloured  slip,  we  never  see  any  part  at  once  to  possess 
two  different  colours. 

The  conclusions  to  which  these  phenomena  lead  are  certainly 
these — that  there  is  a physical  union  in  a cerebral  lobe  of  the 
nerve  impressions  coming  from  the  two  eyes,  and  in  no  other  way 
can  we  account  for  the  two  retinal  images  giving  the  mind  the  im- 
pression of  but  one  object  both  in  natural  and  stereoscopic  vision 
when  corresponding  retinal  fibres  are  excited,  and  of  double  objects 
when  non-corresponding  fibres  are  excited — and  no  other  suppo- 
sition will  account  for  the  increased  brightness  obtained  by  the  use 
of  two  eyes  than  that  suggested,  namely,  that  the  nerve  impressions 
from  both  eyes  are  physically  united  in  the  sensorium. 

Another  conclusion  to  which  we  are  led  is,  that  though  the  cor- 
responding retinal  fibres  are  brought  into  juxtaposition  in  the 
sensory,  yet  they  are  not  there  joined  or  amalgamated  the  one 
with  the  other,  seeing  they  do  not  produce  the  effect  of  an  inter- 
mediate colour,  but  each  fibre  transmits  to  the  sensory  the  distinc- 
tive colour  and  impression  which  it  receives  in  the  retina. 


508  Proceedings  of  the  Royal  Society 

The  reason  why  we  never  see  any  one  part  of  the  overlapping 
stereoscopic  objects  simultaneously  exhibiting  either  two  different 
colours,  or  an  intermediate  colour,  is  a matter  more  difficult  to  ex- 
plain; perhaps  the  following  may  be  considered  sufficient  explana- 
tion. If  the  smallest  visible  point  is  a point  due  to  the  impression 
produced  by  a single  nerve  fibre  from  one  of  the  eyes,  then,  as  on  the 
supposition  of  a decussation  of  the  fibres  in  the  sensory  alternate, 
exceedingly  small  specks  of  different  colours  may  at  any  time  appear 
intermixed,  from  the  circumstance  of  the  supposed  alternate  juxta 
position  of  the  individual  fibres  from  each  retina  in  the  sensory, 
so,  if  this  supposition  is  correct,  it  is  evidently  impossible  that  we 
can  ever  have  the  impression  of  two  different  colours  superimposed 
on  the  same  point  and  at  the  same  moment  of  time. 

3.  On  the  Products  of  the  Oxidation  of  Dimethyl-Thetine, 
and  its  Derivatives.  By  Prof.  Crum  Brown  and  Dr 
E.  A.  Letts. 

The  difficulty  experienced  in  determining  the  sulphur  contained 
in  the  compounds  of  dimethyl-thetine  (described  in  a former  com- 
munication) by  oxidation  to  sulphuric  acid,  induced  the  authors  to 
study  the  effects  of  various  oxidising  agents  on  these  compounds. 

By  acting  on  nitrate  of  dimethyl-thetine  with  dilute  nitric  acid, 
two  bodies  are  produced.  The  one  has  acid  properties,  and  forms 
a well-marked  soluble  salt  with  baryta.  The  other  has  neither 
acid  nor  basic  properties.  It  crystallises  in  very  beautiful  needles 
from  a hot  solution  in  alcohol. 

By  acting  on  the  base  dimethyl-thetine  with  permanganate  of 
potash  solution,  the  same  crystalline  substance  is  produced,  but  the 
presence  of  the  acid  body  could  not  be  ascertained.  The  oxidation 
of  dimethyl-thetine  by  permanganate  of  potash  takes  place  in  acid 
or  alkaline  solution  and  in  the  cold. 

Chromic  acid  has  no  action  whatever  on  dimethyl-thetine  further 
than  combining  with  it  to  form  chromate  of  dimethyl-thetine — a 
yellow  gummy  substance  which  refuses  to  crystallise.  The  same 
body  may  be  produced  by  acting  on  a solution  of  hydrobromate  of 
dimethyl-thetine  with  chromate  of  silver. 

Fuming  nitric  acid  dissolves  solid  hydrobromate  of  dimethyl- 
thetine  without  rise  of  temperature,  but  with  separation  of  bromine. 


509 


of  Edinburgh,  Session  1874-75. 

On  warming  the  solution,  brisk  action  ensues.  When  this  has  ter- 
minated, and  the  nitric  acid  has  been  evaporated  off  on  a water 
bath,  a strongly  acid  syrup  remains,  which  fumes  like  hot  sulphuric 
acid.  This  syrup  also  forms  a soluble  barium  salt. 

The  investigation  of  the  compounds  produced  by  the  oxidation 
of  dimethyl-thetine  and  its  derivatives  is  proceeding,  and  the 
authors  trust  in  a short  time  to  be  able  to  communicate  the  result 
of  their  experiments  to  the  Society. 


Monday , 5 tli  April  1875. 

Professor  KELLAND,  Vice-President,  in  the  Chair. 

The  Council  having  awarded  the  Neill  Prize  for  the 
Triennial  Period,  1871-74,  to  Mr  Charles  William  Peach, 
for  his  contributions  to  Scottish  Zoology  and  Geology,  and 
for  his  recent  contributions  to  Fossil  Botany,  Professor 
Geikie,  on  the  presentation  of  the  medal,  addressed  the  Pre- 
sident as  follows : — 

Sir, — The  Council  of  the  Royal  Society  of  Edinburgh  has  awarded 
the  Neill  Prize  for  the  triennial  period,  1871-74,  to  Mr  Charles 
William  Peach,  and  on  the  part  of  the  Council  I am  requested  to 
describe  briefly  to  the  Society  on  the  present  occasion  the  nature 
of  his  scientific  work,  which  has  been  judged  well  deserving  of  one 
of  the  Society’s  medals.  By  the  terms  of  the  original  bequest  this 
prize  is  reserved  for  the  work  of  a Scottish  naturalist.  Born  in 
Northamptonshire,  Mr  Peach  might  seem  to  be  excluded  from  the 
list  of  those  to  whom  the  prize  can  properly  he  awarded.  But  for 
more  than  a quarter  of  a century  he  has  lived  continuously  in  Scot- 
land, and  during  that  time  has  done  at  least  as  much  as  any  living 
Scotsman  to  extend  our  knowledge  of  the  natural  history  of  his 
adopted  country.  From  the  Kyles  of  Sutherland  to  the  holms  of 
Roxburgh,  he  has  never  resided  in  or  near  any  Scottish  county 
without  adding  something  to  what  was  previously  known  about  its 
flora  and  fauna,  either  living  or  fossil.  The  Neill  bequest  likewise 
provides  that  the  paper  or  work  for  which  the  prize  is  given  shall 
bear  date  within  five  years  previous  to  the  award.  During  the  last 
five  years  Mr  Peach  has  contributed  some  valuable  materials  to- 
wards the  extension  of  our  knowledge  of  the  fossil  plants  and  fishes 


510 


Proceedings  of  the  Royal  Society 

of  the  Carboniferous  rocks  of  the  basin  of  the  Forth.  But  the 
Council  has  considered  that  it  will  best  conform  to  the  liberal  spirit 
of  the  founder,  Dr  Neill,  himself,  by  having  regard  not  only  to 
Mr  Peach’s  work  during  the  last  five  years,  but  to  all  his  labours 
in  Scotland,  which  have  so  frequently  aided  the  researches  of  his 
brother  naturalists,  from  whom,  in  his  old  age,  every  token  of 
grateful  appreciation  and  kindly  feeling  is  justly  due. 

The  naturalist,  not  less  than  the  poet,  is  born,  not  made. 
The  quickness  of  eye  which,  without  effort,  lets  nothing  escape 
notice;  the  fine  instinct  which  divines  the  meaning  of  half-hidden 
phenomena,  and  leads  on  to  where  further  successful  observations 
should  be  made;  the  patience  with  which  repeated  failure  is  borne; 
the  enthusiasm  which,  amid  foul  weather  or  fair,  brings  the 
observer  back  joyously  from  the  cares  of  this  world  to  his  self- 
chosen  task,  whether  it  be  among  the  treasures  of  land  or  of  sea, — 
these  are  qualities  which  no  education  can  supply  to  us,  and  which 
no  want  of  education  can  wholly  repress.  Mr  Peach  has  been  happy 
in  the  possession  of  them  to  no  common  degree.  Appointed  more 
than  half  a century  ago  to  the  Coast  Guard  Service,  and  necessarily 
restricted  in  his  pursuits  by  the  arduous  duties  of  that  calling,  he 
has  everywhere  during  that  extended  period  shown  the  genuine 
characteristics  of  the  born  naturalist.  His  enforced  residence  near 
the  sea  has  been  turned  by  him  to  excellent  account,  for  he  has 
materially  increased  our  acquaintance  with  the  marine  fauna  which 
surrounds  our  islands. 

Somewhere  about  twenty  species,  and  several  genera  of  sponges, 
were  first  made  known  by  him  as  denizens  of  British  seas.  He 
has  considerably  augmented  our  list  of  native  hydrozoa  and  polyzoa. 
The  naked-eyed  Medusae  owe  not  a little  to  his  attention,  and  one 
genus  of  them  (Staurophora)  was  first  introduced  by  him  to  the 
naturalists  of  this  country.  The  Echinoderms,  too,  are  under 
similar  obligations  to  him,  for  besides  bringing  several  new  species 
to  light,  he  found  the  huge  Echinus  melo  of  the  Mediterranean  on 
the  coast  of  Cornwall,  and  supplied  the  twenty- armed  Holothuria 
nigra  to  fill  up  the  blank  pointed  out  by  Edward  Forbes  among 
the  British  Holothuriae. 

Since  his  removal  to  Scotland  in  1849,  Mr  Peach  has  done  further 
and  most  valuable  work  among  the  mollusca  and  fishes,  adding  to 
our  fauna  several  species  of  shell  as  well  as  some  fishes — Yarreli’s 


of  Edinburgh,  Session  1874-75.  511 

Blenny,  Ray’s  Bream,  and  the  Anchovy,  for  example — which  were 
not  before  known  to  occur  so  far  north  as  the  seas  which  wash  the 
northern  shores  of  Scotland.  In  none  of  his  labours  does  the  true 
spirit  of  the  naturalist  appear  more  pre-eminently  than  in  those 
by  which  he  made  known  the  nest-building  habits  of  certain  sea- 
shells  and  fishes.  At  Wick  he  noticed  that  the  jelly-like  masses 
of  the  ascidian  Leptoclinum  very  frequently  contained  small  yellow 
patches  in  the  centre.  Watching  these,  he  found  that  the  central 
yellow  parts  were  really  extraneous  bodies,  and  consisted  of  nests 
containing  ova.  Further  observation  connected  these  ova  with  the 
slug-like  gasteropod  Lamellaria,  and  showed  him  that  this  shell 
comes  every  spring  regularly  to  shore  from  deeper  water  outside, 
and  remains  two  or  three  months  for  the  purpose  of  nidification. 
Again,  at  Peterhead  he  made  himself  intimately  acquainted  with 
the  family  arrangements  of  that  rather  fierce-looking  little  fish, 
the  15-spined  stickle -back  ( Gasterosteus  spinaceus).  In  a rocky 
pool  he  found  a colony  of  them,  and  learnt  how  they  built  their 
nests  and  deposited  their  ova.  He  watched  the  hatching  and  growth 
of  the  young  until  the  whole  colony,  young  and  old,  took  to  the  sea. 
As  he  used  to  visit  them  five  or  six  times  a day,  the  parents  grew 
so  familiar  that  they  would  swim  round  and  touch  his  hand,  though 
on  the  appearance  of  a stranger  they  would  angrily  dash  at  any 
stick  or  incautious  finger  that  was  brought  near  them.  The  same 
habit  of  close  and  cultivated  observation  was  shown  by  his  study  of 
the  maternal  instincts  of  the  female  lobster  in  its  native  haunts. 

Previous  to  Mr  Peach’s  transference  to  Wick,  very  little  was 
known  about  the  fossil  plants  of  the  Old  Red  Sandstone  of  Caith- 
ness. Many  specimens  had  been  found,  but  they  were  commonly 
spoken  of  as  indistinctly  preserved,  and  as  probably  of  marine 
origin.  Setting  to  work  among  the  dark  flagstones  of  that  district, 
he  eventually  succeeded  in  forming  an  admirable  collection,  and  in 
showing  the  truly  terrestrial  nature  of  that  ancient  flora.  Within 
the  last  few  years  he  has  continued  his  services  to  fossil  botany  by 
bringing  to  light  some  new  and  most  interesting  vegetable  forms 
from  the  Carboniferous  strata  of  the  basin  of  the  Forth.  He  has 
shown,  for  example,  the  connection  between  the  flower-like  Antho- 
lites  and  the  usually  detached  fruit,  Cardrocarpon,  and  has  obtained 
in  one  fossil  a conjunction  of  microspores  and  macrospores. 
vol.  viii.  3 u 


512  Proceedings  of  the  Royal  Society 

To  palaeontology  he  has  contributed  several  new  species  of  fishes 
from  the  Old  Eed  Sandstone  and  the  Carboniferous  rocks.  In  great 
measure  to  his  perseverance  do  we  owe  our  present  list  of  the 
ichthyolites  of  Caithness  and  the  Orkney  Islands.  But  perhaps 
the  most  important  item  of  his  labours,  in  this  department,  at  least, 
if  we  regard  questions  alike  in  theoretical  geology  and  in  the  geolo- 
gical structure  of  Britain,  was  the  discovery  of  fossils  in  the  lime- 
stones of  Sutherland,  Previous  to  his  observations  the  rocks  of  the 
Scottish  Highlands  were  usually  grouped  with  the  so-called  “ Azoic” 
rocks,  as  if  they  belonged  to  a time  anterior  to  any  of  the  fossil- 
bearing  formations  of  the  country.  Obscure  organic  remains  had 
neen  indeed  detected  many  years  before  by  Macculloch  in  the 
quartz-rocks  of  Sutherland,  and  these  were  afterwards  brought 
again  into  notice  by  Hay  Cunningham.  But  they  had  gradually 
passed  out  of  mind,  their  organic  nature  being  stoutly  denied  even 
by  such  geologists  as  Sedgwick  and  Murchison.  Mr  Peach,  how- 
ever, brought  to  light  a good  series  of  recognisable  shells  and  corals, 
which  demonstrated  the  limestones  containing  them  to  lie  on  the 
same  geological  horizon  as  some  part  of  the  great  Lower  Silurian 
formations  of  other  regions.  It  was  this  discovery  which  enabled  Sir 
Boderick  Murchison  to  clear  up  the  geological  structure  of  the  High- 
lands, and  entitled  him  to  be  the  first  Brisbane  medallist  of  this 
Society. 

In  every  department  of  natural  science  to  which  Mr  Peach  has 
given  his  attention  he  has  distinguished  himself  as  a keen-eyed 
and  enthusiastic  collector,  wdth  an  almost  unrivalled  shrewdness  in 
detecting  what  was  new,  and  at  the  same  time  with  a disinterested 
readiness  to  hand  over  his  materials  to  those  who  had  more  specially 
studied  the  department  of  natural  history  to  which  these  materials 
belonged.  For  his  varied  contributions  to  science,  carried  on  for 
so  long  a time,  with  a purity  of  motive  and  a generous  helpfulness 
towards  others  which  have  won  for  him  the  esteem  of  all  naturalists, 
and  with  an  enthusiasm  which  the  lapse  of  more  than  threescore 
years  and  ten  has  left  undimmed,  the  Council  has  adjudged  to  him 
the  Neill  prize.  I beg  on  their  part  to  present  him  to  you,  with 
the  cordial  wish  that  he  may  yet  live  for  many  years  among  us  as 
an  honoured  type  of  the  true  collector  and  naturalist. 


of  Edinburgh , Session  1874-75. 


513 


The  following  Communications  were  read : — 

1.  On  the  Physiological  Action  of  Light.  Part  II.  By 
James  Dewrar,  Esq.,  and  Dr  John  G.  M'Kendrick. 

2.  On  the  Structure  and  Systematic  Position  of  Tristi- 
chopterus  alatus,  Egerton.  By  K.  H.  Traquair,  M.D., 
F.G.S. 

The  cranial  osteology  and  the  dentition  of  Tristichopterus  have 
been  hitherto  entirely  unknown,  and  we  were  but  imperfectly 
acquainted  with  the  structure  of  the  pectoral  fins.  Consequently 
great  doubts  have  prevailed  with  regard  to  its  affinities,  though  it 
was  supposed  to  be  allied  in  many  respects  to  Dipterus.  A suite 
of  specimens  from  John  O’Gfroat’s,  in  the  Edinburgh  Museum  of 
Science,  collected  by  Mr  Peach,  the  original  discoverer  of  the  fish, 
subsequent  to  the  publication  of  Sir  Philip  Egerton’s  description, 
throws  great  light  on  the  previously  unknown  points  of  its  struc- 
ture, as  well  as  on  its  affinities.  In  the  osteology  of  the  head  it 
presents  a striking  resemblance  to  the  Saurodipterini , and  to  the 
genus  Gyropty chius,  as  described  by  Pander.  The  teeth  are  acutely 
conical,  and  of  two  sizes,  large  and  small;  the  larger  teeth  have 
their  bases  fluted  externally,  and  internally  the  dentine  is  seen 
to  be  thrown  into  a series  of  simple  folds,  the  pulp  cavity  becoming 
simple  towards  the  apex  of  the  tooth.  The  shoulder  girdle  is 
provided  with  interclaviculars;  the  pectoral  fin  is  subacutely  lobate. 
The  structure  of  the  head,  the  dentition,  and  the  form  of  the 
paired  fins,  show  that  Tristichopterus  has  nothing  whatever  to  do 
with  Dipterus.  It  seems  to  be  more  closely  allied  to  Gyroptychius 
than  to  any  other  known  genus. 

Tho  following  Gentleman  was  duly  elected  a Fellow  of 
the  Society: — 

John  Aitken,  Esq.,  Darroch,  Falkirk. 


51.4 


Proceedings  of  the  Royal  Society 


Monday , 19  th  April  1875. 

Sir  WILLIAM  THOMSON,  President,  in  the  Chair. 
The  following  Communications  were  read  : — 

1.  Note  of  Temperature  Measurements  in  the  Great  Geysir 
of  Iceland — August,  1874.  By  Bobert  Walker,  Esq. 

I have  thought  it  might  be  of  interest  to  the  Society  to  lay  before 
it  a short  account  of  some  temperature  observations  which  I suc- 
ceeded in  making  at  the  Great  Geysir  of  Iceland,  in  the  month 
of  August  last  year.  As  the  circumstances  of  my  visit  to  the 
island  obliged  me  to  limit  my  stay  at  that  remarkable  spring  to  a 
few  hours,  and  as,  during  that  time  and  for  48  hours  previously, 
no  great  eruption  occurred,  I fear  my  results  must  appear  some- 
what meagre  and  unsatisfactory.  The  very  interesting  nature, 
however,  of  the  problem  of  the  action  of  the  Great  Geysir,  and 
the  difficulty  of  securing  any  reliable  observations  at  all  in  so  inac- 
cessible a region,  will  perhaps  be  deemed  sufficient  grounds  for 
my  taking  up  the  time  of  the  Society  with  these  few  remarks. 
So  far  as  my  results  go,  they  confirm  very  remarkably  those  of 
Professor  K.  Bunsen,  who,  with  a companion,  spent  more  than  ten 
days  at  the  spot  in  July  1846,  and  to  whom  science  is  indebted 
for  the  now  generally  received  theory  of  the  action  of  the  Great 
Geysir.  An  account  of  his  observations  was  given  in  the  “Annalen” 
for  1847,  and  to  it  I shall  refer  frequently  in  the  course  of  these 
remarks. 

If  the  difficulty  of  obtaining  thermometer  readings  at  various 
points  in  a column  of  water  from  70  to  80  feet  deep,  and  more  or 
less  in  a constant  state  of  agitation,  be  great,  the  difficulty  of 
reaching  the  place  at  all  I found  to  be  by  no  means  inconsiderable. 
Arriving  in  Reykjavik  on  the  afternoon  of  Monday,  3d  August, 
after  a very  stormy  passage  of  nearly  five  days  from  the  Clyde,  we 
experienced,  owing  to  the  visit  of  His  Majesty  the  King  of  Den- 
mark, more  than  the  usual  trouble  and  delay  in  securing  guides 
and  ponies,  for  the  long  ride  of  nearly  80  miles  up  country.  It  is 


515 


of  Edinburgh,  Session  1874-75. 

jsual  to  take  this  in  two  stages,  halting  at  Thingvalla,  which  is 
rather  less  than  half  way,  or  about  35  miles  from  Reykjavik. 
Starting  with  several  fellow-travellers  on  the  afternoon  of  Tuesday, 
the  4th,  under  orders  to  return  to  our  steamer  on  Saturday  evening, 
it  was  early  morning  next  day  wdien  we  pitched  our  tents  on  that 
classic  plain  where,  on  the  Friday,  the  King  was  to  address  the 
assembled  deputies  from  all  Iceland.  My  companions  decided  to 
remain  and  witness  this  great  national  demonstration.  After  a 
great  deal  of  trouble  I at  last  succeeded  in  finding  a native  who 
had  no  scruple  on  patriotic  motives  to  absent  himself,  and  act  as 
my  guide  on  to  G-eysir;  and,  through  the  goodness  of  some  Iceland 
friends,  I was  able  to  secure  the  companionship  of  a most  intelli- 
gent lad  of  only  15  years  of  age,  a student  at  Reykjavik,  who, 
besides  knowing  Icelandic  and  Danish,  could  speak  English  re- 
markably well.  Making  an  early  start,  then,  with  these  two,  and 
fi  ve  horses,  on  the  morning  of  Thursday,  6th  August,  we  managed 
to  reach  the  G-eysir  in  8 hours,  meeting  the  king  and  his  retinue 
on  their  way  down.  From  one  or  two  members  of  the  American 
party,  and  some  English  travellers,  who  had  preceded  us,  I learned 
that  there  were  great  expectations  that  the  Greysir  was  at  last  to 
go  off.  It  had  erupted  twice  on  the  morning  of  Tuesday  the  4th, 
but  not  since  then,  so  that  the  king  had  been  obliged  to  return, 
after  boiling  an  egg  at  the  edge  of  the  basin.  By  those  who  were 
now  about  to  follow  him  I was  congratulated  as  being  quite  certain 
to  see  an  eruption  before  morning;  but  no  such  good  fortune  was 
in  store  for  us.  Dr  Hayes,  of  Arctic  fame,  kindly  assisted  in  arrang- 
ing the  tackling  of  rope  and  cord  which  I had  brought  with  me 
for  letting  down  the  thermometer,  and  one  of  the  English  party,  a 
Cambridge  man,  the  Rev.  E.  MacCarthy  of  King  Edward’s  School, 
Birmingham,  was  even  so  good  as  to  volunteer  to  remain  behind 
and  help  me  with  my  observations,  an  offer  which  I gladly  accepted. 
I need  hardly  attempt  to  describe  what  travellers  have  so  often 
described  already,  I mean  the  general  situation  and  form  of  the 
Geysir  tumulus,  and  the  beautiful  basin  filled  with  pellucid  water, 
by  which  this  mound  of  deposited  silica  is  crowned.  The  water  in 
the  centre  seemed  three  or  feet  deep  to  the  mouth  of  the  funnel 
proper;  but  of  course  our  measurements  were  necessarily  taken 
from  its  surface  in  the  basin,  and  this  may  account  for  the  fact 


516 


Proceedings  of  the  Royal  Society 

that  my  measurement  of  the  depth  of  the  funnel  is  3 or  4 feet 
in  excess  of  Bunsen’s. 

In  devising  the  apparatus  employed  I was  kindly  assisted  by 
my  friend  Professor  Fuller  of  Aberdeen.  I procured  from  Casella 
of  London  a self-registering  maximum  thermometer,  which  is  now 
on  the  table.  We  had  made  for  it  a case  of  brass,  the  ends  of 
which  were  made  to  unscrew,  and  were  pierced  with  holes.  The 
thermometer  was  kept  in  its  place  in  this  case  by  little  wedges  of 
cork,  which,  however,  allowed  the  water  to  have  free  passage  through 
the  tube  from  end  to  end.  To  protect  the  thermometer  and  case 
against  injury  from  the  sides  of  the  G-eysir-funnel,  we  slid  over  its 
ends  two  large  pieces  of  cork,  and  connected  these  lengthwise  with 
slips  of  wood.  This  arrangement  was  found  to  answer  admirably, 
unless  that  the  large  masses  of  cork  required  so  heavy  a weight 
to  submerge  the  whole  apparatus  that  we  had  some  trouble  in 
hauling  it  in  towards  the  side  when  each  reading  was  taken.  We 
had  also  omitted' to  provide  swivels  to  prevent  twisting  of  the  cord 
when  the  cap  was  unscrewed,  and  from  this  cause  much  time  was 
lost  in  getting  each  successive  reading.  The  following  12  were  all 
that  Mr  MacCarthy  and  I could  obtain,  though  we  worked  well 
all  the  time  we  were  there,  unless  for  6 or  7 hours  when  we  went 
to  rest  in  the  boer  or  farm-house  near  by,  leaving  a watch,  with 
orders  that  we  should  be  called  if  any  unmistakable  signs  of  an 
approaching  eruption  were  given.  From  this  division  of  our  time 
it  resulted  that  of  these  12  readings,  one-half  were  taken  on  the 
evening  of  the  6th  August,  and  the  rest  on  the  morning  of  the  7th. 
Allowance  must  be  made  for  this,  in  accordance  with  one  of  Bunsen’s 
results  as  to  the  general  rise  of  temperature  in  the  whole  column 
as  a great  eruption  is  coming  on. 

Temperature-measurements  at  the  G-reat  Greysir,  6th  and  7th 


August  1874. 

Depth  in  feet 

Observed  temp. 

Calculated 

Diffs. 

from  surface. 

Fahrenheit. 

boiling-point. 

0 

187° 

210° 

23° 

10J 

190° 

224°-3 

34°-3 

18 

197° 

233° 

36 

27 

211° 

241°-8 

30o,8 

o f Edinburgh , Session  187 4-7  5.  517 


Depth  in  feet 

Observed  temp. 

Calculated 

Diffs. 

from  surface. 

Fahrenheit. 

boiling-point. 

36 

243° 

250°-9 

70,9 

39 

247° 

252°*2 

5°*2 

45 

250°-5 

257° 

6°*5 

49-5 

254° 

260°*2 

6°*2 

54 

256°-5 

263°-3 

6°-8 

58*5 

254° 

266°*5 

12°-5 

67-5 

*259°*5 

272°-2 

12°-7 

77 -5 

257° 

278° 

11° 

* Mean  of  two  observations 


Bunsen  s Measurements  in  1846. 


6th  July, 

8.20  p.m. 

7th  July,  2.55  p.m. 

7th  July,  7.58  p.m. 

Height  from 

Temp. 

Height  from 

Temp. 

Height  from 

Temp. 

bottom,  in  feet. 

Fahr. 

bottom,  in  feet. 

Fahr. 

bottom,  in  feet. 

Fahr. 

0 

254-5 

0 

261-5 

0 

259-7 

15-75 

252-8 

16-4 

253-4 

31-5 

235-4 

29-5 

248-7 

32-3 

251-2 

47-25 

186-4 

48-36 

223-5 

48-36 

230-0 

63 

180-7 

64-1 

185-4 

64-1 

184-5 

For  comparison  I give  above  Bunsen’s  results  from  the  “Annalen  ” 
(1847),  with  the  readings  reduced  to  the  same  measures  as  my  own. 
His  heights  are  from  the  bottom ; no  doubt,  because  for  some  time  after 
a great  eruption  the  level  of  the  water  in  the  funnel  is  gradually 
rising.  While  I remained,  the  basin  continued  nearly  full,  the 
level  of  water  in  it  not  changing  more  than  a few  inches. 

Bunsen  draws  the  following  conclusions  from  these  observations: — 

(1.)  That,  omitting  small  irregularities,  the  temperatures  in  the 
Grey  sir- column  diminish  from  beneath  upwards. 

(2.)  That  the  temperature  at  all  points  is  dependent  on  the  time 
since  last  eruption. 

(3.)  That  that  temperature  nowhere  reaches  the  boiling-point 
due  to  the  pressure  until  a few  minutes  before  a great  eruption. 

(4.)  That  the  temperature  about  the  middle  height  of  the 
column  comes  nearest  to  the  boiling-point  corresponding  to  the 


518 


Proceedings  of  the  Royal  Society 

pressure,  and  approaches  it  more  nearly  the  nearer  the  moment  of 
a great  eruption. 

He  argues,  therefore,  that  immediately  before  such  an  eruption 
only  a small  shock  will  be  sufficient  to  vaporise  a large  mass  of 
the  whole  column,  and  so  to  displace  the  whole  column  above. 
Now,  it  is  a fact  that  the  column  is  constantly  subject  to 
such  shocks,  which  occur  at  intervals  of  a few  hours,  and  are 
more  frequent  as  a great  eruption  is  approaching.  Bunsen  accounts 
for  these  shocks,  which  are  in  fact  abortive  attempts  at  an 
eruption,  in  this  manner.  He  observes  that  it  is  a feature  of 
most  of  the  Icelandic  warm  springs  that,  periodically,  at  certain 
points,  great  bubbles  of  steam  get  formed,  and  rising  soon  condense 
in  the  colder  strata  above.  This  is  well  seen  in  these  rocky 
cavities,  10  or  12  feet  deep,  which  exist  in  that  remarkable  region 
of  springs  and  mud-cauldrons  in  the  immediate  vicinity  of  the 
Great  Geysir.  I observed  also  something  of  a like  phenomenon  at 
the  “quhar”  by  the  side  of  the  lake  at  Laugardalr,  where  we  rested 
on  the  way  between  Thingvalla  and  the  Geysir.  At  that  spring, 
however,  as  the  depth  of  water  is  quite  inconsiderable,  the  effect  is 
more  of  a continuous  bursting  of  great  bubbles  of  steam  on  the 
surface,  as  no  condensation  takes  place,  the  water  being  at  a tem- 
perature close  on  the  boiling-point.  Now  Bunsen  argues  that,  if 
at  some  point  in  the  in-carrying  ducts  of  the  Geysir-column  (and 
the  existence  of  these  ducts  is  proved  by  the  constant  overflow  of 
water  from  the  basin),  the  temperature  of  the  layer  of  water  gets 
raised  above  the  boiling-point  due  to  the  pressure,  owing  to  the 
great  heat  of  the  surrounding  rocks,  then  a sudden  generation  of 
steam  is  the  result,  and  a rise  of  that  steam  in  the  column  itself. 
This  great  bubble  is  soon  condensed,  while  at  the  same  time  its 
sudden  formation  cooled  the  water  at  the  point  in  the  duct  where 
it  was  formed.  The  phenomenon,  therefore,  possesses  a periodic 
character,  and  the  explanation,  it  must  be  admitted,  seems  to  account 
well  for  the  conical  water-hill,  as  Bunsen  aptly  terms  it,  the  sudden 
upheaval  of  which  in  the  centre  of  the  basin  is  an  invariable 
accompaniment  of  these  subterranean  explosions,  often  of  very 
great  violence,  which  are  heard  and  felt  recurring  at  intervals 
under  the  Geysir  cone.  The  grand  display  of  a great  eruption, 
however,  does  not  occur  until  the  temperatures  in  the  whole  column 


519 


of  Edinburgh,  Session  1874-75. 

are,  by  the  influx  of  heated  water,  brought  so  near  their  respective 
boiling-points  that  a slight  upheaval  at  a certain  point  of  the  tube 
is  sufficent  to  carry  the  superincumbent  layer  to  a point  where, 
from  its  temperature  and  the  slight  diminution  of  pressure,  a 
further  generation  of  steam  (instead  of  a condensation  of  that 
already  formed)  will  be  the  result. 

Bunsen  has  shown  that  the  mechanical  force  which  this  action 
developes  is  fully  sufficient  to  account  for  the  marvellous  pheno- 
mena of  a great  eruption.  Bunsen’s  observations  and  my  own 
agree  in  showing  that  it  is  somewhere  about  the  middle  of  the 
column  that  the  observed  temperatures  approach  most  nearly  to 
those  of  the  boiling-point  due  to  the  pressure.  An  upheaval  of  the 
layer  at  that  point,  through  only  a few  feet,  will  be  sufficient  to 
generate  instantaneously  an  additional  volume  of  steam,  the  pressure 
of  which  will  again  further  relieve  that  of  the  strata  beneath, 
and  so  cause  an  additional  volume  to  be  generated  there.  The 
enormous  force,  which  the  phenomenon  of  the  sudden  upheaval  of 
a small  column  of  water  is  thus  capable  of  calling  forth  cannot  be 
spent  in  a single  eruptive-shot,  and  hence  the  explanation  of  the 
fact  that  a great  eruption  lasts  sometimes  for  four  minutes. 

No  theory  of  internal  steam-cauldrons,  filled  in  succession  with 
steam  and  water,  seems  at  all  consistent  with  observed  phenomena. 
It  fails  to  explain  how,  in  the  abortive  eruptions,  no  water  seems 
to  flow  from  the  tube  more  than  the  small  rivulet  which  steadily 
finds  its  way  at  the  indentations  over  the  rim  of  the  basin.  What 
flows  over  the  margin,  and  it  was  great  enough,  considering  its 
temperature,  to  cause  considerable  difficulty  in  retaining  hold  of 
the  cord  and  rope,  was  due  solely  to  the  great  commotion  in  the 
basin,  and  was  apparently  equal  to  the  fall  of  a few  inches  in  the 
level  of  water  in  the  pool  when  the  sudden  upheaval  had  subsided. 
Further,  Bunsen  actually  let  his  thermometer  remain  without  injury 
at  the  bottom  of  the  tube  during  a great  eruption,  having  noted 
on  it,  a few  moments  before,  a temperature  of  9°  C.  below  that  of 
the  boiling-point  due  to  the  pressure.  The  column  erupted  on  that 
occasion  he  estimated  at  43'3  metres  or  about  142  feet. 

It  will  be  observed,  that  there  is  a remarkably  sudden  rise  of 
temperature  at  a particular  point  of  the  column.  Thus  while  the 
rise  between  depths  of  10J  feet  and  18  feet  is  only  7°  F.,  and  that 

3 x 


VOL.  VIII. 


520  Proceedings  of  the  Royal  Society 

between  28  feet  and  27  feet,  14°  F.,  the  rise  between  27  feet  and 
36  feet  is  as  much  as  32°.  I regret  that  I did  not  observe  this 
so  as  to  interpolate  one  or  two  additional  observations  between 
these.  But  Bunsen’s  results  (vide  3d  col.)  give  one  intermediate 
measurement,  his  others  being  in  remarkable  accordance  with 
mine. 

We  had  several  displays  of  the  power  of  Strokkur,  a smaller 
G-eysir  about  a 100  yards  from  the  Great  G-eysir.  Unlike  the  latter, 
it  can  be  made  to  erupt  by  throwing  in  turf,  stones,  or  earth,  which 
stop  up  the  funnel  at  a point  about  27  feet  down,  where  it  narrows 
from  a width  at  the  mouth  of  about  8 feet  to  about  8 inches.  The 
people  living  at  the  farm-house  asserted  that  the  long  interval  of 
inaction  of  the  Great  Geysir  was  owing  to  the  very  frequent  erup- 
tions of  Stokkur,  which  had  been  provoked  by  way  of  display  during 
the  king’s  visit. 

Professor  Tait  has  suggested  the  use  of  a thermo-electric 
junction,  after  Becquerel’s  method,  to  determine  with  perfect 
accuracy  the  temperature  at  any  point  of  the  column.  I believe, 
however,  that  no  care  in  packing  would  make  it  possible  to  trans- 
port safely  a galvanometer  and  a thermo-electric  arrangement  over 
80  miles  of  such  country  as  one  has  to  travel  to  the  Great  Geysir. 
I had  the  misery  of  seeing  the  package  containing  my  thermometer 
repeatedly  tossed  from  the  pack-saddle,  without  any  injury  to  the 
instrument,  however,  as  I found  by  comparing  it  carefully  on  my 
return  with  one  tested  at  Kew.  The  packages  are  fastened  usually 
with  hair  ropes,  and  not  only  are  these  constantly  getting  loose, 
but,  when  a marrow  part  of  the  way  is  reached,  the  ponies,  urged  on 
behind  by  their  drivers,  charge  against  each  other,  and  often  leave 
their  loads  behind  ere  they  get  through. 

Setting  out  from  the  Geysir  at  1 p.m.  on  Friday  (7th  August),  I 
reached  Reykjavik  at  6 the  following  evening,  and,  I confess,  was 
grievously  disappointed  to  find  that  our  steamer  was  not  to  sail  for 
other  48  hours,  an  interval  which  would  have  sufficed  to  complete 
my  observations,  and  would,  most  probably,  have  given  me  an 
opportunity  of  witnessing  an  eruption  of  this  world-renowed  spring. 

2.  On  the  Capillary  Surface  of  Revolution.  By 
Sir  William  Thomson  and  Mr  John  Perry. 


of  Edinburgh,  Session  1874-75. 


521 


3.  On  the  Oscillation  of  a System  of  Bodies  with  Rotating 
Portions.  Part  II. — Vibrations  of  a Stretched  String  of 
Gyrostats  (Dynamics  of  Faraday’s  Magneto-optic  Dis- 
covery), with  Experimental  Illustrations.  By  Sir  William 
Thomson. 


4.  On  the  Theory  of  the  Spinning-Top,  with  Experimental 
Illustrations.  By  Sir  William  Thomson. 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 


vol.  viii.  1874-75.  No.  92. 


Ninety-Second  Session. 

Monday , 3 d May  1875. 

DAVID  MILNE  HOME,  Esq.,  Vice-President,  in  the 
Chair. 

The  Portrait  of  Sir  Robert  Christison,  Bart.,  Honorary 
Vice-President  of  the  Society,  executed  by  George  Reid, 
Esq.,  Aberdeen,  was  uncovered. 

The  following  Communications  were  read 

1.  Laboratory  Note. — Analysis  of  Titaniferous  Iron  Sand 

from  North  Berwick.  By  James  Davidson,  Esq.  Com- 
municated by  Professor  Crum  Brown. 

In  an  excursion  of  Professor  Geikie’s  class  to  North  Berwick 
(5th  February),  a layer  of  titaniferous  iron  sand  was  found  lying 
along  the  shore  for  a short  distance. 

The  rocks  at  this  locality  consist  chiefly  of  dull  green  and  red 
trap-tuffs,  traversed  by  dykes  and  veins  of  basalt.  Immediately  in 
front  of  the  spot  where  the  iron  sand  was  met  with  several  intrusive 
masses  of  dark  heavy  basalt  occur.  It  was  evidently  from  the 
decomposition  and  trituration  of  this  rock  that  the  iron  sand  came, 
which  has  been  assorted  by  the  waves  along  the  upper  margin  of 
the  beach. 

3 Y 


VOL.  VIII. 


524  Proceedings  of  the  Royal  Society 

It  was  analysed  with  the  following  result: — 


Magnesia 

0-2 

Ferrous  oxide 

17*6 

Titanic  acid 

6-2 

Ferric  oxide 

75*6 

99-6 

Specific  gravity  4-6. 


The  sand  was  highly  magnetic. 

Assuming  that  the  magnesia  is  present  as  titanate  of  magnesia, 
and  that  the  titanic  acid,  in  excess  of  what  is  required  to  form 
titanate  of  magnesia,  is  united  with  ferrous  oxide  to  form  ferrous 
titanate,  the  residue  of  the  ferrous  oxide  being  united  with  ferric 
oxide,  we  obtain  the  following  proximate  composition : — 


MgO,  Ti02  • 

0*6 

FeO,  Ti02  . 

10-6 

FeO,  Fe,03  . 

42-9 

Fe203  .... 

45-5 

99-6 

The  sand  is  obviously  crystallised,  but  the  grains  are  so  rounded 
by  rolling  as  to  render  it  impossible  to  determine  whether  they  are 
octahedral  or  rhombohedral. 

If  we  calculate  the  quantity  of  oxygen  contained  in  the  several 
oxides  present,  we  find, — 


Oxygen. 

MgO 

0*2 

0-08 

FeO 

17*6 

444 

Ti02  . 

6-2 

1*21 

Fe203  . 

75*6 

22-68 

Or  arranged  as  above. 

Oxygen. 

MgO,  Ti02 

0-6 

0-24 

FeO,  Ti02 

10-6 

3-42 

FeO,  Fe203 

42-9 

12-00 

Fe203  . 

45*5 

13-68 

of  Edinburgh,  Session  1874-75. 


525 


Dividing  into  oxides  having  the  general  formula  M203  and  M304 
respectively  (Fe203,  MgTiOb,  FeTi03;  and  Fe304)  we  have, — 


These  numbers  are  nearly  in  the  proportion  of  3:2,  and  the  compo- 
sition of  this  sand  might  he  nearly  represented  by  the  formula, 


The  composition,  however,  nearly  agrees  with  that  of  sands  held 
by  Rammelsberg,  with  good  reason,  to  be  mixtures. 

2.  On  some  Permian  Fishes,  hitherto  erroneously  referred 
to  the  Genus  Palceoniscus.  By  Dr  Traquair. 

3.  Note  on  the  Action  of  Bile  Salts  on  the  Animal  Economy. 
By  J.  Graham  Brown,  Esq.  Communicated  by  Dr 
M‘Kendrick. 

The  investigations  recorded  in  this  paper  were  undertaken  for 
the  purpose  of  elucidating  the  action  of  the  bile  salts  on  the  ani- 
mal economy.  The  chief  workers  in  this  field  of  inquiry  have 
been  Frerichs  and  Kiihne,  and  the  results  obtained  have  been  to  a 
great  extent  contradictory. 

The  most  important  conclusions  at  which  Frerichs  arrives,  are  : — 
(1.)  That  injections  of  bile  into  the  blood  of  the  lower  animals  are 
followed  by  no  important  derangement  of  the  vital  functions  ; 
(2.)  That  bile  pigment  is  excreted  in  considerable  quantity  by  the 
urine  after  injections  of  decolorised  bile  ; (3.)  That  unchanged  bile 
acids  are  never  found  in  the  urine  after  such  injections. — (“Clinical 
Treatise  on  Diseases  of  Liver,”  vol.  i.  p.  394.) 

Kiihne,  on  the  other  hand,  affirms  with  an  equal  degree  of  posi- 
tiveness : — (1.)  That  biliary  acids  are  not  decomposed  in  the 
blood.  In  whatever  manner  they  find  their  way  into  that  fluid  they 
are  afterwards  excreted  unchanged  by  the  kidneys  ; (2.)  After  in- 
jections into  the  veins  of  colourless  solutions  of  bile  salts,  bile 
pigment  may  appear  in  the  urine  (as  stated  by  Frerichs),  but  it  is 
due  to  the  property  possessed  by  the  bile  acids  of  dissolving  the 


Oxygen  in  M203 

„ „ M 04 


17*34 

12-00 


526 


Proceedings  of  the  Royal  Society 


blood  corpuscles,  and  thus  setting  free  a quantity  of  heematine, 
which  being  acted  on  by  the  bile  acid  is  converted  into  bile  pig- 
ment.— ( Vide  Beale’s  “Archives  of  Medicine,”  vol.  i p.  342.) 

Neither  of  these  observers  notices  any  abnormal  post  mortem 
appearances  in  any  of  the  animals  they  operated  on. 

In  the  prosecution  of  this  investigation  there  were  various 
courses  open  by  which  bile  might  be  introduced  into  the  system. 
It  was  not  desirable  to  administer  it  by  the  mouth,  for  then  its 
absorption  into  the  portal  circulation,  and  consequent  passage  to 
the  liver,  would  tend  to  complicate  its  action.  It  seemed  therefore 
best  to  introduce  the  bile  directly  into  the  general  circulation  by 
hypo-dermic  injection.  Intravenous  injection  was  not  employed, 
in  order  to  avoid  the  error  of  some  who,  injecting  biliary  fluids  into 
the  veins,  attributed  the  immediate  effects  produced  on  the  system 
to  the  bile,  forgetting  that  the  intravenous  injection  of  any  solu- 
tion, or  even  of  distilled  water,  will  produce  such  symptoms. 

Having  then  decided  to  inject  the  bile  into  the  subcutaneous 
cellular  tissue,  it  remained  to  consider  what  preparation  was  best 
for  this  purpose.  Frerichs  used  filtered  bile,  but  this,  though  the 
simplest  way,  was  open  to  many  objections. 

It  seemed  more  advisable  first  to  separate  from  fresh  bile  the 
salts  of  the  biliary  acids,  and  to  inject  these  in  solution  in  water. 
The  method  of  preparation  of  these  salts  corresponded  very  closely 
with  that  described  by  Dr  Lauder  Brunton  in  the  “ Handbook  for 
the  Physiological  Laboratory.”  In  this  manner  a mixture  of 
glycocholate  and  taurocholate  of  soda  is  obtained,  consisting  of 
nearly  equal  quantities  of  these  salts.  This  mixture  was  dissolved 
in  distilled  water  so  as  to  make  a solution  of  known  strength. 
In  these  experiments  the  solution  used  contained  gr.  j.  in  Hpiij. 

The  rabbits  experimented  on  were  placed  in  a cage,  the  floor  of 
which  was  constructed  of  glass  rods,  lying  parallel  to  each  other, 
and  very  close,  and  which  allowed  the  urine  to  pass  through  into 
a porcelain  dish  placed  below  for  its  reception,  while  it  retained  in 
the  cage  the  solid  excreta.  The  urine  was  thus  obtained  in  a very 
pure  state,  as  it  passed  through  the  floor  of  the  cage  immediately 
on  being  voided.  Its  quantity  was  measured  in  cubic  centimeters, 
as  this  rendered  future  calculation  much  more  expeditious. 

The  urine  was  tested  in  the  usual  way  for  albumen,  bile  acids, 


of  Edinburgh,  Session  1874-75.  527 

bile  pigment,  and  blood.  The  estimation  of  the  urea  was  attempted 
by  two  methods  (the  one  to  check  the  other):  Firstly , by  Liebig’s 
process  with  nitrate  of  mercury;  and  secondly , in  an  easier  manner 
by  the  use  of  hypobromite  of  soda  (as  recommended  by  Dr  Graham 
Steele,  in  the  “Edinburgh  Medical  Journal’’  for  August  1874). 
These  two  methods  invariably  gave  results  that  corresponded  very 
closely,  and  thus  led  to  greater  certainty.  But,  unfortunately,  in 
the  case  of  both  of  these  processes,  other  urinary  constituents 
come  in  to  complicate  the  results  of  analysis.  For  not  only  does 
Urea  precipitate  the  mercury  solution,  but  uric  acid,  hippuric  acid, 
creatin,  creatinine,  and  even  perhaps  fibrin,  cause  precipitation. 
The  same  is  true  with  respect  to  the  process  with  the  hypobromite 
of  soda,  as  these  bodies  all  unite  with  urea  in  giving  off  nitrogen. 
It  is  evident,  then,  that  it  is  impossible  by  either  of  these  methods 
to  obtain  an  absolute  knowledge  of  the  quantity  of  urea,  especially 
in  the  urine  of  herbivora,  which  contains  so  much  hippuric  acid. 
It  was  only  possible  to  determine  the  quantity  of  nitrogen  obtain- 
able from  the  urine  by  means  of  the  second  process,  and  to  use 
the  other  merely  as  a check.  The  diet  of  the  animals  experi- 
mented on  was  always  uniform,  consisting  of  cabbage. 

And  now,  in  describing  these  experiments,  it  will  be  best  to  speak 
first  of  those  symptoms  noticed  during  life,  and  second,  of  the  post 
mortem  appearances.  The  former  will  be  given  under  the  system 
to  which  each  belongs,  so  that  they  may  be  arranged  methodically. 

Symptoms  during  Life. 

Alimentary  System. — No  salivation  was  ever  noticed.  The 
appetite  was  much  affected,  sometimes  almost  lost  if  the  dose  was 
large  (grains  xl),  but  with  smaller  doses  (grains  x.)  it  was  not 
much  influenced.  There  was  never  any  vomiting.  The  bowels  were 
not  affected  if  the  dose  was  small,  but  generally  there  was  pro- 
fuse diarrhoea.  In  all  cases  the  faeces  were  well  bile- stained. 

Circulatory  System. — The  cardiac  pulsations  were,  in  most  cases, 
slightly  but  quite  perceptibly  decreased  in  rapidity,  a short  time 
after  injection.  The  respirations  were  similarly  affected. 

Lymphatic  System. — In  one  case  the  blood  was  carefully  ex- 
amined, the  greatest  precautions  being  taken  to  prevent  contact 
with  the  air  as  far  as  possible.  In  this  case  frojn  day  to  day  the 


528 


Proceedings  of  the  Royal  Society 


coloured  corpuscles  were  seen  to  have  their  form  altered,  while  the 
white  increased  relatively  in  number.  At  the  end  sometimes  more 
than  40  white  corpuscles  were  to  be  seen  at  once  in  the  field  of  the 
microscope. 

Integumentary  System. — No  jaundiced  line  was  ever  noticed  in 
the  skin  or  conjunctive. 

Urinary  System.— The  quantity  of  the  urine  was  sometimes 
greatly  increased  after  injection  of  bile  salts,  and  at  other  times 
diminished.  This  difference  depended,  apparently,  on  the  amount 
of  food  taken  during  the  day  following  the  injection.  For  when 
the  sole  food  of  an  animal  consists  of  a vegetable  containing  so 
high  a percentage  of  water  as  cabbage  does,  the  quantity  of  urine 
varies  very  much  according  to  the  appetite ; when,  however,  the 
quantity  of  food  remained  the  same,  the  bile  acids  seemed  to  have 
an  undoubted  diuretic  effect. 

The  colour  of  the  urine  in  health  was  almost  invariably  light. 
It  was  opaque  owing  to  a deposit  of  phosphates.  After  injection 
if  the  quantity  was  increased,  then  it  became  still  lighter  in  colour, 
but  when  it  was  diminished,  it  became  very  dark  and  smoky.  This 
colour  was  no  doubt  owing  partly  to  concentration,  but  its  smoky 
colour  led  to  the  belief  that  some  blood  pigment  was  present. 
This  was  rendered  all  the  more  probable  by  the  fact  that  blood 
corpuscles  were  once  or  twice  seen  in  the  urine  after  injection  of 
bile  salts.  However,  the  spectrum  of  the  urine  did  not  show  the 
characteristic  absorption  bands  of  blood  on  the  two  occasions  on 
which  it  was  in  my  power  to  apply  this  test. 

There  once  appeared  a trace  of  albumen  after  injection  of  bile 
salts.  Small  quantities  of  bile  acids  could  usually  be  detected  after 
injection,  but  only  rarely  was  there  any  trace  of  bile  pigment;  it 
must  be  confessed,  however,  that  the  test  for  the  latter  is  much  less 
satisfactory  than  that  for  the  former.  The  quantity  of  free  nitrogen* 
almost  always  rose  after  injection  of  bile  salts,  as  seen  in  the 
following  tables : — 

* By  free  nitrogen  is  here  meant  the  nitrogen  which  is  liberated  by  the 
action  of  hypobromite  of  soda. 


of  Edinburgh,  Session  1874-75.  529 


First  Injection.  (Grains  x.  of  bile  salts.)  October  6,  1874. 

Total  Nitrogen  obtained. 

Average  of  5 days  (previous  to  injection),  5106  cubic  centimeters. 
First  24  hours  after  injection,  . . 679’ 95  „ 

Second  „ ;,  . 436*0  „ 


Second  Injection.  (Grains  xxv.)  October  9,  1874. 

Total  Nitrogen  obtained. 

Average  of  2 days  (previous  to  injection),  452*37  cubic  cents. 
First  24  hours  after  injection,  . . 676*66  ,, 

Second  „ „ . . 723*75  „ 

Third  „ „ . . 592*665 

Fourth  „ „ . . 643*5  „ 

Fifth  „ . 486*6 


Third  Injection.  (Grains  viii.)  November  2,  1874. 

Total  Nitrogen  obtained. 

Average  of  6 days  previous  to  injection,  456*25  cubic  cents. 

24  hours  after  injection,  . . . 356*25  „ (Death.) 

(Perhaps  the  diminution  of  nitrogenous  excretion  in  this  case  may 
be  explained  in  some  extent  by  the  rapid  death  of  the  animal.) 


Fourth  Injection.  (Grains  viii.)  November  16,  1874. 


First  day,  previous  to  injection, 
Second 
Third 
Fourth 
Fifth 
Sixth 

First  24  hours  following  injection, 
Second  „ „ 

Third  „ 


55  5 5 

5'  55 

5?  55 

55  55 


Total  Nitrogen  obtained. 


673*0  cubic  cents. 


467*6 

474*2 

531*2 

591*6 

300*0 

449*3 

440*0 

288*0 


55 

55 

55 


55 

55 


In  this  fourth  injection  there  was  some  diarrhoea  on  the  5th  day, 
and  this  reduced  the  nitrogenous  excretion  on  the  6th  day,  and  so 
the  rise  after  the  injection  is  not  so  well  seen. 


530 


Proceedings  of  the  Royal  Society 
Fifth  Injection.  (Grains  xxiv.)  November  21,  1874. 


Average  of  3 days  previous  to  injection, 
First  24  hours  after  injection, 

Second  „ ,,  . 

Third  „ „ 

Fourth  „ „ . 


Total  Nitrogen  obtained. 

333*36  cubic  cents. 

666*38 

763*14 

945*0 

881*9  ,,  (Death.) 


The  weights  of  the 
follows  : — 

First  injection, 
Second  „ 
Third  „ 
Fourth  „ 
Fifth  ,, 


these  injections  were  as 

2 lbs.  2 oz. 

2 lbs. 

1 lb.  If  oz. 

1 lb.  7 oz. 

1 lb.  4 oz. 


animals  used  for 


In  the  6th  and  7th  injections  there  was  such  watery  diarrhoea 
that  the  urine  could  not  be  collected  separately,  and  thus  the 
results  of  analysis  were  not  to  be  depended  upon.  In  the  other 
cases  the  urine  was  not  submitted  to  nitrogenous  analysis. 

It  might  be  stated  as  an  objection,  that  as  the  bile  acids  were 
found  in  the  urine,  and  as  they  contained  much  nitrogen,  they 
gave  off  this  nitrogen  when  treated  with  hypobromite  of  soda 
solution,  and  thus  increased  the  nitrogen  of  the  urine.  No  doubt 
this  is  true,  but  only  to  a very  limited  extent ; for  when  the  biliary 
solutions  used  were  separately  analysed  to  ascertain  how  much 
nitrogen  they  gave  off,  it  was  seen  to  be  so  small,  that  even  were 
the  whole  solution  injected  excreted  during  the  next  twenty-four 
hours,  it  would  be  utterly  insufficient  to  account  for  so  great  a rise 
in  the  quantity  of  nitrogen  as  was  seen  to  take  place  after  the  5th 
injection. 

Nervous  System. — Each  injection  of  bile  salts  is  usually  followed 
by  drowsiness.  In  cases  which  are  to  end  fatally  this  deepens,  and 
the  animal  at  last  becomes  almost  comatose.  In  this  state  the 
animal  sleeps  nearly  the  whole  day,  rouses  up  if  touched,  but 
merely  moves  a little,  and  again  falls  asleep.  Convulsions  were 
never  noticed,  but  they  might  have  been  overlooked,  as  the  animals 
never  happened  to  be  under  observation  at  the  time  of  death. 


531 


of  Edinburgh,  Session  1874-75. 

The  pupil  never  showed  any  particular  change. 

Let  us  now  turn  to  a consideration  of  the  Pathological  appear- 
ances noticed  after  death.  Out  of  four  fatal  cases  these  appearances 
were  only  seen  in  three,  as  the  other  animal  died  so  rapidly  as  not 
to  permit  of  their  development.  The  lesion  seemed  to  be  confined 
to  the  liver  and  kidney,  and  was  of  the  following  nature : — 

The  Liver  was  of  natural  size,  but  congested,  and  throughout  its 
substance  were  scattered  numerous  small  white  patches,  which 
contrasted  well  with  the  dark  red  colour  of  the  rest  of  the  organ. 
The  borders  of  these  patches  were  seldom  or  never  well  defined, 
but  the  lesion  seemed  to  affect  particular  lobules.  On  removing  a 
small  piece  from  one  of  those  white  portions  of  a fresh  liver,  and 
teasing  it  out,  one  could  easily  see  with  the  microscope  that  the 
liver  cells  were  altered,  swollen,  with  an  irregular  outline,  and  full 
of  minute,  highly  refractive  granules.  The  nucleus  was  in  some 
cases  obscured,  in  others  more  distinct  than  usual.  There  could 
also  be  seen  what  were  evidently  the  remains  of  hepatic  cells,  a 
nucleus  surrounded  by  a mass  of  fine  oil  globules,  with  perhaps  the 
trace  of  a cell-wall  on  one  side.  If,  on  the  other  hand,  a portion 
of  the  more  healthy  tissue  be  examined,  liver  cells  approaching 
very  closely  to  the  normal  can  be  seen. 

After  hardening  in  alcohol,  or  in  chromic  acid  %),  sections  of 
this  liver  structure  may  be  made,  but  the  changes  described  are  not 
nearly  so  well  seen  then  as  in  fresh  specimens.  This  change  in 
the  hepatic  tissue  is  not  merely  a fatty  infiltration,  such  as  takes 
place,  to  a limited  extent,  normally  after  each  meal,  but  a true 
fatty  degeneration.  Had  it  been  mere  infiltration  the  lesion  would 
have  been  general,  and  not  confined  to  particular  regions  of  the 
organ ; the  oil  would  have  been  in  larger  globules,  and  not  in  the 
fine  molecular  form  seen  in  these  specimens;  and  the  hepatic 
cells  would  not  have  been  broken  down. 

The  Kidneys  were  of  natural  size,  but  rather  pale  and  flabby. 
When  a transverse  section  is  made  across  the  tubules,  the  epi- 
thelium lining  then  is  seen  to  be  granular  and  swollen,  sometimes 
to  such  an  extent  as  to  block  up  the  tubule.  In  order  to  distinguish 
clearly  that  the  obstruction  in  the  tubules  is  composed  of  swollen 
epithelium,  it  is  necessary  to  prepare  the  sections  and  render  them 
transparent  by  treatment  with  oil  of  cloves.  When  this  has  been 

3 z 


VOL.  VIII. 


532  Proceedings  of  the  Royal  Society 

ilone  the  epithelial  cells  lose  their  granular  appearance,  and  their 
outlines  can  be  more  readily  traced.  In  a favourable  specimen  you 
may  then  see  clearly  the  slight  spaces  between  each  cell  converg- 
ing towards  the  centre  of  the  tubule,  the  interstices  taking  some- 
what the  appearance  of  a leech  bite. 

In  other  tubules  the  same  appearance  may  be  seen  in  a more 
modified  degree — the  cells  swollen,  but  not  to  such  an  extent  as 
entirely  to  block  up  the  tubule.  In  other  parts  of  the  section 
tubules  may  be  seen  entirely  denuded  of  their  epithelium.  In 
longitudinal  sections  these  appearances  cannot  be  so  well  seen. 

A consideration  of  these  facts  leads  to  the  following  conclu- 
sions : — 

I.  That  a mixture  of  glycocholate  and  taurocholate  of  soda 
when  injected  hypodermically,  in  rabbits,  in  doses  of  40  grains 
and  under,  does  not  cause  any  immediate  disturbance,  but  is  almost 
always  fatal  (unless  the  dose  be  small)  in  a period  varying  from 
30  hours  to  3 or  4 days. 

II.  That  such  injections  often  cause  an  increased  nitrogenous 
excretion  by  the  urine. 

III.  That  such  injections  frequently  cause  diarrhoea. 

IV.  That  such  injections  are  followed  by  an  excretion  of  a small 
amount  of  bile  acid  by  the  urine  invariably,  and  in  some  cases  that 
bile  figment  is  also  so  excreted. 

V.  That  such  injections  are  followed  by  a fatty  degeneration  of 
the  hepatic  secreting  cells,  and  of  the  renal  epithelium. 

VI.  That  such  injections  cause  a destruction  of  red  blood 
corpuscles,  and  consequently  an  apparent  increase  of  the  white. 

VII.  That  such  injections  are  frequently  followed  by  drowsiness 
and  somnolence. 

It  would  be  out  of  place  to  attempt  to  give  here  a detailed  account 
of  the  bearing  which  those  results  may  have  on  liver  disease.  It 
may,  however,  be  right  to  indicate  in  a brief  way  a few  of  those 
points  which  seem  to  be  of  special  clinical  interest. 

And,  first,  in  regard  to  phosphorus  poisoning , where  the  liver, 
kidneys,  and  muscular  fibre  become  fatty.  No  true  analogy  can  be 
traced  between  the  results  of  these  experiments  and  this  disease, 


533 


of  Edinburgh,  Session  1874-75. 

because  in  poisoning  with  phosphorus  the  lesion  is  fatty  infiltra- 
tion, and  not  degeneration  (according  to  Niemeyer).  There  is  then 
only  an  apparent,  not  a real  similarity  between  the  two  conditions. 

Disintegration  of  the  hepatic  tissue  has  been  occasionally  observed 
to  follow  obstruction  of  the  bile  duct.  Frerichs  has  recorded  such 
a case,  but  he  does  not  think  that  this  result  can  be  owing  to  re- 
tention of  bile  in  the  system;  for  in  some  cases  where  the  bile 
duct  was  undoubtedly  obstructed,  disintegration  of  the  hepatic  tissue 
did  not  occur.  But  it  should  be  remembered  that  the  bile,  though 
prevented  from  reaching  the  intestine,  may  yet  be  excreted  by  the 
urine.  Hence  in  cases  where  the  kidneys  are  acting  rightly  no 
poisonous  effects  need  be  produced.  But  if,  owing  to  any  cause, 
the  urinary  secretion  be  interfered  with  (as  seems  to  have  been  the 
case  in  the  instance  Frerichs  refers  to),  then  the  bile  will  accumu- 
late in  the  system,  and  produce  its  toxic  effects.  In  cases  of 
jaundice,  Graves  states*  that  he  was  always  uneasy  as  to  the  issue 
when  nervous  symptoms  showed  themselves, — symptoms,  moreover, 
which  he  remarked  were  often  coincident  with  a diminished  secretion 
of  urine. 

But  perhaps  the  most  important  bearing  of  the  results  of  these 
experiments  is  upon  acute  yellow  atrophy  of  the  liver.  In  this 
disease  there  is  a rapid  fatty  degeneration  of  the  hepatic  tissue, 
and  of  the  epithelium  of  the  kidney.  In  some  cases  the  fatty 
change  is  universal  through  the  whole  of  the  liver  substance,  but 
in  other  cases  the  altered  appearance  is  only  seen  in  isolated 
portions. 

Now  it  seems  clear  from  these  experiments  that  the  mere  reten- 
tion of  bile  acids  in  the  system  will,  if  long  enough  continued, 
produce  exactly  similar  changes  in  these  organs.  It  may  be  pre- 
mature to  argue  from  this  that  the  appearances  seen  in  acute  yellow 
atrophy  are  invariably  produced  by  biliary  retention,  but  that  they 
may  be  so  produced  is  certainly  true,  and  so  far  as  these  experi- 
ments go  they  point  to  that  conclusion. 

Assuming  this  to  be  correct,  it  will  be  for  consideration  how  far 
the  jaundice,  seen  in  this  disease,  may  be  the  cause  and  not  the 
consequence  of  the  hepatic  lesion,  and  whether  the  efforts  of  the 
physician  should  not  be  directed  more  strenuously  than  heretofore 
* Trousseau’s  “ Clinical  Medicine,”  vol.  iv.  p.  305. 


534  Proceedings  of  the  Roycd  Society 

towards  the  rapid  removal  from  the  system  of  the  accumulated  bile 
salts. 

N.B . — While  this  investigation  was  being  carried  out,  and  after 
the  first  specimen  of  the  peculiar  fatty  degeneration  had  been 
obtained,  there  appeared  in  Robin’s  “ Journal  de  l’Anatomie  et  de  la 
Physiologie  ” for  December  1874  an  account  of  similar  experiments 
by  MM.  Felz  and  Ritter,  professors  in  Nancy.  These  gentlemen 
remarked  the  same  structural  changes  in  the  liver  and  kidneys  as 
have  just  been  described.  They  also  noticed  the  diarrhoea  which 
follows  the  injection,  and  a slight  increase  in  the  nitrogen  elimin- 
ated by  the  urine.  On  some  points,  however,  their  results  are  at 
variance  with  those  recorded  in  this  paper. 

While  the  priority  in  this  investigation  belongs  without  question 
to  MM.  Feltz  and  Ritter,  yet  it  will  be  seen  from  the  dates  of  the 
above  experiments  that  the  most  important  results  were  obtained 
previous  to  the  appearance  of  their  valuable  paper. 

4.  Preliminary  Note  on  the  Auatomy  of  the  Pia  Mater. 

By  Dr  J.  Batty  Tuke. 

5.  Note  on  the  Physiological  Action  of  Light.  By 
James  Dewar,  Esq.,  and  Dr  M‘ Kendrick. 

The  following  Gentlemen  were  elected  Fellows  of  the 
Society : — 

John  Christie,  Esq.,  Cowden,  Dollar. 

James  Thomson,  Esq.,  LL.D.,  University,  Glasgow, 

Michael  Scott,  Memb.  Inst.  C.E. 

William  Jack,  M.A.,  Glasgow. 

James  Bryce,  M.A.,  LL.D. 


A ballot  having  been  taken,  Dr  Alexander  Wood  was 
re-admitted  a Fellow  of  the  Society. 


of  Edinburgh,  Session  1874-75. 


585 


Monday , 17 th  May  1875. 

Professor  KELLAND,  Vice-President,  in  the  Chair. 

The  following  Communications  were  read : — 

1.  On  the  Expiatory  and  Substitutionary  Sacrifices  of  the 
Greeks.  By  Dr  Donaldson. 

The  author  gives  the  results  of  his  examination  of  the  subject  in 
the  following  propositions  : — 

1.  That  the  sacrifices  of  the  Greeks  were  offered  to  the  gods  with 
the  idea  that  the  food  and  drink  would  gratify  them,  and  that  the 
other  offerings  would  in  some  way  or  other  be  pleasing  to  them ; 
that  the  common  people  continued  to  offer  up  sacrifices  with  this 
belief  till  the  end  of  Paganism ; but  that  as  the  more  cultivated 
classes  came  to  believe  that  the  gods  did  not  stand  in  need  of  food, 
drink,  or  of  gifts  from  them,  substitutions  became  more  and  more 
general  with  them. 

2.  That  certain  sacrifices  were  intended  to  appease  the  anger 
or  overcome  the  dislike  of  the  gods,  not  because  any  sin  had  been 
committed,  but  because  the  Greek  worshipper  was  not  sure  of  the 
disposition  of  the  special  god  towards  him,  and  believed  that  the 
wisest  course  was  to  conciliate  him. 

3.  That  no  expiatory  sacrifices  were  offered  up  simply  to  express 
repentance  for  sin  in  general,  but  they  were  always  occasioned  by 
some  offence  against  some  individual  god  or  gods;  that  in  these 
cases  care  must  be  taken  to  distinguish  between  the  purification 
and  the  sacrifice ; that  in  the  case  of  deliberate  murder  no  expia- 
tory sacrifice  was  permissible,  but  the  murderer  or  his  descendants 
must  suffer  death ; and  in  the  case  of  involuntary  murder,  the 
sacrifice  was  of  the  nature  of  a payment  of  damages. 

4.  That  there  is  no  instance  of  a human  sacrifice  in  Homeric 
times.  That  in  the  classical  times  the  one  or  two  allusions  really 
refer  to  mythical  times,  and  that  there  is  only  one  instance  of 
human  sacrifice  for  which  there  is  the  shadow  of  historical 
evidence;  that  the  evidence  for  this  human  sacrifice  breaks  down 
completely  on  close  examination,  and  thus  we  have  the  fact  that 


536  Proceedings  of  the  Boyal  Society 

there  is  no  clear  proof  that  one  human  sacrifice  was  ever  offered 
up  in  G-reece  during  the  historical  period.  We  have,  on  the  con- 
trary, abhorrence  of  such  sacrifices  frequently  expressed.  Herodotus 
denounces  human  sacrifices  as  an  unholy  deed  (jrprjyfxa  ovk 
octlov).  iEschylus  and  Euripides  * employ  language  of  utmost 
detestation  against  it.  The  Delphic  oracle  calls  it  a foreign 
practice.  Pausanias  and  Porphyrius  deem  it  barbarous.  And 
Sextus  Empiricus,  contrasting  the  different  feelings  of  mankind  in 
regard  to  the  same  acts,  says  of  the  G-reeks, — “ But  we  think  that 
the  temples  are  polluted  by  human  blood.”t  The  same  Greek 
detestation  of  human  sacrifices  is  embodied  in  the  tradition  that 
Heracles  gained  renown  by  doing  away  with  human  sacrifice  in 
various  parts  of  the  world  .J 

5.  That  there  is  no  satisfactory  proof  that  the  G-reeks  at  any  time 
or  in  any  place  were  in  the  habit  of  offering  up  human  sacrifices. 
Certain  rites  may  find  an  explanation  in  the  supposition  that 
human  sacrifices  were  at  an  early  period  offered  up ; but  there  is 
no  historical  testimony  to  show  that  the  practice  ever  existed. 
And  even  in  the  cases  where  the  practice  may  by  some  be  regarded 
as  the  best  explanation  of  the  rite,  we  have  not  a genuine 
Greek  race.  The  ceremonial  on  Mount  Lycseus  was  Pelasgic.  And 
the  Agrionia  and  the  sacrifices  of  the  Athamantidse  are  connected 
with  the  Minyan  Orchomenos,  the  seat  of  Pelasgic  worship.  So 
that  we  should  have  in  these  three  cases  the  traditions  of  the  wor- 
ship of  the  race  which  preceded  the  Hellenes,  if  we  were  to  base 
any  conclusion  on  the  unsatisfactory  information  which  we  have 
in  regard  to  them.  And  there  are  really  no  other  decided  cases  of 
what  can  be  regarded  as  survivals. 

6.  That  the  writers  of  the  third  period,  influenced  by  the  belief 
that  the  ordinary  gods  of  the  G-reeks  were  demons  of  savage  pro- 
pensities, lent  a ready  ear  to  any  tale  of  horror  connected  with  their 
worship,  and  that  it  is  in  these  writers  that  we  hear  of  the  human 
sacrifices  of  the  G-reeks ; but  if  we  place  the  evidence  for  these 

* Welcker  thinks  that  human  sacrifices  were  attacked  by  Sophocles  in  his 
Athamas,  by  Achseus  in  his  Azanes,  and  possibly  by  Xenocles  in  his  Lycaon. 
— Die  Griechischen  Tragodien > vol.  iii.  p.  965. 

t Hyp.  iii.  24,  p.  209. 

t Welcker. — Griechische  Gotterlehre,  ii.  p.  769. 


537 


of  Edinburgh,  Session  1874-75. 

sacrifices  fairly  in  the  balance,  we  shall  find  it  not  so  strong  as  that 
which  could  be  adduced  to  prove  that  the  early  Christians  killed 
infants,  drank  their  blood,  and  indulged  in  indiscriminate  sexual 
intercourse.  And  yet  no  one  now  believes  these  accusations 
against  the  Christians. 

In  fact,  the  G-reeks  were  strangers  to  the  idea  of  sin  until  the 
introduction  of  Stoicism,  as  Sir  Alexander  Grant  has  well  shown  in 
his  Aristotle,  and  it  is  likely  that  the  idea  was  not  present  to  the 
minds  of  the  earlier  Stoics.  There  is  therefore,  as  it  seems  to  me, 
no  analogy  between  the  sacrifices  of  the  G-reeks  and  the  sacrifice  of 
G-olgotha.  The  sacrifice  of  Christ  is,  as  Dr  Crawford  has  admir- 
ably brought  out  in  his  “ Mysteries  of  Christianity,”  p.  230, 
“ exceptional  and  unique.”  But  in  the  deeper  meaning  of  sacrifice, 
the  essence  of  which  is  self-renunciation,  there  is  a striking 
parallelism  between  most  of  the  G-reek  mythical  sacrifices,  includ- 
ing also  the  more  or  less  historical  voluntary  deaths  of  Codrus  and 
Leonidas,  and  the  sacrifice  of  Christ.  The  oracle  decrees  that  what 
is  noblest,  and  most  beautiful,  and  most  fair  must  perish.  The 
noblest  and  the  fairest  offer  themselves  up  for  their  country,  and 
present  to  their  country  the  most  beautiful  sacrifice  that  can  be 
offered — a pure  human  soul.  And  in  like  manner  the  sacrifice  of 
Christ,  not  indeed  devoted,  like  the  Grreek  sacrifices,  to  a single 
land,  but  offered  up  for  the  whole  world,  is  an  act  of  obedience  to 
the  will  of  G-od,  and  an  infinitely  grand  exemplification  of  that 
self-renunciation  which  constitutes  the  essence  of  all  true  religion. 

2.  The  Placenta  in  Ruminants. — a Deciduate  Placenta. 

By  Professor  Turner. 

All  zoologists,  who  have  accepted  the  placental  system  of  classifi- 
cation of  the  Mammalia,  agree  in  placing  the  Ruminantia  amongst 
the  Indeciduata. 

As  is  well  known,  the  foetal  portion  of  the  placenta  in  Ruminants 
consists  of  a number  of  distinct  cotyledons.  Each  cotyledon  is 
composed  of  numerous  branched  villi,  which  fit  into  pits  or  depres- 
sions situated  in  mound-like  elevations  of  the  wall  of  the  uterus, 
called  the  maternal  cotyledons.  It  is  generally  believed,  that  in 
the  process  of  parturition  in  these  animals,  the  foetal  villi  are 


538  Proceedings  of  the  Royal  Society 

drawn  out  of  the  maternal  pits  without  removing  any  of  the  mater- 
nal substance  along  with  them,  just  as  the  fingers  are  drawn  out  of 
a glove  without  any  portion  of  the  substance  of  the  glove  accom- 
panying them,  so  that  the  placenta  is  non-deciduate. 

Having  been  engaged  in  the  study  of  the  structure  of  the  pla- 
centa in  the  undelivered  cow  and  sheep,  it  seemed  to  me,  from  the 
mode  in  which  the  foetal  villi  divided  into  branches,  and  from  the 
consequent  subdivision  of  the  maternal  pits  into  smaller  branching 
compartments,  that  the  interlocking  of  the  foetal  and  maternal 
tissues  with  each  other  was  so  great  as  to  render  it  difficult,  if  not 
impossible,  for  the  foetal  villi  to  be  forcibly  expelled  from  the 
maternal  cotyledons,  without  carrying  away  with  them  some  of  the 
uterine  tissue.  With  the  object  of  testing  the  accuracy  of  this  sup- 
position, I procured,  in  the  spring  of  the  present  year,  the  foetal  mem- 
branes, separated  in  normal  parturition,  both  of  the  cow  and  sheep, 
and  submitted  the  foetal  cotyledons  to  microscopic  examination. 

Before  describing  the  microscopic  appearances,  it  may  be  advis- 
able to  say  a few  words  on  the  general  arrangement  of  the  cotyle- 
dons, both  foetal  and  maternal,  in  these  animals. 

I shall  first  describe  the  arrangements  in  the  sheep  from  a 
specimen  where  the  cotyledons  were  well  developed. 

In  this  animal  the  maternal  cotyledons  projected  as  cup-shaped 
mounds  from  the  uterine  wall.  They  were  covered  on  the  outer 
convex  surface  by  the  uterine  mucosa,  which  was  prolonged  as  far 
as  the  free  inverted  edge  of  the  cup.  The  inner  surface  of  the  coty- 
ledon was  composed  of  a soft,  spongy  material,  containing  numerous 
pits,  which  extended  almost  vertically,  and  divided  as  they  passed 
deeper  into  its  substance,  into  smaller  compartments,  which  radiated 
towards  the  outer  wall  of  the  cotyledon,  without  diverging  much 
from  each  other.  The  pits  were  lined  by  well-marked  cells,  most 
of  which  were  irregular  in  shape,  polygonal,  ovoid,  or  even  some- 
what caudate,  and  of  considerable  size,  though  some  few  were  like 
modified  columnar  cells.  They  consisted  of  granular  protoplasm, 
in  which  one,  two,  or  sometimes  three,  well-defined  ovoid  or  elliptical 
nuclei  were  imbedded,  but  without  a cell- wall.  Not  unfrequently 
the  outline  of  the  individual  cells  was  very  indistinct,  and  they 
seemed  as  if  composed  of  a layer  of  protoplasm  studded  with  nuclei. 

The  cells  rested  on  a highly  vascular  sub-epithelial  connective 


539 


of  Edinburgh,  Session  1874-75. 

tissue,  which  formed  the  proper  wall  of  the  pits.  The  mucous 
membrane  investing  the  cotyledon  was  continuous  at  the  mouth  of 
the  cup  with  the  walls  of  the  pits  in  the  spongy  tissue,  so  that 
the  cells  lining  the  pits  were  in  the  same  morphological  plane 
as  the  epithelium  covering  the  mucosa.  The  cotyledons  were 
highly  vascular.  Some  of  the  arteries  in  the  sub-cotyledonary 
connective  tissue  were  corkscrew-like  ; and  in  the  deeper  part 
of  the  cotyledon  itself  I have  seen  tortuous  vessels.  The 
greater  number  of  the  vessels  within  the  cotyledon  passed, 
however,  vertically  towards  the  surface  lying  in  the  connective 
tissue  walls  of  the  pits ; branching  repeatedly,  as  a rule  in  a dicho- 
tomous manner,  prior  to  forming  a compact  maternal  capillary 
plexus, — not  dilating  into  maternal  blood  sinuses. 

The  mucous  membrane  of  the  uterus  between  the  cotyledons 
contained  numerous  tortuous,  branched  tubular  glands.  Some  of 
these  extended  almost  vertically  to  the  surface,  and  could  be  seen 
in  almost  their  entire  length  in  vertical  sections — others  ran  more 
obliquely,  and  owing  to  their  tortuosity,  were  repeatedly  divided 
in  vertical  sections.  The  mouths  of  the  glands  could  readily  be 
seen  with  a pocket  lens  opening  on  the  surface,  the  orifice  being 
partially  surrounded  by  a minute  elevation  of  the  mucosa.  In  the 
mucosa  around  the  base  of  the  cotyledons,  a ring-like  series  of 
gland  openings  were  seen.  In  the  mucosa  covering  the  coty- 
ledons glands  were  also  present,  but  their  orifices  were  much 
stretched,  as  if  by  the  pressure  due  to  the  great  growth  of  the  sub- 
jacent spongy  tissue  of  the  cotyledon.  The  sub-epithelial  connec- 
tive tissue  in  which  the  glands  lay,  was  not  by  any  means  so  vascu- 
lar as  that  which  formed  the  walls  of  the  pits  within  the  cotyledons. 
In  some  sections  through  the  cotyledons  and  adjacent  mucosa  no 
glands  were  to  be  seen  in  the  connective  tissue  intervening  between 
the  cotyledon  and  muscular  wall,  but  they  were  collected  in  consider- 
able numbers  around  the  cotyledon,  as  if  pushed  outwards  by  its 
rapid  growth.  In  other  sections,  however,  tubular  glands  were  seen 
in  the  sub-cotyledonary  connective  tissue ; but  they  seemed  to  be 
the  deep  ends  of  the  branching  glands,  the  stems  of  which  may 
have  inclined  obliquely,  so  as  to  open  on  the  surface  of  the  mucous 
membrane  covering  the  cotyledon.  None  of  these  subjacent  glands, 
or  those  situated  on  the  surface  of  the  cotyledon,  were  seen  to  open 

4 a 


VOL.  VIII, 


540  Proceedings  of  the  Royal  Society 

into,  or  in  any  way  to  communicate  with,  the  pits  within  the  coty- 
ledon itself. 

The  foetal  cotyledons  consisted  of  numerous  villi,  which  collec- 
tively formed  a hall-like  mass,  occupying  the  concavity  of  the 
maternal  cotyledon.  Each  villus  consisted  of  a main  stem,  which 
gave  off  a tuft  or  cluster  of  spatulate  branches.  The  villi  entered 
the  maternal  pits  and  branched  along  with  them,  so  that  every 
compartment  was  occupied  by  a branch  of  the  villus ; hut  there  was 
necessarily  no  great  divergence  of  these  branches  from  the  main 
stem.  At  their  deeper  end  these  spatulate  branches  gave  off 
slender  terminal  offshoots.  The  villi  were  formed  of  gelatinous 
connective  tissue,  in  which  very  distinct  fusiform  and  stellate  cor- 
puscles were  arranged  in  an  anastomosing  network.  At  the  peri- 
phery of  the  villus  was  a layer  of  flattened  cells,  with  small  but 
distinct  nuclei  arranged  so  as  to  form  an  epithelial-like  investment. 
The  umbilical  vessels  ramified  within  the  villus  and  formed  net- 
works of  capillaries.  The  villi  were  in  close  contact  with  the 
epithelial  cells  lining  the  maternal  pits.  Owing  to  the  inversion  of 
the  free  edge  of  the  maternal  cotyledon  and  the  radiated  arrange- 
ment of  the  pits,  with  their  contained  villi,  it  was  impossible  to 
disengage  the  maternal  and  foetal  cotyledons  from  each  other  with- 
out drawing  away  with  the  foetal  villi  portions  of  the  maternal 
cotyledon.  I invariably  found  that,  in  drawing  the  foetal  villi  out 
of  their  compartments,  flakes  of  epithelial  cells  accompanied  them, 
which  showed  how  readily  this  element  of  the  maternal  tissue  is 
shed.  During  parturition,  however,  when  the  parts  are  relaxed, 
the  disengagement  of  the  two  structures  is  necessarily  more  easily 
accomplished. 

In  the  cow  the  maternal  cotyledons  differed  in  form  from  those 
in  the  sheep.  They  were  fungiform  or  umbrella-shaped,  and  were 
connected  to  the  uterine  wall  by  a broad  neck,  around  which  the 
uterine  mucosa  was  prolonged  as  far  as  the  border  of  the  umbrella. 
The  whole  convex  surface  of  the  cotyledon  was  riddled  with  pits, 
which  passed  vertically  into  its  spongy  substance,  and  divided  into 
smaller  compartments  in  the  deeper  part  of  the  cotyledon.  Pro- 
jecting from  the  wall  of  each  pit  were  delicate  bands,  visible  to 
the  naked  eye,  arranged  as  a rule  in  a vertical  direction,  and  in  the 
intervals  between  these  bands  the  wall  was  perforated  by  nume- 


541 


of  Edinburgh,  Session  1874-75. 

rous  orifices,  easily  seen  with  a pocket  lens,  which  were  the 
months  of  depressions  or  crypts  in  the  wall  of  the  pit,  some  lying 
almost  at  right  angles,  others  obliquely  to  the  wall  of  the  pit  itself. 
The  pits,  with  their  numerous  crypts,  were  lined  by  epithelial 
cells,  similar  in  character  to  those  of  the  sheep,  and  these  cells 
rested  on  a highly  vascular  connective  tissue,  in  which  the  mater- 
nal capillaries  formed  a compact  network.  But  I should  state  that 
in  the  cow  a larger  proportion  of  these  cells  had  preserved  the 
columnar  form  of  the  epithelium  of  the  non-gravid  uterine  mucosa. 

The  surface  of  the  uterine  mucosa  between  the  cotyledons  pre- 
sented the  mouths  of  the  tubular,  branched,  utricular  glands,  which 
extended  more  obliquely  to  the  surface  than  in  the  sheep,  so  that 
in  vertical  sections  through  the  membrane  they  were  frequently  cut 
through  and  divided ; segments  of  each  gland  were  as  a rule  seen, 
though  sometimes  the  stem  of  a gland  mounted  to  the  surface  to 
open  by  an  obliquely-directed  orifice.  Gflands  were  also  present  in 
the  connective  tissue  forming  the  neck  of  the  cotyledon,  but  none 
were  seen  to  communicate  with  the  pits. 

The  foetal  cotyledons  were  situated  on  the  umbrella-shaped 
maternal  cotyledons,  and  their  numerous  villi  occupied  the  pits. 
The  stems  of  the  villi  were  comparatively  large,  and  studded  with 
multitudes  of  minute  tufts,  which,  arising  obliquely  or  almost  at 
right  angles  to  the  main  stem,  entered  and  occupied  the  crypts. 
The  minute  villi  forming  these  tufts  were  so  slender  and  filiform 
that  each  terminal  offshoot  contained  only  a single  capillary  loop. 
The  villi  were  in  contact  with  the  epithelium  cells,  and  in  drawing 
them  out  of  the  pits,  more  especially  in  drawing  the  tufts  out  of  the 
crypts,  multitudes  of  the  lining  epithelial  cells  came  away  with  them. 
From  the  differences  in  shape  of  the  maternal  cotyledon  in  the 
cow  and  in  the  sheep,  there  is  not  the  same  difficulty  in  unlocking 
the  foetal  from  the  maternal  placenta  in  the  former  animal  as  in 
the  latter. 

For  the  purpose  of  studying  the  shed  placenta  of  the  sheep,  I 
procured  the  after-birth  from  the  ewe  as  soon  as  it  was  passed,  and 
immersed  it  in  strong  spirit.  Some  foetal  tufts  were  then  exa- 
mined without  any  other  preparation ; but  others  were  immersed  in 
glycerine  jelly,  so  as  to  bind  the  several  constituents  of  the  tuft 
together.  Thin  slices  were  then  removed  from  the  hardened  tufts, 


542  Proceedings  of  the  Royal  Society 

whilst  from  others  small  portions  were  taken  and  teezed  out  with 
needles.  In  the  examination,  a magnifying  power  of  320  diameters 
was  employed.  Quantities  of  cells,  having  the  form  and  appearance 
of  the  epithelial  cells  already  described,  were  seen  to  be  inter- 
mingled with  the  foetal  villi.  In  some  cases  small  patches  of  cells 
were  seen  lying  free  in  the  spaces  between  the  villi,  but  more  fre- 
quently the  cells  were  isolated.  In  a few  instances  I saw  groups  of 
such  cells  in  immediate  contact  with  the  terminal  villi,  as  if  they, 
in  being  drawn  out  of  the  compartments  in  the  maternal  cotyledon, 
had  pulled  an  envelope  of  epithelial  cells  along  with  them. 

When  the  cotyledons  of  the  shed  placenta  of  the  cow  were 
examined  microscopically,  quantities  of  granular  debris  were  to  he 
seen  floating  in  the  fluid  in  which  the  specimens  were  placed. 
Along  with  these  granules  were  small  flakes  of  protoplasm;  rounded 
or  ovoid  bodies,  with  distinct  outlines  looking  like  free  nuclei ; and 
large  cells  composed  of  granular  protoplasm,  containing  one,  two, 
or  three  nuclei,  having  the  anatomical  characters  of  maternal  epi- 
thelial cells. 

The  amount  of  debris  and  of  decidua  cells  varies  considerably  in 
the  different  slides  which  I examined;  in  some  being  so  abundant 
as  to  render  the  fluid  in  which  the  specimen  was  examined  quite 
turbid,  whilst  in  others  only  slight  traces  were  to  be  recognised. 

From  these  observations  I am  of  opinion  that,  both  in  the  sheep 
and  cow,  the  cotyledons  of  the  foetal  placenta  carry  away  with 
them,  during  the  act  of  parturition,  a portion  of  the  maternal  struc- 
ture, so  that  in  these  animals,  and  presumably  in  other  ruminants, 
the  placenta  is  deciduate.  So  far  as  my  observations  have  gone,  I 
have  only  detected  the  epithelial  element  of  the  uterine  mucosa,  or 
the  cells  of  the  decidua  serotina,  intermingled  with  the  foetal  villi; 
but  from  the  bloody  state  of  the  external  parts  of  the  ewe,  for  some 
hours  after  the  birth  of  the  lamb,  I think  it  not  improbable  that 
the  disruption  of  some  of  the  maternal  cotyledons  has  been  deeper 
than  a mere  epithelial  shedding, — that  the  maternal  vessels  have, 
in  some  places  at  least,  been  torn  across,  so  as  to  give  rise  to  the 
haemorrhage. 

From  the  observations  which  I have  made  on  the  structure  of 
the  placenta  in  many  of  the  Mammalia,  both  in  the  deciduata  as 
well  as  in  the  so-called  non-deciduata,  I am  of  opinion  that  the 


of  Edinburgh,  Session  1874-75. 


543 


shedding  or  non-shedding  of  maternal  tissue,  along  with  the  foetal, 
during  the  act  of  parturition,  is  determined  by  the  degree  of  inter- 
locking of  the  foetal  and  maternal  portions  of  the  organ  during 
the  formation  of  the  placenta,  and  not  from  the  presence  in  the 
deciduata  of  a structure  or  structures  which  do  not  exist  in  the 
non-deciduata.  In  both  forms  the  same  anatomical  elements 
exist,  though,  as  in  the  case  of  the  human  placenta,  the  maternal 
constituents  may  become  so  modified  in  arrangement  as  greatly  to 
obscure  their  original  characters.  The  foetal  part  of  the  placenta 
consists  of  a chorion  more  or  less  perfectly  covered  with  vascular 
villi:  the  maternal  part  consists  of  a modified  uterine  mucosa,  the 
surface  of  which  is  composed  of  the  modified  epithelial  cells  of  the 
mucous  membrane,  beneath  which  is  a highly  vascular  connective 
tissue,  the  modified  sub-epithelial  connective  tissue  of  the  mucosa. 

In  those  animals  in  which  the  chorion  remains  almost  entirely 
covered  by  villi,  as  in  the  pig,  mare,  and  cetacean,  the  villi  are  short, 
with  simple  branches,  and  the  depressions,  pits,  or  crypts  in  the 
uterine  mucosa  for  their  reception  are  consequently  shallow.  Dur- 
ing the  act  of  parturition  the  villi  are  so  readily  liberated  from  the 
uterine  crypts  that  no  maternal  tissue  is  necessarily  shed  along  with 
them,  though  even  here  it  is  not  difficult  to  see  that,  should  the 
epithelial  serotina  from  any  cause  become  detached  from  the  sub- 
epithelial  connective  tissue,  flakes  of  it  might  pass  off  along  with 
the  villous  chorion.  In  the  zono-  and  disco-placentary  mammals, 
where  the  villi  are  much  longer,  and,  as  a rule,  much  more  exten- 
sively branched,  the  constituents  of  the  mucosa,  both  epithelial 
and  sub-epithelial,  are  so  intermingled  with  the  foetal  villi  in  the 
region  of  the  placenta  as,  as  is  generally  admitted,  to  be  shed  along 
with  them.  The  ruminants,  therefore,  with  their  scattered  coty- 
ledons, are  seen  to  occupy,  as  regards  deciduation,  an  intermediate 
position  between  the  animals  with  a diffused  placenta  on  the  one 
hand,  and  the  zono-  and  disco-placentary  mammals  on  the  other; 
for  whilst  the  former  are  apparently  non-deciduate  during  the  act 
of  parturition,  and  the  latter  part  with  both  the  epithelial  and  the 
vascular  sub-epithelial  constituents  of  the  uterine  mucosa  in  the 
placental  area,  the  ruminants  shed,  as  a rule  at  least,  only  the 
epithelial  lining  of  the  uterine  pits  into  which  the  foetal  villi  are 
inserted. 


544  Proceedings  of  the  Royal  Society 

I have  hitherto  spoken  of  the  shedding  of  maternal  tissue  along 
with  the  foetal  during  the  act  of  parturition.  But,  to  prevent  mis- 
conception, it  may  be  well  to  state  that,  as  indeed  has  been  pointed 
out  by  Owen,*  by  Ercolani,f  and  by  myself, | in  a memoir  pre- 
viously submitted  to  this  Society,  if  not  during  parturition,  at  least 
afterwards,  all  placental  mammals  are  deciduate;  for  in  the  pig, 
mare,  and  cetacean,  “ during  the  period  of  involution  which  follows 
parturition,  it  is  obvious  that  great  changes,  either  from  actual 
shedding  of  portions  of  its  substance,  or  from  degeneration  and 
interstitial  absorption,  must  take  place  in  the  constituents  of  the 
crypt-layer  before  it  can  be  restored  to  its  proper  non-gravid  con- 
dition.” 

In  the  ruminants  also,  although  the  epithelial  cells  may  be 
the  only  constituent  of  the  uterine  mucosa  which  is  shed  during 
the  act  of  parturition,  yet,  after  that  act  is  accomplished,  the  thick, 
vascular,  spongy  tissue  of  the  maternal  cotyledon  must  disappea  x 
before  the  uterus  can  assume  its  normal  unimpregnated  aspect. 

It  will  be  observed  that  in  this  communication  I have  given  to 
the  term  deciduate  a more  extended  signification  than  has  usually 
been  attached  to  it  by  anatomists.  It  has  been  customary  to  con- 
sider a placenta  as  deciduate,  only  when  both  the  epithelium  and 
the  sub-epithelial  vascular  maternal  tissue  are  parted  along  with 
the  foetal  villi. § But  it  appears  to  me  that  even  when  the  epithelial 
lining  of  the  crypts  only  is  shed,  the  placenta  should  be  regarded 
as  deciduate,  inasmuch  as  there  is  a shedding  of  maternal  struc- 
ture, though,  of  course,  in  an  inferior  degree  to  one  in  which  the 
sub-epithelial  vascular  tissue  is  also  separated. 

3.  An  Essay  towards  the  General  Solution  of  Numerical 
Equations  of  all  Degrees.  By  W.  H.  Fox  Talbot,  Esq., 
Hon.  F.R.S.E. 

* The  Anatomy  of  Vertebrates,  vol.  iii.  p.  727.  1868. 

t Sur  les  Glandes  utriculaires  de  l’uterus,  &c.  Algiers,  1869. 

J Trans.  Roy.  Soc.  Edinburgh,  1871. 

g Huxley — Lectures  on  Comparative  Anatomy,  p.  10.  1864. 


of  Edinburgh,  Session  1874-75. 


545 


4.  Note  on  the  Electrical  Conductivity  of  Saline  Solutions. 
By  J.  G.  MacGregor,  M.A.,  B.Sc.  Communicated  by 

Professor  Tait. 

In  the  Sitzungsberichte  of  the  Munich  Academy,*  Professor  Beetz 
has  recently  published  a review  of  a paper  by  Mr  J.  A.  Ewing  and 
myself  on  “The  Electrical  Conductivity  of  certain  Saline  Solu- 
tions,” which  was  read  before  the  Royal  Society  of  Edinburgh 
during  the  session  of  1872-73,  and  is  published  in  their  Transac- 
tions.! I take  the  earliest  opportunity  of  discussing  the  strength 
of  the  arguments  on  which  his  criticisms  are  based.  Unfortunately, 
on  account  of  Mr  Ewing’s  being  at  present  in  South  America,  I am 
unable  to  communicate  with  him.  I alone  am  therefore  responsible 
for  the  contents  of  the  present  paper. 

Professor  Beetz  begins  by  characterising  the  short  reference 
which  we  made  to  his  valuable  work  on  the  conductivity  of  solu- 
tions of  zincic  sulphate  J as  a “ complete  series  of  mistakes.”  “ My 
only  precaution,”  he  writes,  “ against  polarisation  consisted,  then, 
in  the  use  of  amalgamated  zinc  electrodes  ! Whoever  has  read  and 
understood  my  paper,  must  know  that  the  plan  of  my  work  went 
beyond  the  experiments  with  zincic  sulphate  solutions,  that  it 
rather  consisted  in  finding,  by  a damping  method,  the  conduc- 
tivity of  electrolytes  generally,  relatively  to  that  of  a single  one.” 
We  are  accused  of  having  underrated  his  precautions  against 
polarisation  and  of  being  ignorant  of  the  scope  of  his  work.  There 
were  two  things  which  Professor  Beetz  set  himself  to  accomplish — 
(1.)  to  investigate  absolutely  the  conductivity  of  zincic  sulphate 
solutions ; and  (2.)  to  determine  relatively  to  it  that  of  other  elec- 
trolytes. The  first  part  he  has  carried  out,  and  his  researches  in 
this  field  are  generally  regarded  as  authoritative.  The  second 
part,  however,  he  has  not  carried  out.  He  made  use  of  two 
original  and  very  ingenious  methods  for  the  purpose,  but  both 
failed.  Of  one  he  says  himself,  “ Es  gelang  aber  nicht  brauchbare 
Ausschlage  zu  bekommen § and  of  the  other,  “ Auch  diese  Methode 
hat  mir  noch  keine  Besultate  geliefert .”  ||  Now,  however  one  may 

* Sitzungsberichte  der  Miinchener  Akademie,  6.  Februar,  1875,  pp.  59-70. 

f Trans.  Roy.  Soc.  Edin.,  vol.  xxvii.  part  1,  1872-73,  pp.  51-70. 

X Poggendorff’s  Annalen,  cxvii.  1862,  pp.  1-27. 

§ Ibid,  cxvii.  p.  26.  ||  Ibid,  p.  27. 


546 


Proceedings  of  the  Royal  Society 

admire  the  ingenuity  of  the  methods  which  he  employed,  it  is 
impossible  to  speak  of  them  as  having  been  productive  of  positive 
results,  and  unwarrantable  to  describe  them  as  methods  which  have 
increased  our  knowledge  of  this  department  of  Physics.  Hence 
we  did  not  mention  his  whole  plan,  nor  refer  to  all  the  methods  by 
which  he  endeavoured  to  carry  it  out,  but  confined  our  attention  to 
that  part  of  it  which  he  had  successfully  accomplished.  If  we  are 
justified  in  having  thus  restricted  our  remarks  to  really  fruitful  work, 
we  must  also  be  justified  in  having  given  as  his  only  precautions 
against  polarisation,  those  which  he  adopted  in  his  absolute 
measurements  of  the  sulphate  of  zinc.  Two  sentences  will  show 
what  these  were  : — “ If  we  only  knew  a combination  of  liquid  and 
electrodes,  in  which  the  electric  current  produces  neither  polaris- 
ation nor  new  resistances,  it  could  be  treated,  so  far  as  the 
measurement  of  resistance  is  concerned,  exactly  as  a solid  body.”  * 
Such  a combination  is  easily  obtainable,  for  “ through  du  Bois- 
Keymond’s  investigations  it  is  known  that  amalgamated  zinc 
electrodes  are  not  polarised  in  concentrated  solutions  of  zinc 
vitriol.”f  The  only  necessary  precaution  is  thus  found;  and,  as 
might  be  expected,  one  looks  in  vain  for  an  account  of  any  others. 
Of  course  he  made  his  solutions  as  pure  as  possible,  excluded  air, 
arranged  his  tube  so  that  it  would  always  be  full  of  liquid,  and  kept 
his  electrodes  in  the  same  positions ; but  these  were  not  directed 
immediately  against  polarisation.  His  only  precaution,  in  fact, 
was  the  only  necessary  one,  viz.,  the  use  of  non-polarisable 
electrodes. 

In  describing  Professor  Beetz’  work,  however,  we  fell  into  an 
error  by  assuming  that  pure  zinc  electrodes  are  not  polarisable  in 
solutions  of  zinc  vitriol,  and,  therefore,  regarding  it  as  remarkable 
that  he  should  have  taken  the  unnecessary  trouble  of  amalgama- 
tion ; and  the  same  error  is  seen,  as  he  points  out,  in  our  reference 
to  Paalzow’s  work,  in  which  we  say  that  he  used  pure  zinc 
electrodes,  while  in  reality  he  amalgamated  them.  This  is,  I 
think,  the  only  “ Wissensfehler”  of  which  we  can  be  convicted. 
As  an  error  it  is,  of  course,  to  be  regretted.  But  its  comparative 
triviality  is  shewn  by  the  fact  that  it  not  only  has  no  influence  on 
our  own  work,  but  does  not  even  affect  our  criticism  of  either  Pro- 

* Pogg.  Ann.  cxvii.  p.  3.  + Ibid.  p.  6. 


of  Edinburgh,  Session  1874-75. 


547 


lessor  Beetz  or  of  Paalzow.  In  the  case  of  the  former,  we  attri- 
buted to  the  electrodes  which  he  used  the  same  property  as  he  did 
himself,  and  in  the  case  of  the  latter  we  attributed  to  those  which 
we  described  him  as  having  used,  the  properties  which  belong  to 
the  ones  which  he  really  did  use.  Nevertheless,  Professor  Beetz 
thinks  that  we  did  not  understand  Paalzow’s  method.*  “ The 
authors,”  he  says,  “ call  this  method  4 very  ingenious/  4 Curiously 
enough  ! ’ for  they  did  not  understand  it  at  all.  If  they  only 
had,  how  ingenious  it  would  then  have  appeared  to  them.” 
He  comes  to  this  conclusion  because  he  thinks  that,  had  we  had 
a full  knowledge  of  Paalzow’s  apparatus,  we  could  not  have 
criticised  it  as  we  did.  All  that  is  necessary,  therefore,  for  me  to 
prove,  is  that  the  items  of  description  which  we,  for  shortness’  sake, 
omitted,  do  not  necessitate  a change  in  our  criticism.  Paalzow’s 
apparatus,  according  to  our  description,  consisted  of  two  glasses 
filled  with  sulphate  of  zinc  solution  and  joined  by  a bent  tube  con- 
taining the  solution  under  investigation,  the  electrodes  dipping 
into  the  zinc  sulphate.  Professor  Beetz  thinks  that  we  had  neither 
grasped  the  idea  that  the  tube  did  not  open  into  the  glasses  con- 
taining the  vitriol,  but  into  porous  clay  vessels  which  contained  the 
same  liquid  as  the  tube ; nor  understood  the  meaning  of  his  having 
made  two  or  more  measurements  of  the  same  solution  in  tubes  of 
different  lengths.  Do,  then,  these  facts  destroy  our  criticism  ? 
We  said  that  diffusion  of  the  liquids  must  be  a source  of  error,  and 
that  polarisation  at  the  surface  of  junction  might  be.  These 
dangers  are  not  excluded  even  when  the  clay  vessels  are  used.  Dif- 
fusion may  not  go  on  so  rapidly,  but  it  still  goes  on ; the  mixture 
which  must  take  place  constantly  changes  the  conductivity,  and 
(as  our  experiments  t shew)  possibly  to  a great  extent.  Moreover, 
there  are  still  surfaces  of  contact,  notwithstanding  the  intervention 
of  the  clay  vessels,  the  only  difference  being  that  instead  of  one 
large  one  there  are  numerous  small  ones;  and  there  is  still, 
therefore,  the  danger  of  polarisation  J without  the  possibility  of 
eliminating  its  effects  by  calculation.  The  clay  vessel  not  only 

* Monatsberichte  der  Berliner  Akademie,  30.  Juli,  1868.  p 486.  Pogg. 
Ann.  cxxxvi.  1869,  p.  489. 

t Trans.  Roy.  Soc.  Edin.,  vol.  xxvii.  part  1,  1872-73,  p.  67. 

t Monatsberichte  der  Berliner  Akademie,  17  Juli,  1856,  p.  1. 

VOL.  vui.  4 R 


548 


Proceedings  of  the  Royal  Society 

does  not  obviate  the  two  difficulties  already  cited;  it  may  also  intro- 
duce a new  one,  in  the  form  of  what  du  JBois-Reymond  calls  internal 
( innere ) polarisation.*  Nor  is  the  second  addition  to  our  descrip- 
tion more  destructive  of  the  accuracy  of  our  criticism  than  the  first. 
Professor  Beetz  thinks  that,  by  measuring  the  same  liquid  in  tubes 
of  different  lengths,  one  may  take  the  difference  of  their  resist- 
ances as  the  resistance  of  a column  of  liquid  whose  length  is  the 
difference  of  their  lengths.  But  this  can  only  be  the  case  on  the 
supposition  that  the  state  of  matters  at  the  junction  of  the  liquids 
is  the  same  for  both  determinations.  Now  diffusion  does  not  cease 
at  the  end  of  each  measurement  and  wait  until  the  next  begins. 
Nature  is  not  so  convenient.  Every  moment  adds  to  the  mixture 
of  the  solutions  and  changes  their  resistance.  If,  moreover,  there 
be  polarisation  at  the  surface  of  contact,  or  (clay  vessels  being 
used)  if  there  be  also  internal  polarisation,  it  must  begin  at 
zero  and  increase  from  the  first  moment  of  contact  up  to  the  time 
of  observation  (supposing  that  to  occur  before  the  maximum  is 
reached).  In  order  that  this  condition  may  be  the  same  for  both 
measurements,  the  observations  must  be  made  after  the  same  lapse 
of  time  from  the  first  moment  of  contact,  an  occurrence  which  is 
manifestly  improbable,  and,  if  it  should  happen,  impossible  to 
know.  It  is  true  that  a judicious  choice  of  electrolytes  may 
remove  one  or  more,  though  never  all,  of  these  sources  of  error ; 
but  such  a possibility  cannot  be  taken  into  consideration  in  dis- 
cussing Paalzow’s  as  a general  method;  while,  at  its  best,  as  a 
special  method,  it  has  always  the  defect  arising  from  the  mixture 
of  the  liquids.  How  great  or  how  small  the  error  arising  from 
mixture  and  polarisation  may  be,  it  is  difficult  to  say.  That  can 
only  be  decided  by  future  experiments.  But  it  is  clear  that  the 
error  remains,  and  that  the  method,  as  described  most  minutely,  is 
subject  to  the  same  criticism  as  in  its  simpler  form. 

Passing  from  Paalzow,  Professor  Beetz  proceeds  to  prove  that 
we  did  not  understand  Kohlrausch  and  Nippoldt’s  f work  any  better 

* Monatsberichte  der  Berliner  Akademie,  Aug.  4,  1856,  p.  15,  and  Jan.  31, 
1859,  p.  1. 

t Gottinger  Nachrichten,  Nov.  18,  1868,  p.  415.  Jahresbericht  des  phys. 
Vereins  zu  Frankf.  1867-68,  p.  71.  Pogg.  Ann.  cxxxviii.  1869,  pp.  280  and 
370. 


549 


of  Edinburgh,  Session  1874-75. 

than  that  just  discussed.  We  ourselves  are,  however,  to  a certain 
extent  responsible  for  this  judgment.  The  cause  of  his  misunder- 
standing is  the  careless  structure  of  our  description.  By  the  use 
of  a specific  term  in  the  second  sentence  instead  of  a generic,  the 
thermo-electric  currents  are  made  to  appear  to  have  been  used  as  a 
means  of  reducing  the  electromotive  force  of  the  magneto-electric 
currents,  while  in  reality  the  former  were  substituted  for  the  latter 
in  order  to  obtain  currents  of  low  as  well  as  of  high  electromotive 
force,  that  is,  to  reduce  the  electromotive  force  of  the  currents 
employed.  The  sentence  is  a parenthesis,  in  which  the  words 
“these  currents”  take,  from  the  structure  of  the  preceding  part  of 
the  description,  a narrower  meaning  than  they  were  intended  to 
have.  One  might  almost  have  expected  Professor  Beetz  to  dis- 
cover the  defect,  rather  than  adopt  the  supposition  of  belief  in  the 
reduction  of  the  electromotive  force  of  magneto-electric  currents  by 
means  of  a thermo-electric  pair. 

The  oasual  remark  that  the  resistance  of  either  a wire  or  a 
constant  cell  can  be  easily  measured,  Professor  Beetz  translates 
incorrectly,  and,  in  consequence,  criticises  unfairly.  We  did  not 
affirm  that  the  resistance  of  a galvanic  cell  is  quite  as  easy  ( ebenso 
leicht ) to  measure  as  that  of  a solid  body,  nor  did  we  mean  to  say 
that  there  is  yet  a perfect  means  of  measurement,  but  that  by 
Wheatstone’s  method  (in  our  reference  to  which  Galvanometer  is 
printed  Electrometer)  approximately  accurate  results  may  be  easily 
obtained.  Why  then  have  von  Waltenhofen  and  others  tried  to 
improve  upon  Wheatstone?  Simply  because  they  think  they  can 
reduce  the  already  greatly  diminished  sources  of  error,  or  because 
they  wish  to  have  a method  applicable  to  both  constant  and  incon- 
stant cells. 

I come  next  to  consider  Professor  Beetz’  criticism  of  the  method 
of  resistance  measurement  which  we  used;  and  it  is  interesting  to 
notice  how  even  he,  who,  having  written  what  he  has  written, 
might  be  expected  to  take  all  possible  precautions  against  mistake, 
nevertheless  can  slip  into  what  he  would  call,  if  we  had  been  guilty 
of  them,  die  allerg  rob  sten  Wissens-  und  Verstandnissirrthiimer.  He 
thinks  that  our  method  is  the  same  as  his  own,  except  that  we 
substituted  platinum  for  zinc  electrodes,  and  relied  upon  the  quick- 
ness with  which  we  could  make  and  break  contact  for  the  measuring 


550  Proceedings  of  the  Royal  Society 

of  resistance  during  the  earliest  stages  of  polarisation!  Accordingly, 
his  criticism  is,  that  contact  cannot  be  so  quickly  made  and  broken, 
i.e.,  the  time  of  passage  of  current  cannot  be  made  so  short,  as 
to  warrant  our  neglecting  the  effect  of  polarisation;  and  he  cites  as 
proofs  of  the  fact  the  experience  of  Kohlrausch  and  Nippoldt,*  and 
the  experiments  of  Edlund.f  “If,”  he  writes,  “the  authors  were 
acquainted  with  Edlund’s  experiments,  they  would  know  that 
platinum  electrodes,  between  which  the  current  from  three  Daniell’s 
cells  has  passed  in  dilute  sulphuric  acid  during  only  — th  of  a 
second,  have  already  acquired  a polarisation,  whose  electromotive 
force  is  equal  to  that  of  0*57  of  a Daniell’s  cell.”  Very  interesting, 
hut  unfortunately  not  to  the  point ! Any  one  who  understood  the 
method  of  our  paper  would  know  that  Edlund’s  experiments  were 
quite  irrelevant,  simply  because  our  observation  was  equally  accu- 
rate whether  the  current  flowed  during  yi-g,  1 or  100  seconds.  In 
what  respect  then  did  the  method  differ  from  Professor  Beetz’  idea 
of  it?  In  one  respect,  viz.,  that  while  he  supposed  us  to  have 
used  a heavy  mirror  galvanometer,  we  used  Sir  William  Thomson’s 
“ Dead  Beat  ” galvanometer  J — and  we  distinctly  stated  that  such 
an  one  was  necessary  for  the  use  of  our  method. § This  galvano- 
meter has  four  peculiarities: — (1.)  The  mirror  is  exceedingly  light; 
(2.)  On  the  back  of  it  there  are  four  very  small  magnets;  ||  (3.)  The 
mirror  cell  is  just  large  enough  to  admit  of  deflection;  (4.)  The  front 
and  back  of  the  cell  act  as  stops.  In  virtue  of  the  former  two 
peculiarities  the  mirror  moves  almost  instantaneously  in  obedience 
to  even  a very  weak  current;  and  in  virtue  of  the  latter  two,  there 
is  almost  no  oscillation.  The  effect  of  these  properties  is  seen  by 
comparing  an  observation  made  by  means  of  the  ordinary  galvano- 
meter with  one  made  by  means  of  the  “ Dead  Beat.”  Suppose  the 
ordinary  galvanometer  to  be  used  in  a Wheatstone’s  Bridge,  one  of 
the  arms  of  which  is  a tube  containing  an  electrolyte  with  platinum 
electrodes,  while  the  other  three  are  known  resistances,  and  are 

* Pogg.  Ann.  cxxxviii.  p.  282,  1869. 

t Ibid,  lxxxv.  p.  209,  1852. 

J See  Fleming  Jenkins’  “ Electricity  and  Magnetism,”  p.  198. 

$ P.  58  of  our  paper. 

||  The  mirror  and  magnets  of  our  galvanometer  weighed  together  only 
about  -08  grm. 


551 


of  Edinburgh,  Session  1874-75. 

arranged  in  such  proportion  that,  if  the  tube  were  replaced  by  an 
equal  metallic  resistance,  a very  small  deflection  of  the  mirror,  in 
a positive  direction,  would  be  obtained  on  closing  the  circuit. 
Then,  during  the  time  of  contact,  a large  deflection  is  produced  in 
a negative  direction.  The  moment  of  inertia  of  the  mirror  is  so 
great,  that  before  the  main  current  has  moved  it,  at  least  perceptibly, 
in  the  positive  direction,  the  polarisation  current  carries  it  off  in 
the  negative.  If  contact  lasts  -g^th  of  a second,  the  deflection  is 
due  to  the  sum  of  all  the  forces  acting  upon  the  mirror  during  that 
space  of  time.  Against  such  a method  Professor  Beetz’  criticism 
is  valid;  because  it  is  almost  impossible  to  make  and  break  contact 
in  less  than  ^th  of  a second,  and  we  certainly  did  not  think  that 
we  had  done  so.  But  suppose  that  we  use  the  “ Dead  Beat  ” gal- 
vanometer, the  bridge  being  in  the  same  condition.  During 
contact  the  mirror  makes  two  deflections,— the  first,  very  small 
and  in  a positive  direction,  the  second,  much  larger  and  in  a 
negative  direction, — the  size  of  the  second  deflection  depending, 
within  limits,  upon  the  length  of  time  of  contact,  while  both  the 
occurrence  and  size  of  the  first  are  entirely  independent  of  it.  The 
inertia  of  the  mirror  is  so  small,  that  the  main  current — lessened  of 
course  by  the  first  traces  of  polarisation — produces  its  effect 
before  polarisation  has  had  time  to  gather  its  forces;  and  it  is  this 
first  deflection,  caused  by  the  main  current,  which  is  observed,  and 
which  is  reduced  to  just  nothing  by  changing  the  relation  of  the 
arms,  in  order  to  determine  the  resistance  of  the  tube.  It  is  thus 
evident  that  the  length  of  time  of  contact  has  no  effect  upon  our 
result.  So  far  as  a single  observation  is  concerned,  it  is  quite  the 
same  whether  it  lasts  a long  or  a short  space  of  time.  Edlund’s 
experiments  and  Kohlrausch  and  Nippoldt’s  experience  are  thus 
alike  worthless  to  a critic  of  our  method,  and  Professor  Beetz  cites 
them  simply  because  he  was  criticising  a conception  of  his  own. 
He  was,  perhaps,  led  astray  by  the  importance  we  attached  to 
making  the  time  of  contact  as  short  as  possible.  But  this  precau- 
tion had  reference  to  the  next  following  observation.  The  shorter 
the  contact,  the  less  time  required  for  depolarisation  and  the  less 
change  in  the  constitution  of  the  liquid.  The  same  remarks,  which 
I have  made  to  shew  that  we  did  not  lean  upon  such  a broken  reed 
as  the  shortness  of  contact,  make  it  evident  also  that  we  were  right 


552 


Proceedings  of  the  Royal  Society 

in  our  choice  of  platinum  electrodes.  Professor  Beetz’  own  expe- 
rience,* and  that  of  other  workers  in  this  department,  shew  that 
platinum  electrodes  are  the  best  to  form  part  , of  an  apparatus 
for  the  investigation  of  electrolytes  generally. 

The  method  which  we  used  certainly  cannot  be  regarded  as  com- 
pletely eliminating  the  effects  of  electrolytic  action.  Like  the 
other  general  methods  which  have  been  tried,  it  is  an  approximation 
method.  It  aims,  just  as  Kohlrausch ’s  does,  at  measuring  resistance 
when  the  effects  of  polarisation  are  so  slight  that  they  may  he 
neglected.  If  the  weight  of  the  mirror  were  indefinitely  small, 
its  first  deflection  might  he  regarded  as  due  to  the  main  current 
alone.  But  it  is  impossible  to  obtain  such  a mirror;  and  the 
first  deflection  must  be  regarded  as  caused  by  the  sum  of  the  forces 
of  the  first  few  moments,  which  sum  includes  the  electromotive 
force  of  polarisation.  It  is  generally  admitted,  however,  that 
polarisation,  beginning  at  zero,  must  during  the  first  few  moments 
be  exceedingly  slight.  The  mirror,  therefore,  being  sufficiently 
light,  the  observation  will  take  place  when  its  electromotive  force 
is  so  small  as  to  warrant  its  being  neglected.  The  lighter  the 
mirror,  the  more  rapid  the  deflection,  the  smaller  the  influence  of 
polarisation  and  the  error.  Whether  or  not,  with  the  lightest  mirror 
which  can  at  present  be  made,  the  error  is  really  small  enough  to 
be  neglected,  can  only  be  determined  by  a comparison  of  results  with 
those  of  some  standard  method  which  eliminates  completely  the 
effects  of  electrolytic  action.  Our  method  guards  for  a single 
observation  not  only  against  polarisation,  but  in  the  same  way 
against  the  effect  of  the  production  of  substances  which,  while 
giving  rise  to  no  new  electro  motive  force,  differ  in  conductivity 
from  the  original  liquid.  The  observation  is  made  before  such 
products  can  be  formed  in  any  appreciable  amount.  The  necessity 
of  repeated  observations  in  the  same  liquid,  however,  renders  the 
elimination  of  this  error  only  slightly  less  defective  than  in  the 
methods  of  Kohlrausch  and  Nippoldt,  Kohlrausch  and  G-rotrian, 
Paalzow,  and  perhaps  even  Professor  Beetz. 

In  passing  to  consider  the  numerical  results  which  we  published, 
Professor  Beetz  refers  to  two  remarks  which  we  made  about  his 
results,  in  one  of  which  he  finds  the  only  Verstandnissfehler , of 
* Pogg.  Ann.,  cxvii.  p.  26. 


553 


of  Edinburgh,  Session  1874-75. 

whose  occurrence  in  our  paper  I am  aware.  We  said  that  in  his 
researches  on  the  conductivity  of  solutions  of  different  density,  he 
was  not  careful  to  keep  to  exactly  the  same  temperature  throughout 
a whole  series  of  observations,  so  that  his  results  did  not  admit  of 
accurate  graphic  representation.  This  is  a mistake,  proceeding 
probably  from  a misunderstanding  of  one  of  his  tables,  and  I am 
happy  to  have  this  opportunity  of  making  the  correction.  In 
speaking,  however,  of  our  having  made  observations  at  constant 
temperatures,  Professor  Beetz’  statements  are  somewhat  too  sweep- 
ing. He  proves  it  himself;  for  the  confidence  which  he  places  in 
Paalzow’s*  numbers  shew  that  this  is  not  the  cause  of  his  want  of 
confidence  in  ours.  Our  experience  is  contrary  to  his  opinion.  We 
found  the  method  of  constant  temperatures  somewhat  slow,  but  met 
with  no  great  difficulty  in  making  our  measurements  always  within 
a small  fraction  of  10°  C.  Had  it  not  been  so,  it  would  have  been 
easy  to  adopt  the  method  of  interpolation. 

The  second  remark  was  merely  a statement  of  fact,  and  not 
intended,  as  Professor  Peetz  thinks,  as  a reproach.  Which  of  the 
two  kinds  of  formula  is  the  better,  is,  of  course,  simply  a matter  of 
opinion.  We  wished  merely  to  state  that  Professor  Beetz,  having 
adopted  the  usual  one,  had  not  availed  himself  of  what  we  regarded 
as  one  great  advantage  of  the  other.  He  thinks,  however,  that  we 
not  only  made  the  worse  choice,  but  did  not  produce  good  speci- 
mens of  the  kind  which  we  had  chosen.  “ It  would  be  better,” 
he  says,  u if  there  was  more  agreement  between  their  observed  and 
calculated  numbers.”  As  a comment  upon  this  remark,  I give 
the  tables  of  conductivity  (observed  and  calculated)  of  the  solutions 
which  both  he  and  we  have  examined.  His  results  we  take  from 
the  table  given  in  his  paper, f the  latter  part  of  which  has  been 
omitted,  because  our  formula  (a  manifest  disadvantage)  does  not 
apply  to  solutions  beyond  that  of  maximum  conductivity.  Our 
numbers  are  those  given  in  our  agreement-table,  $ reduced  to  the 
same  form  as  his,  the  first  four  being  omitted  because  they  corres- 
pond to  solutions  weaker  than  any  that  Professor  Beetz  examined. 
All  the  given  numbers  must  be  multiplied  by  10 ~9. 

* Monatsberichte  der  Berliner  Akademie,  30.  Juli,  1868,  p.  488. 

t Pogg.  Ann.  cxvii.  1862,  p.  20. 

X Trans.  Roy.  Soc.  Edin.  xxvii.  part  i.  1872-73,  p.  64. 


Proceedings  of  the  Royal  Society 


f)54 


Beetz’  Table. 

Ewing  and  MacGregor’s  Table. 

Observed. 

Calculated. 

Difference. 

Observed. 

Calculated. 

Difference. 

2387 

2315 

+ 72 

1876 

1883 

- 7 

2864 

2864 

0 

2264 

2264 

0 

3417 

3408 

+ 9 

2828 

2828 

0 

3921 

3992 

-71 

2969 

2997 

-28 

4450 

4487 

-37 

3145 

3166 

-21 

4502 

4502 

0 

3264 

3298 

-34 

4528 

4545 

-17 

3344 

3344 

0 

4594 

4615 

-21 

3367 

3379 

-12 

4638 

4621 

+ 17 

4641 

4630 

+ 11 

4626 

4638 

-12 

4628 

4641 

-13 

4632 

4649 

-17 

4640 

4651 

-11 

4632 

4645 

-13 

A comparison  of  these  tables  shews  that,  within  the  limits  of 
common  observation,  Professor  Beetz’  remark  will  apply  as  well 
to  the  agreement  of  his  own  numbers  as  of  ours.  That  the 
agreement  for  very  dilute  solutions  is  not  so  good  we  have  already 
satisfactorily  explained.*  Professor  Beetz  did  not  attempt  to 
measure  their  conductivity,  because  he  found  that  when  there  was 
less  than  a certain  percentage  of  salt  in  his  solutions,  his  method 
was  no  longer  proof  against  the  effects  of  polarisation. 

I have  already  said  that  the  only  way  of  testing  our  method  is 
the  comparison  of  the  results  which  it  furnishes  with  those  of  a 
known  perfect  method.  But  the  comparison  to  which  I refer  is 
not  such  an  one  as  Professor  Beetz  has  proposed  and  executed. 
Its  first  condition  must  be  the  possession  of  a standard  method ; 
its  second  the  elimination  of  all  unnecessary  variables.  It  must 
be  such  as  to  allowr  suspicion  of  the  cause  of  differences  in  results 
to  rest  only  upon  the  method  itself.  If  there  be  x sources  of 
error,  it  cannot  be  fastened  upon  any  one.  The  solutions  examined 
must  be  the  same,  the  vessels  containing  them  the  same,  the 
standards  of  resistance  the  same.  The  only  pieces  of  apparatus 
which  may , are  those  which  must  be  changed.  The  fulfilment  of 
the  second  condition  is  easy.  The  first  is  generally  regarded  as 
fulfilled  by  the  use  of  Professor  Beetz’  method.  Kohlrausch  and 
* Page  G4  of  our  paper. 


of  Edinburgh,  Session  1874-75.  555 

G-rotrian  used  it  in  testing  the  validity  of  their  method.*  That, 
however,  Professor  Beetz’  method  is  free  from  all  the  disturbing 
effects  of  electrolytic  action  seems  not  yet  to  be  thoroughly  estab- 
lished. Du  Bois-Reymond’s  experiments  show  that  there  is  no 
polarisation.  But  do  Professor  Beetz’  experiments!  prove  that 
new  compounds  are  not  formed  by  the  passage  of  the  current,  of 
different  conductivity  from  that  of  the  original  liquid?  In  the 
tube  which  contained  the  electrolyte  he  placed  several  pieces  of 
amalgamated  zinc,  which  fitted  the  tube  closely  like  pistons 
Holes  were  bored  through  the  axis  to  enable  liquid  to  pass  from 
one  side  to  the  other.  Generally,  he  says,  the  pieces  of  zinc,  so 
soon  as  they  touched,  clung  fast  to  one  another  ( [hafteten  fest  an 
einander ),  but  they  could  always  be  separated  by  inclination  of  the 
tube.  When  all  the  pieces  were  lying  close  together,  and  one  of 
them  close  to  a zinc  electrode,  the  current  would  have  to  pass  only 
once  through  the  electrolyte ; but  when  they  were  separated  from 
one  another,  it  must  several  times  pass  through  the  solution.  If 
any  new  resistance  were  produced  there  would  be  several  times  as 
much  produced  in  the  second  as  in  the  first  case,  and  the  fact 
could  be  observed.  This  would  be  conclusive,  if  it  was  certain 
that  there  was  contact  between  the  pieces  of  zinc  lying  next  one 
another.  If  the  amalgamated  surfaces  had  been  coated  with  liquid 
amalgam,  there  would  be  sufficient  certainty  of  contact  to  warrant 
trust  in  the  experiment.  But  that  does  not  seem  to  have  been 
the  case,  as  Professor  Beetz  does  not  mention  it,  and  therefore 
leaves  bis  readers  free  to  suppose  that  he  did  not  rely  upon  its 
agency.  He  must  then  have  taken  for  granted  that,  without  the 
use  of  any  pressure,  the  pieces  of  zinc  could  be  brought  so  close 
together  as  to  prevent  the  liquid  from  penetrating  between  them, 
— a somewhat  doubtful  supposition.  If  there  was  a layer  of 
electrolyte,  however  thin,  between  each  two  neighbouring  pieces 
of  zinc,  electrolysis  would  occur  at  as  many  points  of  the  tube  as 
when  the  zinc  pieces  were  farther  separated,  and  the  resistances 
observed  would  be  equal  whether  compounds  of  greater  or  less 
resistance  were  formed  or  not.  Hence,  until  more  is  known  of 
the  mode  in  which  Professor  Beetz  assured  himself  of  the  contact 

* Pogg.  Ann.  cliv.  p.  9. 


VOL.  vm. 


t Ibid,  cxvii.  pp.  6-8. 

4 c 


556  Proceedings  of  the  Royal  Society 

of  his  pistons  of  zinc,  his  results  must  be  looked  upon  as 
questionable. 

While  in  Professor  Beetz’  comparison  his  fulfilment  of  the  first 
condition  is  not  without  doubt,  his  fulfilment  of  the  second  is 
certainly  not  faultless.  He  forgets  the  certainty  of  error  arising 
from  the  use  of  different  standards  of  measurement,  as  well  as 
the  certainty  of  still  greater  error  from  the  use  of  different  vessels 
for  holding  the  electrolyte.  He  recognises,  however,  the  necessity 
of  knowing  that  we  worked  with  the  same  substances,  and  this 
fact  he  proves  in  a somewhat  extraordinary  way.  His  argument 
takes  the  form  of  a hypothetical  syllogism  : — If  we  used  the  same 
substances,  both  methods  must  have  indicated  the  same  solution  as 
that  of  maximum  conductivity.  Now  both  methods  have  done  so 
(this  itself  was  only  approximately  the  case).  Ergo , we  used  the 
same  substances.  The  fallacy  is  evident.  He  has  mixed  up  what 
the  logicians  call  the  modus  yonens  with  the  modus  tollens , and 
forgotten  that  a conclusion  can  be  drawn  only  from  a denied, 
never  from  an  affirmed  “ consequent.”  That  Professor  Beetz 
intended  the  “major  premise”  as  we  have  given  it,  is  evident, 
from  the  fact  that,  while  he  could  reasonably  expect  its  admission 
from  his  readers,  he  could  not  expect  them  to  grant  the  converse, 
viz.,  that  if  both  he  and  we  had  indicated  the  same  solution  as 
that  of  maximum  conductivity,  we  must  have  used  the  sanie  sub- 
stances. Such  an  assumption  would  make  his  syllogism  correct. 
But  it  neglects  what  the  syllogism  itself,  according  to  the  first 
version,  neglects,  viz.,  the  fact  of  the  possible  plurality  of  causes. 

While  the  method  which  we  used  cannot,  by  Professor  Beetz’ 
argument,  be  proved  faulty,  the  results  which  we  published  might 
thus  be  shown  to  be  unreliable.  For  that  purpose  it  would  be 
necessary  that  various  methods  of  acknowledged  approximate 
accuracy  should  give  results  approximately  the  same,  and  differing 
widely  from  ours.  Professor  Beetz  thinks  this  has  been  done. 
“ Kohlrausch  and  Nippoldt  have  shown  how  close  is  the  agreement 
between  the  results  which  they,  Paalzow,  and  I have  obtained  in 
three  quite  different  ways.  The  agreement  between  their  measure- 
ments of  zinc- vitriol  solutions  and  mine,  and  between  their 
measurements  of  dilute  sulphuric  acid  and  Paalzow’s,  is  perfectly 
satisfactory  ” One  would  understand  from  these  sentences  that 


557 


of  Edinburgh,  Session  1874-75. 

each  of  the  three  experimenters  mentioned  had  used  in  all  his 
(or  their)  observations  a method  quite  different  from  that  of  the 
others;  and  that,  while  the  results  of  one  pair  on  zinc-vitriol 
agree,  the  results  of  the  other  pair  on  dilute  sulphuric  acid  also 
agree.  Kohlrausch  and  Nippoldt’s  determinations  are  used  as  a 
medium  of  connection  between  those  of  the  other  two ; and  only 
on  the  supposition  that  they  used  throughout  the  same  method  or 
methods  connected  by  compared  results,  can  they  reasonably  be 
used  as  such,  or  the  agreement  between  Kohlrausch  and  Nippoldt 
and  Paalzow  be  supposed  to  assist  in  establishing  the  accuracy 
of  Professor  Beetz’  results.  What,  then,  are  the  facts  ? Professor 
Beetz  has  made  a series  of  observations  of  the  conductivity  of  zinc- 
vitriol  solutions;  Paalzow,  of  dilute  sulphuric  acid.  Kohlrausch 
and  Nippoldt  have  investigated  solutions  of' both,  but  with  different 
and  unconnected,  methods . In  all  cases  in  which  they  investi- 

gated zinc  sulphate  they  used  Professor  Beetz*  method.  The 
principle  of  his  method  is  the  use  of  non-polarisable  electrodes ; 
that  of  Kohlrausch  and  Nippoldt’s,  the  reduction  of  polarisation 
by  means  of  rapidly  alternating  currents  and  large  electrodes  to 
as  small  an  amount  as  possible.  In  one  determination  their 
mode  of  investigation  was  quite  the  same  as  Professor  Beetz’ ; * 
in  the  other  they  used  magneto-electric  alternating  currents  in- 
stead of  the  ordinary  galvanic  current. f It  is  evident,  however, 
that,  even  in  this  determination,  since  they  used  amalgamated 
zinc  electrodes  and  not  platinum  ones,  they  were  working  with 
Professor  Beetz’  method  and  not  their  own ; for  the  alternating 
currents  are  characteristic  of  their  method,  only  in  so  far  as 
they  prevent  the  heaping-up  of  the  polarising  substances  on 
platinum  or  other  polarisable  electrodes.  A link  is  wanting,  then, 
between  the  methods  used  by  Kohlrausch  and  Nippoldt  in  their 
sulphuric  acid  determinations  and  their  zinc  sulphate  determina- 
tions respectively.  Nor  is  this  link  supplied  by  the  comparison  of 
methods  given  by  Kohlrausch  and  Grotrian  ; $ for  they  make  only 
a single  comparative  observation,  and  their  platinum  electrode 
method  is  an  improvement  upon  that  of  Kohlrausch  and  Nippoldt. § 
There  being  no  connecting  link,  Professor  Beetz  cannot  cite 

* Pogg.  Aim.  cxxxviii.  p.  376.  t Ibid.  p.  373. 

X Ibid.  cliv.  p.  10.  § . Ibid.  p.  2. 


558  Proceedings  of  the  Royal  Society 

Paalzow’s  agreement  with  Kolilrausoli  as  evidence  for  his  own 
accuracy,  and  his  <c  agreement  of  results  obtained  by  three  observers 
in  three  quite  different  ways  ” becomes  the  agreement  of  results 
obtained  by  two  observers  in  the  same  way.  We  must  now  inquire 
what  even  this  agreement  amounts  to.  Kohlrausch  and  Nippoldt 
made  two  comparable  observations.  The  first,  however,*  is  ren- 
dered worthless  by  the  fact  that  they  assume  the  resistance  of  two 
vessels  of  the  electrolyte,  apparently  without  having  made  any 
accurate  determination.  The  secondf  agrees  very  well  with  Pro- 
fessor Beetz’  corresponding  determination;  but  in  order  to  conclude 
from  this  single  agreement  to  general  agreement,  the  unwarrant- 
able assumption  must  be  made  that  the  error  found  is  not  less  than 
the  average  error.j:  Kohlrausch  and  G-rotrian,  whom  Professor 

Beetz  also  cites,  make  two  comparable  observations,  but  both  are 
questionable  from  the  fact  of  their  being  unable  to  state  accurately 
the  constitution  of  the  solutions  whose  resistance  they  measured. 
The  authority  with  which  Professor  Beetz  condemns  our  results 
as  inaccurate  on  the  ground  of  non-agreement  with  the  agreeing 
results  of  various  quite  different  methods  may  now  be  judged  by 
the  reader  for  himself. 

That  the  results  of  a new  method  applied  by  young  experimenters 
should  be  even  approximately  accurate  is,  perhaps,  hardly  to  be 
expected,  and  it  will  probably  be  found  that  our  numbers  are  not 
quite  exact.  If  Professor  Beetz’  conclusion  were  well  grounded 
they  would  need  to  be  corrected  only  to  the  extent  to  which 

* Pogg.  Ann.  cxxxviii.  p.  373.  t Ibid.  p.  376. 

t The  “ perfectly  satisfactory  agreement  ” between  Kohlrausch  and 
Nippoldt  and  Paalzow  is  based  also  upon  comparison  of  a single  pair  of 
observations,  the  same  unwarrantable  supposition  being  made.  With  regard 
to  this  agreement  it  is  interesting  to  notice  the  fact  that  Kohlrausch  has 
lately  corrected  his  first  published  numbers  to  the  extent  of  4 per  cent. 
Paalzow’s  observed  conductivity  instead  of  being  a little  more  than  2 per 
cent,  less  than  Kohlrausch’s,  becomes  a little  less  than  2 per  cent,  greater. 
If  Paalzow  were  next  to  make  the  same  discovery  there  would  still  be  the 
same  agreement,  and  Professor  Beetz’  argument  would  be  untouched.  Even 
if  such  corrections  should  proceed  alternately,  ad  infinitum,  his  argument 
would  hold  at  all  stages  of  the  process  as  well  as  at  the  present!  It  would 
still  be  true  that  Professor  Beetz  agreed  with  Kohlrausch  and  Kohlrausch 
with  Paalzow,  and  therefore  Professor  Beetz  would  be  proved  to  be  authori- 
tative. So  long  as  Kohlrausch  and  Paalzow  agree, — it  matters  not  whether 
in  accuracy  or  in  error, — they  nevertheless  prove  Professor  Beetz  accurate  ! 


559 


of  Edinburgh,  Session  1874-75. 

Kohlrausch  Las  already  corrected  his  first  results  to  be  made 
“perfectly  satisfactory.”  We  might  therefore  congratulate  our- 
selves on  having  made  so  close  an  approximation,  and  proceed  to 
lighten  our  mirror.  Whether  or  not,  however,  it  must  be  much 
or  little  or  at  all  lightened,  is  a question  which  must  be  regarded 
as  not  yet  settled.  It  may  be  that  Professor  Beetz’  results  are 
accurate,  and  that  ours  alone  need  correction,  but  that  is  not 
proved ; and,  in  the  meantime,  it  will  be  well  to  hold  to  the 
acknowledged  truth  that  neither  accuracy  nor  error  is  often  found 
to  be  all  on  one  side. 

Professor  Beetz  “would  not  have  pointed  ouF  the  weak  points 
of  our  paper  in  so  searching  a style,  had  we  not  conducted  the 
experiments  under  the  guidance  of  Professor  Tait,”  who,  in  com- 
municating it  for  us  to  the  Boyal  Society,  took  upon  himself,  he 
thinks,  the  responsibility  for  its  contents.  He  did  so,  at  the  very 
least,  to  the  same  extent  as  is  always  done  by  the  secretary  of  a 
learned  Society  who  communicates  a paper  not  written  by  a Fellow. 
The  remarks  which  I have  offered  will,  I venture  to  think,  shew 
the  responsibility  to  be  a lighter  matter  than  Professor  Beetz 
supposes.  If  our  errors  were  as  numerous  as  his  accusations  there 
would  certainly  be  a great  deal  to  answer  for.  But  fortunately  the 
strength  of  the  arguments  on  which  he  bases  them  is  inversely  as 
the  strength  of  language  in  which  he  expresses  them ; and  as  the 
latter  is  great,  so  the  former  is  small. 

Monday , 7 th  June  1875. 

DAVID  STEVENSON,  Esq.,  Vice-President,  in  the  Chair. 
The  following  communications  were  read : — 

1.  On  High  Flood  Marks  on  the  Banks  of  the  Eiver  Tweed 
and  some  of  its  tributaries,  and  on  Drift  Deposits  in 
Tweed  Valley.  By  David  Milne  Home,  LL.D. 

In  many  parts  of  Scotland  there  are  indications  that  our  exist- 
ing rivers  reached  much  higher  levels  than  at  present,  and  that 


560  Proceedings  of  the  Royal  Society 

large  bodies  of  water  prevailed  over  districts  which  are  now  dry- 
land. 

As  these  facts  suggest  important  speculations  as  to  the  physical 
conditions  and  climate  of  the  country,  it  is  desirable  that  they  be 
investigated,  before  becoming  more  indistinct  from  the  combined 
effects  of  weather  and  land  improvements. 

The  author  divided  his  paper  into  the  following  heads  : — 

1.  Water  lines  on  the  banks  of  the  River  Tweed  and  some 

of  its  tributaries. 

2.  Notice  of  drift  deposits,  and  appearances  of  ancient 

lakes. 

3.  Theoretical  explanations  suggested. 

4.  Notice  of  views  by  other  persons. 

I. — Water  Lines  on  Banks  of  the  Tweed. 

(1.)  The  lowest,  and  therefore  the  most  recent,  water  line  is  indi- 
cated by  haugh-lands  bounded  by  a cliff  or  bank,  and  at  a height 
above  the  present  ordinary  summer  level  of  the  river  of  from  14  to 
22  feet,  at  various  places  (which  were  specified)  between  Berwick 
and  Melrose.  The  line  is  low  where  the  floods  have  room  to  ex- 
pand laterally ; high,  where  the  banks  are  near  one  another  and 
vertical.  To  the  above-mentioned  heights  the  river  rose  above 
its  present  channel  on  9th  February  1831,  being  the  greatest  flood 
which  has  occurred  during  the  last  hundred  years. 

(2.)  There  are  two  higher  water  lines,  from  22  to  50  feet  above 
the  present  channel  of  the  river.  These  being  older,  -they  are  less 
continuous  and  less  distinctly  marked.  With  regard  to  them  the 
question  is,  were  they  reached  by  the  river  from  its  present 
channel,  or  when  its  channel  was  higher? 

(3.)  Another  extensive  flat,  more  or  less  horizontal,  but  appa- 
rently not  produced  by  the  river,  is  at  a height  of  from  115  to 
130  feet  above  the  sea.  It  is  seen  on  both  sides  of  the  Tweed, 
but  not  beyond  Kelso. 

(4.)  Traces  of  two  higher  flats  or  terraces  exist  in  the  districts 
adjoining  the  Tweed  Valley — one  from  170  to  180  feet,  the  other 
from  200  to  220  feet  above  the  sea. 


of  Edinburgh,  Session  1874-75.  561 

II. — Notice  of  Ancient  Lakes  and  Drift  Deposits. 

(1.)  There  are  indications  that  lakes  existed  formerly  in  Lauder 
Valley,  at  Huntly,  near  Grant’s  House,  on  the  north  side  of  Tweed 
valley ; and  at  Morebattle  and  Millfield  Plain,  on  the  south  side  of 
the  valley,  as  well  as  at  many  other  places. 

(2.)  The  drift  deposits  consist  of  clay,  gravel,  sand,  and 
boulders.  The  clay  generally  occupies  the  lowest  parts.  Exten- 
sive beds  of  sand  exist  from  the  lowest  parts  up  to  1000  feet  above 
the  sea  and  more.  Gravel  lies  more  frequently  over  sand  than 
below  it.  These  deposits  form  round  hills,  as  also  extensive  elliptic 
shaped  ridges.  These  ridges  are  generally  parallel  to  one  another 
and  to  the  axis  of  the  valley.  To  the  west  and  north  of  Kelso  their 
average  direction  is  (by  compass)  E.N.E ; near  the  sea,  about  E. 
and  W.  There  are  also,  at  a level  of  about  800  feet  above  the  sea, 
remarkable  eskars  or  kaims,  running  continuously  for  more  than  a 
mile,  and  observing  approximately  a parallelism  with  hills  not  far 
distant.  Boulders  are  of  three  classes — some  from  parent  rocks 
situated  in  the  valley,  some  from  rocks  in  the  neighbouring  hills, 
some  from  rocks  in  the  Highlands. 

The  localities  where  striated  rocks  occur  were  pointed  out. 

Ill . — Theoretical  Explanations. 

The  author,  to  account  for  the  beds  of  stratified  sand  and 
gravel,  and  for  their  formation  into  parallel  ridges,  as  well  as  for 
the  transportation  of  boulders,  assumes  that  sea,  loaded  with  ice, 
prevailed  over  the  district  to  a height  of  1500  feet  and  more.  He 
infers  also  that,  after  the  sea  began  to  sink  towards  its  present 
level,  a kyle  or  arm  of  open  sea  prevailed  between  the  Cheviot 
hills  on  the  south  and  the  Lammermuir  range  of  hills  on  the 
north,  the  shallowest  part  of  which  would  be  the  present  water- 
shed between  the  counties  of  Roxburgh  and  Dumfries — viz.,  at 
St  Mary’s  Loch  and  Mosspaul,  which  are  about  800  feet  above  the 
present  sea-level.  During  the  period  that  the  level  of  this  sea  con- 
tinued to  sink  towards  the  present  level,  pauses  probably  occurred 
in  the  process,  which  would  allow  of  the  formation  of  cliffs  by  the 
undermining  or  erosion  of  the  land,  and  also  the  formation  of  flats 
or  terraces  by  the  deposit  of  sediment. 


562  Proceedings  of  the  Royal  Society 

A particular  account  was  given  of  various  localities  where  flat 
land  or  terraces  in  Tweed  valley,  at  various  heights  above  the  sea, 
were  recognisable.  When  the  flat  of  115  to  120  feet  existed,  the 
sea  reached  to  Kelso ; and  there,  at  that  time,  the  Tweed  would 
join  the  sea.  As  the  sea  fell — say  30  or  40  feet,  to  Coldstream — - 
the  River  Tweed  would  cut  out  a deeper  channel  for  itself,  and 
when  the  sea  fell  so  much  more,  its  channel  would  he  still  more 
deepened,  till  it  reached  the  present  sea-level.  During  these 
periods,  when  the  river  ran  in  one  channel  after  another,  flood- 
marks  would  be  made  on  its  banks,  traces  of  which  would  long 
remain,  though  it  is  only  the  most  recent  which  can  be  expected 
to  be  now  visible. 


IV. — Views  of  other  Persons. 

1.  As  to  the  drift  deposits — 

(1.)  Several  geologists  have  ascribed  the  formation  of  the  parallel 
ridges  of  drift  deposits  in  Tweed  Valley  to  the  action  of  land-ice, 
and  suppose  that  some  of  these  ridges  are  lateral , others  terminal 
moraines. 

(2.)  They  have  also  been  ascribed  to  fluviatile  action,  aiding 
that  theory  by  the  supposition  that  enormous  floods  were  in  former 
times  caused  by  the  climate  being  more  rainy,  or  by  the  melting 
of  ice  and  snow  on  the  hills. 

The  author  combated  both  views,  holding  that  as  similar  ridges 
of  sand,  gravel,  and  mud  are  formed  now  in  the  sea,  so  they  may 
have  been  formed  in  this  district,  when  the  district  was  under  the 
sea. 

2.  As  to  the  high  flood-marks  on  the  river,  reference  was  made 
to  the  opinions  of  Mr  Alfred  Tylor,  and  of  the  Rev.  Thomas  Brown, 
of  this  society,  as  to  the  probability  that  those  marks  were  made 
by  the  rivers  flowing  in  their  existing  channels. 

The  author  combated  this  theory,  stating,  that  when  the  sea  stood 
at  higher  levels  all  the  rivers  of  the  country  must  have  likewise 
flowed  in  channels  at  higher  levels,  and  that  the  flood-marks  in ' 
question  were  formed  then. 


of  Edinburgh,  Session  1874-75. 


563 


2.  Observations  on  Mr  Sang’s  Remarks  relative  to  the  Great 
Logarithmic  Table  compiled  at  the  Bureau  du  Cadastre 
under  the  direction  of  M.  Prony.  By  M.  F.  Lefort. 
Communicated  by  Mr  Sang,  who  has  translated  the  paper 
from  the  French. 


To  the  President  and  Council  of  the  Royal  Society  of  Edin- 
burgh, Scotland. 


Paris,  le  29  Mars  1875. 


Monsieur  le  President, 

J’ai  regu  par  une  voie  detournee,  un  article  de  M.  Edward  Sang, 
intitule  “ Remarks  on  the  great  Logarithmic  and  Trigonometrical 
Tables  computed  in  the  Bureau  du  Cadastre  under  the  direction  of 
M.  Prony.”  Cet  article,  qui  parait  avoir  ete  publie  dans  les 
“Proceedings  of  the  Royal  Society  of  Edinburgh,  Session,  1874- 
1875,”  m’a  ete  adresse  a l’Observatoire  de  Paris.  Or  je  n’ai  pas 
l’honneur  d’etre  astronome.  Je  suis  simplement  un  inspecteur 
general  des  Ponts  et  Chaussees,  ami  de  la  science  qu’il  a cultivee  et 
qu’il  cultive  encore  dans  les  trop  courts  instants  de  loisir  que  lui 
laisse  sa  carriere  professionelle.  L’Observatoire  de  Paris  a 
d’ailleurs  bien  voulu  me  renvoyer  la  brochure  a mon  domicile,  rue 
du-bac  No.  38,  a Paris. 

Quoique  j’aie  une  opinion  faite  sur  le  fond  de  la  controverse 
qui  s’est  elevee  entre  la  redacteur  de  la  feuille  periodique,  intitulee 
“Nature”  et  M.  Edward  Sang,  je  crois  qu’il  ne  serait  ni  opportun, 
ni  convenable  que  j’exprimasse  un  avis.  Mais,  il  est  des  questions 
de  fait  et  de  doctrine  soulevees  par  M.  Sang,  qui  me  touchent 
trop  personellement  et  interessent  trop  la  science,  pour  que  je  ne 
regarde  pas  comme  une  devoir  d’eclairer,  dans  les  limites  de  mon 
pouvoir,  des  savants  qui  se  sont  occupes  de  mes  travaux  avec  tant 
de  bienveillance. 

Tel  est  1’objet,  Monsieur  le  Presiden't,  de  la  note  ci  jointe  que 
je  vous  prie  de  vouloir  bien  soumettre  a la  Societe  Royale  d’Edin- 
burgh,  et  de  porter  a la  connaissance  de  M.  Edward  Sang,  dont  le 
domicile  m’est  inconnu. 

Yeuillez  agreer,  Monsieur  le  President,  l’assurance  de  ma  haute 
consideration  et  de  mes  sentiments  respectueux. 


F.  Lefort. 


vol.  VIII. 


D 


564  Proceedings  of  the  Royal  Society 

Observations  relatives  aux  remarques  publics  par  M.  Ed- 
ward Sang  dans  les  “ Proceedings  of  the  Eoyal  Society 
of  Edinburgh,  Session  1874-1875,”  sur  les  grandes  tables 
logarithmiques  et  trigonometriques  calculees  au  Bureau 
du  Cadastre  sous  la  direction  de  Prony ; par  F.  Lefort, 
Inspecteur  general  des  Ponts  et  Chaussees,  membre  cor- 
respondant  de  l’Academie  des  Sciences  de  Naples. 

M.  Edward  Sang,  dans  un  article  dont  je  viens  de  rappeler  le 
titre,  a mentionne  de  la  manure  la  plus  flatteuse  les  travaux  que 
j’ai  publiees  sur  la  matiere  des  logarithmes,  et  notamment  sur  la 
grande  operation  qu’a  dirigee  Prony  a la  fin  du  siecle  dernier. 
Je  ne  puis  que  Ten  remercier;  n’entendant  d’ailleurs  intervenir  en 
aucun  fagon  dans  le  fond  de  la  controverse  qui  s’est  engagee  entre 
ce  savant  et  le  redacteur  de  la  feuille  scientifique  intitulee  “Nature.” 
Mais  je  lui  dois,  autant  qu’a  la  tres  honorable  Societe  Royale 
d’Edimbourg,  des  explications  sur  differents  points  de  fait  et  de 
doctrine,  qu’il  regarde  comme  ressortant  de  mes  ecrits,  ecrits  qu’il 
a mal  interpretes,  sans  doute  par  suite  d’une  connaissance  incomplete 
de  la  langue  Frangaise.  Je  n’ignore  pas  qu’en  redigeant  cette  note 
je  m’expose  a un  danger  de  meme  nature;  mais  je  compte  sur 
l’indulgence  de  M.  Sang,  comme  il  pent  etre  assure  de  la  mienne. 

I.  M.  Edward  Sangn’admet  pas  que  les  tables  de  Vlacq,  corrigees 
au  moyen  de  mon  errata , puissent  suppleer  les  tables  nouvelles 
dont  il  propose  l’impression.  II  etablit  d’abord  qu’on  ne  peut  se 
procurer  les  tables  de  Ylacq  qu’a  un  prix  eleve ; qu’il  est  encore 
assez  difficile  d’avoir  un  exemplaire  du  4e  volume  des  Annales  de 
l’Observatoire  de  Paris;  enfin,  qu’il  n'existe  pas  une  concordance 
parfaite  entre  les  divers  exemplaires  de  l’ouvrage  de  Ylacq.  A 
1’appui  de  cette  derniere  these  il  cite  la  phrase  suivante  qui  serait 
imprimee  a la  page  64  des  tables  de  Taylor;  “ in  about  100  copies ; 
in  about  200  copies;  doubtful  whether  a few  copies  are  erroneous 
or  not;  in  about  half  the  impression;  only  in  one  copy;  and  so  on.” 
Je  possede  une  edition  des  tables  de  Taylor,  publiee  en  1792, 
a Londres,  par  les  soins  de  Maskelyne.  J’y  trouve  a la  page  64 
un  errata,  avec  cette  mention  fort  differente  de  celle  qui  precede : 
“ Errata  of  the  logarithmic  tables,  which  affect  only  part  of  the 
impression  of  the  sheet,  and  have  been  corrected  by  the  printer 


of  Edinburgh,  Session  1874-75.  565 

since  the  impression,  except  any  may  have  escaped  correction 
through  inadvertence.” 

Y-a-t-il  eu  plusieurs  editions  des  tables  de  Taylor?  je  n’en  sais 
rien.  Mais  il  resulte  bien  de  la  preface  placee  en  tete  de  l’edition 
que  je  viens  de  citer,  que  la  publication  a ete  faite  pour  la  premiere 
fois  par  les  soins  de  Maskelyne.  En  tout  cas,  les  deux  citations 
me  paraissent  s’appliquer  exclusivement  a l’ouvrage  de  Taylor,  et 
n’avoir  aucun  trait  a l’ouvrage  de  Vlacq. 

L’errata  que  j’ai  donne  dans  le  4e  volume  des  annales  de  l’Obser- 

vatoire,  est  relatif  a P “ Arithmetica  logarithmica per 

Adrianum  Ylacq  Groudanum,  G-oudae  1628.  Petrus  Rammasenius,” 
et  non  aux  contrefa§ons  qui  ont  pu  se  produire. 

Quant  a l’hypothese  des  caracteres  “ moveable  types”  enleves  par 
Pouvrier  manoeuvrant  le  tampon  a encre  “inking  dabber,”  et  qui 
auraient  ete  mal  replacees  par  Pouvrier  qui  fait  agir  la  presse 
“ pressman,”  je  ne  puis  comprendre  qu’elle  soit  produite ; car  elle 
suppose  l’absence  complete  des  verifications  les  plus  habituelles, 
les  plus  elementaires,  et  dont  Po mission  est  d’autant  moins  probable 
dans  l’espece  que  Vlacq,  l’auteur  de  ces  tables  si  precieuses,  avait  ete 
imprimeur  et  le  predecesseur  immediat  de  Petrus  Rammasenius. 

J’admets  bien  qu’  a la  suite  des  tirages  successifs  on  ait  pu 
rendre  plus  corrects  les  exemplaires  de  Vlacq,  mais  je  n’admets  pas 
qu’on  les  ait  rendus  moins  corrects.  II  est  done  possible  que 
Pexemplaire  dont  on  dispose,  ne  renferme  pas  toutes  les  erreurs 
successivement  signalees  par  Vlacq,  Vega,  et  autres  auteurs  parmi 
lesquels  je  me  range.  Mais  quel  danger  cela  presente-t-il  ? le 
nombre  des  corrections  a faire  sera  moindre,  et  voila  tout. 

Je  reconnais  qu’il  n’est  pas  toujours  tres  facile  de  se  procurer 
un  exemplaire  de  Parithmetica  logarithmica  de  Vlacq,  et  que  la 
rarete  de  l’ouvrage  en  rend  le  prix  assez  eleve.  Tout  fois  on  pent 
y suppleer avantageusement  a l’aide  du  “Thesaurus  logarithmorum 
completus”  de  Vega,  qui  est  un  ouvrage  fort  estimable,  moins  rare 
et  par  suite  moins  cher  que  le  premier.  J;ai  compose  aussi  un 
errata  pour  les  tables  de  Vega.  J’en  joins  la  copie  & cette  note,  et 
j’en  autorise  biens  volontiers  la  publication.  Mon  edition  du 
Thesaurus  porte  la  mention,  “ Leipzig,  1794.” 

La  difficulty  de  consulter  le  4e  volume  des  annales  de  PObserva- 
toire  de  Paris,  n’est  pas  serieuse  pour  des  villes  comme  Edimbourg, 


566  Proceedings  of  the  Royal  Society 

Londres,  &c.,  qui  possedent  des  Bibliotheques  publiques  et  des 
etablissments  scientifiques  de  premier  ordre.  La  copie  de  moil 
errata  ne  demande  que  quelques  heures. 

II.  J’arrive  maintenant  au  grandes  tables  du  Cadastre  et  c’est  a 
leur  sujet,  surtout,  que  j'eprouve  le  besoin  de  rectifier  plusieurs 
des  interpretations  de  M.  Sang. 

Les  observations  presentees  par  M.  Le  Vender,  dans  le  seance 
de  1’Academie  des  Sciences  de  Paris,  en  date  du  17  Mai  1858,  ne 
resultent  pas  d’un  examen  personnel  auquel  se  serait  livre  le 
savant  directeur  de  l’Observatoire,  mais  des  conferences  que  j’ai 
eu  l’honneur  d’avoir  avec  lui.  Ainsi  que  je  Pai  dit  dans  la  note 
presentee  a la  seance  de  21  Mai,  “M.  Le  Verrier  avait  bien  voulu 
mentionner  mes  rechercbes  dans  la  derniere  seance.”  Done  les 
doutes  eleves  par  ce  savanf  sur  la  veritable  originalite  des  calculs 
en  quelques  endroits,  n’ont  ni  plus  ni  moins  de  portee  que  ceux 
que  j’ai  exprimes  moi-meme  dans  cette  seance  de  21  Mai,  et  n’in- 
firment  en  quoi  que  ce  soit  ma  conclusion,  que  je  maintiens  plus 
firmement  que  jamais : “ Les  tables  du  Cadastre,  comme  toutes  les 
oeuvres  humaines,  ne  sont  done  pas  parfaites.  Elies  ne  le  sont,  ni 
dans  l’execution,  ni,  peut-etre,  dans  les  details  de  la  conception. 
Cependant,  elles  surpassent  de  beaucoup,  non  seulement  en  etendue 
mais  encore  et  surtout  en  correction  toutes  les  tables  qui  les  ont 
precedees,  et  les  tables  plus  modernes  qui  ne  lui  ont  pas  ete  com- 
pares avant  la  publication.” 

Le  2e  paragraphe,  pag.  12,  de  la  brochure  qui  m’a  ete  adressee, 
paragrapbe,  que  je  ne  reproduis  pas  a cause  de  son  developpement, 
contient  une  erreur  capitale  que  je  n’ai  pas  conscience  d’avoir  fait 
naitre.  M.  Sang  dit  qu’il  y a un  troisieme  exemplaire  des  tables 
“ third  copy,”  que  avait  ete  laisse  a Prony  a titre  de  minute.  Je 
n’ai  jamais  rien  avarice  de  semblable.  II  n’existe  en  fait  que  deux 
exemplaires  “two  copies”  manuscrits  des  grandes  tables  du  Cadastre. 
L’introduction  de  la  notice  que  j’ai  publiee  dans  le  tome  IV  des 
annales  de  l’Observatoire,  ne  laisse  aucun  doute  a cet  egard.  On 
y voit  comment  j’ai  ete  amene,  apres  de  longues  rechercbes,  a 
decouvrir  l’un  des  .deux  exemplaires  que  l’on  croyait  perdu. 

En  presence  de  ce  fait,  il  serait  inutile  que  je  cherchasse  a com- 
battre  les  consequences  que  tire  M.  Sang  de  l’existence  dune 
transcription  : cette  transcription  est  purement  imaginaire. 


567 


of  Edinburgh,  Session  1874-75. 

III.  M.  Edward  SaDg,  mu  evidemment  par  l’unique  desir  d’ob- 
tenir  des  tables  logarithmiques  parfaites,  met  le  public  savant  en 
defiance  contre  la  valeur  reelle  des  tables  du  Cadastre.  Suivant  lui, 
ces  tables  n’offriraient  de  garanties  serieuses  que  si  la  methode  suivie 
etait  bonne  en  principe,  si  elle  avait  ete  fidelement  executee,  et  si 
les  resultats  etaient  sincerement  produits. 

Sur  ces  trois  chefs  “ on  these  three  heads,”  M.  Sang  se  sert  de 
moi  comme  d’un  belier  pour  demolir  Tedifice  construit  par  Prony, 
et  il  croit  avoir  si  bien  reussi  qu’il  lui  parait  inutile  de  recapi- 
tuler  les  critiques  partielles  aux  quelles  il  s’est  livre.  Je  pense 
qu’il  aurait  congu  une  opinion  tout  autre,  s’il  lui  avait  ete  donne 
de  consacrer  quelques  annees  a l’etude  d’un  travail  qui  se  resume 
par  19  volumes  in  folio. 

Pour  se  rendre  compte  dans  tous  ses  details  de  la  partie  mathe- 
matique  de  la  methode,  il  faudrait  lire  l’expose  qu’en  a fait  Prony 
dans  le  * volume  qui  sert  d’introduction  aux  tables.  Quoique  le 
memoire  ne  soit  pas  tres  volumineux,  et  que  j’en  aie  personnelle- 
ment  pris  copie,  je  n’ai  pas  trouve  d’imprimeur  qui  consentit  a 
courir  les  risques  de  l’impression.  Je  me  suis  alors  borne  a pro- 
fiter  de  la  place  tres  honorable,  mais  restreinte,  que  M.  Le  Yerrier 
voulait  bien  me  donner  dans  l’important  receuil  qu’il  publie,  et 
j’ai  cherche,  par  mon  travail  personnel,  a mettre  en  saillie  tout  ce, 
qui  m’a  paru  capital  dans  l’oeuvre  de  Prony. 

Serait-il  opportun  aujourd’liui  de  repondre  en  detail  aux  critiques 
de  M.  Sang?  Je  l’ignore.  En  tout  cas,  le  temps  me  manquerait 
pour  faire  une  reponse  complete.  Je  dirai  seulement  que  le 
mystere,  “ mystery,”  qui  lui  parait  resulter  de  l’insuffisance  de  la 
collation  operee  par  MM.  Letellier  et  G-uyetant  sur  les  tables  de 
Briggs,  n’en  est  pas  un  pour  quiconque  a recouru  aux  sources  ori- 
ginales. 

IV.  Bien  que  Briggs  ait  du  a Napier,  non  seulement  l’idee  mere 
des  logarithmes,  mais  meme  1’idje  de  leur  construction  dans  le  sys- 
teme  dont  la  base  est  10,  systeme  dont  on  l’a  fort  a tort  considere 
comme  l’inventeur  et  auquel  on  a donne  son  nom,  j’apprecie  & un 
tres  haut  degre  le  travail  de  ce  collaborateur  de  Napier,  mais  l’etude 
de  l’arithmetica  logarithmica  m’a  permis  de  reconnaitre  des  erreurs 
dans  l’etablissement  meme  des  bases  du  calcul,  et  m’a  explique  sur 
abondamment  les  fautes  qui  entachent  le  grand  ouvrage  de  1624. 


568 


Proceedings  of  the  Royal  Society 

La  table  de  la  page  10,  “ numeri  continue  medii  inter  denarium 
et  unitatem”  renferme  des  erreurs,  ainsi  que  cela  resulte  d’une 
table  analogue,  et  plus  etendue,  calculee  par  Callet. 

La  table  de  la  page  32,  u tabula  inventioni  logarithmorura  in- 
serviens”  est  egalement  fautive,  d’apres  les  travaux  de  Leonelli  et 
de  M.  Houel. 

On  ne  peut  done  attribuer  aux  calculs  de  Briggs,  qui  reposent 
sur  des  bases  entachees  de  quelques  erreurs,  aucune  superiority 
sur  les  calculs  effectues  au  bureau  du  Cadastre. 

Cependant M.  Edward  Sang  va  plus  loin.  II  attaque  la  methode  des 
differences  mise  en  usage  par  Prony,  et  parait  lui  preferer  les  pro- 
cedes  de  Briggs,  ou  ceux  que  lui-meme  a recemment  employes.  Je 
ne  parlerai  pas  de  ces  derniers  qui  me  sont  inconnus;  mais, 
ayant  longuement  etudie  les  procedes  de  Briggs,  et  ayant  pratique 
moi-meme  la  methode  des  differences  pour  calculer  a 7 decimales 
des  tables  de  logarithmes  d ’addition  et  de  soustraction,  je  me  crois 
en  droit  de  combattre  les  critiques  elevees  contre  cette  derniere 
methode. 

La  critique  principale  de  M.  Sang  est  enfermee  dans  la  phrase 
suivante : “ Also  an  error  in  the  determination  of  the  first  diffe- 
rence of  the  sixth  order  is  augmented  82  472  326  300  times  in 
the  final  logarithm.”  En  d’autres  termes,  quand  on  veut  calculer 
des  logarithmes  a 14  decimales,  en  faisant  usage  de  6 ordres  des 
differences,  l’approximation  etant  porteepour  le  ler  ordre  a 16  deci- 
males, le  2e  a 18,  le  3e  a 20,  le  4e  a 22,  le  5e  a 24,  et  le  6e  a 26, 
1’erreur  resultant  de  l’incertitude  sur  la  valeur  de  26e  chiffre  de- 
cimal est  multipliee  apres  200  termes  par  82  472  326  300. 

Pour  voir  nettement  ce  qu’il  en  est,  faisons  usage  des  signes 
algebriques.  En  donnant  aux  lettres  le  sens  que  je  leur  ai  assigne 
dans  mon  memoire  insere  au  tome  IY  des  annales  de  l’Observatoire, 
on  a pour  la  determination  du  logarithme  final,  up  en  fonction  du 
logarithme  initial  u0  et  des  differences  successives  de  u0  jusqu’au 
6e  ordre, — 

Up  = u0  + pA u0  + p tl  A %0  + A3^0 

+ . . .t»AS+  . 

Sil’on  designe  par  E0 , Ei}  E,,  Ea , E , . . . .,  la  plus  grande 


of  Edinburgh,  Session  1874-75. 


56  9 


erreur  que  comporte  le  calcul  de  u0 , A uQ , A 2u0 , ....  on  a,  en 
assignant  & toutes  les  erreurs  le  meme  signe,  pour  la  plus  grande 
erreur  possible  sur  le  calcul  de  up, 


E„  = E0  + pE , + p til  e2  + ^2 y-_8  H p - 5 E 

p o r ^ 2 2 r 2 3 4 5 6 5 


p = 200,  de  sorte  que  les  coefficients  successifs  ont  les  valeurs 
suivantes : 


200  = 2. 102,  19  900^2.104,  1313  400^1,4.106 
64  684  950  ^ 1.108,  2535  650  040  ^ 3.109, 

82  408  626  3000  1.1011: 

Ainsi,  la  plus  grande  erreur  finale  sur  la  valeur  de  um)  deter- 
minee  par  la  methode  des  differences,  sera  moindre  que 

0,0145  + 0,0131  f 0,0147  + 0,0I45  + 0,0142  + 0,0155  = 0,013395  ; 


en  sorte  que  par  le  seul  fait  de  la  repetition  des  erreurs  coramises 
sur  les  elements  du  calcul,  l’erreur  totale  ne  pourrait  s’elever  a plus 
de  4 unites  du  14e  ordre  decimal.  On  voit  combien  est  fantas- 
magorique  le  chiffre  82  472  326  300  (d’ailleurs  inexact),  qui  est 
donne  par  M.  Sang. 

En  fait,  l’erreur  s’eleve  en  realite  plus  haut  dans  les  tables  du 
Cadastre,  mais  cela  a lieu  par  suite  des  differences  omises.  Aussi 
ai-je  dit  que  les  logarithmes  ont  ete  calcules  avec  14  decimales, 
mais  en  vue  d’avoir  seulement  12  decimales  exactes,  et  cette  cor- 
rection est  presque  absolument  assuree. 

V.  Loin  de  moi  l’idee  d’inculper  les  intentions  de  M.  Edward 
Sang:  je  suis  convaincu  qu’il  n’a  eu  d’autre  but  que  la  recherche 
de  la  verite.  Le  liberalisme  scientifique  de  l’Angleterre  est  trop 
connu,  et  s’est  manifeste,  il  y a quelques  annees,  d’une  maniere  trop 
honorable  par  la  publication  des  tables  de  la  lune  de  Hansen,  pour 
qu’on  puisse  supposer  qu’un  savant,  appartennant  a cette  nation, 
cherche  de  propos  delibere,  a discrediter  une  grande  oeuvre  Fran- 
caise,  sur  laquelle  il  est  peu  on  mal  renseigne. 

II  n’a  pas  dependu,  et  il  ne  depend  pas  encore  de  moi  de  porter 
plus  de  lumieres  sur  un  sujet  qui  m’a  occupe  pendant  plusieurs 
annees.  En  1857,  j’ai  presente  a l’Academie  des  Sciences  de  Paris 
un  memoire  fort  etendu  sur  la  theorie  des  logarithmes,  la  construe- 


570  Proceedings  of  the  Royal  Society 

tion  et  l’usage  des  tables  logarithmiques.  Dans  ce  travail,  j’ai 
passe  en  revue  tout  ce  qui  a ete  fait  d’important  depuis  Napier 
jusqu’a  nos  jours.  Notamment,  j’ai  fait  connaitre  avec  beaucoup 
de  details  l’oeuvre  de  Briggs,  et  le  monument  eleve,  sons  la  direc- 
tion de  Prony,  par  le  burean  du  Cadastre.  Ce  serait  la  matiere  d’un 
volume  in  4°  de  200  pages  environ.  Je  n’ai  trouve  personne  qui 
consentit  a supporter  les  frais  d’impression. 

J’extrairai  volontiers  de  mon  travail  tout  ce  qui  pourra  interesser 
les  savants,  et,  pour  le  prouver,  je  ne  crois  pouvoir  mieux  faire 
que  de  joindre  a cette  notice  l’errata  que  j’ai  forme  pour  le 
“ Thesaurus  Logarithmorum  Completus  de  Vega.”  Je  n’ai  pas 
souvenance  de  l’avoir  deja  publie. 

J’ai  compose  aussi  un  errata  pour  1’  “ Arithmetica  Logarithmica 
de  Briggs,”  qui  contient  environs  300  (trois  cents)  articles;  mais 
sa  publication  devrait  etre  precede  de  quelques  details  qu’il  m’est 
impossible  de  donner  aujourd’hui.  Je  ferai  remarquer  seulement 
que  M.  Sang  ne  parait  pas  avoir  lu,  dans  mon  memoire  insere  au 
tome  IV  des  annales  de  l’Observatoire  de  Paris,  la  phrase  ou 
j’indique  dans  quelle  mesure  etroite  la  collation  des  tables  de 
Briggs  avec  les  tables  du  Cadastre  a ete  faite  par  MM.  Letellier  et 
G-uyetant : “ La  collation  operee  par  MM.  Letellier  et  Guyetant 
ne  porte  reellement  que  sur  12  chiffres.  Elle  aurait  pu  etre  etendue 
a 14  chiffres  pour  les  dix  milles  premiers  nombres,  dont  les  loga- 
rithmes  ont  ete  calcules  au  bureau  de  Cadastre  avec  19  decimales.” 
Tout  le  mystere  consiste  done  en  ceci.  MM.  Letellier  et  Guye- 
tant  n’etaient  pas  des  calculateurs  de  la  2e  section ; et  il  se  sont 
homes  a comparer  le  travail  de  Briggs  avec  celui  qui  avait  ete  fait 
par  les  calculateurs  du  bureau  de  Cadastre — qui,  comme  eux,  appar- 
tenaient  a la  3e  section. 

On  sait  que  Legendre  a publie,  dans  son  traite  des  fonctions  ellip- 
tiques,  les  logarithmes  a 19  figures,  tels  qu’ils  resultent  des  calculs 
faits  au  bureau  du  Cadastre,  pour  les  nombres  premiers  compris 
entre  1 et  10,000. 

L’errata  qui  suit  ne  reproduit  pas  l’errata  imprime  a la  page 
XXX  du  Thesaurus  Logarithmorum  completus.  On  suppose  que 
les  corrections  indiquees  par  l’auteur  ont  deja  ete  faites  sur  Tex- 
emplaire  que  le  ealculateur  possede. 


of  Edinburgh , Session  1874-75. 


571 


ERRATA. 


Thesaurus  Logarithmorum  completus,  etc.,  a G-eorgio  Vega. 


Emend atis  erroribus  ab  auctore  Semetiposo  prius  signatis , non 
nulli  infra  signati  adhuc  super  sunt. 


I. 

Magnus  Canon  Logarithmorum  vulgarium. 


Locus  corrig. 

Error. 

Correct. 

Locus  corrig. 

Error. 

Correct. 

Log.  558 

90 

89 

Log.  22  312 

2 

3 

863 

8 

7 

22  877 

1 

2 

869 

5 

4 

22  996 

2999 

3000 

10  033 

3 

2 

23  274 

299 

300 

Diff.  10  032 

887 

23  492 

3 

2 

Diff.  10  033 

845 

23  820 

2 

1 

Log.  1 1 003 

29 

30 

24  156 

10 

09 

Diff.  11002 

724 

24  626 

9 

8 

Diff.  11003 

687 

25  173 

9 

8 

Differentiarum 

maculae, 

brevi- 

25  524 

59 

K 

60 

tatis  causa, 

haud  ultra  ad- 

25  586 

0 

6 

seribuntur  : 

attento 

lectori 

25  707 

26  004 

5 

3 

6 

4 

patent. 

26  188 

2 

3 

Log.  11  240 

3 

2 

26  407 

5 

4 

15  620 

6 

5 

26  642 

39 

40 

17  646 

8 

9 

26  717 

4 

5 

17  647 

6 

7 

26  728 

46 

26 

17  648 

0 

L 

27  291 

5 

4 

17  649 

0 

.1 

27  560 

3 • 

2 

20  071 

10 

u9 

27  586 

8 

9 

20  280 

6 

7 

27  861 

2 

3 

20  375 

5 

4 

27  921 

7 

6 

20  645 

3 

2 

28  486 

699 

700 

20  822 

2 

1 

28  680 

69 

70 

20  866 

1 

0 

29  112 

5 

6 

21  245 

5 

4 

29  163 

8 

9 

21  749 

2 

3 

29  226 

799 

800 

21  795 

5 

4 

29  446 

7 

8 

21  904 

9 

8 

29  639 

8 

7 

22  016 

7 

0 

29  703 

3 

2 

22  200 

4 

5 

30  499 

6000 

5999' 

4 E 


VOL.  VITT. 


572 


Proceedings  of  the  Royal  Society 


Locus  corrig. 

Error. 

Correct. 

Locus  corrig. 

Error. 

Correct. 

Log.  30  502 

8 

7 

Log.  48  845 

40 

39 

30  728 

1 

2 

48  980 

9 

8 

31  001 

2 

1 

49  047 

6 

5 

31  627 

5 

6 

49  409 

1 

2 

31  653 

6 

8 

50  211 

9 

8 

31  735 

6 

7 

50  414 

1 

0 

31  817 

79 

80 

50  601 

7 

6 

31  919 

8 

7 

50  828 

3 

2 

32  111 

5 

6 

50  937 

1 

0 

32  633 

9 

10 

50  996 

5 

4 

32  672 

5 

4 

51037 

3 

2 

33  071 

23 

27 

51  096 

2 

1 

33  370 

6 

7 

51 175  ■ 

4 

3 

34  037 

6 

7 

51  299 

3 

2 

34  162 

4 

3 

51  388 

5 

4 

34  358 

4 

3 

51  389 

7 

6 

34  664 

1 

0 

51  606 

1 

0 

34  702 

4 

5 

51  607 

6 

5 

34  734 

7999 

8000 

51  820 

7 

6 

35  053 

8 

9 

51915 

4 

3 

35  298 

7 

8 

52  064 

2 

3 

38  051 

9 

7 

52  533 

8 

7 

38  277 

1 

2 

52  565 

8 

7 

38  321 

7 

6 

52  587 

8 

7 

38  783 

3 

2 

52  620 

8 

7 

39  227 

4 

5 

52  792 

3 

4 

39  802 

5 

4 

52  823 

7 

6 

39  839 

7 

6 

52  986 

2 

1 

40  108 

2 

3 

53  647 

8 

7 

40127 

19 

20 

53  868 

5 

4 

40  966 

6 

7 

54  026 

3 

2 

41  156 

5 

6 

54  145 

1 

0 

41  227 

2 

3 

54  273 

4 

3 

41  385 

6 

5 

54  419 

70 

69 

42  584 

1 

2 

54  708 

3 

2 

44121 

40 

39 

54  825 

4 

3 

44  822 

2 

3 

55  010 

50 

49 

45  060 

3 

4 

55  115 

8 

7 

45  231 

5 

6 

55  313 

9 

8 

45  238 

3 

2 

55  618 

768 

678 

45  474 

5 

4 

57  089 

8 

7 

45  549 

8 

7 

57-202 

7 

6 

45  571 

8 

7 

57  486 

6 

5 

45  697 

7 

6 

57  751 

8 

7 

45  725 

2 

1 

58  081 

2 

1 

45  755 

6 

7 

58  214 

6 

5 

46  073 

9 

8 

58  223 

2 

1 

47  162 

40 

39 

58  301 

1 

0 

47  476 

1 

2 

58  858 

7 

6 

48  305 

5 

4 

59  007 

1 

0 

48  614 

6 

7 

59  488 

4 

3 

48  626 

8 

7 

P.  173,  col.  0 777 

Lin.  5a 

Lin.  6a 

of  Edinburgh , Session  187 4-7 5. 


573 


Locus  corrig. 

Error. 

Correct. 

Locus  corrig. 

Error. 

Correct. 

Log,  60  096 

2 

3 

o g.  73  571 

2 

1 

60  401 

8 

9 

73  655 

9 

8 

60  487 

2 

1 

74  527 

6 

5 

60  704 

1 

2 

74  723 

8 

7 

60  794 

2 

1 

74  733 

5 

4 

61  Oil 

4 

3 

74  932 

5 

4 

61  157 

4 

3 

74  941 

40 

39 

62  038 

5 

4 

75  149 

9 

8 

62  131 

7 

6 

75  386 

2 

1 

62173 

7 

6 

75  395 

6 

5 

62  257 

4 

3 

75  560 

3 

2 

62  273 

4 

3 

75  562 

4 

5 

62  933 

50 

49 

75  590 

4 

3 

63  183 

9 

8 

75  613 

4 

3 

63  357 

50 

49 

75  841 

8 

7 

63  887 

1 

0 

75  353 

4 

3 

64  086 

5 

4 

77  047 

2 

1 

64  639 

1 

0 

77  437 

6 

5 

64  661 

4 

8 

77  663 

7 

6 

64  993 

40 

39 

77  944 

6 

5 

65  143 

1 

0 

78  079 

5 

4 

65  185 

8 

9 

78  259 

2 

1 

65  311 

5 

4 

79  447 

5 

4 

65  659 

1 

0 

79  467 

1 

0 

65  946 

2 

3 

79  666 

20 

19 

66187 

7 

6 

80  060 

7 

8 

66  239 

4 

3 

80  062 

8 

9 

66  423 

7 

6 

80  063 

2 

3 

67  399 

30 

29 

80  090 

6 

7 

69  311 

7 

8 

81212 

60 

59 

69  457 

3 

2 

81  460 

8 

7 

69  477 

5 

4 

82  951 

60 

59 

69  988 

2 

1 

82  991 

7 

6 

70  019 

40 

39 

83  6&3 

6 

5 

70  040 

3 

4 

83  803 

8' 

9 

70  043 

1 

0 

85  651 

9 

8 

70  066 

7 

8 

85  810 

19 

20 

70  599 

6 

5 

86  688 

3 

4 

71  140 

9 

8 

86  708 

90 

89 

71306 

9 

8 

86  898 

0 

1 

71  569 

0 

1 

87  634 

3 

2 

71  653 

3 

4 

89  182 

7 

6 

71  764 

6 

5 

89  185 

6 

7 

72  103 

9 

8 

90  625 

5 

6 

72  675 

5 

4 

91086 

8 

7 

73  046 

90 

89 

91  087 

7 

6 

73  059 

4 

5 

93  155 

1 

2 

73  286 

2 

3 

93  498 

0 

1 

73  303 

90 

89 

96  981 

80 

79 

73  404 

6 

5 

97  674 

5 

6 

73  501 

9 

8 

98  336 

5 

6 

73  570 

1 

0 

98  337 

49 

50 

574 


Proceedings  of  the  Royal  Society 


Locus  corrig. 

Error. 

Correct. 

Locus  corrig. 

Error. 

Correct. 

Log.  98  338 

3 

4 

Log.  98  772 

8 

7 

98  339 

6 

7 

98  936 

7 

8 

98  340 

39 

40 

98  966 

4 

3 

98  341 

1 

2 

99  926 

2 

1 

98  342 

3 

4 

100  330 

3 

2 

98  345 

6 

7 

98  346 

6 

7 

Wolframii  tabula  Logarithmorum 

98  348 

5 

6 

naturalium. 

98  350 
98  352 
98  353 

2 

7 

4 

3 

8 

5 

Log.  1 099 

7 853 

1 0021  1 
9676 

| 0021 5 
1 9686 

98  356 

2 

3 

98  357 

7 

8 

98  358 

2 

3 

Magnus  Canon  Logarithmorum 

98  359 

6 

7 

vulgarium  trigonometricus. 

98  360 

0 

2 

Log.tan.  0°  30'  45" 

1 101 

I 201 

98  362 

6 

7 

Cotg.  0°  30'  45" 

] 899  j 

799 

98  365 

2 

3 

98  366 

3 

4 

Alias  maculae  posterius  signa- 

98  367 

4 

5 

buntur. 

Paris,  le  29  mars  1875. 
F.  Lefort. 


Translation. 

1.  Observations  relative  to  Mr  Edward  Sang’s  “ Remarks  on 
the  Great  Logarithmic  and  Trigonometrical  Tables  calculated 
in  the  Bureau  du  Cadastre  under  the  direction  of  Prony,” 
published  in  the  Proceedings  of  the  Eoyal  Society  of  Edin- 
burgh, Session  1874-1875,  by  M.  E.  Lefort,  Inspecteur 
General  des  Ponts  et  Chaussees,  Corresponding  Member 
of  the  Academy  of  Sciences  of  Naples. 

Mr  Edward  Sang,  in  the  above  cited  article,  makes  most  flatter- 
ing mention  of  the  works  which  I have  published  on  the  subject 
of  Logarithms,  and  particularly  on  the  great  operations  performed 
in  the  end  of  the  last  century  under  the  direction  of  Prony.  I 
cannot  but  thank  him,  yet  without  wishing  to  intervene  in  any 
way  in  the  controversy  between  him  and  the  editor  of  the  scientific 
periodical  “ Nature.”  But  I owe  it  to  him,  as  well  as  to  the 
honourable  Koyal  Society  of  Edinburgh,  to  give  explanations  on 


575 


of  Edinburgh,  Session  1874-75. 

several  points  of  fact  and  of  doctrine  which  he  regards  as  deducible 
from  my  writings;  writings  which  he  has  misinterpreted,  doubtless 
from  an  incomplete  knowledge  of  the  French  language.  In  pre- 
paring the  following  note  I am  aware  that  I am  exposed  to  a 
danger  of  the  same  kind,  and  therefore  count  upon  Mr  Sang’s 
indulgence,  as  he  may  assuredly  count  upon  mine. 

I.  Mr  Edward  Sang  does  not  admit  that  Ylacq’s  Table  corrected 
by  help  of  my  errata  can  supply  the  place  of  the  new  tables  which 
he  proposes  to  print.  He  argues  that  Ylacq’s  Tables  can  only  be 
had  at  a great  price,  and  that  the  4th  volume  of  the  “Annales  de 
l'Observatoire  de  Paris,”  is  not  always  easily  obtainable;  and  also 
that  there  is  not  a complete  agreement  among  the  different  copies 
of  Ylacq’s  work.  In  support  of  this  thesis  he  quotes  the  following 
phrase,  which  should  be  found  on  the  64th  page  of  Taylor’s  Tables: — 
“ In  about  100  copies;  in  about  200  copies;  doubtful  whether  a few 
copies  are  erroneous  or  not;  in  about  half  the  impression;  only  in  one 
copy;  and  so  on.” 

I have  a copy  of  Taylor’s  Tables,  published  in  1792  at  London, 
under  the  care  of  Maskelyne.  Therein  I find  at  page  64  an  errata 
with  this  notice,  very  different  from  the  preceding: — “Errata  of 
the  Logarithmic  Tables  which  affect  only  part  of  the  impressions 
of  the  sheet,  and  have  been  corrected  by  the  printer  since  the 
impression,  except  any  may  have  escaped  correction  through 
inadvertence.” 

Have  there  been  several  editions  of  Taylor’s  Tables?  I know 
nothing  of  it.  But  the  preface  to  the  edition  just  mentioned  shows 
that  the  publication  was  made  for  the  first  time  under  Maskelyne’s 
care.  Any  way  the  two  quotations  seem  to  me  to  apply  exclusively 
to  Taylor’s  work,  and  to  have  no  reference  to  that  of  Ylacq. 

The  errata  which  I have  given  in  vol.  4 of  the  “ Annales  de 
l’Observatoire,”  refer  to  the  Arithmetica  Logarithmica  par  Adrian 
Ylacq,  Gfoudanum,  Gfoudae  1628,  Petrus  Bammasenius,  and  not  to 
any  spurious  copies. 

As  to  the  hypothesis  of  the  types  drawn  out  in  the  working  of 
the  “inking  dabber,”  and  misplaced  by  the  pressman;  I cannot 
imagine  how  it  could  be,  because  it  supposes  the  complete  neglect 
of  the  most  elementary  and  usual  verifications;  an  omission  much 


576  Proceedings  of  the  Royal  Society 

the  less  likely  since  Vlacq,  the  author  of  these  valuable  tables, 
had  been  a printer,  and  was  the  immediate  predecessor  of  Petrus 
Rammasenius. 

I willingly  admit  that,  in  the  course  of  successive  impressions, 
the  copies  of  Vlacq  may  have  been  made  more  correct ; it  is  thus 
possible  that  a particular  copy  may  not  contain  precisely  all  the 
errors  indicated  by  Vlacq,  Vega,  and  other  authors,  among  whom 
I may  count  myself.  But  what  danger  is  there  from  that?  there 
are  fewer  corrections  to  be  made ; that  is  all. 

I admit  that  it  is  not  always  very  easy  to  procure  a copy  of  the 
u Arithmetica  Logarithmica”  of  Vlacq,  and  that  the  scarcity  of  the 
book  enhances  its  price.  However,  the  want  may  be  advantageously 
supplied  by  the  Thesaurus  Logarithmorum  Completus  of  Vega, 
a most  estimable  work,  not  so  rare  and  therefore  not  so  costly  as 
the  other.  I subjoin  a copy  of  a list  of  errors  in  Vega  which  I 
have  made,  and  of  which  I willingly  authorise  the  publication ; 
my  copy  of  the  Thesaurus  has  the  legend  Leipzig,  1794. 

There  can  be  no  serious  difficulty  in  consulting  the  4th  volume 
of  the  (i  Annales  de  l’Observatoire  de  Paris,”  in  such  towns  as 
Edinburgh,  London,  etc.,  where  there  are  public  libraries  and 
scientific  establishments  of  the  first  order.  The  copying  of  my 
errata  is  the  matter  of  a few  hours. 

II.  I come  now  to  the  Great  Tables  of  the  Cadastre,  on  which 
subject  chiefly  I find  it  necessary  to  rectify  several  of  Mr  Sang’s 
interpretations. 

The  observations  made  by  M.  Le  Verrier  at  the  meeting  of  the 
Academy  of  Sciences  of  Paris,  of  date  17th  May  1858,  were  not 
the  results  of  a personal  examination  made  by  the  Director  of  the 
Observatory,  but  of  the  conferences  which  I had  the  honour  of 
having  had  with  him.  As  I have  said  in  the  note  presented  at  the 
Meeting  of  the  24th  May: — “ M.  Le  Verrier  has  been  kind  enongh, 
at  the  previous  meeting,  to  mention  my  researches.”  Hence  the 
doubts  expressed  by  this  philosopher  as  to  the  true  originality  of 
the  calculations  in  some  places,  have  neither  more  nor  less  weight 
than  those  which  I myself  have  expressed  at  this  meeting  of  the 
24th  May,  and  do  not  weaken  in  the  least  the  conclusion  which  I 
maintain  more  firmly  than  ever: — “The  Tables  of  the  Cadastre, 


of  Edinburgh,  Session  1874-75.  577 

like  all  human  works,  are  not  then  perfect;  they  are  so  neither  in 
the  execution  nor  perhaps  in  the  details  of  the  conception;  never- 
theless, they  greatly  surpass,  not  only  in  extent,  but  yet  and  above 
all  in  correctness,  all  the  tables  which  have  preceded  them,  as  well 
as  the  more  modern  tables  which  have  not  been  compared  with 
them  before  publication.” 

The  second  paragraph,  p.  12,  of  the  pamphlet  sent  me,  which  on 
account  of  its  length  I do  not  quote,  contains  a capital  error  for 
which  I cannot  admit  that  I have  given  cause.  Mr  Sang  says  that 
there  is  a third  copy  of  the  tables  which  had  been  allowed  to  Prony 
by  way  of  minutes.  I have  never  said  anything  of  the  kind. 
There  only  exist,  in  fact,  two  manuscript  copies  of  the  Great 
Tables  of  the  Cadastre.  The  introduction  and  notice  which  I 
have  published  in  vol.  4 of  the  Annals  of  the  Observatory  leave 
no  doubt  on  that  subject.  It  may  be  seen  therein  how,  after  long- 
researches,  I was  led  to  discover  that  one  of  the  two  which  was 
believed  to  have  been  lost. 

It  is,  therefore,  unnecessary  for  me  to  seek  to  controvert  the 
consequences  which  Mr  Sang  has  drawn  from  the  existence  of  an 
imaginary  transcription. 

III.  Mr  Edward  Sang,  evidently  led  by  the  sole  desire  to  obtain 
perfect  logarithmic  tables,  would  have  the  learned  world  to  mistrust 
the  Cadastre  Tables.  According  to  him,  these  afford  no  serious 
guarantee  that  the  principle  of  the  method  was  good,  that  these 
principles  were  faithfully  carried  out,  or  that  the  results  were  sin- 
cerely given.  On  these  three  heads  Mr  Sang  uses  me  as  a 
battering  ram  to  demolish  the  edifice  erected  by  Prony,  and  thinks 
he  has  so  well  succeeded  that  it  was  unnecessary  to  recapitulate 
the  special  criticisms  which  he  had  made.  I think  that  he  would 
have  formed  quite  a different  opinion  if  he  had  been  privileged  to 
spend  years  in  the  study  of  a work  which  fills  nineteen  folio  volumes. 

In  order  to  give  an  account  of  all  the  mathematical  details  of 
the  method,  it  would  be  necessary  to  read  Prony’s  explanation  in 
the  (manuscript)  volume  forming  the  introduction  to  the  tables. 
Although  this  memoir  be  not  exceedingly  voluminous,  and  although 
I have  personally  made  a copy  thereof,  I have  not  found  a printer 
willing  to  run  the  risk  of  the  impression,  and  have,  therefore,  been 
confined  to  the  honourable  but  restricted  space  kindly  given  by 


578  Proceedings  of  the  Royal  Society 

M.  Le  Verrier  in  the  annals  which  he  publishes;  and  I have 
endeavoured  by  my  own  exertions  to  exhibit  all  of  Prony’s  work 
that  appeared  to  me  to  be  most  important. 

I do  not  know  that  it  would  be  opportune  at  present  to  reply  in 
detail  to  Mr  Sang’s  criticisms,  and  need  only  say,  that  the  mystery 
which  he  thinks  to  result  from  the  insufficient  collation  of  Briggs’ 
Tables  by  MM.  Letellier  et  Gruyetant  is  no  mystery  to  those  who 
have  had  recourse  to  the  original  sources. 

Although  it  be  true  that  Briggs  owes  to  Napier  not  only  the 
fundamental  idea  of  logarithms,  but  also  that  of  the  system  computed 
according  to  the  basis  10,  of  which  system  Briggs  has  without 
reason  been  held  as  the  inventor,  and  to  which  his  name  has  been 
attached,  I appreciate  in  the  highest  degree  the  work  of  this  fellow 
labourer  with  Napier.  But  the  study  of  the  Arithmetica 
Logarithmica  has  led  me  to  discover  errors  in  the  fundamental 
basis  of  the  calculation,  and  has  superabundantly  explained  the 
faults  which  mar  the  great  work  of  1624. 

The  table  in  page  10,  “Numeri  continue  medii  inter  denarium 
et  unitatem,”  contains  several  errors,  as  is  seen  from  an  analogous 
and  more  extensive  table  calculated  by  Callet. 

The  table  on  page  32,  “ Tabula  inventioni  logarithmorum  inser- 
viens  ” is  equally  faulty,  according  to  the  works  of  Leonelli  and 
of  M.  Houel. 

We  must  not  then  attribute  to  the  calculations  of  Briggs, 
founded  on  pages  containing  various  errors,  any  superiority  over 
those  executed  in  the  Bureau  du  Cadastre. 

For  all  that,  Mr  Edward  Sang  goes  farther;  he  attacks  the 
method  of  differences  made  use  of  by  Prony,  and  seems  to  prefer 
to  it  the  processes  followed  by  Briggs,  or  those  which  he  himself 
has  recently  employed.  I say  nothing  about  these  last,  which  are 
unknown  to  me;  but  having  for  long  studied  Briggs’  processes, 
and  having  myself  practised  the  method  of  differences  while  com- 
puting to  7 decimals  tables  of  logarithms  of  sums  and  differences, 
I believe  myself  to  be  in  a position  to  repel  the  attacks  on  this 
latter  method. 

Mr  Sang’s  principal  objection  is  contained  in  the  following 
phrase: — “ Also  an  error  in  the  denomination  of  the  first  difference 
of  the  sixth  order  is  augmented  82  472  326  300  times  in  the  final 


of  Edinburgh,  Session  1874-75. 


579 


logarithm.”  In  other  words,  when  we  wish  to  calculate  logarithms 
to  14  decimals,  making  use  of  6 orders  of  differences,  the  approxi- 
mation being  carried  for  the  1st  order  to  16,  for  the  2d  to  18,  the 
3d  to  20,  the  4th  to  22,  the  5th  to  24,  and  the  6th  to  26,  the  error 
resulting  from  an  uncertainty  in  the  26th  figure  is  multiplied  after 
200  terms  by  82  472  326  300. 

To  see  exactly  the  state  of  matters,  let  us  make  use  of  algebraic 
signs.  Giving  to  the  letters  the  meaning  which  I have  assigned  to 
them  in  my  memoir  inserted  in  the  4th  volume  of  the  “ Annales 
de  TObservatoire,”  we  have  for  the  determination  of  the  final 
logarithm  uv  in  terms  of  the  initial  logarithm  and  of  the  succes- 
sive differences  up  to  the  sixth  order, 


If  we  denote  by  E0 , Ex , E2 , . . . . the  greatest  error  which 
arises  in  the  calculation  of  u0 , Au0 , A u0  ....  we  have,  on  giving 
the  same  sign  to  all  the  errors,  in  order  to  obtain  the  greatest  pos- 
sible error  in  the  result. 


putting  each  error  in  the  differences  at  ^ of  a unit  in  its  own  last 
place,  and  making  p = 200,  the  successive  coefficients,  have  the  fol- 
lowing values— 200 , 19900 , 13  13400 , 64  684  950 , 2 535  650  040  , 
82  408  626  300  . 

Thus,  the  greatest  final  error  in  the  value  of  um  determined 
by  the  method  of  differences  must  be  less  than  0-5  + 1*0  + 0-7 
+ 0-5  + 0'2  + 0'05  = 3*95  in  the  fourteenth  place;  so  that  by  the 
simple  repetition  of  the  errors  made  in  the  elements  of  the  calcula- 
tion, the  total  error  can  never  rise  to  more  than  four  units  in  the 
14th  decimal  place.  We  see  thus  how  fantasmagoric  is  the  number 
82  472  326  300  (inaccurate  besides)  which  is  given  by  Mr  Sang. 

In  point  of  fact,  the  error  really  rises  higher  than  this  in  the 
Cadastre  tables,  but  that  is  because  of  the  differences  omitted. 


'0 


4 • . .^-SA %0  + . . . ,t4A%  4 . . . . V6AX  . 
4 5 o 


E*  - E0  + p\  + p ^ E2  + 


P-2  V ~ 3 V-  4 P~  5 e 
F 2 3 4 5 6 6 ‘ 


4 F 


VOL.  VI! I. 


580 


Proceedings  of  the  Royal  Society 

Thus,  I have  said  that  the  logarithms  have  been  calculated  with 
14  decimals,  but  with  the  view  only  of  having  12  exact;  and  this 
degree  of  accuracy  is  almost  absolutely  secured. 

Y.  Far  be  it  from  me  to  entertain  the  idea  of  blaming  the  inten- 
tions of  Mr  Edward  Sang.  I am  convinced  that  he  has  had  no 
other  desire  than  to  reach  the  truth.  The  scientific  liberality  of 
England  is  too  well  known,  and  has  recently  been  too  well  shown, 
by  the  publication  of  Hansen’s  Lunar  Tables,  to  allow  us  to  sup- 
pose that  a savant  belonging  to  that  nation  would  deliberately  seek 
to  discredit  a great  French  work,  concerning  which  he  has  been  ill- 
informed. 

It  has  not  depended,  and  it  will  not  depend  on  me,  to  throw 
more  light  on  a subject  which  has  occupied  me  for  several  years. 
In  1857  I presented  to  the  Academy  of  Sciences  of  Paris  a very 
extensive  memoir  on  the  Theory  of  Logarithms,  on  the  construc- 
tion, and  on  the  use  of  Logarithmic  Tables.  In  this  work  I have 
reviewed  everything  important  that  has  been  done  from  Napier’s 
dowm  to  our  times.  Notably,  I have  explained  with  many  details 
the  work  of  Briggs,  and  the  monument  erected  under  the  direction 
of  Prony  by  the  Bureau  du  Cadastre.  It  would  make  a quarto 
volume  of  some  200  pages;  I have  found  no  one  willing  to  bear  the 
expense  of  the  impression. 

I would  willingly  extract  from  my  work  anything  that  would 
interest  the  learned  ; and  to  prove  this  I do  not  think  I can  do 
better  than  annex  to  this  note  the  errata  which  I have  compiled 
for  “ Yega’s  Thesaurus  Completus.”  I have  no  recollection  of 
having  published  it  before. 

I have  prepared  also  an  errata  for  Briggs’  u Arithmetica  Logarith- 
mica,”  which  contains  about  300  entries,  but  its  publication  would 
need  to  be  accompanied  by  some  details  which  I am  just  now  unable 
to  give.  I would  remark  only,  that  M.  Sang  does  not  seem  to  have 
read  in  my  memoir  inserted  in  tome  IY.  des  Annales  de  l’Obser- 
vatoire  de  Paris  the  passage  in  which  I point  out  the  limited  extent 
of  the  comparison  of  Briggs’  tables  with  those  of  the  Cadastre  made 
by  MM.  Letellier  et  G-uyetant.  “ The  comparison  made  by 
MM.  Letellier  et  Gruy^tant  extended  only  to  12  figures.  It  might 


of  Edinburgh,  Session  1874-75.  581 

have  been  extended  to  14  figures  for  the  first  ten  thousand  num- 
bers, whose  logarithms  had  been  computed  to  19  places  at  the 
Bureau  du  Cadastre.”  All  the  mystery  lies  here.  MM.  Letellier 
et  Gruy^tant  were  not  calculators  of  the  second  section,  and  they 
confined  themselves  to  the  comparison  of  the  work  of  Briggs  with 
that  which  was  done  by  the  computers  in  the  Bureau  du  Cadastre, 
who,  like  them,  belonged  to  the  third  section. 

We  know  that  Legendre  has  published  in  his  “ Treatise  on 
Elliptic  Functions  ” the  logarithms  of  all  prime  numbers  from  1 to 
10,000,  as  obtained  from  the  calculations  made  at  the  Bureau  du 
Cadastre. 

The  following  errata  does  not  contain  the  errors  printed  at  page 
xxx.  of  the  Thesaurus  Logarithmorum  Completus;  it  is  taken  for 
granted  that  the  errors  pointed  out  by  the  author  have  been  already 
corrected  on  the  computer’s  copy. 

Eeply  to  M.  Lefort’s  Observations.  By  Edward  Sang. 

From  M.  Lefort’s  opening  sentence  it  appears  that  he  had  only 
recently  received  the  copy  of  my  remarks  which  had  been  posted 
to  him  on  22d  December.  Perhaps  on  this  account  M.  Lefort  has 
been  hurried  in  the  perusal  of  my  paper,  and  so  has  fallen  into 
several  mistakes  as  to  my  meaning.  These  will  be  apparent  to 
any  one  who  peruses  the  writings,  and  I shall  pass  them  over 
entirely,  confining  myself  to  the  very  few  points  which  are  essen- 
tial to  the  subject  in  hand.  The  only  extraneous  matter  to  which 
I shall  allude  is  this,  that  while  M.  Lefort  has  obviously  and  justly 
been  desirous  of  upholding  the  dignity  of  the  Grrandes  Tables  du 
Cadastre,  he  has,  in  the  true  spirit  of  an  inquirer  after  truth, 
clearly  and  faithfully  exhibited  even  those  points  which  press 
most  sorely  on  his  own  position. 

While  disclaiming  any  intention  to  enter  into  the  controversy 
opened  by  “Nature,”  he  at  once  plunges  into  it  in  support  of  the 
thesis  enunciated  by  the  non  nemo  of  that  periodical — “Almost 
all  the  errors  found  by  Mr  Sang  by  means  of  this  table  are  among 
those  there  given  by  Lefort,  and  any  one  who  chooses  can,  without 
much  expenditure  of  trouble,  render  his  copy  of  Ylacq  all  but  free 


582  Proceedings  of  the  Royal  Society 

from  error — much  more  accurate  than  any  neiu  table  could  possibly  be.” 
In  opposition  to  this  gigantic  absurdity,  I had  pointed  out  the  well 
recognised  danger  arising  from  the  use  of  moveable  types : M. 
Lefort  denies  and  yet  admits  this  danger  in  one  sentence : — 
'“J’admets  bien  qu’a  la  suite  des  tirages  successives  on  ait  pu 
rendre  plus  corrects  les  exemplaires  de  Ylacq,  mais  je  n’admets 
pas  qu’on  les  ait  rendus  moins  corrects.”  It  is  enough  for  my 
argument  that  two  copies  may  differ.  In  the  supplementary  table 
to  the  Errata  of  Briggs,  M.  Lefort  supplies  a strong  corroboration 
of  what  I advance.  The  logarithm  of  2087  is  therein  stated  as 
9 . . instead  of  952.  The  two  figures  52  had  been  drawn  out  or 
been  broken  while  the  copy  “ Sainte  Genevieve”  was  being  printed; 
in  my  own  copy  they  are  correctly  given. 

In  order  to  sustain  this  dictum  of  u Nature,”  we  have  to  suppose 
the  Tables  du  Cadastre,  which  were  the  basis  of  Lefort’s  com- 
parison, to  be  absolutely  correct.  Now,  while  composing  the  re- 
marks made  at  the  first  meeting  of  the  Session,  I had  only  access 
to  M.  Lefort’s  papers  in  the  Comptes  Bendus;  but  through  his 
great  kindness  I am  now  in  possession  of  a copy  of  his  most 
valuable  paper  inserted  in  the  Annales  de  TObservatoire  de  Paris, 
and  am  thereby  enabled  much  more  satisfactorily  to  explain  the 
defects  of  Prony's  mode  of  procedure  because  an  example  of  the 
actual  work  is  therein  given. 

The  design  was  to  compute  the  successive  differences  of  the 
logarithms,  carrying  the  decimals  two  places  further  at  each  step ; 
and  by  the  summation  of  these  to  obtain  200  terms  of  the  logarith- 
mic progression.  An  error  of  unit  in  the  last  place  of  each  of 
these  differences  will  produce  an  effect  on  the  final  term,  according 
to  the  following  scale  : — 

Is*,  2-00 
2 d,  1-99  00 

3d,  1-31  34  00 

4:th,  -64  68  49  50 

5th,  *25  35  65  00  40 

6th,  *08  24  08  62  63  00 

making  a total,  if  all  the  errors  should  happen  to  be  in  one  way,  of 


583 


of  Edinburgh , Session  1874-75. 

6-2862.  Wherefore,  if  each  difference  have  been  computed  true 
to  the  nearest  last  figure,  the  maximum  error  arising  from  this 
mode  of  calculation  is  31431.  M.  Lefort,  taking  into  account  the 
maximum  possible  error  in  the  first  logarithm,  makes  it  3-95,  or 
say  four  units  in  the  last  place. 

All  this  looks  exceedingly  well,  but  has  not  the  slightest  reference 
to  the  matter  in  hand.  In  order  to  obtain  such  a miserable  degree 
of  precision,  we  have  the  labour  of  computing  the  first  difference 
of  each  order,  and  then  the  toil  of  writing  6 times  12  times  200, 
or  14  400  unnecessary  figures ; for,  to  make  M.  Lefort’s  formula 
applicable,  each  difference  of  each  order  must  be  carried  to  the 
26th  place. 

Prony  did  not  use  the  method  of  differences;  he  used  a method 
of  vitiated  differences.  To  show  the  nature  of  the  vitiation,  I 
transcribe  a few  lines  of  the  actual  work  from  M.  Lefort’s  example, 
which,  belonging  to  an  advanced  part,  has  only  differences  of  the 
fourth  order. 


Nombres. 

Logarithmes. 

A1 

A2 

A3 

A* 

100  800 

00346  05321  0951 

43084  5563-17 

4274  19-79 

848-03 

2-52 

801 

00346  48405  6514 

43084  1288-97 

4274  11-31 

848-00 

2-52 

802 

00346  91489  7803 

43083  7014-86 

4274  02-83 

847-97 

2-52 

803 

00347  34573  4818 

43083  2740-83 

4273  94-35 

847-94 

2-52 

Here  we  see  that  the  differences,  though  computed  true  to  the 
last  figure,  are  only  used  to  the  second  preceding  figure;  thus  2*52 
is  read  3,  and  the  possible  error  is  augmented  one  hundred  times. 
But  this  is  not  all;  the  difference  of  any  particular  order  only 
comes  to  affect  those  of  lower  orders  by  the  accident  of  some  of  the 
to  be  rejected  figures  being  more  or  less  than  50;  so  that  the  final 
effect  cannot  be  made  the  subject  of  calculation.  I find  nowhere 
any  attempt  to  estimate  the  effect  of  this  systematic  vitiation, 
and  shall  endeavour  to  supply  the  want  by  taking  two  extreme 
imaginary  cases.  In  the  first  case  I shall  assume  each  of  the 
initial  differences  to  be  0-49.  Proceeding  with  these  according  to 
the  method  of  Prony,  we  find 


584  Proceedings  of  the  Boy  at  Society 


V 

u 

A u 

Ahi 

A3u 

A % 

Abu 

A 3u 

0 

0 

0*49 

0-49 

0*49 

0-49 

0-49 

0-49 

1 

0 

0-49 

0-49 

0-49 

0-49 

0*49 

0-49 

200 

o’ 

6-49 

6-49 

0-49 

0-49 

0-49 

0*4*9 

giving  for  um  the  value  0,  whereas  if  computed  according  to  the 
method  of  successive  differences,  the  result  is  um  = 308. 

If,  however,  we  augment  the  sixth  difference  by  two  units  in  its 
last  place,  leaving  the  other  differences  unchanged,  we  get 


p 

u 

A1^ 

A % 

A 3u 

A % 

A bu 

A % 

0 

0 

0-49 

0-49 

0-49 

0-49 

0-49 

0-51 

1 

0 

0-49 

0*49 

0-49 

0-49 

0-50 

0-51 

2 

0 

0-49 

0-49 

0-49 

0-50 

0*51 

0-51 

3 

0 

0-49 

0-49 

0-50 

0-51 

0-52 

0-51 

4 

0 

0-49 

0*50 

0-51 

0-52 

0*53 

0*51 

5 

0 

0*50 

0-51 

0-52 

0*53 

0-54 

0*51 

6 

1 

0-51 

0-52 

0-53 

0-54 

0-55 

0-51 

50 

45 

0-95 

0-96 

0-97 

0*98 

0*99 

0-51 

100 

95 

1-45 

T46 

1-47 

1-48 

1-49 

0*51 

150 

190 

2-41 

2-43 

2*45 

2-47 

1-99 

0-51 

195 

327 

3-80 

3-84 

3-78 

3-37 

2-44 

0-51 

196 

331 

3-84 

3*88 

3-81 

3-39 

2-45 

0-51 

197 

335 

3-88 

3-92 

3-84 

3-41 

2*46 

0-51 

198 

339 

3*92 

3-96 

3-87 

3-43 

2-47 

0-51 

199 

343 

3-96 

4-00 

3-90 

3-45 

2-48 

0-51 

200 

347 

4-00 

4-04 

3-93 

3-47 

2*49 

0-51 

Thus  a change  of  two  units  in  the  last  place  of  the  6th  difference 
has  caused  a change  of  347  in  the  value  of  whereas,  if  it  had 
been  computed  by  the  method  of  differences,  the  change  would 
only  have  been  T64,  and  thus  the  number  which  M.  Lefort  has 
characterised  as  “ phantasmagorique”  has  yet  to  he  augmented 
more  than  two  thousand  times,  and  it  is  possible  that  this  egre- 
giously  absurd  mode  of  proceeding  may  cause  an  uncertainty  of 
three  units  in  the  twelfth  place ; also  it  cannot  be  predicated  that 
this  actually  exemplified  error  is  the  maximum  one. 

I had  treated  as  a mystery  the  fact  that  MM.  Letellier  et 


585 


of  Edinburgh , Session  1874-75. 

Guyetant  had  not  noticed  the  numerous  last  place  errors  in  the 
Arithmetica  Logarithmica.  In  regard  to  this  I now  find  in  M. 
Lefort’s  paper  inserted  in  the  Annales  de  l’Observatoire  the  follow- 
ing statement : — The  comparison  made  by  MM.  Letellier  et 
Guyetant  was  really  only  to  12  figures.  It  might  have  been  ex- 
tended to  14  figures  for  the  first  10,000  numbers  whose  logarithms 
had  been  computed  to  19  places  in  the  Bureau  du  Cadastre,” 
from  which  it  seems  that  the  object  of  the  comparison  was  not  to 
correct  Brigg’s  tables  but  to  verify,  in  so  far,  the  Cadastre  tables 
themselves. 

The  only  other  point  to  which  I would  refer  is  as  to  my  mistake 
concerning  a third  copy . The  explanation  is  simple.  In  common 
with  many  others,  I had  understood  that  the  two  copies  of  the  great 
tables  were  deposited  in  separate  libraries.  Having  read  only  the 
papers  in  the  Comptes  Rendus,  which  contain  no  notice  whatever 
of  the  loss  and  recovery  of  one  of  these  copies,  nor  of  the  important 
service  rendered  by  M.  Lefort  in  that  recovery,  I naturally  regarded 
the  presentation  to  the  Academy  as  that  of  a third  copy.  The  de- 
tail of  these  matters,  interesting  to  all  classes  of  computers,  is  con- 
tained in  the  Annales  de  l’Observatoire,  a sectional  work  consulted 
by  only  a limited  class.  From  this  paper  we  learn  that  one  of  the 
two  copies,  so  like  as  to  be  hardly  distinguishable,  had  been  long 
amissing,  its  whereabouts  unknown,  until  M.  Lefort,  by  untiring 
perseverance,  traced  it  to  the  possession  of  the  Heirs  of  Prony,  to 
whom  it  had  been  allowed  by  way  of  minutes,  “ Cet  exemplaire 
avait  ete  laisse  a Prony  & titre  de  minute.”  That  is  to  say,  the 
Director  had  taken  away  one  half  of  the  result  of  this  enormous 
labour,  lessening  greatly  the  value  of  the  remaining  half  by 
depriving  it  of  the  means  of  verification ; and  that  the  so-called 
presentation  was  only  the  restitution  of  what  should  never  have 
been  taken  away. 

I crave  leave  to  add  one  word  in  regard  to  the  nineteen-place 
table.  On  comparing  the  logarithms  of  primes  from  1163  to 
10007  as  given  by  Legendre  in  his  “ Exercises  de  Calcul  Integral,” 
Tome  III.,  with  my  own  to  twenty-eight  places,  it  is  found  that, 
for  primes  above  1900,  hardly  a logarithm  is  true  to  the  nineteenth 
place;  so  much  so,  that  to  make  a list  of  the  errors  would  be  to 


586  Proceedings  of  the  Royal  Society 

make  a list  of  all  the  primes.  The  only  logarithms  above  1900 
truly  given  are  those  of  2417,  2879,  2903,  6379,  8599,  and  9137 ; 
and,  with  the  exception  of  the  logarithm  of  9479  which  is  unit  in 
excess,  all  those  erring  by  less  than  10  are  in  defect.  A list  of  the 
corrections  exceeding  9 is  subjoined. 


Numb.  Corrn. 

Numb. 

Corrn. 

Numb. 

Corrn. 

1303,  - 10 

4201,  + 

28 

6659,  - 

2494 

1579,  + 10 

4409,  + 

55 

05 

00 

1 

45 

2003,  + 13 

5233,  + 

10 

6827,  - 

25 

2011,  + 12 

5273,  + 

10 

6883,  + 

30 

2203,  + 55 

5813,  - 

245 

7001,  + 

53 

2207,  + 30 

6011,  + 

14 

7109,  - 

295 

2633,  + 13 

6037,  + 

10 

8011,  + 

10 

3307,  + 55 

6269,  + 

15 

8069,  - 

494 

3863,  + 25 

6521,  + 

14 

8353,  + 

12 

3923,  + 10 

6581,  + 

14 

8819,  + 

31 

4007,  + 19 

6619,  + 

29 

9403,  + 

15 

The  only  error  higher  than  the  sixteenth  place  is  in  the 
logarithm  of  4603,  which  should  be  93974  instead  of  93924. 

From  this  it  is  obvious  that  the  mechanical  part  of  the  work 
had  been  carefully  performed,  but  that  the  computers  had  been 
unskilled  in  the  management  of  the  final  figures,  so  as  to  prevent 
the  accumulation  of  small  errors.  The  fact  that  almost  all  the 
errors  lie  in  one  direction  points  to  the  influence  of  some  definite 
but  erroneous  bye  rule. 

Finally,  on  examining  the  list  of  corrections  given  in  vol.  iv.  of 
the  “ Annales  de  FObservatoire,”  by  help  of  which,  according  to 
“Nature,”  Ylacq  is  to  be  made  “much  more  accurate  than  any 
new  table  could  possibly  be,”  I find  between  the  narrow  limits 
from  20000  to  30000  two  omissions,  at  24580  and  26699,  and  two 
mis-corrections,  at  26188  and  29163,  in  all  of  which  M.  Lefort  has 
been  misled  by  errors  of  calculation  made  at  the  Bureau  du  Cadastre, 
as  is  clear  from  the  subjoined  logarithms  set  down  true  to  the  15th 
place — 

24580  *39058  18785  50435 

26188  -41810  23322  49959 

26699  • 42649  49953  49034 

29163  -46483  21978  49968 


of  Edinburgh,  Session  1874-75.  587 

We  must  therefore,  it  seems,  be  careful  lest  in  correcting  Ylacq 
by  help  of  Prony’s  calculations,  we  do  not  put  him  wrong  where 
he  is  right. 

Postscript  by  M.  Lefort . 

Les  erreurs  signalees  sur  le  10rae  chiffre  decimal  pour  les  logar- 
ithmes  des  nombres  24580,  26188,  26699  et  29163  sont  moindres 
qu’une  unite  du  12me  ordre  decimal.  Or  M.  Lefort,  dans  son  article 
sur  les  tables  du  Cadastre  a prevenu  que  “ le  12me  chiffre  decimal 
pent  etre  accidentellement  en  erreur  de  pres  d’une  unite,”  page  26. 

Monday,  21  st  June  1875. 

The  Hon.  LORD  NEAYES,  Vice-President,  in  the  Chair. 

The  following  Communications  were  read : — 

1.  Note  on  Electric  Resistance  of  Solutions.  By  William 
Durham  and  P.  R.  Scott  Lang,  M.A. 

This  note  contains  the  results  of  experiments  we  have  made  on 
the  electric  resistance  of  solutions  by  a method  brought  under  the 
notice  of  this  Society  by  Messrs  Ewing  and  M‘Gfregor,  and  de- 
scribed in  their  paper  printed  in  the  Transactions,  vol.  27,  page 
51.  Our  results,  so  far  as  they  have  gone,  are  as  follows  : — 

1.  Resistance  of  solutions  of  sodium-chloride,  and  potassium- 
chloride,  varying  in  strength  from  *002  grains  to  4 and  5 grains  to 
25  cubic  inches  of  water.  In  these  weak  solutions  the  polarization 
was  very  little  and  easily  got  rid  of,  and  the  results  satisfactory. 
On  plotting  these  out  in  the  usual  manner,  we  found  the  curves 
described  to  be  hyperbolas,  as  shown  in  the  diagram,  where  the 
ordinates  represent  the  strengths  of  the  solutions  and  the  abscissae 
the  resistances.  Becquerel,  in  his  experiments  on  this  subject, 
found  the  hyperbolas  to  be  rectangular  for  the  solutions  he  used, 
while  Ewing  and  M‘Gregor  found  theirs  not  to  be  rectangular. 
We  find  some  of  our  curves  to  be  rectangular  and  others  not. 
Thus  we  have — 


4 G 


vol.  vnr. 


KC1 — not  rectangular. 


588  Proceedings  of  the  Royal  Society 

We  tried  with  the  same  arrangement  the  resistance  of  distilled 
water,  and  found  it  to  be  about  37,000  B.A.  units  per  cubic  centi- 
metre; but  on  carefully  distilling  water  twice,  we  found  the 
resistance  had  risen  as  high  as  47,000  B.A.  units,  showing  the 
great  difference  the  least  impurity  made. 

2.  The  effects  of  heat  on  electric  resistance.  We  experimented 
on  water,  sodium-chloride,  and  potassium-chloride — weak  solutions 
of  the  two  latter.  We  heated  them  to  about  70°  centigrade,  and 
measured  the  resistance  as  they  cooled.  We  found,  as  the  tem- 
perature fell,  the  rate  of  increase  of  resistance  increased,  and  the 
results,  on  being  plotted,  all  described  rectangular  hyperbolas,  as 
shown  in  the  diagram.  Since  making  our  experiments  we  find 
that  Professor  Beetz  of  Munich  has  been  making  experiments  on 
the  same  subject,  using  zinc  electrodes  and  zinc  sulphate,  thus 
avoiding  polarization  almost  entirely.  His  results  and  ours  agree 
generally. 

3.  From  some  phenomena  we  noticed  we  were  led  to  try  the 
effect  of  varying  the  strength  of  the  current  passing  through  the 
solution ; and  as  the  result  of  many  experiments  we  find  that,  as 
the  strength  of  the  current  increases,  the  resistance  seems  to 
diminish.  We  note  the  results  of  two  experiments  on  a weak 
solution  of  sodium-chloride  and  a stronger  one  of  copper-sulphate. 


Resistance  in  Current. 

Resistance  in  Solution. 

10  B.A.  Units 

950  B.A.  Units. 

100  „ 

1000 

1000  „ 

1150  „ 

10,000  „ 

1390 

10  „ 

132 

100  „ 

138 

1000 

158 

10,000 

187 

We  are  not  prepared  as  yet  to  say  to  what  this  effect  is  due.  It 
may  be  due  in  some  way  to  the  polarization,  but  we  cannot  say  for 
certain  till  we  make  further  experiments.  Our  thanks  are  due  to 
Professor  Tait  for  kindly  allowing  us  the  use  of  laboratory  and 
apparatus. 


of  Edinburgh,  Session  1874-75. 


589 


2.  On  the  Circumscribed,  Inscribed,  and  Escribed  Circles  of 
a Spherical  Triangle.  By  C.  G-.  Colson,  Esq.  Communi- 
cated by  Professor  Tait. 

In  the  following  paper  I propose  to  investigate  expressions  for 
the  vector  of  the  following  six  points  of  a spherical  triangle  : — 
(1.)  Pole  of  inscribed  circle. 

(2.)  (3.)  (4.)  Poles  of  escribed  circles. 

(5.)  Pole  of  circumscribed  circle. 

(6.)  The  orthocentre  or  intersection  of  arcs  drawn  perpendicu- 
larly from  angles  upon  the  opposite  sides. 

These  vectors  will  all  be  found  in  terms  of  the  vector  of  the 
corners  of  the  triangle  drawn  from  the  centre  of  the  sphere. 

Throughout  the  investigation  a,  (3,  y will  denote  the  vectors  of 
A,  B,  C,  the  corners  of  triangle  ABC,  A'B'C'  will  represent  the  polar 
triangle  of  ABC  (A!  being  pole  of  BC),  &c. ; a (3'  y will  denote  the 
vectors  of  its  corners ; and  following  the  notation  usual  in  spherical 
trigonometry,  a,  b,  c,  A,  B,  C will  denote  sides  and  angles  of  the 
triangle ; pLi  p2 , p3J  the  perpendicular  arcs  from  A,  B,  C on  BC, 
&c. ; R,  r,  rlt  r2 , r3  the  radii  of  the  circumscribed,  inscribed, 
and  escribed  circles. 

After  finding  these  vectors  we  proceed  to  deduce  certain  well- 
known  results,  among  others,  to  find  the  radius  of  the  circle  (analogous 
to  that  discovered  by  Feuerbach  in  the  case  of  a plane  triangle) 
which  touches  the  inscribed  circle  and  the  three  escribed  circles. 

To  find  the  vector  of  the  pole  of  inscribed  circle.  Let  p be  the 
vector  (from  centre  of  sphere)  of  P,  the  pole  of  inscribed  circle  of 
the  triangle  ABC.  Then  we  may  express  p as  follows : — 

p = xa  -f-  yf3  + zy  , 

where  xyz  are  scalars  to  be  determined.  Operating  by  S .V/?y  on 
the  expression,  we  have 

SpV/?y  = xSoNfiy. 

But 

Y/3y  = a sin  a ( a being  the  vector  of  A')  , 

therefore 

Spa  — xSaa' , 
or 

cos  PA'  «=.  sc  cos  A A' , 


590 


Proceedings  of  the  Royal  Society 


x — — . 

sm  px 

Similarly 

_ sin  r _ sin  r 
^ sin  p’  sin  p3 

Hence 

P = sin  r ) • • (1.) 

\sm  Px  sin  p2  sm  pj 

To  find  the  vectors  of  the  poles  of  the  escribed  circles,  let 
Pi  Pa  Pi  be  the  vectors  of  Pj  P2  P3 , the  poles  of  the  escribed  circles 
opposite  to  ABC  respectively.  Then,  as  before,  we  may  write 

px  - xa  + y/3  + zy  . 

Determining  the  scalars  xyz  as  before,  we  have 

^ _ cos  PjA'  _ cos  PjB'  w _ cos  PjC' 

X " cos  AA'  ’ y ~ ’ 2 ~ cos  GO'  ’ 


By  geometry  of  the  figure  we  see  that 


I*  ^'=1+^  PiB'=g-r,  P,G  '=|-rt. 


Hence 


Therefore 


_ _ sm  rx  _ sm  rx  _ sm  rx 
sin  px  5 ^ sin  p2  5 2 sin  p3 ' 


p.  = sm  rx  ( - PL-  + J—  + 


sin^  sm|)2  sm  p3/ 


Similarly  we  find 


P-2  = sin  r2  ( PL-  _ + -PL-  ^ 

\smj}j  sm  p2  sm  py 

p2  - sin  r3  ( — 1-  ~J— — - PL-  ) 

\sin  pj  sm  p3  sm  pj 


(2.) 

(3.) 

(^) 


Coroll.  : 

Pi  | P-2  + Pi  = a + P 7 = P 

sm  rx  sin  r2  sin  r3  sm  px  sin  p2  sin  p3  sin  r 


(a  result  which  is  useful  further  on). 

To  find  vector  of  the  pole  of  the  circumscribed  circle,  let  cr  be 
the  vector  of  Q,  the  pole  of  the  circumscribed  circle.  Then  since 


of  Edinburgh,  Session  1874-75. 


591 


any  vector  may  be  expressed  in  terms  of  any  three  other  conter- 
minal and  not  complanar  vectors,  we  may  write 

<r  — xa'  + y/3'  + zy'  . 

Operate  now  by  S.a.  Then  noticing  that 
Sa /3'  = 0 Sayr  = 0 


we  have 


Sa <r~  = ccSaa' , 
cos  AQ  = x cos  AA' , 


i.e., 

_ cos  E 

sin  p1  * 

Similarly 

_ cos  E _ cos  E 

^ sin  p2  * ^ sin  pi 

Hence 

er 

= cos  E ( E—  + X-  + 

V sm  px  Sin  p2 

Or  since 

Y /3y  = a'  sin  a , &c., 

we  may  write 

J-) 

mi  pj 


cos  E 


sin  a sin 


Pi 


(V/3y  + Yya  + Y a/3) 


Or  we  might  proceed  thns- 
Since 


QA  = QB  = QC , 

Sera  = S<r/3  = Scry, 

Str  (a  - (3)  = 0 , S cr(j3  - y)  = 0 , 
<r  is  J_r  plane  of  chordal  A . 

cr  = zY  Q3y  + ya  + a/3)  . 
Operate  by  Sa.  Then 

Sacr  = zSaY/3y  = 2 sin  aSaa  , 
cos  E 

sin  a sin  pl  ’ 


therefore 

therefore 

therefore 

Hence 


therefore 


(5.) 


(5.) 


z = 


592 


Proceedings  of  the  Bo  gal  Society 


<r  = C0S  R (V/3y  + V7a+Va/?)  = COSR(  + -A- + / \ 

smasm^  \smp1  siny>2  sinp3/ 

To  find  the  vector  of  the  orthocentre. 

Let  co  be  the  vector  of  X,  the  orthocentre  of  the  triangle.  Then 
co  = xa  + y/3  + zy . 

To  determine  the  scalar,  operate  as  before  by  Sa' 

Sa'co  = #Saa' 
or 

cos  XAy  = x cos  A A' 

(calling  arc  XA  = q1  XB  = q.2  ’ XO  = q 3) 
sin  (pi  — q^)  — x sin  px , 


Hence 


sin  — g,)  _ sin  (?.,-&)  2 = sin  (p3-  g;) 

sin  pl  ’ sin  p3  ’ sin  p3 


= (ft-gi)  g + sin  (pa-?8)  „ + sin  (p:i-gi)  - x 
sin^  sinp2  sin  p3  ' ' 


Or  we  may  proceed  as  follows,  and  express  co  in  terms  of  a ft'  y'. 
Let 

co  = xa  + y/3'  -f-  z-/. 

Then 
therefore 
therefore 


Hence 


Saco  = X Saa/ , 
cos  qx~  x sin  px , 


— C0S  ?1  _ C0S  $2 

x — j y — - i 

sin  px  sin  p2 


cos q.3' 
sin  p3  * 


cos  q,  , . cos  qn  ol  , cos  q , , 
- — a + - — i-2  ft  + - — ^ y 
sin  px  sin  p2  Bin  p3 


(6'.) 


Having  now  found  very  simple  and  symmetrical  expressions  for 
the  vector  of  these  six  points,  we  proceed  to  apply  the  results  to  the 
solution  of  various  well-known  problems. 

Ex.  (1.)  To  find  the  arcual  distances  between  the  poles  of  the 
circumscribed  circle  and  the  inscribed  circle,  also  of  the  escribed 
circles. 


of  Edinburgh . Session  1874-75. 


593 


Taking  Q,  P,  Px , P2 , P3  to  be  these  points,  and  cr~,  p,  px , p2 , p3 
to  be  their  vectors — 


by  (5) 


<T~  = cos  E 


(A--+ A-), 

\ sin  pl  sin  p2  sin  p.2  / 


by  (1)  p = sin  r 

therefore 


\ sin 


p 


+ — 4-  — — — 

px  sin  p2  sin  ■ 


Sa'a  ^ 

Syy_' 

sin2^ 

si»A 

sin2p3 , 

'sin  Pi  + 

sin  P2  + 

sin  pz 

,sin2pi 

sin2_pg 

sin2^ 

(noticing  that  Sa/3  = 0,  &c.), 
therefore 


cos  QP  = cos  E sin  r ( — — + — ^ — + — — ^ . 

V sin  px  sm  p2  sin  p2 ) 

Again,  by  (2) 


therefore 
cos  Px( 
and 

cos  ' 

and 

cos  P„Q  = - Scrp3  = cos  E sin  r,  ( + -r— ^ ^ 

\sm  px  sin  p%  smjp3/ 

Adopting  the  usual  notation,  sin  px  sin  a = &c.,  = zn , we  have  (see 
Todhunter’s  Spherical  Trigonometry) 
cos  E sin  - 


Pi  = sin  rx 

( ~ — r— — + 

A_  + 

— )> 

V sin  pi 

sm  p2 

sin  p%  J 

■■  - Scrpi  = 

cos  E sin  rx  ( 

1 

+A—  + A- 

1 \ 

^ sin  pi 

sin  p,2  sm  p3 

\ = Scrp  = 

cos  E sin  r9  1 

f 1 „ 

A—  + A— Y 

J \ 

vsm  Pi 

sm  Pi  sinjp3y’ 

cos  PQ  = - 


2 n 


(sin  a + sin  b + sin  c) 


cos  PXQ  = cos  ^ s*nTi  ( - sin  a + sin  b + sin  c) . 

&c.  &c. 

Ex.  (2.)  To  find  the  arcual  distances  between  the  orthocentre 
and  the  poles  of  the  inscribed,  escribed,  and  circumscribed  circles. 


594  Proceedings  of  the  Royal  Society 


Calling  the  vector  of  orthocentre  (X)  w,  we  have  from  (6) 

w = sin  + sin  (p8-g3)  „ + sin  (p8-g;i) 

sin  sin  sin  p3  ' ’ 

therefore 

Sour  = cos  E (Sin  Sac'  + m'  + Sin(.Pr?3)  ST7  'l  . 

\ sm*^  sin  7^3  J 

therefore 

cos  XQ  = cos  B f sin  fa  ~ ^ + sinfe~g-^  + !Ln_fe-g8)y 
v sin  Bin  p2  sin  p3  / 


sin 

Again,  from  second  form  of  (6) 


cos  q, 

> = - — ^ c 
sin 


cos  & w + CQS  ?3 

sinp2^  sin  p3 


therefore 


So*  = sin  r ( 22Ml  Saa'  + S fifT  + ^ Syy' ) , 

\ sinV  sm2p2  em2®,  / 


1 Pi 

cos  XP  = sin  r 


/cos_2i 

Vsin^ 


' ' smzp3 

£i  + cos  & + cos  Z»)  t 
sin  p2  sin  p3  / ’ 


Similarly  from  (2)  (6)  we  find 


cos  XP 


1 = B*n  ri(^~ 


cos  qx  cos  $2  COS  q.f 

sin  pj  sin  p2  sinp3/ 


and  similar  expressions  for  cos  XP2,  cos  XP3 . 

Ex.  (3.)  To  find  the  volumes  of  pyramids  OP^Pg,  OP^P,  &c., 
where  0 is  the  centre  of  the  sphere,  in  terms  of  the  volume  of  the 
pyramid  OABC. 

We  have 


therefore  multiplying  these,  and  taking  the  vector  of  each  side, 
we  have 


Again 


of  Edinburgh^  Session  1874-75. 


595 


Ps  = sin  r. 


Vsm. 


therefore 


Pi 


/?  _ y 

iUt>2 


'Pi 


)■ 


Sp3Y/3  p = 2 sin  r sin  r2  sin  r3 
™ n ^ 1 2 3 sin  sin  p2  sin  jp3  ’ 


Now 


therefore 


g <,  sin  r.  sin  r9  sin  r.,  Q 0 

VpiPiPz  ~ 4-. — r ^ ba/?y  . 

sm  sin  p sin  p3 


- Spipipt  = 6 vol.  of  pyramid  OP^Pg  = 6Y 

- So j3y  = 6 vol.  of  pyramid  OABO  = 6Y 


Y,  = 4 


sin  r,  sm  r„  sm  r„ 


V. 


Also 


sm  px  sm  p2  sm  p3 


SpYpx  p2  = 2 sin  r sin  rx  sin  r2  . S<*Yy/?_  + Sff\ya 
sm  px  sm  p2  sm  p3 

0 4 sin  r sin  r,  sin  r9  a 0 

SpPi  Pi  = ^ ^ 1e.;vi<OT8  SaP7  1 


sm  sm  y?2  sm  jp3 

4 sin  r sin  rt  sin  r2 
sin  _pA  sin  p2  sin  p2 


V, 


calling  pyramid  OPPxP2  = Yx , &c. 

Similarly  we  find  the  vols.  of  pyramids  OPP2P3,  &c.,  and  arrive 
at  this  result — 


Yx  sin  r3  + Y2  sin  rx  + Y3  sin  r2  = 3Y4  sin  r. 

Ex.  (4.)  To  find  the  radius  of  Dr  Hart's  circle,  i.e .,  the  circle 
which  touches  the  inscribed  circle  and  the  three  escribed  circles. 

Let  7]  be  the  vector  of  the  pole  of  this  circle,  k its  angular  radius. 
Then  since  the  circle  touches  all  four  circles,  we  must  have,  if  z be 
its  centre 

arc  zPj  = k + rL , zP2  = k + r2 , zP3  = k + r3 , zP  = k - r . 
Hence 

S^pi  = - cos  ( k + rx)  = sin  k sin  rx  - cos  k cos  rx 

S r)p.2  = - cos  (k  -f  r2)  = sin  k sin  r2  - cos  k cos  r2 

S>yp3  = - cos  (k  4-  r3)  = sin  k sin  r8  - cos  k cos  r3 , 

4 ii 


VOL.  VIII. 


596 


Proceedings  of  the  Royal  Society 


therefore 

&v(  Pi  _ + .& + ^ =3.  sin  K-coSfc(cotr14-cotr24-  cotr3)  . 

\sin  rx  sin  r.2  sin  r3  J 

But 

Pi  + P«_  + _Pi_  = ,rP_; 

sin  rx  sin  r2  sin  r3  sin  r 

therefore 

= 3 sin  k - cos  k (cot  rx  + cot  r2  + cot  r3)  . 

sin  r 

But 

S rjp  = - cos  (k  - r)  , 

therefore 

- CQS(K  — 3 sin  k — cos  k (cot  + cot  r2  + cot  r.J  , 
sin  r 

therefore 

4 sin  k = cos  k (cot  rx  + cot  r2  +-  cot  r3  - cot  r) , 
therefore 

cot  r,  + cot  r9  + cot  r3  - cot  r _4an  R 
tan  k ■ ■ . ' " s~\  • 

4 2 

3.  On  some  Remarkable  Changes,  Additions,  and  Omissions 
of  Letters  in  Certain  Cognate  European  Words.  By  the 
Hon.  Lord  Neaves. 

The  subject  of  comparative  philology  has  always  interested 
scholars,  but  latterly  the  study  has  been  carried  on  in  a more 
scientific  manner,  and  I may  also  say  with  more  success,  than  at 
any  former  period.  One  great  object  in  prosecuting  the  study  is 
to  detect  the  various  disguises  which  words  radically  the  same  are 
apt  to  assume  in  different  languages  or  dialects.  The  great 
scholars  of  two  centuries  ago  were  fully  alive  to  the  importance  of 
this  inquiry,  and  although  they  sometimes  indulged  in  too  great 
a latitude  of  conjecture,  there  is  scarcely  an  etymological  affinity 
now  generally  admitted  of  which  traces  and  indications  are  not 
plainly  to  be  found  in  the  works  of  those  learned  men,  and  more 
particularly  in  the  writings  of  Salmasius,  the  greatest  of  them  all. 


597 


of  Edinburgh,  Session  1874-75. 

But  it  cannot  be  denied  that  a strong  impetus  to  this  science 
has  latterly  been  given,  arising  partly  from  a more  extended 
knowledge  of  the  forms  of  speech  since  Europeans  began  to  study 
the  cognate  languages  of  the  East.  Comparative  philology  has 
thus  assumed  a more  definite  shape  within  the  last  fifty  years,  as 
for  instance  in  the  law  of  sound-change  first  pointed  out  by  Bask, 
and  afterwards  confirmed  and  extended  by  Grimm. 

Other  phenomena  of  change  have  still  more  recently  be6n  made 
prominent,  and  to  some  of  these  I now  wish  shortly  to  direct 
attention. 

An  opinion  prevails  among  several  eminent  philologians  that 
the  letter  and  sound  of  l did  not  originally  occur  in  the  Aryan 
family  to  which  our  chief  European  languages  belong.  Its  intro- 
duction, if  it  is  not  original,  is  certainly  not  recent,  for  it  would  be 
difficult  to  maintain  that  it  has  not  existed  for  several  thousand 
years,  as  it  plays  so  conspicuous  a part  in  the  Homeric  writings. 
But  it  appears  that  the  Zend  language — that  is,  the  old  Persian  or 
Bactrian — had  no  such  letter  as  Z,  and  that  European  words  which 
have  that  sound  have  frequently  Zend  forms  where  r supplies  the 
place  of  Z.  It  is  said  also  that  in  the  oldest  Indian  writings  the 
same  peculiarity  appears,  though  the  Z has  been  freely  introduced 
into  the  later  Sanscrit. 

Be  this  as  it  may,  it  must  be  admitted  that  there  is  a great 
affinity  between  the  smooth  and  the  rough  liquids,  Z and  r,  and 
that  they  are  frequently  interchangeable.  We  see  much  of  this  in 
Greek  and  Latin,  and  it  is  not  easy  to  say  that  either  of  the  two 
languages  shows  a preference  for  one  of  those  letters  over  the 
other.  Let  us  take  some  plain  and  undoubted  examples : — 
Aeipiov,  G.;  = lilium,  L. ; paws,  G.,  = Aa/cos,  G.,  a ragged  garment ; 
in  connection  with  which  it  has  been  specially  observed  tha^  the 
Cretan  form  of  Doric  frequently  confounded  p and  A.  The  ter- 
minations -pos,  G.,  and  -lus,  L.,  seem  cognate,  as  in  rpopepos  and 
tremulus.  In  Latin  itself  we  have  two  terminational  forms  that 
seem  identical — alis  and  aris — the  use  of  which  seems  in  a great 
measure  determined  by  euphony,  in  this  way,  that  where  Z occurs 
in  the  radical  word,  the  termination  -aris  is  used  for  the  sake  of 
variety ; and  when  r occurs  in  the  radical,  -alis  is  used.  Thus 
from  jpopulus  comes  popular  is  ; and  from  naturu , naturalis. 


598 


Proceedings  of  the  Royal  Society 

It  is  remarkable  that  in  the  later  Romance  languages,  Z,  when  it 
is  found  in  Latin,  sometimes  disappears,  and  is  replaced  by  r:  as 
apostolus,  apotre;  epistola,  epitre ; capitulum,  chapitre,  &c.  In- 
deed l does  not  very  well  stand  its  ground  in  modern  times.  In 
Italian  it  often  becomes  an  i ; in  French  it  becomes  an  u ; and  in 
the  lower  German  dialects,  such  as  our  own  Scottish,  it  is  similarly 
changed  or  lost. 

Let  us  now  assume  as  an  interim  hypothesis  that  r and  l are 
interchangeable  in  Greek  and  Latin,  and  see  if  that  assumption 
will  afford  us  results  that  tend  to  confirm  its  truth. 

The  names  for  the  swallow  in  those  two  languages  are  respec- 
tively and  hirundo.  Upon  the  hypothesis  suggested, 

XsXlSuv  may  be  changed  into  xepiSwv;  and  then,  by  well-known 
tendencies  of  the  Latin  language,  the  final  v will  be  dropped, 
leaving  xqoiSw,  while  an  n may  be  inserted  before  the  d to 
strengthen  the  syllable,  as  in  tundo,  tudi ; fundo,  fudi ; fmdo,  fidi ; 
frago,  frawgo ; tago,  tango,  &c.  We  thus  get  ^epn/Sto  and  hirundo, 
the  identity  of  which  is  manifest. 

XaAa£a  and  grando,  the  words,  for  hail,  may  be  assimilated 
nearly  in  the  same  way.  XaAa£a  becomes  xaPata : this  when  con- 
tracted becomes  xpa£a,  as  XaPL*  becomes  gratia.  Z is  = to  ds  or 
di,  and  with  an  inserted  n,  xaPa£a  is  equal  to  grandia,  which  is 
close  upon  grando. 

Upon  this  footing  we  see  the  identity  or  near  affinity  of  Kpvimo 
and  KaAu7TT<o;  and  with  these,  perhaps,  kXcttto)  may  be  connected. 

KvkAos,  the  Greek  for  a wheel  or  ring,  may  in  its  more  primitive 
form  be  set  down  as  KVKpos,  which  seems  cognate  to  the  Indian 
form  chakra,  with  the  same  meaning.  But  Ka/cpos  with  a slight 
metathesis  leads  easily  to  the  Latin  circus,  circulus ; and  it  is 
again  possible  that  by  aspirating  and  modifying  the  consonants, 
circus  becomes  identified  with  the  Teutonic  ring  <=  hring,  while 
kvkXos  is  thought  to  be  cognate  to  the  Teutonic  wheel ; so  many 
diversities  of  form  may  thus  be  derived  from  the  same  elements  of 
a guttural  twice  repeated,  and  a liquid  r or  l variously  arranged. 

fEAj uivPs,  by  changing  the  l into  r and  prefixing  a digamma, 
becomes  vermis,  the  relation  of  the  aspirate  and  digamma  being 
the  same  as  in  icnrepos  and  vesper.  The  Greek  iSpa  would  be 
easily  changed  in  Latin  into  sedla , which  by  assimilation  becomes 


599 


of  Edinburgh,  Session  1874-75. 

sella.  Balbus  and  barbarus  seem  in  like  manner  to  be  connected, 
the  meaning  of  barbarus  being  one  who  speaks  unintelligibly. 

We  may  here  give  an  example  of  the  same  radical  word  appear- 
ing in  two  different  forms  in  the  same  language  with  diversified 
but  kindred  meanings.  The  G-reek  d/xipyco  has  the  general  meaning 
of  pressing  or  squeezing,  while  afxeXy co  has  the  special  meaning  of 
pressing  out  milk  from  the  udder.  The  first  of  these  has  not  been 
adopted  by  the  other  European  languages,  but  d/reAyco  is  very 
widely  diffused  as  mulgeo  in  Latin,  and  milk  in  the  Teutonic  lan- 
guages. 

A somewhat  similar  example  may  be  found  in  the  Greek  words 
ypacfju)  and  yXacfxD.  These  two  words  mean  different  methods  of  a 
kindred  operation,  that  of  marking  intelligible  forms  by  some 
sharp  or  cutting  instrument,  the  one  designating  the  process  of 
writing  or  painting,  and  the  other  that  of  carving  or  modelling. 
Another  cognate  seems  to  be  y \vcj>a).  But  of  these  words,  and 
some  others  connected  with  them,  I shall  have  occasion  afterwards 
to  speak  more  fully. 

Examples  of  the  interchange  of  r and  l might  be  further  multi- 
plied, but  those  already  given  will  sufficiently  illustrate  the  subject, 
and  direct  attention  to  this  mode  of  discovering  latent  affinities  in 
words. 

It  has  often  been  surmised  that  a similar  relation  subsists  be- 
tween other  liquids,  as  between  \vfMf>a  and  nympha,  and  it  seems 
clear  that  the  Attic  dialect  frequently  changed  an  v into  A,  as  in 
mpov , At rpov,  &c.  But  this  hypothesis  has  not  as  yet  been  suffi- 
ciently matured,  and  I refrain  from  entering  on  it. 

The  next  point  that  I shall  notice  is  the  peculiarity  that  un- 
doubtedly exists,  of  leaving  out  or  adding  an  initial  sibilant  in 
cognate  words,  so  as  partially  to  disguise  them.  In  some  lan- 
guages combinations  of  letters  are  found  to  be  admissible,  and 
even  frequent,  which  are  not  found  in  other  languages,  though 
nearly  allied.  Neither  G-reek  nor  Latin  seems  to  admit  of  the 
initial  combinations  of  si  or  sn,  and,  accordingly,  it  is  probable 
that  an  affinity  subsists  between  words  in  other  European  languages 
which  show  these  combinations,  and  Latin  and  Greek  words  that 
show  no  sibilant.  Thus  laxus  may  be  a cognate  of  slack,  limus 
of  slime,  &c.  Nix,  undoubtedly,  is  identical  with  snow,  and 


600  Proceedings  of  the  Royal  Society 

nervus  is  supposed  to  be  the  same  as  snare,  which  is  a word  for  a 
string. 

The  Greek  makes  use  of  the  initial  combination  sm,  which  the 
Latin  rejects;  but  the  Greek  is  not  constant  to  that  combination 
of  letters,  and  the  s is  often  dropped,  so  that  we  have  <rfwcpos  and 
/ uKpos , oyxapaySos  and  /xapaySos.  The  word  /mSiaw  does  not  show 
any  initial  or,  but  it  may  be  conjectured  that  the  a was  once  there, 
and  has  been  dropped.  The  prosody  and  form  of  Venus’s  epithet 
cf)i\ofjL/uLeL8ys  would  be  well  explained  by  considering  it  as  a corrup- 
tion of  ^Aocr/xetS^s.  If  we  adopt  this  view,  we  then  establish  an 
affinity  between  the  Greek  /xeiSiaw  and  the  English  smile,  which  is 
further  supported  by  the  well-known  tendency  of  the  Greek  8 to 
become  an  l. 

In  those  words  in  other  languages  which  have  an  initial  s and 
a consonant,  the  s is  often  dropped  in  Latin,  while  the  rest  of 
the  word  is  retained.  We  see  examples  of  this  in  comparing 
Greek  and  Latin  words.  Thus  we  have  the  Greek  o-^aAAco  be- 
coming in  Latin  fallo;  cr^oyyos  becoming  fungus ; and  or^v8ovr], 
funcla.  The  Greek  cn-eyco  and  oreyos  seem  to  be  identical  with 
tego  and  tectum , and  in  other  languages  the  s seems  also  to  be 
lost,  as  in  the  Gaelic  teach,  the  English  thatch,  and  the  German 
decken. 

In  some  cases  we  find  an  initial  s in  the  Teutonic  languages, 
where  it  is  wanting  in  Latin  and  Greek.  Thus  the  Latin  taurus 
and  the  corresponding  Greek  ravpos  seem  to  be  represented  by  the 
Teutonic  word  steer,  of  which  a diminutive  is  stirk.  The  Greek 
KtLpa)  appears  in  English  in  the  form  of  shear,  an  s being  prefixed, 
and  the  other  consonant  thereby  softened.  This  root  in  the 
Teutonic  languages  is  very  productive,  there  being  many  forms  of 
it  connected  with  the  process  of  cutting  or  dividing,  as  shear, 
share,  ploughshare,  scar,  score,  sharp,  &c.  Probably,  also,  short 
comes  from  this  source,  and  fully  represents  the  Latin  curtus  with 
a sibilant  prefixed.  The  Latin  caveo  seems  to  have  a cognate  in 
an  Anglo-Saxon  word  scevian,  from  which  come  our  common 
words  of  shy  and  shun,  for  the  Latin  caveo  has  completely  the 
idea  of  shunning  or  being  shy  of  an  object.  “ Hunc  tu  Eomane 
caveto.”  The  Latin  carus  with  careo  may  possibly  be  connected 
with  the  English  scarce,  for  the  radical  idea  in  carus  is  that  of 


601 


of  Edinburgh , Session  1874-75. 

scarcity  as  adding  to  the  value  of  a tiling,  just  as  the  physical 
dearth  adds  to  the  moral  dearness  of  an  object ; parco  also  in  Latin 
may  be  cognate  with  the  English  spare. 

The  initial  l in  Latin  seems  often  to  disturb  the  formation  of 
words,  and  to  sacrifice  some  letter  that  had  preceded  it.  Besides 
other  examples  already  referred  to,  we  may  notice  the  word  lien, 
which  appears  to  have  lost  the  older  initials  sp , which  would  iden- 
tify it  with  spleen.  But  the  most  remarkable  instance  of  this  is 
found  in  the  word  lis , which  from  the  old  grammarians  we  know  to 
have  been  originally  stlis.  But  acting  on  the  principle  which 
identifies  l and  r , we  see  that  the  original  form  would  give  us  strits 
instead  of  stlis,  and  thus  we  should  have  the  word  commencing 
with  the  same  letters  as  our  Teutonic  words  strife,  sturt,  streit,  G., 
&c.,  which  undoubtedly  are  cognate  in  their  meaning  with  the 
Latin  lis,  though  this  word  by  a strange  metamorphosis  has  lost 
all  trace  of  that  struggle  or  violent  contention  which  it  really 
represents. 

It  is  a peculiarity  of  the  G-reek  language  that  all  words  beginning 
with  p are  supposed  to  have  a prefixed  aspirate  which  is  analogous 
to  a Latin  sibilant.  If  we  transferred  a Greek  word  of  this  kind 
to  a Teutonic  form,  we  should  prefix  a sibilant  to  the  r,  but  as  sr 
is  not  a combination  favoured  by  the  Teutonic  languages,  a t 
might  be  inserted  for  the  sake  of  euphony.  Upon  this  footing  we 
may  plausibly  consider  the  Greek  pevpa  as  identical  with  the 
Teutonic  stream.  It  is  remarkable,  however,  that  the  Gaelic  has 
no  objection  to  the  initial  combination  of  sr,  and  accordingly  we 
find  the  word  srutli,  pronounced  srhu,  meaning  a stream  or  current, 
and  occupying  an  intermediate  position  between  the  Greek  pew, 
pew o),  and  the  Teutonic  stream.  If  we  could  get  over  the  change 
of  vowel,  we  might  in  the  same  way  connect  the  Greek  pcv,  a nose, 
with  the  Gaelic  sron. 

It  seems  a remarkable  circumstance  that  in  Greek  and  Latin 
words  beginning  with  a sibilant  and  another  consonant  there  is  a 
tendency  to  confound  or  corrupt  the  second  consonant  so  as  to 
change  one  for  another  in  a somewhat  arbitrary  way.  In  Latin, 
in  particular,  where  the  consonant  succeeding  the  sibilant  is 
always  a tenuis,  one  tenuis  is  frequently  changed  for  another  in 
comparing  Greek  and  Latin  words.  Thus  <n rovBrj  and  studium 


602  - Proceedings  of  the  Royal  Society 

seem  equivalent,  also  perhaps  oTaSiov  and  spatium,  o-k€7tw  and 
specio,  o-KvXtv (o  and  spolio. 

In  conclusion,  on  this  modification  of  original  roots  by  the 
adjection  of  an  initial  sibilant,  I shall  revert  to  a set  of  words 
already  noticed — viz.,  ypa<£w,  y\acf)a),  y\vcf> to.  These  words  are  of 
analogous  meaning ; and  it  is  interesting  to  see  whether  we  can 
find  corresponding  and  cognate  words  in  Latin.  I think  the  Latin 
words  scalpo  and  sculpo  are  in  this  situation.  These  words  seem 
to  be  formed  by  prefixing  a sibilant  to  the  radical  elements  of  the 
G-reek  forms  which  consist  of  a guttural  y or  c,  a liquid  l or  r,  and 
a labial  or  7 r.  Now  these  elements,  with  a slight  metathesis, 
may  become  ypair  or  glap,  yapir  or  galp ; prefixing  an  s we  have 
scalp  and  sculpo,  which  words  indicate  operations  of  a kindred 
kind,  that  of  carving  or  embossing.  Some  philologists,  of  whom 
Salmasius  is  one,  consider  that  by  a similar  process  ypa^oj  becomes 
scribo. 

I now  conclude  these  few  observations,  not  unconscious  that 
some  of  the  conjectures  and  speculations  which  have  been  ven- 
tured may  be  overstrained,  or  in  some  respects  mistaken.  But  I 
feel  considerable  confidence  that  the  general  views  I have  expressed, 
most  of  which  are  derived  from  higher  sources  than  my  own 
opinions,  are  correct  in  substance,  and  are  calculated  to  afford  con- 
siderable aid  in  the  continuous  progress  which  philology  is  making. 

4.  De  l’interpolation  des  fonctions  irrationnelles  en  general,  et 
des  fonctions  logarithmiques  en  particnlier,  a l’aide  des 
tables  numeriques.  Par  F.  Lefort,  inspecteur  general  des 
Ponts  et  chaussees,  membre  correspondant  de  l’Academie  des 
Sciences  de  Naples. 

Introduction. 

Pour  faire  un  usage  intelligent  destables  des  fonctions  irrationelles 
en  general,  et  des  tables  de  logarithmes  en  particulier,  il  est  indispens- 
able de  conaitre  les  formules  fondamentales  de  l’interpolation,  et 
de  savoir  se  rendre  compte  du  degre  d’approximation  que  1’on 
peut  obtenir  dans  les  differents  cas.  Je  traite  dans  ce  memoire 
ces  deux  points  qui  sont  a peine  indiques  dans  la  plupart  des 


603 


of  Edinburgh , Session  1874-75. 

ouvrages  elementaires,  et  qui  sont  completement  omis  dans  les 
introductions  les  plus  developpees  a des  tables  d’ailleurs  tres  estim- 
ables. 

De  V interpolation  par  le  moyen  des  tables  numeriques  de  fonctions 
irrationnelles. 

Une  table  si  etendue  qu’elle  soit,  ne  peut  contenir,  dans  les 
limites  de  J ’approximation  qu’elle  comporte,  toutes  les  valeurs 
d’une  fonction,  puisque  cette  fonction  est  susceptible  de  croitre  par 
intervalles  infiniment  petits,  et  que  ses  valeurs  successives  sont 
calculees  pour  des  acroissements  finis,  et  generalement  assez  bornes, 
de  la  variable.  Cependant,  on  peut  se  servir  de  la  table  des  valeurs 
inscrites  pour  determiner  approximativement  les  valeurs  interme- 
diaires  de  la  fonction,  et  c’est  a la  solution  de  ce  probleme  que 
s’ applique  la  methode  dite  d’interpolation. 

On  demontre  que  toutes  les  fonctions  qui  entrent  dans  les  tables 
peuvent,  entre  certaines  limites,  etre  developpees  en  series  conver- 
gentes  suivant  les  puissances  entieres  et  positives  de  la  variable,  a 
laquelle  on  donne  le  nom  d’ argument  de  la  table.  Si  done,  dans  le 
calcul  de  ces  fonctions,  on  borne  1’approximation  a l’ordre  n,  elles 
pourront  etre  assimiles  a des  fonctions  rationelles  et  entieres  de  cet 
ordre.  Ainsi  on  aura  generalement 

(1)  u — a0  + x + a2  x2  + . . . . an  x ; 

u etant  une  fonction  quelconque  de  x,  et  aot  a,  . . . des  quantites 
numeriques,  positives  ou  negatives. 

Les  n + 1 coefficients  de  x sont  completement  determines,  quand 
on  connait  n + 1 valeurs  de  u,  repondant  a n -f  1 valeurs  egale- 
ment  connues  de  x.  Par  suite,  la  fonction  generale  de  x doit  etre 
consideree  comme  donnee  par  cela  seul  que  l’on  donne  n + 1 de  ses 
valeurs  locales. 

D’un  autre  cote,  pour  la  meme  fonction  u , on  a,  par  la  formule 
generale  des  differences  finies, 

/0\  A n — 1 „ »-lw-2  ■ 

un  = u0  + n A u0  + n — A z u0  + . . . n — ^ g—  . . . AM  u0i 

ou  n est  un  nombre  entier  tel  qffien  supposant  constant  l’accroisse- 

4 i 


VOL.  vm. 


604 


Proceedings  of  the  Boyal  Society 


ment  Ax  de  la  variable,  n — on  peut  done  4crire  au  lieu 

de  l’equation  (2) 


(6)  un  — u0  -f- 


^ - x0Au0 

Ax  1 + 


Ax 


1-2  + 


Cette  equation  est  du  ne  degre  en  x , et  elle  doit  devenir  identique 
avec  l’equation  (1),  quand  on  fait  dans  cette  derniere  x = xn)  done 
les  coefficients  des  memes  puissances  de  xn  et  de  x sont  egaux,  et 
les  deux  equations  ne  different  qu’en  ce  que  dans  V une  on  emploie 
le  symbole  x et  dans  l’autre  le  symbole  xn.  On  peut  des  lors  ecrire 
d’une  maniere  generale. 


(4) 


x - xQ  A uq  x - xQ  fx  - xn  A A2  u0 

+ -*r  V + ~xr  (-sr*  - V T2 


+ . . . 


x — x0 

formule  tres  differente  de  la  formule  (3),  attendue  que  ^ 

n’est  plus  assujette  a etre  un  nombre  entier,  mais  peut  passer  par 
toutes  les  valeurs  comprises  entre  o et  n. 

L equation  (4)  permet  d’interpoler  dans  la  s^rie  des  valeurs  u0, 
u,  ...  . un , avec  le  meme  degre  d’approximation*  qui  a et6  adopts 
pour  le  calcul  de  ces  premieres  valeurs.  On  doit  remarquer 
d’ailleurs  que,  l’interpolation  se  faisant  toujours  entre  deux  termes 
consecutifs  de  la  s6rie,  et  rorigine  des  indices  etant  arbitraire,  on 

peut  toujours  faire  ensorte  que  X soit  moindre  que  l’unit4. 

Dans  ces  deux  conditions,  et  si  les  differences  sont  petites,  la 
formule  (4)  devient  trbs  convergente,  et  on  peut,  dans  les  ap- 
plications, borner  le  calcul  a un  petit  nombre  des  termes  de  la  serie. 

Par  exemple,  si  l’on  prend  x0  pour  point  de  depart,  et  que  l’on 
considere  x comme  exprimb  en  parties  de  Ax,  on  doit  poser  x0  = o 
et  Ax  = 1,  en  sorte  que  Interpolation  s’op&re  par  la  formule  tres 
simple 

iC  ““  1 

(5)  U - U0  + X A Uq  + X n A2  Uq  + ... 


enti&rement  de  meme  forme  que  l’equation  (2)*  Toutefois  it  ne 
faut  pas  perdre  de  vue  que  x est  une  quantity  plus  petite  que  1,  une 


* Nous  verrons  plus  loin  sous  quelles  reserves. 


of  Edinburgh,  Session  1874-75.  605 


veritable  fraction  de  Ax.  L’usage,  dans  le  calcul  des  differences 
finies,  est  de  denoter  par  des  indices  croissants  les  valenrs  de  la 
fonction  qui  repondent  a des  valenrs  successivement  croissantes  de 
la  variable.  De  cette  maniere,  les  differences  premieres  sont 
toujours  positives,  lorsqne  la  fonction  croit  en  meme  temps  que  la 
variable,  et  negatives  dans  le  cas  contraire*  II  est  indispensable 
d’ avoir  ces  considerations  presentes  a l’esprit  pour  ne  pas  commettre 
d’erreurs  dans  Fapplication  des  formules,  et  surtout  pour  ne  pas 
leur  donner  une  extension  qu’  elles  ne  comportent  pas. 

Par  exemple,  on  ne  pourrait  dans  la  formule  (2)  changer  uQ  en 
un,  et  reciproquement ; mais  on  devrait  ecrire 


(6) 


l - 1 


= un  - n A un  _ ! + n — A2  un _ 2 + ...  ± A™  uQ ; 


ainsi  qu’il  est  facile  de  le.  verifier. 
Lorsque  A”  u0  = An  un,  on  a encore 
n + 1 


(7)  uQ  = un  - n\un  + n a2  un  4-  . . . ± n — ^ g 


n 4- 1 n 4-  2 2 n — 1 


A Un- 


Cette  equation  (7),  comparee  a F equation  (1)  conduit  a la  suivante 


(8) 


rjQ  q 

u = ux  — xAux  4-  x — 


A 2u,  - , 


qui  donne  lieu  aux  memes  remarques  que  l’equation  (5).  La 
formule  (8)  permet  d’interpoler  en  partant  de  la  valeur  superieure 
de  la  fonction.  Ce  mode  d’interpolation  qui  est  sou  vent  avanta- 
geux,  n’est  pas  kabituellement  suivi : on  s’appuie  en  general  sur  la 
formule  (5). 

La  probleme  de  l’interpolation  est  double : il  s’agit  de  deter- 
miner la  fonction  connaissant  la  valeur  de  la  variable,  ou  de  deter- 
miner la  variable  connaissant  la  valeur  de  la  fonction.  Dans  le 
premier  cas,  il  n’y  a qu’a  mettre  en  nombres  la  formule  (5),  en 
cbercbant  dans  les  tables  les  valeurs  u0)  A u0i  &c.,  qui  repondent  ^ 
l’argument  immediatement  inferieur  a la  valeur  de  la  variable. 
Dans  le  second  cas,  on  met  Fexpression  de  x sous  la  forme 


u - u0 

x = q 

A **'  I . o , 

Au0  4“  2 ^ •+■  . . . 

et  on  resout  Fequation  par  des  approximations  successives,  en 


606 


Proceedings  of  the  Royal  Society 

negligeant  d’abord  les  quantitds  de  l’ordre  A2  u0  et  des  ordres  superi- 
eurs.  La  vraie  valeur  de  l’argument  repondant  a la  fonction  u 
sera  x0  + x A u0- 

Si  l'on  voulait  faire  usage  de  la  formule  (8),  on  aurait 
u,  — u 

x = -5 ; 

x + 1 9 

Atq  - — g—  A2  u0  + ... 

et  la  vraie  valeur  de  I’argument  repondant  a la  fonction  u serait 
xl  -xkXi  . x est  toujours  compte  a partir  de  1’ argument  qui  sert 
de  base  a l’interpolation. 

Du  degre  d approximation  que  permettent  les  tables  usuelles . 

On  entend  par  tables  usuelles  celles  qui  ne  necessitent  pas  en 
general  l’emploi  des  differences  secondes. 

Les  tables  usuelles  les  plus  etendues  ne  donnent  que  les  differ- 
ences du  premier  ordre,  c’est  a dire  les  A u.  Les  plus  completes 
presentent  en  outre,  sous  le  titre  de  parties  proportion elles,-  les  pro- 
duits  de  A u par  0,1 ; 0,2  . . . jusqu’a  0,9,  ou  les  produits  de  A u par 
0,01 ; 0,02  ; . . . jusqu’a  0,99.  Elies  ne  fournissent  ainsi  que  les 
deux  premiers  termes  u0  + xAu0  de  la  formule  d ’interpolation,  et 
c’est  a ces  deux  termes  que,  pour  les  cas  ordinaires,  on  borne 
1’approximation  dans  la  recherche  de  u ou  de  x.  On  ecrit  done, 
suivant  le  problem  e a resoudre,  soit 

u — u0 

u = u0  + xA w0;  soita;  = * 

II  convient  d’etre  fixe  sur  1’importance  de  1’erreur  commise  par 
suite  de  l’omission  d’une  partie  des  termes  de  la  formule  generale, 
et  par  suite  de  l’inscription  incomplete  des  valeurs  de  la  fonction, 
de  ses  differences,  et  des  parties  proportionelles. 

Une  table  donnee  suppose  a l’avance  un  certain  ordre  d’ approxi- 
mation admis  dans  le  calcul  des  valeurs  de  la  fonction.  Les  nombres 
in  serifs  pour  ces  valeurs  doivent  etre  exacts  a une  demi-unite  pres 
de  l’ordre  du  dernier  chiffre,  soit  en  plus,  soit  en  moins.  Ainsi 
les  tables  de  logaritbmes  it  7 decimales  doivent  donner  la  valeur 
des  logaritbmes  a une  demi-unite  pres  du  7e  ordre  decimal. 

L’un  autre  cot4,  les  differences  premieres  inscrites  ne  sont  pas 
cedes  qui  resulteraient  du  calcul  direct  par  la  formule 


(307 


of  Edinburgh,  Session  1874-75. 

A x? 

(9)  A u = f (x)  Aa?  + f (x)  -y  + &c., 

en  bornant  1’ approximation  a une  demi-unite  du  dernier  ordre  de 
la  fonction ; ce  sont  les  differences  memes  des  valenrs  inscrites  de 
la  fonction,  valenrs  qui  peuvent  etre  individuellement  en  erreur  de 
pres  d’une  demi-unite  du  dernier  ordre,  de  telle  sorte  que  la  differ- 
ence inscrite  peut  6tre  en  erreur  de  pres  d’une  unite  de  cet  ordre 
sur  la  valuer  complete  que  represente  la  serie  (9). 

Enfin,  les  parties  proportionelles,  quand  elles  resultent  des  pro- 
duits-par  les  neufs  premiers  nombres,  sont  au  plus  donnees  avec  les 
dixiemes  de  l’unite  du  dernier  ordre : par  suite,  les  produits  xAu0 
peuvent  etre  en  erreur  sur  la  vraie  valeur  de  pres  d’une  unite, 
meme  en  supposant  qu’on  ne  neglige  aucune  decimale  dans  la 
somme  des  produits  partiels  qui  les  composent. 

Cherchonsa  apprecier  l’importance  de  ces  diverses  causes  d’erreur 
dans  la  determination  de  la  fonction  par  l’argument,  ou  de  l’argu- 
ment  par  la  fonction. 

Soit  E,  1’ erreur  propre  resultant  de  l’omission  des  differences 
secondes  et  des  differences  des  ordres  superieurs,  on  a evidemment 

x — 1 x 1 x — 2 

E = x — g—  A 2u0  + x g—  A3  u0  + . . . 

Le  maximum  numerique  du  coefficient  %X ^ a pour  valeur 
0,125,  et  a lieu  pour  x — 0,5-  Le  maximum  numerique  du  co- 
efficient x g a pour  valeur  0,064  et  a lieu  pour  x = 0,42. 

Le  maximum  numerique  des  coefficients  qui  suivent  diminue  pro- 
gressivement,  et  repond  a des  valeurs  progressivement  moindre  de  x. 
En  consequence,  si  la  valeur  numerique  des  differences  successives 
des  divers  ordres  diminue  d’une  maniere  notable,  ce  qui  a lieu  dans 
les  tables  de  logarithm es,  par  exemple;  la  serie  qui  exprime  la 
valeur  de  E,  est  tres  convergente,  et  il  suffit  en  general  de  con- 
siderer  son  premier  terme  pour  apprecier  l’erreur  qui  resulte 
de  l’omission  des  differences  secondes  et  des  differences  des  ordres 
superieurs. 

Dans  les  tables  vraiment  usuelles,  bien  construites,  le  produit 


608 


Proceedings  of  the  Royal  Society 


j 

x — 2 — A%0,  en  aucun  point  de  la  tabled  interpoler,  n’atteint  une 

demi-unite  dn  dernier  ordre  de  la  valeur  de  la  fonction ; par  suite, 
l’emploi  de  la  formule  d’interpolation  ux  = u0  + x A u0  n’entraine 
pas  une  erreur  d’une  demi-unite  pour  cause  d’omission  des  differ- 
ences secondes.  C’est  aussi  la  limite  d’exactitude  que  comportent 
les  valeur  inscrites  de  la  fonction. 

Yoyons  maintenant  si  pour  Tusage  de  Interpolation,  en  sup- 
posant  toujours  l’omission  des  differences  secondes,  il  y a avantage 
a preferer  les  differences  tabulaires , c’est  a dire,  les  differences  entre 
deux  valeurs  cons^cutives  de  la  fonction  inscrites  dans  la  table,  aux 
differences  vraies  que  donne  la  formule  de  Taylor. 

Je  designe  par  u}  A u les  valeurs  completes  de  la  fonction  et  de  sa 
difference  premiere,  par  T,  AT  les  valeurs  analogues  inscrites  dans 
les  tables,  par  AY  la  difference  vraie  exprimee  a une  demi-unite 
pres  du  dernier  ordre  de  la  fonction.  On  a 

ux  — uQ  + xA u0.  D’ailleurs  u0  = T0  ± a0;  ux  = Tx  ± cq;  a0etcq 
etant  des  quantites  num4riques  dont  la  valeur  est  inferieure  a une 
demi*unit6  du  dernier  ordre  de  la  table. 

On  peut  obtenir  la  valeur  approximative  de  ux  par  les  formules 
suivantes: 

T,  = T0  + a?AT0 ; ou  Y.  = T0  + #AY0. 

Comparons  entre  elles  les  valeurs  ux  - Tx  et  ux  - V*,  et  nous 
aurons  ainsi  l’importance  de  1’ erreur  commise  dans  les  deux  cas. 

Nous  remarquons  d’abord  que  AY0  et  AT0  ne  peuvent  differer 
que  lorsque  les  corrections  & faire  a T0  et  a Tx  pour  avoir  u0  et  ux 
sont  de  signes  contraires.  La  comparaison  n’est  done  a faire  que 
lorsque 

= To  ± ao ; et  ui  = Ti  t ai ; 

les  signes  superieurs  etant  pris  ensemble  et  les  signes  inferieurs 
ensemble.  On  a alors 

Ai{0  = AT0  *f  (cq  + a0);  et  Ton  peut  avoir  AY0  = AT0  =f  1,  d’ou 
A u0  - AY0  = t (cq  -f  a0)  ± on  deduit  de  la 
ux  — T*  = U0  — T0  + X (A u0  — AT0)  = ± [a0(l  — X)  — #cq]  = to 
ux  ~ Y*  = w0-  T0  + x[Auq-  AY0)  = ± [a0(l  - x)  + «?(l-a1)]=  <o". 


609 


of  Edinburgh,  Session  1874-75. 

x,  1 - x,  et  1 - oq  etant  des  quantites  positives,  la  premiere  valeur 
de  a/'  (avec  le  signe  +)  est  toujours  positive,  et  la  seconde  (avec  le 
signe-)est  toujours  negative.  Les  deux  valeurs  de  J sont  in- 

versement  positives  ou  negatives  suivant  que  x ^ — a^— . Leur 

^ a0  + at 

maximum  numerique,  relatif  a la  variable  x,  repond  aux  deux 
limites  0 et  1 des  valeurs  de  cette  variable. 

Pour  x = 0 , w'  = ± a0  pour  x = 1 , to'  = ax , 

ainsi  la  valeur  numerique  de  to'  est  toujours  plus  petite  que  0,  5 . 

Pour  x = 0 la  valeur  de  to"  est  la  meme  que  celle  de  to',  mais 
pour  x = 1 , w"  = ± (1  - ax) ; la  valeur  numerique  de  to"  pourrait 
ainsi  l’approcher  de  1. 

On  doit  done  preferer  T*  k Yx  : en  d’autres  termes,  il  vaut  mieux 
interpoler  avec  les  differences  tabulaires  qu’avec  les  differences 
vraies. 

Les  raisonnements  precedents  supposent  que  l’on  a affectue  com- 
pletement  le  produit  x(Au0  - AT0)  car  e’est  k cette  condition 
seulement  que  Ton  pent  remplacer  A u0  - AT0  par  =f  (ax  + a0). 
Cependant,  en  faisant  usage  des  tables  des  parties  proportionelles 
les  plus  completes,  telles  que  celles  de  Bremiker  pour  les  logar- 
ithmes  a 7 decimales,  on  ne  calcule  en  general  les  produits  £cAT0  ou 
x\V0  qu’a  une  demi-unite  du  dernier  ordre  pres.  Voyons  ce  que 
deviennent  alors  les  produits  que  nous  avons  consideres. 

En  general,  #AT0  = e ± /,  e etant  la  partie  entiere  du  produit  et 
/<0,5.  Comme  AY0  peut  differer  de  AT0  de  t 1,  on  aura  alors 
xAY0  = #AT0  =f  x — e ± / =f  a?. 

Le  seul  cas  k examiner  est  celui  ou  la  valeur  numerique  de 
± / =f  oo  est  plus  grande  que  0,5,  puisque  Y*  ne  peut  differer  de 
Tx  que  dans  ce  cas.  On  aurait  ainsi  #AY0  = e ± f , f'p 0,5. 

Au  moyen  des  equations  ci-dessus  la  valeur  complete  de  ux  peut 
prendre  les  formes  suivantes  : 

ux  = u0  + xAu0  = T0  ± a0  + xAT0  =F  x(ax  + a0)  = T0  + e + to'  ± / . 

Si  l’on  prend  pour  valeur  de  ux,  Tx  = T0  + e , l’erreur  r^elle 
tor  = to'  ± /.  Elle  est  numdriquement  plus  petite  que  1. 

Si  l’on  prend  au  contraire  pour  ux)  Vx  = T0  -1-  e t % ; Terreur 


610  Proceedings  of  the  Royal  Society 

reelle  est  exprimee  par  a/,.  = to' ± / =f  x,  et  elle  pent  devenir 
numeriquement  pins  grande  que  1. 

Done,  en  interpolant  avec  les  differences  tabulaires,  et  reduisant 
les  parties  proportionelles  a lenrs  parties  entieres,  on  est  sur  de  ne 
pas  commettre  une  erreur  qui  s’eleve  a une  unite.  L’erreur,  au 
contraire,  pourrait  etre  superieure  a une  'unite,  si  l’on  interpolait 
dans  les  memes  conditions  avec  les  differences  vraies  reduites  a 
leur  partie  entiere.  Telle  est  la  raison  qui  doit  faire  preferer,  au 
point  de  vue  des  approximations,  les  differences  tabulaires  aux 
differences  vraies.*  II  y en  a d’autres,  d’ailleurs,  quand  on  envis- 
age la  question  sous  la  rapport  de  la  facilite  des  inscriptions  et 
des  verifications. 

II  est  a peine  utile  de  dire  que  la  difference  tabulaire  a adopter 
est  celle  qui  existe  reellement  entre  les  deux  nombres  consecutifs 
qu’il  s’agir  d’interpoler,  et  non  une  difference  plus  ou  moins  voisine 
inscrite  en  marge  de  la  table. 

Pour  obtenir  avec  surete  la  partie  entiere  de  a?AT0  a une  demi- 
unite  pres,  x etant  generalement  un  nombre  de  deux  chiffres  au 
moins,  il  faut  que  la  table  des  parties  proportionelles  donne  les 
dixiemes,  si  elle  fournit  seulement  le  produit  de  AT0  par  les  neuf 
caracteres  de  la  numeration  decimale. 

Toutes  les  erreurs  que  nous  venons  d’apprecier  s’appliquent  a la 
determination  de  la  fonction  a l’aide  des  valeurs  donnees  de  l’argu- 
ment.  II  importe  aussi  de  se  rendre  compte  de  la  maniere  dont 
les  erreurs  qui  peuvent  entacber  Pexpression  de  la  fonction  et  de 
ses  differences  pesent  sur  la  determination  de  l’argument.  On  y 
parvient,  sans  entrer  dans  de  longs  details  de  calcul,  en  remarquant 
que,  pour  des  amplitudes  locales  et  restreintes,  les  variations  des 
arguments  sont  k tres  peu  pres  proportionelles  aux  variations  des 
fonctions.  Si  done  la  variation  A u de  la  fonction  repond  a la 
variation  Aa?  de  1’argument,  pour  une  variation  a de  la  fonction 

Targument  variera  de  Aa?.  Cette  variation  sera  d’autant  plus 

faible  que  la  difference  de  la  fonction  sera  plus  grande. 

La  meme  consideration  sert  a apprecier  Fetendue  de  Terreur, 

* II  est  facile  de  conclure  de  ce  qui  precede  que  Ton  doit  egalement 
preferer  les  differences  tabulaires  pour  les  ordres  superieures,  lorsqu’il  est 
necessaire  d’en  faire  usage. 


611 


of  Edinburgh , Session  1874-75. 

lorsque  l’argument  qui  sert  a determiner  la  fonction  n’est  lui- 
meme  qu’approximativement  connu.  Si  (3  represente  1’ erreur 
possible  sur  P argument,  la  plus  grande  erreur,  dont  puisse  etre 
entackee  pour  cette  cause  la  fonction  qu’il  determine,  est  exprimee 

par  A u,  et  Ton  voit  qu’inversement  a ce  qui  avait  lieu  dans 

le  cas  precedent,  Perreur  est  d’autant  plus  considerable  que  la 
difference  de  la  fonction  a une  plus  grande  valeur. 

Lorsque  l’on  veut  apprecier  l’influence  totale  possible  de  diverses 
causes  d’erreur  sur  la  determination  d’une  quantite,  il  faut  donner 
le  meme  signe  aux  erreurs  possibles  calculees,  et  les  aj outer. 

Si  1’ on  ajoute  entre  elles  plusieurs  quantites  qui  ne  sont  exacte- 
ment  connues  qu’entre  certaines  limites,  la  plus  grande  erreur 
possible  de  la  somme  sera  egale  a la  somme  arithmetique  des  plus 
grandes  erreurs  de  ckacun  des  termes,  ensorte  que  1’expression  de 
cette  erreur  ne  change  pas  quand  il  s’agit  de  difference  au  lieu 
d’addition. 

Dans  la  multiplication  ou  dans  la  division  d’une  quantite  qui 
n’est  pas  exactement  connue  la  plus  grand  erreur  croit  ou  diminue 
dans  la  meme  proportion  que  la  quantite  elle  meme. 

Les  principes  exposes  dans  cet  article  permettent  de  se  rendre 
compte  de  l’avantage  que  peut  presenter,  suivant  les  cas,  l’emploi  de 
l’une  ou  de  1’autre  des  formules 

ux  - u0  + os^u0 ; ux  = ux  - a?A ux . 

x devient  ainsi  4gal  a 0,5  au  plus,  et  on  attenue  l’erreur  possible 
sur  le  produit  ^AT0 . Si  l’on  consentait  a emplo37er  concurrement 
ces  deux  formules,  dans  les  conditions  que  nous  avons  definies,  on 
pourrait  diminuer  de  pres  de  moitie  1’etendue  des  tables  des  parties 
proportionelles.  On  ne  doit  pas  se  dissimuler  toutefois  que  ce 
double  usage  exige  la  coup  d’oeil  d’un  calculateur  exerce. 

(Extrait  d’un  memoire  sur  la  th4orie  des  logarithmes,  la  con- 
struction et  l’usage  des  tables  logarithm iques,  compose  en  1857  et 
reste  inedit. 

C’est  de  ce  memoire  qu’a  6t4  4galement  extrait  Particle  sur  les 
grandes  tables  du  Cadastre,  publie  en  1858,  dans  le  tome  iv..  des 
Ann  ales  de  l’Observatoire  de  Paris.) 

4 K 


vol.  vni. 


612 


Proceedings  of  the  Royal  Society 


Monday,  5th  July  1875. 

Sir  EOBEET  CHEISTISON,  Bart.,  Hon.  Vice-President, 
in  the  Chair. 

The  following  Communications  were  read 

1.  The  Theory  of  the  Causes  by  which  Storms  Progress  in 

an  Easterly  Direction  over  the  British  Isles,  and  why  the 

Barometer  does  not  always  indicate  real  vertical  pressure. 
By  Eobert  Tennent,  Esq. 

Upwards  of  three  years  ago  the  author  laid  a paper  before  two 
members  of  the  Scottish  Meteorological  Society.  The  question 
taken  up  was,  why  horizontal  movement  takes  off  vertical  pressure  ; 
and  the  conclusion  arrived  at  was,  that  every  such  horizontal  cur- 
rent, owing  to  its  passage  over  a resisting  surface,  and  by  means  of 
rapid  upper  currents,  caused  removal  of  air  and  lifting,  and  thereby 
diminished  pressure.  It  was  inferred  that  the  barometer  which  re- 
presented this  was  consequently  an  “effect”  and  not  a cause  of  wind. 

The  present  remarks  will  be  confined  mainly  to  the  mechanical 
effects  of  motion  and  friction, — the  important  questions  of  tempera- 
ture, vapour,  rotation,  external  high  and  low  pressure,  &c.,  not  being 
now  considered. 

Friction. — This  forms  a very  important  element.  To  it  is  due 
the  retardation  of  the  surface  currents,  while  the  upper  currents 
move  more  rapidly,  being  comparatively  free  and  unimpeded. 
Surface  retardation  is  increased  by  pressure,  which  amounts  to  8J 
tons  on  every  square  yard,  but  this  gradually  diminishes  upwards. 
Tyndal,  by  experiment,  estimated  the  mobility  of  the  uppers  on 
Mont  Blanc  as  being  twice  as  great  as  that  of  the  surface.  When 
the  atmosphere  is  in  a state  of  rest,  its  columns  maybe  represented 
as  being  vertical  or  upright,  but  when  rapid  uppers  and  retarded 
surface  currents  prevail,  it  may  then  be  regarded  as  moving  in 
inclined  columns  at  an  angle  to  the  surface,  and  in  the  direction 
of  the  moving  force. 

Supply. — The  inclination  of  the  columns  will  depend  not  only 
on  surface  friction,  but  also  on  the  supply  of  air  to  the  moving  cur- 


613 


of  Edinburgh , Session  1874-75. 

rents.  This  may  be  sufficient,  insufficient,  or  more  than  sufficient. 
The  supply  to  the  uppers  may  differ  in  amount  from  that  to  the 
surface  currents.  The  position  and  the  distance  of  the  source  of 
supply  are  also  important.  This  may  he  vertically  or  horizontally 
situated.  According  to  Redfield  and  others,  the  horizontal  extent 
of  an  atmospheric  disturbance  is  often  two  hundred  times  greater 
than  its  vertical  height.  The  arresting  effect  of  such  an  extensive 
surface  on  the  supply  drawn  over  it  must  he  great.  But  if  supply  is 
derived  from  a vertical  source,  as  in  the  case  of  a descending  current, 
much  less  retardation  will  take  place.  Hence  when  the  supply  to 
the  surface  current  is  from  a horizontal  source,  great  inclination  of 
columns  will  take  place,  but  when  from  a vertical  source,  there 
will  he  less  inclination.  An  important  difference  in  the  mode  of 
inflow  of  the  different  winds  will  thus  exist  betwixt  those  vertically 
and  those  horizontally  supplied.  The  former  will  move  freely  in 
nearly  upright  columns,  the  latter  in  columns  more  or  less  inclined. 

Gradients. — A.  river  flows  on  an  incline,  by  the  amount  of  which 
its  velocity  and  volume  are  regulated ; hut  the  river  itself  exerts  a 
reactionary  influence  on  this  incline,  which  it  will  tend  to  pull 
down  and  lower,  if  it  is  not  composed  of  rigid  materials,  An  aerial 
gradient  is  not  rigid,  it  is  elastic  and  mobile,  and  being  thus 
subject  to  the  reactionary  influence  of  the  air  which  it  draws  to 
itself,  it  will  not  remain  stationary,  nor  will  its  incline  remain 
unaltered.  Its  efficiency  and  the  amount  of  its  slope  will  there- 
fore depend  on  the  amount  of  facility  with  which  air  inflows  to 
it.  If  the  inflow  takes  place  in  vertical  columns,  little  or  no 
reactionary  influence  or  lowering  will  be  produced;  but  if  the 
inflow  is  in  inclined  columns,  which  therefore  produce  difficult 
supply,  being  from  a horizontal  source,  the  tendency  will  be  to  pull 
down  and  lower  the  gradient,  and  thereby  remove  the  source  of 
supply  to  a greater  distance.  What  thus  takes  place  is  popularly 
expressed  by  the  phrase,  that  the  wind  blows  itself  out,  which  is  in 
fact  accomplished  by  lowering  the  gradient,  and  removing  the 
source  of  supply  to  such  a distance  that  it  is  almost  entirely  arrested 
by  the  extent  of  the  resisting  surface  over  which  it  is  now  com- 
pelled to  pass.  Thus  a gradient  represents  not  only  a motive  force, 
but  also  a reactionary  force  which  is  due  to  it. 

Curve  of  Outward  Propagation. — There  are  thus  two  different 


614  Proceedings  of  the  Royal  Society 

inodes  of  inflow  towards  the  low  central  barometer;  one  is  an 
advantageous,  the  other  is  a disadvantageous  form.  It  is  by  this 
latter  mode  that  the  gradient  is  lowered.  It  takes  place  with 
inclined  columns,  resulting  from  rapid  uppers  and  retarded  surface 
currents.  Much  of  the  work  of  inflow  is  thus  thrown  upon  the 
uppers.  To  enable  them  to  maintain  their  superior  velocity,  they 
themselves  must  be  adequately  supplied  by  the  uppers  in  advance. 
This  is  accomplished  by  outward  extension  ; they  advance  forwards 
to  procure  the  requisite  supply  from  the  still  atmosphere  a-head, 
which  now  begins  to  inflow  spirally.  It  is  to  this  advancing 
line  of  removal,  that  the  term  “ Curve  of  Outward  Propagation” 
is  applied.  It  may  be  illustrated  thus  : — If  a river  flowing  down 
an  incline  does  so  uniformly,  and  at  am- equal  rate  of  speed, 
removal  will  equal  restoration;  but  if  in  the  lower  part  of  its 
course,  a more  rapid  removal  is  inaugurated,  while  restoration  or 
supply  above  remains  as  before,  the  curve  representing  the  poin 
at  which  the  increased  removal  begins  to  travel  upwards  will  repre- 
sent the  forward  movement  of  this  curve  of  outward  propagation  or 
extension. 

When  a rapid  fall  of  the  barometer  takes  place,  if  the  inflow  to 
the  depression  so  formed  assumes  an  advantageous  form,  it  will  fill 
up  at  once  ; but  if,  as  usually  takes  place,  it  assumes  the  disad- 
vantageous form  or  mode  of  inflow,  instead  of  filling  up,  it  will 
open  out  and  extend  itself  outwards  all  round,  like  the  undulations 
produced  by  a stone  thrown  into  still  water.  The  uniformity  of 
this  extension  will  depend  on  the  uniformity  of  the  motive  central 
inflow.  With  inflowing  winds  of  different  degrees  of  density, 
temperature,  and  moisture,  it  may  be  safely  asserted  that  such 
uniformity  of  inflow  will  not  occur.  A disadvantageous  mode  of 
inflow  will  consequently  take  place  in  one  segment,  with  a less 
disadvantageous  mode  in  another.  The  first  is  found  in  the 
advancing  segment,  the  latter  in  the  rear. 

The  effect  of  this  want  of  uniformity  in  the  mode  of  inflow  will 
be,  that  the  depression,  instead  of  extending  itself  uniformly  all 
round,  will  shallow  itself  out  in  one  particular  direction , which  is  that 
in  which  the  disadvantageous  mode  of  inflow  is  found,  and  where 
the  curve  of  outward  propagation  exists.  This  disadvantageous 
mode  of  inflow  is  increased  by  the  circumstance,  that  as  the 


615 


of  Edinburgh,  Session  1874-75. 

uppers  are  rapid,  while  the  surface  winds  are  retarded,  the 
numerous  intermediate  layers  betwixt  these,  must  all  move  at 
different  rates  of  speed  attended  by  much  friction  and  consequent 
retardation. 

The  direction  assumed  by  the  curve,  is  therefore  one  which  is 
nearly  opposite  to  that  of  the  motive  inflow , which  produces  it.  In 
a somewhat  similar  manner  within  the  tropics,  oceanic  currents  are 
in  certain  cases  produced,  moving  in  nearly  an  opposite  direction 
to  that  of  the  North  East  trades,  on  which  they  depend. 

Winds  representing  the  different  Modes  of  Inflow. — On  the  west 
segment  of  a barometric  depression,  Polar  winds  prevail,  which  are 
dry,  cold,  and  dense,  and  are  fed  by  descending  currents,  with  a 
vertical  source  of  supply.  They  may  be  regarded  as  surface  winds. 
On  the  east  segment  are  found  equatorial  winds,  which  are  warm, 
moist,  and  less  dense;  they  are  weakened  by  their  ascending  ten- 
dency,— they  have  not  so  much  the  character  of  surface  winds, 
but  assume  more  the  character  of  rapid  uppers,  and  instead  of  a 
vertical,  have- a horizontal  source  of  supply. 

Progress. — When  a barometic  depression  is  formed,  a spiral 
inflow  towards  the  centre  takes  place  ; if  this  were  equally  uniform 
in  every  direction,  the  great  central  fall  of  the  barometer  would 
extend  itself  all  round,  gradually  diminishing  as  it  proceeds  out- 
wards towards  the  circumference,  and  lowering  the  surrounding 
gradients  as  it  proceeds;  but  if,  as  is  usually  the  case,  the  inflow  is 
not  uniform,  the  depression  will  then  extend  itself  in  one  particu- 
lar direction,  in  the  manner  above  described.  This  extension, 
which  is  due  to  the  mode  of  the  central  inflow,  takes  place  mostly 
in  front,  and  in  an  easterly  direction  : it  will  there  create  a 
scarcity  of  supply,  towards  which  the  low  central  barometer  will 
advance.  What  thus  takes  place  may  be  illustrated  in  this 
manner : — Suppose  that  the  ascent  of  a balloon,  situated  near  the 
surface  of  the  ground,  is  retarded,  though  not  arrested,  by  a chain 
passing  over  it.  This  chain,  where  it  reaches  the  ground  on  each 
side,  is  not  fixed  to  it,  but  is  laid  outwards  along  its  surface,  one 
end  extends  for  a short  distance,  the  other  for  a considerable 
distance.  Under  these  circumstances,  the  ascent  of  the  balloon 
will  not  be  vertical,  but  in  a direction  inclined  towards  that  in 
which  the  chain  extends  for  the  greatest  length  over  the  ground, 


616  Proceedings  of  the  Boyal  Society 

and  where,  consequently,  it  is  most  difficult  to  lift,  and  where  the 
drag  is  greatest. 

In  a somewhat  similar  manner  the  low  central  barometer,  having 
by  means  of  the  peculiar  mode  of  inflow  of  winds  in  that  segment 
caused  supply  there  to  be  scarce,  will  itself  move  in  that  direction , 
to  obtain  the  requisite  supply,  which  it  could  not  procure  if  it 
remained  stationary:  in  so  doing,  it  opens  out  the  depression  in 
front,  and  is  enabled  to  move  forward,  provided  it  is  sufficiently 
supplied  in  the  rear.  If  high  pressure  or  steep  gradients  existed 
in  front  of  one  of  the  segments,  progress  could  not  there  take 
place,  since  supply  being  there  abundant,  no  lowering  of  the 
gradient  could  take  place,  nor  could  it  shallow  itself  out  in  that 
direction. 

Lifting. — From  the  greater  mobility  of  the  atmosphere  in  the 
upper  regions,  it  there  moves  faster,  and  hence  the  air  is  more  easily 
removed  than  it  is  near  the  surface.  The  atmosphere  may  thus 
be  conceived  to  be  divided  into  a number  of  spherical  concentric 
layers,  each  possessing  a different  rate  of  speed,  slipping  or  sliding 
over  those  underneath  with  an  increasing  amount  of  friction,  as 
their  position  becomes  lower.  The  upper  layers  possess  two  sources 
of  supply — one  from  a horizontal  source,  the  other  from  the  layers 
underneath,  while  the  surface  layers  possess  only  a horizontal 
source  of  supply.  The  facility  with  which  the  uppers  are  thus 
supplied,  tends  in  the  first  instance  to  increase  their  speed,  but 
when  this  has  taken  place  to  a certain  extent,  the  source  of 
supply  will  diminish  in  amount.  This  is  accompanied  by  a 
lowering  of  the  gradient,  the  effect  of  which  is  to  remove  the 
source  of  supply  to  a greater  distance,  and  increase  the  diminu- 
tion, until  a point  is  at  last  reached  in  which  it  is  almost  entirely 
arrested.  When  this  begins  to  take  place,  the  uppers  will  tend  to 
lift  and  become  detached  as  it  were  from  the  surface,  thus  causing 
a partial  vacuum  near  the  surface. 

Lifting  may  be  illustrated  by  what  takes  place  on  the  lee  side  of 
a house  or  wall,  over  which  a strong  wind  blows,  a partial  vacuum 
is  here  formed.  The  friction  which  retards  the  air  when  flowing 
over  an  extensive  horizontal  surface,  may  be  represented  by  a 
series  of  such  obstructions  which  enable  the  air  to  be  more  easily 
carried  off  and  removed  than  it  can  be  restored.  This  removal 


617 


of  Edinburgh,  Session  1874-75. 

causes  a local  or  partial  reduction  of  pressure,  while  the  real  ver- 
tical pressure  of  the  atmosphere  overhead  remains  unaltered.  The 
relation  which  exists  betwixt  pressure  and  the  speed  of  the  winds 
is  altered  as  their  velocity  increases,  in  a somewhat  similar  way  to 
that  which  takes  place  when  the  lee  way  of  a ship  is  practically 
diminished  by  an  increase  in  its  head  way. 

It  must  be  observed,  that  lifting  can  only  take  place  where 
scarcity  of  supply  exists.  The  vacuum  formed  behind  a wall  over 
which  the  wind  blows  is  due  to  the  fact,  that  removal  is  there 
greater  than  restoration;  for  if  supply  was  sufficient  no  such 
vacuum  could  exist. 

Water  flowing  from  an  orifice  in  the  side  of  a cistern,  which  is 
only  a little  below  its  surface  level,  will  fall  directly  downwards ; 
but  if  the  level  is  raised  much  above  that  of  the  orifice,  the  water 
passing  through  it  will  he  expelled  with  considerable  force ; it  will 
“lift”  and  take  a form  approaching  to  that  of  a horizontally 
flowing  spout.  The  great  mass  of  water  will  accumulate  in  the 
upper  part  of  the  curve  of  the  spout,  and  will  connect  itself  with 
the  side  of  the  cistern  by  a thin  film  of  water,  which  will  now 
take  the  place  of  the  large  body  of  water  which  fell  vertically  down- 
wards when  the  pressure  was  less.  This  accumulation  may  he 
taken  to  illustrate  what  takes  place  in  the  upper  part  of  the  atmo- 
sphere, while  the  thin  film  may  represent  the  diminished  pressure 
at  the  surface. 

Since  scarcity  of  supply  exists  in  the  advancing  portion  of  a 
progressing  depression,  it  is  there  that  lifting  is  most  highly 
developed.  Copiousness  of  supply  is  found  in  the  rear,  and  hence 
it  is  there  that  lifting  is  least  likely  to  he  found. 

Lifting  takes  place  where  inequality  exists  in  the  movement  of 
the  various  atmospheric  layers,  hence  for  this,  among  other  reasons, 
mountain  heights  cannot  be  measured  during  the  prevalence  of 
strong  winds,  nor  is  the  reduction  of  the  barometer  from  consider- 
able heights  to  sea-level  at  all  to  he  depended  upon.  Lifting  is 
always  preceded  by  removal  of  air;  hut  so  far  as  removal  alone  is 
concerned,  it  is  accurately  represented  by  the  barometer.  The 
diminished  pressure  at  the  surface  due  to  lifting  is  also  correctly 
exhibited  by  the  barometer  there  placed,  but  in  such  cases  the 
barometer  fails  to  exhibit  the  real  vertical  pressure  due  to  the 


618 


Proceedings  of  the  Royal  Society 

mass  of  the  column  existing  overhead.  To  ascertain  this  accu- 
rate^, observations  would  require  to  be  taken  by  a series  of  baro- 
meters placed  at  different  heights,  and  not  very  far  apart. 

This  tendency  of  air  to  accumulate  aloft  with  the  abnormal 
pressure  which  accompanies  it,  will  be  masked  by  the  greater  pro- 
portional removal  of  air  w,hich  takes  place  at  an  upper,  as  compared 
with  a lower  station.  This  is  seen  in  the  observations  at  Geneva 
and  St  Bernard.  The  relations  betwixt  the  pressure  which  exists 
at  an  upper  and  a lower  station  will  thus  be  altered  in  two  ways ; 
first,  by  the  tendency  of  the  air  to  accumulate  aloft,  which  lowers 
the  surface  barometer,  while  it  tends  to  raise  the  upper  barometer; 
and  secondly,  by  the  greater  proportional  removal  of  air  which  takes 
place  aloft,  depending  on  the  height  of  the  upper  station.  For 
this  reason,  the  surface  barometer,  although  it  falls  with  strong 
winds,  will  not  fall  to  the  same  extent  as  the  upper  barometer, 
where  so  much  removal  takes  place. 

Isobarics. — Lifting  takes  place  in  front  of  an  advancing  depres- 
sion where  supply  is  scarce ; the  pressure  there  indicated  is  conse- 
quently less  than  it  ought  to  be.  In  the  rear,  where  supply  is 
more  abundant,  and  where  lifting  to  the  same  extent  does  not  take 
place,  the  barometer  there  will  more  nearly  indicate  real  pressure* 
than  it  does  in  front.  Hence  an  isobar  in  front  is  not  comparable 
with  the  same  isobar  in  the  rear.  An  isobar  therefore  would 
require  to  be  corrected  all  round,  but  in  different  degrees;  when 
corrected,  it-  would  extend  further  forward,  and  be  more  widened 
out  in  the  advancing  segment  where  progress  takes  place.  Until 
such  a correction  is  carried  out,  no  uniformity  of  inflow,  either  in 
point  of  force  or  of  direction  can  be  expected  from  the  present  mode 
of  construction  of  charts.  Instead  of  isobars,  this  might  be  repre- 
sented by  a line  or  curve  of  Isorhoics,  drawn  to  represent  lines 
of  equal  inflow.  Such  an  Isorhoic  Curve  would  neither  coincide 
with  lines  of  equal  observed  pressure,  nor  with  lines  of  real 
pressure. 

The  Weather  Charts  are,  as  at  present  constructed,  drawn  from 

*In  the  subsequent  use  of  the  term  “real  pressure,”  the  meaning  to  be 
conveyed  is  this. — The  real  amount  of  pressure  due  to  the  height  of  the 
atmospheric  column  overhead,  but  which  may  not  be  correctly  indicated  by 
the  surface  barometer. 


619 


of  Edinburgh,  Session  1874-75. 

observed  pressure,  and  they  are  also  supposed  to  indicate  real  pres- 
sure. But  since  the  Isobars  in  front  are  more  under  the  influence 
of  the  dynamical  element  than  those  in  the  rear,  real  pressure  is 
there  represented  as  being  lower  than  it  ought  to  be.  - 

If  the  difficulties  attendant  upon  the  construction  of  a chart  of 
Isorhoics  could  be  overcome,  it  would  exhibit  a practical  standard 
of  reference  as  to  the  real  amount  of  inflow  of  air,  which  cannot  be 
ascertained  by  the  present  system  of  Isobarics.  The  introduction  of 
the  dynamical  element  complicates  the  forms  of  the  Isobaric  curves 
to  such  an  extent  as  often  to  render  them  absolutely  uninterpre- 
table : this  is  done  by  creating  barometric  oscillations,  and  different 
modes  of  inflow  in  the  various  winds,  which  would  not  take  place 
on  a frictionless  surface. 

Barometer , liow  it  represents  Pressure. — It  is  only  when  the  atmo- 
sphere is  in  a state  of  perfect  rest  that  the  surface  barometer 
exhibits  the  real  amount  of  pressure  due  to  the  column  of  air 
overhead,  and  it  is  only  then  that  the  normal  diminution  of 
pressure  due  to  the  diminished  mass  takes  place  in  ascending  up- 
wards. 

But  when  the  atmosphere  is  in  a state  of  motion  and  the  upper 
currents  move  rapidly,  the  dynamical  element  then  enters  more 
largely  into  these,  than  into  the  slower  moving  surface  currents. 
The  consequence  is,  that  the  surface  barometer  will  no  longer 
indicate  real  pressure. 

Owing  to  the  lowering  of  the  gradient  in  front,  this  diminu- 
tion of  surface  pressure  takes  place,  most  in  front  of  a moving  de- 
pression, and  least  in  the  rear.  It  is  due  to  lifting,  hence  the 
barometer,  to  a certain  extent,  represents  dynamical  or  fictitious 
pressure.  In  the  rear  it  more  nearly  indicates  static  or  real  pres- 
sure. No  difference  of  real  pressure,  therefore,  seems  necessarily 
to  exist  here,  setting  aside,  in  the  meantime,  the  effects  of  conden- 
sation, to  which  the  reduction  of  pressure  in  the  advancing  seg- 
ment is  usually  attributed.  Hence  it  is  to  the  difference  betwixt 
static  and  dynamic  pressure  that  progress  is  due. 

When  a gradient  is  lowered  by  friction,  the  accompanying 
lowered  barometer  is  an  effect,  and  in  so  far  as  it  is  so,  it  is  in- 
capable of  attracting  air.  The  gradient  thus  lowered  is  caused  to 
extend  itself  forwards,  and  its  accompanying  barometer  will  con- 

4 l 


vol.  vm. 


620 


Proceedings  of  the  Royal  Society 

sequently  fall  at  places  which  it  would  not  otherwise  have  reached  ; 
it  will  there  exhibit  fictitious  pressure,  and  what  takes  place  may 
be  explained  by  the  use  of  the  term  “ falling  for  sympathy  with 
adjoining  barometers.” 

A very  considerable  portion  of  the  numerous  barometric  oscilla- 
tions, which  so  constantly  take  place,  are  an  effect  due  to  friction 
from  a resisting  surface.  On  a frictionless  surface  their  amount 
would  be  greatly  reduced ; no  difference  would  then  exist  betwixt 
the  speed  of  surface  and  upper  currents;  and  depressions,  with  their 
accompanying  disturbances,  would  then  no  longer  possess  a self- 
moving  power, — they  would  cease  to  move  forward,  except,  perhaps, 
in  imbedding  currents. 

Conclusions. — When  a barometric  depression  is  formed,  the 
winds  inflow  spirally  towards  the  centre,  but  they  very  seldom  do 
so  equally  or  uniformly.  In  front  they  do  so  with  difficulty,  owing 
to  the  peculiar  mode  of  inflow  which  there  takes  place ; in  the  rear, 
they  do  so  with  comparative  facility.  In  these  circumstances,  the 
low  central  barometer  cannot  remain  stationary.  It  will  move 
forward  in  that  direction  in  which  supply  is  most  scarce,  and  by  so 
doing,  it  will  be  enabled  to  procure  the  necessary  amount  of  supply, 
which  it  could  not  have  received  if  it  remained  stationary.  It  is 
in  this  way  that  progress  takes  place.  A depression  thus  possesses 
within  itself  a self-moving  power.  When  a barometer  begins  to 
fall  rapidly,  the  fall  may  extend  itself  uniformly  all  round  over  the 
surrounding  area.  Such  uniformity  of  extension,  however,  does 
not  usually  take  place,  except  when  a depression  remains  stationary. 
It  generally  assumes  some  particular  direction , which  is  that  indi- 
cated by  progress.  This  is  due  to  the  difference  betwixt  dynamical 
and  statical  pressure  in  front  and  rear,  or,  perhaps  more  frequently, 
to  the  difference  betwixt  the  amount  of  dynamical  pressure  to  be 
found  in  these  positions. 

When  the  atmosphere  is  in  a state  of  perfect  rest,  the  barometer 
then  indicates  real  vertical  pressure ; but  when  it  is  in  motion,  and 
the  surface  currents  are  retarded  by  friction,  while  the  dynamical 
element  of  motion  is  introduced  in  a comparatively  larger  propor- 
tion into  the  uppers,  the  process  of  lifting  takes  place,  by  which 
surface  pressure,  as  indicated  by  a barometer  there  placed,  is 
reduced,  while  the  real  vertical  pressure  of  the  column  of  air  aloft 


of  Edinburgh,  Session  187 4-7 5 . 621 

remains  unchanged.  Hence,  in  these  circumstances,  a barometer 
does  not  exhibit  real  vertical  pressure. 

When  horizontal  movement  takes  off  vertical  pressure,  this  is 
accomplished  in  two  ways, — first,  by  actual  removal  of  air,  and 
secondly,  by  lifting.  Strictly  speaking,  however,  no  real  horizontal 
movement  takes  place. 


Addendum. 

Isobarics. — As  above  stated,  these  do  not  indicate  the  existence 
of  real  pressure.  There  are  three  modes  in  which  a barometric 
chart  may  be  constructed.  It  may  be  made  to  exhibit  real  pressure, 
it  may  exhibit  dynamical  pressure,  or  it  may  assume  the  form  of 
isorhoic  curves,  which  will  represent  the  correction  of  barometric 
pressure. 

1.  Charts  of  Real  Pressure. — These  are  the  daily  weather  charts, 
and  the  curves  are  there  drawn  through  figures  of  equal  observed 
pressure,  but  they  do  not  exhibit  the  effects  of  the  introduction  of 
the  dynamical  element,  and  hence  do  not  represent  real  pressure  as 
they  are  supposed  to  do.  To  enable  them  to  do  so  graphically,  the 
curves  in  front  must  be  widened  out  and  extended  forwards  to  such 
a point  that  the  amount  of  pressure  which  they  there  indicate  will 
correspond  with  an  equal  amount  of  observed  pressure  in  the  same 
isobar  in  the  rear.  Let  the  observed  pressure  in  the  rear  of  the 
isobar  in  question  amount  to  30-00,  and  let  it  also  be  supposed  lobe 
real,  the  front  of  it  on  the  chart  will  be  exhibited  as  3CK)0.  Let 
the  dynamical  lowering  there,  however,  amount  to  say  0-20.  An 
isobar,  therefore,  drawn  through  an  observed  and  real  pressure  of 
30-00  in  the  rear,  will  in  front  require  to  be  extended  forwards  and 
drawn  through  an  observed  pressure  of  30*20,  to  make  it  exhibit 
one  which  is  real  and  comparable  with  that  in  the  rear.  All  its 
parts  will  now  be  graphically  comparable.  The  comparative  wide- 
ness of  the  isobars  in  front,  with  the  corresponding  diminution  in 
the  steepness  of  the  gradients  there,  will  thus  represent  a greater 
scarcity  of  supply  there  than  is  to  be  found  on  charts  of  the  usual 
construction. 

A curve  thus  drawn,  although  its  different  portions  are  thus 
rendered  graphically  comparable,  will  not  be  one  of  isobarics,  as  it 
is  not  drawn  through  figures  of  equal  observed  pressure,  nor  will  it 


622  Proceedings  of  the  Royal  Society 

indicate  the  spots  at  which  real  pressure  actually  exists.  This 
may  illustrate  the  result  of  the  present  mode  of  construction  in 
which  the  existence  of  real  pressure  is  assumed. 

2.  Charts  of  Dynamical  Pressure. — If  barometric  charts,  instead 
of  exhibiting  real,  are  supposed  to  indicate  dynamical  pressure,  this 
also  can  be  exhibited  graphically,  and  such  portions  of  its  curve 
also  be  made  comparable  by  using  figures  of  equal  observed  pres- 
sure, corrected,  however,  to  represent  those  of  equal  dynamical 
pressure  through  which  the  curve  will  be  drawn.  As  in  the  former 
case,  such  a chart  will  not  be  one  of  isobarics ; it  will  be  one  of 
isodynamics,  and  will  indicate  approximately  the  spot  at  which 
real  pressure  exists. 

Such  a chart,  therefore,  will  more  nearly  represent  the  real  state 
of  pressure  than  one  of  the  ordinary  construction,  because  in  few 
or  no  instances,  over  the  area  usually  embraced  by  it,  is  the 
atmosphere  in  a state  of  perfect  rest,  hence  real  pressure  is  not 
often  found  to  exist.  In  this  instance  of  graphical  delineation  to 
exhibit  dynamical  pressure,  an  extension  of  the  isobars  will  take 
place,  but  to  a greater  extent  in  front  than  in  the  rear,  though  the 
extension  will  not  be  so  great  as  in  the  former  instance. 

3.  Curve  of  Isorhoics. — Such  a curve  as  this,  which  represents 
uniformity  of  inflow  in  the  various  segments,  besides  aiding  the 
correction  of  the  barometer,  will  also  increase  the  reliability  of  the 
gradients  on  which  they  depend. 

Lifting. — It  is  generally  assumed  that  the  force  of  the  wind 
depends  on  the  steepness  of  the  gradients,  and  not  on  the  absolute 
height  of  the  barometer.  In  the  “ English  Meteorological  Ma- 
gazine,” for  June  1869,  Strachan,  however,  shows  that  strong  winds 
generally  are  also  accompanied  by  a remarkable  reduction  of 
pressure.  This  takes  place  mostly  with  equatorial  winds,  attended 
also,  as  shown  in  a diagram,  with  the  greatest  barometric  oscilla- 
tions. The  reason  of  this  is,  that  these  winds  are  fed  from  a 
horizontal  source  of  supply,  and  are  drawn  over  a resisting  surface 
often  of  great  inequality.  Under  these  circumstances  “ lifting  ” 
takes  place.  With  polar  winds,  which  have  a vertical  source  of 
supply,  removed  from  proximity  to  a resisting  surface,  fewer 
oscillations  take  place,  and  the  barometer  often  rises.  Jenyns  has 
shown  that,  unlike  the  thermometer,  the  barometer  rarely  rises 


of  Edinburgh,  Session  1874-75.  623 

above  its  mean  more  than  one-half  of  the  amount  to  which  it  falls 
below  it.  When  below  the  mean,  equatorial  winds  prevail,  and 
the  greater  range  of  pressure  which  then  takes  place  I attribute  to 
the  cause  above  stated. 

Note. — In  the  “Philosophical  Magazine”  for  September  1874, 
Mr  Tylor  comes  to  the  conclusion  that  “ the  barometer  cannot 
give  a true  indication  of  weight  when  there  is  motion  in  the 
atmosphere.” 

2.  On  Electric  Images.  Professor  Tait. 

3.  Laboratory  Notes.  By  Professor  Tait. 

a.  On  the  Origin  of  Atmospheric  Electricity. 

This  was  a preliminary  notice  of  the  results  of  a series  of  ex- 
periments devised  to  test  the  part  played  by  water-vapour  in  the 
production  of  atmospheric  electricity.  While  water  is  in  the  form 
of  vapour  it  must  be  electrified  by  contact  with  the  gases  of  the 
atmosphere — as  they  are  by  contact  with  one  another.  Precipita- 
tion of  vapour  in  a receiver,  whether  produced  by  cold  or  by 
exhaustion,  was  found  to  be  steadily  accompanied  wrth  a dis- 
engagement of  electricity.  Further  experiments  are  to  be  made 
with  receivers  of  very  great  capacity. 


b.  Preliminary  Experiments  on  the  Thermal  Conductivity  of  some 
Dielectrics.  By  Messrs  C.  M.  Smith  and  C.  Gr.  Knott. 

These  experiments  were  suggested  by  observations  on  the  different 
lengths  of  time  required,  under  different  circumstances,  for  telegraph 
cables  to  assume  the  temperature  of  the  water  in  which  they  were 
submerged.  The  method  employed  was  that  known  as  “ Ang- 
strom’s,” which  has  already  been  described  by  Prof.  Tait  (Proc. 
B.  S.  E.  1872-73  p.  55-61);  the  manner  of  the  application  of  the 
method  being,  however,  somewhat  modified  in  these  experiments, 
we  will  give  a short  description  of  it. 


624 


Proceedings  of  the  Royal  Society 

The  substances  to  be  experimented  on  were  obtained  in  sheets, 
from  which  eight  or  nine  circular  discs  3 inches  in  diameter  were 
cut,  and  piled  one  on  another  so  as  to  form  a cylinder.  Between 
the  first  four  discs  thermo-electric  junctions  of  fine  copper  and 
iron  wires  were  inserted.  A |-in.  copper  plate,  with  three  small 
hooks  on  the  circumference,  was  placed  on  either  end,  and  the 
whole,  having  been  slightly  compressed  in  a Bramah  press,  was 
tied  together  with  strings  stretching  from  hook  to  hook.  The 
cylinder  thus  prepared  was  surrounded  with  cotton  wool,  and  placed 
horizontally  in  a wooden  frame,  with  one  end  projecting  about  a 
quarter  of  an  inch.  Over  this  end  a sheet  of  tinned  iron  was  then 
drawn  so  as  to  screen  all  except  the  copper  plate  from  the  heat. 
The  hitherto  free  ends  of  the  thin  copper  and  iron  wires  were 
attached  to  similar  pieces  of  thick  copper  wire,  and  to  insure 
equality  of  temperature  were  immersed  in  small  vessels  of  water, 
placed  in  a larger  vessel  also  containing  water;  the  other  ends  of 
the  thicker  wires  were  then  carried  to  the  mercury  pools  of  a com- 
mutator, so  arranged  that  the  junctions  could  be  thrown  singly, 
and  in  rapid  succession,  into  the  circuit  of  a Thomson’s  dead  beat 
mirror  galvanometer  of  about  24  ohms  resistance.  A further  resist- 
ance of  about  30  ohms  was  also  placed  in  the  circuit.  The  source 
of  heat  was  a large  vessel  of  boiling  water.  From  one  side  of  this 
vessel,  which  was  placed  on  a movable  retort  stand,  a cylinder,  with  a 
flat  end  3J  inches  in  diameter,  projected  for  about  an  inch  and  a 
half. 

The  method  of  observation  was  as  follows.  The  water  being  kept 
boiling,  the  vessel  was  applied  for  ten  minutes  with  its  flat  surface 
in  contact  with  the  copper  plate,  then  removed  to  a distance  for  ten 
minutes,  then  again  applied  for  ten  minutes,  and  so  on  during  the 
whole  of  the  experiment.  After  this  had  been  continued  for  about 
two  hours  observations  were  begun.  The  galvanometer  deflections 
for  each  of  the  three  junctions  were  read  every  minute,  the  readings 
being  taken  from  the  coldest  to  the  hottest;  15s  were  taken  to  read 
the  three.  These  readings  were  continued  till  two  or  three  com- 
plete periods  had  been  observed  after  the  steady  periodic  state  had 
been  arrived  at.  The  deflections  thus  obtained  were  plotted  in  terms 
of  the  time;  and  from  the  curves  so  obtained  the  necessary  calcula- 
tions were  made. 


625 


of  Edinburgh,  Session  1874-75. 

Making  use  of  Fourier’s  theorem,  in  the  form, — 

o 9_ 

y = A0  + A,  cos  ~t  + A2cos  

+ B,  sin  ~t  + B2  sin  2 

values  of  A and  B were  obtained  from  the  expressions 

= 2/0V2+2/1  - y-i  - 2/4V2  - 2/0 +2/7 

4 x/SBj  = yl  + y.2  J2  + y3  - ys  - y,  V2  - y, , 

where  y0 , y15  &c.,  are  the  measured  values  of  the  ordinates  of  the 
curve,  taken  at  intervals  of  J of  a period,  the  axis  of  t being  a 
tangent  to  two  of  the  vertices,  or  a line  parallel  to  it.  From  these 
values  of  A1  and  B1?  a and  (3  were  calculated,  so  as  to  fulfil  the  con- 
ditions 

a = VA*  + Ba2'  ; p = tan -1  ( - • 

These  having  been  calculated  for  the  curves  representing  the  oscil- 
latory state  of  temperature  at  two  of  the  junctions,  the  value  of  the 
conductivity  (K)  was  obtained  from  the  equation 

K = _771  

cp  T lo ge 03-/3'), 

where  cp  is  the  water  equivalent,  T the  periodic  time,  and  r the 
distance  between  the  two  junctions.  Care  must  be  taken  that  log  — , 

is  the  Naperian  logarithm,  and  that  (3  - (3'  is  measured  in  radians.* 
The  unit  employed  in  measuring  y is  of  no  importance,  but  r and 
T must  be  measured  in  the  units  in  which  the  answer  is  required. 
In  the  following  calculations  the  units  employed  are  millimetres 
and  seconds. 

The  substances  experimented  on  in  these  preliminary  investiga- 
tions were,  Siemens’  gutta-percha,  the  same  as  is  used  by  Messrs 
Siemens  Brothers  in  the  manufacture  of  their  cable  core,  and 
Hooper’s  india-rubber,  which  is  the  insulating  material  used  by  the 

* The  unit  angle  has  been  named  by  Prof.  J.  Thomson  a Radian.  As  there 
is  no  surface  conduction  in  these  experiments,  the  two  quantities  referred  to 
ought  to  be  equal.  Their  more  or  less  close  agreement  may  be  taken  as  a 
test  of  the  accuracy  of  each  experiment. 


626 


Proceedings  of  the  Boyal  Society 


11  Hooper  ” Company.  The  following  are  the  most  important  results 
of  the  experiments  : — 


Gutta-Percha,  No.  I. 

= *99  mm.;  mean  free  temperature,  40°  C. 


Junefc. 

yl 1 

yA 

y-2  1 

y 3 

2/4 

y5 

2/6 

y 7 

Ax 

b, 

a 

I. 

0*0 

4-8 

11*2 

18*6 

24*4 

20-3 

12*9 

5*6 

-11-13 

1 

p 

00 

02 

11*17 

II. 

1*7 

1-8 

oo 

o 

13*4 

18*9 

18*7 

11*7 

6*7 

- 8*46 

- 2-72 

8*89 

175°  34' 
162°  10' 


loge  =0*22835;  /3-/3'*=130  24j|  0*2345  radians  ; 
K 


cp 


= 0*0479  mm.  secs. 


Gutta-Percha,  No.  II. 

t = 2*04  mm.;  mean  free  temperature,  46°  C. 


Junctions. 

y0 

y i 

2/2 

2/3 

2/4 

2/5 

2/6 

2/7 

A, 

a 

I. 

2*0 

6*9 

12*7 

18-0 

17*2 

11*9 

6-7 

1*7 

-7-59 

3*48 

8-35 

11. 

0*0 

1*6 

5*9 

11*1 

13-0 

9*8 

5*6 

1*6 

-6*37 

0*31 

6*38 

24°45' 

2°47' 


log  ft.  = 0-26915;  /3 - <3'  = 21°  58'  = 0-38397  radians; 

6 a 

— = 0*0494  mm.  secs. 

cp 

The  third  junctions  in  the  gutta-percha  did  not  give  reliable 
results,  owing  to  the  very  slight  temperature  variations. 

India-Kubber,  No.  I. 

t — 3-320;  mean  free  temperature,  23°  C. 

P 

42°  10' 
8°  16' 

log  % = 0*27687;  (3  - (3'  = 33°  54'=  0-5923  radians; 

e a 

— = 0-176. 

cp 


Junctions. 

2/o 

2/i 

y^ 

2/3 

2/4 

2/s 

2/6 

2/7 

A, 

a 

I. 

2*1 

5*4 

9-2 

11-9 

9*7 

6*1 

2*1 

0*3 

-4-08 

3-69 

5*50 

II. 

0*1 

1*6 

4*9 

7*8 

8-4 

6*6 

3*7 

1*1 

-4*13 

0-60 

4*17 

* These  values  of  >8-/3'  include  -0006  radians,  being  the  equivalent  for  the 
7-6"  lost  in  reading. 


of  Edinburgh,  Session  1871-75.  627 

Curve  III.  is  in  this  experiment  not  so  good  as  curves  I.  and  II., 


but  the  mean  result  from  it  makes 


perature  of  20  C. 


K 

cp 


'257  with  a mean  free  tem- 


India-Rubber,  No.  II. 


= 2*480  ; mean  free  temperature,  | j 30°  C ; j jjj'  | 0 C. 


Junctions. 

Vo 

2/i 

y-2 

2/3 

2/4 

2/5 

2/6 

2/r 

i 

a 

I. 

9*4 

13-7 

15-6 

13-0 

8*2 

3*2 

0-4 

4*7 

0-69 

7-12 

7J5 

II. 

3*8 

7-7 

11-2 

12-0 

9-0 

5*1 

T4 

0-9 

- 2*80 

oo 

5-62 

III. 

0-5 

2-7 

6'7 

9*8 

9 '4 

6-5 

3-0 

0-8 

-4-49 

op 

4 85 

18 

95°  32' 
60°  06' 
22°  17' 


II 


II. 

III. 


j’  }Ioge  7 = 0'24078;  /?- /S' = 35“ 26' = 0-6190  radians; 

= 0-1080  . 

cp 

} log*  = 0-14739  ; ft  - ft'  = 37°  49'  = 0-6607  radians. 

' a! 


Cp 


- = 0*1653  . 


These  experiments  seem  to  show,  in  the  case  of  the  india-rubber, 

a very  marked  increase  in  the  value  of  — with  a decrease  of  tem- 

cp 

perature;  but,  unfortunately,  the  late  period  of  the  session  at  which 
the  specimens  were  obtained  prevented  our  repeating  the  experi- 
ments, which  probably  give  too  high  values.  We  have  not  yet 
been  able  to  obtain  values  for  c,  but  hope  to  do  so  at  some  future 
time.  The  values  for  p are  roughly — for  gutta-percha,  p = 097; 
for  india-rubber,  p=  1T7  at  the  temperature  of  18'8°  C. 

In  conclusion,  our  thanks  are  due  to  Prof.  Tait  for  the  use  of  his 
laboratory,  and  the  kind  assistance  which  he  gave  us  in  our  experi- 
ments; to  Prof.  Jenkin,  through  whom  we  obtained  the  specimens; 
and  to  Messrs  Siemens  and  Hooper  for  the  care  with  which  these 
specimens  were  prepared. 


4.  A Chapter  on  the  Tides.  By  the  Rev.  James  Pearson, 
M.A.,  Vicar  of  Fleetwood.  Communicated  by  Professor 
Tait. 

4 M 


VOL,  VITI. 


628  Proceedings  of  the  Royal  Society 

5.  Farther  Researches  in  very  perfect  Vacua.  By 
Professors  Dewar  and  Tait. 

(. Abstract .) 

The  paper  commences  with  an  account  of  various  methods  of 
producing  very  perfect  exhaustion  of  a receiver,  especially  that 
recently  devised  by  the  authors,  in  which  the  absorbent  power  of 
charcoal  is  made  use  of.  An  attempt  is  made  to  calculate  the 
amount  of  exhaustion  thus  producible. 

Certain  experiments  described  long  ago  by  Bennett,  Mark  Watt, 
and  others,  and  very  recently  much  extended  and  improved  by 
Crookes,  are  next  referred  to ; with  the  results  obtained  by  the 
authors  when  repeating  them  in  their  charcoal  vacua. 

By  operating  with  discs  of  rock-salt  and  other  materials  under 
various  circumstances  of  absorption,  the  observed  phenomena  are 
traced  to  the  unequal  heating  of  the  movable  parts  of  the  appa- 
ratus; and  their  full  explanation  is  given  from  the  kinetic  theory 
of  gaseous  pressure. 

To  confirm  this  explanation  various  additional  experiments  are 
described — some,  in  particular,  with  amorphous  sulphur.  The 
amount  of  radiation  from  a magnesium  lamp,  as  measured  by  the 
pyrheliometer,  is  shown  to  be  quite  consistent  with  the  explanation 
offered. 


ELECTRIC  RESISTANCE  OF  IRON. 


of  Edinburgh,  Session  1875-76. 


629 


[ Deferred  from  jo.  491.] 

On  the  Electric  Eesistance  of  Iron  at  a High  Temperature. 
By  Messrs  C.  M.  Smith,  C.  Gr.  Knott,  and  A.  Macfarlane. 
(Plate.) 

The  following  paper  is  a continuation  of  a former  brief  one, 
communicated  to  the  Society,  and  printed  in  the  Proceedings , on 
the  change  of  electric  resistance  of  iron  due  to  change  of  tempera- 
ture. In  a note  appended  to  Prof.  Tait’s  paper  on  a “ First 
Approximation  to  a Thermo-electric  Diagram  ” (Trans.  R.  S.E., 
1872-73),  attention  was  drawn  to  the  curious  phenomenon  observed 
by  Grore,  that  at  a temperature  about  dull  red  heat,  iron  wire 
undergoes  sudden  changes  in  length,  and  also  to  the  further  dis- 
covery by  Prof.  Barrett,  that  if  the  wire  be  cooling,  a sudden 
reglow  occurs  simultaneously  with  these  changes.  These  pheno- 
mena seemed  to  be  connected  with  other  known  physical  changes 
which  take  place  in  iron  at  this  critical  temperature,  such  as  the 
loss  of  its  magnetic  properties,  the  remarkable  bend  of  the  iron 
line  in  the  thermo-electric  diagram,  and  the  interesting  alteration  in 
the  rate  of  change  of  electric  resistance  with  respect  to  change  of 
temperature,  observable  in  iron  at  the  same  dull  red  heat.  The 
following  experiments  were  made  mainly  with  the  view  of  more 
thoroughly  investigating  this  last  peculiarity. 

The  method  employed  in  the  first  series  of  experiments  consisted 
in  comparing  the  change  of  resistance  with  time,  the  wire  through- 
out the  whole  of  the  experiment  being  surrounded  for  the  greater 
part  of  its  length  by  an  iron  cylinder  which  had  been  previously 
heated  to  a white  heat  in  a stove,  and  was  then  allowed  to  cool  by 
radiation.  By  this  means  a sufficiently  slow  and  uniform  altera- 
tion of  temperature  was  secured;  and  the  curve  (see  diagram, 
Fig.  I.)  as  plotted  in  terms  of  the  resistance  and  the  time  as 
ordinate  and  abscissa,  shows  the  remarkable  and  sudden  change  of 

^5.  at  a temperature  about  the  dull  red  heat — a change  observable 

in  all  the  experiments  in  connection  with  the  iron  wire.  Upon  the 
substitution  of  an  equal  length  of  platinum  wire  for  the  Iron,  ceteris 
‘ paribus , it  was  found  that  no  similar  change  was  observable— the 


630 


Proceedings  of  the  Royal  Society 

curve  obtained  (see  diagram,  Fig.  II.)  being  throughout  the  same 
range  of  temperature  very  accurately  a straight  line.  The  resistance 
was  measured  by  shunting  the  current  in  the  galvanometer  and 
battery  circuit  through  the  wire  under  consideration.  One  great 
disadvantage  of  this  method  is,  that  the  curves  do  not  represent 
strictly  the  relation  between  temperature  and  resistance,  since  the 
rate  of  cooling  is  not  uniform,  and  the  wire  is  not  at  one  tem- 
perature throughout. 

In  the  second  method,  however,  this  difficulty  was  overcome ; 
for  time,  as  a variable,  was  eliminated  by  combining  the  two  ori- 
ginally separate  experiments  with  iron  and  platinum  into  one,  and 
comparing  the  simultaneous  changes  in  the  resistances  of  these 
wires,  which  were  in  exactly  similar  circumstances.  Equal  lengths 
of  iron  and  platinum  wire  were  led  side  by  side  through  the  hori- 
zontal cylinder,  and  their  extremities  were  so  connected  with  the 
galvanometer  and  battery  circuit,  that  by  simply  rocking  a six- 
footed rocker,  working  in  six  mercury  holes,  the  current  could  be 
shunted  through  each  wire  alternately,  and  thus  their  resistances 
could  be  compared  by  the  effects  produced  upon  the  galvanometer. 

The  curves  obtained  from  these  experiments  with  platinum  and 
iron  (see  diagram,  Fig.  III.),  their  indications  being  here  abscissse 
and  ordinates,  show  the  same  marked  change  at  the  same  critical 
temperature.  When  palladium  was  substituted  for  platinum  the 
same  peculiarity  was  observable  (see  diagram,  Fig.  IV.);  but  when 
palladium  was  substituted  for  iron,  the  curve  obtained  (see  diagram, 
Fig.  V.)  was  an  accurate  straight  line.  It  was  found  expedient, 
after  the  first  few.  preliminary  experiments,  to  introduce  into  the 
battery  circuit  a commutator,  by  which  to  reverse  the  current,  and 
so  eliminate  all  errors  referable  to  thermo-electric  effects  due  to  the 
unequal  heating  (by  radiation  from  the  cylinder,  or  conduction  along 
the  heated  wires),  of  the  various  metallic  junctions  in  the  circuit. 

In  the  third  distinct  series  of  experiments  the  arrangement  was 
more  elaborate.  To  the  platinum  or  other  wire,  whose  resistance 
was  compared  with  that  of  iron,  was  attached  at  the  middle  point 
a third  wire.  By  a mechanical  arrangement  of  rockers  and  com- 
mutators, the  battery  and  iron  wire  could  be  thrown  out  of  the 
galvanometer  circuit,  and  thus  a thermo-electric  standard  of 
temperature  was  obtained,  with  which  the  resistances  of  the  two 


631 


of  Edinburgh,  Session  1874-75. 

wires  could  be  at  any  instant  compared.  One  great  drawback  in 
all  these  experiments  was  the  oxidation  of  the  iron  wire.  In  order 
to  get  rid  of  this  to  some  extent,  an  entirely  new  arrangement  was 
devised,  in  which  the  heating  of  the  wires  was  effected  by  the  same 
current  which  measured  the  resistance ; but  the  results  obtained  by 
this  method  were  far  from  satisfactory,  owing  to  the  many  practical 
difficulties  which  were  continually  cropping  up.  These  experi- 
ments were  conducted  during  March  and  April  of  1874. 

In  the  following  June,  experiments  similar  to  those  of  the  third 
series  above  mentioned  were  made  with  an  iron  wire  and  two 
platinum-iridium  alloys — the  same  which  are  called  M and  N in 
the  thermo-electric  diagram.  The  resistances  of  M were  compared 
with  those  of  iron,  and  readings  as  nearly  simultaneous  as  possible 
were  taken  of  the  deflections  due  to  the  M-N  thermo-electric  junc- 
tion in  the  manner  described  above.  Immediately  upon  the  com- 
pletion of  this  experiment  a triple  junction  was  set  up  of  M,  N, 
and  the  iron  wire  already  used.  The  currents  due  to  the  Fe-M  and 
M-N  junctions  were  then  compared,  and,  from  the  curve  obtained 
(see  diagram,  Fig.  VI.),  which  shows  the  usual  parabolic  charac- 
ters at  and  near  the  neutral  points,  the  iron  line  was  laid  down  with 
reference  to  N (Fig.  VII.).  The  features  of  this  line,  taken  in 
connection  with  the  M-N  deflections  observed  in  the  “ resistance  ” 
experiment,  conclusively  prove  that  the  bend  of  the  iron  line  in  the 
thermo-electric  diagram  occurs  at  almost  exactly  the  temperature 

d It 

at  which  the  sudden  change  in  the  otherwise  nearly  uniform 

of  the  same  iron  wire  is  observable. 

In  the  diagrams  of  the  various  experiments,  all  observed  points 
which  do  not  lie  exactly  on  the  curves  traced  have  been  inserted. 


632 


Proceedings  of  the  lioyal  Society 


Donations  to  the  Eoyal  Society  Library  during  Session 

1874-75  : — 


I.  Authors. 

Asbjornsen  (P.  0.).  Esquisse  Bibliograpkique  et  Litterseire. 
Christiania,  1875.  4to. — From  the  Author. 

Bechmann  (D.  Augustus).  Regiae  Friderico- Alexandrine  Liter- 
arum  LTniversitatis  Prorector.  4to. — From  the  Author. 

Bertin  (L.  E.).  Donnees  theoriques  et  experimentales  sur  les 
Vagues  et  le  Boulis.  Paris,  1874.  8vo. — From  the  Author. 

Note  sur  l’etude  experimentale  des  Yagues.  Paris,  1874. 

8 vo. — From  the  Author . 

- — — Etude  sur  la  Ventilation  dans  Transport-Ecurie.  4to. — 
From  the  Author. 

Notes  sur  la  Theorie  et  l’Observation  de  la  Houle  et  du 

Roulis  suivies  d’une  note  sur  la  resistance  des  Carenes 
dans  le  Roulis  et  sur  les  qualites  nautiques.  1873.  4to. — 
From  the  Author. 

Principes  du  vol  des  Oiseaux.  4to. — From  the  Author. 

Nouvelle  Note  sur  les  Yagues  de  hauteur  et  de  vitesse 

variables.  4to. — From  the  Author. 

Bischoff  (Dr  Theodor  L.  W.)  . Ueber  den  Einfluss  des  Freiherrn 
Justus  von  Liebig  auf  die  Entwicklung  der  Physiologie. 
Munch en,  1874.  4to. — From  the  Author. 

Bindseil  (Dr  Med.  Carl).  Das  Verhalten  der  Korpertemperatur  im 
intermittirenden  Fieber.  Erlangen,  1874.  8vo. — From  the 
Author. 

Boot  (J.  C.  Gr.).  De  Vita  et  Scriptis  Petri  Wesselingil.  Trajecti, 
1874.  8 vo. — From  the  Author. 

Brunton  (T.  Lauder).  On  the  Nature  and  Physiological  Ac- 
tion of  the  Crotalus  Poison  as  compared  with  that  of  Naja 
Tripudians  and  other  Venomous  Snakes.  By  T.  Lauder 
Brunton,  M.D.,  and  J.  Fayrer,  M.D.  8v*o. — From  the 

Authors. 


633 


of  Edinburgh,  Session  1874—75. 

Bursian  (Dr  Conrad).  Ueber  den  Beligiosen  Charakter  des  Grie- 
chischen  Mythos.  Munclien,  1875.  4to. — From  the  Author. 

Coughtrey  (Professor).  Aerial  Locomotion.  Pettigrew  versus 
Marey.  London,  1875.  8vo. — From  the  Author. 

Croizier  (Le  C.  De).  Etude  historique  sur  les  monuments  de 
l’Ancien  Cambodge.  1875.  8vo. — From  the  Author. 

Dana  (James  D.).  Manual  of  Geology,  treating  of  the  Principles 
of  the  Science,  with  special  reference  to  American  Geological 
History.  New  York,  1875.  8vo. — From  the  Author. 

Darwin  (Charles).  A Fajok  Eredete  a Termeszeti  Kivalas  utjan 
vagyis  az  elonoys  valfajok  Fenmaradasa  a leterti  Kuz- 
delemben.  1874.  Yol.  I.,  II.  8vo.- — From  Dr  Theodore 
Margo. 

Demetriades  (Dr  Med.  Al.).  Ueber  Spasmen  der  Kopfrotatoren 
and  deren  Therapie.  Erlangen,  1874.  8vo. — From  the 

Author. 

Dollen  (W.).  Die  Zeitbestimmung  Yermittelst  des  Tragbaren 
Durchgansinstraments  im  verticale  des  Polarsterns.  Part 
2.  St  Petersburg,  1874.  4to. — From  the  Author. 

Dollinger  (J.  Yon).  Gedachtness-Bede  auf  Konig  Johann  von 
Sachsen.  Munchen,  1874.  4to. — From  the  Author. 

Dudgeon  (Patrick).  Historical  Notes  on  the  occurrence  of  Gold  in 
the  South  of  Scotland.  8vo. — From  the  Author. 

Ellis  (A.  J.).  Algebra  identified  with  Geometry.  London,  1874. 
8vo. — From  the  Author. 

Erlenmeyer  (Dr  Emil).  Ueber  den  Einfluss  des  Freiherrn  Justus 
von  Liebig  auf  die  Entwicklung  der  reinen  Chemie.  Mun- 
chen, 1874.  4to. — From  the  Author. 

Etheridge  (Bobert,  jun.).  Notes  on  Carboniferous  Lamellibran- 
chiata.  8vo. — From  the  Author. 

Description  of  a Section  of  the  Burdiehouse  Limestone  and 

connected  Strata  at  Grange  Quarry,  Burntisland.  8vo. — 
From  the  Author. 

Notice  of  Fossils  from  the  Upper  Silurian  Series  of  the 

Pentland  Hills.  8vo. — From  the  Author. 

(Bobert,  jun.).  Bemains  of  Pterygotus  and  other  Crusta- 
ceans, from  the  Upper  Silurian  series  of  the  Pentland  Hills. 

8vo.~  From  the  Author. 


634  Proceedings  of  the  Royal  Society 

Etheridge  (Robert,  jun.).  Note  on  a new  Provisional  Genus  of 
Carboniferous  Polyzoa.  8vo. — From  the  Author. 

On  the  Relationship  existing  between  the  E chin othur idee 

and  the  Perischoechinidce.  8vo. — From  the  Author. 

Fayrer  (J.,  M.D.).  The  Royal  Tiger  of  Bengal.  London,  1875. 
8 vo. — From  the  Author. 

Geyer  (F.).  Inaugural — Dissertation  zur  Erlangung  der  Doctor- 
wiirde.  Jena,  1874.  8vo. — From  the  Author. 

Gumaelius  (Otto).  Bidrag  till  Kaunedomen  on  Sveriges  erratiska 
bildningar,  samlade  a Geologiska  Kartbladet  “Orebro.” 
Stockholm,  1872.  8vo. — From  the  Author. 

Beskrifning  till  Kartbladet  “ Osebro.”  Stockholm,  1873 

8vo. — From  the  Author. 

Handyside  (Dr  P.  D.).  Jubilee  Chronicon  ; a Valedictory  Address 
delivered  on  the  occasion  of  retiring  from  the  Chair  of  the 
Medico-Chirurgical  Society,  7th  January  1874.  Edinburgh, 
1874.  8vo. — From  the  Author. 

Hayden  (F.  V.).  Catalogue  of  the  Publications  of  the  United 
States  Geological  Survey  of  the  Territories.  Washington, 
1874.  8 vo.- — From  the  Author. 

Ilayter  (H.  H.).  A Digest  of  the  Statistics  of  the  Colony  of 
Victoria  for  the  year  1873.  Melbourne,  1874.  8vo. — From 
the  Author. 

Helmkampff  (H.).  Inaugural — Abhandlung  zur  Erlangung  der 

Medizinischen  Doktorwurde.  1874.  8vo. — From  the  Author. 

Henneberg  (Dr).  Inaugural — Abhandlung  der  Medicinischen 

Facultat  zu  Erlangen.  .1874.  8vo. — From  the  Author. 

Heut  (Gottlieb).  Einige  Beobachtungen  uber  Peucedanin  und 
seine  zerselzungs  Producte.  Erlangen,  1874.  8vo. — From 
the  Author. 

Hoeufft  (Jac  Henr.).  Gaudea  Domestica.  8vo.  — From  the 
Author. 

Hooker  (J.  D.).  The  Flora  of  British  India.  Parts  1,  2,  3.  Lon- 
don. 8vo. — From  the  India  Office. 

Hornstein  (C.).  Magnetische  und  Meteorologische  Beobachtungen 
au  der  K.  K.  Sternwarte  zu  Prag  im  Jahre  1873-1874, 
4to. — From  the  Author. 


635 


of  Edinburgh,  Session  1874-75. 

Jalm  (Dr  Max).  Ueber  Fissura  Sterni  Congenita  und  uber  die 
Herz  bewegun  inshesondere  den  Herzsoss.  Erlangen, 
1874.  8 vo. — From  the  Author. 

Jervis  (Guglielmo).  Cenni  G-eologici  sulle  Montagne  Poste  in 
Prossimita  al  G-iacimento  di  Antracite  di  Demonte.  8vo. — 
From  the  Author. 

Joly  (M.  N.).  Notice  sur  les  Travaux  Scientifiques.  4to. — From 
the  Author. 

Etude  sur  les  Metamorphoses  des  Axolotls  du  Mexique. 

8vo. — From  the  Author. 

Etudes  sur  les  Moeurs  le  Developpement  et  les  Metamor- 
phoses d’un  petit  poisson  chinois.  8vo. — From  the  Author. 

Documents  Nouveaux  sur  le  Pygopage  de  Mazires  et  sur 

Millie-Christine.  8vo  From  the  Author. 

Jordan  (Alexis).  Eemarques  sur  le  fait  de  Pexistence  en  societe 
a l’etat  sauvage  des  especes  vegetables  affines.  Lyons, 
1873.  8vo. — From  the  Author. 

Kjerulf  (Professor  Theodor).  Om  Shuringsmoerker,  Glacialforma- 
tionen,  Terrasser  og  Strandlinier  samt  om  grandfjeldets  og 
sparagmitfjedets  maagtighed  i Norge.  1873.  4to. — From  the 
Royal  University  of  Norway. 

Koethe  (Dr  Med.  Hugo).  Der  Phosphor  und  seine  Therapeutische 
Wirksamkeit.  Erlangen,  1874.  8vo. — From  the  Author. 

Koster  (Dr  Fredrich).  Ueber  G-rossere  Darminjectionen  und  deren 
Heilworkungen  inshesondere  bei  Ileus.  Erlangen,  1874.  8vo, 
— From  the  Author . 

Kraussold  (Dr  Hermann).  Zur  Pathologie  und  Therapie  des  Dia- 
betes Mellitus.  Erlangen,  1874.  8vo. — From  the  Author. 

Lea  (Isaac,  LL.D.).  Observations  on  the  Genus  Unio,  together  with 
Descriptions  of  New  Species  in  the  Family  Unionidae,  and 
Descriptions  of  Embryonic  Forms  and  Soft  Parts ; also  New 
Species  of  Strepomatedse,  with  twenty-two  Plates.  Yol.  XIII. 
Index  Vol.  I.  to  XIII.  4to. — From  the  Author. 

Lieblein  (J.).  Die  iEgyptischen  Denkm tiler  in  St  Petersburg,  Hel- 
singfors, Upsala,  und  Copenhagen.  1873.  8vo. — From  the 
Royal  University  of  Norway. 

Lindemann  (Ferdinand).  Ueber  Unendlich  Kleine  Bewegungen  und 
uber  Kraftsyteme.  Leipzig,  1873.  8vo. — From  the  Author. 

4 N 


VOL.  VIII. 


636 


Proceedings  of  the  Royal  Society 

Lloyd  (Humphrey,  D.D.),  A Treatise  on  Magnetism.  1874.  8vo. 
— From  the  Author. 

Loher  (Franz  Yon).  Ueber  Deutschlands  Weltstellung.  Munchen, 
1874.  8vo. — From  the  Author. 

Lowy  (Dr  Med.  Moritz).  Ueber  das  Syphilitische  Fieber  und 
seine  Beliandlung  mit  Jod.  Erlangen.  8vo. — From  the 

Author. 

Lueder  (Dr  C.).  Der  neueste  Codifications-versuch  auf  dem  G-ebiete 
des  Yolkerreclits.  Erlangen,  1874.  8vo. — From  the  Author. 

Luvini  (Griovanni).  Equazione  d’Equilibrio  di  una  Massa  G-assosa 
sotto  1’Azione  della  sua  Elasticita  e della  Forza  Oentrefuga. 
Torino,  1875.  8vo .—From  the  Author. 

Proposta  di  na  Sperienza  che  pno  Risolvere  in  Modo 

decisivo  la  Questione.  Torino,  1875.  8vo. — From  the 

Author. 

II  Dieteroscopio.  8vo. — From  the  Author. 

Lyman  (Theodore).  Commemorative  Notice  of  Louis  Agassiz. 
1873.  8vo. — From  the  Author. 

Macfie  (R.  A.).  The  Patent  Question  in  1875.  The  Lord  Chan- 
cellor’s Bill  and  the  Exigencies  of  Foreign  Competition. 
London.  8vo. — From  the  Author. 

Margb(Dr  Theodore).  NeueUntersucliungen  uber  dieEntwickelung 
das  Wachsthum,  die  Neubildung  und  den  flineren  Bau  der 
Muskelfasern.  Yienna,  1861.  4to. — From  the  Author. 

— Uber  die  Endigung  der  Nerven  in  der  quergestreiften 

Muskelsubstanz.  1862.  4to. — From  the  Author. 

Marie  (M.  Maximilien).  Theorie  des  fonctions  des  variables 
imaginaires.  Tomes  I.,  II.  Paris,  1874-75.  8vo. — From 
the  Author. 

Meunier  (Stanislas).  Cours  de  G-eologie  Comparbe.  Paris,  1874. 
8vo. — From  the  Author. 

Meyer  (Adolf).  Ein  Fall  von  Extrauterinschwangerschaft  mit 
glucklichem  Ausgang.  Erlangen,  1874.  8vo. — From  the 

Author. 

Milroy  (John).  On  Cylindrical  or  Columnar  Foundations  in  Con- 
crete Brickwork  and  Stonework.  1873.  8vo. — From  the  Author. 

Moller  (J.  D.).  Institute  fur  Mikroskopie.  12mo. — From  the 

Author. 


of  Edinburgh,  Session  1874-75.  637 

Muller  (Albert).  Em  Fund  vergeschiclitlicher  Steingerathe. 
Basel,  1875.  4to. — From  the  Author. 

Muller  (Marcus  Joseph).  Philosophic  und  Theologie  von  Averroes. 
Munchen,  1875.  4to. — From  the  Author. 

— G-eschiedenis  der  Noordsche  Compagnie.  Utrecht,  1874. 

8vo. — From  the  Author. 

Muller  (Dr  Med.  Karl).  Statistik  der  Menschlichen  Entozoen. 
Erlangen,  1874.  8vo .—From  the  Author. 

Naumann  (Alexander).  Jahresbericht  iiber  die  Fortschritte  der 
Chemie  fiir  1872-1873.  Heft  1,  2.  G-iessen.  8vo.— From 
the  Editor. 

Nicholson  (H.  A.).  Report  upon  the  Palaeontology  of  the  Province 
of  Ontario,  1874-75.  8vo. — From  the  Author. 

Ostlioff  (Dr  Med.  Carl).  Die  Verlangsamung  der  Schmerzempfindung 
bie  Tabes  Dorsualis.  Ealangen,  1874.  8vo. — From  the  Author. 

Pettenkoffer  (Dr  Max).  Dr  Justas  Freiherrn  von  Liebig  zum 
Gedachtniss.  Munchen,  1874.  4to.  From  the  Author. 

Plantamour  (E.).  Determination  Telegraphique  de  la  Difference 
de  Longitude,  par  E.  Plantamour  et  A.  Hirsh.  Geneve,  1875. 
4to. — From  the  Authors. 

— Nivellement  de  Precision  de  la  Suisse,  par  A.  Hirsh  et 

E.  Plantamour.  Geneve,  1874.  4to. — From  the  Authors. 

Poetschki  (Hans  Nic).  Eineges  uber  die  Therapie  bei  Ovarien- 
systen.  Munchen,  1874.  8vo. — From  the  Author. 

Porr  (Dr  V.).  Ueber  einen  Fall  von  Alaxie  Locomotrice  Progres- 
sive. Erlangen,  1874.  8vo. — From  the  Author. 

Radlkofer  (L.).  Monographic  der  Sapindaceen-Gattung  Serjania. 
Munchen,  1875.  4to. — From  the  Author. 

Reess  (Dr  Max).  Ueber  den  Befruchtungsvergang  bei  d'en  Basi- 
diomyceten.  Erlangen,  1875,  8vo  — From  the  Author. 

Reuschle  (Dr  C.  G.).  Tafelin  complexer  primzahlen  welche  aus 
Wurzeln  der  Einheit  gebildet  sind.  Paris,  1875.  4to. — From 
the  Author. 

Riccardi  (Paolo).  Annuario  della  Societa  dei  Naturalisti  in 
Modena.  1874.  8vo. — From  the  Author . 

Roclie  (Dr  Cazenave  de  la).  Remarks  on  the  Influence  of  the 
Ocean  Winds  in  the  South-Western  Sub-Pyrenean  Basin 
Paris.  8vo — From  the  Author . 


638 


Proceedings  of  the  Royal  Society 

Kotter  (Dr  Med.  Emil).  Arthritis  deformans,  der  Articulatio 
Epistropheo-Atlantiea.  Leipzic,  1874.  8vo. — From  the  Author. 

Schweenfurth  (Dr  G*.).  Discours  prononce  an  Caire  a la  Seance 
d’Inauguration.  Alexandrie,  1875.  8vo — From  the  Author . 

Schmid  (Dr  Med.  Adolf).  Die  haltwasser-behandlung  des  Typhus 
abdominalis.  Leipzig,  1874.  8vo. — From  the  Author. 

Schmidt  (Carolus).  De  Apostolorum  Decreto  Sententia  et  Con- 
silio.  Erlangen,  1874.  8vo. — From  the  Author. 

(Rudolf).  Die  Categorien  des  Aristoteles  in  St  G-allen. 

Erlangen,  1874.  8vo. — From  the  Author. 

Sexe  (S.  A.)  Jaettegryder  og  G-amle  Strandlinier  i fast  Klippe. 
Christiania,  1874.  4to. — From  the  Royal  University  of  Nor- 
way. 

Shuttleworth  (Sir  James  Kay).  Social  Problems.  1873*  8vo. — 
From  the  Author. 

Stevens  (Edwin  A.).  Announcement  of  the  Stevens  Institute 
of  Technology.  1874.  Hoboken,  N.J.  8vo. — From  the 
Author. 

Tommassi  (Dr  Donato).  Action  of  Benzyl-Choloride  on  Laurel 
Camphor  ( Laurus  Camphor  a).  8vo. — From  the  Author . 

— Combinaison  de  Bioxyde  de  Chrome.  8vo. — From  the 

A utlior. 

— . — - Action  of  Ammonia  on  Phenyl-Chloracetamide  and  Cresyl- 
Chloracetamide.  8vo. — From  the  Author. 

Action  de  ITodure  Plombique.  Paris,  1872.  8vo. — From 

the  Author. 

Sur  les  derives  Acides  de  la  Naphtylamine.  4to. — From  the 

Author. 

Toner  (J.  M.).  On  the  Natural  History  and  Distribution  of  Yellow 
Fever  in  the  United  States,  from  1868  to  1874.  Washington. 
8vo. — From  the  Author. 

Unger  (C.  R.).  Postola  Sogur.  Christiania,  1874.  8vo. — From, 
the  Royal  University  of  Norway. 

Yogel  (August).  Justus  Freiherr  von  Liebig  als  Begrunder  der 
Agrikultur-Chemie.  Munchen,  1874.  4to. — From  the  Author. 

Vogt  (Dr  Wilhelm).  Antheil  der  Reichsstadt  Weissenburg  an 
der  reform atorischen  Bewegung  in  den  Jahren  1524-1530. 
Erlangen,  1874.  8vo. — From  the  Author. 


639 


of  Edinburgh,  Session  1874-75. 

Weddell  (H.  A.).  Les  Lichens  du  Massif  Granitique  de  Liguge. 
Paris,  1873.  8vo. — From  the  Author. 

Nouvelle  Eevne  des  Lichens.  Cherbourg,  1873.  8vo. — 

From  the  Author. 

Weiler  (Adolph).  Ueber  die  Yerschiedenen  G-attungen  der  Com- 
plexe  zweiten  G-rades.  Leipzig,  1874.  8vo. — From  the 
Author. 

Weiss  (Dr  Solomon).  Ueber  Stenosis  Arteriae  Pulmonalis  Con- 
genita. Erlangen,  1874.  8vo. — From  the  Author. 

Wex  (Gustav).  Ueber  die  Wasserabnahme  in  den  Quellen  Fliissen, 
und  Stromen.  Wien,  1873.  4to. — From  the  Author. 


II.  Transactions  and  Proceedings  of  Learned  Societies, 
Academies,  etc. 

Alger. — Bulletin  Annuel  de  la  Societe  Protectrice  des  Animaux. 
Liv.  9e.  8 vo. — From  the  Society. 

Amsterdam. — Verslagen  en  Mededeelingen  der  Koninklijke  Aka- 
demie  van  Wetenschappen.  Afdeeling  Letterkunde, 
Deel  IY.  Naturkunde,  Deel  YIII.  8vo. — From  the 

Academy. 

Yerhandelingen  der  Koninklijke  Akademie  van  Wetens- 
chappen. Deel  XI Y.  4to. — From  the  Academy. 

Processen-verbaal  van  de  gewone  Yergaderingen  der 
Koninklijke  Akademie  van  Wetenschappen.  1873- 
1874.  8 vo. — From  the  Academy. 

Jaarboek  van  de  Koninklijke  Akademie  van  Wetenschappen 
gevestigd  te  Amsterdam,  voor  1873.  8vo. — From  the 
Academy . 

Catalogues  van  de  Bockerij  der  Koninklijke  Akademie  van 
Wetenschappen  gevestigd  te  Amsterdam.  Eersteen  Deels, 
Eerste  Stuk.  8vo. — From  the  Academy. 

Flora  Batava,  afbeelding  en  beschrigving  van  Neder- 
landsche  Gewassen  Aangevangen,  door  Wijlen  Ian  Kops 
Hoogleeraar  te  Utrecht  Yoortgezet  door  F.  W.  van  Eeden 
te  Haarlem.  No.  225,  No.  226,  Register,  Deel  I.-XIY. 
4to. — From  the  King  of  Holland . 


640  Proceedings  of  the  Boyal  Society 

Baltimore. — Eighth  Annual  Report  of  the  Provost  to  the  Trustees 
of  the  Peabody  Institute.  1875.  8vo. — From  the  In- 
stitute. 

Berlin.-— Jahresbericht  der  Commission  zur  Wissenschaftlichen 
Untersuchung  der  Deutschen  Meere  in  Kiel  fur  das  Jahre 
1872-73.  Jahrgang  2,  3-.  Fob — From  the  Commission. 

Abhandlungen  der  Koniglichen  Akademie  der  Wissens- 
chaften  zu  Berlin.  1873.  Index.  4to. — From  the  Aca- 
demy. 

Monatsbericht  der  Koniglich  Preussischen  Akademie  der 
Wissenschaften  zu  Berlin.  1874-75.  8vo. — From  the 
Academy. 

Berne. — Beitrage  zur  Geologischen  Karte  der  Schweiz  herausge- 
gehen  von  der  Geologischen  Commission  der  Schweizer 
Naturforschenden  Gesellschaft  auf  kosten  der  Eidge- 
nossenschaft.  1874. — From  the  Commission. 

Mittheilungen  der  Naturforschenden  Gesellschaft  in  Bern 
aus  dem  Jahre  1873.  Nos,  812-827.  8vo. — From  the 
Society. 

Berwickshire. — -Proceedings  of  the  Naturalists’  Club.  Yol.  VII. 
No.  2.  8vo. — From  the  Society. 

Bologna. — Rendiconto  delle  Session!  delle  Accademia  delle  Scienze 
dell  Istituto  di  Bologna,  Anno  Accademico  1873-74. 
8vo. — From  the  Academy. 

Memorie  dell’  Accademia  delle  Scienze  dell  Istituto  di 
Bologna.  Serie  III.  Tomo  III.  Ease.  3-4;  Tomo  IV. 
4to.' — From  the  Academy. 

Bombay. — Journal  of  the  Bombay  Branch  of  the  Royal  Asiatic 
Society  1873-74.  Vol.  X.  Nos.  29-30.  8vo. — From  the 
Society. 

The  Indian  Antiquary.  Vol.  III.  from  January  to  Decem- 
ber 1874-75.  Vol.  IV.  February  to  August.  4to. — From 
the  Publishers. 

General  Report  on  the  Census  of  Bombay  Presidency,  1872. 
Parts  1,  2.  Fol. — From  the  Census  Office. 

Bonn. — Verhandlungen  des  Naturhistorischen  Vereines  der  Preus- 
sischen Rheinlande  und  Westfalens.  Jahrgang  XXX, 

Folge  3 ; XXXI,  Folge  4.  8vo .—From -the  Society, 


641 


of  Edinburgh,  Session  1874-75. 

Bordeaux. — Memoires  de  la  Societe  des  Sciences  Physiques  et 
Naturelles  de  Bordeaux.  Tome  X.  No.  2.  Index 
Tome  X.  Tome  I.  No.  1.  2 Series.  8vo. — From  the 

Society. 

Boston. — Proceedings  of  the  American  Academy  of  Arts  and 
Sciences.  New  Series.  Yol.  I.  8vo. — From  the  Academy . 

Proceedings  of  the  Society  of  Natural  History.  Yol.  XV., 
Parts  3,  4;  Yol.  XVI.,  Parts  1-4;  Yol.  XVIL,  Parts 
1,  2.  8 vo. — From  the  Society. 

Memorial  Meeting  of  the  Society  of  Natural  History,  Octo- 
ber 7,  1874.  8 vo. — From  the  Society. 

Thirty-Seventh  Annual  Report  of  the  Board  of  Education, 
1872-73.  8vo. — From  the  Board  of  Education. 

Brussels. — Bulletin  de  1’Academie  Boyale  des  Sciences,  des  Lettres 
et  des  Beaux-Arts  de  Belgique.  Tome  XXXYII. 
Nos.  6-12;  XXXYIIX.  Nos.  1,  3-6.  8vo .—From  the 
Academy. 

Biographie  Nationale  publiee  par  1’Academie  Boyale  des 
Sciences  des  Lettres  et  des  Beaux-Arts  de  Belgique. 
Tome  IV.  Partie  2.  8vo .—From  the  Academy. 

Annuaire  de  1’Academie  Boyale  des  Bruxelles,  1874-75. 
12mo. — From  the  Academy. 

Memoires  Couronnes  et  Memoires  des  Savants  Etrangers 
publies  par  l’Academie  Boyale  des  Sciences,  des  Lettres 
et  des  Beaux-Arts  de  Belgique.  Tome  XXXYII.  4to. 
— From  the  Academy. 

Congres  International  de  Statistique,  Sessions  de  Bruxelles 
(1853),  Paris  (1855),  Vienne  (1857),  Londres  (1860), 
Berlin  (1865),  Florence  (1867),  La  Haye  (1869),  et  St 
Petersbourg  (1872),  par  A.  Quetelet,  1873.  4to. — From 
the  Commission. 

Memoires  de  l’Academie  Boyale  des  Sciences,  des  Lettres  et 
des  Beaux-Arts  de  Belgique.  Tome  XL.  4to. — From  the 
Academy. 

Memoires  Couronnes  et  Autres  Memoires  publies  par 
l’Academie  Boyale  des  Sciences,  des  Lettres  et  des  Beaux- 
Arts  de  Belgique.  Tome  XXIII.  8vo. — From  the 

Academy. 


642  Proceedings  of  the  Royal  Society 

Brussels. — Annales  de  l’Observatoire  Royal  de  Bruxelles  publies  aux 
frais  de  l’Etat,  par  le  director  A.  Quetelet.  Tome  XXII. 
4to. — From  the  Observatory. 

Calcutta. — Records  of  the  Geological  Survey  of  India.  Yol.  VII. 
Parts  1-4.  8vo. — From  the  Survey. 

Memoirs  of  the  Geological  Survey  of  India.  Vol.  X. 
Part  2;  Vol.  XI.  Part  1.  8vo.  Palaeontologia. — Vol.  I. 
No.  1.  4to. — From  the  Survey. 

Journal  of  the  Asiatic  Society  of  Bengal.  Part  2.  No.  4. 
1873;  Part  2,  No.  1,  1874;  Part  2,  Nos.  1-4;  Parti, 
No.  1,  1875.  8vo. — From  the  Society. 

Proceedings  of  the  Asiatic  Society  of  Bengal.  Nos.  1-9, 
1874;  Nos.  1-5,  1875.  8vo. — From  the  Society. 
Cambridge  (U.S). — The  Organisation  and  Progress  of  the  Anderson 
School  of  Natural  History  at  Penikese  Island.  Report  of 
the  Trustees  for  1873. — From  the  Trustees. 

Illustrated  Catalogue  of  the  Museum  of  Comparative  Zoology 
at  Harvard  College.  No.  VII.  Part  4;  No.  VIII.  Part  1. 
4to. — From  the  College. 

Annual  Report  of  the  Trustees  of  the  Museum  of  Compara- 
tive Zoology  at  Harvard  College,  Cambridge,  for  the  years 
1872-73.  8vo. — From  the  College. 

Bulletin  of  the  Museum  of  Comparative  Zoology  at  Harvard 
College,  Cambridge,  Mass.  Vol.  III.  Nos.  9-10.  8vo. — 
From  the  College. 

Annual  Reports  of  the  President  and  Treasurer  of  Harvard 
College.  1872-73.  8vo. — From  the  College. 

Canada. — Geological  Survey  of  Canada.  Palaeozoic  Fossils.  Vol. 

II.  Part  1.  8vo. — From  the  Director. 

Cape  of  Good  Hope. — Catalogue  of  1159  Stars  deduced  from  Ob- 
servations at  the  Royal  Observatory,  1856-1861.  8vo. — 
From  the  Board  of  Admiralty. 

Cherbourg. — Memoires  de  la  Societd  Nationale  des  Sciences 
Naturelles  de  Cherbourg.  Tome  VIII.  8vo. — From  the 
Society. 

Christiania. — Norsk  Meteorologiske  for  1873.  4to. — From  the 

Meteorological  Institute. 


643 


of  Edinburgh,  Session  1874-75. 

Christiania. — Enumeratio  Insectorum  Norvegicorum.  Fasc.  1. 
1874.  8 vo. — From  the  Royal  University  of  Norway. 

Forhandlinger  i Videnskabs-Selskabet  for  1873.  8vo. — 
From  the  Royal  University  of  Norway. 

Min  Haerramek  ja  Baostamek  Jesus  Kristus  odda  Testa- 
menta.  1874.  8vo. — From  the  Royal  University  of 

Norway. 

Norske  Universitets  og  Skole-Annaler.  Hefte  XII.  XIII. 

8 vo. — From  the  Royal  U iversity  of  Norway. 

Norsk  Ordbog  med  dansk  forklaring  af  Joannasen  1873. 

8vo. — From  the  Royal  University  of  Norway. 

Nyt  Magazin  for  Naturvidenskaberne.  Bind  XX.  Hefte  3. 

8vo. — From  the  Royal  University  of  Norway. 

Det  Kongelige  Norske  Frederiks-Universitets  Aarsberetning 
for  1873.  8vo. — From  the  Royal  University  of  Norway. 
Fattigstatistik  for  1870-71.  4to. — From  the  Government 
of  Norway. 

De  Often tlige  Jernbaner  i Aaret  1872.  4to. — From  the 

Government  of  Norway. 

Oversigt  over  Oplysning-svoesnets  Fonds  Indtaegter  og 
Udgifter  i Aaret  1873.  4to. — From  the  Government  of 
Norway. 

Uddrag  af  Consnlatberetninger  vedkommende  Norges 
Handel  og  Skibsfart,  Aaret  1872-73.  4to. — From  the 
Government  of  Norway. 

Tabeller  vedkommende  De  Faste  Eiendomme,  Aarene 
1865—70.  4to. — From  the  Government  of  Norway. 
Oversigt  over  Kongeriget  Norges  Indtaeger  og  Udgifter, 
for  Aaret  1871-72.  4to. — From  the  Government  of 
Norway. 

Den  Norske  Brevposts  Statistik,  for  Aaret  1872.  4to. — 
From  the  Government  of  Norway. 

Beretninger  om  Norges  Fiskerier,  i Aaret  1868-72.  4to. — 
From  the  Government  of  Norway. 

Den  Hrere  Landbrugsskore  i Aas  for  Aaret  1873-74. 

4to. — From  the  Government  of  Norway. 

Den  Norske  Stats  Telegrafs  Statistik  for  Aaret  1872-73. 
4to. — From  the  Government  of  Norway.  0 

4 0 


vol.  vnr. 


644  Proceedings  of  the  Royal  Society 

Christiania . — Beretning  om  Meclicinalforholdene  i Norge,  i Aaret 
1871.  4to. — From  the  Government  of  Norway . 

Criminalstatistiske  Tabeller  for  Kongeriget  Norge  for  Aaret 
1867-71.  4to. — From  the  Government  of  Norway. 

Beretninger  om  Skolevoesnets  Tilstand  i Kongeriget  Norges 
Landdistrikt  for  Aaret  1870-73.  4to. — From  the 

Government  of  Norway. 

Oversigt  over  det  Nordlandske  Kirke  og  Skolefonds  Ind- 
taegter  og  Udgifter,  i Aaret  1873.  4to. — From  the 

Government  of  Norway. 

Oversigt  over  det  Geistlige  Enkepensionsfonds  Indteegter 
og  Udgifter,  i Aaret  1873.  4to. — From  the  Government 
of  Norway. 

Oversigt  over  Tiendefondets  Indtaegter  og  Udgifter,  i Aaret 
1873.  4to. — From  the  Government  of  Norway. 

Tabeller  vedkommende  Folketaellingerne,  i Aarene  1801-72. 
4to. — From  the  Government  of  Norway. 

Tabeller  vedkommende  Skiftevaesnet  i Norge,  i Aaret 
1871-72.  4to. — From  the  Government  of  Norway. 

Oversigt  over  det  Kongelige  Danske  Yidenskabernes  Sels- 
kabs  Forhandlinger  og  dets  Medlemmers  Arbeider,  i 
Aaret  1874.  Nos.  1-3.  8vo. — From  the  Academy. 

Dehra  Doon. — General  Report  on  the  Operations  on  the  Great 
Trigonometrical  Survey  of  India,  during  1873-74.  Fol. 
— From  the  Survey. 

Dorpat. — Meteorologische  Beobachtungen  in  Jahre  1872-74. 
8 vo. — From  the  University  of  Dorpat. 

Dresden. — Nova  Acta  Academise  Caesareae  Leopold  i-Carolinae 
Germanicae  Naturae  Curiosorum.  Yol.  XXXVI.  4to. — 
From  the  Academy. 

Leopoldina  Amtleches  Organ  der  Kaiserlich  Leopoldenisch- 
Carolinischen  Deutschen  Akademie  der  Naturforscher. 
Heft  7-9.  4to. — From  the  Academy. 

Erlangen. — Sitzungsberichte  der  Physicalisch-Medinischen  Societat 
zu  Erlangen.  Heft  6.  8vo. — From  the  Society. 

Geneva. — M^moires  de  la  Societe  de  Physique  et  d’Histoire 
Naturelle  de  Geneve.  Tome  XXIII.  Part  2.  4to. — 
From  the  Society. 


645 


of  Edinburgh,  Session  1874-75. 

Glasgow. — Proceedings  of  the  Philosophical  Society.  Yol.  IX. 
Nos.  1,  2.  8vo. — From  the  Society. 

Gottingen. — Abhandlnngen  der  Koniglichen  G-esellschaft  der  Wis- 
senchaften  zu  Gottingen.  Band  XIX.  4to. — From 
the  Society. 

Nachrichten  von  der  K.  Gesellschaft  der  Wissenschaften 
nnd  der  Georg- Augusts-Universitat,  aus  dem  Jahre  1874. 
12mo. — From  the  University. 

Greenwich. — Astronomical  and  Magnetical  Observations  made  at 
the  Eoyal  Observatory  in  the  year  1872.  4to.- — From  the 

Observatory. 

Gratz. — Mittheilungen  des  Naturwissensehaftlichen  Yereines  fur 
Steiermark.  1874.  8vo. — From  the  Society. 

Haarlem. — Naturerkundige  Verhanderlingen  der  Hollandsche 
Maatschappij  der  Wetenchappen.  Deel  II.  Nos.  1-4. 
4 to. — From  the  Society. 

Archives  du  Musee  Teyler.  Yol.  III.  Fasc.  4.  8vo.-~ 

From  the  Society. 

Archives  Neerlandaises  des  Sciences  Exactes  et  Naturelles 
publiees  par  la  Societe  Hollandaise  a Haarlem.  Tome 
IX.  Liv  1-5.  8vo. — From  the  Society. 

Helsingfors. — Bidrag  till  Kannedom  af  Findlands  Natur  och 
Folk  utgifna  af  Finska  Yetenskaps-Societeten.  Yols. 
XYIII.,  XIX.,  XXI.,  XXII.,  XXIII.  8vo .—From  the 
Society. 

Ofversigt  af  Finska  Yetenskaps-Societetens  Forhandlingar. 
Yols.  XIV.-XYI.  8vo. — From  the  Society. 

Observations  faites  a-IObservatoire  Magnetique  et  Meteor- 
ologique  de  Helsingfors.  Yol.  Y.  4to. — From  the 

Observatory. 

Hertsberg. — Grundtroekkene  i den  iEldste  Norske  proces.  1874. 
8 vo. —From  the  Royal  University  of  Norway. 

Innsbruck.  — Berichte  des  Naturwissenschaftlich-Medizinischen 
Yereines  in  Innsbruck.  Jahrgang  IY.  Heft  1,  2.  8vo. 
— From  the  Society. 

Jena. — Jenaische  Zeitschrift  fur  Medicin  und  Naturwissenschaft 
herausgegeben  von  der  Medicinisch  Naturwissenschaft- 
lichen  Gesellschaft.  1874 .—From  the  Society . 


646  Proceedings  of  the  Royal  Society 

Kasan. — Reports  of  the  University  of  Kasan.  1874.  Nos.  1-6. 
8 vo. — From  the  University. 

Leeds. — The  Fifty-Fourth  Report  of  the  Council  of  the  Leeds 
Philosophical  and  Literary  Society  for  1873-74.  8vo. — 
From  the  Society. 

Liverpool. — Proceedings  of  the  Literary  and  Philosophical  Society. 
No.  28.  8 vo. — From  the  Society. 

Transactions  of  Historic  Society  of  Lancashire  and  Cheshire. 
Third  Series.  Yol.  II.  Session  1873-74  8vo. — From 
the  Society. 

London. — Journal  of  the  London  Institution  ; Yols.  I.,  II. ; Yol. 

III.  Nos.  18-22;  IY.  Nos.  23-25.  8vo. — From  the  Insti- 
tution. 

Journal  of  the  Royal  Geographical  Society.  Yol.  XLIY. 
8vo. — From  the  Society . 

Proceedings  of  the  Royal  Geographical  Society.  Yol. 
XYIII.  Nos.  4,  5;  Yol.  XIX.  Nos.  1-7.  8vo .—From 

the  Society. 

Journal  of  the  Royal  Horticultural  Society.  Yol.  IY.  Part 
15.  8vo. — From  the  Society. 

Report  on  Weather  Telegraphy  and  Storm  Warnings,  pre- 
sented to  the  Meteorological  Congress  at  Yienna  by  a 
Committee  appointed  at  the  Leipzig  Conference.  8vo. — 
From  the  Meteorological  Committee , 1874. 

Statistical  Report  on  the  Health  of  the  Navy  for  the  year 
1873.  8vo. — From  the  Admiralty. 

Transactions  of  the  Royal  Society.  Yol.  CLXIY.  Parts 
1-3.  List  of  Fellows,  1874.  4to. — From  the  Society. 
Proceedings  of  the  Royal  Society.  Yol.  XXII.  Nos.  153- 
155;  XXIII.  Nos.  156-163;  Yol.  Y.  8vo.— From  the 
Society. 

The  Journal  of  the  British  Archeeological  Association. 

June  1875.  8vo. — From  the  Association. 

Journal  of  the  Chemical  Society.  1874,  Ser.  2.  Yol. 
XII.  July,  August,  September,  October,  November, 
December;  Yol.  XIII.  January,  February,  March,  April, 
May,  June,  July,  August,  September.  8vo. — From  the 
Society. 


of  Edinburgh,  Session  1874-75.  647 

London. — Journal  of  the  East  India  Association.  Yol.  VIII. 

Nos.  2,  3;  Yol.  IX.  Nos.  1,  2.  8vo. — From  the  Associa- 
tion. 

Journal  of  the  Geological  Society.  Yol.  XXX.  Nos.  118- 
120  ; Yol.  XXXI.  Nos.  121-123.  List  of  Members.  8vo. 
— From  the  Society. 

Journal  of  the  Linnean  Society.  Yol.  XIY.  (Botany), 
Nos.  76-80;  Yol.  XII.  (Zoology),  No.  58,59.  8vo. — 
From  the  Society. 

Transactions  of  the  Linnean  Society.  Yol.  XXX.  Parts 
2,  3.  Second  Series.  (Zoology),  Yol.  I.  Part  1;  (Botany) 
Yol.  I.  Part  1.  4to. — From  the  Society. 

Transactions  of  the  Boyal  Society  of  Literature.  Yol.  XI. 

Part  1.  8 vo. — From  the  Society. 

Proceedings  of  the  Zoological  Society.  Part  3,  1873; 

1874,  Parts,  1-4;  1875,  Part  1.  8vo.— From  the  Society. 
Transactions  of  the  Geological  Society.  Yol.  VIII.  Parts 
7-9  ; Yol.  IX.  Parts  1-3.  4to. — From  the  Society. 
Descriptive  Catalogue  of  the  Dermatological  Specimens 
contained  in  the  Museum  of  the  Boyal  College  of  Sur- 
geons of  England.  4to. — From  the  College. 

Quarterly  Weather  Beport  of  the  Meteorological  Office. 
Part  4,  1871 ; Parts  3,  4,  1873 ; Part  1,  1874.  4to._ 
From  the  Meteorological  Committee  of  the  Boyal  Society. 
Beport  of  the  Kew  Committee  for  the  year  ending  1874. 
8vo. — From  the  Committee. 

Beport  of  the  Meteorological  Committee  of  the  Boyal  Society 
for  1873-74.  8vo. — From  the  Committee. 

Beport  of  the  Permanent  Committee  of  the  International 
Meteorological  Congress  at  Vienna  for  the  year  1874. 
8vo. — From  the  Meteorological  Committee  of  the  Boyal 
Society. 

Instructions  in  the  Use  of  the  Meteorological  Instruments. 
8vo.  — From  the  Meteorological  Committee  of  the  Boyal 
Society. 

Beport  of  the  Proceedings  of  the  Conference  on  Maritime 
Meteorology,  held  in  London  1874.  Protocols  and  Ap- 
pendices. 8 vo. — From  the  Meteorological  Committee. 


648 


Proceedings  of  the  Royal  Society 

London. — Memoirs  of  the  Royal  Astronomical  Society.  Yol.  XL. 
4to. — From  the  Society. 

Monthly  Notices  of  the  Royal  Astronomical  Society  for 
1874-75.  8vo. — From  the  Society. 

“ Nature”  for  1874-75.  4to. — From  the  Editor. 

Memoirs  of  the  G-eological  Survey  of  G-reat  Britain — Mineral 
Statistics  of  the  United  Kingdom  of  Great  Britain  and 
Ireland  for  the  years  1871-73.  8vo. — From  the  Survey. 
Proceedings  of  the  Geologists’  Association.  Yol.  III.  Nos. 

6-8  ; Yol.  IV.  Nos.  1-3.  8vo. — From  the  Association. 
Proceedings  of  the  Mathematical  Society.  Nos.  66-76, 
78-82.  8 vo. — From  the  Society. 

Transactions  of  the  Clinical  Society.  Yol.  VII.  8vo. — 
From  the  Society. 

Proceedings  of  the  Royal  Institution  of  Great  Britain. 

Yol.  VII.  Parts  3,  4.  8vo. — From  the  Society. 
Proceedings  of  the  Institution  of  Civil  Engineers.  Yols. 
XXXVII.,  XXXVIII.,  XXXIX.  Parti;  XL.,  XLI.  8vo. 

—Prom  the  Society. 

Transactions  of  the  Medical  and  Chirurgical  Society.  Yols. 

LVI.,  LVII.  8 vo. — From  the  Society. 

Proceedings  of  the  Royal  Medical  and  Chirurgical  Society. 

Yol.  VII.  Nos.  7,  8.  8vo. — From  the  Society. 

Proceedings  of  the  Physical  Society.  Parts  1,  2.  8vo. — 
From  the  Society. 

Transactions  of  the  Pathological  Society.  Yols.  XX  Y.  In- 
dex for  Yols.  XYI.  to  XXV.  8vo. — From  the  Society. 
Proceedings  of  the  Society  of  Antiquaries.  Yol.  VI.  Nos. 
2-4.  8vo. — From  the  Society. 

Journal  of  the  Society  of  Arts  for  1874-75.  8vo. — From 
the  Society. 

Journal  of  the  Statistical  Society.  General  Index,  Yols. 

XXVI.-XXXV.  (1863-72). — From  the  Society. 

Journal  of  the  Statistical  Society.  Yol.  XXXVII.  Parts 
2-4;  XXXVIII.  Parts  1-3.  Almanack  for  1875.  8vo. 
— From  the  Society. 

H.M.  S.  “ Challenger  / — Reports  on  Ocean  Soundings  and 
Temperature — Antarctic  Sea,  Australia,  New  Zealand, 


649 


of  Edinburgh,  Session  1874-75. 

No.  2, 1874.  Reports  on  Ocean  Soundings  and  Tempera- 
ture— New  Zealand  to  Torres  Strait,  Torres  Strait  to 
Manilla  and  Hong  Kong,  No.  3.  1874.  Report  on  Ocean 
Soundings  and  Temperatures — Pacific  Ocean,  China  and 
adjacent  Seas,  No.  4.  1875.  Fol. — From  the  Lords 

Commissioners  of  the  Admiralty. 

Memoirs  of  the  Geological  Survey  of  England  and  Wales, 
Explanation  of  Quarter  Sheet,  88  N.E.,  90  N.E.,  91 
N.W.,  93  N.W.,  98  S.E.,  98  N.W.  8vo.— From  the 

Survey. 

Lyons. — Annales  de  la  Societe  Imperiale  d’Agriculture,  Histoire 
Naturelle  et  Arts  Utiles  de  Lyon.  4 Serie.  Tome  V. 
8 vo. — From  the  Society. 

Memoires  de  L’Academie  Imperiale  des  Sciences  Belles- 
Lettres  et  Arts  de  Lyon.  Classe  des  Lettres — Tome  XV. 
4to.  Classe  des  Sciences — Tome  XX.  8vo. — From  the 
Academy. 

Madras. — Census  of  the  Madras  Presidency,  with  Appendix,  1871. 

Yols.  I.,  II.  Supplementary  Tables.  Fol. — From  the 
Census  Office. 

Madrid. — Memorias  de  la  Comision  del  Mapa  G-eologico  de  Espana 
Bosquejo  de  una,  Descripcion  Fisica  y Geologica  de  la 
Provincie  de  Zaragoza,  per  Don  Felipe  Martin  Donayre. 
8 vo. — From  the  Commission. 

Memorias  de  la  Comision  del  Mapa  G-eologico  de  Espana. 
8vo. — From  the  Commission. 

Boletin  de  la  Comision  del  Mapa  Geologico  de  Espana. — 
From  the  Commission. 

Manchester. — Transactions  of  the  Geological  Society.  Yol.  XIII. 

Parts  5,  7-10.  Catalogue  of  Library.  8vo. — From  the 
Society. 

Massachusetts. — Tenth  Annual  Report  of  State  Charities.  1874. 
8vo. — From  the  Board. 

Twenty-First  Annual  Report  of  the  Board  of  Agriculture. 
1873.  8vo. — From  the  Board. 

Mexico. — Boleten  de  la  Sociedad  de  Geografia-y-Estadistica  de  la 
Republica  Mexicana.  Tomo  I.  Nos.  8-12;  Tomo  II. 
Nos.  1,  2.  8vo .—From  the  Society. 


650  Proceedings  of  the  Royal  Society 

Milan. — Atti  della  Societa  Italiana  di  Scienze  Naturali.  Yol. 

XVI.  Fasc.  3,  4;  Vol.  XVII.  Fasc.  1-3;  Vol.  XVIII. 
Fasc.  1.  8vo. — From  the  Society. 

Rendiconti  Reale  Istitnto  Lombardo  di  Scienze  e Lettere 
Serie  2.  Vol.  V.  Fasc.  17-20;  Vols.  VI.;  VII.  8vo. 
— From  the  Institute. 

Memorie  del  Reale  Istituto  Lombardo  di  Scienze  e Lettere. 
Classe  di  Lettre  e Scienze,  Morali  e Politicbe — Vol.' XII. 
Della  III.  Fasc.  4;  Serie  III.  Vol.  XIII.  Fasc.  1.  Classe 
de  Littere  e Scienze  Mathematiche  e Naturali — Vol. 

XII.  Fasc.  6 ; Vol.  XIII.  Fasc.  L — 4to — From  the 
Institute . 

Missouri. — Preliminary  Report  of  the  Iron  Ores  and  Coal  Fields, 
from  the  Field  Work  of  1872.  8vo. — From  the  Geological 
Survey. 

Reports  on  the  Geological  Survey  of  the  State  of  Missouri, 
1855-71.  8vo. — From  the  Geological  Survey. 

Report  of  the  Geological  Survey  of  the  State  of  Missouri, 
including  Field  Work  of  1873-74.  8vo. — From  the 

Geological  Survey. 

Moscow. — Nouveaux  Memoires  de  la  Societe  Imperiale  des  Natura- 
listes  de  Moscow.  Tome  XIII.  Liv.  4.  4to. — From  the 
Society. 

Bulletin  de  la  Societe  des  Naturalistes.  1873,  No.  4; 
1871,  Nos.  1-4.  8 vo. — From  the  Society. 

Munich. — Sitzungsberichte  der  konigl.  bayer.  Akademie  der  Wis- 
senschaften.  Philosophisch  - Philologischen  — 1873, 
Heft  6;  und  Historischen  Classe — 1874.  8vo. — From  the 
Academy. 

Abhandlungen  der  koniglich.  bayerischen  Akademie  der 
Wissenschaften.  Historischen  Classe — Band  XLIII. 
Abth.  2.  Math.-Physik.  Classe — -Band  XL.  Dritte  Abth. 
Philosophisch  - Philologischen  Classe  — Band  XLVI. 
Zweite  Abth.  4to. — From  the  Academy. 

Verzeichniss  von  5563  telescopischen  Sternen,  Supp.  Band 

XIII.  8vo. — From  the  Royal  Observatory. 

Annalen  der  Koniglichen  Sternwarte  bei  Miinchen.  Band 
XX.  8 vo. — From  the  Royal  Observatory . 


of  Edinburgh,  Session  1874  75.  651 

Neuchatel. — '"Bulletin  de  la  Societe  des  Sciences  Naturelles  de 
Neuchatel.  Tome  X.  Part  1.  8vo. — From  the  Society. 
Memoires  de  la  Societe  des  Sciences  Naturelles  de  Neuchatel. 
Tome  IV.  Part  2.  4to. — From  the  Society. 

New  Haven  ( U.S. ). — Journal  (American)  of  Science  and  Art,  con- 
ducted by  Benjamin  Silliman.  Vol.  VII.  Nos.  42-47; 
Vol.  IX.  Nos.  49-54;  Vol.  X.  Nos.  55,  56.  New  Haven. 
8 vo. — From  the  Editor. 

New  York. — Atlases  of  the  Geological  Survey  of  Missouri.  Fol. 
— From  the  Survey. 

New  Zealand. — Results  of  a Census  of  the  Colony  of  New  Zealand 
taken  for  the  Night  of  the  1st  of  March  1874.  Fol. 
— From  the  New  Zealand  Government. 

Nijmegen. — Nederlandsch  Kruidkundig  Archief.  -Dee!  II.  Stuk  1®. 
8 vo. — From  the  Editors. 

Driemaandelijksch  Botanisch  Literatuuroverzicht.  1874. 
Nos.  1,  2.  8vo. — From  the  Editor. 

Oxford. — Astronomical  and  Meteorological  Observations  made  at 
the  Radcliffe  Observatory,  Oxford,  in  the  year  1871.  Vol. 
XXXI.  1872;  Vol.  XXXII.  8vo .—From  the  Obser- 

vatory. 

Paris. — Bulletin  de  la  Societe  Mathematique  de  France.  Tome 
II.  Nos.  4,  5;  Tome  III,  Nos.  1-4.  8vo. — From  the 
Society. 

Annales  des  Mines.  Tome  V.  Liv.  2me,  3me;  Tome  VI.  Liv. 
le,  5®,  6e;  Tome  VII.  Liv.  le-3e.  8vo. — From  the  Ecole 
des  Mines. 

Bulletin  de  la  Societe  de  Gdographie.  1874,  Mai,  Juin, 
Aout,  Septembre,  Octobre,  Novembre,  Decembre;  1875, 
Janvier,  Avril,  Juin,  Juillet,  Aout.  8vo. — From  the 

Society. 

Comptes-Rendus  Hebdomadaires  des  Seances  de  l’Acad($mie 
des  Sciences.  1874-75.  8vo. — From  the  Academy 
Publications  of  the  Depot  de  la  Marine  (with  Charts).  8vo. 
— From  the  Depot. 

Philadelphia. — Proceedings  of  the  American  Philosophical  Society, 
Vol.  XIV.  Nos.  92,  93.  8vo. — From  the  Society. 
vol,  vnt.  4 p 


652  Proceedings  of  the  Royal  Society 

Philadelphia. — Journal  of  the  Academy  of  Natural  Sciences.  New 
Series.  Vol.  VIII.  Part  1.  8vo. — From  the  Academy. 
Proceedings  of  the  Academy  of  Natural  Sciences.  1873, 
Parts  1-3;  1874,  Parts  1-3.  4to. — From  the  Academy. 
The  Third  Annual  Beport  of  the  Board  of  Managers  of  the 
Zoological  Society.  8vo. — From  the  Society. 

Quebec. — Transactions  of  the  Literary  and  Historical  Society. 

New  Series,  No.  11,  Sessions  1873-74  and  1874-75. 
8vo. — From  the  Society. 

Rome. — Beport  of  the  Proceedings  of  the  Annual  General  Meeting 
of  the  British  Academy  of  Arts,  1875.  8vo. — From  the 
Academy. 

Shanghai. — Journal  of  the  North  China  Branch  of  the  Boyal  Asiatic 
Society.  No.  8.  8vo. — From  the  Society. 

Stockholm. — Sveriges  Gfeologiska  Undersokning.  Nos.  50-53.  8vo. 

(with  Charts).  From  the  Geologica  S ciety  of  Sweden. 

St  Petersburg. — Jahresbericht  fur  1871.  8vo. — From  the  Academy 
of  Sciences. 

Bulletin  de  l’Academie  Imperiale  des  Sciences  de  St  Peters- 
bourg.  Tome  XIX.  Nos.  4,  5 ; XX.  Nos.  1,  2.  4to  — 
From  the  Academy. 

Memoires  de  l’Academie  Imperiale  des  Sciences  de  St. 
Petersbourg.  Tome  XXI.  Nos.  6-12 ; XXII.  Nos.  1-3. 
4to. — From  the  Academy. 

Bepertorium  fur  Meteorologie.  Band  IV.  Heft  1.  4to. — 
From  the  Royal  Academy. 

Jahresbericht  fiir  1874.  8vo.— From  the  Pulkowa  Ob- 

servatory. 

Compte-Bendu  de  la  Commission  Imperiale  Arc  6ologique 
pour  Fannies  1870  et  1871  (with  Atlas).  Fol. — From 
the  Commission. 

Becueil  d’Antiquities  de  la  Scythie.  Livraison  II.  1873. 
4to  (with  Atlas,  Fol.). — From  the  Imperial  Commission  of 
Archaeology. 

Annalen  des  Physikalischen  Centralobservatoriums.  1873. 
4to. — From  the  Russian  Government. 

Salem  ( Mass ). — Bulletin  of  the  Essex  Institute.  Vols.  V.,  VI. 
8 vo. — From  the  Institute. 


653 


of  Edinburgh,  Session  1874-75. 

Schaffhausen . — Verhandlungen  der  Schweizerischen  Naturfersch- 
enden  Gesellschaft  in  Schaffhausen.  Jahresberecht  1872- 
73.  8 vo, — From  the  Society. 

Toronto. — Canadian  Joiirnal  of  Science,  Literature,  and  History. 
Yol.  XI Y.  Nos.  3,  4.  8vo.- — From  the  Society. 

Trevandrum. — Observations  of  Magnetic  Declinations  made  at  Tre- 
vandrum  and  Augustia  Malley,  in  the  Observatories  of  His 
Highness  the  Maharajah  of  Travancore,  G.C.S.I.,  in  the 
years  1852  to  1869.  Discussed  and  Edited  by  John 
Allan  Broun,  F.B.S.  Yol.  I.  4to. — From  His  Highness 
the  Maharajah  of  Travancore,  G.C.S.I. 

Trieste . — Bollettino  della  Societa  Adriatica  di  Scienze  Naturali. 
No.  1.  4to. — From  the  Society. 

Turin. — Atti  della  Beale  Accademia  delle  Scienze  de  Torino. 
Yol.  IX.  Despensa  1-5.  8vo. — From  the  Academy. 

Upsala. — Nova  Acta  Begise  Societatis  Scientiarum  Upsaliensis. 
Yol.  IX.  Fasc.  1.  4to. — From  the  Society. 

Bulletin  Meteorologique  Mensuel  de  l’Observatoire  de  l’Uni- 
versite.  Yol.  Y.  Nos.  7-13.  8vo. — From  the  University. 

Utrecht. — Nederlandsh  Meteorologisch  Jaarboek  voor  1872,  No.  1 ; 
1873,  No.  1. — 4to, — From  the  Meteorological  Institute. 

Aanteekeningen  van  bet  Yerhandelde  in  de  Sectie-Verga- 
deringen  Genootschap  van  Kunsten  en  Wetenshappen 
gehouden  in  het  Jaar  1873.  8vo  — From  the  Society. 

Verslag  van  het  Yerhandelde  in  de  Henderdste  Algemeene 
Yergadering  van  het  Provinciaal  Utrechtsche  genootschap 
van  Kunsten  en  Wetensckeppen  1873,  gehouden  den  21 
Juni.  8vo. — From  the  Society. 

Victoria  (Australia). — Statistics  of  the  Colony,  1872-73.  Inter- 
change— Part  5-7.  Fol.  Production-Part  7.  Fol. 
Population — Parts  3-4.  Fol.  Law,  Crime,  &c. — Part  6. 
Fol.  Beligious,  Moral,  and  Intellectual  Progress — Part 
7.  Fol.  Yital  Statistics,  &c. — Parts  8-9.  Fol.  Ac- 
cumulation— Part  4.  Fol.  Blue  Book — Part  1.  1874. 

Fol.  General  Beport  — Fol.  Friendly  Societies  for 
1873,  with  Introductory  Beport — Fol.  Census  of  Vic- 
toria, 1871.  General  Beport  and  Appendices — Occu- 
pations of  the  People — Detailed  Tables — Part  9.  Fol. 


654 


Proceedings  of  the  Royal  Society 

Report  of  Conference  of  G-overnment  Statistics,  held  in 
Tasmania,  January  1875.  Patents  and  Patentees — Yol. 
VII.  4to. — From  the  Registrar-General. 

Victoria. — Transactions  and  Proceedings  of  the  Royal  Society. 
Vols.  X.,  XI.  8vo. — From  the  Society. 

Vienna. — Sitzungsberichte  der  kaiserlichen  Akademie  der  Wissen 
schaften.  Min.  Bot.  Zool.  G-eo.  Pal.  Band  LXVIII., 
Heft  3 bis  5.  LXIX.,  LXX.  Heft  1-2.— Phys.  Anat. 
Band  LXVIII.,  LXIX.,  LXX.  Heft  1-2.— Phil.  Hist. 
Classe.  Band  LXXV.  Heft  1-3 ; LXXVI.  Heft  1-3; 
LXXVII.  Heft  1-4;  LXXVIII.  Heft  1.— Math.  Nat. 
Classe.  Band  LXVIII.  Heft  3-5;  LXIX.,  LXX.  Heft 
1-2.— Register  Phil.  Hist.  Classe.  Bands  I.-LXX.  Al- 
manack der  Raiserlichen  Akademie  der  Wissenschaften, 
1874.  8 vo. — From  the  Academy. 

Denkschriften  der  kaiserlichen  Akademie  der  Wissen- 
schaften. Math.  Natur.  Classe.  Band  XXXIII. — Phil. 
Hist.  Classe.  Band  XXIII.  4to. — From  the  Academy. 

Jahrbuch  der  kaiserlich-koniglichen  geologischen  Reich- 
sanstalt.  Band  XXIV.  Nos.  2-4;  Band  XXV.  Nos. 
1-2.  8 vo. — From  the  Society. 

Verhandlungen  der  kaiserlich-koniglichen  geologischen 
Reichsanstalt.  1874.  Nos.  7-11,  16-18.  1875.  Nos. 
1-4.  8vo. — From  the  Society. 

Verhandlungen  der  kaiserlich-koniglichen  zoologisch-botan- 
ischen  G-esellschaft  in  Wien.  Band  XXIV.  8vo. — From 
the  Society. 

Die  Palaeozoischen  Gfebilde  Podobens  und  Doren  Verstein- 
erungen  von  Dr  Alois-v.  Alth-Die  Triadischen  Pelecypo- 
den-G-attungen  Daonella  und  Halobia  ven  Edmund 
Mojsisovics  v.  Mojsvar.  Band  VII.  Hefts  1-2.  4to. — 
From  the  Society . 

Die  Culm-Elora  des  Mahaisch-Schlesischen  Dachschiefors 
von  D.  Stur  Abhandlungen  der  k.  k.  G-eologisohen  Reich- 
sanstalt. Band  VIII.  Heft  1.  4to. — From  the  Society. 

Warwick. — Proceedings  of  the  Warwickshire  Naturalists’  and 
Archaeologists’  Field  Club.  1873-74.  8vo. — From  the 
Society . 


655 


of  Edinburgh,  Session  1874-75. 

Warwick. — Thirty-Eighth  and  Thirty-Ninth  Annual  Report  of  the 
Natural  History  and  Archaeological  Society  of  Warwick- 
shire. 8vo. — From  the  Society. 

Washington. — Daily  Bulletin  of  Weather  Reports.  1872-73.  4to. 
— From  the  War  Department. 

Astronomical  and  Meteorological  Observations  made  during 
the  year  1872.  4to. — From  the  TJ.S.  Naval  Observatory. 

Results  of  Observations  made  at  the  U.S.  Naval  Observatory 
in  the  years  1853  to  1860  inclusive.  4to. — From  the 
U.S.  Observatory. 

Teport  of  the  Commissioner  of  Agriculture  for  the  year 
1872.  8vo. — From  the  Commissioner. 

Monthly  Reports  of  the  Department  of  Agriculture  for  the 
year  1873-74.  8vo. — From  the  Commissioner. 

Report  of  Explorations  in  1873  of  Colorado  of  the  West 
and  its  Tributaries,  by  Professor  J.  W.  Powell.  8vo. — 
From  the  Smithsonian  Institution. 

Smithsonian  Miscellaneous  Collections.  Yols.  XI.,  XII. 
8vo. — From  the  Institution . 

Smithsonian  Contributions  to  Knowledge.  Yol.  XIX.  4to. 
— From  the  Institution. 

Annual  Report  of  the  Board  of  Regents  of  the  Smithsonian 
Institution  for  the  year  1873.  8vo. — From  the  Institution. 

Lists  of  Elevations,  principally  in  that  portion  of  the  United 
States  west  of  the  Mississippi  River.  8vo. — From  the 
Geological  Survey. 

Synopsis  of  the  Flora  of  Colorado,  by  Thomas  C.  Porter  and 
John  M.  Coulter.  8vo. — From  the  Geological  Survey. 

Annual  Report  of  the  United  States  Geological  Survey  of 
the  Territories,  embracing  Colorado,  being  a Report  of 
Progress  of  the  Exploration  for  the  year  1873.  8vo. — 
From  the  Geological  Survey. 

Bulletin  of  the  United  States  Geological  and  Geographical 
Survey  of  the  Territories.  No.  1.  1874.  8vo. — From 

the  Geological  Survey. 

Report  of  the  United  States  Geological  Survey  of  the  Pro- 
vinces. Yol.  YI.  Part  1— The  Cretaceous  Flora.  4to.- — 
From  the  Geological  Survey , 


656  Proceedings  of  the  Royal  Society , 1874-75. 

Washington. — Geological  Survey  of  the  Territories  for  the  year 
1874.  Birds  of  the  North- West,  by  Elliott  Coues.  8vo. — 
From  the  Geological  Survey. 

V/ellington  (N.  Z .) — Statistics  of  the  Colony  of  New  Zealand  for 
1873.  Fol. — From  the  Registrar- General. 

Reports  on  the  Durability  of  New  Zealand  Timber  in  Con- 
structive Works.  8 vo. — From  the  Agent- General. 

Meteorological  Report  for  1873,  including  Returns  for  1871- 
72,  and  Abstracts  for  previous  years.  8vo. — From  the 
Geological  Survey  Department. 

Statistics  of  New  Zealand.  1873.  Fol. — From  the  New 
Zealand  Government. 

Eighth  Annual  Report  of  the  Colonial  Museum  and  Labora- 
tory. 8vo. — From  the  Geological  Survey  Department. 

Wisconsin. — Transactions  of  the  Wisconsin  Academy  of  Sciences, 
Arts,  and  Letters,  1873  74.  Yol.  II.  8vo. — From  the 
Academy. 

Zwickau. — Jahresbericht  des  Yeriens  fur  Naturkunde  zu  Zwickau. 
1873-74.  8vo. — From  the  Society. 

Zurich.  — Neue  Denkschriften  der  allgemeinen  schweizerischen 
Gessellschaft  fur  die  gesammten  Naturwissenshaften 
(Nouveaux  Memoires  de  la  Societe  Helvetique  des 
Sciences  Naturelles).  Band  XXYI.  4to. — From  the 

Society. 

Schweizerische  Meteorologische  Beobachtungen  herausge- 
geben  von  der  Meteorologischen  Centralanstalt  der 
Schweizerischen  Naturforschenden  Gesellschaft.  1864  to 
1872;  1873 — Januar,  Februar,  Marz,  April,  Mai,  Juni. 
4to. — From  the  Society. 


INDEX. 


After-glow  of  Cooling  Iron  at  a Dull- 
Red  Heat,  363. 

Alexander  (Rev.  Dr  Lindsay),  Obitu- 
ary Notice  of  the  Rev.  Dr  Guthrie, 
273. 

Obituary  Notice  of  Adam 

Black,  467. 

Andrews  (Professor),  Address  on 
Ozone,  229. 

Balfour  (Professor)  on  the  Formation 
of  Buds  and  Roots  by  the  Leaves 
of  the  Ipecacuan  Plant,  108. 

Barclay  (George),  Obituary  Notice  of 
George  Berry,  476. 

Bile  Salts,  Action  of,  on  the  Animal 
Economy,  525. 

Blackie  (Professor)  on  the  Philologi- 
cal Genius  and  Character  of  the 
Neo-Hellenic  Dialect,  31. 

Bottomly  (J.  T.),  Obituary  Notice  of 
John  Hunter,  322. 

Boulders  in  Scotland,  Second  Report 
by  Committee  on,  137. 

Bromacetic  Acid  and  Sulphide  of 
Methyl,  Compound  formed  by, 
219. 

Brown  (Professor  Crum)  and  Letts 
(Dr  E.  A.)  on  a Compound  formed 
by  the  addition  of  Bromacetic 
Acid  to  Sulphide  of  Methyl,  and 
on  some  of  its  Derivatives,  219. 

Preliminary  Note  on  the 

Sense  of  Rotation  and  the  Function 
of  the  Semicircular  Canals  of  the 
Internal  Ear,  255. 

Obituary  Notice  of  Justus 

Liebig,  307. 

Obituary  Notice  of  Gustav 

Rose,  312. 

On  the  Semicircular  Canals 

of  the  Internal  Ear,  370. 

and  Letts  (Dr  E.  A.)  on  Some 

Compounds  of  Dimethvl-Thetine, 
382. 


Brown  (Professor  Crum),  Rates  of 
Diffusion  of  Salts  in  Solution, 
490. 

and  Letts  (Dr  E.  A.)  on  the 

Products  of  the  Oxidation  of  Dim- 
ethyl-Thetine,  508. 

Brown  (J.  Graham)  on  Bile  Salts, 
525. 

Brown  (Rev.  Thomas)  on  the  Parallel 
Roads  of  Glenroy,  340. 

Brain,  Convolutions  of,  in  Rela- 
tion to  the  Surface  of  the  Head, 
243. 

Buchan  (Alexander),  Meteorology  of 
the  Month  of  May,  79. 

Obituary  Notice  of  Chris- 
topher Hansteen,  473. 

Obituary  Notice  of  Jacques 

Adolphe-Lambert  Quetelet,  474. 

Diurnal  Oscillations  of  the 

Barometer,  505. 

Fluid  Cavities  in  Calcareous 

Spar,  126. 

Caphaelis  Ipecucuctnha , 108. 

Cerebral  Hemispheres  and  Corpora 
Striata  of  Birds,  47. 

Christison  (Sir  Robert),  Opening  Ad- 
dress of  Session  1872-73,  2. 

Fossil  Trees  in  Craigleith 

Quarry,  near  Edinburgh,  Notice 
of,  104,  241. 

Fossil  Trees  of  Granton 

Quarry,  377. 

— Portrait  of,  Presented,  523. 

Cleghorn  (Dr),  Obituary  Notice  of  J. 
Lindsay  Stewart,  321. 

Coal,  Formation  of,  and  Changes  pro- 
duced in  it  by  the  Action  of  Water, 
68. 

Cockburn-Hood  (T.  H.)  Remarks  on 
the  Footprints  of  the  Dinornis  in 
the  Sand  Rock  at  Poverty  Bay, 
New  Zealand,  and  upon  its  Recent 
Extinction,  236. 


658 


Index. 


Cognate  European  Words,  Remark- 
able Changes,  Additions,  and 
Omissions  of  Letters  in  certain, 
596. 

Colson  (C.  G.)  on  the  Circumscribed, 
Inscribed,  and  Escribed  Circles  of 
a Spherical  Triangle,  589. 

Concluding  Remarks  by  D.  Milne 
Home,  Session  1873-74,  390.  ' 

Conductivity,  Electric,  33. 

Conductivity  of  Bars,  Angstrom’s 
Method  for,  55. 

Conductivity,  Thermal  and  Electric, 
32,  33. 

Conductivity  of  Wood,  On  the  Appli- 
cation of  Angstrom’s  Method  to  the, 
481. 

Continuants,  A new  Special  Class  of 
Determinants,  229. 

Further  Note  on,  380. 

Corals  of  the  Palaeozoic  Period,  Mode 
of  Growth  and  Increase  of,  498. 

Council,  1872-73,  1. 

1873-74,  207. 

1874-75,  415. 

Curve  of  Second  Sines  and  its  Varia- 
tions, 356. 

Davidson  (James)  on  Titaniferous 
Iron  Sand,  523. 

Dewar  (James)  on  Physical  Constants 
of  Hydrogenium,  49. 

Thermal  Equivalents  of  the 

Oxide  of  Chlorine,  51. 

- and  M‘Kendrick  (J.  G.), 

on  the  Physiological  Action  of 
Light,  100,  110,  179,  513,  534. 

On  the  Physiological  Action 

of  Ozone,  211. 

On  Latent  Heat  of  Mercury 

Vapour,  380. 

Problems  of  Dissociation  For- 
mation of  Allotropic  Sulphur— Heat 
of  Fermentation,  380,  382. 

and  Tait  (Professor),  Prelimi- 
nary Note  on  a New  Method  of 
obtaining  very  perfect  Vacua, 
348. 

Further  Researches  in  very 

perfect  Vacua,  628. 

Dichroite  and  Amethyst,  Resem- 
blances of  Microscopic  Objects  in, 
to  some  of  the  lower  forms  of 
Organic  Life,  52. 

Dickson  (Professor  A.)  on  the  Embry- 
ogeny  of  Tropazolvm  speciosum  and 
T.  peregrinum , 247. 

Dickson  (William  P.),  Obituary 
Notice  of  Wm.  Euing,  491. 


Diffusivities  of  Fluids,  Mode  of  Deter- 
mining the,  229. 

Dimethyl-Thetine,  On  some  Com- 
pounds of,  382. 

Dimethyl-Thetine,  On  the  Products 
of  the  Oxidation  of,  and  its  Deri- 
vatives, 508. 

Dinornis,  Remarks  on  the  Footprints 
of,  236. 

Donaldson  (Dr)  on  Expiatory  and 
Substitutionary  Sacrifices  of  the 
Greeks,  535. 

Donations  to  Library,  186,  396,  629. 

Drift  Deposits  in  Tweed  Valley, 
559. 

Durham  (Wm.)  on  Electric  Resist- 
ance of  Solution,  587. 

Ear,  Function  of  Semicircular  Canals 
of,  255. 

Electric  Resistance  of  Solutions,  587. 

Electrical  Conductivity  of  Saline 
Solutions,  545. 

Electricity,  Atmospheric,  349. 

Energy,  Kinetic  Theory  of  the  Dissi- 
pation of,  325. 

Ewing  (J.  A.)  and  Macgregor  (J.  G.), 
Saline  Solutions,  the  Electrical 
Conductivity  of,  with  a Note  on 
their  Density,  95. 

Expiatory  and  Substitutionary  Sacri- 
fices of  the  Greeks,  535. 

Fairweather  (James  C.)  on  the  Re- 
sistance of  the  Air  to  the  Motion 
of  Fans,  351. 

Fans,  Resistance  of  the  Air  to  the 
Motion  of,  351. 

Fellows  Elected,  80,  89,  114,  185, 
288,  371,  350,  395,  445,  500,  513, 
534. 

Statement  as  to  Number  of, 

324,  420. 

Fishes  from  West  Africa,  Notice  of, 
89. 

Flow  of  Water  through  Fine  Tubes, 
208. 

Fluid  enclosed  in  Crystal  Cavity, 
singular  property,  Notice  of, 
87. 

Fonctions  logarithmiques,  jtl’aidedes 
tables  numeriques,  602. 

Forbes  (Professor  George),  Zodiacal 
Light,  Note  on,  55. 

Thermal  Conductivity  of  Ice, 

and  New  Method  of  determining 
the  Conductivity  of  Different  Sub- 
stances, 62. 


Index. 


659 


Forbes  (Professor  George)  on  “ Tait’s 
Property  of  the  Retina,”  130. 

Obituary  Notice  of  Auguste 

De  la  Rive,  319. 

On  the  After-glow  of  Cooling 

Iron  at  a Dull-Red  Heat,  363. 

On  a Form  of  Radiation  Dia- 
gram, 366. 

Force  exerted  by  an  Element  of  one 
Linear  Conductor  on  the  Element 
of  another,  220. 

Forests,  On  the  Thermal  Influence 
of,  114. 

Fossil  Trees  of  Craigleith  Quarry, 
near  Edinburgh,  104,  241. 

* of  Granton  Quarry,  377. 

Foulis  (James),  Development  of  the 
Ova,  and  Structure  of  the  Ovary, 
in  Man  and  other  Mammals,  437. 

Fraser  (Professor),  Obituary  Notice  of 
J.  S.  Mill,  259. 

Gamgee  (Dr)  on  the  Muscles  which 
Open  and  Close  the  Mouth,  47. 

Gases,  Diffusion  of,  331. 

Germ  Theory  of  Putrefaction,  89. 

Gey  sir  of  Iceland,  Note  of  Tempera- 
ture Measurements  in  the,  514. 

Glenrov,  On  the  Parallel  Roads  of, 
340/ 

Gordon  (Lewis  D.  B.),  Obituary  Notice 
of  Professor  Rankine,  296. 

Greenheart  Timber,  Ravages  of  Lim- 
noria  terebrans  on,  182. 

Greenland  Shark,  a Contribution  to 
the  Visceral  Anatomy  of  the,  81. 

Grouse  Disease,  Note  on,  378. 

Handyside  (P.  D.)  on  the  Anatomy 
of  Polyodon  gladius  of  Martens,  50, 

136. 

Heating  one  Pole  of  a Magnet,  Effect 
of,  97. 

High  Flood  Marks  on  the  Banks  of 
the  Tweed,  559. 

Home  (David  Milne),  Remarks  on  the 
Deaths  of  Professor  Rankine,  Glas- 
gow ; Dean  Ramsay,  Edinburgh ; 
and  Archibald  Smith  of  Jordanhill, 
34. 

On  the  Supposed  Upheaval  of 

Scotland  in  its  Central  Parts,  49. 

Concluding  Remarks,  Session 

1873-74,  390. 

On  High  Flood  Marks  on  the 

Banks  of  the  Tweed,  and  on  Drift 
Deposits,  559. 

Homocheiral  and  Heterocheiral  Simi- 
larity, 70. 

VOL.  VIII. 


Hunter  (Dr  James),  and  Sang  (Ed- 
ward), Observations  and  Experi- 
ments on  the  Fluid  in  the  Cavities 
of  Calcareous  Spar,  126. 

Hydrogenium,  Physical  Constants  of, 
49. 

Iceland  Spar,  Fluid  enclosed  in 
Crystal  Cavities  in,  247,  249. 

Integrals,  Note  on  the  Transforma- 
tion of  Double  and  Triple,  209. 

Ipecacuan  Plant,  Formation  of  Roots 
and  Buds  from  the  Leaves  of,.  108. 

Jenkin  (Professor  Fleeming),  Obituary 
Notice  of  Mr  R.  W.  Thomson,  278. 

Keith  Prize  for  1871-73,  Presentation 
to  Professor  Tait,  416. 

Knott  (C.  G.),  and  Marshall  (D.  H.), 
on  the  Effect  of  Heating  one  Pole 
of  a Magnet,  the  other  being  kept 
at  a constant  Temperature,  97. 

and  Macfarlane  (A.)  on  the 

Application  of  Angstrom’s  Method 
to  the  Conductivity  of  Wood,  481 

and  Smith  (C.  M.),  Experi- 
ments on  the  Thermal  Conductivity 
of  some  Dielectrics,  623. 

Lcemargus  borealis , Contribution  to 
Anatomy  of,  81. 

Lang  (P.  R.  Scott)  on  Electric  Re- 
sistance of  Solution,  587. 

Laws  for  Election  of  Fellows,  pro- 
posed Alterations  in,  48. 

Lefort  (M.  F.),  Observations  on  Mr 
Sang’s  Remarks  relative  to  the 
great  Logarithmic  Table  compiled 
at  the  Bureau  du  Cadastre  under 
the  direction  of  M.  Prony,  563,  574. 

De  Pinterpolation  des  fonctions 

irrationelles  en  general,  et  des  fonc- 
tions logarithmiques  en  particulier, 
a l’aide  des  tables  numeriques,  602. 

Letts  (Dr  E.  A.)  and  Brown  (Professor 
Crum)  ou  a Compound  formed  by 
the  addition  of  Bromacetic  Acid  to 
Sulphide  of  Methyl,  and  on  some 
of  its  Derivatives,  219. 

On  some  Compounds  of  Dime- 
thyl Thetine,  382. 

On  the  Products  of  the  Oxida- 
tion of  Dimethyl-Thetine,  508. 

Light,  on  the  Physiological  Action  of, 
100,  110,  179,  513,  534. 

Limnoria  terebrans , Notice  of  the 
Ravages  of,  on  Greenheart  Timber. 
182. 

4q 


660 


Index . 


Linotrypane  apogon,  386. 

Lister  (Professor)  on  the  Germ  Theory 
of  Putrefaction,  89. 

Logarithmic  and  Trigonometrical 
Tables,  by  M.  Prony,  421. 

Table  compiled  at  the  Bureau 

du  Cadastre,  503. 

Macfarlane  (A.),  and  Knott  (C.  G.),  on 
the  Application  of  Angstrom’s 
Method  to  the  Conductivity  of 
Wood,  481. 

MacGregor  (J.  G.),  on  the  Electrical 
Conductivity  of  Saline  Solutions, 
545. 

and  Ewing  (J.  A.),  Certain  Sa- 
line Solutions,  The  Electrical  Con- 
ductivity of,  with  a Note  on  their 
Density,  95. 

MTntosh  (W.  C.)  on  a New  Example 
of  the  Opheliidae,  386. 

M‘Kendrick  (Dr  J.  G.)  on  Cerebral 
Hemispheres  and  Corpora  Striata  of 
Birds,  47. 

and  Dewar  (James),  Light, 

Physiological  Action  of,  100,  110, 
179,  513,  534. 

and  Dewar  (James)  on  the 

Physiological  Action  of  Ozone, 

211. 

• Note  on  the  Perception  of 

Musical  Sounds,  342. 

Maclagan  (Professor),  Note  on  Grouse 
Disease,  378. 

— Obituary  Notice  of  Henry 
Stephens,  469. 

Maclagan  (David),  Obituary  Notice  of 
Sheriff  Cleghorn,  468. 

Makdougall-Brisbane  Prize  presented 
to  Professor  Allman,  48. 

- - Biennial  Period,  1872-74,  pre- 
sented to  Professor  Lister,  500. 

Marshall  (D.  H.)  on  Electric  Conduc- 
tivity, 33. 

— — and  Knott  (C.  G.)  on  the  Effect 
of  Heating  one  Pole  of  a Magnet, 
the  other  being  kept  at  a Constant 
Temperature,  97. 

Meteorology  of  the  Month  of  May, 
79. 

Mudbanks  of  Narrakal  and  Allippey 
on  the  Malabar  Coast,  70. 

Muir  (Thomas),  Continuants, — a New 
Special  Class  of  Determinants,  229. 

— — Furthur  Note  on  Continuants, 
380. 

Muscles  that  Open  and  Close  the 
Mouth,  47. 

Musical  Sounds,  Perception  of,  342. 


Neaves  (Hon.  Lord),  Obituary  Notice 
of  Lord  Colonsay,  445. 

— - — - Obituary  Notice  of  Cosmo 
Innes,  453. 

— Obituary  Notice  of  Francis 
Deas,  461. 

On  some  Remarkable  Changes, 

Additions  and  Omissions  of  Letters 
in  certain  Cognate  European 
Words,  596. 

Neill  Prize  for  Triennial  Period, 
1871-74,  presented  to  Mr  C.  W. 
Peach,  509. 

Neo-Hellenic  Dialect,  Character  of, 
Professor  Blackie,  31. 

Nicholson  (H.  Alleyne)  on  the  Mode 
of  Growth  and  Increase  amongst 
the  Corals  of  the  Palaeozoic  Period, 
498. 

Nickel,  Pure,  on  the  Thermo-electric 
Properties  of,  182. 

Niven  (Professor  C.),  on  the  Stresses 
due  to  Compound  Strains,  335. 

Obituary  Notices  of  Barnes  (Dr 
Thomas),  3. 

Berry  (George),  476. 

Black  (Adam),  467. 

- Cleghorn  (Sheriff),  468. 

•  — - Lord  Colonsay,  445. 

Deas  (Francis),  461. 

Ewing  (William),  401. 

- — — Guthrie  (Rev.  Dr),  273. 

Hansteen  (Christopher),  473. 

Hunter  (John),  322. 

•  Innes  (Cosmo),  445. 

Liebig  (Justus),  307. 

Mill  (J.  S.),  259. 

— Miller  (Dr  Patrick),  7. 

von  Mohl  (Hugo),  14. 

— Quetelet  (Jacques  Adolphe 

Lambert),  474. 

Ramsay  (Very  Rev.  Dean),  289. 

Rankine  (Professor),  296. 

— - — • De  la  Rive  (Auguste),  319. 

Rose  (Gustav),  312. 

Smith  (Archibald),  282. 

- — Stephens  (Henry),  469. 

Stevenson  (Rev.  Professor), 

314. 

Stewart  (J.  Lindsay),  321. 

— Symonds  (Dr  John  Adding- 
ton), 4. 

Terrott  (Bishop),  9. 

Opening  Address,  Session  1872-73, 
2 ; 1874-75,  420. 

Opheliidae,  on  a new  Example  of 
the,  386. 

Ophiocephalus  obscurus,  Giinther  89. 


Index. 


661 


Ova,  Development  of,  and  Structure 
of  the  Ovary  in  Man  and  other 
Mammals,  437. 

Oxide  of  Chlorine,  Thermal  Equi- 
valents of,  51. 

Ozone,  On  the  Physiological  Action 
of,  211. 

Address  on,  229. 

Pearson  (Rev.  Jas.),  A Chapter  on  the 
Tides,  627. 

Placenta  of  Ruminants, — a Deciduate 
Placenta,  537. 

Plarr  (G.)  on  the  Establishment  of  the 
Elementary  Principles  of  Quater- 
nions on  an  Analytical  Basis,  348. 

On  the  Elimination  of  a,  j8,  y, 

from  the  condition  of  integrability 
of  S.,  Uadp,  S.  WySSp,  S.  Uydp,  436. 

Polyodon  gladius  of  Martens,  Anatomy 
of,  50,  136. 

Radiation,  Diagram  on  a Form  of,  366. 

Retina,  Tait’s  Property  of  the,  130. 

Robertson  (George)  on  the  Mud  Banks 
of  Narrakal  and  Allippey,  two  Na- 
tural Harbours  of  Refuge  on  the 
Malabar  Coast,  70. 

Saline  Solutions  Electrical  Conducti- 
vity of,  95. 

Sandford  (Rev. D.F.),  Obituary  Notice 
of  the  Very  Rev.  Dean  Ramsay,  289. 

Sang  (Edward)  on  a Singular  Pro- 
perty exhibited  by  the  Fluid  en- 
closed in  Crystal  Cavities,  87. 

and  Hunter  (Dr  James),  Ob- 
servations and  Experiments  on  the 
Fluid  in  the  Cavities  of  Calcareous 
Spar,  126. 

On  the  Curve  of  Second  Sines 

and  its  Variations,  356. 

Remarks  on  the  Great  Lo- 
garithmic and  Trigonometrical 
Tables,  computed  in  the  Bureau 
du  Cadastre  under  the  direction  of 
M.  Prony,  421. 

On  the  Complete  Theory  of 

the  Stone  Arch,  479. 

On  a Faulty  Construction 

common  in  Skewed  Arches,  497. 

Reply  to  the  Lefort’s  Observa*- 

tions  on  Logarithmic  Tables,  581. 

On  Last-Place  Errors  in 

Vlacq’s  Table  of  Logarithms,  371. 

Scott  (J.),  Resemblances  of  Microscopic 
Objects  in  Dichroite  and  Amethyst 
to  some  of  the  lower  forms  of  Or- 
ganic Life,  52. 


Seals,  On  the  Placentation  of  the,  137. 

Sharpey  (Dr.  W.),  Obituary  Notice  of 
Dr.  R.  E.  Grant,  486. 

Skewed  Arches,  On  a Faulty  Construc- 
tion common  in,  497. 

Sloths,  On  the  Placentation  of  the, 
134. 

Small  (John),  Obituary  Notice  of  the 
Rev.  Professor  Stevenson,  D.D.,  314. 

Smith  (C.M.),  and  Knott  (C.G.),  Ex- 
periments on  the  Thermal  Conduc- 
tivity of  some  Dielectrics,  623. 

Smith  (John  Alexander),  New  Fishes 
from  West  Africa,  Notice  of,  89. 

Sodium  and  Potassium,  On  the 
Thermo-electrical  Positions  of,  350, 
362. 

Spherical  Triangle,  Circumscribed, 
Inscribed,  and  Escribed  Circle  of, 
589. 

Statement  regarding  Number  of 
Members,  December  1874,  420. 

Stevenson  (David),  Notice  of  the  Ra- 
vages of  Limnoria  terebrans  on 
Greenheart  Timber,  182. 

Notice  of  Striated  Rock  Sur- 
faces on  North  Berwick  Law,  481. 

Stevenson  (Robert  Louis)  on  the 
Thermal  Influence  of  Forests,  114. 

Stone  Arch,  on  the  Complete  Theory 
of,  479. 

Storms,  Easterly  Direction  of,  over 
the  British  Isles,  612. 

Strain-Function,  &c.,  Additional  Note 
on  the,  84. 

Strains,  Compound,  on  the  Stresses 
due  to,  335. 

Striated  Rock  Surfaces  on  North 
Berwick  Law,  Notice  of,  481. 

Sulphide  of  Methyl,  Compound  formed 
by,  219. 

Swan  (Professor),  Singular  Property 
possessed  by  the  Fluid  enclosed  in 
Crystal  Cavities  in  Iceland  Spar, 
249. 

Synodontis  Robbianus,  J.  A.  Smith,  89. 

Tait  (Professor)  on  Electric  Conduc 
tivity,  32. 

On  a Question  of  Arrangement 

and  Probabilities,  37. 

Thermo-  Electric  Diagram,  47. 

On  Angstrom’s  Method  for 

Conductivity  of  Bars,  55. 

On  the  Thermo-Electric  Posi- 
tions of  Sodium  and  Potassium, 
350,  362. 

and  Dewar  (James)  on  the 

exceedingly  Small  Pressures  of 
Spectra,  363. 


662 


Index. 


Tait  (Professor)  on  a Singular  Theory 
given  by  Abel,  440. 

Equipotential  Surfaces  for  a 

Straight  Wire,  443. 

Fundamental  Principles  in 

Statics,  443. 

Photographic  Records  of  the 

Sparks  from  a Holtz  Machine,  484. 

Capillary  Phenomena  at  the 

Surface  of  Separation,  485. 

Determination  of  the  Surface- 

Tension  of  Liquids,  485. 

Photographs  of  Electric  Sparks 

taken  in  Cold  and  Heated  Air, 
491. 

On  the  Thermo-Electric  Pro- 
perties of  Pure  Nickel,  182. 

On  the  Strain-Function,  84. 

— On  a Thermo-Electric  Dia- 
gram, 208. 

—  Note  on  the  Transformation 

of  Double  and  Triple  Integrals, 
209. 

Note  on  various  Possible  Ex- 
pressions for  the  Force  exerted  by 
an  Element  of  one  Linear  Con- 
ductor on  an  Element  of  another, 
220. 

Notes  on  Mr  Sang’s  Com- 
munication of  7th  April  1873,  on 
Singular  Property  possessed  by  the 
Fluid  enclosed  in  Crystal  Cavities 
in  Iceland  Spar,  247. 

— On  the  Flow  of  Water  through 

Fine  Tubes,  208. 

* and  Dewar  (James),  Preli- 

minary Note,  On  a new  Method  of 
obtaining  very  perfect  Vacua,  348. 

—  On  Atmospheric  Electricity, 

349. 

Application  of  Sir  William 

Thomson’s  Dead  Beat  Arrange- 
ment to  Chemical  Balances,  490. 

Electric  Resistance  of  Iron  at 

High  Temperatures,  491. 

On  Electric  Images,  623. 

On  the  Origin  of  Atmospheric 

Electricity,  623. 

Talbot  (W.  H.  Fox),  Essay  towards 
the  General  Solution  of  Numerical 
Equations  of  all  Degrees,  544. 

Tennent  (Robert),  Theory  of  the 
Causes  by  which  Storms  progress 
in  an  Easterly  Direction  over  the 
British  Isles,  &c.,  612. 

Thermal  Conductivity  of  Ice,  62. 

Thermo-Electric  Diagram,  47,  208. 

Thermo-Electric  Properties  of  Pure 
Nickel,  182. 


Thomson  (R.  W.)  on  the  Formation 
of  Coal  and  Changes  produced  in 
the  Composition  of  the  Strata,  by 
the  Solvent  Action  of  Water,  68. 

Thomson  (Sir  William),  Homocliei- 
ral  and  Heterocheiral  Similarity, 
70. 

On  Vortex  Motion,  80. 

On  New  Method  of  deter- 
mining the  Material  and  Thermal 
Diffusivities  of  Fluids,  229. 

Diagrams  to  illustrate  Capil  • 

lary  Surfaces  of  Revolution,  500. 

Obituary  Notice  of  Archibald 

Smith,  282. 

The  Kinetic  Theory  of  the 

Dissipation  of  Energy,  325. 

Diffusion  of  Gases,  331. 

On  a new  Form  of  Mariners’ 

Compass,  363. 

Tide  Calculating  Machine — 

Tide-Gauge,  445. 

Oscillation  of  a System  of 

Bodies  with  Rotating  Motions,  490, 
521. 

and  Perry  (John)  on  the 

Capillary  Surface  of  Evolution, 

520. 

Theory  of  the  Spining-Top, 

521. 

Titaniferous  Iron  Sand,  North  Ber- 
wick, 523. 

Traquair  (R.  H.)  on  the  Structure 
and  Systematic  Position  of  Tristi- 
chopterus  alatus , Egerton,  513. 

- — On  some  Permian  Fishes, 

525. 

Tristichopterus  alatus,  Structure  and 
Systematic  Position  of,  513. 

Tropmolum  speciosum  and  T.  pere- 
grinum,  Embryogeny  of,  247. 

Tuke  (Dr  Batty),  on  the  Anatomy  of 
Pia  Mater,  534. 

Turner  (Professor),  Contribution  to 
the  Visceral  Anatomy  of  the  Green- 
land Shark  ( Lcemargus  borealis),  81. 

— On  the  Placentation  of  the 

Sloths,  134. 

Placentation  of  the  Seals, 

137. 

• Method  of  Demonstrating  the 

Relations  of  the  Convolutions  of  the 
Brain  to  the  Surface  of  the  Head, 
243. 

Placentation  of  Ruminants, 

537. 

Upheaval  of  Scotland  in  its  Central 
Parts,  49, 


Index. 


668 


Vacua,  On  a new  Method  of  obtain- 
ing very  perfect,  348. 

Vaughan  (Daniel),  Volcanic  Erup- 
tions, A Theory  of,  133. 

Vision,  Single  and  Double,  Pheno- 
mena of,  505. 

Vlacq’s  Table  of  Logarithms,  On  Last- 
Place  Errors  in,  371. 

Volcanic  Eruptions,  a Theory  of,  133. 

Vortex  Motion,  80. 


Walker  (Robert),  Note  of  Tempera- 
ture Measurement  in  the  Great 
Geysir  of  Iceland,  August  1874, 
514. 

Wyld  (R.  S.),  Phenomena  of  Single 
and  Double  Vision,  as  shown  in  the 
Stereoscope,  505. 

Zodiacal  Light,  Note  on,  by  George 
Forbes,  55. 


ERRATA. 

Page  549,  line  23,  instead  of  “Wheatstone’s  method  (in  our  refer- 
ence to  which  Galvanometer  is  printed  Electrometer),”  read:  “the 
Electrometer  method  to  which  we  referred.” 

Page  549,  line  26,  instead  of  “ Wheatstone,”  read:  “ this  method.” 
Page  550,  line  4 from  the  bottom,  After  “p.  198”  add  “Also 
Papers  on  Electrostatics  and  Magnetism  by  Sir  William  Thomson, 
1872,  § 350.” 

Page  555,  line  7,  after  “original  liquid,”  read : “and  that  there 
is  no  special  resistance  to  the  passage  of  the  current  from  the  elect- 
rode to  the  liquid  ? ” 


PRINTED  BY  N KILL  AND  COMPANY,  EDINBURGH. 


r o u . II  | 

% v yj ' vf  I 


\>V'  < 


V'  S. : 8r  s~- 


PROCEEDINGS 

OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 

SESSION  1872-73. 


CONTENTS. 

Monday,  2d  December  1872. 

PAGE 


Opening  Address.  Session  1872-73.  By  Sir  Bobert 

Christison,  Bart.,  . . . . ,2 

Monday , 1 6th  December  1872. 

On  the  Philological  (Genius  and  Character  of  theNeo  Hellenic 

Dialect.  By  Professor  Blackie,  . . .31 

Laboratory  Notes.  By  Professor  Tait.  Communicated,  in 
his  absence,  by  Professor  0.  Forbes — 

On  the  Delation  between  Thermal,  and  Electric,  Con- 
ductivity, . . . . . .32 

On  Electric  Conductivity  at  a Bed  Heat,  . . 32 

On  the  Thermo-Electric  Properties  of  Pure  Iron,  . 32 

Note  on  the  Bate  of  Decrease  of  Electric  Conductivity  with 
Increase  of  Temperature.  By  D.  H.  Marshall,  M.A., 
Assistant  to  the  Professor  of  Natural  Philosophy. 
Communicated  by  Professor  Tait,  . . .33 


Monday , 6 th  January  1873. 

Notices  of  deceased  Fellows.  By  David  Milne  Home,  ior^ 

On  a Question  of  Arrangement  and  Probabilities.  By^Byb-  L,  2.  ^ 
fessor  Tait,  . . . 

[3Y(V«  over. 


11 


PAGE 

Laboratory  Notes.  By  Professor  Tait.  (1.)  On  the  Stiff- 


ness of  "Wires.  (2.)  Preliminary  Sketch  of  the  Thermo- 
Electric  Diagram  for  Iron,  Gtold,  and  Palladium,  , 44 

On  the  Muscles  which  open  and  close  the  Mouth,  with  some 
Observations  on  the  Active  and  Passive  Condition  of 
Muscles' generally.  By  Dr  G-amgee,  . . .47 

Observations  and  Experiments  on  the  Cerebral  Hemispheres 
and  Corpora  Striata  of  Birds  By  Dr  M‘Kendrick. 
Communicated  by  Professor  Turner,  . * .47 

Monday , 2 Oth  January  1873. 

Award  of  Makdougall  Brisbane  Prize  to  Professor  Allman,  48 

Beport  anent  proposed  alteration  of  Laws.  . . .48 

On  the  Physical  Constants  of  Hydrogenium.  I.  By  Mr 

James  Dewar,  ......  49 

On  the  supposed  Upheaval  of  Scotland,  in  its  Central  Parts, 
since  the  time  of  the  Boman  Occupation.  By  D.  Milne 
Home,  LL.D  , ......  49 


Monday , 3d  February  1873. 

On  the  Anatomy  of  a new  Species  of  Polyodon,  the  Polyodon 
Gladius  of  Martens,  taken  from  the  river  Yang-tsze- 
Kiang,  450  miles  above  Woosung.  Part  I.,  being  its 
External  Characters  and  Structure.  By  P.  D.  Handy- 


side,  M.D.,  . . . . . .50 

Note  on  the  Thermal  Equivalents  of  the  Oxide  of  Chlorine. 

By  James  Dewar,  Esq.  . . . .51 

On  the  Besemblances  which  Microscopic  Objects  in  Diehroite 
and  Amethyst  have  to  some  of  the  lower  forms  of 
Organic  Life.  By  J.  Scott,  Tain.  Communicated  by 
Professor  Kell  and,  . . . . .52 

Note  on  the  Zodiacal  Light.  By  George  Forbes,  Esq.,  . 55 


Monday , 17 th  February  1873. 

Note  on  Angstrom’s  Method  for  the  Conductivity  of  Bars. 

By  Professor  Tait,  . . . . .55 

On  the  Thermal  Conductivity  of  Ice,  and  a new  Method  of 
Determining  the  Conductivity  of  Different  Substances. 

By  Professor  G-eorge  Forbes,  . . . .62 

For  continuation  of  Contents , see  pp.  3 and  4 of  Cover. 


r a o ii 


jt- 

iii 

On  the  Formation  of  Coal,  and  on  the  Changes  produced  in 
the  Composition  of  the  Strata  by  the  Solvent  Action  of 
Water  slowly  percolating  through  the  Earth’s  Crust 
during  long  periods  of  Geological  Time.  By  R.  W. 
Thomson,  C.E.,  F.R.S.E.,  . . . .68 

Note  on  Homocheiral  and  Heterocheiral  Similarity.  By 

Sir  William  Thomson,  . . . .•  . . 70 

Monday , 3 d March  1873. 

On  the  Mud  Banks  of  Narrakal  and  Allippey,  two  Natural 
Harbours  of  Refuge  on  the  Malabar  Coast.  By  George 
Robertson,  Esq.,  C.E.,  . . . .70 

The  Meteorology  of  the  Month  of  May.  By  Alexander 

Buchan,  M.A.,  * . . . .79 

On  Vortex  Motion.  By  Sir  William  Thomson;  . . .80 

Monday , 11th  March  1873. 

A Contribution  to  the  Visceral  Anatomy  of  the  Greenland 

Shark  ( Lcemargus  borealis).  By  Professor  Turner,  . 81 

Additional  Note  on  the  Strain-Function,  &c.  -By  Professor 

Taut,  ......  84 

Monday , 1th  April  1873. 

Notice  of  a Singular  Properly  exhibited  by  the  Fluid  en- 
closed in  Crystal  Cavities.  By  Edward  Sang,  Esq.,  . 87 

On  the  Germ  Theory  of  Putrefaction  and  other  Fermenta- 
tive Changes.  By  Professor  Lister,  . . . 89 

Monday , 21  st  April  1873. 

Notice  of  New  Fishes  from  West  Africa  : — (I.)  Ophioceph- 
alus  obscurus,  Gunther.  (II.)  Synodontis  Bobbianus , 
nov.  spec,  milii.  (With  a Plate).  By  John  Alex- 
ander Smith,  M.D.,  . . . . .89 

On  the  Electrical  Conductivity  of  Certain  Saline  Solutions, 
with  a note  on  their  Density.  By  J.  A.  Ewing  and  J. 

G.  MacGregor,  B.A.  Communicated  by  Professor 
Tait,  .......  95 

On  the  Effect  of  Heating  one  Pole  of  a Magnet,  the  other 
being  kept  at  a Constant  Temperature.  By  D.  H.  Mar- 
shall, Esq.,  M.A.,  and  C.  G.  Knott,  Esq.  Communi- 
cated by  Professor  Tait.  (With  a Plate),  . . 97 


\ 

\ 


IV 


I 

If 


TAGL 

On  the  Physiological  Action  of  Light.  No.  I.  By  James  \ 
Dewar,  Esq.,  and  John  G.  McKendrick,  M.D.,  of  the 
University  of  Edinburgh,  . . . ..  10d 

Monday , 5th  May  1873w 

Notice  of  two  Fossil  Trees  lately  uncovered  in  Craigleith 
Quarry,  near  Edinburgh.  By  Sir  R.  Ciiristison,  Bart., 
President  R.S.E.,  .....  104 

On  the  Formation  of  Buds  and  Roots  by  the  Leaves  of  the 
Ipecacuan  Plant  (Cephaelis  Ipecacuanha).  By  Professor 
Baleour.  (With  a Woodcut), . . . v 108! 

On  the  Physiological  Action  of  Light.  No.  II,  By  James 

Dewar,  Esq.,  and  John  Gr.  MTGendrick,  M.D.,  . 110 

Monday , 19 tli  May  1873. 

On  the  Thermal  Influence  of  Forests.  By  Robert  Louis 


Stevenson,  Esq.  Communicated  by  Thomas  Steven- 
son, Esq.,  . . . . . 114 

Observations  and  Experiments  on  the  Fluid  in  the  Cavities 
of  Calcareous  Spar.  By  Dr  James  Hunter  and  Edward 
Sang,  . . . . . . 126' 

On  “Tait’s  Property  of  the  Retina.”  By  George  Forbes, 

Esq.,  . . . . . •'r;'.130J 

A Theory  of  Volcanic  Eruptions.  By  Daniel  Vaughan,  . £ 133 , 
On  the  Placentation  of  the  Sloths.  By  Professor  Turner,  . 1341 


Monday , 2 d June  1873. 

On  the  Anatomy  of  a new  species  of  Polyodon,  the  Polyodon 
Gladius  of  Martens,  taken  from  the  river  Yang-tsze- 
kiang,  450  miles  above  Woosung.  Part  II.,  being  its 
Nervous  and  Muscular  Systems.  By  P.  D.  Handyside, 


M.D., 136 

On  the  Placentation  of  the  Seals.  By  Professor  Turner,  . 137 

Second  Report  by  the  Committee  on  Boulders  appointed  by 

the  Society.  (With  a Plate),  ....  137 

On  the  Physiological  Action  of  Light.  No.  III.  By  James 

Dewar,  Esq.,  and  John  Gr.  M‘Kendrick,  M.D.,  . 179  j 

On  the  Thermo-Electric  Properties  of  Pure  Nickel.  By  Pro- 
fessor Tait,  . . . . . .182 

Notice  of  the  Rayages  of  the  Limnoria  terebrans  on  Green- 
heart  Timber.  By  David  Stevenson,  Esq.,  Civil 
Engineer,  . . . . . 1 82  j 


J 

"4 


PROCEEDINGS 


OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 

SESSION  1873-74. 


CONTENTS. 

Monday.  24dh  November  1873. 

PAGE 

Election  of  Office-Bearers,  ....  « 207 

Monday , ls£  December  1873. 

Laboratory  Notes.  By  Professor  Tait — 

1.  First  Approximation  to  a Thermo-electric  Diagram,  208 

2.  On  the  Flow  of  Water  through  Fine  Tubes,  . 208 

Note  on  the  Transformation  of  Double  and  Triple  Integrals. 

By  Professor  Tait,  .....  209 

On  the  Physiological  Action  of  Ozone.  By  James  Dewar, 

Esq.,  Lecturer  on  Chemistry,  and  John  G-.  M‘Kendrick, 

M.D.,  Physiological  Laboratory,  University  of  Edin- 
burgh, .......  211 

On  a Compound  formed  by  the  addition  of  Bromacetic  Acid 
to  Sulphide  of  Methyl,  and  on  some  of  its  Derivatives. 

By  Professor  Crum  Brown  and  Dr  E.  A.  Letts,  . 219 

Note  on  the  Various  Possible  Expressions  for  the  Force 
Exerted  by  an  Element  of  one  Linear  Conductor  on  an 
Element  of  another.  By  Professor  Tait,  . . 220 

Monday , 22 d December  1873. 

Address  on  Ozone,  by  Professor  Andrews,  Hon.  F.B.S.E., 

Vice-President  of  Queen’s  College,  Belfast,  . . 229 


[Turn  over. 


11 


Monday , 5 th  January  1874. 

A new  Method  of  Determining  the  Material  and  Thermal 
Diffusivities  of  Fluids.  By  Sir  William  Thomson, 


page 


229 


Continuants — A New  Special  Class  of  Determinants.  By 
Thomas  Muir,  M.A.,  Assistant  to  the  Professor  of 
Mathematics  in  the  University  of  Glasgow,  . . 229 

Remarks  upon  the  Footprints  of  the  Dinornis  in  the  Sand 
Rock  at  Poverty  Bay,  New  Zealand,  and  upon  its  recent 
extinction.  By  T.  H.  Cockburn-Hood,  F.G.S.,  . 236 


Monday , 19^  January  1874. 

Supplementary  Notice  of  the  Fossil  Trees  of  Craigleith 
Quarry.  By  Sir  Robert  Ciiristison,  Bart.,  Hon.  Vice- 
President,  R.S.E.,  &c.,  . . . . 241 

On  a Method  of  Demonstrating  the  Relations  of  the  Con- 
volutions of  the  Brain  to  the  Surface  of  the  Head.  By 
Professor  Turner,  .....  243 

On  some  Peculiarities  in  the  Embryogeny  of  Tropceolum 
speciosum,  Endl.  & Poepp.,  and  T.  peregrinum , L.  By 
Professor  Alexander  Dickson,  . . . 247 

Notes  on  Mr  Sang’s  Communication  of  7tli  April  1873  on 
a Singular  Property  possessed  by  the  Fluid  enclosed  in 
Crystal  Cavities  in  Iceland  Spar.  (1.)  By  Professor 
Tait  ; (2.)  By  Professor  Swan,  . . . 247 

Preliminary  Note  on  the  sense  of  Rotation  and  the  Function 
of  the  Semicircular  Canals  of  the  Internal  Ear.  By 
Professor  A.  Crum- Brown,  ....  255 

•'  P tVi 

Monday , 2d  February  1874. 

Biographical  Notice  of  J.  S.  Mill.  By  Professor  Fraser,  . 259 

Obituary  Notice  of  the  Rev.  Dr  Guthrie.  By  the  Rev.  Dr 

Lindsay  Alexander,  . . . . .273 

Obituary  Notice  of  Mr  R.  W,  Thomson.  By  Professor 

Fleeming  Jenkin,  .....  278 

Obituary  Notice  of  Archibald  Smith.  By  Sir  William 

Thomson,  . . . . . 282 

For  continuation  of  Contents,  see  pp.  3 and  4 of  Cover. 


Ill 


PAGE 


Monday , 16^  February  1874. 

Obituary  Notice  of  the  Very  Rev.  Dean  Ramsay.  By  the 

Rev.  D.  F.  Sandford,  . 289 

Obituary  Notice  of  Professor  Rankine.  By  Lewis  D.  B. 

Gordon,  C.E.,  . . . . . 296 

Obituary  Notice  of  Justus  Liebig.  By  Professor  Crum- 

Brown,  ......  307 

Obituary  Notice  of  Gustav  Rose.  By  Professor  Crum- 

Brown,  ......  312 

Obituary  Notice  of  the  Rev.  Professor  Stevenson,  D.D.  By 
John  Small,  M.A.,  Librarian  to  the  University  of 
Edinburgh,  ......  314 

Obituary  Notice  of  Auguste  De  la  Rive.  By  George 

Forbes,  Esq.,  . . . . 319 

Obituary  Notice  of  Dr  J.  Lindsay  Stewart.  By  Dr  Cleg- 

horn,  Stravithy,  . . . . . 321 

' Obituary  Notice  of  John  Hunter.  By  J.  T.  Bottomly, 

Esq.,  University,  Glasgow,  ....  322 

The  Kinetic  Theory  of  the  Dissipation  of  Energy.  By 

Sir  William  Thomson,  ....  325 

On  the  Stresses  due  to  Compound  Strains.  By  Professor  C. 

Niven.  Communicated  by  Professor  Tait,  . . 335 

Monday , 2 d March  1874. 

On  the  Parallel  Roads  of  Glen  Roy.  By  the  Rev.  Thomas 

Brown,  F.R.S.E.,  . . . . . 339 

Note  on  the  Perception  of  Musical  Sounds.  By  John  G. 

M‘Kendrick,  M.D.,  . . . . 342 

On  the  Establishment  of  the  Elementary  Principles  of 
Quaternions  on  an  Analytical  Basis.  By  G.  Plarr, 

Esq.  Communicated  by  Professor  Tait,  . . 348 

Preliminary  Note  “ On  a New  Method  of  obtaining  very 
perfect  Vactia.”  By  Professor  P.  G.  Tait  and  Mr 
J ames  Dewar,  ....  . 348 

Laboratory  Notes.  By  Professor  Tait— 

1.  On  Atmospheric  Electricity,  . . . 349 

2.  On  the  Thermo-Electric  Position  of  Sodium,  . 350 


Monday , 16 th  March  1874. 

On  the  Resistance  of  the  Air  to  the  Motion  of  Fans.  By 
James  C.  Fairweather,  Esq.  Communicated  by 
George  Forbes,  Esq.  (With  two  Plates), 


351 


IV 


PAGE 

On  the  Curve  of  Second  Sines  and  its  Variations.  By 

Edward  Sang,  Esq.,  . . . . 356 

Laboratory  Notes.  By  Professor  Tait — 

On  the  Thermo-electric  Positions  of  Sodium  and 

Potassium,  . . . . 362 

On  a New  Form  of  Mariner’s  Compass.  By  Sir  William 

Thomson,  ......  363 

Monday , 6 th  April  1874. 

Further  Note  on  Spectra  under  exceedingly  Small  Pressures. 

By  Professor  Tait  and  James  Dewar,  Esq.,  . . 363 

On  the  After-Glow  of  Cooling  Iron  at  a Dull-red  Heat. 

By  George  Forbes,  Esq  , 363 

On  a Form  of  Radiation  Diagram.  By  G-eorge  Forbes, 

Esq.,  . ...  . . . 366 

On  the  Semicircular  Canals  of  the  Internal  Ear.  By  Pro- 
fessor Crum  Brown,  . . . . 370 

Monday,  20 th  April  1874. 

On  Last-Place  Errors  in  Vlacq’s  Table  of  Logarithms.  By 

Edward  Sang,  Esq.,  .....  371 

Note  on  the  Submerged  Fossil  Trees  of  Granton  Quarry. 

By  Sir  Robert  Christison,  Bart.,  Hon.  V.P.,  R.S.E.,  . 377 

Note  on  Grouse  Disease.  By  Professor  Maclagan,  , 378 

Latent  Heat  of  Mercury  Vapour.  By  James  Dewar,  Esq.,  380 

Notes  by  James  Dewar,  Esq. — 

(1.)  Problems  of  Dissociation;  (2.)  Formation  of 

Allotropic  Sulphur ; (3.)  Heat  of  Fermentation,  . 380 

Further  Note  on  Continuants.  By  Thomas  Muir,  M.A., 
F.R.S.E.,  Assistant  to  the  Professor  of  Mathematics  in 


Glasgow  University,  .....  380 

Monday , 4 th  May  1874. 

On  the  Formation  of  Allotropic  Sulphur.  By  James  Dewar, 

Esq., .382 

On  Some  Compounds  of  Dimethyl-Thetine.  By  Professor 

Crum  Brown  and  Dr  E.  A.  Letts,  . . . 382 

On  a New  Example  of  the  Opheliidae  ( Linotrypane  apogon) 

from  Shetland.  By  W.  C.  MTntosh,  M.D.,  . .'4  386 

Concluding  Remarks  by  David  Milne  Home,  LL.D.,  . 390 


PROCEEDINGS 

OF  THE 

ROYAL  SOCIETY  OF  EDINBURGH. 

SESSION  IS 74-75. 


CONTENTS. 

Monday , 23c?  November  1874. 


Election  of  Office-Bearers,  . . , , ......  . 416 

Monday,  7th  December  1874. 

Presentation  of  the  Keith  Prize  to  Professor  Tait,  . . 415 

Opening  Address  on  the  Stability  of  Steady  Motion.  By 

the  President,  . . . . . 420 

Monday,  21  st  December  1874. 

Kemarks  on  the  Great  Logarithmic  and  Trigonometrical 
Tables  computed  in  the  Bureau  du  Cadastre  under  the 
direction  of  M.  Prony.  By  Edward  Sang,  . . 421 

On  the  Elimination  of  a,  /3,  y,  from  the  conditions  of  integ- 
ral) ility  of  S.  uaSp,  S.  u/3Sp,  S.  uySp.  By  M.  G-.  Plarr, 
Communicated  by  Professor  Tait,  . . . 436 

The  Development  of  the  Ova,  and  the  Structure  of  the 
Ovary,  in  Man  and  other  Mammals.  By  James  Foulis, 

M.D.  (Edin.)  Communicated  by  Prof.  Turner,  . 437 

Mathematical  Notes.  By  Professor  Tait — 

1.  On  a singular  Theorem  given  by  Abel,  . . 440 

2.  On  the  Equipotential  Surfaces  for  a Straight  Wire,  443 

3.  On  a Fundamental  Principle  in  Statics,  . . 443 


Monday,  4th  January  1875. 

Exhibition  and  Description  by  the  President  of  his  Tide 

Calculating  Machine,  also  his  Improved  Tide-Gauge-  ^ 

. 445 


lie  also  described  certain  Capillary  Phenomen 
Experiments,  ..... 


Monday,  18 th  January  187-5.  o UX 

Biographical  Notice  of  Lord  Colon  say.  By  the  Hon.  Lord'*  ' * 
Njsaves,  . . . . . . Vafions^45 

Biographical  Notice  of  Cosmo  Innes.  By  the  Hon: 

Neaves,  ...  . . . . 453 

Biographical  Notice  of  Francis  Deas.  By  the  Hon.  Lord 

Neaves,  . . . . . . 461 

Biographical  Notice  of  Adam  Black.  By  the  Kev.  Dr 

LiNDSAr  Alexander,  .....  467 

Biographical  Notice  of  Sheriff  Cleghorn.  By  David  MaO- 

lagan,  Esq.,  C.A.,  . . . . ' 468 

Biographical  Notice  of  Henry  Stephens.  By  Professor  Mac- 

lagan,  . . . . . . 469 


Turn  over. 


PAGE 


ii 

Biographical  Notice  of  Christopher  Hansteen.  By  Alex- 
ander Buchan,  Esq.,  . ,.  . . 473 

Biographical  Notice  of  Jacques- Adolphe-Lambert  Quetelet. 

By  Alexander  Buchan,  Esq.,  ....  474 

Biographical  Notice  of  G-eorge  Berry.  By  George  Barclay, 

Esq.,  . . . . . . 476  ' 

Monday , 1st  February  1875. 

On  the  Complete  Theory  of  the  Stone  Arch.  By  Edward 

Sang,  Esq.,  ......  479 

On  the  Application  of  Angstrom’s  Method  to  the  Conduc- 
tivity of  Wood.  By  C.  G.  Knott  and  A.  Macfarlane. 
Communicated  by  Professor  Tait,  . . . 481 

Notice  of  Striated  Rock  Surfaces  on  North  Berwick  Law. 

By  David  Stevenson,  V.P.B.S.E,  Civil  Engineer,  . 481 

Laboratory  Notes.  By  Professor  Tait — 

a.  Photographic  Records  of  the  Sparks  from  a Holtz 

Machine,  484 

b.  Determination  of  the  Surface-Tension  of  Liquids  by 

the  Ripples  produced  by  a Tuning-Fork,  . . 485 

c.  Capillary  Phenomena  at  the  Surface  of  Separation 

of  two  Liquids,  . . . . .485 

Monday , 1 5th  February  1875. 

Obituary  Notice  of  Dr  Robert  Edward  Grant,  late  Professor 
of  Comparative  Anatomy  in  University  College,  Lon- 
don. By  Dr  W.  Sharpey,  . . .486 

An  Illustration  of  the  relative  Rates  of  Diffusion  of  Salts  in 

Solution.  By  Professor  Crum  Brown,  . . 490 

On  the  Oscillation  of  a System  of  Bodies  with  rotating 

Portions.  By  Sir  William  Thomson,  . . . 490 

Laboratory  Notes.  By  Professor  Tait — 

a.  On  the  Application  of  Sir  W.  Thomson’s  Dead-Beat 

Arrangement  to  Chemical  Balances,  . . 490 

b.  Photographs  of  Electric  Sparks  taken  in  Cold  and 

in  Heated  Air,  .....  491 

c.  On  the  Electric  Resistance  of  Iron  at  High  Tem- 

peratures, . . ....  491 

Monday , ls£  March  1875. 

Biographical  Notice  of  William  Euing,  Esq.,  E.R.S.E.  By 

Professor  William  P.  Dickson,  . . .491 

On  a Faulty  Construction  common  in  Skewed  Arches.  By 

Edward  Sang,  Esq.,  .....  497 

On  the  mode  of  Growth  and  Increase  amongst  the  Corals  of 
the  Palaeozoic  Period.  By  H.  Alleyne  Nicholson, 

M.D.,  D.Sc.,  Professor  of  Biology  in  the  Durham  Uni- 
versity College  of  Physical  Science,  . . . 498 

Exhibition  of  Diagrams  in  illustration  of  the  Capillary 

Surfaces  of  Revolution.  By  the  President,  . . 500 

Monday  15th  March  1875. 

Presentation  of  the  Makdougall  Brisbane  Prize  to  Professor 

Lister,  .......  500 

On  the  Diurnal  Oscillations  of  the  Barometer.  By  Alex- 
ander Buchan,  M.A.,  .....  505 

For  continuation  of  Contents , see  pp.  3 and  4 of  Cover. 


FAGE 


The  Phenomena  of  Single  and  Double  Vision,  as  shown  in 

the  Stereoscope.  By  R.  S.  Wyld,  Esq.,  . . 505 

On  the  Products  of  the  Oxidation  of  Dimethyl-Thetine,  and 
its  Derivatives.  By  Prof.  Crum;  Brown  and  Dr  E.  A. 

Letts,  .......  508 

Monday , 5th  April  1875. 

Presentation  of  the  Neill  Prize  to  Charles  Wm.  Peach,  . 509 

On  the  Physiological  Action  of  Light.  Part  II.  By  James 

Dewar,  Esq.,  and  Dr  John  Gr.  M ‘Kendrick,  . . 513 

On  the  Structure  and  Systematic  Position  of  Tristichopterus 

alatus , Egerton.  By  R.  H.  Traquair,  M.D.,  E.G-.S.,  . 513 


Monday , l§th  April  1875. 

Note  of  Temperature  Measurements  in  the  G-reat  Geysir  of 

Iceland — August,  1874.  By  Robert  Walker,  Esq.,  . 514 

On  the  Capillary  Surface  of  Revolution.  By  Sir  William 

Thomson  and  Mr  John  Perry,  ....  520 

On  the  Oscillation  of  a System  of  Bodies  with  Rotating 
Portions.  Part  II.— -Vibrations  of  a Stretched  String 
of  Gyrostats  (Dynamics  of  Faraday’s  Magneto-Optic 
Discovery),  with  Experimental  Illustrations.  By  Sir 


William  Thomson,  .....  521 

On  the  Theory  of  the  Spinning-Top,  with  Experimental 

Illustrations.  By  Sir  William  Thomson,  . . 521 

Monday , 3 d May  1875. 

Laboratory  Note — Analysis  of  Titaniferous  Iron  Sand  from 
North  Berwick.  By  James  Davidson,  Esq.  Com- 
municated by  Professor  Crum  Brown,  . . 523 

On  some  Permian  Eishes,  hitherto  erroneously  referred  to 

the  Genus  Palceoniscus.  By  Dr  Traquair,  . . 525 

Note  on  the  action  of  Bile  Salts  on  the  Animal  Economy. 

By  J.  Graham  Brown,  Esq.  Communicated  by  Dr 
M ‘Kendrick,  . .....  525 

Preliminary  Note  on  the  Anatomy  of  the  Pia  Mater.  By 

Dr  J.  Batty  Tuke,  .....  534 

Note  on  the  Physiological  Action  of  Light.  By  James 

Dewar,  Esq.,  and  Dr  M‘Kendrick,  . # 534 

Monday , 17 th  May  1875. 

On  the  Expiatory  and  Substitutionary  Sacrifices  of  the 

Greeks.  By  Dr  Donaldson,  ....  53.5 

The  Placenta  in  Ruminants — a Deciduate  Placenta.  By 

Professor  Turner,  ....  . 537 

An  Essay  towards  the  General  Solution  of  Numerical 
Equations  of  all  Degrees.  By  W.  H.  Eox  Talbot, 

Esq.,  Hon.  E.R.S.E.,  .....  544 

Note  on  the  Electrical  Conductivity  of  Saline  Solutions. 

By  J.  G.  MacGregor,  M.A.,  B.Sc.  Communicated  by 
Professor  Tait,  . . . . . 545 

Monday , 7th  June  1875. 

On  High  Flood  Marks  on  the  Banks  of  the  River  Tweed 
and  some  of  its  tributaries,  and  on  Drift  Deposits  in 
Tweed  Valley.  By  David  Milne  Home,  LL.D.,  . 559 


pag: 

Observations  on  Mr  Sang’s  Remarks  relative  to  the  Great 
Logarithmic  Table  compiled  at  the  Bureau  du  Cadastre 
under  the  direction  of  M.  Prony.  By  M.  F.  Lefort.  r 
Communicated  by  Mr  Sang,  who  has  translated  the 
paper  from  the  French,  . . . . 563 

Observations  relatives  aux  remarques  publiees  par  M. 
Edward  Sang  dans  les  u Proceedings  of  the  Royal 
Society  of  Edinburgh,  Session  1874-1875,”  sut  les 
grandes  tables  logarithmiques  et  trigonometriques  cal- 
culees  au  Bureau  du  Cadastre  sous  la  direction  de  Prony; 
par  F.  Lefort,  Inspecteur  general  des  Ponts  et  Chaussees, 
membre  correspondant  de  l’Academie  des  Sciences  de 
Naples,  . . . . . . 564 

Observation  relative  to  Mr  Edward  Sang’s  u Remarks  on 
the  Great  Logarithmic  and  Trigonometrical  Tables 
calculated  in  the  Bureau  du  Cadastre  under  the  direction 
of  Prony,”  published  in  the  Proceedings  of  the  Royal 
Society  of  Edinburgh,  Session  1874-1875,  by  M.  F. 

Lefort,  Inspecteur  General  des  Ponts  et  Chaussees, 
Corresponding  Member  of  the  Academy  of  Sciences  of 


Naples,  ......  574 

Reply  to  M.  Lefort’s  Observations.  By  Edward  Sang,  . 581 

Monday , 2 ls£  June  1875. 

Note  on  Electric  Resistance  of  Solutions,  By  William 

Durham  and  P.  R.  Scott  Lang,  M.A.,.  . . 587 

On  the  Circumscribed,  Inscribed,  and  Escribed  Circles  of  a 
Spherical  Triangle.  By  C.  G.  Colson,  Esq.  Com- 
municated by  Professor  Tait,  . . . . 589 

On  some  Remarkable  Changes,  Additions,  and  Omissions  of 

Letters  in  Certain  Cognate  European  Words.  By  the 
Hon.  Lord  Neaves,  , . . . . 596  - 

De  Interpolation  des  fonctions  irrationnelles  en  general,  et 
des  fonctions  logarithmiques  en  particulier,  a l’aide  des 
tables  numeriques.  Par  F.  Lefort,  inspecteur  general 
des  Ponts  et  chaussees,  membre  correspondant  de 
FAcad^mie  des  Sciences  de  Naples,  . . . 602 


Monday , 5th  July  1875. 

The  Theory  of  the  Causes  by  which  Storms  Progress  in  an 
Easterly  Direction  over  the  British  Isles,  and  why  the 
Barometer  does  not  always  indicate  real  vertical  pres- 
sure. By  Robert  Tennent,  Esq.,  . . . 612 

On  Electric  Images.  By  Professor  Tait,  . . . 623 

Laboratory  Notes.  By  Professor  Tait — 

a.  On  the  Origin  of  Atmospheric  Electricity,  . .623 

h.  Experiments  on  the  Thermal  Conductivity  of  some 
Dielectrics.  By  Messrs  C.  M.  Smith  and  C.  G. 

Knott,  . . . . . . 623 

A Chapter  on  the  Tides.  By  the  Rev.  James  Pearson,  M.A., 

Vicar  of  Fleetwood.  Communicated  by  Professor  Tait,  627 
Farther  Researches  in  very  perfect  Yacua.  By  Professors 

Dewar  and  Tait,  .....  628 

On  the  Electric  Resistance  of  Iron  at  a High  Temperature. 

By  Messrs  C.  M.  Smith,  C.  G.  Knott,  and  A.  Mac- 
farlane.  (Plate),  , . ( . yTY  . . 629 

A*  " 'A