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Full text of "Report of the British Association for the Advancement of Science"

^.^' h. 



KEPORT 



OF THE 



FIFTY-SECOND MEETING 



OF THE 



BRITISH ASSOCIATION 



FOR THE 



ADVANCEMENT OF SCIENCE; 



HELD AT 



SOUTHAMPTON IN AUGUST 1882. 



LONDON : 
JOHN MUEKAY, ALBEMAKLE STREET. 

1883. 

Office of the Association : 22 Albemarle Street, Loxdox, W. 




LOSDOK ! rniXTED BY 

BPOTTISVVOOnE AND CO., XEW-STEEET SQOAEB 

yOiD PABLI.VMEXT STUKET 



CONTENTS. 



Pago 
Objects .and Rules of the Association xxi 

Places and Times of Meeting and Officers from commencement xxviii 

Presidents and Secretaries of the Sections of the Association from com- 
mencement XXXV 

Evening Lectures xlviii 

Lectures to the Operative Classes li 

Officers of Sectional Committees present at the Southampton Meeting lii 

Table showing the Attendance and Receipts- at. Annual Meetings liv 

Treasurer's Account hi 

Officers and Council, 1882-83 Ivii 

Report of the Council to the General Committee hiii 

Recommendations of the General Committee for Additional Reports and 
Researches in Science Ix 

Synopsis of Money Grants Ixvi 

Places of Meeting in 1883 and 1884 Ixvii 

General Statement of Sums which have been paid on account of Grants 
for Scientific Purposes Lwiii 

Arrangement of the General Meetings Ixx^iii 

Address by the President, 0. William Siemexs, Esq., D.C.L. (Oxon.), 
LL.D. (Glasc. & Dubl.), Ph.D., F.R.S., F.C.S., Memb. Inst. C.E 1 

EEPOETS ON THE STATE OF SCIENCE. 

Report of the Committee, consisting of Professor Sylvester, Professor 
Catley, and the Rev. Geoege Salmon, D.D., appointed in connection with 
the Calculation of Tables of Fundamental Invariants of Binary Quantics ... 37 

Report (provisional) of the Committee, consisting of Mr. Robert H. Scott 
(Secretary), Mr. J. Norman Lockter, Professor H. J. S. Smith, Professor 
G. G. Stokes, Professor Baleotjr Stewart, and Mr. G. J. Symons, ap- 
pointed for the purpose of co-operating with the Meteorological Society of 
the Mauritius in their proposed publication of Daily Synoptic Charts of" the 
Indian Ocean from the year 1861 ! 38 

Report of the Committee, consisting of Captain Abney (Secretary), Professor 
W. G. Adams, Professor G. C. Foster. Professor Lord Rayleigh, Mr. 

a M 



IV CONTENTS. 

Page 
Prebce, Professor Schuster, Professor Dewar, Professor Vernon 
Harcourt, and Professor Atrton, for the purpose of fixing a Standard of 
White Light 38 

Report on Recent Progress in Hydrodynamics. Part II. — Special Problems. 
By W. M. Hicks, M.A 1 39 

Report of the Committee, consisting of Professor G. Carey Foster, the late 
]Mr. C. HocEiN, Sir William Thomson, Professor Atrton, Mr. J. Perrt, 
Professor W. G. Adams, Professor Lord Ratleigh, Professor F. Jenkin, 
Dr. O. J. Lodge, Dr. John Hopkinson, Dr. A. Muirhead (Secretary), Mr. 
W. H. Preece, Mr. Herbert Taylor, Professor Everett, and Professor 
Schuster, appointed for the purpose of constructing and issuing practical 
Standards for use in Electrical Measurements 70 

Eifteenth Report of the Committee, consisting of Professor Everett, Pro- 
fessor Sir William Thomson, Mr. G. J. Stmons, Sir A. C. Ramsay, Pro- 
fessor A. Geikie, Mr. J. Glaisher, Mr. Pengellt, Professor Edward 
Hull, Dr. C. Le Neve Foster, Professor A. S. Herschel, Professor G. 
A. Lebour, Mr. A. B. Wynne, Mr. Galloway, Mr. Joseph Dickinson, 
Mr. G. F. Deacon, Mr. E. Wethered, and Mr. A. Strahan, appointed 
for the purpose of investigating the Rate of Increase of Underground Tem- 
perature downwards in various Localities of Dry Land and under Water. 
Drawn up by Professor Everett (Secretary) 72 

Summary of Results contained in the First Fifteen Reports of the Underground 
Temperature Committee. By Professor Everett (Secretary) 74 

Report of the Committee, consisting of Professor Schuster (Secretary), Sir 
William Thomson, Professor H. E. Roscoe, Professor A. S. Herschel, 
Captain W. de W. Abney, Mr. R. H. Scott, and Dr. J. H. Gladstone, 
appointed for tlie purpose of investigatiug the practicability of collecting and 
identifying Meteoric Dust, and of considering tlie question of undertaking 
regular observations in various localities 90 

Second Report of the Committee, consisting of Mr. G. H. Darwin, Professor 
Sir William Thomson, Professor Tait, Professor Grant, Dr. Siemens, 
Professor Purser, Professor G. Forbes, and Mr. Horace Darwin, ap- 
pointed for the Measurement of the Lunar Disturbance of Gravity. AVritten 
by Mr. G. H. Darwin 95 

Report of the Committee, consisting of Professor Dewar, Dr. William- 
son, Dr. Marshall AA^atts, Captain Abney, Mr. Stoney, Professor 
Hartley, Professor McLeod, Professor Carey Foster, Professor A. K. 
Huntington, Professor Emerson Reynolds, Professor Reinold, Professor 
Liveing, Lord Rayleigh, Dr. Schuster, and Professor W. Chandler 
Roberts (Secretary), appointed for the purpose of reporting upon the present 
state of our Knowledge of Spectrum Analysis 120 

Report of the Committee, consisting of Professors Odling, Huntington, and 
Hartley, appointed to investigate by means of Photography the Ultra-Violet 
Spark Spectra emitted by Metallic Elements, and their combinations under 
varying conditions. Drawn up by Professor W. N. Hartley (Secretary)... 143 

Report of the Committee, consisting of Professor Roscoe, Mr. Lockyer, 
Professor Dewar, Professor Liveing, Professor Schuster, Captain Abney, 
and Dr. W. Marshall Watts (Secretary), appointed to prepare a new 
series of Tables of Wave Lengths of the Spectra of the Elements 144 

Report of the Committee, consisting of Professor Balfour Stewart, Pro- 
fessor Rucker (Secretary), and Professor T. E. Thorpe, appointed for the 
purpose of reporting on the Methods employed in the Calibration of Mer- 
curial Thermometers 145 



CONTENTS. V 

Page 
Second Report of tbe Committee, consisting of Sir A. C. Eamsat, Mr. Thomas 
Gray, and Professor John Milne (Secretary), appointed for the purpose of 
investigating the Earthquake Phenomena of Japan. Drawn up by the 

Secretary -05 

Eighth Report of the Committee, consisting of Professor E. Hull, the Rev. 
H. W. Crossket, Captain Douglas Galton, Professors G. A. Lebour 
and J. Presxwich, and Messrs. James Glaisher, E. B. Marten, W. 
Moltneux, G. H. ISfoRTON, W. Pengelly, James Plant, James Parker, 
I. Roberts, C. Fox Strangavays, Thos. S. Stooke, G. J. Symons, AV. 
Topley, TYLBEX-AVRiGnT, E. Wethered, W. Whitaeer, and 0. E. De. 
Range (Secretary), appointed for the purpose of investigating the Circula- 
tion of the Underground Waters in the Permeable Formations of England, 
and the Quality and Quantity of the Water supplied to various Towns and 
Districts from these formations 213 

Report of the Committee, consisting of Dr. II. C. Sorby, Profes.sor W. 
Ramsay, and Professor W. J. Sollas. appointed for the purpose of investi- 
gating the Conditions under which ordinary Sedimentary Materials maybe 
converted into Metamorphic Rocks. Drawn up by Professor W. J. Sollas 
(Secretary) 23fi 

Report of the Committee, consisting of the late Professor A. Leith Abams, 
Professor W. Boyd Dawkins, Dr. John Evans, Mr. G. II. Kinahan, and 
Ml-. R. J. UssHER (Secretary), appointed for the purpose of carrying out 
Explorations in Caves of Carboniferous Limestone in the South of Ireland 240 

Report of the Committee, consisting of Sir A. C. Ramsay, Professor J. 
Prestwich, Professor T. McK. Hughes, and Mr. W. Topley, appointed to 
assist in the preparation of an International Geological Map of luirope. 
Drawn up by Mr. W. Topley (Secretary) 241 

Tenth Report of the Committee, consisting of Professor J. Prestwich, Professor 
T. McK. Hughes, Professor W. Boyd Dawkins, Professor T. G. Bonney, 
Dr. Crosskey, Dr. Deaxe, and Messrs. C. E. De Rance, D. Mackintosh, 
R. II. TiDBEMAN, J. E. Lee, James Plant, W. Pengelly, H. G. Foed- 
HAM, and W. Terrill, appointed for the purpose of recording the posi- 
tion, height above the sea, lithological characters, size, and origin of the 
Erratic Blocks of England, Wales, and Ireland, reporting other matters of 
interest connected with the same, and taking measures for their preserva- 
tion. Drawn up by Dr. Crosskey (Secretary) 24.j 

Third Report of the Committee, consisting of Dr. H. C. Sorby and 
Mr. G. R. Vine, appointed for the purpose of reporting on Fossil Polyzoa 
(Jurassic Species — British Area onlv). Drawn up by Mr. Vine (Sec- 
retary) ^. .' •• 240 

Preliminary Report of the Committee, consisting of Professor W. C. Wil- 
liamson" ami Mr. Wm. Cash (Secretary), on the Flora of the 'Halifax 
Hard Bed,' Lower Coal Measures 267 

Report of the Committee, consisting of Dr. Pye-Smith, Dr. M. Foster, and 
Dr. BuRDON Sanderson, appointed for the purpose of investigating the In- 
fluence of Bodily Exercise on the Elimination of Nitrogen (the experiments 
conducted by Mr. North) 269 

First Report of the Committee, consisting of Professor Flower, Dr. Beddoe, 
Mr. Beabrook, Mr. F. Galxon, Mr. J. Park Harrison (Secretary), Dr. 
Muirhead, General Pitt-Rivers, Mr. F. W. Eudler, and Mr. Charles 
Roberts, appointed for the purpose of obtaining Photographs of the 
Typical Races in the British Isles 270 

Preliminary Report of the Committee, consisting of Mr. R. Meldola, General 
Pitt-Rivers, and Mr. W. Cole, appointed to investigate the Ancient 
EarthAvork in Epping Forest, known as theLoughton Camp 274 



VI CONTENTS. 

Page 
Second Reiiort of tlie Committee, consisting of Mr. Sclatee, Mr. Howard 
Saundees, and Mr. Thiselton-Dyee (Secretary), appointed for tbe purpose 
of investigating the Natural History of Timor-laut 275 

Keport of tiie Committee, consisting of Mr. F. Galton, Dr. Beddoe, Mr. 
Brabeooe (Secretary), Major-General Pjit-Rivehs, Mr. J. Paek Hae- 
jii.sox, Mr. J. Heyavood, Mr. Feank P. Fellows, Professor Leone Levi, 
Dr. F. II. Mahomed, Sir PiAwson Rawson, and Mr. C. Robeets, appointed 
for tlie_ purpose of carrying out the recommendations of the Anthropometric 
Committee of 1880, especially, as regards the anthropometry of children and 
of females, and the more complete discussion of the collected facts 278 

Report of the Committee, consisting of Lieut.-Col. Godwin-Axisten, Dr. G. 
Haetlaub, Sir J. Hookee, Dr. GtiNiHEE, Mr. Seebohm, and Mr. Sclatee 
(Secretary), appointed for the purpose of investigating the Natural History 
of Socotraand the adjacent Highlands of Arabia and Somali Land 281 

Report of the Committee, consisting of Dr. M. Fostee, Dr. Pye-Sjiith, Pro- 
fessor Htjxley, Dr. Caepentee, Dr. Gwyn Jeffeeys, the late Professor 
F. M. Balfoue, the late Sir C. Wyvilie Thomson, Professor Ray Lankes- 
TEE, Professor Allman, and Mr. Peecy Sladen (Secretary), appointed for 
the purpose of aiding in the maintenance of the Scottisli Zoological Sta- 
tion 282 

Report of the Committee, consisting of Mr. John Coedeaux, Mr. J. A. 
Haevie-Beown, Professor Newxon, Mr. R. M. Baeeington, Mr. A. G. 
More, Mr. T. Haedy, and Mr. P. M. C. Keemode, appointed for the 
purpose of obtaining (with the consent of the Master and Brethren of 
the Trinity House, and of the Commissioners of Nortliern Lights) observa- 
tions on the Migration of Birds at Lightliouses and Lightships, and of re- 
porting on the same 283 

Report of the Committee, consisting of tlie late Professor F. M. Balfottk, 
Professor Newton, Professor Huxley, Mr. Sclatee, Professor Ray Lan- 
KESTEE, Professor Allman, Dr. M. Foster, and Mr. Peecy Sladen (Sec- 
retary), appointed for the purpose of arranging for the occupation of a Table 
at the Zoological Station at Naples 288 

Report of the Committee, consisting of James Glaishee (Secretary), the Rev. 
Canon Tristram, and tlie Rev. F. Lawrence, appointed for the purpose of 
promoting the Survey of Eastern Palestine 296 

Report of the Committee, consisting of Professor Leone Levi, Mr. Stephen 
BouENE, Dr. Hancock, tlie late Sir Antonio Beady, the late Professor 
Jevons, Mr. ¥. P. Fellows, Mr. E. J. \\'atherston, Mr. Peaeson Hill, 
Mr. Geoege Baden Powell, and Mr. Jeremiah Head, appointed for the 
purpose of continuing the inquiry into and completing the report upon the 
Appropriation of Wages and other sources of income, and considering how 
far it is consonant with the economic progress of the United Kingdom. 
Drawn up by Professor Leone Levi 297 

Report of the Committee, consisting of Mr. James IIeywood, Mr. William 
Shaen, Mr. Stephen Bouene, Mr. Robert Wilkinson, the Rev. W. 
Delany, Professor N. Stoey M\skelyne, Dr. Silvanhs P. Thompson, JNliss 
Lydia E. Becker, Sir John Lebbock, Professor A. W. Williamson, Mrs. 
Aegusxa Webster, Dr. H. W. Ceosskey, Professor Roscoe, Professor G. 
Carey Foster, and Dr. J. H. Gladstone (Secretary), appointed to watch 
and report on tlie woL'kings of the proposed revised New Code, and of other 
legislation affecting the teaching of Science in Elementary Schools 307 

Report of the Committee, consisting of SirFEEDEEiCK Beamwell (Secretary), 
Professor A. W. Williamson, Professor Sir William Thomson, Mr. St. 
John Vincent Day, Dr. C. W. Siemens, Mr. C. W. ]\1eeeifield, Dr. 
Neilson Hancock, Mr. F. A. Abel, Captain Douglas- Galton, Mr. E. H. 



CONTENTS. Vll 

Page 
CAKJiUXT, Mr. ]>:. Macroey, Mr. II. Teueman AVood, Mr. W. II. Baeloav, 
and Mr. A. T. Atchison, appointed for the purpos-e of watching' and re- 
porting to the Council on Patent Legislation 310 

Keport of the Committee, consisting of Sir Joseph VVhttwoeth, Dr. (!. W. 
[SiEJiExs, Sir Feedeeiok Beamavell, Mr. A. SxEon, Mr. Beck, Mr. W. H. 
Teeece, Mr. E. Ceompton, Mr. E. Eigg, Mr. A. Le Neve Fosxee, Mr. 
Latimee Clark, Mr. Buckney, and Mr. II. Trueman Wood (Secretary), 
appointed for the purpose of determining a Gauge for the manufacture of 
the various small screws used in Telegraphic and Electrical Apparatus, in 
Clockwork, and for other analogous purposes 311 

Keport of the Committee, consisting of 3Ir. James Glaisher, Mr. C. W. 
Meerifield, Sir Feedekick Beamwell, Professor (). IIeynolds, Professor 
W. Cawthoene Unwin, Mr. Eogees I'ield, Mr. T. IIawksley, and Mr. A. 
T. Atchison (Secretary), appointed to consider and report upon the best 
means of ascertaining the effective Wind Pressures to which buildings and 
structures are exposed 315 

(Jn the Boiling Points and Vapour Tension of Mercury, of Sulphur, and of 
some Compounds of Carbon, determined by means of the Hydrogen Ther- 
mometer. By Professor J. M. Ceafts 317 

On the Method of Harmonic Analysis used in deducing the Numerical Values 
of the Tides of long period, and on a Misprint in the Tidal Report for 1872. 
By G. H. Daeavin, M.A., F.R.S 319 

List of Works on the Geology and Palaeontology of Oxfordshire, of Berkshire, 
and of Bucldnghamshire. By William Whitakee, B.A., F.G.S 327 

Notes on the oldest Records of the Sea Route to China from Western Asia. 
By Colonel H. Yule, C.B., R.E 347 

The Deserts of Africa and Asia. By P. de Tchihatchef, Member of the 
Academies of Sciences of Paris, Berlin, Munich, St. Petersburg, &c 356 

State of Crime in England, Scotland, and Ireland in 1880. By Professor 
Leone Levi, F.S.A 375 

On the Treatment of Steel for the Construction of Ordnance, and other pur- 
poses. By Sir AViLLiAM Aemsteong, C.B., F.R.S 398 

The (ihannel Tunnel. By J. Clarke Hawkshaw, M.A., F.G.S., M.I.C.E. .., 404 

The Forth Bridge. By B. Baker 419 



TEANSACTIONS OF THE SECTIONS. 



Section A.— MATHEMATICAL AND PHYSICAL SCIENCE. 

THURSDAY, AUGUST 24. 

Page 
Address by the Eight Hon. Professor Lord Eatleigh, M. A., F.E.S., F.E.A.S., 

F.E.G.S., President of the Section 437 

1. Second Eeport of the Committee for the Measurement of the Lmiar Dis- 
turbance of Gra\-ity 441 

'2. Eeport of the Committee upon the present state of our Knowledge of 
Spectrum Analysis 441 

3. On the Tension of Mercury Vapours at Common Temperatures. By 

Professor Lord Eatleigh, F.E.S ,. 441 

4. On the Velocity of White and Coloured Light. By Professor G. Fokbes, 

M.A., F.R.S.E 441 

5. Preliminary Account of Eesults obtained duiiug tlie late total Solar Eclipse 

(May 17, 1882). By Dr. Aethur Schuster, F.E.S. , and Captain Abney, 
F.R.S :. 441 

G. On some Matters relating to the Sun. By Dr. Arthur Schuster, 
F.E.S 442 

7. On the Method of Harmonic Analysis used in deducing the Numerical 

Values of the Tides of long period, and on a Misprint in the Tidal Eeport 
for 1872. By G. H. Darwin, F.E.S , 442 

8. On the Photographic Spectrum of Comet ("S^'ells) 1, 1882. By William 

HuGGiNS, D.C.L., LL.D., F.E.S 442 

'J. On the Photographic Spectrum of the Great Nebida in Orion. By 
William Huggins, D.O.L., LL.D., F.E.S. . .'. 443 



FRIDAY, AUGUST 25. 

1. On the Absolute Measurement of Electric Currents. By Professor Lord 
Eatleigh, F.E.S 445 

2. On the Duration of Free Electric Currents in an Infinite Conductin? 
Cylinder. By Professor Lord Eatleigh, F.E.S .". 44G 



ij. Un tlie Equilibrium of Liquid-conducting Surfaces charged with Electricity. 
By Professor Lord Eatleigh, F.E.S. ! 



447 



CONTENTS. IX 

Page 

4. On a new Hand Dynamo-Machine. By W. II. Preece, F.R.S 447 

5. On Secondary Batteries, with special reference to Local Action. Bv J. II. 

Gladstone, Ph.D., F.R.S .". 447 

6. Demands of a System of Electrical Distribution. By F. J. Sprague, U.S. 
Navy 448 

7. On the Comparison of the Mercury with the Hydrogen Thermometer. 

By Professor J. M. Grafts 449 



SATURDAY, AUGUST 26. 

1. Report on Recent Progress in Hydrodynamics. Part II. — Special Pro- 

blems. By W. M. Hicks, M.A 450 

2. On the Rotation of a Homogeneous Liquid Ellipsoid. By A. G. Greex- 
HiLi, M.A 450 

3. On a Proof of Wilson's Theorem. By Professor Oaylet, F.R.S 450 

4. Integration of an Equation connected with the Elliptic Fimctions. By 

Captain P. A. MacMahon, R.A 450 

5. On the Establishment of the Elementary Principles of Quaternions on an 
Analytical Basis. By Gustate Plaer, D.Sc 451 

G. On Linear Syzygetic Relations between the CoeiScients of Ternary Quad- 
rics. By Professor R. W. Genese, M.A 452 

7. On the Rectifiable Spherical Epicycloid, or Involute of a Small Circle. 

By Hexry M. Jeffert, F.R.S 453 

8. On a Partial Diiferential Equation. By J. W. L. Glaisher, M.A., 
F.R.S 454 

9. On a Theorem in Elliptic Functions. By J. W. L. Glaisher, M.A., 
F.R.S 456 



MOiYBAY, AUGUST 28. 

1. Fifteenth Report of the Committee on Underground Temperature, con- 
taining a Sj'nopsis of all previous Reports of this Committee 453 

2. On the Origin of Hail. By Professor Theodore Schwedofp 453 

3. Notes on Schwedoft's Theory of Hail. By Professor Silvanus P. 
Thompson 458 

4. Second Report of the Committee on Meteoric Dust 459 

5. Sun Light and Sky Light at High Altitudes. By Captain W. de W. 
Abney, F.R.S : 459 

6. On the Distribution of Energy in the Solar Spectrum. .By Professor 

S. P. Langley 459 

7. On a Similarity between Magnetical and Meteorological Weather. By 
Professor Balfour Stewart, M.A., LL.D., F.R.S 4C0 

8. On a supposed Connection between the Heights of Rivers and the Number 
of Sun-spots on the Sun. By Professor Balfour Stewart, M.A., 
LL.D.,F.R.S 462 



K CONTENTS. 

TUESDAY, AUGUST 29. 

Page 

1. Heport of the Committee for constructing and issuing practical Standards 

for use in Electrical Measurements 404 

2. Suggestions regarding the Extension of the Practical System of Units. 
ByDr. C. W. Siemexs, F.R.S 4G4 

3. On a new Form of Galvanometer for Measui-ing Currents and Potentials 

in Absolute Units. By Professor Sir William Thomson, F.E.S 4G4 

4. On Electric Meters. By C. Vernon Bots 464 

5. On a new Electrical Contact Maker. By Professor H. S. Hele Shaw ... 4G5 

6. On a Machine for ruling large Diffraction Gratings. By A. Mallock ... 4GG 

7. A Numerical Estimate of the Rigidity of the Earth. By G. II. Daewin, 

F.RS : 472 

8. On the Transmission of Force through an Elastic Solid. By Professor 

Sir William Thomson, F.R.S 474 

0. On a Method of investigating Magnetic Susceptibility. By Professor 

Sir William Thomson, F.E.S '. 474 

WEBNESDAT, AUGUST dO. 

1. On a Method of investigating experimentally the Absorption of Radiant 
Heat by Gases. By Professor Tait, Sec. R.S.E. (From a letter to Sir 

W. Thomson) 475 

2. On Atmospheric Electricity. By Professor 0. Michie Smith, B.Sc, 
F.R.S.E. : '. : ! 47C 

3. On tlie Alteration in the Dimensions of the Magnetic Metals by tlie act 

of Magnetisation. By Professor W. F. Baereti, F.R.S.E 47G 

4. On an Instrument for measuring the Intensity of Aerial Vibration. By 
Professor Lord Ratleigh, F.R.S 477 

•5. On the Effect of Wind on the Draught of Chimneys. By Professor 
Lord Ratleigh, F.R.S '. 477 

6. On a Mechanical Self-registering Thermometer. By A. Mallock 477 

7. On a Musical Instrument. By J. Philips 478 

8. On an Arithmetical Model. By Sir F. J. Beam^vell, F.R.S 478 



Section B.— CHEMICAL SCIENCE. 

THURSBA Y, A UG UST 24. 

Address by Professor G. D. Livelng, M.A., F.R.S., F.C.S., President of the 

Section , 479 

1. On the Legal Flashing Test for Petroleum. By F. A. Abel, C.B.. F.R.S., 
i-.O.S 486 

2. The Influence of Aqueous Vapour on the Explosion of Carbonic Oxide 

and Oxygen. By H. B. Dixon, M.A 486 

3. The Velocity ot Explosion of a Mixture of Carbonic Oxide and Oxygen 
with varying quantities of Aqueous Vapour. By H. B. Dixon, M.A. ... 487 



CONTENTS. XI 

Page 

4. On the Boiling Points and Vapour Tension of Mercury, of Sulphur, and 

of some Compounds of Carbon, determined by means of the Hydi-ogeu 
Thermometer. By Professor J. M. Crafts 487 

5. On the Occurrence of Tellurium and Selenium in Japan. By Professor 
Edward Diveks, JNI.D., and Masachika Shimose 487 

FRIDA Y, A UG UST 25. 

1. Report of the Committee appointed to investigate by means of Photo- 

graphy the Ultra-Violet Spark Spectra emitted by jMetallic Elements, 
and their combinations under varying conditions 489 

■2. Report of the Committee appointed to prepare a new series of Tables of 
Wave-Lengths of the Spectra of the Elements 489 

3. On the Application of the Diamond to Mineralogical and Chemical Ana- 
lysis. By Professor YOif Batjmhatjer 489 

4. On the Action of the Component Salts as Nuclei on Supersaturated Solu- 

tions of certain Compound Salts. By John M. Thomson, E.C.S 490 

5. On the Decomposition by Heat of Chlorate of Potassium. By Albert 
RiLLiET and Professor J. M. Crafts 493 

6. Hydrocarbons of the Formula (C JIs"),,. By Professor W. A. Tilden, 
F.R.S 494 

7. On the Activity of Oxygen, and the Mode of Formation of Hydrogen 
Dioxide. By C. T. Kingzett, F.I.C., F.C.S 494 

8. Metallic Compounds containing Bivalent Hydrocarbon Radicals. Part 

HI. By Professor Saktjrai, F.C.S 495 

3I0NDAY, AUGUST 22,. 
• 1. Report of the Committee on the Calibration of Mercmdal Thermometers 495 

2. Third Report of the Committee upon the present state of our Knowledge 

of Spectrum Analysis 49o 

3. On the Reversals of the Spectral Lines of Metals. By Professor Liveing, 
F.R.S., and Professor Dewae, F.R.S 495 

4. On the Electric Furnace. By Dr. C. AV. Siemens, F.R.S., and Professor 

A. K. Huntington 496 

5. The Aerorthometer, an Instrument for correcting the Measure of a Gas. 

By A. Vernon Haecourt, M.A., F.R.S 499 

6. A Revision of the Atomic Weight of Rubidium. By Charxes T. Hex- 

cock, B.A 499 

7. On a Method of oliitaining Ammonia from Shoddy and Allied Substances. 

By W. Marriott, F.C.S WO 

Section C— GEOLOGY. 
THURSDAY, AUGUST 21. 

Address by Robert Etheridge, F.R.S.L. and E., F.G.S., President of the 

Section 50- 

1. Notes relating to some of the Drift Phenomena of Hampshire: 1. 
Boulders, Havling Island ; 2. Chert Debris in the Hampshire Gravel ; 
Elephant BedJ Freshwater Gate. By Professor Peestwich, M. A., F.R.S., 
F.G.S 529 



XU C0NTEM8. 

Page 

2. Notes oil the Bure Valley Beds and the Westleton Beds. By Horace B. 

Woodward, F.G.S 530 

3. On the Sources of the Salt Supply of India. By Professor V. Ball, M.A., 
F.R.S.,r.G.S .' '. ; 530 

4. Preliminary Report on the Flora of the ' Halifax Hard Bed,' Lower Coal 
Measures 531 

5. On the Iron and Lead Measures of Tynehead, Alston, By C. E. De 
Range, F.G.S., Assoc. Inst.O.E 531 

6. On the Geology of Cardigan Town. By Walter Keeping, M.A., F.G.S. 531 

FRIDAY, AUGUST 25. 

1. On the Post-Miocene Deposits of the Bovey Basin, South Devon. By W. 

Pengellt, F.R.S., F.G.S 502 

2. On the Origin of the Haematite Deposits in the Carboniferous Limestone. 

By Edward Wethered, F.G.S., F.C.S 533 

3. Report on the Earthquake Phenomena of Japan 534 

4. Report on the Conditions under which ordinary Sedimentary Materials 
may be converted into Metamorphic Rocks 534 

5. On some Fossils of the Inferior Oolite. By the Rev. G. F. Whidborne, 
M.A., and Professor W. J. Sollas, M.A., F.G.S 534 

G. Eighth Report on the Circulation of the Underground Waters in tlie 
Permeable Formations of England, and the Quality and Quantity of the 
Water supplied to various Towns and Districts from these Formations ... 535 

7. Evidence of Wave-Action at a depth of 40 fathoms in the English 
Channel, By Arthur R. Hunt, M.A., F.G.S 535 

8. List of Works on the Geology and Palaeontology of Oxfordshire, Berk- 
shire, and Buckinghamshire. By W. Whitakbr, B.A., F.G.S 535 

MONDAY, AUGUST 28. 

1. Mention of an example of an Early Stage of Metamorphic Change in 
Old Red Sandstone Conglomerate, near Aberfoil. By Professor James 
Thomson, LL.D., F.R.S 53G 

2. On Features in Glacial ^Markings noticed on Sandstone Conglomerates at 

Skelmorlie and Aberfoil. By Professor James Thomson, LL.D., F.R.S. 537 

3. On the Equivalents in England of the ' Sables de Bracheux,' and on the 
southern limits of the Thauet Sands. By Professor Peestwich, F.R.S., 
F.G.S 538 

4. Suggestions for a Revised Classification of British Eocenes. By J. S, 

Gardner, F.G.S 539 

5. On the Classification of Oligocene Strata in the Hampshire Basin. By 

J. W. Elwes 5.39 

G. On the Outcrop of the Brockenhurst Bed, near Lyndhurst. By E. B. 
Tawney, M.A., F.G.S 540 

7. On Subsidence as the Effect of Accumulation. By Charles Rickeits, 
M.D., F.G.S 540 

8. On the Cause of Elevation and Subsidence of Land. By J. S. Gardner, 
F.G.S 541 



CONTENTS. xiii 



TUESDAY, AUGUST 29. 

Page 

1. On tlie Geology of the Channel Tunnel. By Professor W. Boyd Dawkixs, 
M.A., F.R.S 542 

2. On the proposed Channel Tunnels in their Geological Aspects. By C. E. 

De Range, F.G.S., Assoc. Inst. C.E 544 

3. On the Synclinal Structure of the Straits of Dover. By W. Topiey, 

F.G.S., Assoc. Inst. C.E 54G 

4. Report on the Exploration of Caves of Carboniferous Limestone in the 
South of Ireland 546 

5. On the Southampton Artesian Well. By T. W. Shore, F.C.S., and 

E. Westlake, F.G.S 547 

6. Tenth Report on the Erratic Blocks of England, Wales, and Ireland 549 

7. Third Report on the British Fossil Polyzoa 549 

8. On the Formation of Flints. Bv Professor W. J. Sollas, M.A., F.R.S.E 
F.G.S : 549 

WEDNESDA T, A UG UST 30. 

1. Problems in the Geology of the Channel Islands. By the Rev. Edwin 
Hill, M.A., F.G.S '. 550 

2. Notes on Alpine Post-Carboniferous (Dyassic) and Triassic Geoloo-y By 

the Rev. A. Irving, B.Sc, B.A., F.G.S ;;. ;. 551 

u. Summary of Reports of the Committee on Underground Temperature. By 
Professor J. D. Everett, F.R.S 552 

4. Notes on the Geology and Mining of the United States of Colombia, S.A. 

By Robert B. White 552 

5. Report on the progress of the International Geological Map of Europe... 55-3 



Section D.— BIOLOGY. 

Department of Anatomy and Physiology. 

THURSDA T, A UG UST 24. 
Address by Professor Gamgee, M.D., F.R.S., President of the Section 554 

FRIDAY, AUGUST 25. 

1. Report on the Influence of Bodily Exercise on the Elimination of Nitroo-en 574 

2. On the Early Development of certain Rodents. By Dr. Alex. Eraser... 574 

3. On the Homologies of the Long Flexor Muscles of the Feet of Mammalia 

By G. E. DoBSON. M.A., M.B 574 



4. On the Nature of the 'Telson' and 'Caudal Furca' of the Q-ustacea. 
By Dr. M. M. IIartog 57 



XIV CONTENTS. 



MONDAY, AUGUST 28. 

Page 

1. On tlie Perception of Colour in Man and tlie Lower Animals. By J. D. 
Macdonalb, M.D., F.RS 575 

2. An improved Method of directly determining the Velocity of the Con- 
traction-Wave in Curarised Muscle. By Professor E. A. SciaAFER, F.R.S. 575 

3. Note on the Structure of the Muscular Tissue of the Leech. By T. W. 
Shoee, Jun., B.Sc 577 

4. On the Kidneys of Teleostei. By W. Newton Parker 577 

5. On the presence of a ' Tympanum ' in the genus Eaia. By George Bond 
Howes 577 

6. On some Toxic Conditions of the Blood, illustrated hy the action of 
Hydrocyanic Acid. By Thomas S. Ralph, M.R.G.S 577 

7. On some new Methods of investio-ating the Physiology of the Mamma- 
lian Heart. By Professor H. N. Martin 578 



TUESDAY, AUGUST 29. 

1. Considerations arising from Koch's Discovery of the Bacillus of Tuber- 
culosis. By F. J. Faraday, F.L.S 578 

2. Remarks on Filaria Sanguinis Hominis. By Dr. Cob'bold, F.R.S 579 

3. On the Destiny of the Filaria in the Blood. By Dr. P. Hanson 579 

4. Note on the Early Development of Lacerta Muralis. By W. R. Weldon, 

B.A 570 



Department of Zoology and Botany. 



FRIDAY, AUGUST 25. 

Address by Professor M. A. Lawson, M.A., F.L.S., Chairman of the Depart- 
ment 580 

1. Second Report of the Committee for the Investigation of the Natural 
History of Timor-laut 589 

2. Report of the Committee for the Livestigation of the Natural History of 

Socotra and the adjacent Highlands of Arabia and Somali Land 589 

3. Report on the Record of Zoological Literature 589 

4. On the Brown Coloration of the Southampton Water. By A. Angell, 
Ph.D., F.O.S 589 

5. On the Distribution and Dates of Spring Migrants in Yorkshire, compared 
with West of England and Ireland. By T. Lister 589 

MONDAY, AUGUST 2^. 

1. Report of the Committee for arranging for the occupation of a Table at the 
Zoological Station at Naples 591 

2. Report of the Committee for aiding in the maintenance of the Scottish 

Zoological Station 691 

3. Report on the Migration of Birds 591 



CONTENTS. XV 

Page 
4. The injurious Parasites of Egypt in relation to Water-Drinking. By Dr. 
CoBBOLD, F.R.S ". 592 

6. On a new Principle affecting the systematic Distribution of the To)-- 
2)ediniclce, and on the probahle occurrence of the T. occidentalis (Storer) 
on the British Coast. By E. dtt Bois-Eeymond, F.R.S., Professor of 
Physiology in the University of Berlin 592 

6. Preliminary Note on Cep/ial6discus, a new form allied to Prof. Allman's 
Rhahdopleura — dredged in H.M.S. 'Challenger.' By Professor McIntosh, 
F.R.S 596 

7. On an Instructional System of Arrangement in Provincial Museums. Bv 

F. T. MoTT, F.R.G.S ;. 597 



Department op Anthropology. 

THURSDAY, AUGUST 24. 

Address by Professor W. BotdDawkins, M.A., F.E.S., F.S.A.,F.G.S., Chair- 
man of the Department 507 

FRIDA Y, A UG UST 25. 

1. Report of the Committee for obtaining Photographs of the Typical Races 

in the British Isles 604 

2. Report of the Committee on the Investigation of Longhton Camp 604 

3. Report of the Anthropometric Committee 604 

4. The Names Britannia and Hibernia, with their Iberian relations. By 
Hyde Clarke, V.P.A.I 604 

5. Evidence as to the Scene of Man's Evolution and the Prospects of proving 
the same by Palseontological Discovery. By W. Stewart Duncan', 
M.A.I 605 

6. On the Length of the Second Toe of the Human Foot. By J. Park 

Harrison, M.A 606 

7. Ebb and Flow in Mental Endowment. By George Harris, LL.D., 
F.S.A 606 

MONDAY, AUGUST 28. 

1. On some Customs of the Aborigines of the River Darling, New South 

AVales. By F. Bonney 607 

2. Prehistoric Remains in the Deposits of the Bovey Basin, South Devon. 

By AV. Pengelly, F.R.S 607 

i3. The Light thrown by the Exploration of Caves on the Conquest of Britain. 
By Professor W. Boyd Dawkins, M.A., F.R.S 607 

4. The Jutes of the Isle of Wight. By J. Park Harrison, M.A 607 

5. On the Physical Characteristics of the Saxon. By J. Park Harrison, 
M.A 607 

6. The Lolo Character of Western Cliina. By Hyde Clarke, V.P.A.I. ... 607 

7. On the Formula of Alfred R. Wallace in its relations to Characters and 

Alphabets. By Hyde Clarke, V.P.A.I 60S 



xvi CONTENTS. 

Page 

8. The City of the Tarquins. By Miss A. W. Buckland 609 

9. The Influence of the Intellectual Faculties in relation to the Direction and 
Operation of the Material Organs. By George Harris, LL.D., F.S.A. 609 

Section E.— GEOGRAPHY. 
THURSDAY, AUGUST 2i. 

1 The Arctic Campaign of 1882. — Its Origin, Constitution, and Otjects. By 
Lieutenant G. T. Temple, E.N., F.R.G.S 611 

2. Notes on a visit to the Chukchi Peninsula in 1881, based on letters from 

Drs. Arthur and Aurel Krause. Communicated by the Bremen Geo- 
graphical Society 612 

3. The question of an Overland Route to China from India via Assam, with 

some remarks on the Source of the Irrawaddi River. By Charles II. 
Lepper, F.R.G.S., M.R.A.S 612 

4 Notes on the oldest Records of the Sea Route to China from Western Asia. 
By Colonel H. Yule, C.B., R.E 61 



q 



FRIDAY, AUGUST 2^. 

Address by the President, Sir Richard Temple, Bart., D.C.L., G.C.S.I., 

F.R.G.S 613 

1. Some points of Physical Geographv observed during a recent tour round 
South America. By JoHX Ball, M.A., F.R.S 622 

2 On the Geographical Evolution of the Tanganvika Basin. Bv Joseph 
Thomsok, F.R:G.S ". .■ 622 

3. On the Royal Geographical Society's Map of Eastern Equatorial Africa. 

By E. G. Ravenstein, F.R.G.S 623 

4. On Senegal, Gambia, and the Gold Coast. By Commander V. L. 

Cameron, R.N., C.B 623 

3I0KDAY. AUGUST 28. 

1. The Deserts of Africa and Asia. By P. de Tchihatchef 624 

2. OnMerv. By E. O'Doxoyax 624 

3 On the Identification of certain Ancient Diamond Mines in India. By 
Professor Y. Ball, M.A., F.R.S., F.G.S 625 

4 The Geography and Meteorologv of Kansas. By Litton Forbes, M.D., 
F.R.G.S .' 625 

5. The Spanish Territories of North America. By E. von Hesse Wartegg 627 

6. The Dominion of Canada, especiallv with regard to the Geography of the 
North- West Territory. By Cyril Graham, C.M.G., F.R.G.S. .." 628 

TUESDAY, AUGUST 29. 

1. Report of the Committee appointed for the purpose of promoting the Sur- 
vey of Eastern Palestine 628 

2. Vn some unexplored or little known parts of Persia. By Colonel Sir 
Oliver St. John, R.E., K.C.S.I 628 

3. On the various means of communication between Central Persia and the 

Sea. By Lieut.-Colonel J. W. Bateman Champain, R.E., F.R.G.S 628 

4. On Tongkin and the new Approach to Yunnan. By D. Boxtlger 629 



CONTENTS. XVll 

Section F.— ECONOMIC SCIENCE AND STATISTICS. 

THUllSDA Y, A UG UST 2 1. 

Page 

1. Report of tlie Autliropometric Committee 630 

2. State of Crime in England, Scotland, and Ireland in 1880. Bv Professor 
Leone Levi, F.S.A .". 630 

3. Report on the workings of the proposed revised New Code, and of other - 
legislation affecting the teaching of Science in Elementary Schools 630 

4. Statistical Account of Railway Accidents for the year 1881. By the 
Rev. Daniel Ace, D.D., F.R.A.S 630 

5. Agricultural Statistics, Tenure, and Aspects. By William Botlt, 
M.R.A.S.E 631 

FRIDA Y, A UG UST 23. 

Address Ijy the Right Hon. G. Sclater-Booth, M.P., F.R.S., President of 

the Section 631 

1. On the Revenue from the Taxation of Alcohol. By George Baden 
Powell, M.A.> F.R.A.S., F.S.S 636 

2. On the Taxation of Alcohol. By Stephen Bourne, F.S.S 637 

3. The Influences of the Beer Duty. By H. Sxopes, F.G.S 638 

4. The North Sea Fisheries. By 0. T. Olsen, F.R.A.S., F.R.G.S 640 

SATURDAY, AUGUST 26. 

1. On some Influences affecting the Progress of our Shipping and Carrying 
Trade. By Hyde Clarke, F.S.S 640 

2. Our Sailors — for Defence and Commerce. At Home and Abroad. By 

C. Pfotjnbes, F.R.G.S 641 

MOXDAY, AUGUST 28. 

1. Report of the Committee for continuing the inquiry into and completing 
the report upon the present Appropriation of Wages and other sources 
of Income, and considering how far it is consonant with the Economic 
Progress of the United Kingdom 642 

2. The Abstract Theory of Rent. By F. Y. Edgeworth 642 

3. The Ricardo Theory of Rent. By Alfred Milnes, M.A., F.S.S 642 

4. On Artisan Education. By Professor Silvantts P. Thompson, B.A., D.Sc. 643 

TUESDAY, AUGUST 29. 

1. Railways — a Plea for Unity of Administration. By Edward J. 

Watherston 643 

2. Cottagers and Open Wastes in the District of the New Forest. By 

G. E. Briscoe Eyre (a Verderer) 645 

3. On Decimal Coinage and Measures in America. By R. de Tracy 
Gould 653 

4. On a proposed International Congress to diminish the Casualties at Sea. 

By Don Arturo de Marcoartu 653 

1882. a 



XViii CONTENTS. 

Section G.— MECHANICAL SCIENCE. 

THURSDA Y, A UG UST 24. 

Page 

Address by John Fowler, O.E., E.G.S., President of the Section 655 

1. On the Forth Bridge. By B, Bakeb 663 

2. On the Treatment of Steel for the Construction of Ordnance and other 
purposes. By Sir William A.hmstrong, C.B., F.R.S G6S 

3. On the increased Tenacity in perforated Test Bars of Steel and Iron. By 

T. Wbighison, M.I.C.E 664 

FRIDAY, AUGUST 25. 

1. Report of the Committee on Patent Legislation 664 

2. The Channel Tunnel. By J. Clarke Haavkshaw, M.A.,F.G.S.,M.LC.E. 664 

3. A System of Excavating the Channel Tunnel by Hydraulic Machinery. 

By T. R. Crampton 664 

4. Improved Continental Communication. By James Abernetht, C.E. ... 665 

5. On Unsteady Motion in Open Channels. By Major Allan Cunningham, 

R.E 665 

6. Convexity of Surface of Streams. By Major Allan Cunningham, R.E. 665 

7. Depression of Maximum Velocity. By Major Allan Cunningham, R.E. 665 

MONDAY, AUGUST 28. 

1 On Compressed Air as applied to Locomotion. Bv Sir Frederick 
Bramwell, r.R.S '. 666 

2. Recent Progress in Telephony. By W. XL Preece, F.R.S 666 

3. On a new Arc Lamp. By W. II. Preece, F.R.S 667 

4. Recent Progress in Electric Railways. By Dr. Fleming 667 

5. On Electric Light Engineering. By Dr. Fleming 667 

6. On the Efficiency of the Edison Steam Dynamo. By Dr. Fleming 667 

7. On some Apparatus for use in connection with Electric Light Measure- 

ment. By Robert Sabine 667 

8. On a new form of Arc Lamp. By Professor G. Forbes, M.A., F.R.S.E. 668 

9. On the Laws defining the strength of Current which can be sent through 
Wires of different diameters without raising the external temperature 
above a certain limit. By Professor G. Forbes, M. A., F.R.S.E QQB 

TUESDAY, AUGUST 29. 

1. Report of the Committee on Wind Pressure 668 

2. On the Mechanical Properties of Aluminium. By W. H. Barlow, F.R.S. 668 

3. On the Southampton Docks. By A. Giles 669 

4. On the Reclamation of Brading Harbour. By R. F. Grantham, Assoc. 
M.Inst. C.E 669 

5. Improvements in Gas Illumination. By W. Sugg 669 

6. On Sound Signals. By E. Price Edwards 670 

7. Some of the Causes of Collision at Sea. By Captain Colomb, R.N 670 

8. On the Engine Power Meter. By C. Vernon Boys 672 



CONTENTS. XIX 

WJSBjYUSBAY, august 30. 

Page 

1. Report of the Committee on Screw Gauges 672 

2. Torpedo-boats. B}' J. Donaldson, M.Inst. C.E 672 

3. Current Meter Observations in the Tidal Compartment of tlie Thames. 

By Professor W. C. Unwin, M.I.C.E 676 

4. An Apparatus for recording the results of Experiments with Itailwaj^ 
Braies. By Sir Frederick Bramwell, F.R.S 677 

5. On a combined Gas Motor and Cold Air Machine. By J. J. Colmax 678 

0. Collapsible Boats. By E. L. Berthon 678 

7. The Pressure of Wheat stored in Elongated Cells or Bins. Bv Isaac 
Roberts, F.G.S '. 678 

INDEX 070 



» 



\ 



LIST OF PLATES, 



PLATES I., II., AND HI. 

Illustrative of the Eeport of the Committee on the Calibration of Jlerciirial 

Thermometeis. 



PLATE IV. 

Illustrative of Professor Ltooxe Levi's Communication, 'On the State of Crime 
in England, Scotland, and Ireland in 1880.' 



PLATES v., VI., AND VIL 

Illustrative of Mr. J. Clabke IIaavkshaw's Communication, ' The Channel 

Tunnel.' 



PLATE VIII. 

Illustrative of Mr. B. Baker's Communication, 'The Forth Bridge.' 

PLATE IX. 

Illustrative of Dr. IIuggins's Communication, 'On the Photographic Spectrum of 

Comet (Wells) 1, 1882.' 

PLATE X. 

Illustrative of I'r. IIuggins's Communication, ' On the Photographic Spectrum of 

the Great Nebula in Orion.' 



OBJECTS AND RULES 



OF 



THE ASSOCIATION. 



OBJECTS. 

The Association contemplates no interference with the ground occupied 
by other institutions. Its objects are : — To give a stronger impulse and 
a more systematic direction to scientific inquiry, — to promote the inter- 
course of those who cultivate Science in different parts of the British 
Empire, with one another and with foreign philosophers, — to obtain a 
more general attention to the objects of Science, and a removal of any 
disadvantages of a public kind which impede its progress. 

RULES. 

Admission of Members and Associates. 

All persons who have attended the first Meeting shall be entitled to 
become Members of the Association, upon subscribing an obligation to 
conform to its Rules. 

The Fellows and Members of Chartered Literary and Philosophical 
Societies publishing Transactions, in the British Empire, shall be entitled, 
in like manner, to become Members of the Association. 

The OfBcers and Members of the Councils, or Managing Committees, 
of Philosophical Institutions shall be entitled, in like manner, to become 
Membei's of the Association. 

All Members of a Philosophical Institution recommended by its Coun- 
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Members of the Association. 

Persona not belonging to such Institutions shall be elected by the 
General Committee or Council, to become Life Members of the Associa- 
tion, Annual Subscribers, or Associates for the year, subject to the 
approval oi a General Meeting. 

Compositions, Subscriptions, and Privileges. 

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offices of the Association. 

Annual Subscribers shall pay, on admission, the sum of Two Pounds, 
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and for the years in which they continue to pay toitliout intermissicn their 
Annual Subscription. By omitting to pay this subscription in any par- 
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XXli EULES OF THE ASSOCIATION. 

all future years tlie privilege of receiving the volumes of the Association 
gratis : but they may resume their Membership aud other privileges at 
any subsequent Meeting of the Association, paying on each such occasion 
the sum of One Pound. They are eligible to all the Offices of the Asso- 
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Associates for the year shall pay on admission the sum of One Pound. 
They shall not receive gratuitously the Reports of the Association, nor be 
eligible to serve on Committees, or to hold any office. 

The Association consists of the following classes : — 

1. Life Members admitted from 1831 to 1845 inclusive, who have paid 
on admission Pive Pounds as a composition. 

2. Life Members who in 1846, or in subsequent years, have paid on 
admission Ten Pounds as a composition. 

3. Annual Members admitted from 1831 to 1839 inclusive, subject to 
the payment of One Pound annually. [May resume their Membership 
after intermission of Annual Payment.] 

4. Annual Members admitted in any year since 1839, subject to the 
payment of Two Pounds for the first year, and One Pound in each 
following year. [May resume their Membership after intermission of 
Annual Payment.] 

5. Associates for the year, subject to the payment of One Pound. 

6. Corresponding Members nominated by the Council. 

And the Members and Associates will be entitled to receive the annual 
volume of Reports, gratis, or to purchase it at reduced (or Members') 
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1. Gratis. — Old Life Members who have paid Five Pounds as a com- 

position for Annual Payments, and previous to 1845 a fur- 
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New Life Members who have paid Ten Pounds as a compo- 
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Annual Membei'S ivho have not intermitted their Annual Sub- 
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as a composition for Annual Payments, but no further sum 
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3. Members may purcbase (for the purpose of completing their sets) 

any of the volumes of the Reports of the Association up 
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Application to be made at the Office of the Association, 22 Albemarle 
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Volumes not claimed within two years of the date of publication can 
only be issued by direction of the Council. 

Subscriptions shall be received by the Treasurer or Secretaries. 

' A few complete sets, 1831 to IST-t, are on sale, £10 the set. 



EULES OK THE ASSOCIATION. XXlll 

Meetings. 

The Association sLall meet aunnally, for one week, or longer. The 
place of each Meeting shall be appointed by the Greneral Committee two 
years in advance ; and the arrangements for it shall be entrusted to the 
Officers of the Association. 

General Covimittee. 

The General Committee shall sit during the week of the Meeting, or 
longer, to transact the business of the Association. It shall consist of the 
following persons : — 

Class A. Permanent Membees. 

1. Members of the Council, Presidents of the Association, and Presi- 
dents of Sections for the pi-esent and preceding years, with Authors of 
Reports in the Transactions of the Association. 

2. Members who by the publication of Works or Papers have fur- 
thered the advancement of those subjects which are taken into considera- 
tion at the Sectional Meetings of the Association. With a view of suh- 
mitting new claims under ihis BuJe to the decision of the Council, they must 
be sent to the Secretanj at least one month before the Meeting of the 
Association. The decision of the Council on the claims of any Member 
of the Association to he placed on the list of the General Committee to he 
final. 

Class B. Temporart Members. 

1. The President for the time being of any Scientific Society publish- 
ing Transactions or, in his absence, a delegate representing him.' Claims 
imcler this Rule to be sent to the Secretary before the opening of the Meeting. 

2. Office-bearers for the time being, or delegates, altogether not ex- 
ceeding three, from Scientific Institutions established in the place of 
Meeting. Claims binder this liule to be approved by the Local Secretaries 
before the opening of the Meeting. 

3. Foreigners and other individuals whose assistance is desired, and 
who are specially nominated in writing, for the Meeting of the year, by 

"the President and General Secretaries. 

4. Vice-Presidents and Secretaries of Sections. 

Organizing Sectional Committees."^ 

The Presidents, Vice-Presidents, and Secretaries of the several Sec- 
tions are nominated by the Council, and have power to act until their 
names are submitted to the General Committee lor election. 

From the time of their nomination they constitute Organizing Com- 
mittees for the purpose of obtaining information upon the Memoirs and 
Reports hkely to be submitted to the Sections,^ and of preparing Reports 
thereon, and on the order in which it is desirable that they should be 

■ Eevised by the General Committee, Southampton, 1882. 

^ Passed by the General Committee, Edinburgh, 1871. 

' Avtioc to Contributors of 3/c'vioirs.— Authors are reminded that, under an 
arrangement dating from 1871, the acceptance of Memoirs, and the days on \yhich 
they are to be read, are now as far as possible determined by Organizing Committees 
for the several Sections before, the beginning of the Meeting. It has therefore become 
necessary, in order to give an opportunity to the Committees of doing justice to the 
several Communications, that each Author should prepare an Abstract of his Memoir, 
of a length suitable for insertion in the published Transactions of the Association, 



XXIV RULES OF THE ASSOCIATION. 

read, to be presented to the Committees of the Sections at their first 
meeting. The Sectional Presidents of former years are ex officio members 
of the Organizing Sectional Committees.' 

An Organizing Committee may also hold such preliminary meetings as 
the President of the Committee thinks expedient, but shall, under any 
circumstances, meet on the first Wednesday of the Annual Meeting, at 
11 A.M., to nominate the first members of the Sectional Committee, if 
they shall consider it expedient to do so, and to settle the terms of their 
report to the General Committee, after which their functions as an 
Organizing Committee shall cease.^ 

Constitution of the Sectional Coinraittees.^ 

On the first day of the Annual Meeting, the President, Vice-Presi- 
dents, and Secretaries of each Section having been appointed by the 
General Committee, these Officers, and those previous Presidents and 
Vice-Presidents of the Section who may desire to attend, are to meet, at 
2 P.M., in their Committee Rooms, and enlarge the Sectional Committees 
by selecting individuals from among the Menibers (not Associates) present 
at the Meeting Avhose assistance they may particularly desire. The Sec- 
tional Committees thus constituted shall have power to add to their 
number from day to day. 

The List thus formed is to be entered dailj* in the Sectional Minute- 
Book, and a copy forwarded without delay to the Printer, who is charged 
with publishing the same before 8 a.m. on the next day in the Journal of 
the Sectional Pi'oceedings. 

Business of the Sectional Committees. 

Committee Meetings are to be held on the Wednesday at 2 p.m., on the 
following Thursday, Friday, Saturday, Monday, and Tuesday, from 10 to 
11 A.M., punctually, for the objects stated in the Rules of the Association, 
and specified below. 

The business is to be conducted in the following manner : — 

1. The President shall call on the Secretary to read the minutes of 

the previous Meeting of the Committee. 

2. No paper shall be read until it has been formally accepted by the 

Committee of the Section, and entered on the minutes accord- 
ingly. 

3. Papers Avhich have been reported on unfavourably bj' the Organiz- 

ing Committees shall not be brought before the Sectional 
Committees.'' 
At the first meeting, one of the Secretaries will read the ]\Iinutes of 
last year's proceedings, as recorded in the Minute-Book, and the Synopsis 

and that he should send it, together with the original Memoir, by book-post, on or 
before .addressed thus — 'General Secretaries, British Associa- 
tion, 22 Albemarle Street, London, \V. For Section ' If it should be incon- 
venient to the Author that his paper should be read on any particular daj's, he is 
requested to send information thereof to the Secretaries in a separate note. Authors 
who send in their MSS. three complete weeks before the Meeting, and whose papers 
are accepted, will be furnished, before the Meeting, with printed copies of their 
Reports and Abstracts. No Report, Paper, or Abstract can be in.serted in the Annual 
Volume unless it is handed either to the Recorder of the Section or to the Secretary, 
before the conclusiun of the Meetiiif/. 

• Added by the General Committee, Sheffield, 1879. 

- Revised by the General Committee, Swansea, 1880. 
3 Passed by the General Committee, Edinburgh, 1871. 

* These rules were adopted by the General Committee, Plymouth, 1877. 



RULES OF THE ASSOCIATION. XXV 

of Recomniendatious adopted at the last Meeting of the Association and 
printed in the last volume of the Transactions. He will next proceed to 
read the Report of the Organizing Committee.* The list of Communi- 
cations to be read on Thursday shall he then arranged, and the general 
distribution of business throughout the week shall be provisionally ap- 
pointed. At the close of the Committee Meeting the Secretaries shall 
forward to the Printer a List of the Papers appointed to be read. The 
Printer is charged with publishing the same before 8 a.m. on Thursday in 
the Journal. 

On the second day of the Annual Meeting, and the following days, 
the Secretaries are to correct, on a copy of the Journal, the list of papers 
which have been read on that day, to add to it a list of those appointed 
to be read on the next day, and to send this copy of the Journal as early 
in the day as possible to the Printer, who is charged with printing the 
same before 8 a.m. next morning in the Journal. It is necessary that one 
of the Secretaries of each Section (generally the Recorder) should call 
at the Printing Office and revise the proof each evening. 

Minutes of the proceedings of every Committee are to be entered daily 
in the Minute- Book, which should be confirmed at the next meeting of 
the Committee. 

Lists of the Reports and Memoirs read in the Sections are to be entered 
in the Minute-Book daily, which, with all Memoirs and Copies or Abstracts 
of Memoirs furnished hy Autliors, are to he fonvarded, at the close of the Sec- 
tional Meetings, to the Secretary. 

The Vice-Presidents and Secretaries of Sections become ex officio tem- 
porary Members of the General Committee {vide p. xxiii), and will receive, 
on application to the Treasurer in the Reception Room, Tickets entitling 
them to attend its Meetings. 

The Committees will take into consideration any suggestions which may 
be offered by their Members for the advancement of Science. They are 
specially requested to review the recommendations adopted at preceding 
Meetings, as published in the volumes of the Association and the com- 
munications made to the Sections at this Meeting, for the purposes of 
selecting definite points of research to which individual or combined 
exertion may be usefully directed, and branches of knowledge on the state 
and progress of which Reports are wanted ; to name individuals or Com- 
mittees for the execution of such Reports or researches ; and to state 
whethei*, and to what degree, these objects may be usefully advanced by 
the appropriation of the funds of the Association, by application to 
Government, Philosophical Institutions, or Local Authorities. 

In case of appointment of Committees for special objects of Science, 
it is expedient that all Memlters of the Committee should he named, and 
one of them, appointed to act as Secretary, for insuring attention to husiness. 

Committees have power to add to their number persons whose assist- 
ance they may require. 

The recommendations adopted by the Committees of Sections are to 
be registered in the Forms furnished to their Secretaries, and one Copy of 
each is to be forwarded, without delay, to the Secretary for presentation 
to the Committee of Recommendations. Unless this he done, the liecom- 
mendations cannot receive the sanction of the Association. 

N.B. — Recommendations which may originate in any one of the Sec- 
tions must first he sanctioned hy the Committee of that Section before they 

• This and the following sentence were added by the General Committee, 1871. 



XXVI EULES OF THE ASSOCIATION. 

can be referred to the Cominittee of Recommendations or confirmed by 
the General Committee. 

The Committees of the Sections shall ascertain whether a Report 
has been made by every Committee appointed at the previous Meeting 
to whom a sum of money has been granted, and shall report to the Com- 
mittee of Recommendations in every case where no such Report has been 
received.' 

Notices regarding Grants of Money. 

Committees and individuals, to whom grants of money have been 
entrusted by the Association for the prosecution of particular researches 
in science, ai'e required to present to each following Meeting of the 
Association a Report of the progress which has been made ; and the 
Individual or the Member first named of a Committee to whom a money 
grant has been made must (previously to the next Meeting of the Associa- 
tion) forward to the General Secretaries or Treasurer a statement of the 
sums which have been expended, and the balance which i-emains dispos- 
able on each grant. 

Grants of money sanctioned at any one Meeting of the Association 
expire a weelc he/ore the opening of the ensuing Meeting: nor is the 
Treasurer authorized, after that date, to allow any claims on account of 
such grants, unless they be renewed in the original or a modified form by 
the General Committee. 

No Committee shall raise money in the name or under the auspices of 
the British Association without special permission from the General Com- 
mittee to do so ; and no money so raised shall be expended except in 
accordance with the rules of the Association. 

In each Committee, the Member first named Is the only person entitled 
to call on the Treasurer, Professor A. W. Williamson, University College, 
London, W.C., for such portion of the sums granted as may from time to 
time be required. 

In grants of money to Committees, the Association does not contem- 
plate the payment of personal expenses to the members. 

In all cases where additional grants of money are made for the con- 
tinuation of Researches at the cost of the Association, the sum named is 
deemed to include, as a part of the amount, whatever balance may remain 
unpaid on the former grant for the same object. 

All Instruments, Papers, Drawings, and other property of the Associa- 
tion are to be deposited at the Office of the Association, 22 Albemarle 
Street, Piccadilly, London, "W"., when not employed in carrying on scien- 
tific inquiries for the Association. 

Business of the Sections. 

The Meeting Room of each Section is opened for conversation from 
10 to 11 daily. The Section Rooms and cqjproaches thereto can be used for 
no notices, exhibitions, or other purposes than those of the Association. 

At 11 precisely the Chair will be taken, and the reading of communi- 
cations, in the order previously made public, commenced. At 3 p.m. the 
Sections will close. 

Sections may, by the desire of the Committees, divide themselves into 
Departments, as often as the number and nature of the communications 
delivered in may render such divisions desirable. 

' Passed by the General Committee at Sheffield, 1879. 



KULES OF THE ASSOCIATION. XXVI 

A Report presented to the Association, and read to the Section which 
orio-inally called for it, may be read in another Section, at the request of 
the Officers of that Section, with the consent of the Author. 

Duties of the Doorkeepers. 

1. — To remain constantly at the Doors of the Rooms to which they are 
appointed during the whole time for which they are engaged. 

2. — To require of every person desirous of entering the Rooms the ex- 
hibition of a Member's, Associate's, or Lady's Ticket, or Reporter's 
Ticket, signed by the Treasurer, or a Special Ticket signed by the 
Secretary. 

3. — Persons unprovided with any of these Tickets can only be admitted 
to any particular Room by order of the Secretary in that Room. 
No person is exempt from these Rules, except those Officers of the 

Association whose names are printed in the programme, p. 1. 

Duties of the Messengers. 

To remain constantly at the Rooms to which they are appointed, dur- 
ing the whole time for which tbey are engaged, except when employed on 
messages by one of the Officers directing these Rooms. 

Committee of Recoininiendations. 

The General Committee shall appoint at each Meeting a Committee, 
which shall receive and consider the Recommendations of the Sectional 
Committees, and report to the General Committee the measures which 
they would advise to be adopted for the advancement of Science. 

All Recommendations of Grants of I\Ioney, Requests for Special Re- 
searches, and Reports on Scientific Subjects shall be submitted to the 
Committee of Recommendations, and not taken into consideration by the 
General Committee unless previously recommended by the Committee of 
Recommendations . 

Local Committees. 

Local Committees shall be formed by the Officers of the Association 
to assist in making arrangements for the Meetings. 

Local Committees shall have the power of adding to their numbers 
those Members of the Association whose assistance they may desire. 

Officers. 

A President, two or more Vice-Presidents, one or more Secretaries, 
and a Treasurer shall be annually appointed by the General Committee. 

Council. 

In the intervals of the Meetings, the affairs of the Association shall 
be managed by a Council appointed by the General Committee. The 
Council may also assemble for the despatch of business during the week 
of the Meeting. 

Papers and Communicatlo7is. 

The Author of any paper or communication shall be at liberty to 
reserve his right of property therein. 

Accounts. 

The Accounts of the Association shall be audited annually, by Auditors 
appointed by the General Committee. 



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PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



XXXV 



Presidents and SecretoA'les of the Sections of the Association. 



Date and Place 



Presidents 



Secretaries 



MATHEMATICAL AND PHYSICAL SCIENCES. 



COMMITTEE OF SCIENCES, I. — MATHEMATICS AND GENERAL PHYSICS. 

Rev. H. Coddington. 

Prof. Forbes. 

Prof. Forbes, Prof. Lloyd. 



1832. Oxford 

18."53. Cambridge 
1834. Edinburgh 



Davies Gilbert, D.C.L.,F.R.S. 

Sir D. Brewster, F.R.S 

Rev. W. Whcwcll, F.R.S. 



1835. Dublin 

1836. Bristol 

1837. Liverpool... 

1838. Newcastle 
1S.".0. Birmingham 

1840. Glasgow ... 

1841. Plymouth 

1842. Manchester 



1843. Cork 

1844. York 

1845. Cambridge 

1846. SouthamjD- 
ton. 

1847. Oxford 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 

1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 



SECTION A. — MATHEMATICS AND PHYSICS 
Rev. Dr. Robinson 



1858. Leeds 



Rev. William Whewell, F.R.S. 

Sir D. Brewster, F.R.S 

Sir J. F. AV. Herschel, Bart., 

F.R.S. 
Rev. Prof. Whewell, F.R.S.... 

Prof. Forbes. F.R.S 

Rev. Prof. Lloyd, F.R.S 

Very Rev. G. Peacock, D.D., 

F.R.S. 
Prof. M'Culloch, M.R.I.A. ... 
The Earl of Rosse, F.R.S. ... 
The Very Rev. the Dean of 

Ely. 
Sir John F. W. Herschel, 

Bart., F.R.S. 
Rev. Prof. Powell, M.A., 

F.R.S. 

Lord Wrottesley, F.R.S 

William Hopkins, F.R.S 

Prof. J. D. Forbes, F.R.S., 

Sec. R.S.E. 
Rev. W. Wliewell, D.D., 

F.R.S., &c. 
Prof. W. Thomson, M.A., 

F.R.S. L. & E. 
The Very Rev. the Dean of 

Ely, F.R.S. 
Prof. G. G. Stokes, M.A., Sec. 

R.S. 
Rev. Prof. Kelland, M.A., 

F.R.S. L. &; E. 
Rev. R. Walker, M. A., F.R.S. 

Rev. T. R. Robinson, D.D., 
F.R.S., M.R.LA. 

Rev. W. Whewell, D.D., 
V.P.R.S. 

b2 



Prof. Sir W. R. Hamilton, Prof. 

Wheatstone. 
Prof. Forbes, W. S. Harris, F. W. 

Jerrard. 
W. S. Harris, Rev. Prof. Powell, 

Prof. Stevelly. 
Rev. Prof. Chevallier, Major Sabine, 

Prof. Stevelly. 
J. D. Chance, W. Snow Harris, Prof. 

Stevelly. 
Rev. Dr. Forbes, Prof. Stevelly, 

Arch. Smith. 
Prof. Stevelly. 
Prof. M'Culloch, Prof. Stevelly, Rev. 

W. Scoresby. 
J. Nott, Prof.' Stevelly. 
Rev. Wm. Hey, Prof. Stevelly. 
Rev. H. Goodwin, Prof. Stevelly, G. 

G. Stokes. 
John Drew, Dr. Stevelly, G. G. 

Stokes. 
Rev. H. Price, Prof. Stevelly, G. G. 

Stokes. 
Dr. Stevelly, G. G. Stokes. 
Prof. Stevelly, G. G. Stokes, W. 

Ridout Wills. 
W. J.Macquorn Rankine, Prof .Smyth, 

Prof. Stevelly, Prof. G. G. Stokes. 
S. Jackson, W. J. Macquorn Rankine, 

Prof. Stevelly, Prof. G. G. Stokes. 
Prof. Dixon, ^K. J. Macquorn Ran- 
kine, Prof. Stevelly, J. Tyndall. 

B. Blaydes Haworlh, J. D. SoUitt, 
Prof. Stevelly, J. Welsh. 

J. Hartnup, H. G. Puckle, Prof. 

Stevelly, J. Tyndall, J. Welsh. 
Rev. Dr. Forbes, Prof. D.Gray, Prof. 

Tyndall. 

C. Brooke, Rev. T. A. Southwood. 
Prof. Stevelly, Rev. J. C. Turnbull. 

Prof. Curtis, Prof. Hennessy, P. A. 

Ninnis, W. J. Macquorn Rankine, 

Prof. Stevelly. 
Rev. S. Earnshaw, J. P. Hennessy, 

Prof. Stevelly, H. J. S. Smith, Prof 

Tyndall. 



XX XVI 



REPORT — 1882. 



Dat 


e and Place 


Presidents 


1859. 


Aberdeen... 


The Earl of Rosse, M.A.,K.P., 
F.R.S. 


18C0. 


Oxford 


Rev. B. Price, M.A., F.R.S.... 


1861. 


Manchester 


G. B. Airy, M.A., D.C.L., 
F.R.S. 


1862. 


Cambridge 


Prof. G. G. Stokes, M.A., 
F.R.S. 


1863. 


Newcastle 


Prof . W. J. ]\Tacquorn Rankine, 
C.E., F.R.S. 


ISOi. 


Bath 


Prof. Cavley, M.A., F.R.S., 
F.R.A.S. 






1865. 


Birmingham 


W. Spottiswoode,M.A.,F.R.S., 
F.R.A.S. 


1866. 


Nottingham 


Prof. ■V\'Tieatstone, D.C.L., 
F.R.S. 


1867. 


Dundee ... 


Prof. Sir W. Thomson, D.C.L., 
F.R.S. 


1868. 


Norwich ... 


Prof. J. Tyndall, LL.D., 
F.R.S. 


1800. 


Exeter 


Prof. J. J. Sylvester, LL.D., 
F.R.S. 


1870. 


Liverpool... 


J. Clerk Maxwell, M.A., 
LL.D., F.R.S. 


1871. 


Edinburgh 


Prof. P. G. Tait, F.R.S.E. ... 


1872. 


Brighton ... 


\V. De La Rue, D.C.L., F.R.S. 


187:?. 


Bradford ... 


Prof. 11. J. S. Smith, F.R.S. 


1874. 


Belfast 


Rev. Prof. J. H. Jellett, M.A.. 
M.R.I.A. 


1875. 


Bristol 


Prof. Balfour Stewart, M.A., 
LL.D., F.R.S. 


1870. 


Glasgow ... 


Prof. Sir W. Thomson, M.A., 
D.C.L., F.R.S. 


1877. 


ri--mouth... 


Prof, G. C. Foster, B.A., F.R.S., 
Pres. Physical Soc. 


1878. 


Dublin 


Rev. Prof. Salmon, D.D., 
D.C.L., F.R.S. 


1870. 


Sheffield ... 


George Johnstone Stoney, 
M.A., F.R.S. 


1880. 


Swansea ... 


Prof. W. Grylls Adams, M.A., 
F.R.S. 


1881. 


York 


Prof. Sii- W. Thomson, M.A., 
LL.D., D.C.L., F.R.S. 


1882. 


Southamp- 


Rt. Hon. Prof. Lord Rayleigh, 




ton. 


M.A., F.R.S. 



Secretaries 



J. P. Hennessy, Prof. Ma.xwell, H. 

J. S. Smith, Prof. Stevellv. 
Rev. G C. Bell, Rev. T. Rennison, 

Prof. Stevellv. 
Prof. R. B. Clifton, Prof. H. J. S. 

Smith, Prof. Stevelly. 
Prof. R. B. Clifton, Prof. H. J. S. 

Smith, Prof. Stevelly. 
Rev.N.Ferrers,Prof.Fuller,F..Tenkin, 

Prof. Stevellj', Rev. C. T. Whitley. 
Prof. Fuller, F. .lenkin. Rev. G. 

Buckle, Prof. Stevelly. 
Rev. T. N. Hutchinson, F. .Jenkin, G. 

S. Mathews, Prof. H. J. S. Smith, 

J. M. Wilson. 
Fleeming Jenkin, Prof. H. J.S.Smith, 

Rev. S. N. Swann. 
Rev. G. Buckle, Prof. G. C. Foster, 

Prof. Fuller, Prof. Swan. 
Prof. G. C. Foster, Rev. R. Harley, 

R. B. Hayward. 
Prof. G. C. Foster, R. B. Hayward, 

W. K. Clifford. 
Prof. W. G. Adams, W. K. Clifford, 

Prof. G. C. Foster, Rev. W. Allen 

Whitworth. 
Prof. W. G. Adams, J. T. Bottomlev, 

Prof. W. K. Clifford, Prof. J. D. 

Everett, Rev. R. Harley. 
Prof. W.K.Clifford, J. W.L.Glaisher, 

Prof. A. S. Herschel, G. F. Rod well. 
Prof. W. K. Clifford, Prof. Forbes, J. 

W.L. Glaisher, Prof. A. S. Herschel. 
J. W. L. Glaisher, Prof. Herschel, 

Randal Nixon, J. Perry, G. F. 

Rodwell. 
Prof. W. F. Barrett, J. W.L. Glaisher, 

C. T. Hudson, G. F. Rodwell. 
Prof. W. F. liarrett, J. T. Bottomley, 

Prof. G. Forbes, J. W. L. Glaislier, 

T. Muir. 
Prof. W. F. Barrett, J. T. Bottomley, 

J. W. L. Glaisher, F. G. Landon. 
Prof. J. Casej-, G. F. Fitzgerald, J. 

W. L. Glaisher, Dr. O. J. Lodge. 
A. H. Allen, J.- W. L. Glaisher, Dr. 

0. J. Lodge, D. McAlister. 
W. E. Ayrton, J. W. L. Glaisher, 

Dr. 0. J. Lodge, D. McAlister. 
Prof. W. E. Ayrton, Prof. 0. J. Lodge, 

D. McAlister, Rev. W. Routh. 

W. M. Hicks, Prof. O. J. Lodge, 
D. McAlister, Rev. G. Richardson. 



CHEMICAL SCIENCE. 

COMMITTEE OF SCIENCES, U. — CHEMISTRY, MINERALOGY. 



1832. 
1833. 
1831. 



Oxford 

Cambridge 
E'linburgh 



John Dalton, D.C.L., F.R.S. 
John Dalton, D.C.L., F.R.S. 
Dr. Hope 



James F. W. Johnston. 

Prof. Miller. 

Mr. Johnston, Dr. Christ ison. 



PRESIDENTS AND SECRETA?.IES OF THE SECTIONS. 
SECTION B. — CHEMISTRY AND MINERALOGY. 



XXXVll 



Date and Place 



1835. Dublin. 

1836. Bristol. 



1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge 

1846. Southamp- 

ton 

1847. Oxford 



Presidents 



Dr. T. Thomson, F.Pi.S. . 
Ilev. Prof. Cumming .... 



Secretaries 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 



1853. Hull 



1854. Liverpool 

1855. Glasgow ... 

1856. Cheltenham 



1857. Dublin 

1858. Leeds 

1859. Aberdeen.. 
18G0. Oxford 



Dr. Apjohn, Prof. Johnston. 

Dr. Apjohn, Dr. C. Henrj', W. Hera- 
path. 

Prof. Johnston, Prof. Miller, Dr. 
Keynolds. 

Rev. William Whewell.F.R.S. ' Prof. Miller, H. L. Pattinson, Thomas 

Richardson. 

Dr. Golding Bird, Dr. J. B. Melson. 

Dr. R. D. Thomson, Dr. T. Clark, 
Dr. L. Playfair. 

J. Prideaux, Robert Hunt, W. M. 
Tweedy. 

Dr. L. Plaj'fair, R. Hunt, J. Graham. 

R. Hunt, Dr. Sweeny. 

Dr. L. Playfair, E. Solly, T. H. Barker. 

R. Hunt, J. P. Joule, Prof. Miller, 
E. Solly. 

Dr. Miller, R. Hunt, W. Randall. 



Michael Faraday, F.R.S.... 



Prof. T.Graham, F.R.S 

Dr. Thomas Thomson, F.R.S. 

Dr. Daubeny, F.R.S 

John Dalton, D.C.L., F.R.S. 

Prof. Apjohn, M.R.I. A 

Prof. T. Graham, F.R.S 

Rev. Prof. Cumming 



Michael Farada)', D.C.L., 

F P S 
Rev! W. V. Harcourt, M.A., 

F.R.S. 

Richard Phillips, F.R.S 

John Percy, M.D., F.R.S 

Dr. Christison, V.P.R.S.E. 
Prof. Thomas Graham, F.R.S 
Tliomas Andrews,M.D.,F.R.S 



B. C. Brodie, R. Hunt, Prof. Solly. 



1861. Manchester 

1862. Cambridge 

1863. Newcastle 



1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 



T. H. Henry, R. Hunt, T. Williams. 

R. Hunt, G. Shaw. 

Dr. Anderson, R. Hunt, Dr. Wilson. 

T. J. Pearsall, W. S. Ward. 

Dr. Gladstone, Prof. Hodges, Prof. 
Ronalds. 

H. S. Blundell, Prof. R. Hunt, T. J. 
Pearsall. 

Dr. Ed wards,Dr.Gladstone, Dr.Price. 

Prof. Frankland, Di'. H. E. Roscoe. 

J. Horsley, P. J. Worsley, Prof. 
Voelcker. 

Dr. Davy, Dr. Gladstone, Prof. Sul- 
livan. 

Dr. Gladstone, W. Odling, R. Rey- 
nolds. 

J. S. Brazier, Dr. Gladstone, G. D. 
Liveing, Dr. Odling. 

A. Vernon Harcourt, G. D. Liveing, 
A. B. Northcote. 

A. Vernon Harcourt, G. D. Liveing. 

H. W. Elphinstone, W. Odling, Prof. 
Roscoe. 

Prof. Liveing, H. L. Pattinson, J. C. 
Stevenson. 

A.V.Harcourt,Prof.Liveing,R.Biggs. 

A. V. Harcourt, II. Adkins, Prof. 
Wanklyn, A. Winkler Wills. 

J. H. Atherton, Prof. Liveing, W. J. 
Russell, J. White. 

A. Crum Brown, Prof. G. D. Liveing, 
W. J. Russell. 

Dr. A. Crum Brown, Dr. W. J. Rus- 
sell, F. Sutton. 

Prof. A. Crum Brown, Dr. W. J. 
Russell, Dr. Atkinson. 
Prof. H. E. Roscoe, B.A., Prof. A. Crum Brown. A. E.Fletcher 
F.R.S., F.C.S. I Dr. W. J. Russell. 



Prof. J. F. AV. Johnston, M.A., 

F.R.S. 
Prof.W. A.Miller, M.D.,F.R.S. 
Dr. Lyon Playfair,C.B.,F.R.S. 
Prof. B. C. Brodie, F.R.S. ... 

Prof. Apjohn, M.D., F.R.S., 

M.R.LA. 
Sir J. F. W. Herschel, Bart., 

D.CL. 
Dr. Lyon Playfair, C.B., F.R.S. 

Prof. B. C. Brodie, F.R.S 

Prof. W.A.Miller, M.D.,F.R.S. 
Prof. W.A.Miller, M.D.,F.R.S. 

Dr. Alex. W. Williamson, 

F.R.S. 
W.Odling, M.B.,F.R.S.,F.C.S. 
Prof. W. A. Miller, M.D., 

V.P.R.S. 
H. Bence Jones, M.D., F.R.S. 

Prof. T. Anderson, M.D., 

F.R.S.E. 
Prof. E. Frankland, F.R.S.. 

F.C.S. 
Dr. H. Debus, F.R.S., F.C.S. 



XXXVlll 



llEPORT 1882. 



Date and Place 


Presidents 


Secretaries 


1871. 


Edinburgh 


Prof. T. Andrews, M.D.,F.K.S. 


J. T. Buchanan, W. N. Hartley, T. 
E. Thorpe. 


1872. 


Brighton ... 


Dr. .7. H. Gladstone, F.E.S.... 


Dr. Mills, W. Chandler Roberts, Dr. 








W. J. Russell. Dr. T. AVood. 


1873. 


Bradford ... 


Prof. W. J. Russell, F.E.S.... 


Dr. Armstrong, Dr. Mills, W. Chand- 
ler Roberts, Dr. Thorpe. 


1874. 


Belfast 


Prof. A. Crura Brown, M.D., 


Dr. T. Cranstoun Charles, W. Chand- 






F.R.S.E., F.C.S. 


ler Roberts, Prof. Thorpe. 


1875. 


Bristol 


A. G. Vernon Harcourt, M.A., 


Dr. H. E. Armstrong, W. Chandler 






F.R.S., F.C.S. 


Roberts, W. A. Tilden. 


187C. 


Glasgow ... 


W. H. Perkin, F.E.S 


W. Dittmar, W. Chandler Roberts, 
J. M. Thomson, W. A. Tilden. 


1877. 


Plymouth... 


F.A.Abel, F.K.S., F.C.S. ... 


Dr. Oxland, AV. Chandler Roberts, 








J. M. Thomson. 


187S. 


Dublin 


Prof. Maxwell Simpson, M.D., 


W. Chandler Roberts, J. M. Thom- 






F.R.S., F.C.S. 


son, Dr. C. E. Tichborne, T. AA'ills. 


1879. 


Sheffield ... 


Prof. Dewar, M.A., F.E.S. 


H. S. Bell, AA^ Chandler Eoberts, J. 
M. Thomson. 


1880. 


Swansea ... 


Joseph Henry Gilbert, Ph.D., 


H. B. Dixon, Dr. W. R. Eaton Hodg- 






F.B.S. 


kinson, P. Phillips Bedson, J. M. 
Thomson. 


1881. 


York 


Prof. A . AV. Williamson. Ph.D., 
F.E.S. 


P. Phillips Bedson, H. B. Dixon, 






T. Gough. 


1882. 


Southamp- 


Prof. G. D. Liveing, M.A., 


P. Phillips Bedson, H. B. Dixon, 




ton. 


F.R.S. 


J. L. Notter. 



GEOLOGICAL (and. until 1851, GEOGRAPHICAL) SCIE2s^CE. 

COMMITTEE OF SCTENCES, III. — GEOLOGY AND GEOGRAPHY. 



1832. Oxford |R. I. Mmchison, F.E.S. 

1S33. Cambridge. G. B. Greenough, F.E.S. 
1831. Edinburgh . Prof . Jameson 



. . . j John Taylor. 
...'\V\ Lonsdale, John Phillips. 
... Prof. Phillips, T. Jameson Torrie, 
Eev. J. Yates. 



SECTION C. — GEOLOGY AND GEOGRAPHY. 



1S3.5. 
1836. 



Dtiblin . 
Bristol . 



1837. Liverpool. 



1838. 


Newcastle. . 


1830. 


Birmingham 


1340. 


Glasgow ... 


1811. 


Plymouth... 


1842. 


Manchester 


1843. 


Cork 







,E. J. Griffith 

I Rev. Dr. Buckland, F.E.S.— 

Gvo(iriiphy, R. I. Murchison, 

F.R.S. 
Rev. Prof. Sedgwick, F.R.S.— 

ft'w/?'(?/;/i'?/,G.B.Greenough, 

F.E.S. 
C. Lyell, F.E.S., A^P.G.S.— 

GuotiTdpliy, Lord Prudhope. 
Eev. Dr. Buckland, F.E.S.— 

6'«)c/?Yy;Z!y, G.B. Greenough, 

F.E.S. 
Charles Lyell, F.E.S.— G'eo- 

qraphii, G. B. Greenough, 

'f.r.s'. 

H. T. De laBeolie, F.R.S. ... 

R. I. Murchison, F.R.S 

Richard E. Griffith, F.R.S., 
M.R.I.A. 



Captain Port lock, T. J. Torrie. 
William Sanders, S. Stutchburj', 
T. J. Torrie. 

Captain Portlock, R. Hunter. — Geo- 
qraiyhij, Captain H. M. Denham, 
R.N. 

\A^. C. Trevelyan, Capt. Portlock.— 
Geor/rapliii, Capt. AVashington. 

George Lloyd, M.D., H. E. Strick- 
land, Charles Darwin. 

W. J. Hamilton, D. Milne, Hugh 
Murray, H. E. Strickland, John 
Scoular, M.D. 

AA''. J. Hamilt on, Edward Moore, M.D., 
R. Hutton. 

E. W. Binney, E. Hutton, Dr. E. 
Lloyd, H. E. Strickland. 

Francis M. Jennings, H. E. Strick- 
land. 



PRESIDENTS AND SECRETAKIES OF THE SECTIONS. 



XXXIX 



Date and Place 


Presidents 


Secretaries 


1844. York 


Henry Warbiurton, M.P.,Pres. 
Geol. Soc. 


Prof. Ansted, E. H. Bunbury. 






1845. Cambridge. 


Rev. Prof. Sedgwick, M.A., 


Rev. J. C. Gumming, A. C. Ramsay, 




F.R.S. 


Rev. W. Thorp. 


1846. Southamp- 


Leonard Homer,F.K.S. — Geo- 


Robert A. Austen, Dr. J. H. Norton, 


tOK. 


graphy, G. B. Greenough, 


Prof. Oldham. — Gcograjjhy, Dr. C. 




F.K.S. 


T. Beke. 


1847. Oxford 


Very Kev.Dr.Buckland,F.E.S. 


Prof. Ansted, Prof. Oldham, A. C. 
Ramsay, J. Ruskin. 


1848. Swansea ... 


Sir H. T. De la Beche, C.B., 


Starling Benson, Prof. Oldham, 




F.R.S. 


Prof. Ramsay. 


1849.Birminghain 


Sir Charles Lyell, F.R.S., 


J. Beete Jukes', Prof. Oldham, Prof. 




F.G.S. 


A. C. Ramsay. 


1850. Edinbm-gh> 


Sir Roderick I. Murchison, 


A. Keith Johnston, Hugh Miller, 




F.R.S. 


Prof. Nicol. 



SECTION c {continued'). — GEOLOGT. 



1851. Ipswich ,..|WilliamHopkins,M.A., F.R.S. 

1852. Belfast Lieut.-Col. Portlock, R.E., 

F.R.S. 

1853. Hull Prof. Sedgwick, F.R.S 

1854. Liverpool . . Prof. Edward Forbes, F.R.S. 

1855. Glasgow ... Sir R. L Murchison, F.R.S.... 

1856. Cheltenham Prof. A. C. Ramsay, F.R.S.... 

1857. Dublin The Lord Talbot de Malahide 

1858. Leeds WilliamHopkins,M.A..LL.D., 

F.R.S. 

1859. Aberdeen... Sir Charles Lyell, LL.D.^ 

D.C.L., F.R.S. 

1860. Oxford Rev. Prof. Sedgwick, LL.D., 

F.R.S., F.G.S. 

1861. Manchester Sir R. I. Murchison, D.C.L., 

LL.D., F.R.S. 

1862. Cambridge J. Beete Jukes, M.A., F.R.S. 

1863. Newcastle Prof. Warington W. Smyth, 

F.R.S., F.G.S. 

1864. Batli Prof. J. Phillips, LL.D., 

F.R.S., F.G.S. 

1865. Birmingham Sir R. I. Mm-chison, Bart,, 

K.C.B. 

1866. Nottingham Prof. A. C. Ramsay. LL.D., 

F.R.S. 

1867. Dundee ... Archibald Geikie, F.E.S., 

F.G.S. 



C. J. F. Bunbury, G. W. Ormerod- 

Searles Wood. 
James Bryce, James MacAdam, 

Prof. M'Coy, Prof. Nicol. 
Prof. Harkness, William Lawton. 
John Cunningham, Prof. Harkness, 

G. W. Ormerod, J. AV. AVoodall. 
James Bryce, Prof. Harkness, Prof. 

Nicol. 
Rev. P. B. Brodie, Rev. E. Hep- 
worth, Edward Hull, J. Scovigall, 

T. Wright. 
Prof. Harkness, Gilbert Sanders, 

Robert H. Scott. 
Prof. Nicol, H. C. Sorby, E. W. 

Shaw. 
Prof. Harkness, Rev. J. Longmuir, 

H. C. Sorby. 
Prof. Harkness, Edward Hull, Capt. 

D. C. L. Woodall. 
Prof. Harkness, Edward Hull, T. 

Rupert Jones, G. W. Ormerod. 
Lucas Barrett, Prof. T. Rupert 

Jones, H. C. Sorby. 
E. F. Boyd, John Daglish, H. C. 

Sorby, Thomas Sopwith. 
W. B. bawkins, J. Johnston, H. C. 

Sorbj^ W. Pengelly. 
Rev. P. B. Brodie, J. Jones, Rev. E. 

Myers, H. C. Sorby, W. Pengelly. 
R. Etheridge, W. Pengelly, T. Wil- 
son, G. H. Wright. 
Edward Hull, W. Pengelly, Henry 

Woodward. 



> At a meeting of the General Committee held in 1850, it was resolved « That 
the subject of Geography be separated from Geology and combined with Ethnology, 
to constitute a separate Section, under the title of the " Geographical and Ethno- 
logical Section," ' for Presidents and Secretaries of which see page xliv. 



xl 



REPORT — 1882. 



Dat 


i and Place 


Presidents 


Secretaries 


1868. 


Norwich ... 


R. A. C. Godwin-Austen, 


Rev. 0. Fisher, Rev. J. Gunn, W. 






F.R.S., F.G.S. 


Pengelly, Rev. H. H. Winwood. 


1869. 


Exeter 


Prof. R. Harkness, F.R.S., 


W. Pengelly, W. Boyd Dawkins, 






F.G.S. 


Rev. 11. H. Winwood. 


1870. 


Liverpool... 


SirPhilipde M.Grey Egerton, 


W. Pengelly, Rev. H. H. Winwood, 






Bart., M.P., F.R.S. 


W. Boyd Dawkins, G. H. Morton. 


1871. 


Edinburgh 


Prof. A. Geikie, F.R.S., F.G.S. 


R. Etheridge, J. Geikie, T. McKennv 
Hughes,''L. C. Miall. 


1872. 


Brighton ... 


R. A. C. Godwin-.Vustcn, 


L. C. Miall, George Scott, AVilliam 






F.R.S. 


Topley, Henry Woodward. 


1873. 


Bradford ... 


Prof. J. Phillips, D.C.L., 


L. C. Miall, R. H. Tiddeman, W. 






F.R.S., F.G.S. 


Toplev. 


1871. 


Belfast 


Prof. Hull, M.A., F.R.S., 


F. Drew, L. C. Miall, R. G. Symes, 






F.G.S. 


R. H. Tiddeman. 


1875. 


Bristol 


Dr. Thomas Wright, F.R.S. E., 


L. C. Miall, E. B. Tawnej-, W. Top- 






F.G.S. 


ley. 


1876. 


Glasgow ... 


Prof. John Young, M.D 


J. Armstrong, F. W. Rudler, W. 
Topley. 


1877. 


Plj-mouth... 


W. Pengelly, F.R.S 


Dr. Le Neve Foster, R. H. Tidde- 
man, AV. Topley. 


1878. 


Dublin 


John Evans, D.C.L., F.R.S., 


E. T. Hardman, Prof. J. O'Reilly, 






F.S.A., F.G.S. 


R. H. Tiddeman. 


1879. 


Sheffield ... 


Prof. P. Martin Duncan, M.B., 
F.R.S., F.G.S. 


W. Topley, G. Blake Walker. 


1880. 


Swansea ... 


H. C. Sorby, LL.D., F.R.S., 
F.G.S. 


W. Topley, W. Whitaker. 


1881. 


York 


A. C. Ramsay, LL.D., F.R.S., 


J. E. Clark, W. Keeping, W. Topley, 






F.G.S. 


W. Whitaker. 


1882. 


Southamp- 


R. Etheridge, F.R.S., F.G.S. 


T. W. Sliore, W. Topley, E. West- 




ton. 




lake, W. Whitaker. 



BIOLOGICAL SCIENCES. 

COMMITTEE OF SCIENCES, IV. — ZOOLOGY, BOTAXT, PHYSIOLOGY, ANATOMY. 



1832. Oxford 'Rev. P. B. Duncan, F.G.S. ... 

1833. Cambridge' Rev. W. L. P. Garnons, F.L.S. 

1834. Edinburgh. Prof. Graham 



Rev. Prof. J. S. Henslow. 
C. C. Babington, D. Don. 
W. Yarrell, Prof. Burnett. 



SECTION D. — ZOOLOGY AND BOTANY. 



183.5. Dublin. 
1836. Bristol. 



1837. Liverpool... 

1838. Newcastle 

1 839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 



1843. Cork. 



Dr. Allman 

Rev. Prof. Henslow 



W. S. MacLeay 

Sir W. Jardine, Bart. 



Prof. Owen, F.R.S 

Sir W. J. Hooker, LL.D. 



John Richardson, M.D., F.R.S. 
Hon. and Very Rev. W. Her- 
bert, LL.D., F.L.S. 
William Thompson, F.L.S. ... 



J. Curtis, Dr. Litton. 

J. Curtis, Prof. Don, Dr. Riley, S. 
Rootsey. 

C. C. Babington, Rev. L. Jenyns, W. 
Swainson. 

J. E. Gray, Prof. Jones, R. Owen, 
Dr. Richardson. 

E. Forbes, W. Ick, R. Patterson. 

Prof. W. Couper, E. Forbes, R. Pat- 
terson. 

J. Couch, Dr. Lankester, E. Patterson. 

Dr. Lankester, R. Patterson, J. A. 
Turner. 

G. J. Allman, Dr. Lankester, E. 
Patterson. 



' At this Meeting Physiology and Anatomy were made a separate Committee, 
for Presidents and Secretaries of which see p. xliii. 



rUESIDENTS AND SECRETARIES OF THE SECTION'S. 



xli 



Date and Place 


Presidents 


Secretaries 


1844. York 

1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 


Very Rov. the Dean of Man- 
chester. 

Rev. Prof. Henslow, F.L.S..., 

Sir J. Richardson, BI.D., 
F.R.S. 

H. E. Strickland, M.A.,F.R.S. 


Prof. Allman, H. Goodsir, Dr. King, 

Dr. Lankester. 
Dr. Lankester, T. V. Wollaston. 
Dr. Lankester, T. V. Wollaston, H. 

Wooldridge. 
Dr. Lankest'er, Dr. Melville, T. V. 

Wollaston. 



1848. 


Swansea ... 


1849. Birmingham 

1850. Edinburgh 


1851. 


Ipswich ... 


1852. 


Belfast 


1853. 
1854. 
1855. 
1856. 


Hull 

Liverpool... 
Glasgow ... 
Cheltenham 


1857. 


Dublin 


1858. 


Leeds 


1859. 


Aberdeen... 


1860. 


Oxford 


1861. 


Manchester 


1862. 
1863. 


Cambridge 

Newcastle 


1864 


Bath 


1865. 


Birmingham 



L. W. Dilhvyn, F.R.S 



Prof. Goodsir, F.R.S. L. & E. 

Rev. Prof. Henslow, M.A., 

F.R.S. 
W. Ogilby 



SECTION D (continued). — zoologv and botany, including physiology. 

[For tlie Presidents and Secretaries of the Anatomical and Physiological Subsec- 
tions and the temijorary Section E of Anatomy and Medicine, see p. xliii.] 

Dr. R. Wilbraham Falconer, A. Hen- 

frey. Dr. Lankester. 
Dr. Lankester, Dr. Russell. 
Prof. J. H. Bennett, M.D., Dr. Lan- 
kester, Dr. DoiTglas Maclagan. 
Prof. Allman, F. W. Johnston, Dr. E. 

Lankester. 
Dr. Dickie, George C. Hyndman, Dr. 

Edwin Lankester. 
Robert Harrison, Dr. E. Lankester. 
Isaac Byerley, Dr. E. Lankester. 
William Keddie, Dr. Lankester. 
Dr. J. Abercrombie, Prof. Buckman, 

Dr. Lankester. 
Prof. J. R. Kinahan, Dr. E. Lankester, 

Robert Patterson, Dr. W. E. Steele 
Henry Denn.y, Dr. Heaton, Dr. E. 

Lankester, Dr. E. Perceval Wright. 
Prof. Dickie, M.D., Dr. E. Lankester, 

Dr. Ogilvy. 
W. S. Church, Dr. E. Lankester, P. 

L. Sclater, Dr. E. Perceval Wright. 
Dr. T. Alcock, Dr. E. Lankester, Dr. 

P. L. Sclater, Dr. E. P. Wright. 
Alfred Newton, Dr. E. P. Wright. 
Dr. E. Charlton, A.Newton, Rev. H, 

B. Tristram, Dr. E. P. Wright. 
H. B. Bradj', C. E. Broom, H. T. 

Stainton, Dr. E. P. Wright. 
Dr. J. Anthony, Rev. C. Clarke, Rev. 

H. B. Tristram, Dr. E. P. Wright. 



C. C. Babington, M.A., F.R.S. 
Prof. Balfour, M.D., F.R.S.... 
Rev. Dr. Fleeming, F.R.S.E. 
Thomas Bell, F.R.S., Pres.L.S. 

Prof. W. H. Harvev, M.D., 

F.R.S. 
C. C. Babington, M.A., F.R.S. 

Sir W. Jardine, Bart., F.R.S.E. 

Rev. Prof. Henslow, F.L.S... . 

Prof. C. C. Babington, F.R.S. 

Prof. Huxlev, F.R.S 

Prof. Balfour, M.D., F.R.S.... 

Dr. John E. Gray, F.R.S. ... 

T; Thomson, M.D., F.R.S. ... 



SECTION D {continued), — biology.^ 



1866. Nottingham 



1867. Dundee ... 



Prof. Huxley, LL.D., F.R.S. 
— PhyaioUujical Dcjj., Prof. 
Humphry, M.D., F.R.S.— 
Anthrojmlogical Bvp., Alf. 
R. Wallace, F.R.G.S. 

Prof. Sharpey, M.D., Sec. R.S. 
— Bep. of Zool. and Bot., 
George Busk, M.D., F.R.S. 



Dr. J. Beddard, W. Felkin, Rev. H. 
B. Tristram, W. Turner, E. B. 
Tylor, Dr. E. P. Wright. 



C. Spence Bate, Dr. S. Cobbold, Dr. 
M. Foster, H. T. Stainton, Rev. H. 
B. Tristram, Prof. W. Turner. 



' At a meeting of the General Committee in 1805, it was resolved : — 'That the title 
of Section D be changed to Bioloa-y ; ' and ' That for the word " Subsection," in the 
rules for conducting the business of the Sect ions, the word " Department" be substituted.' 



xlii 



REPORT — 1882. 



Date and Place 



1868. Norwich ... 



1869. Exeter, 



1870. Liverpool. 



1871. Edinburgh 



1872. Brighton .. 



1873. Bradford ... 



1874. Belfast. 



1875. Bristol 



1876. Glasgow ... 



1877. Plymouth. 



1878. Dublin 



1879. Sheffield 



1880. Swansea .. 



Presidents 



Rev. M. J. Berkeley, F.L.S. 
— Be p. of Phiisiuloijy, AV. 
H. Flower, F.R.S. 

George Busk, F.E.S., F.L.S. 
— JJip. of Hot. and Zool., 
C. Spence Bate, F.R.S. — 
Brp. oflithno., E. B. Tylor. 

Prof. G. Rolleston, M.A., M.D., 
F.R.S., F.L.S. — -D^'i;. of 
Altai, and Phymtl^VxoiM. 
Foster, M.D., F.L.S.— -D^v^ 
of Etlino., J. Evans, F.R.S. 

Prof. Allen Thomson, M.D., 
F.R.S.— Z'c/^ of Bot. and 
ir(wZ.,Prof.WyvilleThorason, 
F.R.S. — Beji. of Anthropol., 
Prof. W. Turner, M.D. 

Sir J. Lubbock, Bart., F.R.S.— 
Bcji- of Anat. and Pliyswl., 
Dr. Burdon Sanderson, 
F.H.fi.—Bej). of Anthrojwl. 
Col. A. Lane Fox, P.G.S. 

Prof. Allman, F.Tl.ii.—BcjK of 
Anat.andPhi/siol.,l?iot. Rn- 
t\\ertovd,M.t).—B('2).ofAn- 
throjwl, Dr. Beddoe, F.R.S. 

Prof. Redfern, M.D.—Brj}. of 
Zuol. and Bot., Dr. Hooker, 
C.B.,Pres.R.S.— i>(7;. o/'.-l «- 
/7,?vv>.,Sir W.R.Wilde, M.D. 

P. L. Sclater, Y.'R.'t^.—Bi'p.of 
Anat.andPhysiol.A'roi.Cle 
land, M.D., ¥.B..ii.—Bc2).of 
Anthropol., Prof. Rolleston, 
M.D., F.R.S. 

A. Russel Wallace, F.R.G.S., 
F.L.S. — Bcj). of Zool. and 
Bot., Prof. A. Newton, M.A., 
F.R.S.— Z'c^.'. of Anat. and 
Phi/U'wl... Dr. J. G. McKen- 
drick, F.R.S.E. 

J.GwynJeffreys,LL.D.,F.R.S., 
F.L.S. — Bej). of Anat. and 
Physiol, Prof. Macalister, 
M.D. — Bi'j}. of Anthrojiol., 
Francis Gait on, M.A.,F.R.S. 

Prof. W. H. Flower, F.R.S.— 
Bc2). of AnthrojJol., Prof. 
Huxley, Sec. R.S. — Btp. 
of Anat. and Phydol., R. 
McDonnell, M.D., F.R.S. 

Prof. St. Geo]-ge Mivart, 
F.R.S.— 2)^/;. ofAntJirojJol, 
B. B. Tylor, D.C.L., F.R.S. 
— Bc^). of Anat. and P/nj- 
sioL, Dr. Pye- Smith. 

A. C. L. Giinther, M.D., F.R.S. 
• — Brp. of Anat. and Phy- 
siol., F. M. Balfour, M.A., 
F.R.S. — Bep. of Anthropol., 
F. W. Eudler,"r.G.S. 



Secretaries 



Dr. T. S. Cobbold, G. W. Firth, Dr. 
M. Foster, Prof. Lawson, H. T. 
Stainton, Rev. Dr. H. B. Tristram, 
Dr. E. P. Wright. 

Dr. T. S. Cobbold, Prof. M. Foster, 
E. Ray Lankester, Prof. Lawson, 
H. T Stainton, Rev. H. B. Tris- 
tram. 

Dr. T. S. Cobbold, Sebastian Evans, 
Prof. Lawson, Thos. J. Moore, H. 
T. Stainton, Rev. H. B. Tristram, 
C. Staniland Wake, E. Ray Lan- 
kester. 

Dr. T. R. Eraser, Dr. Arthur Gamgee, 
E. Ray Lankester, Prof. Lawson, 
H. T. Stainton, C. Staniland Wake, 
Dr. W. Rutherford, Dr. Kelburne 
King. 

Prof. Thiselton-Dyer,H. T. Stainton, 
Prof. Lawson, F. W. Rudler, J. H. 
Lamprey, Dr. Gamgee, E. Ray 
Lankester, Dr. Pye- Smith. 

Prof. Thiselton-Dyer, Prof. Lawson. 

R. M'Lachlan, Dr. Pye-Smith, E. 

Ray Lankester, F. W. Rudler, J. 

H. Lamprey. 
W.T. Thiselton- Dyer, R. 0. Cunning- 
ham, Dr. J. J. Charles, Dr. P. H. 

Pye-Smith, J. J. Murphy, F. W. 

Rudler. 
E. R. Alston, Dr. McKendrick, Prof. 

W. R. M'Nab, Dr. Martyn, F. "W. 

Rudler, Dr. P. H. Pye-Smith, Dr. 

"W. Spencer. 

E. R. Alston, Hyde Clarke, Dr. 
Knox, Prof. W. R. M'Nab, Dr. 
Muirhead, Prof. Morrison Wat- 
son. 



E. R. Alston, F. Brent, Dr. D. J. 
Cunningham, Dr. C. A. Kingston, 
Prof. W. R. M'Nab, J. B. Rowe, 
F. W. Rudler. 

Dr. R. J. Harvey, Dr. T. Hayden, 
Prof. AV. R. M'Nab, Prof. J. M. 
Purser, J. B . Rowe, F. W. Rudler. 



Arthur Jackson, Prof. W. R. M'Nab, 
J. B. Rowe, F. W. Rudler, Prof. 
Schafer. 



G. W. Bloxam, John Priestlej^ 
Howard Saunders, Adam Sedg- 
wick. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



xliii 



Date and Place 



1881. York. 



1882. Southamp- 
ton. 



Presidents 



Richard Owen, C.B., M.D., 

V.W.^.—Dep.of AnthropoL, 
Prof. W. H. Flower, LL.D., 
F.R.S. — Dej). of Anaf. and 
Fhysii)l., Prof. J. S. Burdon 
Sanderson, M.D., F.R.S. 
Prof. A. Gamgee, M.D., F.R.S. 
— Dep. of Zool. and Bot., 
Prof. M. A. Lawson, M.A., 
F.L.S. — Bep.of Anthropul., 
Prof. W. Boyd Dawkins, 
M.A., F.R.S. 



Secretaries 



G. W. Bloxam, W. A. Forbes, Rev. 
AV. C. Hey, Prof. W. R. M'Nab, 
W. North, John Priestley, Howard 
Saunders, H. E. Spencer. 



G. W. Bloxam, W. Heape, J. B. 
Nias, Howard Saunders, A. Sedg- 
wick, T. W. Shore, jun. 



ANATOMICAL AND PHYSIOLOGICAL SCIENCES. 

COMMITTEE OP SCIENCES, V.— ANATOMY AND PHYSIOLOGY. 

183.3. Cambridge jDr. Haviland iDr. Bond, Mr. Paget. 

1834. Edinburgh [Dr. Abercrombie |Dr. Roget, Dr. William Thomson. 

SECTION E (until 1847). — ANATOMY AND MEDICINE. 



183.5. Dublin 

183G. Bristol 

1837. Liverpool... 

1838. Newcastle 
183!). Birmingham 
1810. Glasgow ... 

18-11. Plymouth... 

1842. Manchester 

1843. Cork 

1844 York 



Dr. Pritchard 

Dr. Rosfet, F.R.S 

Prof. W. Clark, M.D 

T. E. Headlam, M.D 

John Yelloly, M.D., F.R.S.... 
James Watson, M.D 

P. M. Roget, M.D., Sec. R.S. 

Edward Holme, M.D., F.L.S. 
Sir James I'itcairn, M.D. ... 
J. C. Pritchard, M.D 



Dr. Harrison, Dr. Hart. 

Dr. Symonds. 

Dr. J. Carson, jun., James Long, 

Dr. J. R. W. Vose. 
T. M. Greenhow, Dr. J. R. W. Vose. 
Dr. G. 0. Rees, F. Ryland. 
Dr. J. Brown, Prof. Couper, Prof. 

Reid. 
Dr. J. Butter, J. Fuge, Dr. R. S. 

Sargent. 
Dr. Ghaytor, Dr. R. S. Sargent. 
Dr. John Popham, Dr. R. S. Sargent. 
I. Erichsen, Dr. R. S. Sargent. 



SECTION E. PHYSIOLOGY. 



184.5. Cambridge jProf. J. Haviland, M.D iDr. R. S. Sargent, Dr. Webster. 

1846. Southamp- jProf. Owen, M.D., F.R.S. ...{C. P. Keele, Dr. Laj-cock, Dr. Sar- 

ton. j I gent. 

1847. Oxford' ...[ Prof. Ogle, M.D., F.R.S Dr. Thomas K. Chambers, W. P. 

I i Ormerod. 

PHYSIOLOGICAL SUE.SECTIONS OF SECTION D. 

18.50. Edinburgh Prof. Bennett, M.D. , F.R.S.E. 

1855. Glasgow ...I Prof. Allen Thomson, F.R.S. 

1857. Dublin ; Prof . R. Harrison, M.D 

Sir Benjamin Brodie, Bart., 
F.R.S. 

Prof. Sharpey, M.D., Scc.R.S. 

1860. Oxford jProf. G. Rolleston, M.D.,;Dr. R. M'Donnell, Dr. Edward 

I F.L.S. I Smith. 

1861. Manchester Dr. Jolin Davy, F.R.S.L.& E.'Dr. W. Roberts, Dr. Edward Smith. 

1862. Cambridge | C. E. Paget, M.D IG. F. Helm, Dr. Edward Smith. 

' By direction of the General Committee at Oxford, Sections D and E were 
incorporated under the name of ' Section D — Zoology and Botany, including Phy- 
siology ' (see p. xl). The Section being then vacant was assigned in 1851 to 
Geography. 



1858. Leeds 

1859. Aberdeen 



Prof. J. H. Corbett, Dr. J. Struthers. 
Dr. R. D. Lj'ons, Prof. Redfern. 
C. G. Wheelhouse. 

Prof. Bennett, Prof. Redfern. 



xliv 



BEl'OET 1882. 



Date and Place 



1863. Newcastle 

1864. Bath 



1865. Binnino;hin.' 



Presidents 



Prof. Rolleston, M.D., F.R.S. 
Dr. Edward Smith, LL.D., 

F.E.S. 
Prof. Acland, M.D., LL.D., 

F.R.S. 



Secretaries 



Dr. D. Embleton, Dr. W. Turner. 
J. S. Bartrum, Dr. W. Turner. 

Dr. A. Fleming, Dr. P. Heslop, 
Oliver Pembleton, Dr. W. Turner. 



GEOGRAPHICAL AND ETHNOLOGICAL SCIENCES. 

[For Presidents and Secretaries for Geography previous to 18ol, see Section C, 
p. x-xxviii.] 

ETHNOLOGICAL SUBSECTIONS OF SECTION D. 



1846. Southampton 

1847. Oxford 

1848. Swansea ... 
184'.). Birmingham 
1850. Edinburgh 



1851. Ipswich ... 

1852. Belfast 

1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 

1858. Leeds 



Dr. Pritchard 

Prof. H. H. Wilson, M.A. 



Dr. King. 
Prof. Buckley. 
G. Grant Francis, 
Dr. E. G. Latham. 
Daniel Wilson. 



1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 



Vice-Admiral Sir A. Malcolm 
SECTION E. — GEOGRAPHT AND ETHNOLOGT. 

Sir R. L Murchison, F.R.S, 

Pres. R.G.S. 
Col. Chesney, R.A., D.C.L 

F.R.S. 
R. G. Latham, M.D., F.R.S. 



Sir R. L Murchison, D.C.L., 

F.R.S. 
Sir J. Richardson, M.D., 

F.R.S. 
Col. Sir H. C. Rawlinson, 

K.C.B. 
Rev. Dr. J. Henthorn Todd, 

Pres. R.I.A. 
Sir R.L Murchison, G.C.St.S., 

F.R.S. 

Rear - Admiral Sir James 
Clerk Ross, D.C.L., F.R.S. 

Sir R. I. Murchison, D.C.L.. 
F.R.S. 

John Crawfurd, F.R.S 

Francis Galton, F.R.S 



Sir R. L Murchison, K.C.B., 
F.R.S. 

Sir R. I. Murchison, K.C.B., 
F.R.S. 

Major-General Sir H. Raw- 
linson, M.P.,K.C.B., F.R.S. 

Sir Charles Nicholson, Bart., 
LL.D. 

Sir Samuel Baker, F.R.G.S. 



Capt. G. H. Richards, E.N., 
F.R.S. 



R. Cull, Rev. J. W. Donaldson, Dr. 

Norton Shaw. 
R. Cull, R. MacAdam, Dr. Norton 

Shaw. 
R. Cull, Rev. H. W. Kemp, Dr. 

Norton Shaw. 
Richard Cull, Rev. H. Higgins, Dr. 

Ihne, Dr. Norton Shaw. 
Dr. W. G. Blackie, R. Cull, Dr. 

Norton Shaw. 
R. Cull, F. D. Havtland, W. H. 

Rumsey, Dr. Norton Shaw. 
R. Cull, S. Ferguson, Dr. R. R. 

.Madden, Dr. Norton Shaw. 
R. Cull, Francis Galton, P. O'Calla- 

ghan, Dr. Norton Shaw, Thomas 

Wright. 
Richard Cull, Prof. Geddes, Dr. Nor- 
ton Shaw. 
Capt. Burrows, Dr. J. Hunt, Dr. C. 

Lempri^re, Dr. Norton Shaw. 
Dr. J. Hunt, J. Kingsley, Dr. Nor- 
ton Shaw, W. Spottiswoode. 
J. W. Clarke, Rev. J. Glover, Dr. 

Hunt, Dr. Norton Shaw, T. 

Wright. 
C. Carter Blake, Hume Greenfield, 

C. R. Markham, R. S. Watson. 

H. W. Bates, C. R. Markham, Capt. 

R. M. Murchison, T. Wright. 
H. W. Bales, S. Evans, G. Jabet, C. 

R. Markham, Thomas Wright. 
H. W. Bates, Rev. E. T. Cusins, R. 

H. Major, Clements R. Markham, 

D. W. Nash, T. Wright. 

H. W.Bates, Cyril Graham, Clements 
R. Markham, S. J. Mackie, E. 
Sturrock. 

T. Baines, H. W. Bates, Clements R. 
Markham, T. Wright. 



' Tide note on page xli. 



TKESIDENTS AND SECRETARIES OF THE SECTIONS. 



xlv 



Date and Place 



Presidents 



Secretaries 



SECTION E (continued). — geography. 



1860. Exeter 

1S70. Liverpool.. 

1871. Edinburgh 

1872. Brighton .. 

1873. Bradford .. 

1874. Belfast 

1875. Bristol 

1876. Glasgow .. 

1877. Plymouth.. 

1878. Dublin 

1879. Sheffield .. 

1880. Swansea .. 

1881. York 

1882. Southamp- 

ton. 



Sir Bartle Frere, K.C.B., 

LL.D., F.K.G.S. 
Sir R. I.Murchison, Bt.,K.C.B., 
LL.D., D.C.L., F.R.S., F.G.S. 
Colonel Yule, C.B., F.R.G.S. 

Francis Galton, F.R.S 

Sir Rutherford Alcock,K.C.B. 



H. W. Bates, Clements R. Markham, 

J. H. Thomas. 
H.W.Bates, David Buxton. Albert J. 

Mott, Clements R. Markham. 
Clements R. Markham, A. Buchan, 
J. H. Thomas, A. Keith Johnston. 
H. W. Bates, A. Keith Johnston, 

Rev. J. Newton, J. H. Thomas. 
H. W. Bates, A. Keith Johnston, 
Clements R. Markham. 
Major Wilson, R.E., F.R.S., E. G. Ravenstein, E. C. Rj'e, J. H. 

F.R.G.S. Thomas. 

Lieut. - General SIrachey, H. W. Bates, E. C. Rye, F. F. 
R.E.,C.S.L,F.R.S., F.R.G.S., \ Tuckett. 
F.L.S., F.G.S. 

Capt. Evans, C.B., F.R.S iH. W. Bates, E. C. Rye, R. Oliphant 

j AVood. 
Adm. Sir E. Ommannev, C.B., H. W. Bates, F. E. Fox, E. C. Rye. 
F.R.S., F.R.G.S., F.R.A.S. 

John Coles, E. C. Rye. 



Prof. Sir C. Wyville Thom- 
son, LL.D., F.R.S.L.&E. 

Clements R. Markham, C.B., 
F.R.S., Sec. R.G.S. 

Lieut.-Gen. Sir J. H. Lefro}', 
C.B., K.C.M.G., R.A., F.B.8., 
F.R.G.S. 

Sir J. D. Hooker, K.C.S.I., 

Sir R. Temple," Bart., G.C.S.L, 
F.R.G.S. 



H. W. Bates, C. E. D. Black, E. C. 

Rye. 
H. W. Bates, E. C. Rye. 



J. W. Barry, H. W. Bates. 
E. G. Ravenstein, E. C. Rye. 



18.S3. Cambridge 
1834. Edinburgh I 



STATISTICAL SCIENCE. 

COMMITTEE OF SCIENCES, VI. — STATISTICS. 

J. E. Drinkwater. 



Prof. Babbage, F.R.S 



Sir Charles Lemon, Bart., 



Dr. Cleland, C. Hope Maclean. 



SECTION F. STATISTICS. 



1835. Dublin. 

1836. Bristol. 



1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Pl3Tnouth... 

1842. Manchester 



1843. Cork. 

1844. York. 



1845. Cambridge 



Charles Babbage, F.R.S 

Sir Chas. Lemon, Bart., F.R.S. 

Rt. Hon. Lord Sandon 

Colonel Sykes, F.R.S 

Henry Hallam, F.R.S 

Rt. Hon. Lord Sandon, M.P., 

F.R.S. 
Lieut.-Col. Sykes, F.R.S 

G. W. Wood, M.P., F.L.S. ... 

Sir C. Lemon, Bart., M.P. ... 
Lieut.-Col. Sykes, F.R.S., 

F.L.S. 
Rt.Hon. the Earl Fitzwilliam 



W. Greg, Prof. Longtield, 

Rev. J. E. Bromby, C, B. Fripp, 

James Heywood. 
W. R. Greg, W. Langton, Dr. W. C. 

Tayler. 
W. Cargill, J. Heywood, W.R.Wood. 
F. Clarke, R. W. Rawson, Dr. W. C. 

Tayler. 
C. R. Baird, Prof. Ramsay, R. W. 

Rawson. 
Rev. Dr. Byrth, Rev. R. Luney, R. 

W. Rawson. 
Rev. R. Lunev, G. W. Ormerod, Dr. 

W. C. Tayler. 
Dr. D. Bullen, Dr. W. Cooke Tayler. 
J. Fletcher, J. Heywood, Dr. Lay- 
cock. 
J. Fletcher, Dr. W. Cooke Tayler 



xlvi 



HEPORT— 1882. 



Date and Place 



Presidents 



1846. 

1847. 

1848. 
1849. 

1850. 

1851. 

1852. 

1853. 
1854. 

1855. 



Southamp- G. K. Porter, F.R.S 

ton. 
Oxford Travers Twiss, D.C.L.. F.R.S. 



Swansea ... J. H. Vivian, M.P., F.R.S 
Birmingham Rt. Hon, Lord Lyttelton. 



Secretaries 



J. Fletcher, F. G. P. Neison, Dr. W. 

C. Ta}'ler, Rev. T. L. Shapcott. 
Rev. W. H. Cox, J. J. Danson, F. G. 

P. Neison. 
J. Fletcher, Capt. R. Shortrede. 
Dr. Finch, Prof. Hancock, F. G. P. 
Neison. 
Edinburgh Very Rev. Dr. John Lee, Prof. Hancock, J. Fletcher, Dr. J. 

V.P.R.S.E. Stark. 

Ipswich ... Sir John P. P.oileau, Bart. ... J. Fletcher, Prof. Hancock. 

Belfast His Grace the Archbishop of Prof. Hancock, Prof . Ingram, James 

' Dublin. , MacAdam, jun. 

Hull James Heywood, M.P., F.R.S. Edward Cheshire, W. Newmarch. 

Liverpool... Thomas Tooke, F.R.S E. Cheshire, J. T. Danson, Dr. W. H. 

Duncan, W. Newmarch. 
Glasgow ...R. Monckton Milnes, M.P. ... J. A. Campbell, E. Cheshire, W. New- 
I i march. Prof. R. H. Walsh. 

SECTION F (continued). — ECONOMIC SCIENCE AND STATISTICS. 



1856. Cheltenham 



1857. 
1858. 
1859. 
1800. 
L8G1. 

1802. 
1803. 

1804. 

1805. 

18G6. 

1867. 

1868. 

1809. 

1870. 

1871. 
1872. 
] 873. 
1874. 

1875. 

1876. 



Dublin 

Leeds 

Aberdeen . . . 

Oxford 

Manchester 



Cambridge 
Newcastle . 



Rt. Hon. Lord Stanley, M.P. 



His Grace the Archbishop of 

Dublin, M.R.LA. 
Edward Baines 



Col. Sykes, M.P., F.R.S 

Nassau W. Senior, M.A. ... 
William Newmarch, F.R.S., 



Edwin Chadwick, C.B 

William Tite, M.P., F.R.S. 



Bath William Farr, M.D., D.C.L. 

F.R.S. 
Birmingham Rt. Hon. Lord Stanley, LL.D., 

M.P. 
Nottin.oham Prof. J. E. T. Rogers 



Dundee .... 

Norwich .... 

Exeter 

Liverpool.. 

Edinburgh 
Brighton ... 
Bradford ... 
Belfast 



Bristol... 
Glasgow 



M. E. Grant Duff, M.P 

Samuel Brown, Prcs. Instit. 

Actuaries. 
Rt.Hon.SirStatfordH. Norlh- 

cote, Bart., C.B., M.P. 
Prof. W. Stanley Jevons, M.A. 

Rt. Hon. Lord Neaves 

Prof. Henry Fawcett, M.P. ... 
Rt. Hon. W. E. Forster, M.P. 
Lord 0"Hao'an 



James Heywood, M.A. , F.R.S. 

Pres.S.S. 
SirGeorge Cami^bell, K.C.S.I., 

M.P. 



Rev. C. H. Bromby, E. Cheshire, Dr. 

W. N. Hancock, W. Newmarch, W. 

M. Tartt. 
Prof. Cairns, Dr. H. D. Hutton, W. 

Newmarch. 
T. B. Baines, Prof. Cairns, S. Brown, 

Cai^t. Fishbourne, Dr. J. Strang. 
Prof. Cairns, Edmund Macrory, A. M, 

Smith, Dr. John Strang. 
Edmund Macrorv, ^V. Newmarch, 

Rev. Prof. J. E." T. Rogers. 
David Chadwick. Prof. R. C. Christie, 

E. Macrory, Rev. Prof. J. E. T. 

Rogers. 
H. D. Macleod, Edmund Macrory. 
T. Doubleday, Edmund Macrory, 

Frederick Purdy, James Potts. 

E. Jlacrory, E. T. Payne. F. Purdy. 

G. J. D. Goodman, G. J. Johnston, 

E. Macrory. 
R. Birkin, jun.. Prof. Leone Levi, E. 

Macrory. 
Prof. Leone Levi, E. Macrory, A. J. 

Warden. 
Rev. W. C. Davie, Prof. Leone Levi. 

Edmund Macrorv, Frederick Purdy, 

Charles T. D. Acland. 
Chas. R. Dudlej' Baxter, E. Macrorj-, 

J. Miles Moss. 
J. G. Fitch, James Meikle. 
J. G. Fitch, Barclay Phillips. 
.1. G. Fitch, Swire Smith. 
Prof. Donnell, Frank P. Fellows, 

Hans MacMordie. 

F. P. Fellows, T. G. P. Hallett, E. 
Macrory. 

A. M'Neel Caird, T. G. P. Hallett, Dr. 
W. Neilson Hancock, Dr. W. Jack. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



xlvii 



Date and Place 


Presidents 


Secretaries 


1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 

1880. Swansea ... 
1881 York 


Rt. Hon. the Earl Fortescue 
Prof. J. K. Ingram, LL.D., 

M.R.I.A. 
G. Shaw Lefevre, M.P., Pres. 

S.S. 

G. W. Hastings, M.P 

Rt. Hon. M. E. Grant Dufe, 

M.A., F.R.S. 
Rt. Hon. G. Sclater-Booth, 

M.P., F.R.S. 


W. F. Collier, P. Hallett, J. T. Pim. 
W. J. Hancock, C. Molloy, J. T. Pim. 

Prof. Adamson, R. E. Leader, C. 

Molloy. 
N. A. Humphreys, C. Molloy. 
C. Molloy, W." W. Morrell, J. F. 


1882. Southamp- 
ton. 


Moss. 
G. Baden Powell, Prof. H. S. Fox- 
well, A. Milnes, C. Molloy. 



1836. Bristol 

1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow .... 

1841. Plymouth 

1842. Manchester 



1843. Cork 

1844. York 

1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 



MECHANICAL SCIENCE. 

SECTION G. — MECHANICAL SCIENCE. 
Davies Gilbert, D.C.L., F.R.S. T. G. Bunt, G. T. Clark, W. West. 



Rev. Dr. Robinson 

Charles Babbage, F.R.S 

Prof. Willis, F.R.S., and Robt. 

SteiDhenson. 
Sir John Robinson 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich 



John Taylor, F.R.S 

Rev. Prof. Willis, F.R.S 

Prof. J. Macneill, M.R.LA. ... 

John Taylor, F.R.S 

George Rennie, F.R.S. 

Rev. Prof. Willis, M.A., F.R.S. 



Rev. Professor Walker, M.A., 

F.R.S. 
Rev. Professor Walker, M.A., 

F.R.S. 
Robert Stephenson, M.P., 

F.R.S. 

Rev. R. Robinson 

William Cubitt, F.R.S 

1852. Belfast John Walker, C.E., LL.D., 

F.R.S. 

1853. Hull William Fairbairn, C.E., 

F.R.S. 

1854. Liverpool... John Scott Russell, F.R.S. 



1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 



1858. Leeds .... 
1850. Aberdeen. 



1860. Oxford 

1861. Manchester 

1862. Cambridge 



W. J. Macquorn Rankine, 

C.E., F.R.S. 
George Eennie, F.R.S 

Rt. Hon. the Earl of Rosse, 

F.R.S. 
William Fairbairn, F.R.S. ... 
Rev. Prof. Willis, M.A., F.R.S. 

Prof . W. J. Macquorn Rankine, 

LL.D., F.R.S. 
J. F. Bateman, C.B., F.R.S. 

Wm. Fairbairn, LL.D., F.R.S. 



Charles Vignoles, Thomas Webster. 
R. Hawthorn, C. A^iguoles, T. 

Webster. 
W. Carjjmael, William Hawkes, T. 

Webster. 
J. Scott Russell, J. Thomson, J. Tod, 

C. Vignoles. 
Henry Chatfield, Thomas Webster. 
J. F. Bateman, J. Scott Russell, J. 

Thomson, Cliarles Vignoles. 
James Thomson, Robert Mallet. 
Charles Vianoles, Thomas Webster. 
Rev. W. T.' Kingsley. 
William Betts, jun., Charles Manby. 

J. Glynn, R. A. Le Mesurier. 

R. A. Le Mesurier, W. P. Struve 

Charles Manby, W. P. Marshall. 

Dr. Lees, David Stephenson. 

Jolm Head, Charles Manby. 

John F. Bateman, C. B. Hancock, 

Charles Manby, James Thomson. 
James Oldham, J. Thomson, W. 

Sykes Ward. 
John Grantham, J. Oldham, J. 

Thomson. 
L. Hill, jun., William Ramsay, J. 

Thomson. 
C. Atherton, B. Jones, jun., H. M. 

Jetferj-. 
Prof. Downing, AV.T. Doyne, A. Tate, 

James Thomson, Henry Wright. 
J. C. Dennis, J. Dixon, H. Wright. 
R. Abernethy, P. Le Neve Foster, H. 

Wright. 
P. Le Neve Foster, Rev. F. Harrison, 

Henry Wright. 
P. Le Neve Foster, John Robinson, 

H. Wright. 
W. BI. Fawcett, P. Le Neve Foster. 



xlviii 



REPORT — 1882. 



Date and Place 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton ... 

1873. Bradford ... 

lS7i. Belfast 

1875. Bristol 

1876. Glasgow ... 

1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 

1880. Swansea ... 

1881. York 



Presidents 



1882. Southamp- 
ton. 



Rev. Prof. Willis, M.A.,F.R.S. 

J. Hawkshaw, F.R.S 

Sir W. G. Armstrong, LL.D., 

F.R.S. 
Thomas Hawkslej", V.P.Inst. 

C.E., F.G.S. 
Prof .W. J. Macquorn Kankine, 

LL.D., F.R.S. 
G. P. Bidder, C.E., F.R.G.S. 

C. W. Siemens, F.R.S 

Chas. B. Viguoles, C.E., F.R.S. 

Prof. Fleeming Jenkin, F.R.S. 

F. J. Bramwell, C.E 

W. H. Barlow, F.R.S 

I 

I 

Prof. James Thomson, LL.D., 
! C.E., F.R.S.E. 
W. Froude, C.E., M.A., F.R.S. 

I 
C. W. Merrifield, F.R.S 

Edward Woods, C.E 

Edward Easton, C.E 

J. Robinson, Pres. Inst. Mech. 

Eng. 
James Abernethy, V.P. Inst. 

O.E., F.R.S.E. 
Sir W. G. Armstrons-, C.B., 

LL.D., D.C.L., F.R.S. 
John Fowler, C.E., F.G.S. ... 



Secretaries 



P. Le Neve Foster, P. Westmacott, 

J. F. Spencer. 
P. Le Neve Foster, Robert Pitt. 
P. Le Neve Foster, Henry Lea, W. 

P. Marshall, Walter May. 
P. Le Neve Foster, J. F. Iselin, M. 

0. Tarbotton. 
P. Le Neve Foster, John P. Smith, 

W. W. Urquhart. 
P. Le Neve Foster, J. F. Iselin, C. 

Manby, W. Smith. 
P. Le Neve Foster, H. Bauerman. 
H. Bauerman, P. Le Neve Foster, T. 

King, J. N. Shoolbred. 
H. Bauerman, Alexander Leslie, J. 

P. Smith. 
H. M. Brunei, P. Le Neve Foster, 

J. G. Gamble, J. N. Shoolbred. 
Crawford Barlow, H. Bauerman, 

E. H. Carbutt, J. C. Hawkshaw, 

J. N. Shoolbred. 
A. T. Atchison, J. N. Shoolbred, John 

Smyth, jun. 
W. R. Browne, H. M. Brunei, J. G. 

Gamble, J. N. Shoolbred. 
W. Bottomlev, jun., W. J. Millar, 

J. N. Shoolbred, J. P. Smith. 
A. T. Atchison, Dr. Merrifield, J. N. 

Shoolbred. 
A. T. Atchison, R. G. Svmes, H. T. 

AVood. 
A. T. Atchison, Emerson Bainbridge, 

H. T. Wood. 
A. T. Atchison, H. T. Wood. 

A. T. Atchison, J. F. Stephenson, 

H. T. Wood. 
A. V. Atchison, F. Churton, H. T. 

Wood. 



List of Evening Lectures. 



Date and Place 


Lecturer 


Subject of Discourse 


1842. Manchester 


Charles Vignoles, F.R.S 

Sir M. I. Brunei 


The Principles and Construction of 

Atmospheric Railways. 
The Thames Tunnel. 




R. I. Murchison 


The Geology of Russia. 

The Dinornis of New Zealand. 


1843. Cork 


Prof. Owen. M.D., F.R.S 

Prof. E Forbes, F.R.S 




The Distribution of Animal Life in 




Dr. Robinson 


the J5gean Sea. 
The Earl of Rosse"s Telescope. 


1844. York 


Charles Lyell, F.R.S 

Dr. Falconer, F.R.S 

G.B.Airy,F.R.S.,Astron.Royal 
R. L Murchison, F.R.S 


Geology of North America. 

The Gigantic Tortoise of the Siwalik 

Hills in India. 
Progress of Terrestrial Magnetism. 
Geology of Russia. 


1845. Cambridge 



LIST OB^ EVENING LECTURES. 



xlix 



Date and Place 



1846. Southamp- 
ton. 



1847. Oxford. 



1848. Swansea ... 



1849. Birmino-bam 



1830. Edinburofh 



1851. Ipswich 



1852. Belfast. 



1853. Hull. 



1854. Liverpool... 

1855. Glasgow ... 
1836. Cheltenliam 

1857. Dublin 

1858. Leeds 

1839. Aberdeen... 

1860. Oxford 

1801. Manchester 

1862. Cambridge 

1863. Newcastle 

1882. 



Lecturer 



Prof. Owen, M.D., F.R.S. 

Charles Lj'ell, F.Pt.S 

W. E. Grove, F.R.S 



Rev. Prof. B. Powell, F.R.S. 
Prof. M. Faraday, F.R.S 

Hugh E. Strickland, F.G.S.... 
John Percy, M.D., F.R.S 

W. Carpenter, M.D., F.R.S.... 

Dr. Faradav, F.R.S 

Rev. Prof. Willis, M.A., F.R.S. 



Subject of Discourse 



Prof. J. H. Bennett, M.D., 
F.R.S.E. 

Dr. Mantell, F.R.S 

Prof. R. Owen, JLD., F.R.S. 

G.B.Airy,F.R.S.,Astron. Royal 
Prof. G. G. Stokes, D.C.L., 

F.R.S. 
Colonel Portlo3k, R.E., F.R.S. 



Prof. J. Phillips, LL.D., F.R.S., 
F.G.S. 

Robert Hunt, F.R.S 

Prof. R. Owen, M.D., F.R.S. 
Col. E. Sabine, V.P.R.S 

Dr. W. B. Carpenter, F.R.S. 
Lieut. -Col. H. Rawlinson ... 

Col. Sir H. Rawlinson 



W. R. Grove, F.R.S 

Prof. W. Thomson, F.R.S ... 
Rev. Dr. Livingstone, D.C.L. 
Prof. J. Pliillips.LL.D., F.R.S. 
Prof. R. Owen, M.D., F.R.S. 
Sir R. I. Murchison, D.C.L... . 
Rev. Dr. Robinson, F.R.S. ... 

Rev. Prof. Walker, F.R.S. ... 
Captain Sherard Osborn, R.N. 
Prof.W. A. Miller, M.A., F.R.S. 
G.B.Air}',F.R.S.,Astron. Royal 
Prof. Tyndall, LL.D., F.R.S. 

Prof. Odling, F.R.S 

Prof. Williamson, F.R.S 



Fossil Mammalia of the British Isles. 

Vallej- and Delta of the Mississijipi. 

Propert ies of the Explosive substance 
discovered by Dr. Schonbein ; also 
some Researches of his own on the 
Decomposition of Water bj^ Heat. 

Shooting Stars. 

Magnetic and Diamagnetic Pheno- 
mena. 

The Dodo (Bidiis inrjitus). 

Metallurgical Operations of Swansea 
and its neighbourhood. 

Recent Microscopical Discoveries. 

Mr. Gassiot's Batterj\ 

Transit of different Weights with 
varying velocities on Railways. 

Passage of the Blood through the 
minute vessels of Animals in con- 
nexion with Nutrition. 

Extinct Birds of New Zealand. 

Distinction between Plants and Ani- 
mals, and their chansics of Form. 

Total Solar Eclipse of July 28, 1851. 

Recent discoveries in the properties 
of Light. 

Recent discovery of Rock-salt at 
Carrickfergus, and geological and 
pract ical considerat ions connect ed 
with it. 

Some iseculiar Phenomena in the 
Geology and Physical Geographj- 
of Yorkshire. 

The present state of Photography. 

Anthropomorphous Apes. 

Progress of researches in Terrestrial 
Magnetism. 

Characters of Species. 

Assyrian and Babj-lonian Antiquities 
and Ethnology. 

Recent Discoveries in Assj-ria and 
Babj'lonia, with the results of 
Cuneiform research uj) to tl.eiDre- 
sent time. 

Correlation of Physical Forces. 

The Atlantic Telegraph. 

Recent Discoveries in Africa. 

The Ironstones of Yorkshire. 

The Fossil Mammalia of Australia. 

Geology of the Northern Highlands. 

Electrical Discharges in highly 
rarefied Media. 

Phj'sical Constitution of the Sun. 

Arctic Discovery. 

Spectrum Analysis. 

The late Eclipse of the Sun. 

The Forms and Action of Water. 

Organic Chemistry. 

The Chemistry of the Galvanic Bat- 
tery considered in relation to Dy- 
namics. 



EEPORT 1882. 



Date and Place 



1863. Newcastle 

(ft'Mf.) 

1864. Bath 



Lecturer 



1865. Birmingham 



1866. Nottingham 



1867. Dundee. 



1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton ... 

1873. Bradford ... 

1874. Belfast 



1878. Dublin 



1881. York. 



1875. Bristol 

1876. Glasgow ... 

1877. Plymouth.., 



1879. Sheffield .. 

1880. Swansea .. 



James Glaisher, F.E.S... 

Prof, Eoscoe, F.R.S 

Dr. Livingstone, F.ll.S. 
J. Beete Jukes, F.R.S. ... 



William HiTggins, F.R.S. ... 

Dr. J. D. Hooker, F.R.S 

Archibald Geikie, F.R.S 

Alexander Herschel, F.R.A.S. 

J. Fergusson, F.R.S 

Dr. W. Odling, F.R.S 

Prof. J. Phillips, LL.D., F.R.S. 
J. Norman Lockj-er, F.R.S.... 

Prof. J. Tjmdall, LL.D., F.R.S. 
Prof .W. J. Macquorn Rankine, 

LL.D., F.R.S. 
F. A. Abel, F.R.S 

E. B. Tylor, F.R.S 

Prof. P. Martin Duncan, M.B., 

F.R.S. 
Prof. W. K. Clifford 



Subject of Discourse 



1883. Southamp- 
ton. 



Prof. W. C.Williamson, F.R.S. 
Prof. Clerk Maxwell, F.R.S. 
Sir John Lubbock,Bart.,M.P., 

F.R.S. 
Prof. Huxley, F.R.S 

W.Spottiswoode,LL.D.,F.R.S. 

F. J. Bramwell, F.R.S 

Prof. Tait, F.R.S.E 

Sir Wyville Thomson, F.R.S. 
W. Warington Smyth, M.A., 
F.R.S. 

Prof. Odling, F.R.S 

G. J. Romanes, F.L.S 

Prof. Dewar, F.R.S 

W. Crookes, F.R.S 

Prof. E. Ray Lankester, F.R.S. 
Prof. AV. Boyd Dawkins, 
F.R.S. 

Francis Galton, F.R.S 

Prof. Huxley, Sec. R.S. 

W. Spottiswoode, Pres. R.S. 

Prof. Sir Wm. Thomson, F.R.S. 
Prof. H. N. Moseley, F.R.S. 



The Balloon Ascents made for the 
British Association. 

The Chemical Action of Light. 

Recent Travels in Africa. 

Probabilities as to the position and 
extent of the Coal-measures be- 
neath the red rocks of the Mid- 
land Counties. 

The results of Spectrum Analysis 
applied to Heavenly Bodies. 

Insular Floras. 

The Geological Origin of the present 
Scenery of Scotland. 

The present state of knowledge re- 
garding Meteors and Meteorites. 

Archieology of the early Buddhist 
Monuments. 

Reverse Chemical Actions. 

Vesuvius. 

The Physical Constitution of the 
Stars and Nebulse. 

The Scientific Use of the Imagination. 

Stream-lines and Waves, in connec- 
tion with Naval Architecture. 

Some recent investigations and ap- 
plications of Explosive Agents. 

The Relation of Primitive to Modern 
Civilization. 

Insect Metamorpliosis. 

The Aims and Instruments of Scien- 

titic Thought. 
Coal and Coal Plants. 
Molecules. 
Common Wild Flowers considered 

in relation to Insects. 
The Hj'pothesis that Animals are 

Automata, and its History. 
The Colours of Polarized Light. 
Railway Safety Apijliances. 
B^orce. 

The Challenficr Expedition. 
The Physical Phenomena connected 

with the Mines of Cornwall and 

Devon. 
The new Element, Gallium. 
Animal Intelligence. 
Dissociation, or Modern Ideas of 

Chemical Action. 
Radiant Matter. 
Degeneration. 
Primeval Man. 

Mental Imagery. 

The Rise and Progress of Palaeon- 
tology. 

The Electric Discharge, its Forms 
and its Fimctions. 

Tides. 

Pelagic Life. 



LECTURES TO THE OPERATIVE CLASSES. 



Lectures to the Operative Classes, 



Date and Place 


Lecturer 


Subject of Discourse 


1867. 


Dundee 


Prof. J. Tyndall, LL.D.,F.E.S. 


Matter and Force. 


1868. 


Norwich ... 


Prof. Huxley, LL.D., F.R.S. 


A Piece of Chalk. 


1869. 


Exeter 


Prof. Miller, M.D., F.R.S. ... 


Experimental illustrations of the 
modes of detecting the Composi- 
tion of the Sun and other Heavenly 
Bodies by the Spectrum. 


1870. 


Liv'erpool... 


Sir .John Lubbock, Bart.,M.P., 
F.R.S. 


Savages, 


1872. 


Brighton ... 


W.Spottiswoode,LL.D.,F.R.S. 


Sunshine, Sea, and Sky. 


1873. 


Bradford ... 


C. W. Siemens, D.C.L., F.R.S. 


Fuel. 


1874. 


Belfast ...... 


Prof. Odling, F.R.S 


The Discovery of Oxygen. 


1875. 


Bristol 


Dr. W. B. Carpenter, F.R.S. 


A Piece of Limestone. 


1876. 


Glasgow ... 


Commander Cameron, C.B., 
R.N. 


A Journej' through Africa. 


1877. 


Plymouth... 
Sheffield 


W. H. Preece 


Telegraphj' and the Telephone. 
Electricity as a iMotive Power. 
The North-East Passage. 


1879. 


W. E. Ayrton 


1880. 


^-^ LX V^ L^A V^ A\„V • 4 • 

Swansea ... 


H. Seebohm, F.Z.S 


1881. 


York 


Prof. Osborne Reynolds, 
F.R.S. 


Raindrops, Hailstones, and Snow- 
flakes. 






1882. 


Southamp- 


John Evan.?, D.C.L. Treas.R.S. 


Unwritten History, and how to 




ton. 




read it. 



lii 



OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE 
SOUTHAMPTON MEETING. 

SECTION A. — MATHEMATICAL AND PHYSICAL SCIENCE. 
President.— K\ght Hon. Professor Lord Rayleigh, M.A., F.R.S. 

Vice-Presidents.— G. H. Darwin, M.A., F.R.S. ; Professor W. G. Adams, 
M.A., F.R.S. ; Dr. Werner Siemens ; J. W. L. Glaister, M.A., F.R.S. ; 
W. Spottiswoode, D.C.L., Pres. R.S. ; Professor Cajley, F.R.S.; Sir 
W. Thomson, D.C.L., F.R.S. 

Secretaries.— W. M. Hieks, M.A. ; Professor 0. J. Lodge, D.Sc. ; D. 
McAlister, M.A., M.B., B.Sc. (Eccorder); Rev. G. Richardson, M.A. 

SECTION B. — CHEMICAL SCIENCE. 

President. — Professor G. D. Liveing, M.A., F.R.S. 

Vice-Presidents. — P. A. Abel, C.B., F.R.S.; Profe.=sor Baumhauer; W. 
Crookes, F.R.S. ; Profes.sor J. Ci-afts ; Professor De Chaumont, F.R.S. ; 
J. H. Gladstone, Ph.D., F.R.S.; A. G. Vernon Harcourt, M.A., 
F.R.S. ; Dr. Longstaff, F.C.S. ; Professor H. E. Roscoe, Ph.D., 
LL.D., F.R.S.; W. Weldon, F.R.S.; Professor A. W. Williamson, 
LL.D., F.R.S. 

Secretaries. — Harold B. Dixon, ]\I.A. ; Professor P. Phillips Bedson, 

D.Sc. (Recorder). 

SECTION C. — GEOLOGY. 

President.— U. Etheridge, F.R.S. 

Vice-Presidents.— 3. Evans, D.C.L., F.R.S. ; Professor T. R. Jones, F.R.S. ; 
W. Pengelly, F.R.S. ; Professor J. Prestwich, M.A., F.R.S. 

Secretaries.— T. W. Shore, F.G.S. ; W. Topley, F.G.S. (Recorder); 
E. Westlake, F.G.S. ; W. Whitaker, B.A., F.G.S. 

SECTION D. — BIOLOGY. 

President. — Professor A. Gamgce, M.D., F.R.S. 

Vice-Presidents.— Pmii'ssov W. Boyd Davvkin.-, F.R.S. ; Dr. G. E. Dobson, 
F.L.S. ; Dr. J. Evans, F.R.S. ; tr. U. Foster, F.R.S. ; Sir .T. D. Hooker, 
F.R.S.; Professor M. A. Luwson, F.L.S. ; Sir J Lubbock, F.R.S.; 



OFFICERS OF SECTIONAL COMMITTEES. liii 

Professor J. D. Macdonald, M.D., F.R.S. ; Professor Moseley, F.R.S. ; 
P. L. Sclater, F.R.S. ; Dr. Allen Thomson, F.R.S. ; Professor Da Bois- 
Reymond. 

Secretaries. — Gr. W. Bloxani, M.A., F.L.S. (Recorder); George Haslam, 
M.D. ; W. Heape; W. Hurst ; J. B. Nias, B.A. ; Howard Saunders, 
F.L.S. (Becorder); A. Sedgwick, M.A. (Recorder); T. W. Shore, 
jun., B.Sc. 

SECTION E. — GEOGKAPHT. 

President.— Sir R. Temple, Bart., G.C.S.I., F.R.G.S. 

Vice-Presidents. — H. W. Bates, F.R.S.; Major-General A. C. Cooke, 
R.E., C.B. ; Sir F. J. Evans, K.C.B., F.R.S. ; Sir Joseph D. Hooker, 
K.C.S.I., C.B., F.R.S. ; Admiral Sir Erasmus Ommanney, C.B., F.R.S. ; 
Colonel Sir Oliver St. John, R.E., K.C.S.I. 

Secretaries. — B. G. Ravenstein ; E. C. Rye (Recorder). 



SECTION F. — ECONOMIC SCIENCE AND STATISTICS. 

President.— Right Hon. G. Sclater-Booth, M.P., F.R.S. 

Vice-Presidents. — W. E. Darwin ; R. H. Inglis Palgrave ; the Mayor of 
Southampton ; Professor Leone Levi ; Hyde Clarke. 

Secretaries. — Professor H. S. Foxwell, M.A. ; A. Milnes, M.A. ; Con- 
stantine Molloy, M.A. (Recorder) ; George Baden Powell, M.A. 

SECTION G. — MECHANICAL SCIENCE. 

President.- John Fowler, C.E., F.G.S. 

Vice-Presidents.— A. Giles ; W. H. Preece, F.R.S. ; W. H. Barlow, F.R.S.; 
Sir F. J. Bramwell, F.R.S.; Sir J. Hawkshaw, F.R.S.; Captain 
Douglas Galton, C.B., F.R.S. ; T. Hawksley, F.R.S. ; F. J. Bateman, 
F.R.S.; Sir W. G. Armstrong, C.B., F.R.S. 

\ Secretaries.— A. T. Atchison, M.A. ; F. Churton; H. T. Wood, B.A. 
I (Recorder), 



liv 



REPORT — 1882. 

Table showing the Attendance and Receipts 



Date of Meeting 


Where held 


Presidents 




Old Life 
Members 


New Life 
Members 


1831, Sept. 27 ... 

1832, June 19 ... 

1833, June 25 ... 

1834, Sept. 8 ... 

1835, Aug. 10 ... 

1836, Aug. 22 ... 

1837, Sept. 11 ... 

1838, Aug. 10 ... 

1839, AiTg. 26 ... 

1840, Sept, 17 ... 

1841, July 20 ... 

1842, .June 23 ... 

1843, Aug. 17 ... 

1844, Sept. 26 ... 

1845, June 19 ... 

1846, Sept, 10 ... 

1847, June 23 ... 

1848, Aug. 9 ... 

1849, Sept. 12 ... 

1850, July 21 ... 

1851, July 2 ... 

1852, Sept. 1 ... 

1853, Sept. 3 ... 

1854, Sept. 20 ... 

1855, Sept. 12 ... 

1856, Aug. 6 ... 

1857, Aug. 26 ... 

1858, Sept, 22 ... 

1859, Sept. 14 ... 

1860, June 27 ... 

1861, Sept. 4 .. 

1862, Oct. 1 ... 

1863, Aug. 26 ... 

1864, Sept. 13 ... 

1865, Sept. 6 ... 

1866, Aug. 22 ... 

1867, Sept. 4 ... 
18i;8, Aug. 19 ... 
'1869, Aug. 18 ... 

1870, Sept. 14 ... 

1871, Aug. 2 ... 

1872, Aug. 14 ... 

1873, Sept. 17 .. 

1874, Aug. 19 ... 

1875, Aug. 25 ... 

1876, Sept. 6 ... 

1877, Aug. 15 ... 

1878, Aug. 14 ... 

1879, Aug. 20 ... 

1880, Aug. 25 ... 

1881, Aug. 31 ... 

1882, Aug. 23 ... 

i 


York 


The Earl Fitzwilliam, D.C.L. 
The Eev. W. Buckland, F.K.S. 
The Kev. A. Sedgwick, F.R.S. 

Sir T. M. Brisbane, D.C.L 

The Rev. Provost Lloyd, LL.D. 
The Marquis of Lansdowne . . . 
The Earl of Burlington, F.E.S. 
The Duke of Northumberland 
The Eev. W. Vernon Harcourt 
The Marquis of Breadalbane... 
The Eev. W. Whewell, F.E.S. 

The Lord Francis Eaerton 

The Earl of Eosse, F.E.S 

The Eev. G. Peacock, D.D. ... 
Sir John F. W. Herschel, Bart. 
Sir Eoderick I. Murchison,Bart. 

Sir Eobert H. Inglis, Bart 

The Marquis of Northampton 
The Eev. T. E. Eobinson, D.D. 

Sir David Brewster, K.H 

G. B. Airy, Astronomer Eo\-al 
Lieut.-General Sabine, F.E.S. 

William Hopkins, F.E.S 

The Earl of Harrowby, F.E.S. 
Tlie Duke of Argyll, F.E.S. ... 
Prof. C. G. B. Danbeny, M.D. 
The Eev.Humphrey Lloyd, D.D. 
Eichard Owen, M.D., D.C.L.... 
H.E.H. the Prince Consort ... 
The Lord Wrottesley, M.A. .. 
WilliamFairbairn,LL.D.,F.E.S. 
The Eev. Prof essor AVillis, i\I.A. 
Sir William G.Armstrong, C.B. 
Sir Charles Lyell, Bart., M.A. 
Prof. J. Phillips, M.A., LL.D. 
William E. Grove, Q.C., F.E.S. 
The Duke of Buccleuch,K.C.B. 
Dr. Joseph D. Hooker, F.E.S. 

Prof. G. G. Stokes, D.C.L 

Prof. T. H. Huxley, LL.D 

Prof. Sir W. Thomson, LL.D. 
Dr. W. B. Carpenter, F.E.S. ... 
Prof. A. W. Williamson, F.E.S. 
Prof. J. Tyndall, LL.D., F.E.S. 
SirJohnHawkshaw,C.E.,F.E.S. 
Prof. T. Andrews, M.D., F.E.S. 
Prof. A. Thomson, M.D., F.E.S. 
W. Spottiswoode, M.A., F.R.S. 
Prof.G. J. Allman, M.D., F.E.S. 
A. C. Eamsay, LL.D., F.E.S.... 
Sir John Lubbock, Bart., F E.S. 
Dr. C. W. Siemens, F.E.S 


169 

303 

109 

226 

313 

241 

314 

149 

227 

235 

172 

164 

141 

238 

194 

182 

236 

222 

184 

286 

321 

239 

203 

287 

292 

207 

167 

196 

204 

314 

246 

245 

212 

162 

239 

221 

173 

201 

184 

144 

272 

178 


65 
169 
28 
150 
36 
10 
18 
3 
12 
9 
8 
10 
13 
23 
33 
14 
15 
42 
27 
21 
113 
15 
36 
40 
44 
31 
25 
18 
21 
39 
28 
36 
27 
13 
36 
35 
19 
18 
16 
11 
28 
17 


Oxford 


OaTnhrido*e 




Dublin 


Bristol 




Newcastle-on-Tyne 


(rlnscow 




Manchester 


Cork 

York 


Southampton 

Oxford 


Swansea 




Edinburgh 


Ins wich 


Belfast 


Hull 


LiverDOol 


Glasgow 


Cheltenh.am 

Dublin 


Leeds 


Aberdeen 

Oxford 


Manchester 


Cambrid"e 


Newcastle-on-Tyne 
Bath 


Birmingham 


Nottingham 


Dundee 


Norwich 


Exeter 


Liverpool 


Edinburgh 


Brighton 


Bradford 


Belfast 


Bristol 


Glasarow 


Plymout h 


Dublin 


Sheffield 


Swansea 


York 


Southampton 



ATTENDANCE AND RECEIPTS AT ANNUAL MEETINGS. 



Iv 



at Annual Meetings 


of the Association. 










Attended by 


Amount 

received 

during the 

Meeting 


Sums paid on 

Account of 

Grants for 

Scientific 

Purposes 


Year 


Old 

Annual 

Members 


New 

Annual 

Members 


Asso- 
ciates 


Ladies 


For- 
eigners 


Total 














£ s. d. 


£ s. d. 




46 
75 
71 
45 
94 
65 
107 
54 


::: 

317 

376 

185 

190 

22 

39 

40 

25 




1100* 

60* 
331* 
160 
260 
172 
196 
203 
197 


34 
40 

28 

35 
36 
53 
15 


353 

900 
1298 

1350 
1840 
2400 
1438 
1353 
891 
1315 

1079 

857 

1320 

819 






1831 
1832 
1833 
1834 
1835 
1836 
1837 
1838 
1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 
1848 
















"20' "6" "o 

167 

435 

922 12 6 

932 2 2 

1695 11 

1546 16 4 

1235 10 11 

1449 17 8 

1665 10 2 

981 12 8 

831 9 9 

685 16 

208 5 4 

275 1 8 
















"'9t 

407 

270 

495 

376 














707 'o'o 


93 


33 


447 


237 


22 


1071 


963 


159 19 6 


1849 


128 


42 


610 


273 


44 


1241 


1085 


345 18 


1850 


61 


47 


244 


141 


37 


710 


620 


391 9 7 


1851 


6i> 


60 


510 


292 


9 


1108 


1085 


304 6 7 


1852 


56 


67 


367 


236 


6 


876 


903 


205 


1853 


121 


121 


765 


624 


10 


1802 


1882 


380 19 7 


1854 


142 


101 


1094 


543 


26 


2133 


2311 


480 16 4 


1855 


104 


48 


412 


346 


9 


1115 


1098 


734 13 9 


1856 


156 


120 


900 


■669 


26 


2022 


2015 


507 15 4 


1857 


111 


91 


710 


509 


13 


1698 


1931 


618 18 2 


1858 


125 


179 


1206 


821 


22 


2564 


2782 


684 11 1 


1859 


177 


59 


636 


463 


47 


1689 


1604 


766 19 6 


1860 


184 


125 


1589 


791 


15 


3138 


3944 


1111 5 10 


1861 


150 


57 


433 


242 


25 


1161 


1089 


1293 16 6 


1862 


154 


209 


1704 


1004 


25 


3335 


3640 


1608 3 10 


1863 


182 


103 


1119 


1058 


13 


2802 


2965 


1289 15 8 


1864 


215 


149 


766 


508 


23 


1997 


2227 


1591 7 10 


1865 


218 


105 


960 


771 


11 


2303 


2469 


1750 13 4 


1866 


193 


118 


1163 


771 


7 


2444 


2613 


1739 4 


1867 


226 


117 


720 


682 


45t 


2004 


2042 


1940 


1868 


229 


107 


678 


600 


17 


1856 


1931 


1 622 


1869 


303 


195 


1103 


910 


14 


2878 


3096 


1572 


1870 


311 


127 


976 


754 


21 


2463 


2575 


1472 2 6 


1871 


280 


80 


937 


912 


43 


2533 


2649 


1285 


1872 


237 


99 


796 


601 


11 


1983 


2120 


1685 


1873 


232 


85 


817 


630 


12 


1951 


1979 


1151 16 


1874 


307 


93 


884 


672 


17 


2248 


2397 


960 


1875 


331 


185 


1265 


712 


25 


2774 


3023 


1092 4 2 


1876 


238 


59 


446 


283 


11 


1229 


1268 


1128 9 7 


1877 


290 


93 


1285 


674 


17 


2578 


2615 


726 16 6 


1878 


239 


74 


529 


349 


13 


1404 


1425 


1080 11 11 


1879 


171 


41 


389 


147 


12 


915 


899 


731 7 7 


1880 


313 


176 


1230 


514 


24 


2557 


2689 


476 3 1 


1881 


253 


79 


516 


189 


21 


1253 


1286 


1126 1 11 


1882 




t T 


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of Adn 


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ted by purch 
tions only. 


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XI 


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OFFICERS AND COUNCIL, 1882-83. 



PRESIDENT. 

C. W. SIEMENS, Esq., D.C.L., LL.D., F.R.S., F.C.S., M.T.C.E. 

VICE-PRESIDENTS. 



Major-Gciieral A. C. Cooke, R.E., C.B., F.R.G.S., 
Director-General of the (Jrduiuice Survey. 

Wyxdham S. Pohtal, Esq. 

Professor Puestwich, M.A., F.R.S., F.G.S., F.C.S. 

Philip Lutley Scxateii, Esq., M,A., Ph. D., 
F.R.S., F.L.S., F.G.S. 



The Right Hon. the Lord Mount-Tkjiple. 

Captain Sir F. J. EVAXS, K.C.B., F.R.S., F.R.A.S., 
F.R.G.S., Hydrographer to the Ailmiralty. 

F. A. Abel, Esq., C.B., F.R.S., V.P.C.S., Director of 
the Chemical Establishment of the War Depart- 
ment. 

Professor De Chaumo.nt, M.D., F.R.S. 

PRESIDENT ELECT. 
ARTHUR CAYLET, Esq., LL.D., F.R.S., V.P.R.A.S., Sadlerian Professor of JIathematics in the University 

of Cambridge. 

VICE-PRESIDENTS ELECT. 

The Right Hon. the EAiiL of Derby, M.A., LL.D., F.R.S., F.R.G.S. 

The Right Hon. tlie Eaul of CiiAWFoun and Lalcahuep, LL.D., F.R.S., F.R.A.S. 

The Right Hon. the Earl of La'ihom. 

Professor J. G. Grel.;n'\voud, LL.D. 

Professor H. E. RoscoE, B.A., Ph.D., LL.D., F.R.S., F.C.S. 

Professor H. J. S. Smith, M.A., LL.D., F.R.S., P.R.A.S., F.C.S. 

LOCAL SECRETARIES FOR THE MEETING AT SOUTHPORT. 
J H. Ellis, Es i. Dr. Veukon'. T. W. Wili.i.s, Esq. 

LOCAL TREASURER FOR THE MEETING AT SOUTHPORT. 

The Mayor of SouTHroiiT. 

ORDINARY MEMBERS OF THE COUNCIL. 



Adams, Professor W. G , F.R.S. 
Bateman, J. F., Esq., C.E., F.R.S. 
Cayley, Professor, F.R.S. 
Dabwin, F., Esq., F.R.S. 
Dawki.ns, Professor W. Boyd, F.R.S. 
De la Rue. Warren, Esq., F.R.S. 
Evans, Captain Sir F. J., K.C.B., F.R.S. 
Flower, Professor W. H., F.R.S. 
Gladstone, Dr. J. H., F.R.S. 
Glaisuer, J. W. L., Esq., F.R.S. 
H.'i.RCOURT, A. G. "Vernon. Esq., F.R.S. 
Hastings, G. W., Esq., M.P. 
Hawkshaw, J. Clai:ke, Esq., F.G.S. 



Heywood, J., Esq., F.R.S. 

Huggins, W., Esq., F.K.S. 

Hughes, Professor T. McK., F.G.S. 

Jeffreys, Dr. J. Gwyn, F.K.S. 

Pengelly, W., Esq., F.K.S. 

Perkin, W. H., Esq., F.R.S. 

PiiESTWIcii, Professor, F.R.S. 

Rayleigh, Lord, F.K.S. 

Sanderson, Prof. J. S. Burdon, F.R.S. 

Smith, Professor H. J. S., F.R.S. 

SORBY, Dr. H. C, F.R.S. 

Thuillier, Geu. Sir H. E. L., C.S.I., F.R.S. 



GENERAL SECRETARIES. 
Capt. Douglas Galton, C.B., D.C.L., F.R.S., F.G.S., 12 Chester Street, Grosvenor Place, London, S.W. 
A. G. VhRNON Harcourt, Esq., M.A., F.R.S., F.C.S., Cowley Grange, Oxford. {Nominuhd by llie 
Council.) 

SECRETARY. 
Professor T. G. Bonney, il.A., F.R.S., F.S.A., F.G.S., 22 Albemarle Street, Loudon, W. 

GENERAL TREASURER. 
Professor A. W. Williamson, Ph.D., LL.D., F.R.S., F.C.S., University College, London, W.C. 
EX-OFFICIO MEMBERS OF THE COUNCIL. 
The Trustees, the President and President Elect, the Presidents of former years, the Vice-Prc.'idents and 
Vice-Presidents Elect, the General and Assistant General Secretaries for the present and forn.er years, 
the Secretary, the General Treasurers for the present and former years, and the Local Treasuieraud 
Secretaries for the ensuing Meeting. 

TRUSTEES (PERMANENT). 
General Sir Edward Sabine, K.C.B., R.A., D.C.L., F.R.S. 
Sir John Lubbock, Bart., M.P., D.C.L., LL.D., F.K.S., Pres.L.S. 
William Si-uTOSWOode, Esq., M.A.,D.C.L., LL.D., Pres. R.S. 



PRESIDENTS OF FORMER YEARS. 



Tlie Duke of Devonshire, K.G. 
Sir G. B. Ah-y, K.i'.B., F.R.S. I 

General Su- E. Sabine, K.C.B. 
The Duke of Aryyll, K.T. 
Dr. Richard Owen, U.B., F.R.S. 
Sir W. U. Annstruntr, C.B., LL.D. 
Sir William R. Grove, F.R.S. I 

The Duke of Bu.cleuch, K.G. | 



Sir Joseph D. Hooker, K.C.S.I. 
Prof. Stokes, D.C.L., Sec. R.S. 
Prof. Huxley, LL.D., F.R.S. 
Prof. Sir Wm. Tliomson, D.C.L. 
Dr. Carpenter, C.B., F.R.S. 
Prof. Williamson, Ph.D., F.R S. 
Prof. Tyndall, D.O.L., F.R.S. 
Sir John Hawkshaw, C.E., F.R.S. 



Dr. T. Andrews, F.R.S. 
Dr. Allen Thomson, F.R.S. 
W. Spottiswoode, Esq., Pres. R.S. 
Prof. AUman, M.D., F.R.S. 
Sir A. C. Ramsay, LL.D., F.R.S. 
Sir John Lubbock, Bart., F.R.S. 



GENERAL OFFICERS OF FORMER YEARS. 



F. Galton, Esq., F.R.S. 
Dr. T. A. Hirst, F.R.S. 
Gen. Sir E. Sabine, K.C.B., F.R.S. 



Dr. W. J. Russell, F.R.S. 



W. Spottiswoode, Esq., Pres. K.3. 
Dr. Michael Foster, Sec. R.S. 

AUDITORS. 
Professor G. C. Foster. F.R.S. 



G. Griffith, Esq., M.A., F.C.S. 
P. L. Sclater, Esq., F.R.S. 



1 G. Griffith, Esq., M.A., F.C.S. 



Iviii 



REPORT OF THE COUNCIL. 

Report of the GouncAl for the year 1881-82, presented to tlio General 
Committee at Southamjjton, on Wednesday, August 23, 1882. 

Tlie Council have received reports during the past year from the 
General Treasurei% and his account for the year will be laid before the 
General Committee this day. 

Since the meeting at York the following have been elected Corre- 
sponding Members of the Association : — • , 

Barker, Professor G. F. 
Cooke, Px'ofessor J. P. 
Eads, Captain J. B. 



Gariel, M. 
Halphen, M. 
Hall, Dr. B. H. 
Hubrecht, Dr. A. A. W. 



Johnson, Professoi' "W. "W. 
Marsh, Professor O. C. 
Rowland, Professor H. A. 
Stephanos, M. 
Sturm, Professor. 
Whitney, Professor H. M. 



It is with the deepest regret that the Council announce the untimely 
death of Professor F. M. Balfour, F.R.S., so lately appointed a General 
Secretary. In him science has lost a student of i-are genius and un- 
wearied industry, the Association one who would have served it well and 
ably. 

In respect of the Resolution referred by the General Committee : — 
' That the Council be I'equested to consider the number and position of 
delegates from Scientific Societies, and the regulations which should 
be adopted for governing their relations to the Association,' the Council 
beg leave to make the following recommendations to the General Com- 
mittee :■ — (1) The omission in the rules (General Committee, Class B 
Temporaiy Members § 1) of the words 'and the Secretary of such 
Society ' ■which follow the words ' or, in his absence, a delegate repre- 
senting him.' (2) The appointment of a Committee in order to draw up 
suggestions upon methods of more systematic observation and plans of 
operation ibr local societies, together with a more uniform mode of pub- 
lication of the results of their work. If is recommended that this Com- 
mittee should draw up a list of local societies which publish their 
proceedings. 

Upon the resolution of the General Committee requesting the Council 
to consider how far it may be expedient to take steps to ascertain the 
feeling of foreign Scientific Associations as to the advisability of holding 
an International Scientific Congress, the Council have to report that 
while recognising the difficulties which will attend the endeavour they 
recommend that steps be taken to ascertain the feeling of foreign 
Scientific Associations, similar in character to the British Association, 



EEPOET OF THE COUNCIL. 



lix 



upon this question, and they request authority to make the necessary 
communications to foi-eign Societies. 

In regard to the resolution of the General Committee empowering the 
Council to confer with the Royal Geographical Society on the subject of 
the Exploration of the Snowy Mountain Range of Eastern Equatorial 
Africa, and to contribute the sum of 100/. towards the expenses of an 
expedition, the Council have been informed by the Council of the Royal 
Geographical Society, in a letter dated June 26, that they have decided 
upon undertaking the expedition, and have secured the services of the 
well-known and experienced explorer, Mr. Thomson; the Treasurer has 
accordingly paid the above-named contribution. 

An invitation to visit Canada in 1883, warmly supported by the 
Governor-General, His Excellency the Marquis of Lome, was received at 
the end of last year, but the Council were obliged to reply that the vote 
of the General Committee at York accepting the invitation to Oxford 
precluded them from entertaining the question for that year. With 
reference, however, to the Meeting for 1883, the Council regret to inform 
the General Committee that unforeseen difficulties have recently obliged 
their intended hosts at Oxford to express a desire that the proposed visit 
of the Association should be for a time postponed. Under these circum- 
stances Southport and Birmingham have renewed their invitation for 
1883, and invitations for 1884 have been received from Birmingham, 
Southport, Aberdeen, and Nottingham. 

The Council propose that, in accordance with the regulations, the five 



retiring members shall be the foUowino- : — 

Mr. Abel. 
Mr. J. Evans. 
Professor G. C. Foster. 



Professor Newton. 
General Pitt-Rivers. 



The Council recommend the re-election of the other ordinary members 
of the Council, with the addition of those whose names are distinguished 
by an asterisk in the following list : — - 



Adams, Professor W. G., F.R.S. 
Bateman, J. P., Esq., C.B., F.R.S. 
Cayley, Professor, F.R.S. 
*Darwin, F., Esq., F.R.S. 
*Dawkins, Professor W. Boyd, 

F.R.S. 
De la Rue, Warren, Esq., F.R.S. 
Evans, Captain Sir F. J., K.C.B., 

F.R.S. 
*Flower, Professor W. H., F.R.S. 
*Gladstone, Dr. J. H., F.R.S. 
Glaisher; J. W. L., Esq., F.R.S. 
Harcourt, A. G.Vernon, Esq., F.R.S. 
Hastings, G. W., Esq., M.P. 
Hawkshaw, J. Clarke, Esq., F.G.S. 



Heywood, J., Esq., F.R.S. 
Huggins, W., Esq., F.R.S. 
Hughes, Professor T. McK., F.G.S. 
Jeffreys, Dr. J. Gwyn, F.R.S. 
Pengelly, W., Esq., F.R.S. 
Perkin, W. H., Esq., F.R.S. 
Prestwich, Professor J., F.R.S. 
Rayleigh, Lord, F.R.S. 
Sanderson, Professor J. S. Burdon, 

F R S 
*Sniith, Professor H. J. S., F.R.S. 
Soi-by, Dr. H. C, F.R.S. 
Thuillier, General Sir H. E. L., 

C.S.L, F.R.S. 



Ix REPORT 1882. 



Recommendations adopted by the General Cohmittee at the 
Southampton Meeting in August 1882. 

[When Committees are appointed, tlie Member first named is regarded as tlie 
Secretary, except there is a specific nomination.] 

Involving Grants of Money. 

That Professor Crum Brown, Mr. Milne-Home, Mr. John Murray, and 
Mr. Bucban be a Committee for the purpose of co-operating with the 
Scottish Meteoi'oloa:ical Society in making meteorological observations on 
Ben Nevis ; that Professor Cram Brown be the Secretary, and that the 
sum of 50/. be placed at their disposal for the purpose. 

That Mr. Robert H. Scott, Mr. J. Norman Lockyer, Professor H. J. 
S. Smith, Professor Gr. G. Stokes, Professor Balfour Stewart, and Mr. 
G. J. Symons be reappointed a Committee for the purpose of co- 
operating with the Meteorological Society of the Mauritius in their 
proposed publication of Daily Synoptic Charts of the Indian Ocean from 
the year 1861 ; that Mr. R. H. Scott be the Secretary, and that the un- 
expended sum of 50/. be again placed at their disposal for the purpose. 

That Mr. G. H. Darwin and Professor J. C. Adams be a Committee 
for the Harmonic Analysis of Tidal Observations ; that Mr. Darwin be 
the Secretai'y, and that the sum of 50Z. be placed at their disposal for 
the purpose. 

That Professors W. A. Tilden and H. B. Armstrong be a Committee 
for the purpose of investigating Isomeric Naphthalene Derivatives ; that 
Professor H. E. Armstrong be the Secretary, and that the sum of 15/. be 
placed at their disposal for the purpose. 

That Professors Odling, Huntington, and Hartley be a Committee for 
the purpose of investigating by means of Photography the Ultra- Violet 
Spark-Spectra emitted by Metallic Elements and their combinations 
under varying conditions ; that Professor VV. N. Hartley be the Secretary, 
and that the sum of 20/. be placed at their disposal for the purpose. 

That Mr. R. Etheridge, Mr. Thomas Gray, and Professor John Milne 
be a Committee for the purpose of investigating the Earthquake Phe- 
nomena of Japan ; that Professor J. Milne be the Secretary, and that the 
sum of 50/. be placed at their disposal for the purpo.se. 

That Professor W. C. Williamson, Mr. Thos. Hick, and Mr. W. 
Cash be a Committee for the purpose of investigating the Fossil Plants 
of Halifax ; that Mr. W. Cash be the Secretary, and that the sum of 20/. 
be placed at their disposal for the purpose. 

That Dr. H. C. Sorby and Mr. G. R. Vine be a Committee for the 
purpose of reporting on the British Fossil Polyzoa ; that Mr. Vine be 
the Secretary, and that the sum of 10/. be placed at their disposal for the 
purpose. 

That Mr. R. Etheridge, Dr. H. •Woodward, and Professor T. R. Jones 



KECOMMENDATIONS Ar.OPXED BY THE GENERAL COMMITTEE. Ixi 

be a Committee for the purpose of reporting on the Fossil Phyllopoda of 
the Pah^ozoic Rocks; tliat Professor T. 1{. Jones be the Secretary, and 
that the sum of 25Z. be placed at their disposal for the purpose. 

That Sir John Havvkshaw, and Messrs. R. B. Grantham, J. B. Red- 
min, J. W. Woodall, W. Whitaker, W. Topley, and C. E. De Ranee be a 
Committee for the purpose of inquiring into the rate of Erosion of the 
Sea-coasts of England and Wales, and the influence of the Artificial 
abstraction of shingle and other material in that action ; that Messrs. 
W. Topley and C. E. De Ranee be the Secretaries, and that the sum of 
101. be placed at their disposal for the purpose. 

That Professor E. Hull, the Rev. H. W. Crosskey, Captain Douglas 
Galton, Professors G. A. Lebour and J. Prestwich, and Messrs. James 
Glaisher, E. B. Marten, W. Molyneux, G. H. Morton, James Parker, W. 
Pengelly, James Plant, I. Roberts, Fox Strangways, T. S. Stooke, G. J. 
Symons, W. Topley, Tylden- Wright, E. Wethered, W. Whitaker, and 
C. E. De Ranee be a Committee for the purpose of investigatin"- the 
Circulation of the Underground Waters in the Permeable Formatio^ns of 
England, and the Quality and Quantity of the Waters supplied to various 
towns and districts from these formations ; that Mr. C. E. De Ranee be 
the Secretary, and that the sum of 151. be placed at their disposal for 
the purpose. 

That Dr. J. Evans, Professor J. F. Blake, and Messrs. W. Carrnthers 
F. Drew, F. W. Rudler, E. B. Tawney, W. Topley, E. Wethered, and w! 
Whitaker be a Committee for the purpose of carrying on the Geoloo-ical 
Record ; that Mr. Whitaker be the Secretary, and that the sum of 50°. be 
jjlaced at their disposal for the purpose. 

That Professor V. Ball, Professor W. Boyd Dawkins, Dr. J. Evans, 
Mr. G. H. Kinahan, and Mr. R. J. Ussher be a Committee for the pur.1 
pose of carrying out Explorations in Caves in the Carboniferous Lime- 
stone of the South of Irelnnd ; that Mr. R. J. Ussher be the Secretary, 
and that the sum of 20/. be placed at their disposal for the purpose. 

That Mr. R. Etheridge and Mr. Walter Keeping be a Committee for 
the purpose of reporting on the Llandovery Rocks of Central Wales ; 
that Mr. W. Keeping be the Secretary, and that the sum of 101. be placed 
at their disposal for the purpose. 

That General Pitt- Rivers, Professor Flower, Dr. Beddoe, Mr. Brabrook, 
Mr. F. Galton, Mr. J. Park Harrison, Dr. Muirhead, Mr. F. W. Rudler^ 
and Mr. Charles Roberts be a Committee for the purpose of definino- the 
Facial Characteristics of the Races and Principal Crosses in the British 
Isles, and obtaining illustrative Photographs with a view to their pub- 
lication ; that Mr. J. Park Harrison be the Secretary, and that the sum 
of 101. be placed at their disposal for the purpose. 

That Mr. Stainton, Sir John Lubbock, and Mr. E. C. Rye be reappointed 
a Committee for the purpose of continuing a Record of Zoological Litera- 
ture ; that Mr. Stainton be the Secretary, and that the sum'' of 100^. be 
placed at their disposal for the purpose. 

That Mr. J. Cordeaux, Mr. J. A. Harvie Brown, Professor Newton 
Mr. R. M. Barrington, Mr. A. G. IMore, Mr. J. Hardy, and Mr. P. Kermode 
be a Committee for the purpose of obtaining (with the consent of the 
Master and Elder Brethren of the Trinity House and of the Commis- 
sioners of Northern Lights) observations on the Migration of Birds at 
Lighthouses and Lightships, and of reporting upon the same at the 



Ixii EEPOBT — 1882. 



meeting of 1883 ; that Mr. J. Cordeaux be the Secretary, and that the sum 
of 20Z. be placed at their disposal for the purpose. 

That Professor Ray Laukester, Professor Newton, Professor Huxley, 
Mr. P. L. Sclater, Professor Allman, Dr. M. Foster, Mr. A. Sedgwick, 
and Mr. Percy Sladen be a Committee for the purpose of arranging 
for the Occupation of a Table at the Zoological Station at Naples ; 
that Mr. Percy Sladen be the Secretary, and that the sum of SOL be 
placed at their disposal for the purpose. 

That Dr. Pye-Smith, Dr. M. Foster, Professor Huxley, Dr. Carpenter, 
Dr. Gwyn Jeffreys, Professor Lankester, Professor Allman, and Mr. 
Percy Sladen be a Committee for the purpose of aiding in the mainte- 
nance of the Scottish Zoological Station ; that Mr. Percy Sladen be the 
Secretary, and that the sum of 251. be placed at their disposal for the 
purpose. 

That Dr. Pye-Smith, Professor de Chaumont, Dr. M. Foster, and 
Dr. Burdon Sanderson be reappointed a Committee for the purpose of 
investigating the Influence of Bodily Exercise on the Elimination of 
Nitrogen (the experiments to be conducted by Mr. North) ; that Dr. 
Burdon Sanderson be the Secretary, and that the sum of 30Z. be placed 
at their disposal for the pm-pose. 

That Sir Joseph Hooker, Dr. Gilnther, Mr. Howard Saunders, and 
Mr. P. L. Sclater be a Committee for the purpose of exploring Kilimand- 
jaro and the adjoining mountains of Eastern Equatorial Africa ; that Mr. 
P. L. Sclater be the Secretary, and that the sum of 500Z. be placed at 
their disposal for the purpose. 

That Mr. Raphael Meldola, General Pitt-Rivers, Mr. Worthington G. 
Smith, and Mr. William Cole be a Committee for the purpose of investi- 
gating the Ancient Earthwoi-k in Epping Forest known as the Longhton 
Camp ; that Mr. William Cole be tlie Secretary, and that the sum of 10/. 
be placed at their disposal for the purpose. 

That Mr. Sclater, Mr. Howard Saunders, and Mr. W. Thiselton-Dyer 
be reappointed a Committee for the purpose of investigating the Natural 
History of Timor-laut ; that Mr. W. Thiselton Dyer be the Secretary, 
and that the sum of 501. be placed at their disposal for the purpose. 

That Sir F. J. Bramwell, Mr. James Glaisher, Mr. C. W. Merrifield, 
Captain D. Galton, Professor W. C. Unwin, Mr. T. Hawksley, Major 
A. Cunningham, Mr. A. G. Greenhill, and Mr. A. T. Atchison be 
a Committee for the purpose of ascertaining by experiments and 
observations the relation between the pressure at different points of 
a surface on which water or air impinges and the velocity of the fluid, 
especially in the case of large actual structures, and thus to throw light 
upon some of the points on which information is much required, as 
stated in the report of the Committee on Wind Pressure ; that Mr. Arthur 
T. Atchison be the Secretary, and that the sum of 251. be placed at their 
disposal for the purpose. 

That Sir Joseph Whitworth, Dr. Siemens, Sir F. J. Bramwell, Mr. 
A. Stroh, Mr. Beck, Mr. W. H. Preece, Mr. E. Crompton, Mr. B. Rigg. 
Mr. A. Le Neve Foster, Mr. Latimer Clark, Mr. H. Trueman Wood, 
Mr. Buckney, and Sir William Thomson be a Committee for the purpose 
of determining a Gauge for the manufacture of the various small Screws 
used in Telegraphic and Electrical Apparatus, in Clockwork, and for 
other analogous purposes; that Mr. H. Trueman Wood be the Secretary, 
and that the sum of 201. be placed at their disposal for the purpose. 



BECOMMEHDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixiii 

Not involving Grants of Money. 

That Professor G. Carey Foster, Sir William Thomson, Professor 
Ayrton, Professor J. Perry, Professor W. G. Adams, Lord Rayleigh, 
Professor Jenkin, Dr. O. J. Lodge, Dr. John Hopkinson, Dr. A. Muir- 
head, Mr. W. H. Preece, Mr. Herbert Taylor, Professor Everett, and 
Professor Schnster be reappointed a Committee for the purpose of con- 
structing and issuing practical Standards for use in Electrical Measiire- 
ments, with the addition of the names of Dr. C. W. Siemens, Dr. J. A. 
Fleming, Professor G. F. Fitzgerald, Mr. R,. T. Glazebrook, and Professor 
Chrystal ; and that Dr. Muirhead be the Secretary. 

That Professor Sylvester, Professor Cayley, and Pi'ofessor Salmon 
be reappointed a Committee for the purpose of Calculating Tables of 
the Fundamental Invariants of Algebraic Forms ; and that Professor 
Sylvester be the Secretary. 

That Professor Schuster, Sir William Thomson, Professor H. E. 
Roscoe, Professor A. S. Herschel, Captain W. de W. Abney, Mr. R. H. 
Soott, and Dr. J. H. Gladstone be reappointed a Committee for the purpose 
of investigating the practicability of collecting and identifying Meteoric 
Dust, and of considering the question of undertaking regular observa- 
tions in various localities ; and that Professor Schuster be the Secretary. 

That Mr. Spottiswoode, Professor Stokes, Professor Cayley, Professor 
Smith, Sir William Thomson, Professor Henrici, Lord Rayleigh, and 
Mr. J. W. L. Glaisher be reappointed a Committee on Mathematical 
Notation and Printing ; and that Mr. J. W. L. Glaisher be the Sec- 
retary. 

That Professor Cayley, Professor Stokes, Professor H. J. S. Smith, 
Sir William Thomson, Mr. James Glaisher, and Mr. J. W. L. Glaisher 
be reappointed a Committee on Mathematical Tables ; and that Mr. 
J. W. L. Glaisher be the Secretary. 

That Captain Abney, Professor W. G. Adams, Professor G. C. Foster, 
Lord Rayleigh, Mr. Preece, Professor Schuster, Professor Dewar, Pro- 
fessor Vernon Harcourt, and Professor Ayrton be reappointed a Com- 
mittee for the purpose of fixing a Standard of White Light ; and that 
Captain Abney be the Secretary. 

That Captain Abney, Professor Stokes, and Professor Schuster be a 
Committee for the purpose of determining the best experimental methods 
that can be used in observing total Solar Eclipses ; and that Professor 
Schuster be the Secretary. 

That Professor Roscoe, Mr. Lockyer, Professor Dewar, Professor 
Liveing, Professor Schuster, Captain Abney, and Dr. Marshall Watts be 
reappointed a Committee for the purpose of preparing a new series of 
Wave-lengths Tables of the S^DCctra of the Elements ; and that Dr. 
Marshall Watts be the Secretary, 

That Prof essoins Williamson, Prankland, Roscoe, Crum Brown, and 
Odling, and Messrs. J. Millar Thomson, V. H. Veley, and H. B. Dixon 
be a Committee for the purpose of drawing up a statement of the 
varieties of Chemical Names which have come into use, for indicating: 
the causes which have led to their adoption, and for considering what can 
be done to bring about some convergence of the views on Chemical 
Nomenclature obtaining among English and foreign chemists ; and that 
Mr. H. B. Dixon be the Secretary. 

That Professors Dewar and A. W. Williamson, Dr. Marshall Watts, 



Ixiv KEPOBX — 1882. 

Captain Abney, 'Mv. Stoney, and Professors W. N. Hartley, McLeod, 
Carey Foster, A. K. Huntington, Emerson Reynolds, Keinold, Liveing, 
Lord Rayleigh, Schuster, and W. Chandler Robei'ts be a Committee for 
the purpose of reporting upon the present state of our knowledge of 
Spectrum Analysis ; and that Professor W. Chandler Roberts be the 
Secretary. 

That Professors F. A. Abel, A. K. Huntington. McLeod, Chandler 
Roberts, W. G. Adams, and Tilden and Mr. F. J. Bateman be a Com- 
mittee for the purpose of collecting and arranging in a suitable form for 
reference the already published literature on the subject of Metallic 
Alloys; and that Professor A. K. Huntington be the Secretary. 

That Professors J. Prestwich, V. Ball, J. W. Judd, and W. J. Sollas 
and Messrs. W. T. Blanford and W. Topley be a Committee for the pur- 
pose of inquiring into the possibility of securing the co-operation of 
foreign geologists in obtaining an International Geological Record ; and 
that Professor W. J. Sollas be the Secretary. 

That Professors J. Prestwich, W. Boyd Dawkins, T. McK. Hughes, 
and T. G. Bonney, the Rev. H. W. Crosskey, Dr. Deane, and Messrs. C. E. 
De Ranee, H. G. Fordham, J. E. Lee, 1). Mackintosh, W. Pengelly, J. 
Plant, and R. H. Tiddeman be a Committee for the purpose of recording 
the position, height above the sea, lithological charactei'S, size, and 
origin of the Erratic Blocks of England, Wales, and Ireland, reporting 
other matters of interest connected with the same, and taking measures 
for their preservation ; and that the Rev. H. W. Crosskey be the Secretary. 

That Lieut.-Colonel H. H. Godwin-Austen, Dr. G. Hartlaub, Sir 
J. Hooker, Dr. Giintlier, Mr. Seebohm, and Mr. Sclater be reappointed a 
Committee for the purpose of investigating the Natural History of 
Socotra, and the adjacent Highlands of Arabia and Somali-land; and 
that Mr. Sclater be the Secretary. 

That the Committee for promoting the Survey of Eastern Palestine, 
consisting of Mr. James Glaisher (Secretary), the Rev. Canon Tristram, 
and the Rev. F. Lawrence, be reappointed. 

Tiiat Mr. James Heywood, Mr. William Shaen, Mr. Stephen Bourue, 
Mr. Robert Wilkinson, the Rev. W. Delany, Professor N. Story Maske- 
lyne, Dr. Silvanus P. Thompson, Miss Lydia E. Becker, Sir John 
Lubbock, Professor A. W. Williamson, Mrs. Augusta Webster, the Rev. 
H. W. Crosskey, Professor Roscoe, Professor G. Carey Foster, and Dr. J. 
H. Gladstone (Secretary) be reappointed a Committee for the ])urpose 
of reporting on^ the workings of the Education Code and of other 
legislation aifecting the Teaching of Science in Elementary Schools. 

That Mr. F. Galton, Dr. Beddoe, Mr. Brabrook (Secretary and 
Rsporter), Major-General Pitt-Rivers, Mr. Frank Fellows, Mr. J. P. 
Harrison, Mr. J. Heywood, Professor Leone Levi, Dr. F. A. Mahomed, 
Sir Rawson Rawson, Mr. J. E. Price, and Mr. C. Roberts be a Committee 
for the purpose of carrying out the recommendations of the Anthropo- 
metric Committee of last year and the more complete discussion of 
the collected facts. 

That Sir Frederick Bramwell, Dr. A. W. Williamson, Professor 
Sir William Thomson, Mr. St. John Vincent Day, Dr. C. W. Siemens, 
Mr. C. "W. Merrifield, Dr. Neilson Hancock, Mr. Abel, Captain Douglas 
Galton, Mr. JSTewmarch, Mr. E. H. Carbutt, Mr. Macrory, Mr. H. 
Trueman Wood, Mr. W. H. Barlow, and Mr. A. T. Atchison be re- 
appointed a Committee for the purpose of watching and reporting to 



E „.JM END AXIOMS ADOPTED Br THE GENERAL COMMITTEE. Ixv 

tlie Council on Patent Legislation ; and that Sir Frederick Bramwell be 
the Secretary. 

That Sir' William Thomson, Dr. C. W. Siemens, Mr. W. H. Barlow, 
Dr. A. W. Williamson, Mr. W. H. Preece, and Mr. J. M. Thomson be a 
Comraittee for the purpose of promoting arrangements for facilitating the 
use of Weights and Measux-es in accordance with the permissive clauses 
of the Weights and Measures Act, 1878 ; and that Mr. J. M. Thomson be 
the Secretary. 

Communications ordered to be printed in extenso in the Annual Report of 

the Association. 

Professor J. M. Crafts' paper, 'On the Boiling Points and Tension of 
Vapour of a number of Organic Substances determined with the Air- 
Thermometer.' 

Mr. G. H. Darwin's paper, ' On a Misprint in the Tidal B<eport for 
1872.' 

Mr. W. Whitaker's ' List of Works on the Geology and Pala3ontology 
of Oxfordshire, Berkshire, and Buckinghamshire.' 

Colonel Yule's paper. ' On the Oldest Records of the Sea Route to 
China from Western Asia.' 

M. Pierre de Tchihatchef's paper, ' On the Deserts of Africa and 
Asia.' 

Professor Leone Levi's paper, ' On the State of Crime in England, 
Scotland, and Ireland in 1880,' with accompanying diagrams and shaded 
map. 

Sir W. G. Armstrong's paper, ' On the Treatment of Steel for the 
Construction of Ordnance, and other purposes.' 

Mr. J. Clarke Hawkshaw's paper, ' On the Cliannel Tunnel,' with the 
necessary plans. 

Mr. Baker's paper, ' On the Forth Bridge,' with the necessary cuts. 

Besolutions referred to the Council for Consideration, and Action if 

desirable. 

That the Council be empowered to take steps for amalgamating the 
Departments of Zoology and Botany and of Anatomy and Physiology 
for the ensuing year, should this seem desirable. 

That the Council be empowered to appoint a Committee, as recom- 
mended in their report adopted by the General Committee on August 23, 
in order to draw up suggestions upon methods of more systematic obser- 
vation and plans of operation for local societies, together with a more 
uniform mode of publication of the results of their work. It is recom- 
mended that this Committee should draw up a list of local societies 
which publish their pi'oceedings. 

That the Council be empowered to communicate with Foreign Scientific 
Associations with the view of promoting the organization of an Inter- 
national Scientific Congress. 

That the Council be empowered to appoint a Committee, upon which 
the several sections of the Association be equally represented, for the 
purpose of co-operating with the Council in considering the best arrange- 
ments for securing a representative gathering of the Association at the 
meeting pi-oposed to be held at Montreal. 
1882. d 



Ixvi EEPORT — 1882. 



Synopsis of Grants of Money appropriated to Scientific Purposes 
by the General Committee at the Southampton Meeting in 
August 1882. The Names of the Members ivho would be 
entitled to call on the General Treasurer for the respective 
Grants are prefixed. 

Mathematics and Physics. 

£ s. d. 
Brown, Professor Crum. — Meteorological Observations on 

BenNevis 50 

*Scott, Mr. R. H. — Synoptic Charts of the Indian Ocean 50 

Darwin, Mr. G. H. — Harmonic Analysis of Tidal Observa- 
tions 50 



Chemistry. 

Tilden, Professor W. A. — Investigating Isomeric Naphtha- 
lene Derivatives 15 

*Odling, Professor. — Photographing the Ultra- Violet Spark- 
Spectra 20 



Geology. 

*Etheridge, Mr. R. — Earthquake Phenomena of Japan 50 

*WiUiamson, Professor W. C— Fossil Plants of Halifax 20 

*Sorby, Dr. H. C— British Fossil Polyzoa 10 

Etheridge, Mr. R. — Fossil Phyllopoda of the Paloeozoic 

Rocks 25 

*Hawkshaw, Sir John. — Erosion of the Sea-coasts of Eng- 
land and Wales 10 

* Hull, Professor E. — Circulation of Underground Waters ... 15 

*Evans, Dr. J. — Geological Record 50 

*Ball, Professor V. — Carboniferous Limestone Caves in the 

South of Ireland 20 

Etheridge, Mr. R.— Llandovery Rocks of Central Wales ... 10 

Carried forward :e395 

* Eeappointed. 



SYNOPSIS OF GRANTS OF MONET. Ixvii 



£ s. d. 
Brought forward 395 Q 



Biology. 

*Pitt-Rivers, General. — Photographs of the Races and princi- 
pal Crosses in the British Isles 10 

*Stainton, Mr, — Record of Zoological Literature 100 

*Cordeaux, Mr. J. — Migration of Birds 20 

*Lankester, Professor Ray. — Table at the Zoological Station 

at Naples 80 

*Pje-Smith, Dr. — Scottish Zoological Station 25 

*Pye-Smith, Dr. — Influence of Bodily Exercise on the 

Elimination of Nitrogen 30 

Hooker, Sir J. — Exploring Kilimandjaro and the adjoining 

Mountains of Eastern Equatorial Africa 500 

*Meldo]a, Mr. R. — Investigation of Loughton Camp 10 

*Sclater, Mr. P. L. — Natural History of Timor-laut 50 



Mechanics. 

Bramwell, Sir P. J. — Relation between the pressure at 
different points of a structtire on which water and air 
impinge 25 

*Whitwortb, Sir Joseph. — Screw Gauges 20 

£1265 
* Eeappointed. 



TJie Annual Meeting in 1883. 

The Meeting will commence on Wednesday, September 19, at Soutbport, 
instead of Oxford (see Council Report, p. lix). 



Place of Meeting in 1884. 
The Annual Meeting of the Association in 1884 will be lield at Montreal. 



d2 



Ixviii 



REPORT — 1882. 



General Statement of Sums tvhich have been paid on Account of 
Grants for Scinntific Purposes. 



£ s. d. 



1831. 



Tide Discussions 20 



1835. 

Tide Discussions 

Britisli Fossil Ichtlij-olos 



y ••• 



62 
105 



1838. 

Tide Discussions 29 

British Fossil Fishes 100 

Meteorological Observations 
and Anemometer (construc- 
tion) 100 

Cast Iron (Strength of) 60 

Animal and Vegetable Sub- 
stances (Preservation of )... 10 

Railway Constants 41 

Bristol Tides 50 

Growtli of Plants 75 

Mud in Kivers 3 

Education Committee 50 

Heart Experiments 5 

Land and Sea Level 267 

Steam- vessels 100 

Meteorological Committee ... 31 



£167 



1836. 

Tide Discussions 163 

British Fossil Ichthyology ... 105 
Thermometric Observations, 

&c 50 

Experiments on long-con- 
tinued Heat 17 1 

Eain-Gauges 9 13 

Eefraction Experiments 15 

Lunar Nutation 60 

Thermometers 15 6 



£435 



1837. 

Tide Discussions 284 1 

Chemical Constants 24 13 6 

Lunar Nutation 70 

Observations on Waves 100 12 

Tides at Bristol 150 

Meteorology and Subterra- 
nean Temperature 93 3 

Vitrification Experiments ... 150 

Heart Experiments 8 4 6 

Barometric Observations 30 

Barometers 11 18 6 



£922 12 6 



1 


10 


2 


10 














6 


6 








3 





8 


7 








9 


5 



£932 2 2 



1839. 

Fossil Ichthyology no 

Meteorological Observations 
at Plymouth, &c 63 10 



Mechanism of Waves 144 

Bristol Tides 35 

Meteorology and Subterra- 
nean Temperature 21 

Vitrification Experiments ... 9 

Cast-iron Experiments 100 

Railway Constants 28 

Land and Sea Level 274 

Steam-vessels' Engines 100 

Stars in Histoire Celeste 171 

Stars in Lacaille 11 

Stars in K.A.S. Catalogue ...166 

Animal Secretions 10 

Steam Engines in Cornwall... 50 

Atmospheric Air 16 

Cast and Wrought Iron 40 

Heat on Organic Bodies 3 

Gases on Solar Spectrum 22 

Hourly Meteorological Ob- 
servations, Inverness and 

Kingussie 49 

FossirReptiles 118 

Mining Statistics 50 



18 

11 
4 

7 
1 


18 


16 

10 


1 







d. 

6 


7 

2 
4 

6 











1841. 
Observations on Waves ... 
Meteorology and Subterra- 
nean Temperature 8 

Actinometcrs 10 

Earthquake Shocks 17 

Acrid Poisons 6 

Veins and Absorbents .. 3 

Mud in Rivers 5 



8 
9 




£1595 11 



1840. 

Bristol Tides 100 

Subterranean Temperature ... 13 13 6 

Heart Experiments 18 19 

Lungs Experiments 8 13 

Tide Discussions 50 

Land and Sea Level 6 11 1 

Stars (Histoire Celeste) 242 10 

Stars (Lacaille) 4 15 

Stars (Catalogue) 264 

Atmospheric Air 15 15 

Water on Iron 10 

Heat on Organic Bodies 7 

Meteorological Observations . 52 17 6 

Foreign Scientific Memoirs... 112 1 

Working Population 100 

School Statistics .50 

Forms of Vessels 184 7 

Chemical and Electrical Phe- 
nomena 40 

Meteorological Observations 

at Plymouth 80 

Magnetical Observations 185 13 9 



£1546 16 



30 



8 











7 
























GENEEAL STATEMENT. 



Ixix 



£ .■>. d. 

Marine Zoology 15 12 8 

Skeleton Maps 20 

Mountain Barometers 6 18 fi 

Stars (Histoire Celeste) 185 

Stars (Lacaille) 79 5 

Stars (Nomenclature of ) 17 19 'i 

Stars (Catalogue of) 40 

"Water on Iron 50 

Meteorological Observations 

at Inverness 20 

Meteorological Observations 

(reduction of) 25 

Fossil Reptiles 50 

Foreign Memoirs 62 6 

Railway Sections 38 1 

Forms of Vessels 193 12 

Meteorological Observations 

at Plymouth 55 

Magnetical Observations 61 18 8 

Fishes of the Old Red Sand- 
stone 100 

Tides at Leith 50 

Anemometer at Edinburgh... 69 1 10 

Tabulating Observations 9 6 3 

Races of Men 5 

Radiate Animals 2 

^■1235 10 11 



1812. 
Dynamometric Instruments... 113 

Anoplura Britanniae 52 

Tides at Bristol 59 

Gases on Light 30 

Chronometers .... 26 

Marine Zoology 1 

British Fossil Mammalia 100 

Statistics of Education 20 

Marine Steam-vessels' En- 
gines 28 

Stars (Histoire Celeste) 59 

Stars (Brit. Assoc. Cat. of)... 110 

Railway Sections 161 

British Belemnites 50 

Fossil Reptiles (publication 

of Report) 210 

Forms of Vessels 180 

■Galvanic Experiments on 

Rocks 5 

Meteorological Experiments 

at Plymouth 68 

Constant Indicator aad Dyna- 
mometric Instruments 90 

Force of Wind 10 

Light on Growth of Seeds ... 8 

Vital Statistics 50 

Vegetative Power of Seeds... 8 
Questions on Human Race ... 7 

£Ui9 



n 


2 


12 





8 





14 


7 


17 


6 


5 



































10 
























8 6 











1 11 

9 



17 8 



1843. 
Revision of the Nomenclature 
of Stars 



2 



Reduction of Stars, British 
Association Catalogue 25 

Anomalous Tides, Frith of 
Forth 120 

Hourly Meteorological Obser- 
vations at Kingussie and 
Inverness 77 

Meteorological Observations 
at Plymouth 55 

Whewell's Meteorological 
Anemometer at Plymouth . 10 

Meteorological Observations, 
Osier's Anemometer at Ply- 
mouth 20 

Reduction of Meteorological 
Observations 30 

Meteorological Instruments 
and Gratuities 39 

Construction of Anemometer 
at Inverness 56 

Magnetic Co-operation 10 

Meteorological Recorder for 
Kew Observatory 50 

Action of Gases on Light 18 

Establishment at Kew Obser- 
vatory, Wages, Repairs, 
Furniture, and Sundries ... 133 

Experiments by Captive Bal- 
loons 81 

Oxidation of the Rails of Rail- 
ways 20 

Publication of Report on Fos- 
sil Reptiles 40 

Coloured Drawings of Rail- 
way Sections 147 

Registration of Earthquake 
Shocks 30 

Report on Zoological Nomen- 
clature 10 

Uncovering Lower Red Sand- 
stone near Manchester 4 

Vegetative Power of Seeds... 5 

Marine Testacea (Habits of) . 10 

Marine Zoology 10 

Marine Zoology 2 

Preparation of Report on Bri- 
tish Fossil Mammalia 100 

Physiological Operations of 
Medicinal Agents 20 

Vital Statistics 36 

Additional Experiments on 
the Forms of Vessels 70 

Additional Experiments on 
the Forms of Vessels 100 

Reduction of Experiments on 
the Forms of Vessels 100 

Morin's Instrument and Con- 
stant Indicator 69 

Experiments on the Strength 

of Materials .^^ 60^ 

£1565 



s. 


d. 














12 


8 


























6 





12 

■ 8 


2 

10 



16 



1 


4 


7 


8 

















18 


3 














4 
3 


14 


6 
8 


11 









5 




8 




















14 


10 









10 2 



Ixs 



REPORT — 1882. 



£ s. d. 
1844. 
Meteorological Observations 

at Kingussie and Inverness 12 
Completing Observations at 

Plymouth 35 

Magnetic and Meteorological. 

Co-operation 25 8 4 

Publication of the British 

Association Catalogue of 

Stars 35 

Observations on Tides on the 

East Coast of Scotland ... 100 
Revision of the Nomenclature 

of Stars 1842 2 9 6 

Maintaining the Establish- 
ment in Kew Observa- 

torj- 117 17 3 

Instruments for Kew Obser- 
vatory ... 56 7 3 

Influence of Light on Plants 10 
Subterraneous Temperature 

in Ireland 5 

Coloured Drawings of Kail- 
way Sections 15 17 6 

Investigation of Fossil Fishes 

ofthe Lower Tertiary Strata 100 
Registering the Shocks of 

Earthquakes 1842 23 11 10 

St ructm-e of Fossil Shells ... 20 
Radiata and Mollusca of the 

^gean and Red Seas 1842 100 
Geographical Distributions of 

Marine Zoology 1842 , 10 

Marine Zoology of Devon and 

Cornwall 10 

Marine Zoology of Corf u 10 

Experiments on the Vitality 

of Seeds 9 

Experiments on the Vitality 

of Seeds 1842 8 7 3 

Exotic Anoplura 15 

Strength of Materials 100 

Completing Experiments on 

the Forms of Sliips 100 

Inquiries into Asphyxia 10 

Investigations on the Internal 

Constitution of Metals 50 

Constant Indicator and Mo- 

rin's Instrument 1842 10 

£'981 12 8 



184.5. 

Publications of the British As- 
sociation Catalogue of Stars 351 14 

Meteorological Observations 
at Inverness 30 IS 

Magnetic and Meteorological 

Co-operation 16 ]G 

Meteorological Instruments 

at Edinbtn-gh 18 11 

Reduction of Anemometrical 

Observations at Plymouth 25 



11 



£ 
Electrical Experiments at 

Kew Observatory 43 

Maintaining the Establisli- 

ment in Kew Observatory 149 

For Kreifs Barometrograph 25 

Gases from Iron Furnaces... 50 

The Actinograpli 15 

jMicroscopic Structure of 

Shells 20 

Exotic Anoplura 1843 10 

Vitality of Seeds 1843 2 

Vitality of Seeds 1844 7 

Marine Zoology of Cornwall 10 
Pliysiological Action of Medi- 
cines 20 

Statistics of Sickness and 

Mortality in York 20 

Earthquake Shocks 1843 15 



17 8 



ir 



5 
































(» 





7 




















14 




8 



£831 


9 


9 


184G. 
British Association Catalogue 

of Stars 1844 

Fossil Fishes of the London 

Clay 


211 
100 

50 

146 
CO 

6 
10 

2 

7 
10 
10 

n 

3 

8 

7 
12 


15 



16 


16 


15 

12 




7 

3 

3 

19 

6 







Computation of the Gaussian 
Constants for 1829 


(» 


Maintaining the Establisli- 
ment at Kew Observatory 

Strength of Materials 

Researches in Asphyxia 

Examination of Fossil Shells 

Vitality of Seeds 1844 

Vitality of Seeds 1845 

Marine Zoology of Cornwall 
Marine Zoology of Britain . . . 
Exotic Anoplura 1844 


7 
t> 
2 

10 
3 





Expenses attending Anemo- 
meters 


r> 


Anemometers' Repairs 


6 


Atmospheric Waves 


3 


Captive Balloons 1844 

Varieties of the Human Race 

1844 

Statistics of Sickness and 

Mortality in York 


8 
3 



£(585 


16 





1847. 
Computation of the Gaussian 
Constants for 1829 


50 
10 

20 

10 

6 

4 

107 








9 

7 

8 





Habits of Marine Animals ... 
Physiological Action of Medi- 
cines 




(> 


Marine Zoology of Cornwall 

Atmospheric Waves 

Vitality of Seeds 



3 


Maintaining the Establish- 
ment at Kew Observatory 


6 


£208 


5 


4 



GENERAL STATEMENT. 



Ixxi 



£ s. d. 
1848. 
Maintaining: the Establish- 
ment at Kew Observatory 171 15 11 

Atmospheric Waves 3 10 9 

Vitality of Seeds 9 15 

Comijletion of Catalogue of 

Stars 70 

On Colouring Matters 5 

On Growth of Plants 15 

£275 1 "8 



1850. 
Maintaining the Establish- 
ment at Kew Observatory 255 
Transit of Earthquake Waves 50 

Periodical Phenomena 15 

Meteorological Instruments, 
Azores 25 



1849. 
Electrical Observations at 

Kew Observatory 50 

Maintaining Establishment 

at ditto 76 2 5 

Vitality of Seeds 5 8 1 

On Growth of Plants 5 

Registration of Periodical 

Phenomena 10 

Bill on Account of Anemo- 

metrical Observations 13 9 

£159 19 6 



8 






















£345 18 



1851. 
Maintaining the Establish- 
ment at Kew Observatory 
(includes jDart of grant in 

1849) 309 2 2 

Theory of Heat 20 1 1 

Periodical Phenomena of Ani- 
mals and Plants 5 

Vitality of Seeds 5 6 4 

Influence of Solar Kadiation 30 

Ethnological Inquiries 12 

Eesearches on Annelida 10 

£391 9 7 



1853. 

Maintaining the Establish- 
ment at Kew Observatory 
(including balance of grant 
for 1850) 233 17 8 

Experiments on the Conduc- 
tion of Heat 5 2 9 

Influence of Solar Radiations 20 

Geological Map of Ireland ... 15 

Researches on the British An- 
nelida 10 

Vitality of Seeds 10 6 2 

Strength of Boiler Plates 10 

£304 6 7 



£ s. (L 
1853. 
Maintaining the Establish- 
ment at Kew Observatory 165 
Experiments on the Influence 

of Solar Radiation 15 

Researches on the British An- 
nelida 10 

Dredging on the East Coast 

of Scotland 10 

Ethnological Queries 5 

£205 



1854. 

Maintaining the Establish- 
ment at Kew Observatory 
(including balance of 
former grant) 330 15 4 

Investigations on Flax 11 

Effects of Temperature on 

Wrought Iron 10 

Registration of Periodical 

Phenomena 10 

British Annelida 10 

Vitality of Seeds 5 2 3 

Conduction of Heat 4 2 

£380 19 7 



1855. 
Maintaining the Establish- 
ment at Kew Observatory 425 

Earthquake Movements 10 

Physical Aspect of the Moon 11 8 5 

Vitality of Seeds 10 7 11 

Map of the World 15 

Ethnological Queries 5 

Dredging near Belfast 4 



£480 16 4 

1856. "'^'^""^^^^ 
Maintaining the Establish- 
ment at Kew Observa- 
tory : — 

1854- £ 75 01 ^-k n n 

1855 £500 0/ "^ 

Strickland's Ornithological 

Synonyms 100 

Dredging and Dredging 

Forms 9 13 9 

Chemical Action of Light ... 20 

Strength of Iron Plates 10 

Registration of Periodical 

Phenomena 10 

Propagation of Salmon 10 

£734 13 9 



1857. 

Maintaining the Establish- 
ment at Kew Observatory 350 

Earthquake Wave Experi- 
ments 40 

Dredging near Belfast 10 

Dredging on the West Coast 

of Scotland 10 



Ixxii 



REPORT — 1882. 



£ $. d. 

Investigations into the Mol- 

lusca of California 10 

Experiments on Flax 5 

Natural History of Mada- 
gascar 20 

Kesearches on British Anne- 
lida 25 

Eeport on Natural Products 

imported into Liverpool ... 10 

Artificial Propagation of Sal- 
mon 10 

Temperature of Mines 7 8 

Thermometers for Subterra- 
nean Observations 5 7 4 

Life-boats ■■ 5 

£507 15 4 

1858. 

Maintaining the Establish- 
ment at Kew Observatory 500 

Earthquake Wave Experi- 
ments 25 

Dredging on the West Coast 
of Scotland 10 

Dredging near Dublin 5 

Vitality of Seeds 5 5 

Dredging near Belfast 18 13 2 

Eeport on the British Anne- 
lida 25 

Experiments on the produc- 
tion of Heat by Motion in 
Fluids 20 

Eeport on the Natural Pro- 
ducts imported into Scot- 
land 10 

£618 18 2 

1859. 
Maintaining the Establish- 
ment at Kew Observatory 500 

Dredging near Dublin 15 

Osteology of Birds 50 

Irish Tunicata ' 5 

Manure Experiments 20 

British Medusidie 5 

Dredging Committee 5 

Steam-vessels' Performance... 5 
Marine Fauna of South and 

West of Ireland 10 

Photographic Chemistry 10 

Lanarkshire Fossils 20 1 

Balloon Ascents 39 11 

Ji«8-rTi 1 

1860. 

Maintaining the Establish- 
ment of Kew Observatory 500 

Dredging near Belfast 16 6 

Dredging in Dublin Bay 15 

Inquiry into the Performance 

of Steam-vessels 124 

Explorations in the Yellow 
Sandstone of Dura Den ... 20 



Chemico-mccbanical Analysis 

of Rocks and Minerals 25 

Eesearches on the Growth of 

Plants 10 

Eesearches on the Solubility 

of Salts 30 

Eesearches on the Constituents 

of Manures 25 

Balance of Captive Balloon 

Accounts 1 13 6 

^^766 19~~6 

1861. ™™'™™°'*'^ 
Maintaining the Establish- 
ment of Kew Observatory.. .500 

Earthquake Experiments 25 

Dredging North and East 

Coasts of Scotland 23 

Dredging Committee : — 

1860 £50 "\ ^, 

1861 £22 0/'^ 

Excavations at Dura Den 20 

Solubility of Salts 20 

Steam- vessel Performance ... 1 50 

Fossils of Lesmahago 15 

Explorations at Uriconium... 20 

Chemical Alloys 20 

Classified Index to the Trans- 
actions 100 

Dredging in the Mersey and 

Dee 5 

Dip Circle 30 

Photoheliographic Observa- 
tions 50 

Prison Diet 20 

Gauging of Water 10 

Alpine Ascents 6 

Constituents of Manures 25 



£1111 






























5 10 
O^O 
5 10 



1862. 

Maintaining the Establish- 
ment of Kew Observatory 500 

Patent Laws 21 6 

Mollusca of N.-W. of America 10 

Natural History by Mercantile 

Marine 5 

Tidal Observations 25 

Photoheliometer at Kew 40 

Photographic Pictures of the 

Sun 150 

Eocks of Donegal 25 

Dredging Durham and North- 
umberland 25 

Connexion, of Storms 20 

Dredging North-east Coast 

of Scotland 6 9 6 

Eavages of Teredo 3 11 

Standards of Electrical Ee- 

sistance 50 

Eailway Accidents 10 

Balloon Committee 200 

Dredging Dublin Bay 10 



GENERAL STATEMENT. 



Ixxiii 



£ g. d. 

Dredging the Mersey 5 

Prison Diet 20 

Gauging of Water 12 10 

Steamships' Performance 150 

Thermo-Electric Currents 5 

£1293 16 6 



1863. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 
Balloon Committee deficiency 70 
Balloon Ascents (other ex- 
penses) 25 

Entozoa 25 

Coal Fossils 20 

Herrings 20 

Oranitesof Donegal 5 

Prison Diet 20 

Vertical Atmospheric Move- 
ments 13 

Dredging Shetland 50 

Dredging North-east coast of 

Scotland 25 

Dredging Northumberland 

and Durham 17 

Dredging Committee superin- 
tendence 10 

Steamship Performance 100 

Balloon Committee 200 

Carbon under pressure 10 

Volcanic Temperature 100 

Bromide of Ammonium 8 

Electrical Standards 100 

Construction and Distri- 
bution 40 

Luminous Meteors 17 

Kew Additional Buildings for 

Photoheliograph 100 

Thermo-Electricity 15 

Analysis of Rocks 8 

Hydroida .^ 10 

£1608 
































































5 



3 10 


















































































3 10 



1864. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 

Coal Fossils 20 

Vertical Atmospheric Move- 
ments 20 

Dredging Shetland 75 

Dredging Northumberland ... 25 

Balloon Committee 200 

Carbon under pressure 10 

Standards of Electric Re- 
sistance 100 

Analysis of Rocks 10 

Hydroida 10 

Askham's Gift 50 

Nitrite of Amyle 10 

Nomenclature Committee ... 5 

Rain-Gauges 19 15 8 

Cast-Iron Investigation 20 



£ s. (I. 
Tidal Observations in the 

Humber 50 

Spectral Rays 45 

Luminous Meteors .•• 20 

£1289 15 8 

1865. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 

Balloon Committee 100 

Hydroida 13 

Rain-Gauges 30 

Tidal Observations in the 

Humber 6 8 

Hexylic Compounds 20 

Amyl Compounds 20 

Irish Flora 25 

American Mollusca 3 !» 

Organic Acids 20 

Lingula Flags Excavation ... 10 

Eurypterus 50 

Electrical Standards 100 

Malta Caves Researches 30 

Oyster Breeding 25 

Gibraltar Caves Researches... 150 

Kent's Hole Excavations 100 

Moon's Surface Observations 35 

Marine Fauna 25 

Dredging Aberdeenshire 25 

Dredging Channel Islands ... 50 

Zoological Nomenclature 5 

Resistance of Floating Bodies 

in Water 100 

Bath Waters Analysis 8 10 10 

Luminous Meteors 40 

^59i 7 10 

1866. ~ 
Maintaining the Establish- 
ment of Kew Observatory.. 600 

Lunar Committee 64 13 4 

Balloon Committee 50 

Metrical Committee 50 

British Rainfall 50 

Kilkenny Coal Fields 16 

Alum Bay Fossil Leaf -Bed ... 15 

Luminous Meteors 50 

Lingula Flags Excavation ... 20 
Chemical Constitution of 

Cast Iron 60 

Amyl Compounds 25 

Electrical Standards 100 

Malta Caves Exploration 30 

Kent's Hole Exploration 200 

Marine Fauna, &c., Devon 

and Cornwall 25 

Dredging Aberdeenshire Coast 25 

Dredging Hebrides Coast ... 50 

Dredging the Mersey 5 

Resistance of Floating Bodies 

in Water 50 

Polycyanides of Organic Radi- 
cals 20 



Ixxiv 



REPOET — 1882. 



£ 

Eigor Mortis 10 

Irish Annelida 15 

Catalogue of Crania 50 

Didine Birds of Mascarene 

Islands 50 

Typical Crania Kesearches ... 30 
Palestine Exploration Fun d... 100 

£1750 

1867. 
Maintaining tlie Establish- 
ment of Kew Observatory.. 600 
Meteorological Instruments, 

Palestine 50 

Lunar Committee 120 

Metrical Committee 30 

Kent's Hole Explorations ... 100 

Palestine Explorations 50 

Insect Fauna, Palestine 30 

British Rainfall 50 

Kilkenny Coal Fields 25 

Almn Bay Fossil Leaf-Bed ... 25 

Luminous Meteors 50 

Bournemouth, &c., Leaf-Beds 30 

Dredging Shetland 75 

Steamship Reports Condensa- 
tion 100 

Electrical Standards 100 

Ethyl and Methyl series 25 

Fossil Crustacea 25 

Sound under Water 24 

North Greenland Fauna 75 

Do. Plant Beds 100 

Iron and Steel Manufacture... 25 

Patent Laws 30 

£7739" 

1868. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 

Lunar Committee ]20 

Metrical Committee 50 

Zoological Record 100 

Kent's Hole Explorations ... 150 

Steamship Performances 100 

British Rainfall 60 

Luminous Meteors 60 

Organic Acids 60 

Fossil Crustacea 25 

Methyl Series 25 

Mercury and Bile 25 

Organic Remains in Lime- 
stone Rocks 25 

Scottish Earthquakes 20 

Fauna, Devon and Cornwall.. 30 

British Fossil Corals 50 

Bagshot Leaf-Beds 50 

Greenland Explorations 100 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature ... 50 
Spectroscopic Investigations 
of Animal Substances 5 



«. 


d. 






































13 


4 







































































































4 






























4 






































































































































£ 

Secondary Reptiles, 4;c 30 

British Marine Invertebrate 

Faima 100 

£1940 

1869. ""^^^ 
Maintaining the Establish- 
ment of Kew Observatory. . 606 

Lunar Committee 50 

Metrical Committee 25 

Zoological Record ,... 100 

Committee on Gases in Deep- 
well Water 25 

British Rainfall 50 

Thermal Conductivity of Iron, 

&c 30 

Kent's Hole Explorations 150 

Steamship Performances 30 

Chemical Constitution of 

Cast Iron 80 

Iron and Steel Manufacture 100 

Methyl Series 30 

Organic Remains in Lime- 
stone Rocks >.... 10 

Earthquakes in Scotland 10 

British Fossil Corals 50 

Bagshot Leaf-Beds 30 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature... 30 
Spectroscopic Investigations 

of Animal Substances 5 

Organic Acids 12 

Kiltorcan Fossils 20 

Chemical Constitution and 
Physiological Action Rela- 
tions 15 

Mountain Limestone Fossils 25 

Utilization of Sewage 10 

Products of Digestion 10 

£162^ 

1870. ^"^~" 
Maintaining the Establisli- 

ment of Kew Observatory 600 

Metrical Committee 25 

Zoological Record 100 

Committee on Marine Famia 20 

Ears in Fishes 10 

Chemical Nature of Cast Iron 80 

Luminous Meteors 30 

Heat in the Blood 15 

British Rainfall.. 100 

Thermal Conductivity of 

Iron, &c 20 

British Fossil Corals 50 

Kent's Hole Explorations ... 150 

Scottish Earthquakes 4 

Bagshot Leaf- Beds 15 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature ... 50 
Kiltorcon Quatries Fossils ... 20 



i. d. 


















































































































































(» 




























yt 









































































































GENERAL STATEMENT. 



Ixxv 



... 50 












£1572 









£ s. d. 

Mountain Limestone Fossils 25 

Utilization of Sewage 50 

Organic Chemical Compounds 30 

Onny River Sediment 3 

Mechanical Equivalent of 
Heat 

J871. 
Maintaining the Establish- 
ment of Kew Observatory 600 
Monthly Reports of Progress 

in Chemistry 100 

Metrical Committee 25 

Zoological Record 100 

Thermal Equivalents of the 

Oxides of Chlorine 10 

Tidal Observations 100 

Fossil Flora 25 

Luminous Meteors 30 

British Fossil Corals 25 

Heat in the Blood 7 

British Rainfall 50 

Kent's Hole Explorations ... 150 

Fossil Crustacea 25 

Methyl Compounds 25 

Lunar Objects 20 

Fossil Coral Sections, for 

Photographing 20 

Bagshot^Leaf-Beds 20 

Moab Explorations 100 

Gaussian Constants 40 

£1472 2 6 

1872. 
Maintaining the Establish- 
ment of Kew Observatory 300 

Metrical Committee 75 

Zoological Record 100 

Tidal Committee 200 

Carboniferous Corals 25 

Organic Chemical Compounds 25 

Exploration of Moab 100 

Terato-Embryological Inqui- 
ries 10 

Kent's Cavern Exploration... 100 

Luminous Meteors 20 

Heat in the Blood 15 

Fossil Crustacea 25 

Fossil Elephants of Malta ... 25 

Lunar Objects 20 

Inverse Wave-Lengths 20 

British Rainfall 100 

Poisonous Substances Antago- 
nism 10 

Essential Oils, Chemical Con- 
stitution, &c 40 

Mathematical Tables 50 

Thermal Conductivity of Me- 
tals 25 

£1285 



















































2 


6 












































































































































































£ s. d. 
1873. 

Zoological Record 100 

Chemistry Record 200 

Tidal Committee 400 

Sewage Committee 100 

Kent's Cavern Exploration ... 1 50 

Carboniferous Corals 25 

Fossil Elephants 25 

Wave-Lengths 150 

British Rainfall 100 

Essential Oils 30 

Mathematical Tables 100 

Gaussian Constants 10 

Sub-Wealden Explorations... 25 

Underground Temperature ... 150 

Settle Cave Exploration 50 

Fossil Flora, Ireland 20 

Timber Denudation and Rain- 
fall 20 

Luminous Meteors 30 

£1(585 

1874. " 

Zoological Record 100 

Chemistry Record 100 

Mathematical Tables 100 

Elliptic Fimctions 100 

Lightning Conductors 10 

Thermal Conductivity of 

Rocks 10 

Anthropological Instructions, 

&c 50 

Kent's Cavern Exploration... 150 

Luminous Meteors 30 

Intestinal Secretions 15 

British Rainfall 100 

Essential Oils 10 

Sub-Wealden Explorations ... 25 

Settle Cave Exploration 50 

Mam-itius Meteorological Re- 
search 100 

Magnetizat ion of Iron 20 

Marine Organisms 30 

Fossils, North- West of Scot- 
land 2 10 

Physiological Action of Light 20 

Trades Unions 25 

Mountain Limestone-Corals 25 

Erratic Blocks 10 

Dredging, Durham and York- 
shire Coasts 28 5 

High Temperature of Bodies 30 

Siemens 's Pyrometer 3 6 

Labyrinthodonts of Coal- 

Measures 7 15 

£1151 16 

1875. ~ 

Eliptic Functions 100 

Magnetization of Iron 20 

British Rainfall 120 

Luminous Meteors 30 

Chemistry Record 100 



Ixxvi 



BEPORT — ] 882. 



£ 
Specific Volume of Liquids... 25 
Estimation of Potash and 

Piiosphoric Acid 10 

Isometric Cresols 20 

Sub-Wealden Explorations ... 100 
Kent's Cavern Exploration... 100 

Settle Cave Exploration 50 

Earthquakes in Scotland 15 

Underground Waters 10 

Development of Myxinoid 

Fishes 20 

Zoological Kecord 100 

Instructions for Travellers ... 20 

Intestinal Secretions 20 

Palestine Exploration 100 

£960 



g. 


d. 





















































































1876. 

Printing Mathematical Tables 1 50 

British Rainfall 100 

Ohm's Law 9 

Tide Calculating Machine ... 200 

Specific Volume of Liquids... 25 

Isomeric Cresols 10 

Action of Ethyl Bromobut}-- 
rate or Ethyl Sodaceto- 

acetate 5 

Estimation of Potash and 

Phosphoric Acid 13 

Exploration of Victoria Cave, 

Settle 100 

Geological Eecord 100 

Kent's Cavern Exploration... 100 
Thermal Conductivities of 

Rocks 10 

Underground Waters 10 

Earthquakes in Scotland 1 

Zoological Record 100 

Close Time 5 

Physiological Action of Sound 25 

Zoological Station 75 

Intestinal Secretions 15 

Physical Characters of Inha- 
bitants of British Isles 13 

Measuring Speed of Ships ... 10 
Effect of Propeller on turning 
of Steam Vessels .... 



4 2 

15 












































10 



































15 












5 









£1092 i 


2 



1877. 
Liquid Carbonic Acids in 

Minerals 20 

Elliptic Functions 250 

Thermal Conductivity of 

Rocks 117 

Zoological Record 100 

Kent's Cavern lOO 

Zoological Station at Naples 75 

Luminous Meteors 30 

Elasticity of Wires 100 

Dipterocarpae, Report on 20 



£ s. d. 
Mechanical Equivalent of 

Heat 35 

Double Compounds of Cobalt 

and Nickel 8 

Underground Temperatures 50 

Sottle^Cave Exploration 100 

Underground Waters in New 

Red'Sandstone 10 

Action of Ethyl Bromobuty- 

rate on Ethyl Sodaceto- 

acetate 10 

British Earthworks 25 

Atmospheric Elasticity in 

India 15 

Development of Light from 

Coal-gas 20 

Estimation of Potash and 

Phosphoric Acid 1 18 

Geological Record 100 

Anthropometric Committee 3-t 
Physiological Action of Phos- 

pliuric Acid, &c 15 

£1128 9 7 



1878. 
Exploration of Settle Caves 100 

Geological Record 100 

Investigation of Pulse Pheno- 
mena by means of Syphon 

Recorder 10 

Zoological Station at Naples 75 
In ve.stigation of Underground 

Waters 15 

Transmission of Electrical 

Impulses through Nerve 

Structure 30 

Calculation of Factor Table 

of Fourth Million 100 

Anthropometric Committee... 66 
Chemical Composition and 

Structure of less known 

Alkaloids 25 

Exploration of Kent's Cavern 50 

Zoological Eecord 100 

Fermanagh Caves Exploration 15 
Thermal Conductivity of 

Rocks 4 16 

Luminous Meteors 10 

Ancient Earthworks 25 

£725 16 6 

1879. 

Table at the Zoological 

Station, Naples 75 

Miocene Flora of the Basalt 

of the North of Ireland ... 20 

Illustrations for a Monograph 

on the Mammoth 17 

Record of Zoological Litera- 
ture 100 

Composition and Structure of 
less-known Alkaloids 25 



GENERAL STATEMENT. 



Ixxvii 



£ s. d. 

Exploration of Caves in 
Borneo 50 

Kent's Cavern Exploration ... 100 

Record of the Progress of 
Geology 100 

Fermanagh Caves Exploration 5 

Electrolysis of Metallic Solu- 
tions and Solutions of 
Compound Salts 2.5 

Anthropometric Committee... 50 

Natural History of Socotra ... 100 

Calculation of Factor Tables 
for 5th and 6th Millions ... 150 

Circulation of Underground 
Waters 10 

Steering of Screw Steamers... 10 

Improvements in Astrono- 
mical Clocks 30 

Marine Zoology of South 
Devon 20 

Determination of Mechanical 
Equivalent of Heat 12 

Specific Inductive Capacity 
of Sprengel Vacuum 40 

Tables of Sun-heat Co- 
efficients 30 

Datum Level of the Ordnance 
Survey _. 10 

Tables of Fundamental In- 
variants of Algebraic Forms 36 

Atmospheric Electricity Ob- 
servations in Madeira 15 

Instrument for Detecting 
Fire-damp in Mines 22 

Instruments for Measuring 
the Speed of Ships 17 

Tidal Observations in the 

English Channel 10 

£1080 11 11 











































































15 


G 




















14 


9 














1 


8 









1880. 

New Form of High Insulation 

Key 10 

Underground Temperature ... 10 

Determination of the Me- 
chanical Equivalent of 
Heat 8 5 

Elasticity of Wires 50 

Luminous Meteors 30 

Lunar Disturbance of Gravity 30 

Fundamental Invariants 8 5 

Laws of Water Friction 20 

Sjaecific Inductive Capacity 

of Sprengel Vacuum 20 

Completion of Tables of Sun- 
heat Co-efficients 50 

Instrument for Detection of 

Fire-damp in Mines 10 

Inductive Capacity of Crystals 

and Paraffines -1 1" 7 

Report on Carboniferous 

Poljzoa 10 



£ s. d. 

Caves of South Ireland 10 

Viviparous Nature of Ichthyo- 
saurus 10 

Kent's Cavern Exploration... 50 

Geological Record 100 

Miocene Flora of the Basalt 

of North Ireland 15 

Underground Waters of Per- 
mian Formations 5 

Record of Zoological Litera- 
ture 100 

Table at Zoological Station 

at Naples 75 

Investigation of the Geology 

and Zoology of Mexico 50 

Anthropometry 50 

Patent Laws 5 

£731 7 7 



1881. 

Lunar Disturbance of Gravity 30 

Underground Temperature ... 20 

High Insulation Key 5 

Tidal Observations 10 

Fossil Polyzoa 10 

Underground Waters 10 

Earthquakes in Japan 25 

Tertiary Flora 20 

Scottisli Zoological Station ... 50 

Naples Zoological Station ... 75 

Natural History of Socotra ... 50 

Zoological Record 100 

Weights and Heights of 

Human Beings 30 

Electrical Standards 25 

Antln-opological Notes and 

Queries 9 

Specific Refractions 7 

£476 

























































































3 1 



3 1 



1882. 
Tertiary Flora of North of 

Ireland 20 

Exploration of Caves of South 

of Ireland 10 

Fossil Plants of Halifax 15 

Fundamental Invariants of 

Algebraical Forms 76 1 11 

Record of Zoological Litera- 
ture 100 

British Fossil Polyzoa 10 

Naples Zoological Station ... 80 
Natural History of Timor-laut 100 
Conversion of Sedimentary 

Materials into Metamorphic 

Rocks 10 

Natural History of Socotra... 100 
Circulation of Underground 

Waters 15 

Migral ion of Birds 15 

Earthquake Phenomena of 

Japan 25 



IxxTiii 



KEPOET 1882. 



£ s. d. 

Geological Map of Europe ... 25 

Elimination of Nitrogen by 

Bodily Exercise 50 

Anthroi)ometric Committee... 50 

Photographing Ultra- Violet 

Spark Spectra 25 

Exploration of Raygill Fis- 
sure 20 

Calibration of Jlercurial Ther- 
mometers 20 



£ s. d. 

Wave-lengths Tables of Spec- 
tra of Elements 50 

Geological Kecord 100 

Standards for Electrical 
Measurements 100 

Exploration of Central Africa 100 

Albuminoid Substances of 

Serum 10 

£1120 1 11 




























General Meetings. 

On Wednesday, August 23, at 8 p.m., in tlie Skating Rink, Sir John 
Lubbock, Bart., M.P., D.C.L., LL.D., F.R.S., F.L.S., F.G.S., resigned the 
office of President to C. W. Siemens, Esq.,D.C.L., LL.D., F.R.S., F.C.S., 
M.I.C.E., who took the Chair, and dehvered an Address, for which see 
page 1. • 

On Thursday, August 24, at 8 p.m., a Soiree took place in the Hartley 
Institution. 

On Friday, August 25, at 8.30 p.m., in the Skating Rink, Professor 
Sir William Thomson, M.A., LL.D., D.C.L., F.R.S. , delivered a Discourse 
on ' Tides.' 

On Monday, August 28, at 8.30 p.m., in the Skating Rink, Professor 
H. N. Moseley, M.A., F.R.S., delivered a Discourse on ' Pelagic Life.' 

On Tuesday, August 29, at 8 p.m., a Soiree took place in the Hartley 
Institution. 

On Wednesday, August 30, at 2.30 p.m., the concluding General 
Meeting took place in the Skating Rink, when the Proceedings of the 
General Committee, and the Grants of Money for Scientific purposes, 
were explained to the Members. 

The meeting was then adjourned to Southport. [The Meeting is 
appointed to commence on Wednesday, September 19, 1883.] 



PEESIDENT'S ADDEESS. 



ADDEESS 

BY 

C. WILLIAM SIEMENS, 

D.C.L. (Oxon), LL.D. (Glasc. and Dabl.), Ph.D., F.R.S., F.C.S., 

Member Inst.C.E., 

PRESIDENT. 



In venturing to address the British Association from this chair, I feel 
that I have taken upon myself a task involving very serious responsibility. 
The Association has for half a century fulfilled the important mission of 
drawing together, once every year, scientists from all parts of the country 
for the purpose of discussing questions of mutual interest, of endowing 
research, and of cultivating those personal relations which aid so power- 
fully in harmonising views, and in stimulating concerted action for the 
advancement of science. 

A sad event casts a shadow over our gathering. While still mourning 
the irreparable loss Science had sustained in the person of Chai-les Darwin, 
whose bold conceptions, patient labour, and genial mind made him almost 
a type of unsurpassed excellence, telegraphic news reached Cambridge, 
just a month ago, to the effect that our General Secretary, Professor 
F. M. Balfour, had lost his life during an attempted ascent of the Aiguille 
Blanche de Peteret. Although only thirty years of age, few men have 
won distinction so rapidly and so deservedly. After attending the 
lectures of Dr. Michael Foster, he completed his studies of Biology under 
Dr. Anton Dohrn at the Zoological Station of Naples in 1875. In 1878 
he was elected a Fellow, and in November last a member of Council 
of the Royal Society, when he was also awarded one of the Royal Medals 
for his embryological researches. Within a short interval of time Glasgow 
University conferred on him their honorary degree of LL.D., he was 
elected President of the Cambridge Philosophical Society, and after having 
declined very tempting offers from the Universities of Oxford and Edin- 
burgh, he accepted a professorship of Animal Morphology created for 
him by his own University. Few men could have borne without hurt 
such a stream of honourable distinctions, but in j^oung Balfour genius 
and independence of thought were happily blended with industry and 
personal modesty ; these won for him the friendship, esteem, and admira- 
tion of all who knew him. 

It affords me gi-eat satisfaction to qualify the sad impression produced 

1882. B 



2 iiEPORT — 1882. 

by this event, by the happy one of the safe return to these shores of that 
most persistent and disinterested Arctic explorer, Mr. B. Leigh Smith, 
together -with his much enduring crew and valiant rescuers. 

Since the days of the first meeting of the Association in York in 
1831, great changes have taken place in the means at our disposal 
for exchanging views, either personally or through the medium of type. 
The creation of the railway system has enabled congenial minds to 
attend frequent meetings of those special Societies which have sprung 
into existence since the foundation of the British Association, amongst 
which I need only name here the Physical, Geographical, Meteorological, 
and Anthropological, cultivating abstract science, and the Institution of 
Mechanical Engineers, of Naval Architects, the Iron and Steel Institute, 
the Society of Telegraph Engineers and Electricians, the Gas Institute, 
the Sanitary Institute, and the Society of Chemical Industry, repre- 
senting applied science. These meet at frequent intervals in London, 
whilst others, having similar objects in view, hold their meetings at 
the University towns, and at other centres of intelligence and industry 
throughout the country, giving evidence of great mental activity, and 
producing some of those very results which the founders of the British 
Association wished to see realised. If we consider fui-ther the extra- 
ordinary development of scientific journalism which has taken place, 
it cannot surprise us when we meet with expressions of opinion to the 
effect that the British Association has fulfilled its mission, and should 
now yield its place to those special Societies it has served to call into 
existence. On the other hand, it may be urged that the brilliant success 
of last year's Anniversary Meeting, enhanced by the comprehensive address 
delivered on that occasion by my distinguished predecessor in ofiice, 
Sir John Lubbock, has proved, at least, that the British Association is 
not dead in the aflections of its members, and it behoves us at this, the 
first ordinary gathering in the second half-century, to consider what are 
the strong points to rely upon for the continuance of a career of success 
and usefulness. 

If the facilities brought home to our doors of acquiring scientific 
information have increased, the necessities for scientific inquiry have 
increased in a greater ratio. The time was when science was cultivated 
only by the few, who looked npon its application to the arts and 
manufactures as almost beneath their consideration ; this they were 
content to leave in the hands of others, who, with only commercial aims 
in view, did not aspire to further the objects of science for its own sake, 
but thought only of benefiting by its teachings. Progress could not be 
rapid under this condition of things, because the man of pure science 
rarely pursued his inquiry beyond the mere enunciation of a physical 
or chemical principle, whilst the simple practitioner was at a loss how 
to harmonise the new knowledge with the stock of information which 
formed his mental capital in trade. 



I 



ADDRESS. 3 

The advancement of the last fifty years has, I venture to submit, 
rendered theory and practice so interdependent, that an intimate union 
between them is a matter of absolute necessity for our future progress. 
Take, for instance, the art of dyeing, and we find that the discovery of 
new colouring matters derived from waste products, such as coal-tar, 
completely changes its practice, and renders an intimate knowledge of 
the science of chemistry a matter of absolute necessity to the practitioner. 
In telegraphy and in the new arts of applying electricity to lighting, to 
the transmission of power, and to metallurgical operations, problems 
arise at every turn, requiring for their solution not only an intimate 
acquaintance with, but a positive advance upon, electrical science as 
established by purely theoretical research in the laboratory. In general 
engineering the mere practical art of constructing a machine so designed 
and proportioned as to produce mechanically the desired effect, would 
suffice no longer. Our increased knowledge of the nature of the mutual 
relations between the difierent forms of energy makes us see clearly 
what are the theoretical limits of effect; these, although beyond our 
absolute reach, may be looked upon as the asymptotes to be approached 
indefinitely by the hyperbolic course of practical progress. Cases arise, 
moreover, where the introduction of new materials of construction, or the 
call for new effects, renders former rules wholly insufiicient. In all theso 
cases practical knowledge has to go hand in hand with advanced science 
in order to accomplish the desired end. 

Far be it from me to think lightly of the ardent students of nature, 
who, in their devotion to research, do not allow their minds to travel into 
the regions of utilitarianism and of self-interest. These, the high priests 
of science, command our utmost admiration ; but it is not to them that we 
can look for our current progress in practical science, much less can we 
look for it to the ' rule of thumb ' practitioner, who is guided by what 
comes nearer to instinct than to reason. It is to the man of science 
who also gives attention to practical questions, and to the practitioner 
who devotes part of his time to the prosecution of strictly scientific 
investigations, that we owe the rapid progress of the present day, both 
merging more and more into one class, that of pioneers in the domain of 
nature. It is such men that Archimedes must have desired when he 
refused to teach his disciples the art of constructing his powerful ballistic 
engines, exhorting them to give their attention to the principles involved 
in their construction, and that Telford, the founder of the Institution of 
Civil Engineers, must have had in his mind's eye, when he (at the sug- 
gestion of Tredgold) defined civil engineering as ' the art of directing the 
great sources of power in nature.' 

These considerations may serve to show that although we see the men 
of both abstract and applied science group themselves in minor bodies for 
the better prosecution of special objects, the points of contact between 
the difierent branches of knowledge are ever multiplying, all tending to 
form part of a mighty tree— the tree of modern science— under whose 

B2 



4 REPORT — 1882. 

ample shadow its cultivators will find it both profitable and pleasant to 
meet, at least once a year; and considering that this tree is not the 
growth of one country only, but spreads both its roots and branches 
far and wide, it appears desirable that at these yearly gatherings other 
nations should be more fully represented than has hitherto been the case. 
The subjects discussed at our meetings are without exception of general 
interest, but many of them bear an international character, such as the 
systematic collection of magnetic, astronomical, meteorological, and 
geodetical observations, the formation of a universal code for signalling 
at sea, and for distinguishing lighthouses, and especially the settle- 
ment of scientific nomenclatures and units of measurement, regarding all 
of which an international accord is a matter of the utmost practical im- 
portance. 

As regards the measures of length and weight it is to be regretted 
that this country still stands aloof from the movement initiated in France 
towards the close of last century ; but, considering that in scientific 
work metrical measure is now almost universally adopted, and that its 
use has been already legalised in this country, I venture to hope that 
its universal adoption for commercial purposes will soon follow as a 
matter of course. The practical advantages of such a measure to the 
trade of this country would, I am convinced, bo very great, for English 
goods, such as machinery or metal rolled to current sections, are now 
almost excluded from the continental market, owing to the unit measure 
employed in their production. The principal impediment to the adoption 
of the metre consists in the strange anomaly that although it is legal 
to use that measure in commerce, and although a copy of the standard 
metre is kept in the Standards' Department of the Board of Trade, it 
is impossible to procure legalised rods representing it, and to use a non- 
legalised copy of a standard in commerce is deemed fraudulent. Would 
it not be desirable that the British Association should endeavour to brino- 
about the use in this country of the metre and kilogramme, and, as a 
preliminai-y stop, ask the Government to be represented on the Inter- 
national Metrical Commission, whoso admirable establishment at Sevreg 
possesses, independently of its practical work, considerable scientific in- 
terest, as a well-found laboratory for developing methods of precise 
measurement ? 

Next in importance to accurate measures of length, weight, and time, 
stand, for the purposes of modern science, those of electricity. 

The remarkably clear lines separating conductors from non-con- 
ductors of electricity, and magnetic from non-magnetic substances, enable 
us to measure electrical quantities and efi'ects with almost mathematical 
precision ; and, although the ultimate nature of this, the youngest 
scientifically investigated form of energy, is yet wrapt in mystery, its 
laws are the most clearly established, and its measuring instruments 
(galvanometers, electrometers, and magnetometers) are amongst the. 



ADDBESS. 6 

most accurate in physical science. Nor could any branch of science or 
industry be named in which electrical phenomena do not occur, to exer- 
cise their direct and important influence. 

If, then, electricity stands foremost amongst the exact sciences, it 
follows that its unit measures should be determined with the utmost 
accuracy. Yet, twenty years ago, very little advance had been made 
towards the adoption of a rational system. Ohm had, it is true, given 
us the fixed relations existing between electromotive force, resistance and 
quantity of cnrrent ; Joule had established the dynamical equivalent of 
heat and electricity, and Gauss and Weber had proposed their elaborate 
system of absolute magnetic measurement. But these invaluable re- 
searches appeared only as isolated efforts, when, in 1862, the Electric 
Unit Committee was appointed by the British Association, at the instance 
of Sir William Thomson, and it is to the long-continued activity of this 
Committee that the world is indebted for a consistent and practical 
system of measurement, which, after being modified in details, received 
universal sanction last year by the International Electrical Congress 
assembled at Paris. 

At this Congress, which was attended officially by the leading 
physicists of all civilised countries, the attempt was successfully made to 
bring about a union between the statical system of measurement that had 
been followed in Germany and some other countries, and the magnetic or 
dynamical system developed by the British Association, also between the 
geometrical measure of resistance, the (Werner) Siemens unit, that had 
been generally adopted abroad, and the British Association unit in- 
tended as a multiple of Weber's absolute unit, though not entirely fulfil- 
ling that condition. The Congress, while adopting the absolute system 
of the British Association, referred the final determination of the unit 
measure of resistance to an International Committee, to be appointed by 
the representatives of the several Governments ; they decided to retain 
the mercury standard for reproduction and comparison, by which means 
the advantages of both systems are happily combined, and much valuable 
labour is utilised ; only, instead of expressing electrical quantities directly 
in absolute measure, the Congress has embodied a consistent system, 
based on the Ohm, the Centimetre, the Gramme, and the Second, in which 
the units are of a value convenient for practical measurements. In this, 
which we must hereafter know as the ' practical system,' as distinguished 
from the ' absolute system,' the units are named after leading physicists, 
the Ohm, Ampere, Volt, Coulomb, and Farad. 

I would venture to suggest that two further units might, with advan- 
tage, be added to the system decided on by the International Congress 
at Paris. The first of these is the unit of magnetic quantity or pole. 
It is of much importance, and few will regard otherwise than with 
satisfaction the suggestion of Clauslus that the unit should be called a 
' Weber,' thus retaining a name most closely connected with electrical 
measurements, and only omitted by the Congress in order to avoid the 



6 Heport— 1882. 

risk of confusion in the magnitude of the unit cilrtent with which his 
name had been formerly associated. 

The other unit I would suggest adding to the list is that of power. 
The power conveyed by a current of an Ampere through the diiFerence of 
potential of a Volt is the unit consistent with the practical system. It 
might be appropriately called a Watt, in honour of that master mind 
in mechanical science, James Watt. He ifc was who first had a clear 
physical conception of power, and gave a rational method of measuring it. 
A Watt, then, expresses the rate of an Ampere multiplied by a Volt, 
whilst a horse-power is 746 Watts, and a Cheval de Vapeur 735. 

The system of electro-magnetic units would then be : — 

(1) Weber, the unit of magnetic quantity = 10* C.G.S. Units. 

(2) Ohm ,, „ resistance = 10^ ,, 



(3) Volt 

(4) Ampere 

(5) Coulomb 

(6) Watt 

(7) Farad 



electromotive force = 10^ 
current = 10"' 

quantity =10"' 

power =: 10'^ 

capacity := 10-^ 



Before the list can be looked ujion as complete two other units may 
have to be added, the one expressing that of magnetic field, and the 
other of heat in terms of the electro-magnetic system. Sir William 
Thomson suggested the former at the Paris Congress, and pointed out 
that it would be proper to attach to ifc the name of Gauss, who first 
theoretically and practically reduced observations of terrestrial magnetism 
to absolute measure. A Gauss will, then, be defined as the intensity of 
field produced by a Weber at a distance of one centimetre ; and the 
Weber will be the absolute C.G.S. unit strength of magnetic pole. 
Thus the mutual force between two ideal point-poles, each of one Weber 
strength held at unit distance asunder, will be one dyne; that is to 
say, the force which, acting for a second of time on a gramme of matter, 
generates a velocity of one centimetre per second. 

The unit of heat has hitherto been taken variously as the heat re- 
quired to raise a pound of water at the freezing-point through 1° Fahren- 
heit or Centigrade, or, again, the heat necessary to raise a kilogramme of 
water 1° Centigrade. The inconvenience of a unit so entirely arbitrary 
is sufficiently apparent to justify the introduction of one based on the 
electro-magnetic system, viz. the heat generated in one second by the 
current of an Ampere flowing through the resistance of an Ohm. In 
absolute measure its value is 10^ C.G.S. units, and, assuming Joule's 
equivalent as 42,000,000, it is the heat necessary to raise 0*238 grammes 
of water 1° Centigrade, or, approximately, the riyoo^^ part of the arbitrary 
unit of a pound of water raised 1° Fahrenheit and the ^Vij^h of the 
kUogramme of water raised 1° Centigrade. Such a heat unit, if found 
acceptable, might with great propriety, I think, be called the Joule, 



ADDRESS. 7 

after the man who has done so mucli to develop the dynamical theory 
of heat. 

Professor Clausius urges the advantages of the statical system of 
measurement for simplicity, and shows that the numerical values of the 
two systems can readily be compared by the introduction of a factor, 
which he proposes to call the critical velocity ; this, Weber has already 
shown to be nearly the same as the velocity of light. It is not imme- 
diately evident how by the introduction of a simple multiple, signifying 
a velocity, the statical can be changed into dynamical values, and I am 
indebted to my friend Sir William Thomson for an illustration which 
struck me as remarkably happy and convincing. Imagine a ball of con- 
ducting matter so constituted that it can at pleasure be caused to shrink. 
Now let it first be electrified and left insulated with any quantity of 
electricity on it. After that, let it be connected with the earth by an 
excessively fine wire or a not perfectly dry silk fibre ; and let it shrink 
just so rapidly as to keep its potential constant, till the whole charge is 
carried ofi". The velocity with which its surface approaches its centre is 
the electrostatic measure of the conducting power of the fibre. Thus we 
see how 'conducting power' is, in electrostatic theory, properly measured 
in terms of a velocity. Weber had shown how, in electromagnetic 
theory, the resistance, or the reciprocal of the conducting power of a 
conductor, is properly measured by a velocity. The critical velocity, 
which measures the conducting power in electrostatic reckoning and the 
resistance in electromagnetic, of one and the same conductor, measures 
the number of electrostatic units in the electromagnetic unit of electric 
quantity. 

Without waiting for the assembling of the International Committee 
charged with the final determination of the Ohm, one of its most dis- 
tinguished members, Lord Rayleigh, has, with his collaborateure, Mrs. 
Sidgwick, continued his important investigation in this direction at the 
Cavendish Laboratory, and has lately placed before the Royal Society a 
result which will prolaably not be surpassed in accuracy. His redetermi- 
nation brings him into close accord with Dr. Werner Siemens, their two 
values of the mercury unit being 0-95418 and 0-9536 of the B.A. unit 
respectively, or 1 mercury unit = 0-941.3 X 10^ C.G.S. units. 

Shortly after the publication of Lord Rayleigh's recent results, Messrs. 
Glazebrook, Dodds, and Sargant, of Cambridge, communicated to the 
Royal Society two determinations of the Ohm, by difierent methods; 
and it is satisfactory to find that their final values differ only in the fourth 
decimal, the figures being, according to 

T T -n 1 • 1 1 nr. r\.c\QaK^ Earth Quadrant 
Lord Rayleigh , , 1 Ohm = 0-98651 ^-^^^ — 

Messrs. Glazebrook, etc. = 0*986271 „ 

Professor E. Wiedemann, of Leipzig, has lately called attention to the 



8 REPORT— 1882. 

importance of having the Ohm detei'mined in the most accurate manner 
possible, and enumerates four distinct methods, all of which should 
unquestionably be tried with a view of obtaining concordant results, 
because upon its accuracy will depend the whole future system of 
measurement of energy of whatever form. 

The word Energy was first used by Young in a scientific sense, and 
represents a conception of recent date, being the outcome of the labours 
of Carnot, Mayer, Joule, Grove, Clausius, Clerk-Maxwell, Thomson, 
. Stokes, Helmholtz, Macquorn-Rankine, and other labourers, who have 
accomplished for the science regarding the forces in Nature what we owe 
to Lavoisier, Dalton, Berzelius, Liebig, and others, as regards Chemistry. 
In this short word Energy we find all the efforts in nature, including 
electricity, heat, light, chemical action, and dynamics, equally represented, 
forming, to use Dr. Tyndall's apt expression, so many 'modes of motion.' It 
will readily be conceived that when we have established a fixed numerical 
relation between these different modes of motion, we know beforehand 
what is the utmost result we can possibly attain in converting one form 
of energy into another, and to what extent our apparatus for effecting 
the conversion falls short of realising it. The difference between 
ultimate theoretical effect and that actually obtained is commonly called 
loss, but, considering that energy is indestructible, represents really 
secondary effect which we obtain without desiring it. Thus friction in 
the working parts of a machine represents a loss of mechanical effect, but 
is a gain of heat, and in like manner the loss sustained in transfen-ing 
electrical energy from one point to another is accounted for by heat 
genei'ated in the conductor. It sometimes suits our purpose to augment 
the transformation of electrical into heat energy at certain points of the 
circuit, when the heat rays become visible, and we have the incandescence 
electric light. In effecting a complete severance of the conductor for a 
short distance, after the current has been established, a very great local 
resistance is occasioned, giving rise to the electric arc, the highest develop- 
ment of heat ever attained. Vibration is another form of lost energy in 
mechanism, but who would call it a loss if it proceeded from the violin of 
a Joachim or a Norman-Neruda ? 

Electricity is the form of energy best suited for transmitting an effect 
from one place to another ; the electric current passes through certain 
substances^the metals — with a velocity limited only by the retarding 
influence caused by electric charge of the surrounding dielectric, but 
approaching probably under favourable conditions that of radiant heat 
and light, or 300,000 kilometres per second; it refuses, however, to pass 
through oxidised substances, glass, gums, or through gases except when 
in a highly rarefied condition. It is easy therefore to confine the electric 
current within bounds, and to direct it through narrow channels of 
extraordinary length. The conducting wire of an Atlantic cable is 
such a narrow channel; it consists of a copper wire, or strand of 



ADDBESS. 9 

wires, 5 mm. in diameter, by nearly 5,000 kilometres in length, con. 
fined electrically by a coating of guttapercha about 4 mm. in thick- 
ness. The electricity from a small galvanic battery passing into 
this channel prefers the long journey to America in the good con- 
ductor, and back thi'ough the earth, to the shorter journey across the 
4 mm. in thickness of insulating material. By an improved arrange- 
ment the alternating currents employed to work long submarine cables 
do not actually complete the circuit, but are merged in a condenser at 
the receiving station after having produced their extremely slight but 
certain effect upon the receiving instrument, the beautiful syphon recorder 
of Sir William Thomson. So perfect is the channel and so precise the 
action of both the transmitting and receiviug instruments employed, that 
two systems of electric signals may be passed simultaneously through the 
same cable in opposite directions, producing independent records at either 
end. By the application of this duplex mode of working to the Direct 
United States cable nnder the superintendence of Dr. Muirhead, its 
transmitting power was increased from twenty-five to sixty words a 
minute, being equivalent to about twelve currents or primary impulses 
per second. In transmitting these impulse-currents simultaneously from 
both ends of the line, it must not be imagined, however, that they pass 
each other in the manner of liquid waves belonging to separate systems ; 
such a supposition would involve momentum in the electric flow, and 
although the effect produced is analogous to such an action, it rests upon 
totally different grounds — namely, that of a local circuit at each terminus 
being called into action automatically whenever two similar currents are 
passed into the line simultaneously from both ends. In extending this 
principle of action quadruples telegraphy has been rendered possible, 
although not yet for long submarine lines. 

The minute currents here employed are far surpassed as regards delicacy 
and frequency by those revealed to us by that marvel of the present day, the 
telephone. The electric currents caused by the vibrations of a diaphragm 
acted upon by the human voice naturally vary in frequency and intensity 
according to the number and degree of those vibrations, and each motor 
current in exciting the electro-magnet forming part of the receiving 
instrument deflects the iron diaphragm occupying the position of an 
armature to a greater or smaller extent according to its strength. Savart 
found that the fundamental la springs from 440 complete vibrations in a 
second, but what must be the frequency and modulations of the motor 
current and of magnetic variations necessary to convey to the ear, 
through the medium of a vibrating armature, such a complex of human 
voices and of musical instruments as constitutes an opera perforroftnce ? 
And yet such performances could be distinctly heard and even enjoyed, 
as an artistic treat, by applying to the ears a pair of the double tele- 
phonic receivers at the Paris Electrical Exhibition, when connected with 
a pair of transmitting instruments in front of the footlights of the Grand 
Opera. In connection with the telei^hone, and with its equally remarkable 



10 EEPORT— 1882. 

adjunct the microphone, the names of Riess, Graham Bell, Edison, and 
Hughes will ever be remembered. 

Considering the extreme delicacy of the currents working a telephone, 
it is obvious that those caused by induction from neighbouring tele- 
graphic line wires would seriously interfere with the former, and mar the 
speech or other sounds produced through their action. To avoid such 
interference the telephone wires if suspended in the air require to be 
placed at some distance from telegraphic line wires, and to be supported 
by separate posts. Another way of neutralising interference consists in 
twisting two separately insulated telephone wires together, so as to form 
a strand, and in using the two conductors as a metallic circuit to the 
exclusion of the earth ; the working current will, in that case, receive 
equal and opposite inductive influences, and will therefore remain un- 
affected by them. On the other hand two insulated wires instead of one 
are required for working one set of instruments ; and a serious increase 
in the cost of installation is thus caiiscd. To avoid this Mr. Jacob 
has lately suggested a plan of combining pairs of such metallic circuits 
again into separate working pairs, and these again with other 
workiflg pairs, whereby the total number of telephones capable of being 
worked without interference is made to equal the total number of 
single wires em^sloyed. The working of telephones and telegraphs in 
metallic circuit has the fui'ther advantage that mutual volta induction 
between the outgoing and returning currents favours the transit, and 
neutralises on the other hand the retarding influence caused by change in 
underground or submarine conductors. These conditions are particularly 
favourable to underground line wii'cs, which possess other important 
advantages over the still prevailing overground sj'stem, in that they 
are unaffected by atmospheric electricity, or by snowstorms and heavy 
gales, which at not very rare intervals of time put us back to pre- 
telegraphic days, when the letter-carrier was our swiftest messenger. 

The underground system of telegraphs, first introduced into Germany 
by Werner Siemens in the years 1847-48, had to yield for a time to the 
overground system owing to technical difficulties ; but it has been again 
resorted to within the last four years, and multiple land cables of solid 
construction now connect all the important towns of that country. The 
first cost of such a system is no doubt considerable (being about 38L per 
kilometre of conductor as against 81. 10s. the cost of land lines) ; but as 
the underground wires are exempt from frequent repairs and renewals, 
and as they insui-e continuity of service, they are decidedly the cheaper 
and better in the end. The experience aff"orded by the early introduction 
of the underground system in Germany was not, however, without its 
beneficial results, as it brought to light the phenomena of lateral 
induction, and of faults in the insulating coating, matters which had to be 
understood before submarine telegraphy could be attempted with any 
reasonable prospect of success. 

Regarding the transmission of power to a distance the electric current 



ADDRESS. 11 

has now entered the lists in competition with compressed air, the 
hydraulic accumulator, and the quick running rope as used at Schaff- 
hausen to utilise the power of the Rhine fall. The transformation of 
electrical into mechanical energy can be accomplished with no further 
loss than is due to such incidental causes as friction and the heating of 
wires ; these in a properly designed dynamo-electric machine do not exceed 
ten per cent., as shown by Dr. John Hopkinson, and, judging from recent 
experiments of my own, a still nearer approach to ultimate perfection is 
attainable. Adhering, however, to Dr. Hopkinson's determination for 
safety's sake, and assuming the same percentage in reconverting the 
current into mechanical effect, a total loss of 19 per cent, results. To 
this loss must be added that through electrical resistance in the connecting 
line wires, which depends upon their length and conductivity, and that 
due to heating by friction of the working parts of the machine. Taking 
these as being equal to the internal losses incurred in the double pro- 
cess of conversion, there remains a useful effect of 100 — 38 = 62 per 
cent., attainable at a distance, which agrees with experimental results, 
although in actual practice it would not be safe at present to expect more 
than 50 per cent, of ultimate useful effect, to allow for all incidental losses. 

In using compressed air or water for the transmission of power, the 
loss cannot be taken at less than 50 per cent., and, as it depends upon 
fluid resistance, it increases with distance more rapidly than in the case of 
electricity. Taking the loss of effect in all cases as 50 per cent., electric 
transmission presents the advantage that an insulated wire does the work 
of a pipo capable of withstanding high internal pressure, which latter 
must be more costly to put down and to maintain. A second metallic 
conductor is required, however, to complete the electrical circuit, as the 
conducting power of the earth alone is found unreliable for passing 
quantity currents, owing to the effects of polarization ; but as this second 
conductor need not be insulated, water or gas pipes, railway metals 
or fencing wire, may be called into requisition for this purpose. The 
small space occupied by the electi-o-motor, its high working speed, 
and the absence of waste products, render it specially available for the 
general distribution of power to cranes and light machinery of every 
description, A loss of effect of 50 per cent, does not stand in the way 
of such applications, for it must be remembered that a powerful central 
engine of best construction produces motive power with a consumption 
of two pounds of coal per horse-power per hour, whereas small engines 
distributed over a district would consume not less than five ; we thus 
see that there is an advantage in favour of electric transmission as 
regards fuel, independently of the saving of labour and other collateral 
benefits, which more than compensate for interest on the cost of instal- 
lation. 

To agriculture, electric transmission of power seems well adapted for 
effecting the various operations of the farm and fields from one centre. 
Having worked such a system myself in combination with electric lighting 



12 REPOBT— 1882. 

and horticulture for upwards of two years, I can speak with confidence 
of its economy, and of the facility with which the work is accomplished 
in charge of untrained persons. 

As regards the eflPect of the electric light upon vegetation there is 
little to add to what was stated in my paper read before Section A 
last year, and ordered to be printed with the Keport, except that in 
experimenting upon wheat, barley, oats, and other cereals sown in the 
open air, there was a marked difference between the growth of the plants 
influenced and those uninfluenced by the electric light. This was not 
very apparent till towards the end of February, when, with the first 
appearance of mild weather, the plants under the influence of an electric 
lamp of 4,000 candle power placed about 5 metres above the surface, 
developed with extreme rapidity, so that by the end of May they stood 
above 4 feet high, with the ears in full bloom, when those not under its 
influence were under 2 feet in height, and showed no sign of the ear. 

In the electric railway first constructed by Dr. Werner Siemens, at 
Berlin, in 1879, electric energy was transmitted to the moving carriage 
or train of carriages, through the two rails upon which it moved, these 
being sufficiently insulated from each other by being placed upon well 
creosoted cross sleepers. At the Paris Electrical Exhibition the current 
was conveyed through two separate conductors making sliding or 
rolling contact with the carriage, wliereas in the electric railway now in 
course of construction in the north of Ireland (which when completed 
will have a length of twelve miles) a separate conductor will be pro- 
vided by the side of the railway, and the return circuit completed 
through the rails themselves, which in that case need not be insulated ; 
secondary batteries will be used to store the surplus energy created in 
running downhill, to be restored in ascending steep inclines, and for passing 
roadways where the separate insulated conductor is not pi-acticable. 
The electric railway possesses great advantages over horse or steam-power 
for towns, in tunnels, and in all cases where natural sources of energy, 
such as waterfalls, are available ; but it would not be reasonable to sup- 
pose that it will in its present condition compete with steam propulsion 
upon ordinary railways. The transmission of power by means of electric 
conductors possesses the further advantage over other means of trans- 
mission that, provided the resistance of the rails be not very great, the 
power communicated to the locomotive reaches its maximum when the 
motion is at its minimum — that is, in commencing to work, or when 
encountering an exceptional resistance — 'whereas the utmost economy is 
produced in the normal condition of working when the velocity of the 
power-absorbing nearly equals that of tl^e current-producing machine. 

The deposition of metals from their solutions is perhaps the oldest of 
all useful applications of the electric current, but it is only in very recent 
times that the dynamo current has been practically applied to the refining 
of copper and other metals, as now practised at Birmingham and else- 
where, and upon an exceptionally large scale at Ocker, in Germany, 



I 



ADDRESS. 1 3 

■where the motive power is derived from a water-wheel. The dynamo 
machine there employed was exhibited at the Paris Electrical Exhibition 
by Dr. Werner Siemens, its peculiar feature being that the conductors 
upon the rotating armature consisted of solid bars of copper 30 mm. 
square, in section, which were found only just sufficient to transmit the 
large quantity of electricity of low tension necessary for this operation. 
One such machine consuming 4-horse power deposits about 300 kilo- 
grammes of copper per 24 hours. 

Electric energy may also be employed for heating purposes, but in 
this case it would obviously be impossible for it to compete in point of 
economy with the direct combustion of fuel for the attainment of ordinary 
degrees of heat. Bunsen and St. Claire De Ville have taught us, how- 
ever, that combustion becomes extremely sluggish when a temperature of 
1,800° C. has been reached, and for effects at temperatures exceeding that 
limit the electric furnace will pi'obably find advantageous applications. 
Its specific advantage consists in being apparently unlimited in the degree 
of heat attainable, thus opening out a new field of investigation to the 
chemist and metallurgist. Tungsten has been melted in such a furnace, 
and 8 pounds of platinum have been reduced from the cold to the liquid 
condition in 20 minutes. 

The largest and most extensive application of electric energy at the 
present time is to lighting, but, considering how much has of late been 
said and written for and against this new illuminant, I shall here 
confine myself to a few general remarks. Joule has shown that if an 
electric current is passed through a conductor the whole of the energy 
lost by the current is converted into heat; or, if the resistance be 
localised, into radiant energy, comprising heat, light, and actinic rays. 
Neither the low heat rays nor the ultra-violet of highest refrangibility 
affect the retina, and may be regarded as lost energy, the effective rays 
being those between the red and violet of the spectrum, which in their 
combination produce the effect of white light. 

Regarding the proportion of luminous to non-luminous rays proceeding 
from an electric arc or incandescent wire, we have a most, valuable 
investigation by Dr. Tyndall, recorded in his work on ' Radiant Heat.' 
Dr. Tyndall shows that the luminous rays from a platinum wire heated 
to its highest point of incandescence, which may be taken at 1,700° C, 
formed oV^h part of the total radiant energy emitted, and ^^V^^ P^^^ i^ 
the case of an arc light worked by a battery of 60 Grove's elements. 
In order to apply these valuable data to the case of electric lighting 
by means of dynamo currents, it is necessary in the first place to deter- 
mine what is the power of 50 Grove's elements of the size iised by 
Dr. Tyndall, expressed in the practical scale of units as now established. 
From a few experiments lately undertaken for myself, it would appear 
that .50 such cells have an electro-motive force of 98-5 Volts, and an 
internal resistance of 13'5 Ohms, giving a current of 7"o Amperes when 
the cells are short-circuited. The resistance of a regulator such as Dr. 



14 BEPORT — 1882. 

Tyndall used in his experiments may be taken at 10 Ohms, the current 

qg.g 
produced in the arc would be - " lo i i ~ "^ ^™peres (allowing one 

Ohm for the leads), and the power consumed 10x4^ = 160 Watts; the 
light power of such an arc would be about 150 candles, and, compai'ing 
this with an arc of 3,308 candles produced by 1,162 Watts, wc find that 

r V i.e., 7-3 times the electric energy produce (-TTTr )> i.e., 22 

times the amount of light measured horizontally. If, therefore, in Dr. 

Tyndall's arc -jyth of the radiant energy emitted was visible as light, it 

1 22'0 
follows that in a powerful arc of 3,300 candles, — - x -— -, or fully ^-, are 

luminous rays. In the case of the incandescent light (say a Swan light 
of 20 candle power) we find in practice that 9 times as much power has 
to be expended as in the case of the arc light ; hence ^ x J- = ^V P^''*' of 
the power is given out as luminous rays, as against ^'jth in Dr. Tyndall's 
incandescent platinum — a result suificiently approximate considering the 
wide difference of conditions under which the two are compared. 

These results are not only of obvious practical value, but they seem to 
establish a fixed relation between current, temperature, and light produced, 
which may serve as a means to determine temperatures exceeding the 
melting point of platinum with greater accuracy than has hitherto been 
possible by actinimetric methods in which the thickness of the luminous 
atmosphere must necessarily exercise a disturbing influence. It is probably 
owing to this circumstance that the temperature of the electric arc as well 
as that of the solar photosphere has frequently been greatly over-estimated. 

The principal argument in favour of the electric light is furnished by 
its immunity from products of combustion which not only heat the 
lighted apartments, but substitute carbonic acid and deleterious sulphur 
compounds for the oxygen upon which respiration depends ; the electric 
light is white instead of yellow, and thus enables us to see pictures, furni- 
ture, and flowers as by daylight ; it supports growing plants instead of 
poisoning them, and by its means we can carry on photography and 
many other industries at night as well as during the day. The objec- 
tion frequently urged against the electric light, that it depends upon 
the continuous motion of steam or gas engines, which are liable to 
accidental stoppage, is met by the introduction into practical use of the 
secondary battery ; this, although not embodying a new conception, has 
lately been gi-eatly improved in power and constancy by Plante, Faure, 
Volckmar, Sellon, and others, and promises to accomplish for electricity 
what the gas-holder has done for the supply of gas and the accumulator 
for hydraulic transmission of power. 

It can no longer be a matter of reasonable doubt, therefore, that 
electric lighting will take its place as a public illuminant, and that, even 
though its cost should be found greater than that of gas, it will be 
preferred for the lighting of drawing-rooms and dining-rooms, theatres 



ADDRESS. 15 

and concert-rooms, museums, cliurclies, warehouses, show-rooms, print- 
ing establishments and factoiries, and also the cabins and engine-rooms of 
passenger steamers. In the cheaper and more powerful form of the arc 
light, it has proved itself superior to any other illuminant for spreading 
artificial daylight over the large areas of harbours, railway stations, and 
the sites of public works. When placed within a holophote the electric 
lamp has already become a powerful auxiliary in effecting military opera- 
tions both by sea and land. 

The electric light may be worked by natural sources of power such as 
waterfalls, the tidal wave, or the wind, and it is conceivable that these 
may be utilised at considerable distances by means of metallic conductors. 
Some five years ago I called attention to the vastness of those sources 
of energy, and the facility oS'ered by electrical conduction in rendering 
them available for lighting and power-supply, while Sir William Thomson 
made this important matter the subject of his admirable address to 
Section A last year at York, and dealt with it in an exhaustive manner. 

The advantages of the electric light and of the distribution of power 
by electricity have lately been recognised by the British Government, which 
has just passed a Bill through Parliament to facilitate the establishment 
of electrical conductors in towns, subject to certain regulating clauses to 
protect the interests of the public and of local authorities. Assuming the 
cost of electric light to be practically the same as gas, the preference for 
one or other will in each application be decided iipon grounds of relative 
convenience, but I venture to think that gas-lighting will hold its own 
as the poor man's friend. 

Gaa is an institution of the utmost value to the artisan ; it requires 
hardly any attention, is supplied upon regulated terms, and gives with 
what should be a cheerful light a genial warmth, which often saves the 
lighting of a fire. The time is moreover not far distant, I venture to 
think, when both rich and poor will largely resort to gas as the most 
convenient, the cleanest, and the cheapest of heating agents, and when 
raw coal will be seen only at the colliery or the gasworks. In all 
cases where the town to be supplied is within say 30 miles of the 
colliery, the gasworks may with advantage be planted at the mouth, or 
still better at the bottom of the pit, whereby all haulage of fuel would 
be avoided, and the gas, in its ascent from the bottom of the collieiy, 
would acquire an onward pressure sufficient probably to impel it to its 
destination. The possibility of transporting combustible gas through 
pipes for such a distance has been proved at Pittsburg, where natural gas 
from the oil district is used in large quantities for heating purposes. 

The quasi monopoly so long enjoyed by gas companies has had the 
inevitable effect of checking progress. The gas being supplied by meter, 
it has been seemingly to the advantage of the companies to give 
merely the prescribed illuminating power, and to discourage the inven- 
tion of economical burners, in order that the consumption might reach a 



16 REPOET— 1882. 

maximum. The application of gas for heating purposes has not been 
encouraged, and is still made diflScalt in consequence of the objectionable 
practice of reducing the pressure in the mains during daytime to the 
lowest possible point consistent with prevention of atmospheric indraught. 
The introduction of the electric light has convinced gas managers and 
directors that such a policy is no longer tenable, but must give way to 
one of technical progress ; new processes for cheapening the production 
and increasing the purity and illuminating power of gas are being fully 
discussed before the Gas Institute ; and improved burners, rivalling the 
electric light in brilliancy, greet our eyes as we pass along our principal 
thoroughfares. 

Regarding the importance of the gas supply as it exists at present, 
we find from a Government return that the capital invested in gasworks 
in England, other than those of local authorities, amounts to 80,000,000Z.; 
in these 4,281,048 tons of coal are converted annually, producing 43,000 
million cubic feet of gas, and about 2,800,000 tons of coke ; whereas the 
total amount of coal annually converted in the United Kingdom may be 
estimated at 9,000,000 tons, and the by-products therefrom at 500,000 
tons of tar, 1,000,000 tons of ammonia liquor, and 4,000,000 tons of coke, 
according to the returns kindly furnished me by the managers of many 
of the gasworks and corporations. To these may be added say 120,000 
tons of sulphur, which up to the present time is a waste product. 

Previous to the year 1856 — that is to say, before Mr. W. H. Perkin 
had invented his practical process, based chiefly upon the theoretical 
investigations of Hofman, regarding the coal-tar bases and the chemical 
constitution of indigo — the value of coal-tar in London was scarcely a 
halfpenny a gallon, and in country places gas-makers were glad to give 
it away. Up to that time the coal-tar industry had consisted chiefly in 
separating the tar by distillation into naphtha, creosote, oils, and pitch. 
A tew distillers, however, made small quantities of benzene, which had 
been first shown — by Mansfield, in 1849 — to exist in coal-tar naphtha 
mixed with toluene, cumene, &c. The discovery, in 1856, of the mauve 
or aniline purple gave a great impetus to the coal-tar trade, inasmuch 
as it necessitated the separation of large quantities of benzene, or a 
mixture of benzene and toluene, from the naphtha. The trade was 
further increased by the discovery of the magenta or rosaniline dye, 
which required the same products for its preparation. In the mean- 
time, carbolic acid was gradually introduced into commerce, chiefly as 
a disinfectant, but also for the production of colouring matter. 

The next most important development arose fi-om the discovery by 
Grsebe and Liebermann that alizarine, the colouring pi*inciple of the 
madder root, was allied to anthracene, a hydrocarbon existing in coal-tar. 
The production of this colouring matter from anthracene followed, and 
is now one of the most important operations connected with tar-distilling. 
The success of the alizarine made in this manner has been so great that 
it has almost entirely superseded the use of madder, which is now culti- 



ADDKESS. 17 

Vated to only a coinparatively small extent. Tlie most important colour- 
ing matters recently introduced are the azo-scarlets. They have called 
into use the coal-tar hydrocarbons, xylene and cumene. Naphthalene is 
also used in their preparation. These splendid dyes have replaced 
cochineal in many of its applications, and have thus seriously interfered 
■with its use. The discovery of artificial indigo by Professor Baeyer is 
of great interest. For the preparation of this colouring matter toluene is 
required. At present artificial indigo does not compete seriously with 
the natural product ; but should it eventually be prepared in quantity 
from toluene, a further stimulus will be given to the coal-tar trade. 

The colour industry utilises even now practically all the benzene, a 
large proportion of the solvent naphtha, all the anthracene, and a portion 
of the naphthalene resulting from the distillation of coal-tar ; and the 
value of the colouring matter thus produced is estimated by Mr. Perkin 
at 3,350,000Z. 

The demand for ammonia may be taken as unlimited, on account of 
its high agricultural value as a manure ; and, considering the failing 
supply of guano and the growing necessity for stimulating the fertility of 
our soil, an increased production of ammonia may be regarded as a matter 
of national importance, for the supply of which we have to look almost 
exclusively to our gasworks. The present production of 1,000,000 tons 
of liquor yields 95,000 tons of sulphate of ammonia ; which, taken at 
20Z. 10s. a ton, represents an annual value of 1,947,500L 

The total annual value of the gasworks' by-products may be estimated 
as follows : — 

Colouring matter £3,350,000 

Sulphate of ammonia 1,947,500 

Pitch (325,000 tons) 365,000 

Creosote (25,000,000 gallons) 208,000 

Crude carbolic acid (1,000,000 gallons) . . . 100,000 
Gas coke, 4,000,000 tons (after allowing 2,000,000 tons 

consumption in working the retorts) at I2s. . . 2,400,000 

Total ... . . £8,370,500 

Taking the coal used, 9,000,000 tons, at 12.s., equal 5,400,000Z. ; it 
follows that the by-products alone exceed in value the coal used by 
very nearly 3,000,000?. 

In using raw coal for heating purposes these valuable products are 
not only absolutely lost to us, but in their stead we are favoured with 
those semi-gaseous by-products in the atmosphere too well known to the 
denizens of London and other large towns as smoke. Professor Roberts 
has calculated that the soot in the pall hanging over London on a 
winter's day amounts to fifty tons, and that the carbon present as 
hydrocarbons and in the half-burnt form of carbonic oxide, a poisonous 
compound, resulting from the imperfect combustion of coal, may be 
taken as at least five times that amount. Mr. Aitken has shown, 
moreover, in an interesting paper communicated to the Royal Society of 

1882. c 



18 REPORT— 1882. 

Bdinburgh, last year, that the fine dust resulting from the imperfect 
combustion of coal is mainly instrumental in the formation of fog ; each 
particle of solid matter attracting to itself aqueous vapour ; these glo- 
bules of fog are rendered particularly tenacious and disagreeable by the 
presence of tar vapour, another result of imperfect combustion of raw 
fuel, which might be turned to much better account at the dye-works. 
The hurtful influence of smoke upon public health, the great personal 
discomfort to which it gives rise, and the vast expense it indirectly 
causes through the destruction of our monuments, pictures, furniture, 
and apparel, are now being recognised, as is evinced by the success of 
recent Smoke Abatement Exhibitions. The most effectual remedy would 
result from a general recognition of the fact that wherever smoke is 
produced, fuel is being consumed wastefnlly, and that all our calorific 
effects, from the largest down to the domestic fire, can be realised as 
completely and more economically, without allowing any of the fuel 
employed to reach the atmosphere unburnt. This most desirable result 
may be effected by the use of gas for all heating purposes, with or without 
the addition of coke or anthracite. 

The cheapest form of gas is that obtained through the entire distilla- 
tion of fuel in such gas-producers as are now largely used in working 
the furnaces of glass,i iron, and steel works ; but gas of this description 
would not be available for the supply of towns, owing to its bulk, about 
two-thirds of its volume being nitrogen. The use of water-gas, resulting 
from the decomposition of steam in passing through a hot chamber filled 
with coke, has been suggested, but this gas also is objectionable, because 
it contains, besides hydrogen, the poisonous and inodorous gas carbonic 
oxide, the introduction of which into dwelling-houses could not be 
effected without considerable danger. A more satisfactory mode of 
supplying heating separately from illuminating gas would consist in 
connecting the retort at different periods of the distillation with two 
separate systems of mains for the delivery of the respective gases, as 
has been proposed by me elsewhere. Experiments made some years ago 
by Mr. ElLisen of the Paris gasworks have shown that the gases rich in 
carbon, such as defiant and acetylene, are developed chiefly during an 
interval of time beginning half an hour after the commencement and 
terminating at half the whole period of distillation, whilst during the 
remainder of the time marsh gas and hydrogen are chiefly developed, 
which, while possessing little illuminating power, are most advantageous 
for heating purposes. By resorting to improved means of heating the 
retorts with gaseous fuel, such as have been in use at the Paris gasworks 
for a considerable number of years, the length of time for effecting each 
distillation may be shortened from six hours, the usual period in former 
years, to four, or even three hours, as now practised at Glasgow and else- 
where. By this means a given number of retorts can be made to produce, 
in addition to the former quantity of illuminating gas of superior quality, a 
similar quantity of heating gas, resulting in a diminished cost of production 



ADDRESS. 19 

and an increased supply of the valuable by-products previously referred 
to. The quantity of both ammonia and heating gas may be further 
increased by the simple expedient of passing a streamlet of steam through 
the heated retorts towards the end of each operation, whereby the 
ammonia and hydrocarbons still occluded in the heated coke will be 
evolved, and the volume of heating gas produced be augmented by the 
products of decomposition of the steam itself. It has been shown that 
gas may be used advantageously for domestic purposes with judicious 
management even under present conditions, and it is easy to conceive 
that its consumption for heating would soon increase, perhaps tenfold, if 
supplied separately at, say, Is. a thousand cubic feet. At this price gas 
would be not only the cleanest and most convenient, but also the cheapest 
form of fuel, and the enormous increase of consumption, the superior 
quality of the illuminating gas obtained by selection, and the propor- 
tionate increase of by-products, would amply compensate the gas com- 
pany or corporation for the comparatively low price of the heating gas. 

The greater efficiency of gas as a fuel results chiefly from the cir- 
cumstance that a pound of gas yields in combustion 22,000 heat units, 
or exactly double the heat produced in the combustion of a pound of 
ordinary coal. This extra heating power is due partly to the freedom 
of the gas from earthy constituents, but chiefly to the heat imparted to it 
in efiecting its distillation. Recent experiments with gas-burners have 
shown that in this direction also there is much room for improvement. 

The amount of light given out by a gas flame depends upon the 
temperature to which the particles of solid carbon in the flame are raised, 
and Dr. Tyndall has shown that, of the radiant energy set up in such a 
flame, only the o^th part is luminous ; the hot products of combustion 
carry ofi" at least four times as much energy as is radiated, so that not more 
than one hundredth part of the heat evolved in combustion is converted 
into light. This proportion could be improved, however, by increasing 
the temperature of combustion, which maybe effected either by intensified 
air currents or by regenerative action. Supposing that the heat of the 
products of combustion could be communicated to metallic surfaces, and 
be transferred by conduction or otherwise to the atmospheric air sup- 
porting combustion in the flame, we should be able to increase the tem- 
perature accumulatively to any point within the limit of dissociation ; 
this limit may be fixed at about 2,300° C, and cannot be very much 
below that of the electric arc. At such a temperature the proportion of 
luminous rays to the total heat produced in combustion would certainly be 
more than doubled, and the brilliancy of the light would at the same time 
be greatly increased. Thus improved, gas-lighting may continue its rivalry 
with electric lighting both as regards economy and brilliancy, and such 
rivalry must necessarily result in great public advantage. 

In the domestic grate radiant energy of inferior intensity is reqiiired, 
and I for one do not agree with those who would like to see the open 
fireplace of this country superseded by the continental stove. The 

C2 



20 REPORT— 1882. 

advantages nslially claimed for the open fireplace are, that it is cliecrful, 
* pokable,' and conducive to ventilation, but to these may be added another 
of even greater importance, viz. that the radiant heat which it emits passes 
through the transpai'ent air without warming it, and imparts heat only 
to the solid walls, floor, and fui'niture of the room, which are thus con- 
stituted the heating surfaces of the comparatively cool air of the apart- 
ments in contact with them. In the case of stoves the heated air of 
the room causes deposit of moisture upon the walls in heating them, 
and gives rise to mildew and germs injurious to health. It is, I think, 
owing to this circumstance that upon entering an apartment one can 
immediately perceive whether or not it is heated by an open fireplace ; 
nor is the unpleasant sensation due to stove-heating completely removed 
by mechanical ventilation ; there is, moreover, no good reason why an 
open fireplace should not be made as economical and smokeless as a stove 
or hot- water apparatus. 

In the production of mechanical efiect from heat, gaseous fuel also 
pi'esents most striking advantages, as will appear from the following con. 
sideration. When we have to deal with the question of converting 
mechanical into electrical effect, or vice versa, by means of the dynamo- 
electrical machine, we have only to consider what are the equivalent 
values of the two forms of energy, and what precautions are necessary to 
avoid losses by the electrical resistance of conductors and by friction. 
The transformation of mechanical efiect into heat involves no losses, except 
those resulting from imperfect installation, and these may be so completely 
avoided that Dr. Joule was able by this method to determine the equivalent 
values of the two forms of energy. But in attempting the inverse operation, 
of efi"ecting the conversion of heat into mechanical energy, we find our- 
selves confronted by the second law of thermo-dynamics, which says, that 
whenever a given amount of heat is converted into mechanical efiect, 
another but variable amount descends from a higher to a lower potential, 
and is thus rendered unavailable. 

In the condensing steam engine this waste heat comprises that 
communicated to the condensing water, whilst the useful heat, or that 
converted into mechanical efiect, depends ui3on the diS'erence of tem- 
perature between the boiler and condenser. The boiler pressure is 
limited, however, by considerations of safety and convenience of con- 
struction, and the range of working temperature rarely exceeds 120° C. 
except in the engines constructed by Mr. Perkins, in which a range 
of 160° C, or an expansive action commencing at 14 atmospheres, 
has been adopted with considerable success, as appears from an able 
report on this engine by Sir Fredei-ick Bramwell. To obtain more ad- 
vantageous primary conditions we have to turn to the caloric or gas engine, 

because m them the coefficient of efiiciency expressed by ■ may be 

greatly increased. This value would reach a maximum if the initial 



ADDRESS. 21 

absolute temperature x could be raised to that of combustion, and t' 
reduced to atmospheric temperaturOj and these maximum limits can bo 
much more nearly approached in the gas engine, worked by a combustible 
mixture of air and hydro-carbons, than in the steam engine. 

Assuming, then, in an explosive gas engine a temperature of 1,500° C. 
at a pressure of 4 atmospheres, we should, in accordance with the second 
law of thermo-dynamics, find a temperature after expansion to atmospheric 
pressure of 600° C, and therefore a working range of 1500° - 600°= 900°, 

and a theoretical efficiency of ' — — — = about one-half, contrasting 

very favourably with that of a good expansive condensing steam engine, 

in which the range is 150 — 30 = 120° C, and the efSciency " ^ =^- 

A good expansive steam engine is therefore capable of yielding as 
mechanical work -f th parts of the heat communicated to the boiler, which 
does not include the heat lost by imperfect combustion and that 
carried away in the chimney. Adding to these the losses by friction and 
radiation in the engine, we find that the best steam engine yet con- 
structed does not yield in mechanical efi'ect more than |th part of the 
heat energy residing in the fuel consumed. In the gas engine we have 
also to make reductions from the theoretical efiiciency, on account of the 
rather serious loss of heat by absorption into the working cylinder, which 
has to be cooled artificially in order to keep its temperature down to a 
point at which lubrication is possible ; this, together with frictional loss, 
cannot be taken at less than one-half, and reduces the factor of efficiency 
of the engine to jth. 

It follows from these considerations that the gas or caloric engine 
combines the conditions most favourable to the attainment of maximum 
results, and it may reasonably be supposed that the difficulties still in 
the way of their application on a large scale will gradually be removed. 
Before many years have elapsed we shall find in our factories and on 
board our ships engines with a fuel consumption not exceeding 1 pound 
of coal per eSective horse power per hour, in which the gas producer takes 
the place of the somewhat complex and dangerous steam boiler. The 
advent of such an engine and of the dynamo-machine must mark a new 
era of material progress at least equal to that produced by the intro- 
duction of steam power in the early part of our century. Let us con- 
sider what would be the probable eSect of such an engine upon that most 
important interest of this country — the merchant navy. 

According to returns kindly furnished me by the Board of Trade and 
' Lloyds' Register of Shipping,' the total value of the merchant shipping 
of the United Kingdom may be estimated at 126,000,000^., of which 
90,000,000^. represent steamers having a net tonnage of 3,003,988 tons ; 
and 36,000,000^. sailing vessels, of 3,688,008 tons. The safety of this vast 
g,mount of shipping, car:ryiDg about five-sevenths of our total impprts 



22 EEPOET— 1882. 

and exports, or 500,000,000Z. of goods in the year, and of the more 
precious lives connected with it, is a question of paramount importance. 
It involves considerations of the most varied kind : comprising the con- 
struction of the vessel itself, and the material employed in building it ; its 
furniture of engines, pumps, sails, tackle, compass, sextant, and sounding 
apparatus, the preparation of reliable charts for the guidance of the 
navigator, and the construction of harbours of refuge, lighthouses, 
beacons, bells, and buoys, for channel navigation. Yet notwithstanding 
the combined efforts of science, inventive skill, and practical experience — 
the accumulation of centuries— we are startled with statements to the 
effect that during last year as many as 1,007 British-owned ships were lost, 
of which fully two-thirds were wrecked upon our shores, representing a 
total value of nearly 10,000,000Z. Of these ships 870 were sailing vessels 
and 137 steamers. The number of sailing vessels included in these 
returns being 19,325, and of steamers 5,505, it appears that the steamer 
is the safer vessel, in the proportion of 4'43 to 3'46 ; but the steamer 
makes on an average three voyages for one of the sailing ship taken over 
the year, which reduces the relative risk of the steamer as compared 
with the sailing ship per voyage in the proportion of 13-29 to 3"46. Com- 
mercially speaking, this large factor of safety in favour of steam- shipping 
is to a great extent counterbalanced by the value of the steamship, 
which bears to that of the sailing vessel per net carrying ton the pro- 
portion of 3 : 1, thus reducing the ratio in favour of steam shipping as 
13"29 to 10'38, or in round numbers as 4:3. In testing this result 
by the charges of premium for insurance, the variable circumstances 
of distance, nature of cargo, season and voyage have to be taken into 
account ; but judging from information received from shipowners and 
underwriters of undoubted authority, I find that the relative insurance 
paid for the two classes of vessel represents an advantage of 30 per cent, 
m favour of steam- shipping, agreeing very closely with the above de- 
ductions derived from statistical information. 

In considering the question how the advantages thus established in 
favour of steam-shipping could be further improved, attention should be 
called in the first place to the material employed in their construction. 
A new material was introduced for this purpose by the Admiralty in 
1876, when they constructed at Pembroke dockyard the two steam 
corvettes, the Iris and Mercury, of mild steel. The peculiar qualities of 
this material are such as to have enabled shipbuilders to save 20 per 
cent, in the weight of the ship's hull, and to increase to that extent 
its carrying capacity. It combines with a strength 30 per cent, 
superior to that of iron, such extreme toughness that in the case of 
collision the side of the vessel has been found to yield or bulge several 
feet without showing any signs of rupture, a quality affecting the 
question of sea risk very favourably. When to the use of this material 
there are added the advantages derived from a double bottom and 
from the division of the ship's hold by means of bulkheads of solid 



ADDRESS. 23 

construction, it is difficult to conceive how sucli a vessel could perish by 
collision either with another vessel or with a sunken rock. The spaces 
between the two bottoms are not lost, because they form convenient 
chambers for water ballast, but powerful pumps should in all cases be 
added to meet emergencies. 

The following statement of the number and tonnage of vessels building 
and preparing to be built in the United Kingdom on the 30th of June last, 
which has been kindly furnished me by Lloyds', is of interest as showing 
that wooden ships are fast becoming obsolete, and that even iron is 
beginning to yield its place, both as regards steamers and sailing ships, to 
the new material mild steel ; it also shows that by far the greater number 
of vessels now building are ships of large dimensions propelled by engine 
power : — 





Mild Steel 




Iron 


Wood 


Total 




No. Tons gross 


No. 


Tons gross 


No. Tons gross 


No. Tons gross 


Steam 


. 89 159,751 . 


555 


929,921 . 


6 460 . 


659 1,090,132 


Sailing 


. 11 16,800 . 


70 


120,259 . 


49 4,635 . 


130 141,694 




100 170,551 . 


625 


1,050,180 . 


55 5,095 . 


780 1,232,826 



If, to the improvements already achieved, could be added an engine 
of half the weight of the present steam engine and boilers, and working 
with only half the present expenditure of fuel, a further addition of 30 
per cent, could be made to the cargo of an Atlantic propeller vessel — no 
longer to be called a steamer — and the balance of advantages in favour 
of such vessels would be sufficient to restrict the use of sailing craft 
chiefly to the regattas of this and neighbouring ports. 

The admirable work on the ' British Navy,' lately published by Sir 
Thomas Brassey, the Civil Chief Lord of the Admiralty, shows that the 
naval department of this country is fully alive to all improvements having 
regard to the safety as well as to the fighting qualities of Her Majesty's 
ships of war, and recent experience goes far to prove that although high 
speed and manoeuvring qualities are of the utmost value, the armour 
plate, which appeared to be fast sinking in public favour, is not without its 
value in actual warfare. 

The progressive views perceptible in the construction of the navy are 
further evidenced in a remarkable degree in the hydrographic department. 
Captain Sir Frederick Evans, the hydrographer, gave us at York last year 
a very interesting account of the progress made in that department, which, 
while dealing chiefly with the preparation of charts showing the depth of 
water, the direction and force of currents, and the rise of tides near our 
shores, contains also valuable statistical information regarding the more 
general questions of the physical conditions of the sea, its temperature at 
various depths, its flora and fauna, as also the rainfall and the nature and 
force of prevailing winds. In connection with this subject the American 
Naval Department has taken an important part, under the guidance of 
Captain Maury and the Agassiz, father and son, whilst in this country the 



24, REPORT— 1882. 

persistent labours of Dr. William B. Carpenter deserve the highest com- 
mendation. 

Our knowledge of tidal action has received a most powerful impulse 
through the invention of a self-recording gauge and tide-predicter, 
which will form the subject of one of the discourses to be delivered 
at our present meeting by its principal originator, Sir William Thom- 
son ; when I hope he will furnish us with an explanation of some 
extraordinary irregularities in tidal records, observed some years ago 
by Sir John Coode at Portland, and due apparently to atmospherio 
influence. 

The application of iron and steel in naval construction rendered the 
use of the compass for some time illusory, but in 1839 Sir George Airy 
showed how the errors of the compass, due to the influence experienced 
from the iron of the ship, may be perfectly corrected by magnets and soft 
iron placed in the neighbourhood of the binnacle ; but the great size of the 
needles in the ordinary compasses rendered the correction of the quadrantal 
errors practically unattainable. In 1876 Sir William Thomson invented 
a compass with much smaller needles than those previously used, which 
allows Sir George Airy's pi-inciples to be applied completely. With this 
compass correctors can be arranged so that the needle shall point ac- 
curately in all directions, and these correctors can be adjusted at sea 
from time to time, so as to eliminate any error which may arise through 
change in the ship's magnetism or in the magnetism induced by the 
earth through change of the shijj's position. By giving the compass card 
a long period of free oscillation great steadiness is obtained when the ship 
is rolling. 

Sir William Thomson has also eni'iched the art of navigation by the 
invention of two sounding machines; the one being devised for ascertaining 
great depths very accurately, in less than one-quarter the time formerly 
necessary, and the other for taking depths up to 130 fathoms without 
stopping the ship in its onward course. In both these instruments steel 
pianoforte wire is used instead of the hempen or silken lines formerly 
employed ; in the latter machine the record of depth is obtained not 
by the quantity of wire run over its counter and brake wheel, but through 
the indications produced upon a simple pressure gauge consisting of an 
inverted glass tube, whose internal surface is covered beforehand with 
a preparation of chromate of silver, rendered colourless by the sea- water 
up to the height to which it penetrates. The value of this instrument for 
guiding the navigator within what he calls ' soundings ' can hardly be 
exaggerated ; with the sounding machine and a good chart he can generally 
make out his position correctly by a succession of three or four casts in 
a given direction at given intervals, and thus in foggy weather is made 
independent of astronomical observations and of the sight of lighthouses 
or the shore. By the proper use of this apparatus, accidents such as 
happened to the mail steamer Mosel, not a fortnight ago, would not be 
possible. As regards the value of the deep-sea instrument I can 



ADDRESS, 25 

speak from personal experience ; on one occasion it enabled tbose in 
charge of the cable s.s. Faraday to find the end of an Atlantic cable, 
which had parted in a gale of wind, with no other indication of the 
locality than a single sounding, giving a depth of 950 fathoms. To 
recover the cable a number of soundings in the supposed neighbourhood 
of the broken end were taken, the 950 fathom contour line was then 
traced upon a chart, and the vessel thereupon trailed its grapnel two 
miles to the eastward of this line, when it soon engaged the cable 
20 miles away from the point where dead reckoning had placed the 
ruptured end. 

Whether or not it will ever be practicable to determine oceanic depths 
without a sounding line, by means of an instrument based upon gravi- 
metric differences, remains to be seen. Hitherto the indications obtained 
by such an instrument have been encouraging, but its delicacy has been 
such as to unfit it for ordinary use on board a ship when rolling. 

The time allowed me for addressing you on this occasion is wholly 
insufficient to do justice to the great engineering works of the present 
day, and I must therefore limit myself to making a short allusion to a few 
only of the more remarkable enterprises. 

The great success, both technically and commercially, of the Suez 
Canal, has stimulated M. de Lesseps to undertake a similar work of even 
jiore gigantic proportions, namely, the piercing of the Isthmus of 
Panama by a ship canal, 40 miles long, 50 yards wide on the surface, 
and 20 yards at the bottom, upon a dead level from sea to sea. The 
estimated cost of this work is 20,000,000Z., and, more than this sum 
having been subscribed, it appears unlikely that political or climatic 
difficulties will stop M. de Lesseps in its speedy accomplishment. 
Through it, China, Japan, and the whole of the Pacific coasts will be 
brought to half their present distance, as measured by the length of 
voyage, and an impulse to navigation and to progress will be given 
which it will be difficult to over-estimate. 

Side by side with this gigantic work. Captain Eads, the successful 
improver of the Mississippi navigation, intends to erect his ship railway, to 
take the largest vessels, fully laden and equipped, from sea to sea, over a 
gigantic railway across the Isthmus of Tehuantepec, a distance of 95 
miles. Mr. Barnaby, the chief constructor of the navy, and Mr. John 
Fowler have expressed a favourable opinion regarding this enterprise, 
and it is to be hoped that both the canal and the ship railway will be 
accomplished, as it may be safely anticipated that the ti'affio will be 
amply sufficient to support both these undertakings. 

Whether or not M. de Lesseps will be successful also in carrying into 
effect the third great enterprise with which his name has been promi- 
nently connected, the flooding of the Tunis-Algerian Chotts, thei-eby 
re-establishing the Lake Tritonis of the ancients, with its verdure-clad 
chores, is a question which could only be decided upon the evidence of 



26 REPORT— 1882. 

accurate surveys ; but the beneficial influence of a large sheet of water 
within the African desert could hardly be matter of doubt. 

It is with a feeling not unmixed with regret that I have to record 
the completion of a new Eddystone Lighthouse, in substitution for the 
chef-cVwuvre of engineering erected by John Smeaton more than 100 
years ago. The condemnation of that structure was not, however, the 
consequence of any fault of construction, but was caused by inroads of 
the sea upon the rock supporting it. The new lighthouse, designed and 
executed by Mr., now Sir, James Douglass, engineer of Trinity House, 
has been erected in the incredibly short time of less than two years, and 
bids fair to be worthy of its famed predecessor. Its height above high 
water is 130 feet, as compared with 72 feet (the height of Smeaton's 
structure), which gives its powerful light a considerably increased range. 
The system originally suggested by Sir William Thomson some years ago, 
of distinguishing one light from another by flashes following at varied 
intervals, has been adopted by the Elder Brethren in this as in other 
recent lights in the modified form introduced by Dr. John Hopkinson, in 
which the principle is applied to revolving lights, so as to obtain a 
greater amount of light in the flash. 

The geological difliculties which for some time threatened the accom- 
plishment of the St. Gothard Tunnel have been happily overcome, and 
this second and most important sub- Alpine thoroughfare now connects 
the Italian railway system with that of Switzerland and the south of 
Germany, whereby Genoa will be constituted the shipping port for those 
parts. 

Whether we shall be able to connect the English with the French 
I'ailway system by moans of a tunnel below the English Channel is 
a question that appears dependent, at this moment, rather upon military 
and political than technical and financial considerations. The occurrence 
of a stratum of impervious grey chalk, at a convenient depth below the 
bed of the Channel, minimises the engineering difficulties in the way, and 
must influence the financial question involved. The protest lately raised 
against its accomplishment can hardly be looked upon as a public verdict, 
but seems to be the result of a natural desire to pause, pending the institu- 
tion of careful inquiries. Such inquiries have lately been made by a Royal 
scientific Commission, and will be referred for further consideration to a 
mixed Parliamentary Committee, upon whose Report it must depend 
whether the natural spirit of commercial enterprise has to yield in this 
instance to political and military considerations. Whether the Channel 
Tunnel is constructed or not, the plan proposed some years ago by Mr. 
John Fowler of connecting England and France by means of a ferry boat 
capable of taking railway trains would be a desideratum justified by the 
ever-increasing intercommunication between this and Continental countries. 

The public inconvenience arising through the obstruction to traffic 
by a sheet of water is well illustrated by the circumstance that both 
the estuaries of the Severn and of the Mersey are being undermined in 



ADDRESS. 27 

order to connect the railway systems on the two sides, and that the 
Frith of Forth is about to be spanned by a bridge exceeding in grandeur 
anything as yet attempted by the engineer. The roadway of this bridge 
will stand 150 feet above high- water mark, and its two principal 
spans will measure a third of a statute mile each. Messrs. Fowler and 
Baker, the engineers to whom this great work has been entrusted, could 
hardly accomplish their task without having recourse to steel for their 
material of construction, nor need the steel used be of the extra mild 
quality particularly applicable for naval structures to withstand collision, 
for, when such extreme toughness is not required, steel of very homo- 
geneous quality can be produced, bearing a tensile strain fully double 
that of iron. 

The tensile strength of steel, as is well known, is the result of an ad- 
mixture of carbon with the iron, varying between -j^th and 2 per cent., and 
the nature of this combination of carbon with iron is a matter of great 
interest both from a theoretical and practical point of view. It could 
not be a chemical compound which would necessitate a definite propor- 
tion, nor could a mere dissolution of the one in the other exercise such 
remarkable influence upon the strength and hardness of the resulting 
metal. A recent investigation by Mr. Abel has thrown considerable 
light upon this question. A definite carbide of iron is formed, it appears, 
soluble at high temperatures in iron, but separating upon cooling the 
steel gradually, and influencing only to a moderate degree the physical 
properties of the metal as a whole. In cooling rapidly there is no time 
for the carbide to separate from the iron, and the metal is thus rendered 
both hard and brittle. Cooling the metal gradually under the influence 
of great compressive force, appears to have a similar effect to rapid 
cooling in preventing the separation of the carbide from the metal, 
with this difference, that the effect is more equal throughout the mass, 
and that more uniform temper is likely to result. 

When the British Association met at Southampton on a former 
occasion, Schonbein announced to the world his discovery of gun-cotton. 
This discovery has led the way to many valuable researches on explosives 
generally, in which Mr. Abel has taken a leading part. Recent investiga- 
tions by him, in connection with Captain Noble, upon the explosive action 
of gun-cotton and gunpowder confined in a strong chamber, (which have 
not yet been published), deserve particular attention. They show that 
while by the method of investigation pursued about twenty years ago by 
Karolye (of exploding gunpowder in very small charges in shells con- 
fined within a large shell partially exhausted of air), the composition of 
the gaseous products was found to be complicated and liable to variation, 
the chemical metamorphosis which gun-cotton sustains, when exploded 
under conditions such as obtain in its practical application, is simple and 
very uniform. Among other interesting points noticed in this direction 
was the fact that, as in the case of gunpowder, the proportion of 
carbonic acid increases, while that of carbonic oxide diminishes with 



') 



28 EEPOET— 1882. 

the density of the charge. The explosion of gun-cotton, whether in 
the form of wool or loosely spun thread, or in the packed compressed 
form devised by Abel, furnished practically the same results if fired 
under pressure, that is, under strong confinement — the conditions being 
favourable to the full development of its explosive force ; but some 
marked differences in the composition of the products of metamorphosis 
were observed when gun-cotton was fired by detonation. With regard to 
the tension exerted by the jji'oducts of explosion, some interesting points 
were observed, wliich introduce very considerable difficulties into the 
investigation of the action of fired gun-cotton. Thus whereas no marked 
differences are observed in the tension developed by small charges and by 
very much larger charges of gunpowder having the same density (i.e. 
occupying the same volume relatively to the entire space in which they 
are exploded) the I'everse is the case with respect to gun-cotton. Under 
similar conditions in regard to density of charge, 100 gi'ammes of gun- 
cotton gave a measured tension of about 20 tons on the square inch, 
1,500 grammes gave a tension of about 29 tons (in several very con- 
cordant observations), while a charge of 2'5 kilos gave a pressure of 
about 4.5 tons, this being the maximum measured tension obtained with 
a charge of gunpowder of five times the density of the above. 

The extreme violence of the explosion of gun-cotton as compared with 
gunpowder when fired in a closed space was a feature attended with 
formidable difficulties. In whatever way the charge was arranged in the 
firing cylinder, if it had free access to the inclosed crusher gauge, the 
pressures recoi'ded by the latter were always much greater than Avhen 
means were taken to prevent the wave of matter suddenly set in motion 
from acting directly upon the gauge. The abnormal or wave-pressures 
recorded at the same time that the general tension in the cylinder was 
measured amounted in the experiment to 42'3 tons, when the general 
tension was recorded at 20 tons ; and in another, when the pressure was 
measured at 29 tons, the wave-pressure recorded was 44 tons. Measure- 
ments of the temperature of explosion of gun-cotton showed it to be about 
double that of the explosion of gunpowder. One of the effects observed 
to be produced by this sudden enormous development of heat was the 
covering of the inner surfaces of the steel explosion-vessel with a network 
of cracks, small portions of the surface being sometimes actually fractured. 
The explosion of charges of gun-cotton up to 2'5 kilos in perfectly closed 
chambers, with development of pressures approaching to 50 tons on the 
square inch, constitutes alone a perfectly novel feat in investigations of 
this class. 

Messrs. Noble and Abel are also continuing their researches upon fired 
gunpowder, being at present occupied with an inquiry into the influence 
exerted upon the chemical metamorphosis and ballistic effects of fired 
gunpowder by variation in its composition, their attention being directed 
especially to the discovery of the cause of the more or less considerable 
prosion of the interior surface of guns pi'oduced by the exploding charge — : 



an effect wlilcb, notwitbstanding the application of devices in the building 
up of the charge specially directed to the preservation of the gun's bore, 
have become so serious that, with the enormous charges now iised in our 
heavy guns, the erosive action on the surface of the bore produced by a 
single round is distinctly perceptible. As there appeared to be primii 
facie reasons why the erosive action of powder upon the surface of the 
bore, at the high temperatures developed, should bo at any rate in part due 
to its one component sulphur, Noble and Abel have made comparative 
experiments with powders of the usual composition and with otters in 
which the proportion of sulphur was considerably increased, the extent of 
erosive action of the products escaping from the explosion vessel under 
high tension being carefully determined. With small charges a particular 
powder containing no sulphur was found to exert very little erosive action 
as compared with ordinary cannon powder ; but another powder, contain- 
ing the maximum proportion of sulphur tried (15 per cent.), was found 
equal to it under these conditions, and exerted very decidedly less erosive 
action than it, when larger charges were reached. Other important con- 
tributions to our knowledge of the action of fired gunpowder in guns, as 
well as decided improvements in the gunpowder manufactured for the 
very heavy ordnance of the present day, may be expected to result from a 
continuance of these investigations. Professor Carl Himly, of Kiel, having 
been engaged upon investigations of a similar nature, has lately pi'oposeda 
gunpowder in which hydrocarbons (precipitated from solution in naphtha) 
take the place of the charcoal and sulphur of ordinary powder; this 
powder has amongst others the peculiar property of completely resisting 
the action of water, so that the old caution, ' Keep your powder dry,' may 
hereafter be unnecessary. 

The extraordinary difference of condition, before and after its ignition, 
of such matter as constitutes an exjDlosive agent, leads us up to a con- 
sideration of the aggregate state of matter under other circumstances. 
As early as 1776 Alexander Volta observed that the volume of glass was 
changed under the influence of electrification, by what he termed electrical 
pressure. Dr. Kerr, Govi, and others have followed up the same inquiry, 
which is at present continued chiefly by Dr. George Quincke, of Heidel- 
berg, who finds that temperature, as well as chemical constitution of the 
dielectric under examination, exercises a detei'mining influence upon the 
amount and character of the change of volume effected by electrification ; 
that the change of volume may under certain circumstances be effected 
instantaneously as in flint glass, or only slowly as in crown glass, and 
that the elastic limit of both is diminished by electrification, whereas in 
the case of mica and of guttapercha an increase of elasticity takes place. 

Still greater strides are being made at the present time towards a clearer 
pei'ception of the condition of matter when particles are left some liberty 
to obey individually the forces brought to bear upon them. By the dis- 
charge of high tension electricity through tubes containing highly rarefied 



30 REPORT — 1882. 

gases (Geissler's tubes), phenomena of discharge were produced whicli 
were at once most striking and suggestive. The Sprengel pump afforded 
a means of pushing the exhaustion to limits which had formerly been 
scarcely reached by the imagination. At each step, the condition of 
attenuated matter revealed varying properties, when acted upon by elec- 
trical discharge and magnetic force. The radiometer of Crookes imported 
a new feature into these inquiries, which at the present time occupy tho 
attention of leading physicists in all countries. 

The means usually employed to produce electrical discharge in vacuum 
tubes was Ruhmkorff's coil ; but Mr. Gassiot first succeeded in obtaining 
the phenomena by means of a galvanic battery of 3,000 Leclanche cells. 
Dr. De La Rue, in conjunction with his friend Dr. Hugo Miiller, has gone 
far beyond his predecessors in the production of batteries of high potential. 
At his lecture ' On the Phenomena of Electric Discharge,' delivered at 
the Royal Institution in January 1881, he employed a battery of his own 
invention consisting of 14,400 cells (14,832 Volts), which gave a current 
of 0'054 Ampere, and produced a discharge at a distance of 0'71 inch 
between the terminals. During last year he increased the number of 
cells to 15,000 (15,450 Volts), and increased the current to 0-4 Ampere, 
or eight times that of the battery he used at the Royal Institution. 

With the enormous potential and perfectly steady current at his dis- 
posal, Mr. De La Rue has been able to contribute many interesting facts 
to the science of electricity. He has shown, for example, that the beautiful 
phenomena of the stratified discharge in exhausted tubes are but a modi- 
fication and a magnification of those of the electric arc at ordinary atmo- 
spheric pressure. Photography was used in his experiments to record the 
appearance of the discharge, so as to give a degree of precision otherwise 
unattainable in the comparison of the phenomena. He has shown that 
between two points the length of the spark, provided the insulation of the 
battery is efficacious, is as the square of the number of cells employed. 
Mr. De La Rue's expei-iments have proved that at all pressures the 
discharge in gases is not a current in the ordinary acceptation of the 
term, but is of the nature of a disruptive discharge. Even in an appa- 
rently perfectly steady dischai^ge in a vacuum tube, when the strata as 
seen in a rapidly revolving mirror are immovable, he has shown that 
the discharge is a pulsating one ; but, of course, the period must be of a 
very high order. 

At the Royal Institution, nn the occasion of his lecture, he pro- 
duced, in a very large vacuum tube, an imitation of the Aurora Borealis ; 
and he has deduced from his experiments that the greatest brilliancy 
of Aurora displays must be at an altitude of from thirfcy-seven to 
thirty-eight miles — a conclusion of the highest interest, and in opposi- 
tion to the extravagant estimate of 281 miles, at which it had been pre- 
viously put. 

The President of the Royal Society has made the phenomena of elec- 
trical discharge his study for several years, and resorted in his important 



ADDRESS. 31 

experiments to a special source of electric power. In a note addressed 
to me, Dr. Spottiswoode describes the nature of Lis investigations much 
more clearly than I could venture to give them. He says : ' It had 
long been my opinion that the dissymmetry, shown in electrical discharges 
through rarefied gases, must be an essential element of every disruptive 
discharge, and that the phenomena of stratification might be regarded 
as magnified images of features always present, but concealed under 
ordinary circumstances. It was with a view to the study of this ques- 
tion that the researches by Moulton and myself were undertaken. The 
method chiefly used consisted in introducing into the circuit intermittence 
of a particular kind, whereby one luminous discharge was rendered 
sensitive to the approach of a conductor outside the tube. The applica- 
tion of this method enabled us to produce artificially a variety of pheno- 
mena, including that of stratification. We were thus led to a series of 
conclusions relating to the mechanism of the discharge, among which 
the following may be mentioned : — 

' 1. That a stria, with its attendant dark space, forms a physical unit 
of a striated discharge ; that a striated column is an aggregate of such 
units formed by means of a step-by-step j^rocess ; and that the negative 
glow is merely a localised stria, modified by local circumstances. 

' 2. That the origin of the luminous column is to be sought for at its 
negative end ; that the luminosity is an expression of a demand for 
negative electricity ; and that the dark spaces are those regions where 
the negative terminal, whether metallic or gaseous, is capable of exerting 
sufficient influence to prevent such demand. 

' 3. That the time occupied by electricity of either name in traversing 
tube is greater than that occupied in traversing an equal length of wire, 
but less than that occupied by molecular streams (Crookes' radiations) in 
traversing the tubes. Also that, especially in high vacua, the discharge 
from the negative terminal exhibits a durational character not found at 
the positive. 

' 4. That the brilliancy of the light with so little heat may be due in 
part to brevity in the duration of the discharge ; and that for action so 
rapid as that of individual discharges, the mobility of the medium may 
count as nothing ; and that for these infinitesimal iieriods of time gas 
may itself be as rigid and as brittle as glass. 

' 5. That strise are not merely loci in which electrical is converted into 
luminous energy, but are actual aggregations of matter. 

' This last conclusion was based mainly upon experiments made with 
an induction coil excited in a new way — viz. directly by an alternating 
machine, without the intervention of a commutator or condenser. This 
mode of excitement promises to be one of great importance in spectro- 
scopic work, as well as in the study of the discharge in a magnetic field, 
partly on account of the simplification which it permits in the construction 
of induction coils, but mainly on account of the very great increase of 
strength in the secondary currents to which it gives rise.' 



32 EEPORT — 1882. 

These investigations Sssume additional importance wten we vidW 
them in connection with solar — I may even say stellar — physics, for evi- 
dence is augmenting in favour of the view that interstellar space is not 
empty, but is filled with highly attenuated matter of a nature such as 
may be put into our vacuum tubes. Nor can the matter occupying 
stellar space be said any longer to be beyond our reach for chemical and 
physical test. The spectroscope has already thrown a flood of light upon 
the chemical constitution and physical condition of the sun, the stars, the 
comets, and the far distant nebulte, which latter have yielded spectro- 
scopic photographs under the skilful management of Dr. Huggins, and 
Dr. Draper of New York. Armed with greatly improved apparatus the 
physical astronomer has been able to reap a rich harvest of scientific 
information during the short periods of the last two solar eclipses ; that 
of 1879, visible in America, and that of May last, observed in Egypt 
by Lockyer, Schuster, and by Continental observers of high standing. 
The result of this last eclijjsc expedition has been summed up as follows : 
* Different temperature levels have been discovered in the solar atmo- 
sphere ; the constitution of the corona has now the possibility of being 
determined, and it is proved to shine with its own light. A suspicion 
has been aroused once more as to the existence of a lunar atmosphere, 
and the position of an important line has been discovered. Hydro-carbons 
do not exist close to the sun, but may in space between us and it.' 

To me personally these reported results possess peculiar interest, for 
in March last I ventured to bring before the Royal Society a speculation 
regarding the conservation of solar energy, which was based upon the 
three following postulates, viz. : — 

1. That aqueous vapour and carbon compounds are present in stellar 
or interplanetary space. 

2. That these gaseous compounds are capable of being dissociated by 
radiant solar energy while in a state of extreme attenuation. 

3. That the effect of solar rotation is to draw in dissociated vapours 
upon the polar surfaces, and to eject them after combustion back into 
space equatorially. 

It is therefore a matter of peculiar gratification to me that the results 
of observation here recorded give considerable support to that speculation. 
The luminous equatorial extensions of the sun which the American ob- 
servations revealed in such a striking manner (with which I was not 
acquainted when writing my paper) were absent in Egypt; bat the 
outflowing equatorial streams (I suppose to exist) could only be rendered 
visible by reflected sunlight, or by electric discharge when mixed with 
dust produced by exceptional solar disturbances; and the occasional 
appearance of such luminous extensions would serve only to disprove 
the hypothesis entertained by some, that they are divided planetary 
matter, in which case their appearance should be permanent. Professor 
Langley, of Pittsburg, has shown by means of his bolometer, that the 
solar actinic rays are absorbed chiefly in the solar instead of in the 



ADDRESS. 33 

terrestrial atmosphere, and Captain Abney has found, by his new 
photometric method, that absorption, due to hydro-carbons, takes place 
somewhere between the solar and terrestrial atmosphere. In order to test 
this interesting result still further, he has lately taken his apparatus to the 
top of the RifFel with a view of diminishing the amount of terrestrial 
atmospheric air between it and the sun, and intends to bring a paper on 
this subject befoi-e Section A. Stellar space filled with such matter as 
hydro-carbon and aqueous vapour would establish a material continuity 
between the sun and his planets, and between the innumerable solar 
systems of which the universe is composed. If chemical action and 
reaction can further be admitted, we may be able to trace certain con- 
ditions of thermal dependence and maintenance, in which we may 
recognise principles of high perfection, applicable also to comparatively 
humble purposes of human life. 

We shall thus find that in the great workshop of nature there are no 
lines of demai'cation to be drawn between the most exalted speculation 
and commonplace practice, and that all knowledge must lead up to one 
great result, that of an intelligent recognition of the Creator through His 
works. So then, we members of the British Association and fellow- 
workers in every branch of science may exhort one another in the words 
of the American bard who has so lately departed from amongst us : — 

Let VIS then be up and doing, 

With a heart for any fate ; 
Still achieving, still pursuing, 

Learn to labour and to wait. 



1882. 



EEPOETS 



I ON THE 



STATE OF SCIENCE. 



d2 



EEPOETS 



ON THE 



STATE OF SCIENCE. 



Report of the Comniittee, consisting of Professor Sylvester, Pro- 
fessor Cayley, a7id the Eev. Gteorge Salmon, D.D., appointed in 
connection with the Calculation of Tables of Fundamental In- 
variants of Binary Quantics. 

It has been thought advisable to extend the calculation of tables of 
invai-iants (proper) to ternary systems of binary quantics, and the follow- 
ing systems have been selected for the purpose. 

Two quadrics and a quartic ; a quadric and two quartics ; three 
quartics : a quadi'ic, cubic, and quartic : say the systems (2) (2) (4) ; 
(2) (4) (4); (4) (4) (4); (2) (3) (4). 

By far the most considerable amount of the work belongs to the cal- 
culations connected with the last-named system. 

The entire work covers 52 sheets of paper of dimensions 31 in. by 23 
in., divided into 93x69, i.e. 6417 ^rd-inch squares, each enclosing one 
numerical coefficient ; the total number of such spaces, of which only a 
moderately small fraction remains vacant, being accordingly 333,684. 

The work of compilation was actually performed by Messrs. Healy 
and Durfee (fellows), under the able superintendence of Dr. F. Franklin 
(associate) of the Johns Hopkins University — who is of opinion that 
at least nine-tenths of the labour and time that would otherwise have been 
required for the calculations has been saved by the method of operation 
above indicated : a method called by its presumable inventor or originator, 
Professor Sylvester, the method of cage-work or occlusion, which has 
also been found by Dr. Franklin applicable with very considerable 
advantage to certain operose astronomical computations with which he 
has been entrusted in connection with one of the public departments in 
Washington. 

The leading results will be published in the ' American Journal of 
Mathematics ' in a form similar to that of the tables of like kind, calcu- 
lated at the expense of the British Association, which have already 
appeared there. 



38 REPOET— 1882. 

It is sufficient for present purposes to state that the fundamental in- 
variants (the absolute constant not included) for the systems (2) (2) (4) ; 
(2) (4) (4) ; (4) (4) (4) ; (2) (3) (4) are respectively 19, 29, 25 and 
04 in number ; the first, second, and fourth of these totals, viz. 19, 
29, 64, it will be noticed, are very nearly the same as the numbers of 
invariants of the systems (1) (2) (4) ; (1) (4) (4) ; (1) (3) (4) which 
are, as is well known, identical with the numbers 18, 28, 61, of the in- 
and CO- variants belonging to the quadri-quartic, quarto- quartic, and cnbo- 
quartic systems respectively. 

It may also be stated that the invariants of the three systems in which 
only quadrics or qnartics are contained are all unique for a given type ; 
that is, in each of the three systems there is never more than a single 
invariant of given degrees in the coefficients of the three constituent 
quantics resjpectively. 



Report {'provisional) of the Committee, consisting of Mr. Robert 
H. Scott {Secretary), Mr. J. Norman Lockyer, Professor H. J. S. 
Smith, Professor Gr. Gr. Stokes, Professor Balfour Stewart, and 
Mr. Gr. J. Symons, appointed for tlie jpurpose of co-operating 
with the Meteorological Society of the Mauritius in their pro- 
posed publication of Daily Synoptic Charts of the Indian Ocean 
from the year 1861. 

The Committee have no report to submit, for it appears from the latest 
letters received from Dr. Meldrum that the actual printing ofi" of the pro- 
posed Synoptic Charts for the Indian Ocean has not yet been com- 
menced. 

No expense has therefore been incurred as yet, and there has been no 
occasion to apply for any portion of the grant of 50Z. made at the York 
meeting. 

However, the Meteorological Society of the Mauritius contemplates 
the issue of the charts in the course of the coming year, so that the 
Committee request that they may be re-appointed, and the grant re- 
newed. 



Report of Committee, consisting of Captain Abney {Secretary), 
Professor W. G. Adams, Professor Gr. C. Foster, Professor Lord 
Eayleigh, Mr. Preece, Professor Schuster, Professor Dewar, Pro- 
fessor Vernon Harcourt, and Professor Ayrton, for the purpose 
of fixing a Standard of White Light. 

As the experiments conducted by the Committee are still in progress, 
the Report cannot be ready for presentation this year. 



RECENT PROGRESS IN HYDRODYNAMICS. 39 



Report on Recent Progress in Hydrodynamics. 
By W. IM. Hicks, M.A. 

Part II. Special Problems. 

This second part of tlie report will deal with matters of more purely 
mathematical interest than the first, and will chiefly comprise the con- 
sideration of those particular solutions of the equation ^-(j) = o, which 
satisfy conditions given over the boundaries of various surfaces, and the 
determination of the effective inertia of the surrounding fluid when 
solids of diSerent forms move in it. The problems here considered may 
be regarded in different lights, according as the investigator has 
accustomed himself to think from a hydrodynamical, an electrical, or a 
conduction of heat point of view. Consequently, it will be found that 
several of the hydrodynamical solutions will bo found in papers with 
electrical or other titles. In the following the motion of a perfect 
fluid in (a) two and (6) three dimensions, and (c) of a viscous fluid, will 
be taken in order, the latter from a mathematical standpoint, without 
reference to the experimental researches which have been carried out by 
a large number of investigators. But, before passing on, it may be well 
here to add a few remarks in the way of correction or addition to the 
first part of the Report published last year. 

Professor Larmor has drawn my attention to the fact that the theory 
of the ignoration of co-ordinates, mentioned on page 60, is essentially 
due to Ronth, who gave the complete theory in his Adams' prize essay 
'On the Stability of Motion' (p. 60). The application of the theory to 
fluid motion is due to Thomson and Tait. The statement on p. 65, 
* that the circulation round any closed curve in the fluid is equal to twice 
the surface integral of the resolved part of the vortices perpendicular to 
the surface over any surface whose boundary is the curve,' is a theorem 
due to Thomson, is not correct. Beltrami • states that Hankel gave the 
theorem in 1861, in a paper ^ which I have not been able to obtain ; but 
it seems to have been given by Stokes, in 1854, in a Smith's prize ^ paper 
for that year. This would, therefore, appear to be the first publication. 

In the consideration of viscosity on p. 81 a notice of a paper by 
Helmholtz ' ought to have been given, in which he proves two general 
theorems. These are that, if squares and products of the velocity be 
neglected, and if the fluid be not supposed to glide over the surfaces of 
bodies immersed in it, then, (1) if the motion be steady, the currents in 
the viscous fluids are so distributed that the loss of energy due to 
viscosity is a minimum, on the supposition that the velocities along the 
boundaries of the fluid are given ; and (2) a floating body is in equi- 
librium in a viscous fluid flowing with slow steady motion, if the loss is 
also a minimum, when the velocities of the fluid along the surface of the 

' Sui princijnifondamentaK delV idrodinamica razionalc. 

^ Zur allgcmeineii Theorio der Bmvegwig der Fliissiglieiten. Gott. 1861. Now 
out of print. 

' .See Camh. JJnir. Calendar for 1854, p. 415. 

* ' Zur Theorie der stationilren StriJme in reibenden FKLssigkeiten,' Verh. 
natrirhist, Vereim. Heidelberg. V. p. 1. (18GS.) Also Collected Works, i. p, 223, 



40 BEPOET— 1882. 

body are varied in the same way as if the solid were to have one of its 
possible motions. 

On the same page it should be noted that the theory of similitude 
given by Helmholtz had already, more than twenty years before, been 
stated by Stokes,' though not so fully as to include different coefficients 
of gliding over the surfaces of bodies immersed. The applications by 
Helmholtz are new. 

On page 80, line 20, for ' its i-ate of variation,' I'ead, ' the jrate of 
variation of the energy.' 

The following letters have throughout, nnless specially not%|Bd, the 
meanings here given, viz. : — 

Where on denotes the mass of a body, in' denotes the mass of the 
fluid displaced by it. 

p denotes the density of the fluid. 

(j) „ ,, velocity potential. 

if/ „ „ stream function. 

fj.' ,, „ coefficient of viscosity. 

H „ ,, kinematic coefficient of viscosity = /''/p- 



a. Motion in Ttvo Dimensions. 

Sources and SinJcs. — The simplest motion possible is that where fluid 
moves in an infinite plane, streaming from certain points (sources) and 
into others (sinks). Its importance consists in this, that all potential 
functions can be considered as due to certain distributions of sources or 
sinks at definite points, or along certain lines and surfaces, as has been 
shown by Stokes.^ Regarded from this point of view they have been 
called the ' Green's functions of the given distribution of matter.' Many 
examples will occur in the succeeding pages of their application. W. R. 
Smith ^ has developed some of the general properties of the stream-linos 
and equipotential lines for two dimensional motion when the number of 
singular points is finite and all are of the same magnitude. When the 
system is complete, i.e. when the numbers of sources and sinks are equal, 
the degrees of both the stream-lines and equipotential lines are equal to 
the whole number of singular points. When the numbers are unequal 
this is still true for the stream-lines, but the degree of the equipotential 
line is double the greater number. The general nature of the lines is 
clearly different, according as the system is complete or not. In the 
former case one stream-line goes to infinity, and is, at most, of a degree 
one less than the number of singular points, whilst if the system be not 
complete, eveiy complete stream-line has a number of asymptotes equal 
to the difference of the numbers of sources and sinks. More jjarticularly 
he considers the cases of two, three, and four singular points, and gives 
figures when they are at the corners of a rectangle and of a regular 
trapezium. Cases of the same kind have also been noticed by Kirchhoff "^ 

' Cami. Phil. Trans, ix. 

^ ' On the internal distribution of matter which shall produce a given potential 
at the surfaces of a gravitating mass,' Proc. Roy. Soc, xv., p. 482 ; and Phil. Mag., 
xxxiv. p. 235 (1867). 

^ ' On the flow of electricity in conducting surfaces,' Proc. Roy. Soc. Edin., vii. 
p. 79. 1870. 

* ' Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbeson- 
dere durch eine kreisformige,' Pogg. Ann. Ixiv. 15, 497, or Gemni, Ahhantl, p. 1. 



EECENT PKOGEESS IN HTDRODf NAMICS. 41 

(1845), Qaiuckci (185G), Auerbach^ (1878), and ■ Chwolson ^ (1878), 
from the electrical point of view. 

As sources and sinks may be regarded as the origin of all non-cyclic 
motion, so may the vortex-filament bo looked upon as the basis for cyclic 
motion. The cases of one or two vortices, discovered by Helmholtz, 
have been already referred to.^ When more than two are present the 
general treatment of their motions involves mathematical difficulties of 
calculation, though the theory is quite straightforward. Particular cases 
have been worked out with much detail by W. Grobli''' (1877), in a 
paper which has much interest from the number of figures it contains 
illustrating the paths in certain cases. He considers the cases (1) of 
three vortices («) equal, but one of different sign from the other two, 
(/3) equal and of the same sign, (y) two equal and opposite and double the 
third ; also the conditions that they shall always lie at the angles of a 
triangle (o) of constant size and form, (e) of constant form (4) with two 
equal sides ; (2) of four equal vortices with a plane of symmetry — which 
comes to the same thing as two equal vortices in an infinite fluid 
bounded by a plane ; and (3) of 2n equal vortices with n planes of 
symmetry, or one vortex in the fluid bounded by two planes inchned 
at an angle win. In this last case each describes the Cotes' spiral, 
r sin nd = const. It would lead us too far to describe more fully the 
results arrived at, which, after all, are only particular cases of the 
general problem. The last question has also been discussed by Green- 
hill^ (1878), who shows that a vortex of strength m, in an angle w/n, 
will describe its Cotes' spiral as if it were a particle under the attraction 
of a force varying inversely as the cube of the distance from the angle, 
and strength = ^ (v^ — 1) i'^''^- 

The theory of the fluid motions resulting when portions of planes are 
held in a stream has been referred to in the last report,^ and it will be 
sufficient here to give for reference the cases already solved. The case of 
fluid flowing from an infinite space into a canal bounded by two parallel 
planes is historically the most interesting, being the first example of dis- 
continuous motion which yielded to the genius of Helmholtz.* The only 
other solutions at present known are those discovered by Kirchhoff.^ 
These reduce to special cases of the two general jn-oblems (1) where fluid 
issues from between two straight lines drawn in any direction from two 
points, and (2) where a straight line is opposed in a stream of fluid at any 
angle. The solution of the equation of continuity for all the space outside 

■ ' Ueber die Verbreitung eiries clektrisclien Stromes iu Metallplatten,' Pof/ff. Ann. 
xcvii. p. 382. He considers space bounded by two infinite lines at right angles. 

- ' Ueber die Verbreitung stationarer electrisclier Strome in leLtenden Fliichen,' 
Wied. Ann. iii. p. 498. 

^ 'Ueber das Problem der Stromverzweigimg in einer ebenen Platte,' 
Sclilbm. Z. xxiii, p. 47. 

^ Brit. Ass. HejK, 1881, p. 64. 

* ' Specielle Probleme iiber die Bewegung geradliniger paralleler Wirbelfaden,' 
Inavff. Diss. Gott. pp. 8G ; also, VicHeljahrschHft der naturforschcndcn GescUsclmft 
in Zurich, sxii. 

* ' Plane vortex motion,' Quart. Jour. xv. p. 10. 
' Brit. Ass. Rep. 1881, p. 69. 

^ 'Ueber discontinuirliche Fliissigkeitsbewegungen,' Monatsh. Altad. Berl. 1868, 
p. 215. Phil. Mag. (4) xxxvi. p. 337 ; also reprinted in Helmholtz' Wissen. Ahhand, 
Bd. i. p. 146. 

» ' Zur Theoric freier Fliissigkeitsstrahlen,' Crclle, Ixx. p, 289 ; and reprinted in 
Ges. Werke, p. 416, and Vorlesungoi U. 3lath. Fhi/sik. Vorles. 21, 22. 



42 REPORT— 1882. 

a line can be deduced from the case of the ellipse referred to below. It 
is of importance from an electrical point of view, but is only of purely 
mathematical interest as far as hydrodynamics is concerned. 

Passing on now to spaces bounded by straight lines, we have to notice 
the cases of two parallel lines, triangles, and rectangles. Sources and 
sinks between parallel planes have been discussed by the writer, but they 
may be regarded as limiting cases of the rectangle, which is referred to 
below. When the triangle is equilateral, the motion for a rotation was 
discovered by F. D. Thomson,' and Stokes^ has shown that for this the 
effective moment of inertia of the equivalent solid is two-fifths of that of 
the solidified fluid. The potential and stream functions for a vortex inside 
Buch a triangle have been given by Greenhill,^ and the path described by 
the vortex, also the same functions when there is a source at one corner 
and a sink at the other. For the right-angled isosceles triangle the case 
for a source and sink at the base angles have been given by the writer,'' 
and are, I believe, the only ones solved for this triangle. If the vertex of 
a triangle move off to infinity jierpendicular to the base, we get the space 
bounded on three sides by two infinite parallel lines, and a third line per- 
pendicular to them. The potential and stream function for a source, or a 
vortex (electric point) in such a space are given in the same paper, as well 
as figures illustrating them in particular cases. This may be regarded as 
a limiting case of the rectangle, to which we now proceed. 

This form has received much attention from the time when Stokes^ 
first discussed it in ] 843. He determined the velocity potential for the 
internal motion when the boundary rotates, in the form of an infinite series, 
and in the same form evaluated the moment of inertia of the equivalent 
solid. His method is based on determining the coefficients of an infinite 
series to represent the motion of rotation of two opposite sides when the 
other pair are at rest, and then combining them for the whole motion. 
The same problem is considered in * Thomson and Tait's Natural Philo- 
sophy.' ^ Ferrers^ (1878) attacks the question differently. He first 
shows that if the density of matter at every part of a plane be given by 
p cos mx cos vy, its potential is 4<7rp cos vix cos ny /(m^ + n^). Now the 
analytical conditions for the stream function of the motion of fluid in a 
rotating rectangle are the same as for the potential for a distribution of 
matter of density + 1, and — 1, in alternate equal rectangles. This 
density is expressed as the product of two Fourier's series, and the before- 
mentioned theorem applied. Greenhill* (1878) gives expressions for the 
velocities at any point in a very compact form as definite integrals of 
certain elliptic functions of the position of the point. He arrives at this 

' ' On certain cases of fluid motion,' Ox. Cam. and Dub. Mess. Math. iii. p. 238. 
^ Reprint of papers, p. 65. 

' ' Solutions by means of elliptic functions of some problems in the conduction of 
electricity and of heat in plane figures,' Qua7't. Jour. xvii. p. 28-t. 

* ' On velocity and electric potentials between parallel planes,' Qiuwt. Jour. xv. 
p. 313. 

* ' On some cases of fluid motion,' Trans. Camh. Phil. Soc. viii. p. 105 (1843). 
Supplement to a memoir ' On some cases of fluid motion' (1846), Ibid. p. 409. ' On 
the critical values of the sums of periodic series' (1849), Ibid. p. 533, sec. iv. In 
the reprint of papers these are vol. i. pp. 60, 188, and 288. 

' Vol. i. 1st ed. p. 541. 

' ' Solution of certain questions in potentials and motion of liquids,' Quart. Jour, 
XV. p. 83. 

" ' Notes on hydrodynamics : on the motion of water in a rotating rectangular 
prism,' Quart. Jour. xv. 144. 



HECENT rUOGRESS IN lIYDrvODYNAMlCS. 43 

1*08016 by taking tlie series for the velocity and stream functions given 
in Thomson and Tait, and expressing the series for the velocities derived 
from them in the above way. The upper limits of the integrals are the 
co-ordinates of the point. Definite integral expressions, with constant 
limits for the velocity and stream functions, and the velocities, have 
been determined by myself,' by taking the values of these functions for 
a source inside a rectangle, and distributing sources and sinks over the 
sides of the rectangle, proportional to the normal motion of the boundary 
at the point. 

The two functions for a source inside a rectangle were first (1865) 
determined by Jochmann^ by summation of the corresponding functions 
for the whole set of images of the source. They depend in general on the 
Theta functions, and for particular positions take simple forms. The same 
problem for vortices has been solved by Greenhill,^ who has also found 
the equation to the path of a single vortex inside the boundary. The 
form is so simple that I venture to reproduce it here. If the origin be at 
the centre, and if K : K' be the ratio of the sides, the equation to the path 
of a vortex is ctn2(Ka;/a., Zc) + ctji^(K'y jb, h') = const, whilst, if the vortex 
is at the centre, the stream-lines are cn(K,i;/a, h) cn(K'7//6, Jc') = tanh>^/m. 

The Circle. — This naturally was amongst one of the first boundaries 
for which the velocity potential was fonnd. It was given by Stokes* in 
1843 as a particular case of the general motion of the surfaces of two 
concentric circles, and he showed that the mass of the equivalent solid 
was equal to that of the fluid displaced. A very full discussion of the 
motion of the particles of the fluid, by Clerk-Maxwell,^ will be found in 
the ' Proceedings ' of the Mathematical Society, a discussion which is ren- 
dered all the more insti'uctive from the figures which accompany it. Both 
these papers treat of non-cyclic motion ; but the space in two dimensions 
about a circle being cyclic, admits of a many-valued velocity potential. 
Rayleigh ^ and Greenhill ^ have shown that when there is a cyclic motion 
about the circle it will itself move in a circle in the same direction as that 
motion, whilst the latter has shown that if it also moves under the action 
of gravity it will describe a trochoid. The image of a source in a circle 
has long been known, and that of a vortex is a natural corollary. 

Two Circles. — This is another boundary for which we owe the first 
discussion to Stokes^ (1843). He considered them concentric, with any 
general motion of the points of the surface, and in particular for the 

' ' On velocity and electric potentials between parallel planes,' Quart. Jour, xv, 
p. 274. 

^ ' Ueber einige Aufgabeu, welcbe die Tbeoric des logarithmisclien Potentials und 
den Durchgang eines constanten elektrisclien Stroms durcb eine Ebene betreflfen.' 
Schlbm Z. X. jDp. 48 and 89. Tbey are also given in my paper referred to above, and 
a particular case when the source and sink bisect opposite sides of the rectangle by 
Betti. Sopra la diHtrihuziune (Idle corrcnti elettriche in mio lustra rettangolare. 
N. Cim. (2) iii. (1870) ; also Heine (1874), ' Ueber die constante electrische Stromung 
in ebenen Flatten,' Bwch. Ixxix. p. 1, and Berl. Mcniats. (1874) p. 186. 

* ' On plane vortex motion,' Quart. Jour. xv. p. 10 ; also ' Solution by means of 
elliptic functions of some problems in the conduction of electricity and heat in plane 
figures. Ibid. xvii. p. 284. 

■* ' On some cases of fluid motion,' Camb. Phil. Trans, viii. p. 105 (184.3). 

° ' On the displacement in a case of fluid motion,' Proc. Math. Soc. iii. p. 82 
(1870). 

" ' On the irregular flight of a tennis ball,' Mess. Math. vii. p. 14 (1877). By 
some oversight the circle is made to move in the wrong direction. 

' ' Notes on hydrodynamics,' Mess, Math. vs.. p. 11.3, 

8 ' On some cases,' &c. 



44 BEPOiiT — 1882. 

initial motion, when one circle has a motion of translation. He shows 
that in this case, which serves very approximately to determine the small 
vibration under gravity of the inner circle, the mass of the equivalent 
solid is (5^ + a.^)/(6^ — a^) times the mass of the flaid displaced ; a, b 
being the radii of the circles. I ' have discussed the most general motion 
of two circles, either internal, or external to one another, treating the 
two cases separately where the circles touch or not. The velocity and 
potential functions are given for any motion of the two circles, and the 
following particular cases are considered more in detail : (a) the motion 
of a pendulum inside a circular case, (/3) of a circle in fluid bounded by a 
straight line, (y) of two circles rigidly connected, (I) the motion of one 
when the other is fixed, and lastly (e) some properties of the general 
motion of two free circles, in all cases without cyclic motion. It may be 
interesting to give some of the results, which admit of quantitative de- 
termination in finite terms. If (as in /3) a circle be projected from con- 
tact with the boundary line, in a direction perpendicular to it, the limiting 
velocity as it moves off to an infinite distance is increased in the ratio 
(jTT- + () — 1)- (p + l)""'- If it be projected from any point, the future 
path will have its concavity turned towards the plane, and will turn 
round and meet the plane or not, according as the direction of projection 
makes an angle with the perpendicular to the plane greater or less than 
a certain angle a, which depends only on the distance from the plane. 
When the circle is projected from contact, the values of a for densities of 
the circle 0, 1, 10 are about 41° 22'; 51° 14' ; 70° 15' respectively. If in 
(ci) the circles are equal, and one is projected directly from contact with 
the other, the limiting velocity is (^tt"^ + p —1)- (p + 1)"^' times the 
initial velocity. If it were projected in any way it will move as if attracted 
on the whole by the fixed circle, the path will have its concavity turned 
towards it, and will have two asymptotes, whose distances from the 
centre of the fixed circle are (p + F^^y (p + 1)"- times the apsidal dis- 
tance, where Po is a certain number depending only on this distance. If, 
for example, they touch when nearest Pq = ^ tt- — 1. If, on the contrary, 
both are free to move (as in e), and they are projected so that the whole 
'momentum' of the system is zero, they move as if they repel one 
another, and the jDatli of one relatively to the other has its convexity 
towards that other. If they are equal and touch one another at their 
nearest distance, the distance of the asymptote of the path of one from 
the centre of the other is Q tt- + p — ly (p + l)"-x sum of radii. 
If there is cyclic motion between the circles it is possible to have them 
moving steadily forward through the fluid, always keeping at the same 
distance, provided the circles are equal. The discussion^ of this motion 
shows that when the radii and distance of the centres are given there are 
two possible relations between the velocity of translation and the relative 
motion, one in which they are in the same direction between the circles 
and the other in the opposite. If 2 a be the angle between the two 
internal tangents to the circles, then when a is not nearly ^ tt, the two 
ratios of the velocity due to cyclic motion alone, at the point half-way 
between the cylinders, to the velocity of translation is very approximately 
2 sec a {+ V (1 — cos a sin* o) — 1} , 

' ' On the motion of two cylinders in a fluid,' Quart. Jour. xvi. pp. 113 and 193, 
and Proc. Camb. Phil. Soo. iii. p. 227 (1878). 

- ' On the condition of steady motion of two cylinders in a fluid,' (Juart. Jour. 
xvii. p. 194 (1879). 



RECENT PROOBESS IN HYDEODYNAMICS. 45 

When the boundary consists of two intevsccting circles, the deter- 
mination of the motion can bo made in a manner similar to that for two 
non-intersecting circles. When the two circles ai'e equal and pass 
through each other's centres, the velocity potential for the system moving 
parallel to the line of centres is f = — aW (r~^ + r''^), where r. r' are 
the distances of a point from the centres. This example was given before 
Section A at York last year by Professor A. W. Eiiiclcer.' 

Straight Lines and Circles. — Here again our first reference must be to 

Stokes. In his paper ' On the critical values of the sums of periodic 

scries' he finds the velocity potential for the fluid inside a rotating sector 

of a circle of angle 2 a in the two forms of an infinite series and of a 

definite integral, and expresses in the same two forms the moment of 

inertia of the equivalent solid. The square of the radius of gyration is 

16 f* tanh ax 

— — — ^ — T^ dx. For special values of the angle «, the velocity poten- 

Trajo x{x' + 4>)-' 

tial and stream functions admit of finite expression in terms of logarithmic 

and circular functions. The semicircle is the simplest,^ next comes the 

quadrant of a circle, and a sector of 60°, the two last given by Greenhill,^ 

who has investigated the case of the sector very fully. In this paper 

the case when the angle is any sub-multiple of two right angles is also 

considered. The expressions obtained are naturally rather complicated, 

but they are finite and in terms of circular and logarithmic functions. 

For the two particular cases of the semicircle and quadrant he shows 

that the ratios of the squares of the radii of gyration of the equivalent 

solid, and the solidified fluid, are IG/tt^ — 1, and (16 log 2)1^^—^, 

respectively. He again takes up the question in a later paper'' (1880), 

and obtains a finite expression for the functions when the angle of the 

sector is commensurable with two right angles. The square of the ratio 

of the radius of gyration of the equivalent solid to the radius of the 

circle is in this case 

where ^ («) = ^ log r (x) . 

When sources and sinks exist inside a sector the motion may easily be 
determined by means of what is already known for the space between 
two lines. The position of rest of a vortex inside a sector has been de- 
termined by Lewis.^ It lies on the line bisecting the angle at a distance 
from it = { V (4)2-2 ^ i) _ 2n] ^'2" times the radius, the angle of the sector 
being x/^i. The general motion both for vortices outside and inside a 
circle — either for a single vortex in a sector, or symmeti'ical vortices, 
without straight boundaries, is given by Greenhill ^ with figures illustrating 
the paths for two, four, and six vortices respectively. 

The same author has also discussed the motion in the space bounded 
by two concentric circles and two radii. The values of f and -^ for a 

' ' On a problem in stream lines,' Brit. Assoc. Hep. 1881, p. 554. 
- 'Fluid motion in a rotating semi-circular cvlinder/ Mess. Math. viii. p. •12 
(1878). 

3 'Fluid motion in a rotating quadrantal cylinder,' Mess. Math. viii,' p. 89 (1877). 

* 'On the motion of a frictionlcss liqiiid in a rotating sector,' Mess. Math. x. p. 83. 

* 'Some cases of vortex motion,' 3Iess. Math. Ix. p. 93 (1879). 
" 'Plane vortex motion,' Quart. Jour. xv. p. 10 (1877). 



46 REPORT— 1882. 

rotating rectangle are given in infinite series.' The path of a vortex 
inside such a rectangle ^ admits of a very elegant expression by means of 
elliptic functions ; as well as the <•/> and \p for sources and sinks at the 
corners.^ For instance, for a source and a sink at two adjacent comers on 

the same radius <f> + \pi = log sn — { + i log - J with analogous expres- 
sions in en and dn for the other corners. Here the value of q is (a/b)\ 
The position of rest of a single vortex is at a distance from the centre 
equal to the geometrical mean of the radii.* The solution for sources is 
also given by Allen. ^ 

Ellipse (axes a, b ; a > h). If the elliptic cylinder be considered as 
the limiting case of an ellipsoid when one axis becomes indefinitely large. 
Green may be regarded as the first worker in this field (1833) ; but the 
first to consider definitely the ellipse was Stokes (1843) in his before- 
mentioned paper 'On some cases of fluid motion'; but in this he only con- 
sidered the motion approximately, in the space outside an ellipse of small 
eccentricity, for translation and rotation. He*' has also shown that con- 
focal conies are possible forms for stream lines, though the motion is only 
irrotational in the case of the rectangular hyperbola. In 1873 Beltrami^ 
gave the velocity potential for the motion of an elliptic cylinder as a case 
of the ellipsoid, whilst Ferrers ^ determined the stream function two years 
later (1875) for motions of translation and rotation. In the latter year 
also Lamb-' published the expressions for ^j and \p in the forms which 
are now generally used, and given in KirchhofF's ' Vorlesungen ' and 
Lamb's ' Theory of Motion.' In this paper will be found diagrams of 
the lines of flow. The path and motion of an ellipse moving in an infinite 
fluid have been worked out by Greenhill, '" who has given figures illustrating 
the motion for the three cases when it is projected, so as to make (1) 
oscillations, (2) whole revolutions, and (3) when it is projected in the 
direction of the major axis with infinitely small angular displacement. 

The same author ' ' has also investigated the motion of an ellipse 
whose centre is fixed in a stream. In this case the time of a small 
oscillation is 27r ^,/ [kaah(a'^ + 1^) l(a~ — l'')Y'^} . Problems connected with 
two confocal ellipses are also considered, and the initial motions of the 
inner, due to any sudden motions impressed on the outer, are found. 

Coates '- has worked out the values of \p for a vortex outside and 

' ' Fluid motion in a rotating rectangle, formed by two concentric circular arcs 
and two radii,' 3Iess. Math. ix. p. 35 (1879). 

- ' Solution by means of elliptic functions of some problems in the conduction of 
electricity and heat in plane ligures,' Quart. Jour. xvii. p. 284 (1881). 

» Ibid. 

•* ' Plane vortex motion,' Quart. Jour. xv. p. 10 (1877). 

' 'On .some prolilems in the conduction of electricity,' Quart. Jour. xvii. -p. 65; 
also Brit. Assoc. Brjj. (1879) p. 261. 

'* ' On the steady motion of incompressible fluids,' Cajuh. Phil. Trans, vii. p. 439, 
and Reprint, vol. i. p. 10. 

'■ ' Sui principii fondaraentali dell'idrodinamica razionale,' Mem. di Bologna, iii. 

** ' On the motion of a mass of water about a moving cylinder,' Quart, jour. xiii. 
p. 115. 

" ' Rome hydrodynamical solutions,' Quart. .lour. xiv. p. 40. 

'» ' Notes on Hydrodynamics,' ii. Me.ss. Math. ix. p. 117 (1880). 

" ' Fluid motion between confocal elliptic cylinders, &:c.,' Quart. Jour. xvi. p. 227 
(1879). 

'2 'Vortex motion n and about elliptic cylinders,' Quart. Jour. xy. p. 356, and 
xvi. p. 81 (1878.) 



RECENT TROGRESS IN HYDRODYNAMICS. 47 

iuside au ellipse, and inside a semi-ellipse, by the elliptic transformation 
from the solations for the circle obtained by Greenhill. 

The images inside an ellipse due to either a source, or a doublet 
outside it, have been determined by the writer.' In general it may be 
taken to consist of a line distribution of sources and doublets along the 
straight line joining the foci, and of an isolated image or not, according 
to the position of the original soni'co. When this lies beyond a certain 
confocal ellipse, determined by the size of the bounding ellipse, there is 
no isolated image, -whereas, if it lies within, there is an isolated imago 
lying on the confocal hyperbola through the 'object.' 

Where the ellipse degenerates into the line joining the foci the 
isolated image is always absent, and there is only a distribution of 
doublets along the line. The densities at a point are given throughout 
in terms of the position of the point and of the object soui'ce or doublet ; 
these expressions for certain particular positions of the source become 
very simple. Thus, in the case of a line AB, and a doublet at P,, on 
,AB produced, and perpendicular to it, the line doublet density at a point 
P on the line is proportional to 



PiV Upi.bpJ- 



pp 

The motion of a mass of fluid in the form of an elliptic cylinder 
rotating about its axis under the attraction of its own mass has been 
touched upon by Dirichlet and Riemann in their investigations on the 
similar problem for the ellipsoid referred to below. More particularly, 
Lipschitz 2 gives equations for the motion of such an ellipse, both for 
vibrations of form and rotation, and shows that they are purely periodic 
between definite limits. Kirchhoff '^ has given a simple case, where the 
boundary rotates without change of form — a case which is embraced in a 
more general solution of the same problem given by Greenhill.^ The 
latter considers the motion to be generated by supposing the fluid to 
rotate within a rigid boundary as a solid body with angular velocity w, and 
an additional angular velocity w' to be impressed on the boundary. He 
finds that we may suppose the boundary removed, provided the relation 
between these quantities and the axes is given by 

The paths of the particles are in general pericycloids, which, (1) 
when w' = w (a^ _ h'^) {(a- + h^) are epicycloids, (2) when w + w' = o, or 
boundary at rest, are ellipses (Stokes's case referred to above, p. 8), 
(3) when w = o are circles, and (4) when w' = — w (a + hyj^a"^ + h^) 
are circles, which last is Kirchhoff's case. 

OtJier Curves. — Any number of possible fluid motions can be deter- 
mined by taking any solution of the equation V"^ = o» ^n<i determining 
the stream lines, any one of which may serve as a boundary. But this 

' ' On functional images in ellipses,' Quart. Jour. xvii. p. 327 (1881.) 

- ' Reduction der Bewegung eines fiiissigen homogenen Ellipsoids aiif das 
Variationsproblem eines einfachen Integrals, nnd Bestimmung der Bewegung fiir 
den GrenzfaJl eines nnendlichen elliptischcn Cylinders,' Borcli. Ixxviii. p. 245 
(1874). 

« ' Vorlesungen,' &c. p. 262. Aufi. ii. 

' ' On the rotation of a liquid ellipsoid about its mean axis,' Proc. Camb. PMl. 
Soc. iii. p. 233. 



48 EEPOET — 1882. 

method, as a rule, clocs not afford useful results, as tbo curves are in 
general too complicated. The mathematical interest attaches itself to 
solutions for the case of given boundaries or given conditions, and 
reduces itself often to a suitable transfoi'mation by conjugate functions, 
whereby the given boundary maybe transformed to one consisting of lines 
or circles, the solution of which is known. This has been applied in 
some of the preceding examples. Of direct solutions other than those 
already mentioned two require notice here. One by Ferrers,' who has 
determined the (]i and -^ functions for the spaces (1) inside an ellipse and 
between the two branches of a confocal hyperbola, and (2) between an 
ellipse and one branch of a confocal hyperbola, when the boundary 
rotates; also for two confocal parabolas, the limiting case of (2). The 
functions ai-e given in infinite series. The other is by Greenhill.^ He 
has investigated expressions for the f and i^, due to a source, a doublet, 
or a vortex, in the space bounded by Cartesians, in terms of the con- 
jugate functions given by a; + ii/ = sn"^(| + iij), in which £,»/ give the 
confocal Cartesians, whose vectorial equations are r' — rdn4' = cuE, and 
r' + rdniij = cn»/, the foci being at the points x = o, 1, 1//.-^ and y =■ o. 

Non-plane Two-dimensional Motion. — The hydrodynamical interest of 
plane two-dimensional motion consists in its physical application to the 
motion of cylinders in an infinite fluid, or of cylinders of finite length in 
the space between two planes perpendicular to and touching the ends of 
the cylinder. When the space considered is not plane, the motion may 
be represented physically by the steady motion of electricity, the surface 
being supposed a conductor. The surface of a s^iherc is one which has 
received some attention. The case of the motion for a source and sink 
at opposite extremities of a diameter was discussed by Robertson Smith ^ 
in his paper referred to above. Beltrami* has given the general 
solution of the equation of continuity for the surface of a sphere which is 
analogous to that for plane space in terms of polar co-ordinates. He 
shows that, d and (p being the co-latitude and longitude of a point, the 
general solution for the potential is in the form 

(a log tang + B j (af -f &) 4- 2 i Antan^^ 2 + B„cot" ^ jcos(?i^ 4- a). 

This he applies to the case of the motion of a spherical cap on the sphere, 
and finds that, a being the spherical radius of the cap and (6q . ^tt) the 
co-ordinates of the instantaneous centre of rotation, the potential is pro- 
portional to sin fio(sin ^aycot ^0 cos <j>, the centre of the cap being at the 
pole. The lines of flow are given by cot ^9 sin (j) = const., and of flow 
relative to the cap by (cos a — cos 0) cot ^0 sin f + cot 0^ cos = const. 
These are the intersections with the sphere of hyperbolic cylinders 
whose asymptotic planes are, one parallel to the boundary of the cap (a 
small circle of the sphere), and the other to the great circle of the sphere 
which gives the instantaneous direction of motion of the centre of the 
cap. He also discusses the time a particle takes to describe its path, and 
particular forms of the paths. The f and \p functions for sources and 
sinks on a sphere, or certain portions of spheres, bounded by circles, have 

' ' On the motion of water contained in certain cylindrical vessels,' Quart. Jour. 
xvii. p. 227 (1880). 

- ' On functional images in Cartesians,' Quart. Jour, xviii. p. 231, 846 (1882). 

3 ' On the flow of electricity, &c.' Proc. Boy. Soo. Edin. vii. p. 79 (1870). 

■* 'Intorno ad un caso di moto a due co-ordinate.' Jiendiconti d. reale, 1st. 
Lovib. (II.) xi. p. 199 (1878). 



EECENT rEOGtRESS IN HTDnODYNAMICS. 49 

been investigated by Hill,' who arrives at the necessary expressions by 
transforming the variables so as to make the equation of continuity of 
the same form as in plane motion, and taking similar functions of those 
variables. Amongst many interesting results may be mentioned those 
for equal source and sink. Hero the stream lines ai'e the small circles 
through the source and sink (intersections of sphere with planes through 
the chord joining the points), and the potential lines are the system of 
small circles orthogonal to the foregoing (the intersections with planes 
passing through the line of intersection of the tangents to the sphere 
at the source and sink). Allen '^ has made a valuable remark, that the 
transformation which Hill has used is geometrically equivalent to trans- 
forming the equipotential and stream lines for any motion on a plane by 
a stereographical projection into a corresponding motion on the sphere. 
This might be regarded as making the theory for the spherical surface as 
complete as for the plane, were it not that the projections do not always 
correspond in simplicity to the original curves. For instance, he shows 
that confocal conies project into quartic curves, and that confocal sphero- 
conics are the projections of quartic curves. The case of motion on 
the surface of a cylinder is also touched upon, as it has also been by 
Boltzmann.^ 

b. Motion in three dimensions. 

Planes. — The image of a source in presence of an infinite plane has 
long been known, and is obvious. Stokes was, I believe, the first to 
employ it. The velocity-potential for a source between two parallel 
planes — which is the sum of the same functions for the infinite train of 
images — has been given by myself,* whilst Greenhill ^ has solved the 
corresponding problem for the case of a rectangular box. When the 
origin is at one corner and a single source at the point Xi-y^.z^ the poten- 
tial is 



TT 



H ttH 



+ similar terms in i/j, z-^. 

In any actual case this has to be combined with an equal sink at some 
other point ; it gives the power of solving the general problem of any 
motion of the sides, and has been used by Kirchhofi" to determine the 
electrical resistance of a conducting parallelepipedon. 

The Sphere. — The velocity-potential for the sphere was first found by 
Poisson ^ in 1831, in discussing the effect of the air on the motion of a 
ball-pendulum in it. If the elasticity of the air be neglected we get the 

' ' The steady motion of electricity in spherical current sheets,' Quart. Jovr, 
xvi. p. 306 (1879). 

* ' On some problems in the conduction of electricity,' Qtiart. Jour. xvii. p. 65 
(1880). 

' ' Bewegung cler Electricitat auf einer cylindrischen Flache,' Wien. Sitzher. Hi. 
(2) p. 220. 

■* ' On velocity and electric potentials between parallel planes,' Quart. Jov/r. 
XV. p. 293 (1878). 

* ' On Green's functions for a rectangular parallelepiped,' Proc. Cnmh. Plnl. Soc. 
iii. p. 289. 

* ' Memoire sur los mouvemcnts simultanfis d'uu pendule et tie I'air environnant. 
Mem. (le VAcatl. d. Sc. Paris, xl. p. 621 (1832). 
1882. E 



OO EEPORX— 1882, 

case of a liquid, and he showed that the effect of an incompressible fluid 
is to increase the inertia of the sphere by one-half the mass of the fluid 
displaced by the sphere. His investigation was published in 1832, and, 
the year after, Green read a paper on the same subject before the Royal 
Society of Edinburgh, in which he considered the ball of the pendulum to 
be ellipsoidal. His investigation was carried out without a knowledge of 
Poisson's work, but he gives the same result as to the effect of the sur- 
rounding fluid. In 1835 Plana • also took up the subject in a long paper 
of 166 pages, in which he attempted to take account of the friction, and 
of small differences from the spherical form of the pendulum. He con- 
sidered the friction on the spherical surface to be proportional to the 
relative motion of the fluid over the surface, and that this relative motion 
was the same as if there were no friction. For frictionless fluid his 
results agree with Poisson's, as do Stokes^ deduced in 1843 as a special 
case of a more general one. 

In 1852 the same problem was solved by Dirichlet ' independently. 
He found, in addition, the equation to the stream lines. The chief im- 
portance of this paper lies in the impulse it gave in Germany to the study 
of hydrodynamics, forming as it does the first of a series of important 
papers by himself, Clebsch, Riemann, Helmholtz, and Kirchhoff . Clebsch * 
(1856) also gives the stream lines as a particular case of those for the 
ellipsoid, and discusses with more detail the motion of a spherical ball- 
pendulum. Amongst new results may be mentioned the equations to the 
paths of particles, the co-ordinates being expressed very elegantly in 
terms of elliptic functions of one arbitrary parameter. The motion of a 
sphere in fluid when its centre of gravity is eccentric is the subject of a 
paper by G. J. Michaelis.^ 

It is well known how Thomson discovered that the electrification 
induced on a sphere by a quantity of electricity at a point outside it, 
produces the same effect on an external point as another portion of elec- 
tricity at the optical image of the first, and how from this he developed 
his theory of electric images. This theory suggested to Stokes to search 
for an analogous theorem in fluid motion, and he found ^ that a doublet 
(n) outside a sphere, with its axis directed to the centre of the sphere, 
has an image also at the inverse point, whose magnitude is — fia^jr^, 
\7here a is the radius of the sphere and r the distance of the external 
doublet from the centre. The importance of this lies in the fact that the 
motion of a sphere produces the same motion in the fluid as a doublet at 
its centre, and thus it gives the means of solving the case of two spheres 
moving along the line joining their centres. The general case, of which 
the preceding is a particular instance, for the image of a source of fluid 

1 ' Memoire sur le mouvement d'uu pendule dans un milieu resistant,' il/t'»t. d. r . 
Ace. di Sc. Turin, xxxviii. p. 209. 

'^ On some cases, &c., see below. 

» Monatsber. d. herl. Ahad. 1852- 

It is curious how, even down to the present moment, Dirichlet is regarded on 
the Continent as the first investigator in this region, and how the work of Green and 
ycokes is ignored. 

•• ' Ueber die Bewegung eines Ellipsoids in eiaer tropfbaren Fliissigkeit,' Crelle, 
lii. p. 103 (1856). 

s ' Over eenige gevallen van beweging in eene onsamendrukbare vloeislof,' 
Nicem. Arch. iii. p. 163. 

6 Brit. Ass. Ec]). 1817, ii. p. 6. ' On the resistance of a fluid to two oBoillating 
spheres.' Be^rint, vol. i. p. 230. 



DECENT PEOGKESS IN HYBRODYNAMICS. 51 

outside a sphere has been given by myself ' (1879), and may be thus 
stated. If a source, of strength ;h, is placed at a distance r, from the 
centre of a sphere of radius a, the 'image' consists of (1) a source at 
the optical image of m, and of magnitude majr ; and (2) a constant 
line-sink extending from this isolated image to the centre, and of line- 
density, mja. The image of a doublet (/u) with its axis in any direction 
is then easily deduced by making a source and sink approach indefinitely 
near to one another. When the axis points towards the centre, it is 
clear that the line-distribution disappears, and we get the result found by 
Stokes ; when the axis is perpendicular to the line joining it to the 
centre, the image consists of an isolated doublet ^ /xa^'/r^ at the inverse 
point, and a line doublet thence to the centre, whose line-density at a 
distance p is — fipjar. It is curious ^ that if there is a source at a point 
P and a constant line-sink betAveen P and Q, where Q is a point on the 
line from P to the centre, then, provided the whole amount of the line- 
sink is equal to the amount of the source, the * image ' of this arrange- 
ment is an arrangement of the same form — viz., a source at P' the inverse 
of P, and a constant line-sink between P' and Q', the inverse of Q, the 
whole amount of the line-sink being equal to that of the source at P'. 
This is of importance in the treatment of the motion of two sjDheres, 
when one at least changes its volume. 

The image of another kind of singular point, that of the element of a 
vortex filament, has been determined by Lewis. ^ In this case the image 
of a small element of a vortex line is the optical image of the element, 
and their strengths are iuvei'sely proportional to the square roots of their 
distances from the centre. Hence, any complete vortex filament has a 
complete image, provided it lies on a concentric sphere. By means of 
this theorem Lewis has investigated the motion of a circular vortex fila- 
ment inside a sphere when it moves symmetrically with respect to a 
diameter. When it occupies a position of rest, its radius (r) is given by 
(0,2 _ }-2^ jQg f3j^j.3^Q,2 _ r'^yi^a^h^} —■ 4a^ ; where a is the radius of the 
sphere, and b is the radius of the sphere whose volume is equal to that of 
the filament. 

The motion standing next in simplicity is that of the initial motion of 
the fluid contained between two concentric spheres when the inner begins 
to move. This forms one of the examples considered by Stokes * in his 
paper ' On some cases of fluid motion' (1843). He first finds the velocity 
potential for any motion of the bounding surfaces, and shows that if the 
inner sphere performs a small oscillation within the outer as a fixed boun- 
dary, the motion is the same as if the inertia be supposed increased by a 
mass equal to ^(P + 1a^)l{h^ — a^) times the mass of the fluid displaced, 
where a, h denote the radii of the inner and outer spheres respectively. 
He then passes on to the case where a sphere moves in fluid bounded by 
an infinite plane. This is important as the first application in hydrody- 
namics of the principle of successive ' reflection ' of motion. Taking first 
the motion of the sphere perpendicular to the plane, he finds the normal 
motion at points of the plane due to the motion of the sphere on the 

' ' On the motion of two spheres in a fluid,' Tram. Boy. Soc. part ii. (1880), 
p. 455. 

^ ' On the problem of two pulsating spheres in a fluid,' Proc. Camb. Phil. Soc. 
iii. p. 276. 

' ' On the images of vortices in a spherical vessel,' Quart. Jour, xvi, p. 338 (1879). 

* Trans. Camb. Phil. Soc. viii. 105. 

e2 



52 BEPOET — 1882. 

supposition that the plane docs not exist, and then adds the motion 
obtained by impressing on every point of the plane velocities equal and 
opposite to those at the same point produced by the motion of the sphere, 
and again, takes account of the ' reflected ' motion of this from the surface 
of the sphere. If the fourth powers of the ratio of the radius to the 
distance from the plane be neglected he found that the mass of the 
equivalent solid is i(l + Sa^/Sh^) times the mass of fluid displaced. When 
the sphere moves parallel to the plane, the problem is treated by supposing 
the plane removed, and an equal sphere to move as the optical image of 
the first. Here under the same circumstances the mass of the equivalent 
solid is -5(1 + oa^ jlGP) times the mass of the fluid displaced. In both 
cases h denotes the distance of the centre from the plane. His discovery 
of the image of a doublet whose axis goes through the centre of the sphere 
enabled him to solve further problems ' which, however, he did not 
publish at the time. One of them is printed in the first volume of his 
collected works and is referred to below. The fact that a sphere projected 
from the bounding plane moves as if accelerated, whilst if it is projected 
parallel to the plane it moves as if attracted to it, was deduced from 
general reasoning in Thomson andTait's ' Natural Philosophy,' published 
in 1866. 

The whole question of the general motion of two or more spheres has 
been considered very fully by Bjerknes in a series of papers dating from 
18G8 onwards. In his first paper ' he treats of the movement of two 
spheres moving in their line of centres, and shows how a series for the 
velocity-potential may be obtained. He investigates more particularly 
the case when their distances are so great that inverse powers of the 
distance greater than the seventh may be neglected, and shows that the 
uniform motion of one sphere, along the line of centres produces an 
apparent repulsive force towards the centre of the other : also the general 
movement of several spheres whose distances from each are so large com- 
pared with their radii, that inverse powers of this ratio greater than the 
fourtb can be neglected. Under these circumstances the action between 
any two spheres is independent of the presence of the others. Forces occur 
depending on the acceleration and the kinetic energy of the spheres, that due 
to acceleration varying inversely as the third power of the distance, whilst 
that due to the square of the velocity depends on the inverse fourth power. 

In 1871 Guthrie 3 published a curious theorem, due to Thomson, 
Thomson found that if two spheres are in fluid and oscillating along the 
line joining their centres, then, if the density of one of the spheres is less 

' In the introduction to Lis p.aper on ' The internal friction of fluids on the motion 
of Pendulums' {Trana. Camb. Phil. Soc. ix. 1850), he says, speaking of this discovery : 
' It enabled mc to calculate the resistance to a sphere oscillating in presence of a 
fixed sphere or within a spherical envelope, or the resistance to a pair of spheres 
either in contact, or connected by a narrow rod, the direction of oscillation being, in 
all these oases, that of the line joining the centres of the spheres. . . . Tlie method 
even applies, as Professor Thomson pointed out to me, to the uncouth solid bounded 
by the exterior segments of two intersecting spheres, provided the exterior angle of 
intersection be a snbmultiple of two riglit angles.' 

- ' Om den samtidige Bevaelgelse af kugleformige Legemer i et inkompressibelt 
Fluidum.'— i^)r/(«Mf/. iikand. Naturfors. Christiania (1868). 

' ' On approach caused by Vibration,' Phil. Mag. xli. (4) p. 423. There is clearly a 
printer's error in the result. In the formula the fifth root occurs ; in the numerical 
example the third root. I have ventured in the text to svibstitute the correct value, 
viz. the fourth. This paper of Guthrie's contains experiments on the action between 
bodies moving in fluids and also references to the work of others, For fxuther notices 
see below. 



IIECENT PROGRESS IH HYDRODYNAMICS. 63 

than that of the fluid it is repelled or attracted according as the ratio of 
its radius to the distance between the centres is less or greater than 
1 _4/||(l + 2p)}. In the same year also, Bjerknes^ extended his 
former investigations by taking into consideration changes of volume. 
The velocity-potential is obtained in an infinite series in which the terms 
are multiple integrals, which are integrable when the spheres move along 
the line of centres. This was followed by a series of papers ^ in 1875 and 
]876, in which the consequences of the motion were developed more fully. 
If inverse powers of the distance above the fourth be neglected, the vibra- 
tions of one sphere produce only oscillations of the other, if that other 
does not also vibrate. Simultaneous vibrations of the same period produce 
mean forces of the second, third, and fourth powers of the inverse dis- 
tance ; thus, two spheres with concordant pulsations attract proportionally 
to the inverse square of the distance, and repel according to the same law, 
if they are in opposite phases. If a, b be the radii of the spheres then the 

force on (h) due to pulsations of (a) is 1^ j( a~h '-^\ the density of 

the fluid being unity. Two oscillating spheres behave in the opposite man- 
ner to two magnetic poles. These actions have suggested to Herr Bjerknes 
analogies with electricity and magnetism, which he has illustrated by a 
series of beautiful and striking experiments.^ It must be remembered, 

■ 'Sur le mouvement simultane des corps splieriques variables dans un fluide 
Ind^fini et incompressible,' Forh. Vidensli. Christiania, 1871. 

■ ' Forelobige Meddelelser om de Kriif ter der opstaa, naar kuglef ormige Legemer 
idet de udfore Dilatations; og Kontraktions Svingninger bcviige sig i et inkom- 
pressibelt Fluidum. — Mirh. Vidensk. p. 386, Christiania, 1875. 

For an abstract and description of this, see Koenigsberger's Rejjeriorium fur reine 
und an§ewandte Math. i. p. 264. ' Ueber die Druck-Krafte, die dvirch gleichzeitige 
mit Contractionen und Dilatationen verbundene Bewegnngen von mehreren kugel- 
formigen, in einer incompressiblen Fliissigkeit befindlichen, Korpern entstehen.' — 
Gm. Nach. 1876, p. 245. 

» For descriptions of these, see ' Versuche iiber die scheiubare Anziehung und 
Abstossung zwischen Korpern welche sich in Wasser bewegen.' Von Schiotz und B j erknes, 
Gott. Nauh. 1877, p. 291. 

' Hydroelectricite et hydromagnetisme, r^sultats analytiques,' C. E. 1879. 

' Do. r^sultats experimentaux,' lb. 1879. 

' Experiences hydro dynamiques avec des corps vibrants et imitation dans un sens 
invarse des forces de I'electricite statique et du magnetisme,' C. R. 1879. 

' Ph^nom&nes dits hydroelectriques et hydromagnetiques, theorfemes fondamentaux 
et teur verification exp6rimentale,' Scaiicgg Soc. Phys. Paris (1877), Jovr. Phi/s. 
Jloroh, 1880. 

* Hydrodynamiske analogier til de statlsk clektriske og do magnetiske Kriif cer,' 
Naturen (Christiania) 1880. Also Forh. Sh. N. (Stockolm). 

' Sur I'imitationpar voie hydrodynamique des actions electriques et magnetiques,' 
a R. 1881. 

On the same or analogous questions see also Hydrodynamic analogies to electricity 
and magnetism by G. Forbes, Nature, xxiv. p. 360 (1881). This is a description of 
Bjerknes' experiments. 

* Phenomlnes hydrodynamiques inversement analogues 3, ceus de I'electricite et du 
magnetisme.' — Comptes Rendus, par M. Bertin, Ann. de Chimie ct de Phys. (5) xxv. 
p. 257, 1882. This is a systematic description of Herr Bjerknes' work. 

'Experiences hydrodynamiques, imitation par les courants liquidcs, des pheno- 
mSnes electromagnetiques et d'induction.' Decharme, C. R. xciv. p. 440, and p. 527. 
• Do. des actions des courants electriques les uns sur les autres,' p. 643. ' Do. des 
anneaux de Nobili, obtenus avec les courants electriques,' p. 722 (1882). 

« Backlund : Om en siirskild art af rorelse i en obegriinsad, osammantrykbar viitske, 
i hvilken sammantrykbare kroppar iiro utspridda,' Lund. Arsshr. xv. 

Experimental Researches into the Pro2)ert'>xs and Motions of Fluids, mitli Theoretical 
Deductians therefrom by W. Ford Stanley. London, Spon, 1881. 



54 ' REPORT — 1882. 

however, that the actions are the opposite of those of electricity and 
magnetism — for instance, like oscillations attract — nor is it easy to see 
how the rotatory effects of magnetism can be illustrated in this manner. 
In his ' Vorlesnngen iiber mathematische Physik' (1876), Kirchhoff 
has given a short treatment of the question of two moving spheres, and 
this has been carried somewliat further by Lamb in his treatise on the 
motion of fluids. The present writer' has also applied the theory of 
images, referred to above, to the solution of the same problems, and has 
attempted^ to sketch out an explanation of gravitation on Thomson's 
vortex-atom theory of matter. When two spheres intersect at an angle 
which is a submultiple of two right angles, the number of successive 
images is finite, and the velocity-potential has a finite form. Stokes,^ in 
the reprint of his papers, has worked out in detail the case when two 
spheres cut at right angles. 1£ r,d; r', 6' • r,, 8^, be the polar co-ordinates 
of any point referred to the centres of the spheres, and the middle point 
of the common chord respectively, then the velocity-potential when they 
move along the line of centres is — ^Y {a^ cos jr'^ — a%^ cos d^/ch^^ 
+ b^ cos 0' /)•'-}, c being the distance between the centres. In this case 
the mass of the equivalent solid is 

1 Trpc-^ {4c3(«3 + P) -2(a^ + Z-6) - 3a%''(a + by} . 

The Ellipsoid. — The solution of the problem of the most general motion 
of an ellipsoid in fluid is due to the successive labours of Green (1833), 
Clebsch (1856), and Bjerknes (1873). To the first we owe the velocity- 
potential for a motion of translation, to the second that for a motion of 
rotation and the stream-lines both for translation and rotation, whilst 
the third has given us the solution when the axes of the ellipsoid change 
in any manner with the time. 

Green's^ paper was read in 1833. In this he finds the velocity 
potential for translation only, and the effective momentum of the fluid. 
In finding the effective momentum Green neglected the term in the ex- 
pression for the pressure at a point which depends on the square of the 
velocity, and he supposed, therefore, that his result was only true for 
small vibrations. It was not till ten years later, when Stokes proved that 
this term produces no effect on the i-esultant pressure on a single body in 
an infinite fluid, that it could be seen that Green's value of this momentum 
was rigorously true. His solution for the sphere has already been men- 
tioned ; he also gave the analogous expressions for the spheroids. In 1835 
Plana, in his before-mentioned paper, showed how to determine the velocity, 
potential for a surface of revolution only slightly differing from a sphere 
and moving parallel to its axis. Nothing more seems to have been done 
for twenty- three years, until Clebsch's^ investigations were published in 
1856, although the paper seems to have been finished in 1854. The first 
part deals with the general theory of fluid motion, and has already been 
referred to in the portion of this report presented to the Association last 
year. Here we confine ourselves to his results bearing directly on the 

' ' On the motion of two spheres in a fluid,' Trans. Roy. Soc, pt. ii. p. 455 (1880). 

'^ ' On the problem of two pulsating spheres in a fluid,' Proc, Camb. Phil. Soc. iii. 
p. 276, and iv. p. 29. 

3 ' On the resistance of a fluid to two oscillating spheres,' reprint, vol. i. p. 2.30 
(1880). 

■• ' Researches on the vibration of pendulums in fluid media,' Trans. Eoy. Soc, Edin., 
vol. xiii. ; also reprint, p. 315. 

* ♦ Ueber die Bewegung eipes Ellipsoids in einer Fliissigkeit,' Crelle, Hi. p. H9. 



RECENT PROGRESS IN HYDRODYNAMICS. 55 

ellipsoid. Clebsch was unacquainted with Green's work, and rediscovered 
his values of the velocity-potential for a motion of translation. In addition 
to the potentials for translation and rotation he gives the equations of the 
lines of flow for translation, in terms of eUipsoidal co-ordinates, in the 

form log y = fV(^)<^^> ^liere X.fi.v are the ellipsoidal co-ordinates of a 

point (xAj.z), with a similar expression for log z, which is so related to 
the former that yz may be expressed in terms of an elliptic integral of the 
second kind. The case of rotation is a more complicated one, and was 
only completed in a note^ to this paper. Here the co-ordinates fi.i' are 
expressed as integrals of functions of X, and thus the solution is reduced 
to a question of quadratures. All these simplify very much when tho 
ellipsoids are spheroids. Another period of nearly twenty years followed, 
until Bjerknes ^ completed the general solution by investigating the poten- 
tials when the boundary itself changes its form, yet so as to remain ellip- 
soidal. He considers the generalised problem of motion in space of ?* 
dimensions, and extends the former results to this case. The second paper 
is divided into two parts, the first devoted to the motion in the infinite 
fluid outside the ellipsoid, the second to that inside. His results are 
given below, for space of three dimensions. 

As the results are important, and extremely interesting, I have thought 
it would be well to give a short notice of the results of the three foregoing 
writers, expressed in a consistent notation. 

n O 2 

Let E = 1 - ~ — > so that Eq = o is the equation to the 

a^ + X b'^ + X c^ + X 

boundary at any time, the axes being a.h.c. Further, let D denote the 
product ./[l + 4) (^ + p) (■'■■'■ ^) • '^^^^ ^^^ the velocity-potentials 
can be expressed in terms of fl where 

B 



o = .|" 



dX 
D 



viz., the constants A.B.C. being properly chosen, we have for translation 
parallel to the axis (a) 

fl) =^ A '— (Green) ; 

dm 

for rotation about the axis (a) 

^^Bfy^-z^) (Clebsch); 

V"" dz dyj 

for variation of the axis (a) 

<6 = Ca— (Bjerknes). 

'^ da 

In the last case, if the axes vary so as to keep the volume constant, 
then the sum of the C must vanish, whereas if they vary so that the 

' Crelle, liii. p. 287. 

2 ' Verallgemeinerung des Problems von dem ruhenden Ellipsoid, in emer 
bewegten unendlichen Fliissigkeit,' G6tt. Nach. (1873) p. 448. 'Verallgemeinerung 
des Problems von den Bewegungen welche in einer ruhenden, nnelastischen Fliissig- 
keit die Bewegving eines Ellipsoids hervorbringt,' IMd, p. 829. 



56 BEPOKT — 1882. 

ellipsoid always remains similar to itself, the potential takes the very 
simple form of 

The effective mass and the effective moment of inertia have been given 
by Green and Clebsch respectively in not very comjDlicated forms, but it 
does not seem worth while to reproduce them here. The function il also 
serves to determine the stream-lines for a spheroid moving parallel to its 
axis. They are given by Kirchhoff in his ' Vorlesungen ' in the form 

< C — +|-p > = const, (p.a;) being the cylindrical co-ordinates of any 

point, and the other equation being given by any plane through the axis. 

When the space in question is that inside an ellipsoid, the functions 

become extremely simple. For translation the velocity is, of course, a 

linear function of the rectangular co-ordinates, whilst for rotation about 

J2 g2 

the axis (a) the velocity-potential is given by ^ = w— -yz. "When the 

0" ~\~ c 

axes change, the fluid being incompressible, the volume must remain 

unaltered, or dja + Ijh -\- cjc = o. For this motion Bjerknes has shown 

that 

\a b c J 

He has also shown that if we suppose the density to change with the time 
alone, yet so as to preserve the same mass of fluid within the ellipsoid, we 

may dispense with the condition S cl/a = o. If now E = 1 



2 



'-\ 



a,2 a.^ 



and D^ = n ( 1 + — 5 )) all the above results still hold for 11 variables. 

I have not been able to discover who first determined the potential 
for the internal motion when the boundary rotates. It was given by 
Bjerknes,' Beltrami,^ and Clerk Maxwell,^ all in 1873, but I believe tho 
results must have been known before. Maxwell set it in a fellowship 
examination at Trinity College, Cambridge, with a rider, that after a 
certain number of revolutions, all the liquid particles would occupy the 
same positions relatively to the boundary. 

Several other writers have discussed the motion of the ellipsoid, but 
their work has either been based on that of Green or Clebsch, or their 
results have been developed anew. A short notice, in order of the several 
papers, will therefore suffice here. Ferrers ■• (1875) deduces the velocity- 
potential for translation and rotation, and finds the vis viva of the fluid 
motion by showing that the velocity-potential for a point just outside the 
surface, bears a constant ratio to that just inside. This is a valuable re- 
mark, and shortens the calculation very much, for since the normal motion 
is the same in both cases, it follows that the energy of the motion outside 
has the same ratio to that within. It is seen at once how this enables 
us to deduce immediately the energy for translation. Sharpe^ (1876) 

' See above. = S\d Principii, <5'c., § 26. 3Iem. di Boloffiia, iii. 

' The question is given in the last edition of Besant's Hydromechauics amongst 
the examples. 

•* ' On the motion of an infinite mass of water about a moving ellipsoid,' 
Quart. Joiir. xiii. p. 3.30. 

'■• ' On fluid motion,' Mens. Math. v. p. 12j"). 



KECENT PROGRESS IN HYDRODYNAMICS. 57 

uses the methods of Green developed in his memoir on the determination 
of the attractions of elHpsoids of variable densities, to obtain the velocity- 
potentials for translation and rotation, but he does not refer to Green's 
memoir on the same subject. In 1879 GreenhilP discussed the motion of 
an ellipsoid in general, and in particular of a spheroid. Amongst the 
results obtained may be mentioned the condition that a prolate spheroid 
projected through a fluid may keep its point in front. He found that it 
must have an angular velocity about the axis 

> 2^ (C33C44(1 — C33/C1,)} /Cg5 

where Cn, C33 are the effective masses along and perpendicular to the axis, 
and Cgg, c^^ the effective momenta of inertia about the axis, and a line 
perpendicular to it.^ In this same paper he has determined the initial 
motion of an ellipsoidal solid within a confocal ellipsoidal shell, when the 
shell has any motion of translation or rotation impressed on it, also the 
small oscillations of such a body about the jjosition of confocality. In 
the same year also Craig-* published a paper dealing with the same 
questions with reference to a single ellipsoid, and containing transforma- 
tions to the notation of elliptic functions. 

By making one of the axes of an ellipsoid indefinitely small we arrive 
at a solution of the equation of continuity with conditions over a jDlano 
elliptic disc, but which does not satisfy the hydrodynamic conditions that 
the pressure must be everywhere finite. The solution of the discon- 
tinuous motion which ensues when a disc is moved perpendicular to itself 
through a perfect fluid has yet to be found. 

Another motion in connection with surfaces of the second degree is 
that where the stream-lines are the lines of curvature on a family of one 
kind of confocal quadrics — or are the intersections of two families and 
orthogonal to the third. By supposing the hyperboloid of one sheet to 
degrade into the space outside the focal ellipse we get the solution of the 
equation of continuity for fluid flowing through an elliptic hole in a 
plane. 

Fluid ElUpsoid and Sphere under their oion Attractions. — The problem 
of the ellipsoidal forms of equilibrium of a rotating fluid, under the attrac- 
tion of its own particles, is naturally the next object for consideration. 
Since Maclaurin's discovery of the spheroidal form of equilibrium, and 
Laplace's discussion of it, little seems to have been done until Jacobi 
announced to the French Academy, in 1834, that particular ellipsoids, 
with three unequal axes, could also be forms of equilibrium for fluid rota- 
ting about the least axis. The fact being discovered, several proofs were 
given by different writers, Liouville,"* Ivory, '^ Pontecoulant,^ and others. 
The first to discuss the case with any fulness was C. O. Meyer,'' of 
Koenigsberg, who set himself to do for Jacobi's case what Laplace had 
done for Maclaurin's. If w be the angular velocity, and if the ratio of 
w-/27r to the force between two unit volumes of the fluid at unit distance, be 

' ' Motion of liquid between two confocal ellipsoids,' Quart. Jour. xvi. p. 234. 

= For a simpler proof of this see a paper by the same author : ' Steady motion of 
a top and of a solid of revolution moving in an infinite fluid,' Quart. Jour. xvii. p. 
86 (1880). 

* ' On the motion of an ellipsoid in fluid,' Amer. Jour. Math. ii. p. 260. 

* Journal de Vecolo 'polytechniqiw, T. xiv. p. 289. 
5 PUl. Trans, pt. i. for 1838, p. 57. 

^ Siixtrme dn 3Iondc, T. ii. , 

' ' l)e Aequilibrii formis ellipsoidicis, Crellc, xxiv. p. H. 



58 REPORT— 1882. 

denoted by V, then the combination of Meyer's investigation and Laplace's, 
gives the following results. If an ellipsoid is to be a form of equi- 
librium, V must lie between the values V = and V = -2246. ... If V 
lies between and Vq = •18711 . . . then for a given value of V there is 
one ellipsoidal form with unequal axes, and two spheroidal forms, whilst 
for V = Vq the former coalesces into that spheroidal form which has the 
less axis of rotation. When V is between Vq and V there can only be hvo 
spheroidal forms, which for V = V coalesce into one. The ultimate 
spheroid to which the ellipsoid approximates when V := Vq has the ratio 
of its axes equal to •5827. . . . For V = the limit for the ellipsoid is the 
circular cylinder, whilst the spheroids are — one a sphere and the other an 
infinite disc. It is clear that the most natural datum to take is not the 
angular velocity but the angular momentum, which remains constant, 
however the fluid may change its form. This was a point of view adopted 
by Laplace in treating of the spheroidal form, and Liouville ' took up 
Meyer's problem in the same way in a paper read before the French Aca- 
demy of Sciences in 184.3, in which he showed that the ellipsoidal form 
with unequal axes is only possible provided the ratio of the angular mo- 
mentum to the mass is greater than a certain limit, thus differing from 
the spheroids, which are forms of equilibrium for any given angular mo- 
mentum. What happens when the angular velocity of a spheroid is too 
great for it to keep its form ? This could be answered generally from 
the foregoing theories, viz., that tbe spheroid would become flatter, so 
decreasing its angular velocity, and that it would vibrate about some 
mean position ; but whether its external form would always be spheroidal, 
or what the precise manner of the movement might be, could not be 
decided. This question was answered, and the complete theory of the 
motion of sjiheroids of fluid investigated, in a posthumous paper by 
Dirichlet,2 edited and enlarged by Dedekind. The extremely beautiful, 
and in its fundamental idea simple, theory of Dirichlet threw open to 
mathematicians a new and rich field for further investigations, of 
which they were not slow to avail themselves, so that now it may be said 
that we know the general pi'operties of the motion of a mass of fluid 
moving with a free ellipsoidal surface under its own attraction. Dirichlet's 
first conception dates from the winter of 1850-1857, so his editor, Dedekind, 
says ; but the author, wishing to extend them further, did not publish his 
results in full, and they did not appear until 1859, after his death, when 
Dedekind published them with some further results of his own. I will 
first attempt to give a genei'al idea of his method, then refer to the chief 
results of his investigation, and afterwards pass on to notice the work 
done by other mathematicians, following on the lines laid down by him. 

Considering that the Lagrangrian method of treating fluid motion is 
better fitted than the Eulerian when the boundary surface changes with 
the time, he asks the question. Is it possible to have the co-ordinates of a 
particle at any time linear functions of its original co-ordinates, and if 
BO, to what kind of motion does it refer ? It is clear at once that those 
particles originally lying on an ellipsoid must always do so, though not 

' This was piiblished in the Additions a la Connaiasance ties Temps for 1846, and 
also in 1851 in lAonrille's Journal, xvi. p. 241, under the title ' Sur les figures ellip- 
so'idales i\ trois axes inegaux, qui peiivent convcnir ;\ I'equilibre d'un masse liquide 
homogene, douee d'un movivemeut de rotation.' 

- ' Ueber ein Problem dor Hydrodj'namik,' AbJiand, ¥6n. Gcs. Wiss. Gott. viii. p. 
1, and Borck. Iviii. p. 181, 



EECENT PEOflPvESS IN HYDRODYNAMICS. 59 

in general tlie same. The coefficients of the original co-ordinates will be 
nine in number, and functions of the time alone. Substituting the 
velocities and the attractive forces in the equations of motion, it is found 
that the initial co-ordinates enter linearly, and hence, in order to have a 
free surface, the pressure must be of the form 

P + ,, A _ ^ _ ^' _ V>^ 

where the coefficient of a equated to zero gives the initial surface, and o- 
is a function of the time alone. Equating to zero the coefficients of 
^Oi 2/0. ^0 there result, with the equation of continuity, ten equations to 
determine ff and the nine coefficients. This is the fundamental idea • 
for the development I must refer the reader to the paper itself, contenting 
myself here with giving some of the chief physical results of Dirichlet's 
investigation. This was confined, so far as he worked it out in detail, to 
surfaces of revolution. When there is no rotation, and the original form 
is an oblate or prolate spheroid at rest, the form vibrates through the 
sphere to a prolate or oblate spheroid respectively, and he finds equations 
to determine the limits and the time of vibration. If in any position the 
velocity of change of an axis surpasses a certain limit the form does not 
vibrate, but the spheroid either lengthens infinitely or flattens infinitely, 
but the presence of the slightest amount of rotation prevents the former 
ultimate state, a result easily foreseen from the constancy of ano-ular 
momentum. When rotation occurs three cases present themselves, dis- 
tinguished by the relation of the angular velocity to the momentary form. 
The first gives no change of form, and leads to Maclaurin's spheroid ; in 
the second the spheroid vibrates as well as rotates ; and in the third it 
rotates and either flattens itself without limit, or, in the reverse direction 
tends to an ultimate form not of infinite length. In the second case the 
motion is only possible without a uniform external pressure over the 
surface, provided the angular velocity at the moment of greatest 
lengthening is less than a certain limit. The last section of this paper is 
nearly all due to Dedekind. In the foregoing the same particles always 
form the principal axes of the ellipsoid. Dedekind states here that there 
are only two other cases in which this is the case, one in which an ellip- 
soid vibrates without rotation, for which the co-ordinates are propor- 
tionate to their initial values, and the other is Jacobi's ellipsoid. He 
further states another possible motion where an ellipsoid satisfying 
Jacobi's conditions retains its form stationary in space, with an internal 
motion of the particles given by 

X — Xq cos ht + J jIq sin Id, y = —xq- sin Id + t/q cos M, z = Zq. 

U (J, 

This may be referred to as Dedekind's ellipsoid. 

The proof of these theorems Dedekind gave in an appendix ' to 
Du-ichlet's paper republished in Borchardt's Journal, and in addition a 
remarkable reciprocal law between two correlated motions with the same 
boundary surface. It is thus stated by him. To every motion of a fluid 
ellipsoid expressed by the equations x = Itiq + myo + nzo, y = I'xq +m'yo 
+ n';s„, z = l"x(, + m"yo + n"zQ whose original surface has the equation 

'-Y +-J^ + 2 ~^ corresponds, by changing the initial state of motion, 
' ' Zusatz zu der yorstehenden Abhandlmig,' Borch. Iviii, p. 217. 



60 REPORT— 1882. 

a second motion of tho same ellipsoid expressed by tlie equations 
X = Ixq +.^l'yQ + ^l"za, ?/ = - mxQ + m'tj^ + - m"za, 



z—-nxQ +-n'yo + ?i'%, 
a 

This law of reciprocity, applied to Jacobi's case, gives Dedekind's at once. 

The unknowns adopted by Dirichlet are not well adapted for consider- 
ing the changes of shape and position of the fluid boundary ; what is 
really wanted is the variation of the axes, their motion, and the motion of 
the fluid relative to the ellipsoidal axes at any time. Riemann,^ taking 
up the problem where left by Dirichlet and Dedekind, adopted as his 
unknowns, a, the axes, their instantaneous rotations about themselves, 
and the instantaneous rotations of a second set of axes, which give the 
relative motion of the fluid, and which may be defined as follows. The 
particles originally lying on the axes, at all future time lie on a set of 
conjugate axes of the momentary ellipsoid — are, in fact, tho lines to which 
the axes are deformed by a pure strain. If the momcntaiy ellipsoid be 
changed by a pure strain to a sphere these become an orthogonal system, 
and are the second system referred to. 

Having formed the difierential equations, and the integrals equivalent 
to constant impulsive couple, the equation of energy, and the surface 
integral of vortex strength, Riemann devotes his attention to considering 
the general question of persistence of form, where therefore the axes 
are constant, and for which his form of the equations is very suitable. 
He proves that if the form is to be persistent the axis of rotation of the 
fluid must lie in a principal plane of the ellipsoid, and must be fixed rela- 
tively to it. Calling a h c the axes in descending order of magnitude we 
may state his results as follows. For the more general case where tho 
axis of rotation lies in a principal plane there are three sub-cases ; (a) 
axis in plane of greatest and least axis, with a + c ^2b; (/3) axis also 

in same plane with « - c > 26 and c- < ^^, ~ f* ^ ; (y) axis in 

a^ — h^ 

plane of mean and greatest axis, with a — h > 2c and 

where B^ = fl + A^ A + M /'l + M. In this case there is neces- 

sary an external pressure in order to preserve the continuity of the fluid, 
unless a, h, c are subject to another condition. In the more special case (^) 
of motion about a principal axis, this axis must be either the least or the 
mean. In fact calling c the axis of rotation and a the greatest axis, c 
must lie between h + a and h — a' where a, a' depend on the solution of 
a transcendental equation. If a decreases towards coincidence with I, 
these limits for c become h and -303327 l, but if a = 6 exactly (Mac- 
laurin's spheroid) c can have any value between o and a. Jacobi's and 
Dedekind's motions belong to this case, which also serves to connect con- 
tinuously cases (a) and (y), whilst case (/3) remains isolated. 

Riemann gives the following way of representing the foregoing per- 

1 'Ein Beitrag zn den Untersiichungen liber die Bewegiing eines fiussigen 
gleichartigen Ellipsoides,' Ahh. lionifj. Ges. Wiss, Gott. Math. Class, ix. p. 3. 



KECBNT PROGRESS IN HYDRODYNAMICS. 61 

sistent motions. Suppose the particles to describe similar ellipses in 
parallel planes perpendicular to a principal section of tlie ellipsoid in the 
same way as if attracted to the centres of their paths. Then the actual 
motion may be represented by supposing the whole system to have an 
extra motion of uniform rotation about an axis in that principal plane. 
In other words we may suppose the motion set up in the same way as 
imagined by Greenhill, referred to below. In the latter part of his paper 
he shows that when the axis of rotation is not a principal axis the motion 
is unstable, that Jacobi's and Dedekind's ellipsoidal forms are stable, and 
that in the other cases the motions are not stable if the two rotations 
which represent the motion are in the same direction. 

In the same year as Riemann's researches appeared, Brioschi ' pub- 
lished a paper in which he investigated equations for the moving axes 
of the ellipsoid and the molecular rotations. Dedekind's reciprocal law 
follows also easily from his forms of the differential equations. The in- 
vestigations of Dirichlet and Riemann have been co-ordinated and pub- 
lished in Italian by Padova^ with some extensions of his own, when the 
ellipsoid changes its form periodically. 

In 1879 and 1880, in the ' Proceedings ' of the Cambridge Philosophical 
Society, GreenhilP took up the same problem so far as it relates to 
motions with persistent form, but from quite a different point of view 
from that of Dirichlet. Instead of the Lagrangian equations he uses 
the Eulerian referred to moving axes. The fluid is supposed enclosed in 
a rigid envelope without mass, the whole system to have a rotation as a 
rigid body communicated to it about one line through the centre, and 
then a rotation of the shell alone about another. This is quite as general 
as Dirichlet's, and has the advantage of expressing the motion in terms 
of quantities whose dynamical meanings are evident. As the velocity- 
potentials for the last rotations are known, the equations are obtained 
with the greatest ease, and it only remains to find the condition that the 
pressure of the fluid on the shell may be everywhere the same, in which 
case the shell may be removed and the fluid mass will move as before. 
In the first paper the case of rotation about the principal axis is alone 
considered, and the relations between the axes and two rotations deduced. 
This is case (3) of Riemann. In the second paper he takes up the 
general question, and gives the condition for a free surface, but does not 
discuss the equation giving the condition. The calculations can be even 
here much simplified by considerations adduced at the end of the paper. 

On the same subject reference may be made to papers by Lipschitz^ 
(1874) and Hagen^ (1879). The former uses Riemann's form of 
Dirichlet's expressions for the positions of the particles, finds the action, 
and applies Hamilton's principle. The latter does not refer to any of the 

> ' Devcloppements relalifs au § 3 des Eecherches de Dirichlet sur un probl&me 
d'hydrodynamiqiie,' Borrh. lis. p. 63. 1861 (dated Nov. 1860). 

- ' Sul moto di un ellissoide fiuido ed omogenco,' Ann d. Sc. Korni. Pisa. 18G8-9. 

3 ' On the rotation of a liquid ellipsoid about its mean axis,' Proe. Camh. Phil. 
Soc. iii. p. 233. 

' On the general motion of a liquid ellipsoid under the gravitation of its own 
parts,' Proo. Camb. Phil. Soc. iv. p. 4. 

■• ' Reduction der Bewegung eines fliissigen homogenen ellipsoids auf das Varia- 
tioiispi'oblcm eines einfachen Integrals, und Bestimmung der Bewegung fiir den 
Qjen^^^'ill eines unendlichen elliptischen Cylinders,' Porch. Ixxviii. p. 245. 

i 'Zur Theorie der drei elUpsoidischen Gleichgewiclitsfiguren frei rotirender 
homoSener Fliissigkeiten,' ScMdm. Zeits Math. sxiv. p. 104. 



62 EBPOST — 1882. 

foregoing investigations, but gives approximations when the eftcentricitiea 
are very small or very large. The motion of a sphere under its own 
attraction vrhen slightly deformed, according to a spherical harmonic of 
order n, is the subject of a paper by Thomson.' The time of oscillation 
is shown to be 2ir\/ {(2n + l)a/2«(ii — 1)</}, where g is the acceleration 
at the surface produced by the gravitation. This is independent of the 
size, and depends only on the density of the sphere. The forced oscilla- 
tions of liquid spheres have been shortly treated by G. H. Darwin ^ in a 
similar manner. 

All the foregoing go upon the supposition that the density throughout 
the mass is constant, but this is not the case with the planetary masses, 
at least with the earth. This led Betti^ to take up the question of the 
equilibrium of heterogeneous ellipsoids, the surfaces of equal density 
being similar to the external surface. The investigation is not pressed to 
qualitative results, and is chiefly of mathematical interest. 

Other Surfaces. — When the meridian curve of a surface of revolution 
can be expressed in the form V = S cjr'^ = 1 where the r denotes the dis- 
tances of a point from each of a set of fixed points on the axis, the 
velocity-potential for a motion of translation pai-allel to the axis is easily 
wi'itteu down. The solution is duo to Hoppe,"* and takes the simple 
forms (^ — X [x + \ '^ c{x — a)jr^} and i// = p^ (1 _ y)^ in which X is a 
constant, a the distance from the origin of the point from which r is 
measured, and p the distance of the variable point from the axis. 
He has drawn figures of the lines of flow for the particular case 
81 /r^ — 16 /r'^ = 1. Another sui-face of revolution is that formed when 
a circle rotates about a line in its own plane. An investigation of this, 
based on notes taken at a course of lectures delivered by Riemann, has 
been published by Godecker,-^ the velocity-potential being obtained as 
an infinite series. The velocity-potential when the ring moves per- 
pendicularly to its plane was given independently by myself" in 1881. 
For an infinitely small wire of any foi'm with cyclic motion through the 
opening the sokition flows at once from Helmholtz's theory of the vortex 
filament. This has been treated of by Kirchhoff ^ and Boltzmann.^ 



c. Viscous Fluid. 

Motion in Tubes and Canals. — Naturally the first problem to which 
the equations of viscous motion were applied was that of the flow of 

1 ' Oscillations of a liquid sphere," PMl. Trans. 15.3 (1863) p. 608. 

' ' On problems connected with the tides of a viscous spheroid,' PMl. Trani. 
Part. II. 1879, p. 585. 

' ' Sopra i moti che conservando la fignra ellissoidale a una massa fluida etero- 
genea,' Annali di Matem. (2) X. p. 173 (1881). 

■* ' Vom Widerstande der Fltissigkeiten gegen die Bewegung fester Kiirper,' 
-P()^,9. ^7)«. xciii. 1854. 'Determination of the motion of conoidal bodies through 
an incompressible fluid,' Quart. Jour. i. p. 301. 

^ ' Die Bewegung eines kreisformigen Einges in einer unendlichen incompresBiblen 
Fliissigkeit,' Pr. Gdttiiiffeii, 1870. 

< On Toroidal Functions,' Trans. Bay. Soc. Part. III. 1881, p. 609. 

' ' Ueber die Kriltte, welche zwei unendlich diinne, starre Kinge in einer Flussig- 
keit scheinbar auf einander ausiiben konnen,' Crelle, Ixxi. and Keprint, p. 404. 

' ' Ueber die Druckkriifte, welche auf Pdnge wirksam sind, die in bewegte Fliis- 
sigkeit tauchen,' Crelle, Ixxiii. p. 111. 

See Part I. of this report, p. 74. 



RECENT rnOGRES^ IN HYDRODYNAMICS. 63 

fluids througli tubes and along canals. Stokes,' in Lis fii'sfc paper on vis- 
cosity, worked out the case of watei' flowing down an inclined circular 
cylinder under the action of gravity, as an example of the methods 
developed in the paper. In a cylinder of radius a, inclined at an angle a, 
the velocity at a distance r from the axis is h(a'^ — r'-) + U, U being 
the velocity at the surface, and lc = ^g sin a jfj. In 1860 Helmholtz - 
considered the analogous question where the motion is caused by a dif- 
ference of pressure at the two ends, allowing also for a certain amount of 
slipping at the surface of the tube. Here the velocity is given by 
A;(a* -1- 2Xa — r^), where h = (diff. of pressures) /4/iZ, which gives a 
flow of ^Trkp(a'*' + Xa^), agreeing well with experiments. The same 
question has also been treated by Stefan, Boussinesq, Butcher, Graetz, and 
Greenhill. Stefan ^ takes into consideration a motion of rotation of the 
vessel as well. Boussinesq's * investigations are more general than the 
others, and extend to tubes of non-circular sections. Considering the 

equation — - + -4r + 4Z.- = 0, which gives the velocity parallel to the axis, 

he shows, from the principle of similitude, that in tubes of similar sections 
the velocities at corresponding points are proportional to h and the areas 
of sections, and that the flows in the same times are proportional to the 
fourth powers of the constant of similarity — the forces acting being the 
same. He then solves for the j^articular cases where the sections of the 
tubes are — (1) elliptic, (2) rectangular, and (3), in a note at the end of 
the paper, where the section is an equilateral triangle. If A be the area 
of the section, the flow for the elliptic tube is kAa-b"^ l(a^ +■ h'^) for the 
triangular (sides = 2a) is IcLa^jh, whilst for the rectangular the expres- 
sion is naturally more complicated. After noticing the case where in 
a straight tube the section gradually changes, he passes on to consider 
the motion where the axis of the tube is circular. This is interesting, as 
a steady motion in circles is impossible if the boundary is at rest. Treat- 
ing the velocities in any section of the tube as small compared with the 
velocity across it, he solves the equation when the section is a rectangle 
whose height is small compared with its breadth. The motion consists 
of two circulations combined with a translatory motion along the tube of 
greater magnitude. If the rectangular section be divided by a medial 
line in the plane of the tube, the circulations may be represented by 
supposing the particles of fluid near it to move outwards, increasing 
their distance from it, and at last, on nearing the outer boundary, revers- 
ing their direction, and coming back nearer the longer sides. A similar 
result was also subsequently (1875) arrived at by Oberbeck. Boussinesq^ 

' 'On the theories of the internal friction of fluids in motion, &C.' Camh. Phil. 
Trans, viii. p. 287. 

■■* ' Ueber die Rcibung tropfbarer Fliissigkeiten,' Sitzhcr. d. li. Ahad. Wins. 
Wien. xl. p. 652, and Collected Warhs, Bd. I. p. 215. 

' ' Ueber die Bewegung fliissiger Korper,' Sitzber. d. h. Ahul. Wicn. xlvi. p. 495. 
The dimensions of the coefficient of viscosity are wrongly given. He seems to regard 
the vortex rotations as if the small elements of fluid turned round as rigid bodies. 

* ' Memoire sur I'influence des frottements dans les mouvements reguliers des 
fluides,' Ziour. (2) xiii. p. 377 (1868). 

* ' Essai sur la theorie des eaux courantes,' Acad, des Soienees. Paris. Mem. 
par divers Savants, xxiii. xxiv. 1877. This is a long memoir, consisting of 680 quarto 
pages of printing. The latter part is devoted to wave motion, and this contains 
some results of value — especially the theory of the solitary wave ; but this Lad been 
published before in Liouville. (See first part of this report.) 



64 REPORT — 1882. 

lias publislied fartlier investigations on tlio same subject, but more from 
the point of view of tlie liydraulic engineer. 

In 1876 Bntcher, in Lis paper before referred to,^ also touches on 
the question of the motion in straiglit tubes, but without adducing new 
results. Besides this he finds the general form for Stokes's stream func- 
tion for a motion taking jjlace in planes through an axis. Graetz ^ has 
worked out precisely the same questions as Boussinesq, to whose work 
he does not refer. He has taken the trouble to calculate numerical 
results for a tube with a square section, and has also followed out St. 
Venant's idea by taking algebraical solutions of the equations, and finding 
for what shaped tubes tbey are the solutions. 

Greenhill ^ has made a valuable remark by which the motion of a 
viscous fluid in a straight tube of any section, without gliding at the 
surface, may be deduced at once from the solution for the case of the 
motion of a perfect fluid in a cylinder of the same section rotating about 
its axis. This is seen at once when it is noticed that the difierential 
equation for the velocity parallel to the axis in the first case has precisely 
the same form as that for the stream function relative to the boundary, 
rotating with an angular velocity 21c ; and that the bounding condition for 
the two functions is the same, if in the first case the fluid is supposed to 
stick fast to the boundary. In this way the velocities in tubes whose 
sections are a circle, an ellipse, an equilateral triangle, two hyperbolas, 
a sector of a circle, and a rectangle, are written down at once. 

Cylinders. — If two co-axial cylinders rotate with difiereut velocities, 
wi, m, the velocity of the fluid between at a distance r from the common 
axis, when steady, has been given by Stokes,'* with a single cylinder in 
an infinite fluid as a particular case. When the motion takes place 
between two co-axial cylinders at rest — being produced and kept up by 
pressures across two plane sections through the axis — the expression for 
the velocity is not algebraical as in the previous case. The solution for 
this is due to Boussinesq, and is given in his paper in Liouville just 
referred to. Rohrs ^ treats a similar question, taking account of non- 
permanent motion. The determination of the motion of the fluid when a 
cylinder oscillates in a direction perpendicular to its axis, forms one of 
the chief problems considered by Stokes ^ in the second of his classical 
papers on viscosity. The method employed is precisely similar to that 
adopted for the corresponding problein for the sphere (noticed below) ; 
but, unfortunately, the solution of the differential equations occurring 
cannot be represented in finite forms, as in that case. The functions 
entei'ing are cyliudric harmonics, and this introduces a diSiculty in ap- 
plying the condition of finite motion at an infinite distance, to determine 
the arbitrary constants appearing in the solution, but that is surmounted. 

• ' On Viscous Fluids,' Proe. Lond. Math. Soc. viii. p. 120. (See first part of 
report, p. 79.) His analysis is wrono; where he considers the determination of the 
arbitrary constants in the solution from the bounding conditions. 

- ' Ueber die Bewegung von Fliissigkeiten in Rohren,' Zeits. f. Math. u. Phys. 
XXV. pp. 316, 375 (1880). 

^ ' On the flow of viscous fluid in a pipe or channel,' Proc. Lond. Math. Soc, xiii. 
p. 43 (1881). 

* ' On the friction of fluids, &;c.' (1845). 

* « Spherical and cylindric motion in viscous fluids,' Proc. Lond. Math, Soc. v, 
p. 133 (1874), 

« ' On the effect of the internal friction of fluids on the motion of pendulums,' 
Camh. Phil. Trans, ix. part ii. p. 35. 



RECENT PKOGRESS IN HTDEODYNAMICS. 65 

The results are used to determine the effect of the wire by which it is 
suspended on the time of oscillation of a ball-pendulum. If it be pro- 
posed to determine the state of motion of the fluid due to a uniform 
translation of the cylinder, it will be found that a steady motion of the 
fluid will be impossible, but that as the time increases the quantity of 
fluid carried forward with the cylinder continually increases. In fact, if 
the differential equation for the stream function be integrated on the 
supposition of steady motion, it will be found that, though the integral 
takes a simple finite form, there are not arbitrary constants sufficient to 
satisfy the conditions. 

Plane and Disc. — The determination of the motion of a disc in a viscous 
fluid is important, as it forms a useful method to determine experimen- 
tally the value of the coefficient of viscosity for different fluids. The 
method was first employed by Coulomb, but first received mathematical 
treatment by Stokes (1850), and afterwards (1861) by Meyer. Stokes * 
begins by investigating the motion when an infinite plane oscillates in its 
own plane, so that its displacement at any time is given by c sin nt. The 
displacement at any point in the fluid at a distance x is then given by 
c sin {nt — .r\/(?i/2^4)} x exp — x v/(ii./2^). A given phase is therefore 
propagated with a velocity ^/2im. This for air, treated as incompres- 
sible, andfor a time of vibration of one second, is about "2908 inch per 
second. The solution for a disc oscillating in its own plane can then be 
obtained by treating each element of it as a portion of the above plane, a 
solution which is exact if the squares of the velocities are neglected, except 
in so far as the action of the rim is concerned. In this way he finds the 
change in the'time of vibration due to viscosity, and also the logarithmic 
decrement of the arc of oscillation, with a correction to be applied, 
because the observations are made soon after the disc is set in motion, 
and before the motions, due to the starting in a fluid at rest, have dis- 
appeared. The results obtained enable him to discuss the observations of 
Coulomb. 

Without a knowledge of Stokes' work, O. E. Meyer ^ attacked the 
same problem about ten years later. He supposes the angular velocity 
of the fluid to depend only on the distance from the disc, and not on the 
distance from the axis of rotation. This is equivalent to Stokes' appli- 
cation of the motion for a plane to that for a disc. He also determines 
the logarithmic decrement. 

The Sphere. — The analytical difficulties connected with this surface 
may be considered to have been surmounted, chiefly through the work of 
Stokes, Meyer, and Oberbeck. In his second paper on viscosity of 
fluids Stokes ' attacks the problem of the motion by expressing the velo- 
cities in terms of the stream function — first introduced by him — ana 
making the determination of this stream function the basis of the investi- 
gation. The motion is supposed so small that squares and products of 
the velocities may be neglected. In this case the stream function -^ must 
satisfy the differential equation ^ V^(^^ X ofi~^dlJt)\p = 0, the solution 
of which can be represented in the form ;// = i//, + \p.2 where v'^i/'i = 0, 
(v^ + pfi~^d/dt)\l^.2 ^ O- The complete solution of this is not entered 

' ' On the effect of the internal friction of fluids on tlie motion of pendulums,' 
Carnb Phil. Trans, ix. part 2, p. 8 (1850). 

^ ' Ueber die Reibung der Fliissigkeiten,' Borcli. lix. p. 229. 

^ I use — V" to denote the operation d^jda.'- + d-jdi/- + d-jdz", or, in this case, 
d-jdx- + d-jdw- — m- ^djdw, as v denotes the vector operator idjdx + jdjdy + Jidjdz. 
1882. F 



66 EBPOKT— 1882. 

upon, but the simpler and more important case where the motion begins 
from rest is worked out in detail. If the displacement of the centre of 
the sphere be given by the equation £ = c sin nt, then the stream func- 
tion, when the surrounding fluid is infinite, is 

^L = ^a?c?.m^d\{ ( 1 +-^')cosn< + -^fl + -\innt )- 

- — ( cos Oat - vr + va) + f 1 + — ") sin (...)) e-"-"^! 

where r = v'(?;,/2^), whence the pressure and resultant force on the 
sphere are easily deduced in simple forms. The latter consists of two 
terms, whose effects on the motion of a pendulum are different. If r 
is the time of oscillation, the effect of one term is to produce an apparent 
increase of inertia equal to ItM! , whilst the other has most effect on the 



TT Ic'W 



amplitude of vibration, the log decrement being -— . -— — —-, , where 

^ ' & ° 2r M + IM.' 

M , M' denote the masses of the sphere, and of the fluid displaced by 



it, and 



He then passes on to investigate the effect of a concentric spherical 
boundary. When the effect of the boundaiy is small it is sufiicient to 
treat it as absent, and then add small corrections to the results. If the 
viscosity is small, or if the time of oscillation is small, this correction is 
the same as if there were no viscosity.' 

We have seen (p. 27) that a steady motion of the fluid when a 
cylinder moves uniformly through it is impossible. This is not so with 
the sphere. In this case Stokes shows, that, if V be the velocity of the 
sphere, ip = :j aW(Srja — ajr) sin ^6 (axes fixed in the sphere), and 
that the force necessary to maintain the motion is G-rrf^iaV. This varies 
only as the radius of the sphere, ' accordingly, fine powders remain 
nearly suspended in a fluid of widely different specific gravity.' If a 
sphere of density o- be descending through a fluid under gravity, the 
limiting velocity (if it is not very great) is 2g(t7 — p)a^/9/u'; this for a 
globule of water in air, of "001 inch diameter, is 1"593 inch per second, 
whilst for one with a diameter of "0001 inch, it is less than one-sixteenth 
of an inch per second. 

In a note at the end of this paper it is shown that if a sphere rotate 
about a diameter the particles of the fluid move, when the motion is 
steady, in annuli, with velocities given hjv = a'w sin 6 jr^, w being the 
angular velocity of the sphere ; and that, in general, the motion is given 
by V = v' sin d, where v' is a function of r alone. This steady motion in 
annuli is only possible when the motion is slow ; if it is not so, then with 
the annular motion is combined one in planes through the axis : ' In 
fact it is easy to see that, from the excess of centrifugal force in the 
neighbourhood of the equator of the revolving sphere, the particles in 
that part will recede from the sphere and approach it again in the 
neighbourhood of the poles, and this circulating motion will be com- 

• See above, p. 61. 



RECENT PROGRESS IN HYDRODYNAMICS. 67 

bined with a motion about the axis.' ' This may be compared with 
Boussinesq's results for a circular tube of rectangular section, referred to 
above. 

This investigation by Stokes is a most important one, forming as it 
does the first application of mathematical reasoning with any success to 
the problem of the motion of pendulums in non-perfect fluids. The second 
part of the paper, forming about one-third of the whole, is devoted to the 
discussion of the observations of Baily, Bessel, Coulomb, and Dubuat, and 
the values of /u for water and air are deduced from their experiments. The 
investigations with reference to cylinders and vibrating discs have been 
already referred to. 

Stokes had considered the case when the fluid was originally at rest 
without vortex motion in any part, and had, therefore, taken only those 
particular solutions of the difierential equations which i/^i, \p2 satisfy, in 
which d enters as the factor sin ^d. In 1870, O. B. Meyer ^ took up this 
question and showed that the general solutions are expressed in the forms 

^b^ = S(Aen + BZ„)E„ exp (XH), .//^ = 2(09^ + DZ„)Sn exp (XH) 

where 9, Z are functions of d alone, and R, S of r, both of flnite forms. 
In fact, the 9, Z are proportional ^ to sin ddP /dd, where P is a zonal 
spherical harmonic. The work is too complicated to be described with 
any fulness here, but it is carried out with much skill, account being 
taken of a concentric boundary. He proves, amongst other things, that 
the motion due to the original state of the fluid decreases indefinitely with 
the time, i.e., that the equation giving the values of X has all its roots 
pure imaginaries except for the case ?i = 1 or 9; = sin^fl (Stokes' case), 
in which it is complex, giving periodic vibrations with decreasing ampli- 
tudes. In the particular case where the external boundary is infinitely 
large, Meyer's results agree with those of Stokes for the time, but there 
is a slight difference for the log decrement. When the surrounding fluid 
is elastic the results must be modified ; this has also been considered by 
Meyer '' who has determined the log decrement under these conditions, 
and has shown that when the velocity of sound in the fluid is very great 
the correction may be neglected without sensible error. Meyer refers to 
a paper by 0. J. H. Lampe ^ on the same subject, but this I have not 
seen. 

The investigations both of Stokes and Meyer are based on the stream 
function, but this is only suitable when the motion takes place in planes 
through an axis. When this is not so, recourse must be had to the 
quaternion potential first introduced by Helmholtz ^ in his paper on 
vortex motion. The investigation on these lines has been carried out by 

' ' On the theories of the internal friction of fluids in motion,' &c. Camh. Phil. 
Trans., viii. ; or reprint, vol. i. p. 103, 1845. The connection of this with part of 
Siemens' theory of the conservaiion of the sun's heat is evident. 

- ' Ueber die pendelnde Bewegnng einer Kugel unter dem Einflusse der inneren 
Eeibung des umgebenden Jlediums,' Bmxh. Ixsiii. p. 31. 

' ' Ueber die Bewegung einer Pendelkugel in der Luft,' Borcli. Ixxv. p. 336, 
1873. 

* Ibid. 

* ' Ueber die Bewegung einer Kugel, welche in einer reibenden Fliissiglceit um 
einen senkrechten Durchmes.ser als feststehende Axe rotirend schwingt,' Frogramme 
des iStddtiscIien Gymnasiums zu Danzig, 1866. 

« See Part I. of this report, Brit.- Assoc. Bep. 1881, p. 60. 

F 2 



68 REPORT— 1882. 

Oberbeck,' and later and independently by Craig.'^ As is known the velo- 
cities are in this method expressed by functions P, L, M, N, so that 
u = clVjdx + cmifly - cZM/c?2 with v2P = 0. (Hjjdx + dMjchj + d'N/dz = o, 
and the vortex rotations given by ^ = V^L, &c. He takes the most general 
form for P in spherical harmonics with no normal velocity at the surface 
of the sphere ; in other words, if Yn be any solid harmonic of degree n, 
then 



'^^i^-^i^TV- 



By means of an important theorem of Borchardt's, L, M, N are then 
expressed in the form h^= z dFJdy — y dF/dz, with similar expressions 
for M, N, where 

The above theory applied to a sphere moving uniformly gives values 
for the velocities which agree with those of Stokes. Expressions are also 
given for the vortex rotations, from which it can be easily proved that the 
vortices of equal strength lie on concentric spheres, and that the strengths 
are inversely as the squares of the radii of the spheres on which they lie. 
The theory given by Craig is almost identically the same, as indeed any 
theory, starting from the basis of Borchardt's theorem and the quaternion 
potential, must be. 

The motion of fluid inside a sphere was first investigated by Helm- 
holtz,-' allowance being made for a slipping of the fluid over the surface 
of the boundary. The paper in which his investigation appeared was 
a joint one, containing the mathematical theory by Helmholtz, and the 
experimental by Piotrowski. The motion is considered so small that 
squares of the velocities may be neglected, and in this case the motion is 
such that it may be represented by supposing concentric shells of the 
fluid to revolve as if rigid with an angular velocity depending on the 
radius of the shell, the most general expression for which is a sum of 
terms of the form 

w„= Ae"* < -^ cosli /3r sinh (Sr > where /3 = ± >/(o//i'), 

and a is in general a complex. The motion can be represented as a series 
of waves propagated to the centre with rapidly decreasing intensity, and 
there reflected. If, for example, the boundary have a simple har- 
monic motion of period -, the velocity of propagation of these waves 
will be 2^ (^iTr/r), and is therefore dependent on the time of vibration. 
Whilst the wave moves through a wave-length 2\/(/i7rr), the amplitude 
diminishes in the ratio 1 to exp.( — 27r), or from 1 to 1/535. Helmholtz 
works out the motion for the sphere as applicable to the data in 
Piotrowski's experiments. These experiments contain the first attempt 
to approximate to the value of the coefficient of gliding. The values 
of this found for alcohol and ether are so small that they are probably 

' ' Ueber stationiire Fliissigkeitsbewegungen mit Beriicksichtigung der inneren 
Eeibung,' Bvrch. Ixxxi. p. 62, 1875. 

2 ' On steady motion in an incompressible viscous fluid,' Phil. Mag. (.5) x. p. 342 
(1880) 

' ' Ueber Eeibung tropfbaver Fliissigkeiten,' Sitzber. d. h. Akad. ^S'iss. Mien., si. 
p. 607 (1860), and WissemchaftUchen Abhandlungen, i. p. 172. 



KECENT PROGRESS IN HYDRODYNAMICS. 69 

evanescent, whilst for water in contact with a gilded surface it is con- 
siderable. 

The same problem has been investigated by Liibeck ' (1873), starting 
from Meyer's solution of the equation for the stream function, and by 
Rohrs - (1874), who took up the question from the point of view of pre- 
cession, and considers the case where the axis of rotation slowly changes. 

The Ellipsoid. — The expressions for the velocities when a sphere moves 
through a viscous fluid have suggested to Oberbeck ^ the form of the solu- 
tion for an ellipsoid moving parallel to one of its axes. He shows that if ii 
denote the potential of the ellipsoid at an external point, in the form given 

on page 17, and Q = 2 tt — then the velocities of the fluid, when the 

Jo l-^j . 

ellipsoid moves parallel to the axis a with velocity V, are given by 



L dy dxdij i 

r dQ , 2 f?'" 1 



f/\ 



where a = — s— with A = — = I /, X^ 



with A = —5 \ /, \^\t^ 

Qo + a^A .^J^(l-f-^)D. 



Tbe force on the ellipsoid necessary to keep up uniform motion is then 
STT^t'ciE, where £ is the measure of the charge of electricity induced on the 
ellipsoid when it is charged to potential Qq. 

The oscillations of a viscous spheroid have been treated by G. H. 
Darwin and Lamb. In the investigations of the former,'' which are devoted 
more directly to researches on the past history of the earth, the motions 
are treated as very slow, and the coefficient of viscosity as large, so that 
the problems considered belong more to the domain of elastic solids than 
to that of hydrodynamics. The latter ^ has considered the general solution 
of the equations of motion when the velocities are so small that their 
squares can be neglected. The first part of his paper is devoted to the 
solution of the system of equations 

(y2 _ 7i2) u= 0, (v2 _ /,2) ^ = o,(v' - Ji^)io = 0, and 
dujdx + dv/dy + dwjdz = 0. 

This is then applied to investigate the oscillations of a sphere slightly 
distorted and moving under its own gravitation, and an equation is 
obtained on whose roots depend the time of oscillation and the logarithmic 
decrement of the amplitude. This equation is easily solved either for the 

' ' Ueber den Einfluss, welchen auf die Bewegung eines Pendels mit einem kugel- 
formigen Hohlraume eine in ihm enthaltene reibende Flussigkeit ausubt,' Borch. 
Ixxvii. p. 1. 

2 ' Spherical and cylindric motion in viscous fluid,' Proc. Lond. Math. Soc, v. p. 
125. 

' ' Ueber stationare Fliissigkeitsbewegungen,' &c. Borch. Ixxxi. p. 62. 

* • Bodily tides of viscous spheroids,' Phil Trans., part i. 1879. 

'Problems connected with tides of a viscous spheroid,' Phil. Trans, part ii. 1879. 

5 ' On the oscillations of a viscous spheroid,' Proc. Lond. Math. Soc. xiii. p. 51, 
1881. 



70 BEPOET— 1882. 

case of very large viscosity or very small. For very large viscosity the 
result agrees with that of Darwin's and the displacement subsides without 
oscillation. For very small, the time of oscillation agrees with that for a 
perfect fluid, found by Thomson,' whilst the 'modulus of decay,' i.e. the 
time in which the amplitude decreases to 1/e of its original value, is 
(w — l)(2n + VjiJtja^, for an harmonic displacement of order n. This 
for a sphere of water of the size of the earth is 1'84 x 10^' years. For 
a globule of water oscillating under the action of its surface tension, the 
time of oscillation is 2ir/j3, where /3^ = n(n — l)(n + 2)T/pa^ where T is 
the surface tension. For the slowest oscillation (n = 2) the modulus of 
decay of a globule of water is 14-3 a^ seconds, the radius a being ex- 
pressed in centimetres. 

The effect of viscosity on the motion of waves has been discussed by 
Stokes,^ Boussinesq,' Lamb,* and others. The rate of decay of the motion 
obtained by Stokes is double the true value — an error caused, as both 
Boussinesq and Lamb have pointed out, by an oversight of the former in 
neglecting the potential energy of the motion. 



Postscript. 

I find I have omitted to notice a paper by Lodge ' On some Problems 
connected with tlie Flow of Electricity in a Plane,' Phil. Mag. (V.), 
vol. 1. (1870), in which the motions in plane triangles, rectangles, and 
circles are treated. 



Report of the Committee, consisting of Professor Gr. Carey P^oster, 
the late Mr. C. Hockin, Sir William Thomson, Professor Ayrton, 
Mr. J. Perry, Professor W. G. Adams, Professor Lord Eayleigh, 
Professor F. Jenkev, Dr. 0. J. Lodge, Dr. Johx Hopkixsox, Dr. A. 
MuiRHEAD (Secretary), Mr. W. H. Preece, INIr. Herbert Taylor, 
Professor Everett, and Professor Schuster, appointed for the 
piorpose of constructing and issuing practical Standards for 
use in Electrical Measurements. 

The Committee have to report that Mr. Taylor has continued the experi- 
ments upon the temperature-coefficient of the resistance of metals and 
alloys, the first results of which were communicated at the York meeting. 
In consequence of Mr. Taylor's absence from the country, the details of 
the farther experiments cannot be communicated at present ; but it may 
be stated that they have shown the possible influence of the process of 

' See above p. 24. 

^ ' On the effect of the internal friction,' &:c., cited above. 

" 'Additions et eclaircissements au memoire intitule Essai sur la thfiorie,' &c. 
Mem. de Sav. Etran. xxiv. (1877). 

* ' On the oscillations,' k.c., cited above. 



ON STANDAEDS FOR USE IN ELECTRICAL MEASUREMENTS. 71 

annealing on the specific resistance of wires and on the temperature- 
coefficient to be much greater than has hitherto been commonly supposed. 
The following are examples of some of the results obtained : — 

German Silver. — Wire drawn to be extremely hard and brittle. The 
percentage variation of resistance, for 1° between 13° and 100° C, was 
0'0296. After annealing, the percentage variation of the same wire was 
0-0421. 

Steel. — "Wire, 0'025 inch diameter, thoroughly hardened, and then 
tempered in paraffin wax at 230° C. : — 

Percentage variation of resistance for 1°, 0'267. 

Same wire annealed ; percentage variation for 1°, 'SIG. 

At 9° C, the ratio of the absolute resistance of this wire in the hard 
state to that of the same wire when annealed was 1"229. 

Platinum- Silver Alloy. — A piece of wire made from a particular bar 
of the alloy was hardened by being drawn down through a couple of 
holes of the draw-plate. In this state the variation of resistance was 
0"0255 per cent, per degree. After annealing in the ordinary way, the 
variation of resistance per degree was 0'0258 per cent. The same wire 
was next placed in an iron tube which was filled up with sand and left 
all night in the fire. After this treatment, the percentage variation of 
resistance per degree was 00344. 

Platinum- Silver Alloy, another specimen. — A wire from a second 
bar of the alloy was annealed at a very high temperature and left to soak 
in the fire and cool slowly, as in the last-mentioned experiment. The 
variation of resistance was now 0'095 per cent, per degree, and the wire 
was as soft as pure silver and very fragile. After being heated to red- 
ness and quenched in water, the corresponding variation of resistance of 
the same wire was 0076 ; and when the wire had been drawn down 
through two or three jewel-holes, it was 0'0732. 

These results indicate a connection between the temperature-coefficient 
of wires and their degree of hardness, and tend to reopen the question as 
to the most trustworthy material for a permanent standard of resistance. 
The Committee understand that Mr. Taylor will continue his experiments 
with the co-operation of Dr. Muirhead. 

The Committee are pleased to be able to report that there is a pro- 
spect that Lord Rayleigh may be able to organise, at the Cavendish 
Laboratory, Cambridge, a system of testing resistance-coils and issuing 
certificates of their correct value at a specified temperature. 

As stated in the Report presented last year, Dr. Muirhead has con- 
sented, at the request of the Committee, to issue standards of capacity 
upon his own responsibility. 

The Committee regret that they are not able to report any progress 
towards the construction of a standard of Electromotive Force. 

They are unwilling to conclude without expressing their deep sense of 
the loss which not only they, but all friends of physical science, have 
snffisred in the death of one of the most valued of their colleagues, Mr, 
Charles Hockin. 



BEPORT — 1882. 



Fifteenth Report of the Committee, consisting of Professor Everett, 
Professor Sir William Thomson, Mr. G. J. Symons, Sir A. C. 
Eamsay, Professor A. Geikie, Mr. J. Glaisher, Mr. Pengelly, 
Professor Edward Hull, Dr. C. Le Neve Foster, Professor A. S. 
Herschel, Professor G. A. Lebour, Mr. A. B. Wynne, Mr. Gallo- 
way, Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wethered, 
and Mr. A. Strahan, appointed for the purpose of investigating 
the Rate of Increase of Underground Tertipjerature doivmoards 
in various Localities of Dry Land and under Water. Dragon 
up by Professor Everett (^Secretary). 

One portion of the duty assigned to the Committee is the investigation 
of the rate of increase of underground temperature downwards under 
luater. This part of their task has remained in abeyance until the past year, 
but through the good oflSces of Professors Lebour and Merivale observa- 
tions have now been obtained from a colliery which runs to a considerable 
distance under the sea at Whitehaven, Cumberland. 

The observations were taken in holes bored upwards for the purpose 
to a distance of 4 feet in the roof of the ' Main Band,' at Croft Pit, under 
the direction of the manager, Mr. G. H. Liddell. 

The holes were well plugged with clay, and the thermometer (one of 
the Committee's slow-action instruments) was in each case left in the 
hole for 7 days. The distance beyond low-water mark was 430 yards in 
the case of two of the boreholes, and 1,340 yards in the case of the other 
two. The depths below ordnance datum were 1,140 feet for the two 
former, and 1,250 feet for the two latter. The depth of the sea in all 
four cases is estimated at 12 fathoms. The temperature observed was 
exactly the same in all four holes, namely, 73° F., and, in one instance, 
this was verified by reinserting the thermometer with its bulb upwards 
instead of downwards. These data give 1,195 feet as the mean depth 
below ordnance datum, and 1,123 feet as the mean depth below the bottom 
of the sea. Assuming 48° as the mean temperature of the bottom of 
the sea, we have, therefore, an increase of 25° F. in 1,123 feet of ground, 
which is at the rate of 1° F. in 45 feet. 

Mr. E. Garside has furnished two more observations, one of them 
from the same neighbourhood as his previous observations — the East 
Manchester coal-field — and the other from South Stafibrdshire. They 
were made with the slow-action thermometer, used in precisely the same 
manner as before. 

The former observation was taken on May 4, 1882, in Denton Colliery, 
Lancashire. The hole was drilled at 1,317 feet from the surface, nearly 
vertically below the bed of the river Tame, which divides the estate of 
Denton Colliery from that of Bredbury Colliery, and the temperature 
observed was 66° P. Assuming a surface temperature of 49°, this gives 
an increase of 17° in 1,317 feet, which is at the rate of 1° in 77^ feet, 
being nearly identical with that found at Bredbury Colliery. 

The other observation was made at Lye Cross Colliery, Dudley (north 
of Wolverhampton). The thermometer was placed, as usual, ia a hole 
about 4 feet deep, drilled for the purpose in ground newly opened, free 
from cracks or other visible irregularities, and also free from any strong 
air-current. It was at the depth of 700 feet from the surface, in the hard 



ON THE EATE OF INCREASE OF UNDERGROUND TEMPERATURE. 73 

shales which are 8 feet in thickness, forming the floor of the ten yards 
coal and roof of the Heythen coal, the total thickness of the seam worked 
(with small parting) being about 52 feet. The temperature observed 
was 57°-5 F. which, with an assumed surface temperature of 49°, gives 
an increase of 8°-5 in 700 feet, being at the rate of 1° F. in 82 feet. 

The colliery is situated on the summit of a hill 822 feet above sea- 
level, so that the point at which the observation was taken was 122 feet 
above sea-level. The convexity of the ground must be taken into account 
as one element in endeavouring to account for the slowness of the ob- 
served rate of increase. Of the 700 feet of superincumbent shales, about 
470 consist of coal measures, 165 of clay marl, and 65 of basalt, connected 
with dykes whose many branches traverse the coal at slopes varying from 
vertical to horizontal. The basalt is found to contain, when newly cut 
open, a remarkable quantity of salt water ; and the charred coal next to 
the dyke is as porous as ordinary coal cinders for a distance of several inches 
from the dyke. 

The Secretary has had a correspondence with Mr. Garside respecting 
the quantity of water found in the East Manchester coal-field. This 
quantity is very large, as appears from a list furnished by Mr. Garside of 
the number of gallons pumped per minute from each of thirteen pits 
during the sinking, the list being given on the authority of William 
Seddon, Esq., mining engineer, who was contractor for the sinking of 
them. The average is 360 gallons per minute for each pit, the highest 
being Denton Colliery with 1,000 gallons, and the lowest Valley Pit, 
Denton, with 120 gallons. Particulars are also given of the quantity 
now pumped from some of the collieries, amounting in some cases to 800 or 
900 gallons per minute. Some of the collieries have been repeatedly 
flooded, and one is mentioned (Lord's Field Colliery) which was aban- 
doned on account of water, though its owners were makers of hydraulic 
machinery, and tried their utmost to keep the water down. Some of the 
pits were formerly the sources of water-supply for towns in the district. 
In Astley Deep Pit, Dukinfield, the shaft is ' tubbed ' with cast-iron rings 
to keep the water back ; and most of the shafts in the district are made 
as water-tight as possible. Mr. Garside refers to the ' Memoir of the 
Geological Survey round Oldham,' as stating, on page 45, that five million 
gallons a day are estimated as being raised from the New Red Sandstone. 

The question naturally arises whether this abundance of water does 
not exert a powerful cdnvective action, and furnish the explanation of the 
slow increase of temperature downwards, which has been observed not 
only in the coal mines of this district but also in a still more marked 
degree at the Liverpool waterworks at Bootle. 

Nine years having elapsed since the last observations were furnished 
from the great well at La Chapelle in the north of Paris, which was then 
in course of sinking, the Secretary has put himself in communication with 
the contractors to learn what progress has been made, and has received a 
letter dated July 8, 1882, giving a history of the undertaking during the 
interval. 

The continual crumbling down of the sides rendered tubing necessary, 
and a tube was accordingly constructed 677m. long, l-3m. in diameter, 
and 2 centimetres thick. During the lowering of it, a portion 120m. 
long broke ofi" and fell to the bottom, leaving another piece 100m. long 
suspended. This suspended piece was successfully extracted without 
difficulty, but the fallen piece was not easily dealt with. It was first cut 



74 REPORT — 1882. 

into four lengths by a new and special tool, and three of these were 
raised ; but the fourth was so broken and jammed that the extracting 
tool could not remove it. Dynamite was tried, but its explosive violence 
was so deadened by the superincumbent pressure, that it proved power- 
less, and a special engine had to be constructed for crushing the broken 
pieces. This task has now been successfully accomplished, and the work 
is accordingly just as forward as it was before the tubing was com- 
menced. The Municipal Council of Paris have now ordered the con- 
tinuance of the operations, and the tubing will be recommenced. Owing 
to the difficulties above described, the well is now no deeper than it was 
when the last observations of temperature were taken in it nine years 
ago. 

Two slow-action thermometers have been sent to Mr. "W. Galloway 
(Member of the Committee and Inspector of Mines, Cardilf), for obser- 
vationa in mines. 

One slow-acting and one Negretti maximum thermometer have been 
sent to Mr. T. W. Rumble, Engineer of the Southwark and Vauxhall 
Water Company, for observations in a deep well now sinking at Tooting. 

A slow-acting thermometer has also been supplied to Mr. Grifi&th, 
Manager of a Colliery at Wrexham. 

This, the iifteenth Report of the Committee, is accompanied by a 
summary, which has been made by the Secretary, of the fourteen pre- 
ceding Reports, together with as much as it was possible to include of 
the present Report. 



Summary of Results contained in the First Fifteen Reports of the 
Underground Temperature Committee. By Professor Everett {Secre- 
tary). 

The fourteen reports hitherto published are contained in the consecu- 
tive volumes of British Association Reports, commencing with that for 
1868, except that the report for 1874 having been by mistake omitted 
from the volume for that year, is inserted in the volume for 1875 instead. 

The following Table, showing the page at which each report com- 
mences, will facilitate reference : — 



Eeport 

I. . 

II. . 

ni. . 

IV. . 

V. . 

VI. . 

VII. . 



Volume 

1868 , 

1869 , 

1870 , 

1871 . 

1872 . 

1873 , 

1874 . 



Page 

510 

176 

29 

14 

128 

252 

14 



Eeport 


A''olume 


Page 


VIII. 


. . 1875 


. 156 


IX. 


. . 1876 


. . 204 


X. 


. . 1877 


. 194 


XI. 


. . 1878 


. 178 


XII. 


. . 1879 


. 40 


XIII. 


. . 1880 


. 26 


XIV. 


. . 1881 


. 90 



In the references which we shall have to make, the number of the 
report will be indicated by Roman, and the page by Arabic figures. 

We shall classify the results as follows : — 

A. Instruments. B. Methods of observation. C. Questions afiect- 
ing correctness of observations. D. Questions affecting deductions from 
observations. E. Comparison of results. F. Mean rate of increase of 
temperature with depth, and mean upward flow of heat. 

A. Instruments. — Under this head we have — 

1. Instruments for observing temperature. 2. Subsidiary apparatus. 

1. The thermometers which the Committee have employed have been 



I 



ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 75 

of two kinds — slow-action thermometers and maximum thermometers. 
The present pattern of slow-action thermometer consists of a thermometer 
having its biilb surrounded by stearine or tallow, the whole instrument 
being hermetically sealed within a glass jacket, and had its origin in a 
conference between the Secretaiy and Dr. Stapff in the St. Gothard 
tunnel (VIII., IX., XI.) Other slow-action methods described in the 
reports are — Angstrom's thermometer in bottle of water (I.), large spirit 
thermometer (I.), Symons' thermometer in a thick casing of felt (II.). 

Our present patterns of maximum thermometer are two — the Phillips, 
and the Inverted Negretti — both being hermetically sealed in strong glass 
jackets to prevent the bulbs from receiving pressure when lowered to a 
great depth in water. 

Both instruments are used in a vertical position, and it is necessary 
that they register truly in spite of jolts in hauling up. The Phillips pat- 
tern was used fii'st (I., II., III.), and there were continual complaints of 
the detached column shaking down, till it was pointed out by Professor 
Phillips himself, that the fault arose from the bore not being small enough. 
This defect was remedied (VI.), and the instilment has since worked 
perfectly, but it requires good light and sharp eyes to read it. 

The Inverted Negretti (IV.) was contrived by the Secretary with the 
view of overcoming the difficulty as to jolts, but the contrivance had been 
anticipated many years before by Messrs. Negretti & Zambra themselves. 
It is easily read and managed, but it has a theoretical defect in requiring 
a slight correction for the difference between the tem^Dcrature at the time 
of taking the reading and the maximum temperature recorded. 

References to some other kinds of maximum thermometer will be found 
in some of the reports, namely, to Walferdin's (IV.), Lubimofif's (IV., 
v.), and Magnus' (IX.), all these being of the class of overflow ther- 
mometers. 

References to Becquerel's thermo-electric method of observing under- 
ground temperature were made in three of the reports (1., XI., XII.), and 
some laboratory experiments were subsequently carried out by the 
Secretary which led to the conclusion that the method could not he re- 
lied on to yield sufl&ciently accurate results. It may be mentioned that 
Becquerel's observations are only carried to the depth of 100 feet, whereas 
we require observations at the -depth of 1,000 or 2,000 feet. 

2. As regards subsidiary (that is non-thermo metric) apparatus, Mr. 
Symons' apparatus for lowering and raising thermometers to and from 
any required depth in a deep well (1,000 feet deep in this case), is de- 
scribed with an illustration in the second report. 

Plugs for preventing convection-currents in a bore or well are suggested 
in the first report, Herr Bunker's two forms of plug successfully employed 
by him at Sperenberg, are described in the ninth, and Professor Lebour's 
umbrella-like plug in the ninth, tenth, and twelfth. In its final form 
(XII.) it appears to be very convenient, as it requires only one wire. It 
remains collapsed so long as the wire is taut, but opens out and plugs the 
hole when ib becomes slack. 

B. Methods of Observation. These have chiefly been of two kinds. 

1. Observations in holes bored to the depth of a few feet in newly 
opened rock, either in the workings of a mine or a tunnel, or in a shaft 
during the sinking. The rock should not have been exposed for more 
than a week when the hole is bored, and a day may be allowed to elapse 
for the heat generated by boring to escape before the thermometer is 



76 REPORT— 1882. 

inserted. Very complete plugging is necessary to exclude the influence 
of the external air. Ifc is desirable to use about two feet of plugging, of 
which the outer part should be made airtight with plastic clay or greased 
rag. After the lapse of a few days, the tliermometer is to be drawn out 
by means of a string attached to the handle of its copper case, and the 
reading taken. The slow-action thermometer above described is employed 
for this purpose, and there is time to read it with suGBcient deliberation 
before any appreciable change occurs in its indication. It is recommended 
that the thermometer be then reinserted and plugged as before, and a 
second reading taken after the lapse of a week. The majority of our 
successful observations have been made by this method. 

2. Observations in deep bores of small diameter. 

The first report contained a successful application of this method to a 
bore about 350 feet deep, near Glasgow, which gave very regular results in 
a series of observations at every sixtieth foot of depth ; but in the majority 
of instances in which it has since been applied, there have been marked 
irregularities, due apparently to the influx of water from springs at 
particular points. One of the most valuable of our results was obtained 
by the application of the method to a bore 863 feet deep, executed at the 
bottom of a coal mine 1,066 feet deep, giving a total depth of 1,929 feet. 
The bore in this case was dry at the time of its execution, though full of 
water at the time of the observation. It was in South Hetton Colliery, 
Dui-ham, and the observer was Mr. J. B. Atkinson (V., VI.). The instru- 
ment generally employed in the observations of this class was a maximum 
thermometer of either the Phillips or the Inverted Negretti construction, 
as described above. 

The larger the diameter of the bore the more uncertain does this 
mode of observation become. The South Hetton bore had a diameter of 
2h inches. The Kentish Town well, 1,000 feet deep, in which Mr. Symons' 
observations were made, had a diameter of 8 inches (II., III., IV.), and 
the well 660 metres deep at La Chapelle, in the north of Paris, had a 
diameter of 4^ feet (V., VI., VII.). The temperatures in this last were 
proved to be largely afiiected by convection, the water at the top being too 
warm, and that at the bottom not warm enough. The observations of 
Herr Dunker, in the bore at Sperenberg, near Berlin, with a depth of 
3,390 feet and a diameter of 12 inches, proved a similar disturbance, 
amounting at the top and especially at the bottom to several degrees. As 
regards the bottom, the proof consisted in showing that when a ther- 
mometer at the bottom was protected by a tight plug from the influence 
of the water above, its indications were higher by 3° R. (= 6|° F.), than 
when this precaution was not employed. 

3. Where a shaft contains only a few feet of water at the bottom, a 
thermometer lowered to the bottom of this water may be assumed to give 
pretty nearly the normal temperature of the soil at this depth, and a few 
of our observations have been taken in this way. 'No observations of any 
valne for our purpose can be made in the portion of a shaft or well occu- 
pied by air, as the temperature of such air is largely influenced by that 
of the air at the surface. This is clearly proved by Mr. Symons' observa- 
tion in 200 feet of air at Kentish Town (II., III.). 

C. Questions affecting the Correctness of the Observations made 
might theoretically include questions as to the correct working of the 
instruments employed, and as to the personal reliability of observers ; but 
the latter topic has not come into discussion, and the former has not arisen 



ON TIIK EATE OF INCEEASE OF UNnERGEOUND TEMPERATDEE. 77 

since our present patterns of instrument came into use. The questions 
for discussion are thus confined to those which relate to possible diiferences 
between the temperature of the point at which the thermometer was 
placed and the normal temperature at the same depth in its vicinity. 

1. The heat generated by the action of the boring tool will vitiate the 
observation if snfScient time is not allowed for its escape. 

A very full discussion of this subject in connection witli the great 
artesian well at La Chapelle will be found in reports V., VI., and VII., 
clearly establishing the fact that the temperature at the bottom both on 
the third and the sixth day after the cessation of boring opei'ations, was 
7j° F. higher than after the lapse of four months, though the water had 
been left to itself during this interval. Further evidence showing that 
the temperature in the lower part of a bore full of water may thus be 
raised several degrees, is furnished by the Snb-Wealden bore (VI. 255). 

The heat generated by boring will increase with the hardness of the 
rock, and Mr. Garside, in report XIV., testifies that he has found two 
hours a sufiScient time to give the permanent temperature in holes 3^ feet 
deep and 2 inches in diameter drilled in the sides of a deep mine in the 
East Manchester coalfield. 

2. The generation of heat by local chemical action is well known to 
be a powerful disturbing cause when pyrites is present. In the tentli 
report, the observers in the mines of Schemnitz say, ' Pyrites and also 
decaying timber were avoided, as being known to generate heat.' In the 
uinth report, p. 210, the observations in the coal mines of Anzin show 
a temperature of 70f ° F. in shaft IV. (a very dry one) at the depth of 
21'2 metres, or less than 70 feet. This must be about 15° F. above the 
normal temperature. In shaft II. the observer mentions that there was at 
a depth of 90 m. a seam of coal in which heat was generated by oxidation. 

At Talargoch lead mine in Flintshire (XIII., XIV.), the discrepancies 
between the temperatures at the six observing stations are suggestive of 
local chemical action. 

3. Convection of heat has proved a very troublesome disturbing cause. 
As to convection of heat by air in a shaft or well not filled with water, 

evidence will be found in the second report, both in the case of Mr. 
Hunter's observations in the shafts of two salt mines at Carrickfei'gus, 
having the depths of 570 and 770 feet respectively, and in the case of 
Mr. Symons' observations at Kentish Town, where the first 210 feet of the 
well are occupied with air. At the depth of 150 feet the temperature was 
52'1 in January and 54'7 in July. 

Convection of heat by water in old shafts whicli have heen allowed to 
become flooded, is very manifest in some of the observations communicated 
by Mr. Burns in the second and fourth reports. In Allendale shaft 
(Northumberland), 300 feet deep, with about 150 feet of water, the 
temperature was practically the same at all depths in the water, and this 
was also the case in Breckon Hill shaft, where the observations extended 
from the depth of 42 feet to that of 350 feet. A similar state of things 
was found in a shaft at Ashburton (Devon), by Mr. Amery (III. 7), who 
observed at every fiftieth foot of depth down to 350 feet. 

Convection by water in the great well at La Chapelle, 660 m. (2,165 
feet) deep, and 1 35 m. (4 feet 5 inches) in diameter at the bottom, 
appears probable from the following comparisons. 

Very concordant observations (communicated by M. Walferdin to 
Compies Bendus for 1838) at three different wells in the Paris basin of 



78 KEPOET— 1882. 

the respective depths of 263 m. 400 m. and 600 m., show, by comparison 
with one another and with the constant temperature in the artificial 
caves under the Paris Observatory, a rate of increase of 1° F. in 56 or 
57 feet (IV. 24, 25). These data would give at the depth of 100 m., or 
328 feet, a temperature of 57°, and at the depth of 660m., or 2,165 feet, 
a temperature of 90° ; whereas the temperatures actually observed at those 
depths in the well at La Chapelle in October 1873, when the water had 
been undisturbed for a year and four months, were 59°'5 and 76° (VI. 254) . 
It thus appears probable that the upper part of the well is warmed, and 
the lower part cooled, by convection. Further light may be expected to 
be thrown on this point when the well reaches the springs, and the water 
spouts above the surface, as it does at the Puits de Grenelle. A letter 
received by the Secretary in July 1882 states that engineering difficulties 
have prevented any deepening of "the well since the above observations, 
but that arrangements for this purpose have now been made. 

More certain and pi'ecise information as to the effect of convection in 
deep bores is furnished by the experiments of Herr Dunker at Speren- 
berg (IX. 204-208). The principal bore at Sperenberg has a depth of 
4,052 Rhenish, or 4,172 English feet, and is entirely in rock salt, with 
the exception of the first 283 feet. Observations were first taken (with 
a maximum thermometer on the overflow principle) at numerous depths, 
from 100 feet to the bottom, and showed a fairly regular increase of tem- 
perature downwards. The temperature at 700 feet was 16°"08 R., and at 
3,390 feet 34°-l R. Plugs were then contrived which could be fixed 
tight in the bore at any depth with the thermometer between them, or 
could be fixed above the thermometer for observinfj at the bottom. 
Convection was thus prevented, and a difference of one or two degrees 
Reaumur was found in the temperatures at most of the depths ; at 700 feet 
the temperature was now 17°'06 R., and at 3,390 feet 36°-15. We have 
thus direct evidence that convection had made the temperature at 
3,390 feet 2°-05 R., or 4°-6 F. too low ; and this, as Herr Dunker 
remarks, is an under-estimate of the error, inasmuch as convection had 
been exerting its equalising action for a long time, and its effect could 
not be completely destroyed in the compai'atively short time that the 
plugs were in position. Again, as regards the effect of convection on the 
upper part of the bore, the temperature 11°'0 R. was observed at the 
depth of 100 feet in the principal bore when no plugs were employed, 
while a second bore only 100 feet deep in its immediate vicinity showed 
a temperature 9°*0 R. at the bottom. This is direct evidence that the 
water near the top of the great bore had been warmed 2° R. or 4^° F. by 
convection. 

Suggestions for observations in filled-up bores will be found in the 
eleventh report, but they have not yet taken a practical shape. 

D. Questions affecting deductions from Obseevations. 

1. In many instances the observations of temperature have been con- 
fined to considerable depths, and in order to deduce the mean rate of 
increase from the surface downwards it has been necessary to assume the 
mean temperature of the surface. To do this cori'ectly is all the more 
difficult, because there seems to be a sensible difference between the mean, 
temperature of the surface and that of the air a few feet above it. 

In the third report some information on this point is given, based on 
observations of thermometers 22 inches deep at some of the stations of 
the Scottish Meteorological Society, and of thermometers 3 (French) feet 



ON THE BATE OF INCEEASE OF UNDERGROUND TEMPERATURE. 79 

deep at Greenwich and at Edinburgh. These observations point to an 
excess of surface temperature above air temperature, ranging from half a 
degree to nearly two degrees, and having an average value of about one 
degree. 

Dr. Schwartz, Professor of Physics in the Imperial School of Mines 
at Schemnitz, in sending his observations made in the mines at that 
place (X. 195), remarks on this point : — 

' Observations in various localities show that in sandy soils the excess 
in question amounts, on the average, to about half a degree Centigrade. 
In this locality the surface is a compact rock, which is highly heated by 
the sun in summer, and is protected from radiation by a covering of 
snow iu winter ; and the conformation of the hills in the neighbourhood 
is such as to give protection against the prevailing winds. Hence the 
excess is probably greater here than in most places, and may fairly be 
assumed to be double the above average.' 

Some excellent observations of underground temperature at small 
depths were made at the Botanic Gardens, Regent's Park, London, for 
the six years 1871-76, along with observations of air temperature, and 
have been reduced by Mr. Symons. They are at depths of 3, 6, 12, 24, 
and 48 inches beneath a surface of grass, and their joint mean derived 
from readings at 9 a.m. and 9 p.m. for the six years is 49 '9, the mean for 
the 48-inch thermometer being 60'05. The mean air temperature derived 
in the same way from the readings of the dry-bulb thermometer is 
49 '6. Hence it appears that the excess of soil above air is in this case 
about 0°-4. 

Quetelet's observations for thi-ee years at Brussels (p. 48 of his 
'Memoire') make the earth, at depths less than 1^ foot, colder than 
the air, and at greater depths warmer than the air. 

Caldecott's observations for three years at Trevandrum, in India, 
make the ground at the depth of three feet warmer than the air by 5°'7 F. 

Dr. Stapff, in his elaborate publications on the temperature of the 
St. Gothard tunnel, arrives at the conclusion that the mean temperature 
of the soil on the surface of the mountain above the tunnel is some degrees 
higher than that of the air, the excess increasing with the height of the 
surface and ranging from 2° or 3° C. near the ends of the tunnel to 5° or 
6'^ C. in the neighbourhood of the central ridge. 

Connected with this is the question — 

2. Whether the mean annual temperature of the soil increases down- 
wards from the surface itself, or whether, as is sometimes asserted, the 
increase only begins where annual range ceases to be sensible — say at a 
depth of 50 or 60 feet. 

The general answer is obvious from the nature of conduction. Start- 
ing with the fact that temperature increases downwards at depths where 
the annual range is insensible, it follows that heat is travelling upwards, 
because heat will always pass from a hotter to a colder stratum. This 
heat must make its way to the surface and escape there. But it could 
not make its way to the surface unless the mean temperature diminished 
iu approaching the surface ; for if two superposed layers had the same 
mean temperature, just as much heat would pass from the upper to the 
lower as from the lower to the upper, and there would not be that excess 
of upward flow which is necessary to carry off the perennial supply from 
below. 

This reasoning is rigorously true if the conductivity at a given depth 



3 feet 


12 feet 


24 feet 


51-85 


53-69 


53-71 


45-88 


45-92 


46-07 


46-13 


46-76 


47-09 


46-27 


46-92 


47-18 


85-71 


86-12 


— 


50-92 


50-61 


50-28 



80 EEPORT — 1882. 

be independent of the temperature, and be the same all the year round. 
By ' conductivity ' we are to understand the ' flux of heat ' divided by the 
' temperature-gradient ; ' -where by the ' flux of heat ' is meant the quantity 
of heat -which flows in one second across unit area at the depth considered, 
and by the ' temperature-gradient ' is meant the difference of temperature 
per foot of descent at the depth and time considered. 

Convection of heat by the percolation of water is here to be regarded 
as included in conduction. If the conductivity as thus defined were the 
same all the year round, the increase of mean temperature per foot of 
depth would be independent of the annual range, and would be the same 
as if this range did not exist. 

As a matter of fact, out of six stations at which first-class under- 
ground thermometers have been observed, five show an increase down- 
wards and one a decrease. The following are the results obtained for the 
depths of 3, 12, and 24 Trench feet :— 

Brussels, three years .... 
Edinburgh (Craigleith), five years 

„ (Gardens), five years . 

„ (Observatory), seventeen years 

Trevandrum, India, three years 
Greenwich, fourteen years 

In calculating the mean temperature at 12 feet for Trevandrum, we 
have assumed the temperature of May, which is wanting, to be the same 
as that of April. 

Omitting Trevandrum, and taking the mean values at 3 and 24 
French feet, we find an increase of -656 of a degree in 21 French feet, 
which is at the rate of 1° for 32 French, or about 84 English feet. 

3. Another question which it has sometimes been necessary to discuss 
is the influence which the form of the surface exerts on the rate of 
increase of temperature with depth. 

The surface itself is not in general isothermal, but its temperature is 
least where its elevation is greatest; the rate of decrease upwards 
or increase downwards being generally estimated at 1° F. for 300 feet. 
This is only about one-fifth of the average rate of increase downwards in 
the substance of the earth itself beneath a level surface. If the two rates 
were the same, the isotherms in the interior of a mountain would be 
horizontal, and the form of the surface would have no influence on the 
rate of increase of temperatui'e with depth. The two extreme assump- 
tions that the surface is an isotherm, and that the isotherms are hori- 
zontal, lie on opposite sides of the truth. The isotherms, where they 
meet the sides of the mountain, slope in the same direction as the sides of 
the mountain, but to a less degree. Probably the tangents of the two 
slopes are generally about as 3 to 4. ^ 

Further, if we draw a vertical line cutting two isotherms, the lower 
one must have less slope than the upper, because the elevations and 
depressions are smoothed off as the depth increases. 

The practical inference is that the distance between the isotherms (in 
other words, the number of feet for 1° of increase), is greatest under 
mountain crests and ridges, and is least under bowl-shaped or trough- 
shaped hollows. 

The observations in the Mont Cenis tunnel, and the much more com- 
plete observations made by Dr, Stapfi" in the St. Gothard tunnel, fully 



ON THE RATE OF INCREASE OF UNDERGROUND TEAirERATURE. 81 

bear oafc these predictions from theory. The discussion of the former 
occurs in the fourth report, p. 15, 

As regards the St. Gothard tunnel, Dr. Stapff reports (XII. 41) : — 
' The mean rate of increase downwards in the whole length of the 
tunnel is "02068 of a degree Centigrade per metre of depth, measured 
from the surface directly over. This is 1° F. for 88 feet. Where the 
surface is a steep ridge the increase is less rapid than this average ; where 
the surface is a valley or plain the increase is more rapid.' 

4. The question whether the rate of increase downwards is upon the 
whole the same at all depths, was raised by Professor Mohr in his com- 
ments upon the Sperenberg observations, and is discussed, so far as these 
observations bear upon it, in the 9 th and 11th reports. 

Against the Sperenberg observations, which upon the whole show a 
retardation of the rate of increase as we go deeper, may now be set the 
Dukinfield observations begun by Sir William Fairbairn (III.), and con- 
tinued by Mr. Garside (XIII. 3). Taking Mr. Garside's observations, and 
assuming a surface temperature of 49°, the increase in the first 1,987^ 
feet is at the rate of 1° in 79-5 feet; in tlae next 420 feet it is at the rate 
of 1° in 70 feet, and in the last 283^ feet it is at the rate of 1° in 51^ feet. 

From a theoretical point of view, in places where there is no local 
generation of heat by chemical action, the case stands thus : — 

The flow of heat upwards must be the same at all depths, and this 
flow is equal to the rate of increase downwards multiplied by the conduc- 
tivity, using the word 'conductivity' (as above explained) in such a sense 
as to include convection. The rate of increase downwards must, there- 
fore, be the same at all depths at which this conductivity is the same. 

This reasoning applies to superposed strata at the same place, and 
assumes them to be sufficiently regular in their arrangement to ensure that 
the flow of heat shall be in parallel lines, not in converging or diverging 
lines. 

5. If we have reason to believe that the flow of heat upwards is nearly 
the same at all places, then the above reasoning can also be applied 
approximately to the comparison of one place with another — that is to 
say, the rates of increase downwards in two masses of rock at two difierent 
places must be approximately in the inverse ratio of their conductivities. 
In the cooling of a heated sphere of heterogeneous composition, the rates 
of flow would at first be very unequal through different parts of the sur- 
face, being most rapid through those portions of the substance which 
conducted best ; but these portions would thus be more rapidly drained 
of their heat than the other portions, and thus their rate of flow would 
fall ofl" more rapidly than the rates of flow in the other portions. If the 
only differences in the material were diff'erences of conductivity, we might 
on this account expect the outflow to be after a long time nearly the 
same at all parts of the surface. But when we come to consider 
differences of ' thermal capacity per unit volume,' it is clear that with 
equal values of ' diff'usivity ' that is of ' conductivity divided by thermal 
capacity of unit volume ' in two places, say in two adjacent sectors of 
the globe, there would be the same distribution of temperatures in both, 
but not the same flow of heat, this latter being greatest in the sector in 
which the capacity and conductivity were greatest. 

Where we find, as in Mr. Deacon's observations at Bootle, near 
Liverpool, and to a less marked degree in the observations of Sir William 
Fairbairn and Mr. Garside, near ]\Ianchester, an exceptionally slow rate 
1882. G 



82 EEPOET — 1882. 

of increase, -without exceptionally good conductivity, it is open to us to 
fall back on the explanation of exceptionally small thermal capacity per 
■unit volume in the underlying region of the earth, perhaps at depths of 
from a few miles to a few hundred miles. 

6. A question which was brought into consideration by Professor Hull, 
in connection with the great difference between the rate of increase at 
Dukinfield and that at Rosebridge (III. 33), is the effect of the dip of the 
strata upon the vertical conduction of heat. Laminated rocks conduct 
heat much better along the planes of lamination than at right angles to 
them. If ki denote the conductivity along, and k.2 the conductivity 
normal to the planes of lamination, and if these planes are inclined at an 
angle 6 to the horizon, the number of feet per degree of increase down- 
wards corresponding to a given rate of outflow through the surface, will 
be the same as if the flow were vertical with a vertical conductivity : — 

7i;, sin^ + Jc^ cos^ 0, 

The following is the proof. Let the number of feet per degree of in- 
crease in the vertical direction be n, so that - of a degree is the increase 

n 

for a foot measured vertically. Then the increase for a foot measured in 
the direction of dip is - sin 6, and the increase for a foot measured per- 

nendicular to the laminae is - cos d. The flow of heat in the direction 
^ n 

of dip is, therefore, - Ici sin 6, and the flow perpendicular to the laminae 

- Tc2 COS Q. Resolving each of these in the vertical direction, and adding, 
n 

we eet the vertical flow - (Jci sin- + Icc, cos- 0), which must be equal to 
° n 

the vertical rate of increase - multiplied by the effective vertical conduc- 

n 

tivity. 

Professor Herschel finds about I"3 as the ratio of the two principal 
conductivities in Loch Rannoch flagstone, and 1'875 as the ratio in Fes- 
tiniog slate. 

The dip of the strata at Dukinfield is stated by Mr. Garside to be 15°, 
and we have sin^ 15° = '07, cos^ 15° = -93. 

If we assume Ti^ = 1"3 h.2, as in the case of flagstone, we find for the 
•effective vertical conductivity 1;^ (-09 + "93) = 1-02 h.^, so that the number 
of feet per degree would only be increased by 2 per cent. 

If we assume ^i = 1"875, as in the case of slate, we find 

7^2 (13 + -93) = 1-06 1-2, 

or the number of feet per degree would be 6 per cent, more than if the 
strata were horizontal. 

It is not likely that the two conductivities in the strata at Dukinfield 
are so unequal as even in the case of flagstone, so that 2 per cent, is a 
high estimate of the effect of their dip on the vertical rate of increase so 
far as pure conduction is concerned. The effect of dip in promoting the 
jiercolation of water (III. 32) is a distinct consideration, but the workings 



ON THE BATE OF INCREASE OF UNDERGBOUND TEMPEBATUBE. 83 

in the Dakinfield mines are so dry that this action does not seem to be 
important.^ 

E. We now proceed to a comparison of results. The localities at 
which definite results have been obtained may be thus classified : — 

1, Metallic mines. 2. Coal mines. 3. Wells and wet borings. 
4. Tunnels. 

1. The mines at Pkzibbam in Bohemia (VII. 15), with a depth of 1,900 
feet, are in very quartzose rock, and give a very slow rate of increase, 
viz. 1°-1 in 136 feet. As all the shafts are in lofty hills, an allowance of 
-jLmay be made for convexity, leaving 1° F. in 126 feet. Quartz is found 
by Professor Herschel to have a conductivity of about '0086. 

The mines at Schemnitz in Hungary (X. 194), with a depth of 1,368 
feet, give an average rate of 1° F. in 74 feet, the rock being a green 
hornblende-andesite (in German, G^-ihistein-Trachjt), which is a compact, 
igneous, more or less vitreous rock. Professor Lebour estimates its 
conductivity as being probably nearly the same as that of Calton Hill 
trap-rock, which Professor Herschel found to be about •0029. 

The Talakgoch lead mine (Flintshire) (XIII., XIV.), with its veins 
running across carboniferous limestone, has a depth of 1,041 feet, and gives 
in various parts rates varying from 1° in 47 feet to 1° in 113 feet. The 
average may be taken as 1° in 80 feet. 

2. The results from coal mines are as follows, beginning with foreign 
mines : — 

The mines of the Societe Cocqueril at Seraing (Belgium) (VII. 17), 
with a depth of 1,657 feet, give an average rate of 1° F. in 60 feet. The 
reck is coal shale. Professor Herschel found for shale the low conduc- 
tivity of -0019. 

The mines of Anzin, in the north of France (IX. 210) with a depth of 
658 feet, gave in the deepest shaft an increase of 1° in 47 feet. 

EosEBRiDGE CoLLiERT, near Wigan (III.), with a depth of 2,445 feet, 
gave a mean rate of 1° in 64 feet. 

The four following are in the East Manchester coalfield : — 

Astlet Pit, Dukinfield (III., XIII.), with a depth of 2,700 feet, gave 
1° in 72 ft. 

AsHTON Moss Colliery (XIV.), with a depth of 2,790 feet, gave 1° in 
77 feet. 

Bredburt Colliery (XIV.), with a depth of 1,020 feet, gave 1° in 78-5 
feet. 

Nook Pit (XIV.), with a depth of 1,050 feet, gave 1° in 79 feet. 

Denton Colliery, Lancashire (XV.), with a depth of 1,317 feet, gave 
an increase of 1° in about 77 feet. 

South Hetton CotLiERY, Durham (V. 132, VI. 254), with a depth of 
1,929 feet, including a borehole at bottom, gives very consistent observa- 
tions at various depths, and an average rate of 1° in 57'5 feet. 

Boldon Colliery, between Newcastle and Sunderland (X. 197), with a 
depth of 1,514 feet, and excellent conditions of observation, gives an 
average rate of 1° in 49 feet. 

Whitehaven Colliery, Cumberland (XV.), in workings under the sea, 
with a depth of 1 ,250 feet beneath sea-level, or about 1,178 feet beneath the 
sea-bottom, gave an increase (from the sea-bottom) of about 1° in 45 feet. 

KiNGSWooD Colliery, near Bristol (XII.), with a depth of 1,769 feet, and 

• Though the workings are dry, there is a large quantity of water in the super- 
incumbent strata. See Report XV. 

g2 



84 REPORT— 1882. 

remarkable consistency between observations at various points, gives 1° in 
68 feet. 

Radstock Collieries, near Bath (XIV.), witb a depth of 1,000 feet, give 
a doubtful average of 1° in between 60 and 70 feet, the results in different 
parts being irregular. We have adopted 1° in 62 feet. 

Fowlee's Collieet, Ponttpeidd, with a depth of 8-55 feet, gave, by one 
observation at the bottom compared vpith the known surface-temperature, 
a rate of 1° in 76 feet. 

Professor Phillips' observations in Monkwearmouth Colliery, published 
in ' Phil. Mag.' for December 1834, showed a temperature of 71°2 in a hole 
bored in the floor of a recently exposed part at the depth of 1,584 feet. 
The surface of the ground is 87 feet above high water, and the mean 
temperature of the air is assumed by Professor Phillips to be 47°'6. If, as 
usual, we add 1" to get the soil temperature, instead of assuming, as 
Professor Phillips does, that the temperature 100 feet deep is identical 
■with the air temperature at the surface, we obtain a rate of increase of 
1° in 70 feet. 

3. The following are the most trustworthy results from wells and 
borings : — 

The Sperenberg bore, near Berlin (IX. 204), in rock salt, with a depth 
of 3,492 English feet, to the deepest reliable observation, gave an average 
of 1° in 51'5 feet. This result is entitled to special weight, not only on 
account of the great depth, but also on account of the powerful means 
employed to exclude convection. 

Rock salt, according to Professor Herschel, has the very high conduc- 
tivity -0113. 

Three artesian wells in the chalk of the Paris Basix gave the following- 
results (IV. 24) :— 

St. Andri3, depth of observation . 8.S0 ft. . rate 1° in .564 ft. 

Grenelle l,iU2 „ . „ 1° in 56 9 „ 

Military School .... 568 „ . „ 1° in 56-2 „ 

The great well of La Chapelle, in the same basin, is not yet finished, 
and a very great change in its indications may be expected when it 
strikes the strong springs which it is intended to bring to the surface. 
Up to the present time the deepest observation has been at 2,165 feet, 
and this, by comparison with the known temperature in the artificial caves 
under the Paris Observatory, gives a rate of 1° in 90-5 feet, which is 
probably much slower than the truth, by reason of convection. The 
temperature at 328 feet compared with that at 2,1 65 feet, gives 1° in 
111 feet, this result being affected by convection at both ends. 

An artesian well at St. Petersburg (IV. 22), in the Lower Silurian 
strata, with a depth of 656 feet, gives about 1° in 44 feet. 

A -well sunk at Takoutsk, in Siberia (IV. 22), to the depth of 540 feet, 
disclosed the fact that the ground -was permanently frozen to this depth, 
and probably to the depth of 700 feet. The rate of increase of tempera- 
ture -was 1° in 52 feet. 

Of the English wells in which observations have been taken, the most 
important is that at Kentish Town (II., III., IV.), in which Mr. G. J. 
Symons, F.R.S., has taken observations to the depth of 1,100 feet. The 
temperatures at different depths form a smooth series, and have been con- 
fii'med by observations repeated at long intervals. The only question that 
can arise as to the accuracy of the results is the possibility of their being 
affected by convection. 



ON THE BATE OF INCREASE OF UNDERGROUND TEJU'ERATURE. 85 

The well is 8 feet in diameter, with brickwork to the depth of 540 feet, 

and this part of it is traversed by an iron tube 8 inches in diameter, which 

is continued to the depth of more than 1,300 feet from the surface. The 

tube is choked with mud to the depth of about 1,080 feet, so that the 

deepest observations were taken under 20 feet of mud. The temperature 

at 1,100 feet was 69°"9, and by combining this with the surface temperature 

of 49°'9 observed at the Botanic Gardens, Regent's Park, we obtain a rate 

of 1° in 55 feet. These data would give at 250 feet a calculated tem- 

peratui'e of 54'5, whereas the temperature actually observed at this depth 

was 56'1, or 1°"6 higher; the temperature at 300 feet and at 350 feet being 

also 56'1. This seems to indicate convection, but it can be accounted for 

by convection in the 8-foot well which surrounds the tube, and does not 

imply convection currents within the tube. Convection currents are 

much more easily formed in water columns of large diameter than in small 

ones, and the 20 feet of mud at the bottom give some security against 

convection at the deepest point of observation. It is important to remark 

that the increase from 1,050 to 1,100 feet is rather less than the average, 

instead of being decidedly greater, as it would be if there were convection 

above, but not in, the mud. The rate of 1° in 55 feet may therefore be 

adopted as correct. 

Mr. Symons also made numerous observations in this well (VI., TX., 
XII.) to determine whether the temperature at the depth of 1,000 feet 
remained exactly the same at all seasons and from year to year. The 
result was that the changes, if any, were so small as not to be distinguish- 
able from the necessaiy errors of observation. The research was finally 
abandoned, because the gradual silting up of the well, which was found 
to be going on, would itself be competent to account for any small secular 
change that might have been detected by further observation. 

The strata, consisting of tertiary sti-ata, chalk (586 feet thick), upper 
greensand and gault, are given in detail on the last page of the third 
report. 

The Kentish Town temperature at the depth of 400 feet (58°) is con- 
firmed by observations in Mr. Sich's well at Chiswick (VIII. 159), which 
is 395 feet deep, and has a temperature varying from 58° to 57°'5. 

The BoOTLE well, belonging to the Liverpool Waterworks, is 1,302 feet 
deep, and the observations were taken in it during the sinking (XI., XII.) 
The diameter of the bore is 24 inches, and convection might have been 
suspected but for the circumstance that there was a gradual upward flow 
of water from the bottom, which escaped from the upper part of the well 
by percolation to an underground reservoir near at hand. This would 
check the tendency to downflow of colder water from the top ; and as the 
observations of temperature were always made at the bottom, they would 
thus be protected against convective disturbance. 

The temperature at 226 feet was 52°, at 750 feet 56°, at 1,302 feet 
59°, giving hj comparison of the first and last of these a mean rate of 1° 
in 154 feet. The circumstance that the boring ceased for six weeks at 
the depth of 1,004 feet, and the temperature fell during this interval from 
58°'l, to 57°"0, would seem to indicate an elevation of 1° due to the heat 
generated by the boring tool. An assumed surface temperature of 49° 
(only 0°-9 lower than that of the Botanic Gardens in London), would give 
by comparison with 57°, at 1,004 feet, a rate of 1° in 125^ feet, and by 
comparison with 59°, at 1,302 feet, a rate of 1° in 130 fe'et, which last 
may be adopted as the best determination. The rock consists of the 



86 BEPORT— 1882. 

pebble beds of the Bunter or Lower Trias, and the boring was executed at 
the rate of nearly 100 feet per month. 

The boring at Swinderby, near Scaele (Lincoln), in search of coal 
(VIII., IX.), was carried to a depth of 2,000 feet, with a diameter at the 
lower part of only 3^ inches — a circumstance favourable to accuracy, both 
as impeding convection and as promoting the rapid escape of the heat of 
boring. The temperature at the bottom was 79°, the water having been 
undisturbed for a month, and this by comparison with an assumed surface 
temperature of 50° gives a rate of 1° in 69 feet. 

The rocks are Lower Lias, New Red Marl (569 feet thick), New Eed 
Sandstone (790 feet thick). Red Marl, and earthy Limestone. 

The following results have been obtained from shallow borings. The 
first three were made under Sir William Thomson's direction, with a 
thermometer which could be read by estimation to hundredths of a 
degree : — 

Bltthswood bore, near Glasgow (I.), with a depth of 347 feet, gave a 
very regular increase of 1° in 50 feet. 

KiRKLAND Neuk bore, in the immediate vicinity of the above (II.), 
gave consistent observations at difPerent seasons of the year from 180 feet 
to the bottom (354 feet), the rate being 1° in 53 feet. This bore passed 
through coal which had been ' very much burned or charred.' 

South Balgeat bore, near Glasgow, and north of the Clyde, with an 
available depth of 625 feet, gave, by comparing the temperature at the 
bottom with that at 60 feet, a rate of 1° in 41 feet. 

Shale extends continuously from 390 to 450 feet from the surface, and 
the increase in these 60 feet of shale was 2°-02, which is at the rate of 
1° in 30 feet. This rapid increase agrees with the fact that shale has 
very low conductivity, averaging -0019 in Professor Herschel's experi- 
ments. 

The only small bore remaining to be mentioned is that at Manegaon, 
in India (X. 198), which had 310 feet available, and gave by comparing 
the temperature at this depth with that at 60 feet a rate of 1° in 68 feet. 
The rocks consist of fine softish sandstones and hard siltv clays, the dip 
being 10°. J J ' f 

The following results, obtained from observations at the bottom of 
shafts with only a small depth of water, are not altogether without value, 
^ihough the circumstances are not favourable to accuracy : — 

Two shafts of salt mines near Cakrickfergus (Ireland) (II. 12, 13), 
with depths of 570 feet and 770 feet, gave by comparison with an assumed 
surface temperature of 48° rates of 1° in 40 feet and 1° in 43 feet. The 
sod in both cases was yellow clay, a substance for which Professor 
Herschel finds the low conductivity of "0025. 

In a ' sump ' at the bottom of Slitt mine, in the Allenheads lead 
mines, Weardale (Northumberland) (IV.), at 660 feet from the surface, 
the temperature 65°-0 was found, which, by comparison with the surface 
temperature, 45°-3, assumed by the observer (Mr. Burns, of H.M. Geo- 
logical Survey), being a degree higher than the observed air temperature 
in the neighbourhood, gives a rate of 1° in 34 feet. The strata consist 
of alternate beds of sandstone and shale, with a few beds of limestone, 
158 feet of basalt, and 55 feet of fluor spar. 

4. Tunnels.— The Mont Cenis tunnel (IV. 15), which is about 7 miles 
long, is at a depth of exactly a mile (5,280 feet) beneath the crest of Mont 
Frejus overhead. This was the warmest part of the tunnel, and had a 



ON TUE RATE OF II^CREASE OF UNDEllGROUND TEMPERATURE. 87 

temperature of 85°1 F. The mean air temperature at the crest overhead 
was calculated by the engineer of the tunnel, M. Giordano, by interpolating 
between the known temperature of the pass of San Theodule and that of 
the city of Turin, the former being 430 metres higher, and the latter 
2,650 metres lower, than the point in question. It is thus calculated to 
be — 2°-6 C. or 27°'3 F. If, according to our usual rule, we assume the 
ground to be 1° warmer than the air, we have 28°-3 to compare with 85°-l. 
This gives a rate of 1' in 93 feet ; but, inasmuch as the convexity of the 
surface increases the distance between the isotherms, a correction will be 
necessary before we can fairly compare this result with rates under level 
ground. As a rough estimate we may take § of 93, and adopt 1° in 79 feet 
as the corrected result. 

* The rocks on which the observations have been made are absolutely 
the same, geologically and otherwise, from the entrance to the tunnel, on 
the Italian side, for a distance of nearly 10,000 yards. They are not 
faulted to any extent, though, highly inclined, contorted, and subjected to 
slight slips and slides. They consist, to a very large extent indeed, of 
silicates, chiefly of alumina, and the small quantity of lime they contain 
is a crystalline carbonate.' 

The St. Gothaed Tunnel (VIII., XI., XII.), which has a length of 
about 9 miles, has been subjected to much more minute observation, a 
skilled geologist. Dr. StapiF, having, under Government direction, devoted 
bis whole time to investigating its geology and physics. He not only 
observed the temperature of the rock in the tunnel at very numerous 
points, but also determined, by observations of springs, the mean tempera- 
tures of the surface of the mountain at various points, and compared 
these with an empirical formula for air temperature deduced from the- 
known mean temperatures of the air at Gbschenen, Andermatt, Airolo, 
and the Hospice of St. Bernard. He infers from bis comparisons a con- 
siderable excess of soil above air temperature, increasing from 2° C. at the 
ends of the tunnel to 6° C. at the crest of the mountain over the centre 
of the tunnel. The highest temperature of the rocks in the tunnel was 
at this central part, and was about 30°-6 C. or 87° F. The soil tempera- 
ture at the crest above it was about — 0°'6 C. or 31° F., giving a difference- 
of 56° F. The height of the crest above sea-level was about 2,850 m., and 
that of the tunnel at this part 1,150 m., giving a difference of 1,700 m^ 
or 5,578 feet. The rate of increase here is, therefore, about 1° F. in 100- 
feet ; and if we apply the same correction for convexity as in the case of 
the Mont Cenis tunnel, this will be reduced to about 1° F. in 87 feet, as 
the equivalent rate under a level surface. From combining his observa- 
tions in all parts of the tunnel, through the medium of empirical 
formulEe, Dr. Stapff deduces an average rate of 1° F. for every 88 feet 
measured from the surface directly overhead. Where the surface is a 
steep ridge, the increase was lesj rapid than this average ; where the sur- 
face was a valley or plain, the increase was more rapid. As this average 
merely applies to the actual temperatures, the application of a correction 
for the general convexity of the surface would give a more rapid rate. 
If we bring the isotherms nearer by one part in 15, which seems a fair 
assumption, we shall obtain a rate of 1° F. in 82 feet. 

Collecting together the foregoing results, and arranging them mainly 
in the order of their rates of increase, but also with some reference to 
locality, we have the following list : — 



88 



EEroRT — 1882. 








Depth 


Feet 




feet 


for 1° F 


Bootle waterworks (Liverpool) . . . . 


1,392 


130 


Przibram mines (Bohemia) . . . . . 


1,900 


126 


St. Gothard tunnel 


5,578 


82 


Mont Cenis tunnel ...... 


5,280 


79 


Talargoch lead mine (Flint) 


1,041 


80 


Nook Pit, colliery \ / . . 


1,050 


79 


Bredbury „ East 


1,020 


781 


Ashton Moss „ ■ Manchester - 
Denton „ coalfield. 
Astley Pit, Dukinfield / \ . 


2,790 


77 


1,317 


77 


2,700 


72 


Schemnitz mines (Hungary) 


1,368 


74 


Scarle boring (Lincoln) .... 


2,000 


69 


Manegaon boring (India) .... 


310 


68 


Pontypridd colliery (S. Wales) 


855 


76 


Kings wood colliery (Bristol) .... 


1,769 


68 


Kadstock „ (Bath) .... 


620 


62 


Paris artesian well, Grenelle 


1,312 


S7 


„ „ St. Andre 


830 


56 


„ „ Military School 


568 


56 


London „ Kentish Town 


. 1,100 


55 


Rosebridge colliery (Wigan) 


2,445 


54 


Takoutsk, frozen ground (Siberia) 


510 


52 


Sperenberg, boring in salt (Berlin) 


3,492 


511 


Seraing coUeries (Belgium) .... 


1,657 


50 


Monkwearmouth collieries (Durham) . 


. 1,684 


70 


South Hetton ,, ,, . . 


. 1,929 


57i 


Boldon „ „ . . 


. 1,514 


49 


Whitehaven „ (Cumberland) 


1,250 


45 


Kirkland Neuk bore (Glasgow) 


354 


53 


Blythswood „ „ ... 


347 


50 


South Balgray „ ,, ... 


625 


41 


Anzin collieries (North of France) 


658 


47 


St. Petersburg, well (Russia) 


656 


44 


Carrickfergus, shaft of salt mine (Ireland) . 


770 


43 


»» ,» ,, 


670 


40 


Slitt mine, Weardale (Northumberland) 


660 


34 



The depth stated is, in each case, that of the deepest observation that 
has been utilised. 

F. In deducing a mean from these very various results, it is better to 
operate not npon the number of feet per degree, but upon its reciprocal 
— the increase of temperature per foot. Assigning to the results in the 
foregoing list weights proportional to the depths, the mean increase of 
temperature per foot is found to be -01563, or about J^ of a degree per 
foot— that is, 1° F. in 64 feet. 

It would be more just to assign greater weight to those single results 
which represent a large district or an extensive group of mines, especially 
where the data are known to be very accurate. Doubling the weights 
above assigned to Przibram, St. Gothard, Mont Cenis, Schemnitz, Kentish 
Town, Rosebridge, and Seraing, and quadrupling that assigned to 
Sperenberg, no material difference is made in the result. The mean still 
comes out 1° F. in 64 feet, or more exactly -01566 of a degree per foot. 

This is a slower rate than has been generally assumed, but it has been 
fairly deduced from the evidence contained in the Committee's Reports ; 
and there is no reason to throw doubt on the results in the upper portion 
of the above list more than on those in its lower portion. Any error that 
can reasonably be attributed to the data used in the calculations for the 



ON THE KATE OF INCnEASB OP UNDERGROUND TEMPERATURE. 89 



Sfc. Gotharrl tunnel and for the numerous deep mines of the East Man- 
Chester coalfield, will have only a trifling effect on the rates of increase 
assigned to these localities. 

To obtain an approximation to the rate at which heat escapes annually 
from the earth, we will first reduce the above rate of increase "01566 to 
Centigrade degrees per centimetre of depth. For this purpose we must 
multiply by -0182, giving -000285. 

To calculate the rate of escape of heat, this must be multiplied by the 
conductivity. 

The most certain determinations yet made of the conductivity of a 
portion of the earth's substance are those deduced by Sir William 
Thomson by an indirect method, involving observations of underground 
thermometers at three stations at Edinburgh, combined with laboratory 
measurements of the specific heats and densities of the rocks in which 
the thermometers were planted. The specific heats were determined by 
Regnault, and the densities by Forbes. Specific heats and densities can 
be determined with great accuracy in the laboratory, but the direct 
determination of conductivity in the laboratory is exceedingly difficult, it 
being almost impossible to avoid sources of error which make the con- 
ductivity appear less than it really is. 

Professor Herschel, in conjunction with a Committee of the British 
Association, has made a very extensive and valuable series of direct 
measurements of the conductivities of a great variety of rocks, and 
has given additional certainty to his results by selecting as two of the 
subjects of his experiments the Calton Hill trap and Craigleith sand- 
stone, to which Sir "William Thomson's determinations apply. Comparison 
shows that Professor Herschel's results for these two substances, as given 
in the fifth Report of the Conductivity Committee (1878), must be multi- 
plied by about 1"4 to make them agree with Sir William Thomson's.' 

The following list, condensed from that Report, will be useful for our 
purpose : — 

Mean Conductivities in C.G.S. measure, from Professor HersclieVs Determinations. 



Eock salt 

Quartz 

Sandstone 

Flagstone 

Slate 

Granite 

Limestone 

Serpentine 

Trap . 



•0113 


Clay slate . 


•0086 


Clay . 


•0060 


Chalk 


•0046 


Firestone . 


•0040 


Shale 


0053 


Sand, dry . 


0052 


„ saturated 


0044 


Coal 


0038 


Pumice 



•0027 
•0023 
•0026 
■0021 
•0019 
•0009 
•0070 
•0008 
•0006 



The mean of these 18 values is -00413, which, if multiplied by the 
correcting factor 1-4 above mentioned, gives •0058. 

Sir William Thomson's three determinations were : — 

Trap rock of Calton Hill -00415 

Sand of Experimental Garden -00262 

Sandstone of Craigleith Quarry •OlOeS 

These give a mean of "00582, which is sensibly the same as the above. 

' The sixth Report of the Conductivity Committee states that a mistake was made 
in the factor employed for reducing the results to C. G. S., and that the results as 
given in the fifth Report require to be increased by one-eighth part of their 
respective amounts. 



90 BEPORT— 1882. 

Adopting -0058 as the mean conductivity of the outer crust of the 
earth, we have 

•0058 X -000285 = 16330 x lO-'" 

as the flow of heat in a second across a square centimetre. Multiplying by 
the number of seconds in a year, which is approximately 31^ millions, 
we have 

1633 X 315 X 10-' = 41-4 

This then is our estimate of the average number of gramme-degrees 
of heat that escape annually through each square centimetre of a hori- 
zontal section of the earth's substance. 



Report of the Committee, consist! nr/ of Professor Schuster (Secre- 
tary), Sir William Thomson, Professor H. E. Eoscoe, Professor 
A. S. Heeschel, Captain W. de W. Abney, Mr. E. H. Scott, and 
Dr. J. H. Gladstone, appointed for the purpose of investigating 
the practicability of collecting and identifying Meteoric Dust, 
and of considering the question of undertaking regular observa- 
tions in various localities. 

1. In their first Report the Committee confined itself to giving a short 
abstract of some of the work which had hitherto been done to clear up the 
important question with which they are concerned. Since that time the 
previous literature has been more thoroughly studied, and a microscopic 
investigation of different specimens of magnetic dust derived from various 
sources has been undertaken. 

A good deal of the literature confines itself to the dust-falls which 
are frequently observed in the Atlantic, in the southern parts of Italy, 
and sometimes in the Red Sea. These dust-falls were at one time sup- 
posed to be of meteoric origin, but it has now been conclusively proved 
that the dust has its origin in the sandy deserts of Northern Africa, 
whence it is carried by the winds often through considerable distances ; 
the grosser particles falling down first, so that ultimately only the finest 
remain in suspension. With these dust-falls we are not directly con- 
cerned, but we wish to point out that because as a whole they are proved 
to be of terrestrial origin it does not follow that everything they contain 
is terrestrial. Granting for a moment that meteoric dust exists, that 
dust would accumulate in the desert as well as anywhere else, we should 
expect that some of the magnetic particles carried hj these dust-storms 
would show the same peculiarities which, in other cases, have led to the 
supposition of their meteoric origin. Such indeed is the case ; but before 
entering into details on this point we must give a short account of the 
very clear line of argument by means of which Tissandier has to most 
minds established the existence and general prevalence of meteoric dust. 

Tissandier has fully discussed the question in his interesting little 
book 'Les poussieres de I'air,'' and has described the result of the micro- 
scopic examination of the dust gradually settled down in dry weather, or 

' Paris, Gauthier Villars, 1877. 



ON METEORIC DUST. 91 

precipitated by rain and snow. We are concerned here chiefly with the 
magnetic particles contained in this dust. These particles are of various 
shapes, but the most remarkable form is perfectly spherical, which at 
once conveys the obvious information that the particles at one time must 
have been in a state of fusion. These spherules have been found in the 
snows on the slopes of Mont Blanc, at a height of nearly 9,000 feet in the 
sediment of rain collected at the Observatory of Sainte-Marie-du-Mont, 
and in the dust collected at different elevated positions. There are other 
particles, not spherical but of equally characteristic forms, which generally 
accompany these spherules, and some of these shapes we find in the 
iron dust extracted by Nordenskjold from the sand of the polar regions. 
If we confine ourselves, however, at present to the spherical particles, 
and accept the conclusion that they have been in a state of fusion, we 
are practically reduced to three alternatives. The particles may be of 
volcanic origin, they raay have been fused in our terrestrial fires, or they 
may be meteoric. All the volcanic dust which the writer has had at his 
disposal was carefully examined under the microscope, and its appearance 
was found to be altogether diffei'ent from the supposed meteoric dust. 
Such also seems to be the conclusion arrived at by Tissandier. No iron 
spherules have, as far as I know, been found in volcanic dust. 

The smoke issuing from the chimneys of our manufacturing towns 
can and does contain iron particles similar in appearance to those to 
which Tissandier ascribes a meteoric origin. That some of these particles 
are found very far from any terrestrial sources which can produce them 
would not perhaps tell conclusively against their terrestrial origin, but 
chemical analysis seems to settle the point. The iron particles issuing 
from our chimneys contain neither nickel nor cobalt ; while these metals 
were found by Tissandier to exist in the microscopic magnetic particles 
found in rain-water collected at the Observatory of Sainte-Marie-du-Mont. 
We are, therefore, driven to ascribe a cosmic origin to these particles. 

2. The author of this Report has, during the last year, made a few 

microscopic investigations of small iron particles found in different places. 

He has obtained in the first place sand col- ^ , „,,-,,. 

1 J. J r J.T. J J. • J.1, • 1,1, 1, 1 Fig. 1- — Globular Pieces of Iron 

lected from the desert m the neighbourhood ^^ geen under the microscope 

of the Great Pyramids. This sand contains (objective J inch), March 16, 

an appreciable quantity of magnetic particles 1882. Specimen of Sand col- 

ai. • T 7^ AAA^ T? • J V J.1 lected near the Pyramids m the 

part m 144,000). Examined by the Desert of Sahara. 

microscope the greater part of these particles 

were found to be angular in shape, and there 

can be no doubt that they form an integral 

part of the sand, and are due to the debris 

of magnetic rocks. But here and there we 

find perfect spheres of iron exactly like those 

described by Tissandier and about the same 

diameter, that is, 0'2 to O'l millimetre; 

some of them are even larger. Fig. 1 shows 

some of these spherules as seen under the microscope. Figs. 2 and 3 

give another form of frequent occurrence. 

The greater part of these latter particles are metallic iron, as is shown 

by the deposition of copper on them when a drop of a solution of sulphate 

of copper is added. In fig. 2 all the light parts represent the metallic 

iron. The total quantity of this metallic iron must, however, have been 

small, for it could not be traced by chemical analysis. 




92 



EEPORT — 1882. 



Mr. J. B. B. Hennessey was kind enongli to forward me some sand 
•which was collected at his request, and with proper precautions specified 
by him, in desert of Rajpatana, in lat. N, 27° 40' 25", long. E. 72° 43' 
39" ; the nearest village beins: fall 13 miles distant. The examination of 
this sand has not as yet been completed, but at present no spherical 

Fig. 2. — Iron Particle in Sahara Sand. The light parts are metallic. Enlargement, 100 : 1. 




Fig. 



3. — Metallic Iron in Sahara 
Sand, 100:1. 



particles have been found, nor is there any appearance of metallic iron. 
But the sand contains a comparatively large quantity of magnetic oxide 
(O'l per cent.). This magnetic oxide, which is of undoubted terrestrial 

origin, will naturally hide any traces of me- 
teoric dust, which could only form a small 
percentage of the total magnetic part. 

Similar negative results were obtained 
with some specimens of mud collected on 
the banks of the Nile near the village of 
Sohag (lat. 26° 33', long. E. 2^ 07'"), on the 
occasion of the last total solar eclipse. Here 
also a very large quantity of debris from mag- 
netic rocks was found in the mud, hiding any 
meteoric particles which might have been 
there. 
3. "We may approach the question from yet another point of view. A 
shooting star is not an uncommon phenomenon, and on certain nights in 
the year we often find them counted by hundreds. Each of these meteors 
will leave traces behind in our atmosphere, for it seems hardly possible 
that when white hot, owing to the friction with our atmosphere, part of 
this surface should not fuse and be left behind in a finely divided state. 




ON MKTEOEIC DUST. 93 

In addition to this we also hear of larger meteors passing through the 
air more slowly, but leaving behind trains of luminous clouds remaining 
visible for a considerable length of time. What becomes of all this 
matter, and how should we expect it to look after it has settled down on 
the surface of our earth ? Tissandier has examined microscopically some 
powder which he has detached from the surface of a meteoric stone found 
in Bohemia, and it was found to resemble in appearance the magnetic 
particles found in different places to which he had attributed a meteoric 
origin. 

4. An interesting question arises in connection with the iron particles 
which are found in the metallic state in the sand of the desert of Sahara 
and in other localities. How did they escape oxidation, either when first 
detached from the molten mass of the meteoric dust, or subsequently. 
Several explanations of this fact may be offered. If the particles are 
really meteoric they would contain a considerable proportion of nickel, 
and such iron is able to resist oxidation to a high degree. But the pre- 
sence of nickel would not prevent their transformation into magnetic 
oxide when red hot, as they must have been when they separated from 
the meteor. I wish, however, to point out that possibly, and even pro- 
bably, the separation has taken place at a height at which the atmosphere 
contains only comparatively small quantities of oxygen. It is known by 
the laws of diffusion that, assuming everything to be in a state of equili- 
brium, each gas will form an atmosphere round the terrestrial globe 
independently of any other gas which may be present. It follows that at 
great heights the lighter gases will be present in preponderating propor- 
tions, as compared with the lower regions. Calculating, for instance, the 
proportion of oxygen which we should expect at different heights if the 
temperature is the same throughout, we find as follows : — 

At a height of kilometres 21 per cent, of oxygen. 
,, 5 ,, 19'5 ,, ,, 

„ 10 „ 18 „ „ 

„ 100 „ 4-2 

,, 150 „ 2 ,, „ 

„ 200 „ 0-8 

Convection currents would, no doubt, especially within the lower 
regions, tend to equalise the difference between the higher and lower 
parts, but the fact must remain that, at a height at which luminous, 
meteors have been seen luminous, the oxygen can only form a small 
fraction of the atmosphere. But matters become still more striking if 
we consider that probably some other and lighter gas is present in ad- 
dition to the oxygen and nitrogen. 

Spectroscopic observations of the Aurora Borealis show the presence 
of a green line which no one has as yet obtained from any known constituent 
of the atmosphere. I have myself observed nitrogen, and oxygen and 
some of the carbon compounds, under so many different conditions that 
I am fully convinced that the line is not due to them, but must be due to 
the presence of some unknown gaseous body. As we cannot detect it 
near the surface of the earth, this gas must be very light. Supposing, for 
the sake of argument, that it is as dense as hydrogen, and that at the surface 
of the earth its quantity per cubic centimetre is only the millionth part 
of the oxygen present in the same space, it would certainly escape all our 
methods of analysis. But from these suppositions we can calculate that, 



94 EEPOBT— 1882. 

at a height of 200 kilometres, it must exceed the oxygen in proportion of 
170,000 to 1 — that is to say, at that height the atmosphere would practi- 
cally contain no oxygen. If the gas is less dense than hydrogen this 
proportion would still further be increased. Even those who do not feel 
inclined to assume the presence of an unknown gas will not deny the 
possibility that free hydrogen may be present in our atmosphere in such 
small quantities as we have assumed. Electric discharges which are 
• constantly going on partially decompose the aqueous vapour of the 
atmosphere, and some of it will escape recombination. If then free 
hydrogen exists even in quantities only which are very small on the 
surface of the earth, it may be hi preponderating proportion in the upper 
regions. 

After having considered the above explanation of the fact that some 
of the meteoric iron may be in the metallic state, I have made a few 
experiments which tend to show that iron dust may separate from a red- 
hot meteor even in atmosphere containing considerable quantities of 
oxygen, and yet escape oxidation. Tissandier has shown how by burning 
an iron wire in oxygen we may often obtain iron spherules of exactly 
the same nature as those floating in our atmosphere. I have obtained 
similar spherules by using an iron file as one pole of a dynamo-machine, 
and pas.sing the file over a copper wire connected with the other pole. 
The sparks flying off in all directions are found to consist chiefly of iron 
globules like those to which Tissandier ascribes a meteoric origin ; but 
in addition we have small spongy masses which are metallic, and present 
exactly the same appearance as the metallic iron found in the Saharah 
desert. The most remarkable fact, however, is this, that we find even a 
few globules of iron which are metallic. These globules must have been 
in a state of f asion, and yet they did not oxidise at the contact of the air, 
no doubt owing to the fact that a large number of particles used up the 
free oxygen of the air in the neighbourhood of the few particles which 
thus escaped, 

5. The question of meteoric dust suggests another interesting reflec- 
tion. Mr. Aitken has recently shown how a condensation of aqueous 
vapour only takes place round a nucleus of solid matter. It is no doubt 
one of the most interesting questions to decide what forms in different 
localities the most common nucleus for fogs, rain, snow, or hail. We 
conclude this Report by mentioning the very suggestive fact, that 
Nordenskjold has found iron particles as a nucleus to hailstones at Stock- 
holm, and that observations of the same kind have been made in Spain, 
where also hailstones were found to contain iron particles as a nucleus. 
Other observations of the same nature seem to exist. 

There is every reason to believe that the blue colour of the sky is due 
to minute particles scattering the light. These particles must be much 
more minute than any which the Committee has at present investigated ; 
they must, in fact, be beyond the limits of microscopic power. It might, 
however, be possible ultimately to find out the nature of these small 
particles. It is interesting to record the observation made by the author 
of this Report, that in the valleys of the Himalayas which are cultivated, 
the colour of the sky is much whiter than in the valleys which are 
barren and devoid of any vegetation. 



ON THE MEASUBEMENT OF THE LUNAU DISTURBANCE OF GBAVITY. 95 



Second Report of the CoviTtiittee, consisting of Mr. Gr. H. Darwin, 
Professor Sir William Thomson, Professor Tait, Professor Grant, 
Dr. Siemens, Professor Purser, Professor Gr. Forbes, aoid Mr. 
Horace Darwin, appointed for the Measurement of the Lunar 
Disturbance of Gravity. Written by Mr. Gr. H. Darwin. 

Shortly after the meeting of the British Association last year (1881), 
the instrument with which my brother and I were experimenting at the 
Cavendish Laboratory, at Cambridge, broke down, through the snapping 
of the wire which supported the pendulum. A succession of unforeseen 
circumstances have prevented us, up to the present time, from resuming 
our experiments. 

The body of the present Report, therefore, will merely contain an 
account of such observations by other observers as have come to our 
knowledge within the past year, and it must be taken as supplementary to 
the second part of the Report for 1881 . The Appendix, however, contains 
certain theoretical investigations, which appear to me to throw doubt 
on the utility of very minute gravitational observations. 

The readers of the Report for 1881 will remember that, in the course 
of our experiments, we were led away from the primary object of the 
Committee, namely the measurement of the Lunar Disturbance of Gravity, 
and found ourselves compelled to investigate the slower oscillations of 
the soil. 

It would be beyond the scope of the present Report to enter on the 
literature of seismology. But, the slower changes in the vertical having 
been found to be intimately connected with earthquakes, it would not 
have been possible, even if desirable, to eliminate all reference to seismo- 
logy from the present Report. 

The papers which are quoted below present evidence of a very mis- 
cellaneous character, and therefore this Report must necessarily be rather 
disjointed. It has seemed best in our account of work done rather to 
classify together the observers than the subjects. This rule will, however, 
be occasionally departed from, when it may seem desirable to do so. 

The interesting researches in this field made during the last ten years 
by the Italians, are, I believe, but little known in this country, and as the 
accounts of their investigations are not easily accessible (there being, for 
example, no copy of the 'Bulletino' referred to below at Cambridge), it 
will be well to give a tolerably full account of the results attained. I 
have myself only seen the ' Transactions ' for four years. 

The great extension which these investigations have attained in Italy 
has been no doubt due to the fact of the presence of active volcanos and 
of frequent sensible earthquakes in that country. But it is probable that 
many of the same phenomena occur in all countries. 

In 1874 the publication of the ' Bulletino del Vulcanismo Italiano ' 
was commenced at Rome under the editorship of Professor S. M. de 
Rossi, of Rome.' As the title of this publication shows, it is principally 
occupied with accounts of earthquakes, but the extracts made will refer 
almost entirely to the slower oscillations of level. 

' I am compelled to make this abstract from manuscript notes ; but my papers 
having become somewhat disarranged, I am not absolutely certain, in one or two 
places, of the year to which the observations refer. 



96 REPORT— 1882. 

I learn from the ' Bulletino ' that in 1873 Professor Timoteo Bertelli, 
of Florence, had published an historical account of small spontaneous 
movements of the pendulum, observed since the seventeenth century up to 
that time.' 

In 1874 (Anno 1 of the ' Bulletino ') Rossi draws attention to the 
fact that there are periods lasting from a few days to a week or more, in 
which the soil is in incessant movement, followed by a comparative cessation 
of such movement. This he calls a 'seismic period.' In the midst or at 
the end of a seismic period there is frequently a sensible earthquake. 

At page 51 he remarks, in a review of some observations of Professor 
Pietro Monte (Director of the Observatory of Leghorn), that he was led 
to suspect that the crust of the earth is in continuous and slow movement 
during the seismic period, and that this movement is influenced by varia- 
tions of barometric pressure. This suspicion was, he says, confirmed by 
finding, in his observations of a pendulum at Rocca di Papa (of which 
we shall speak again below), that during the seismic period the excursions 
of the pendulum were mostly in the S.W. and N.E. azimuth. This is 
perpendicular to the volcanic fracture, which runs towards the Alban 
lake and the sea. The lips of the fracture rise and fall, and there result 
two sets of waves along and perpendicular to the fracture. In an earth- 
quake these waves are propagated with great velocity (the phenomenon 
being in fact dynamical), but during the seismic period the same class of 
changes takes place slowly. This view accords with observations at 
Velletri made by Professor D. G. Galli. 

With regard to the influence of barometric pressure Rossi elsewhere 
quotes M. Poey (October 15, 1857 ?) as having attributed the deviations 
of the vertical to this cause, and remarks : — 

' Although he (Poey) gave too much weight to the baro-seismic action 
of large variations of atmospheric pressure, yet after very numerous ob- 
servations made by me in these last three years (I suppose 1871-4), I 
can affirm that no marked barometric depression has occurred without 
having been immediately preceded, accompanied, or followed by marked 
micro-seismic movements ; but besides these there are other irregular, 
often considerable and instantaneous movements, which occur under high 
pressure. To distinguish them, I have called the first baro-seismic, and 
the second vulcano-seismic, movements.' The reader will find a theoretical 
investigation on this subject in the Appendix to the present Report. 

Rossi states (page 118, Anno 1 ?) that whilst Etna was in a condition 
of activity his pendulums at Rocca di Papa were extraordinarily agitated 
at the beginning of each barometric storm. 

At page 90 of the second year are given graphical illustrations of the 
simultaneous deflections of pendulums at Rome, Rocca di Papa, Florence, 
Leghorn, and Bologna. There is some appearance of concordance between 
them, and this shows that the agitations sometimes affect considerable 
tracts of land, but that the minor deflections are purely local phenomena. 

M. d'Abbadie, in presenting a memoir on micro-seismic movements 
by Father Bertelli to the French Academy, relates (' Comptes Rendus,' 
1875, vol. 81, p. 297) the following experiment made by Count Malvasia, 
as proving the independence of the disturbances of the pendulum from 
the tremors produced by traffic. Two batteries of artillery were marching 

' Bulletino Soncamj>affni, t. vi. Gennaio, 1873. Eeprinted Via Lata, No. 2114, 
Kome. 



ox* THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 97 

through Bologna, and it was arranged that at 30 meters from the Palazzo 
Malvasia they should break into a trot. The pendulum, situated only 6 
meters from the street, was observed to be unaffected by this, and continued 
its oscillations in the B.W. azimuth. A pool of mercury was violently 
agitated, and it was concluded that the motion communicated to the 
ground by the artillery was exclusively vertical. 

At page 5 of the ' Bulletino ' for 1876 (January to May), Rossi 
writes a ' Guida pratica per le osservazioni sismiche.' This article con. 
tains a description of the instruments which have been used by the 
Italian observers. 

Bertelli used a pendulum protected from the air, with a microscope 
and micrometer for. evaluating the oscillations. The upper part of the 
support of the pendulum consisted of a spiral spring, so that vertical 
movements of the ground could be recorded. This instrument he calls a 
tromo-seismometer. 

Professor Kgidi, of Anagni, proposed to use the reflection from mer- 
cury. The object observed was to be a mark fixed on a wall, and the 
reflected image of the mark was to be observed with a telescope. The 
deviation of the vertical was to be evaluated by noting the amount of 
movement required to bring the cross-wires of the telescope on to the 
mark. This instrument has not, I think, the advantages of M. d'Abbadie's, 
because the light was incident at about 45° on the mercury, and thus 
the mark and telescope were remote from one another ; whereas in the 
arrangement of M. d'Abbadie the mark and microscope are close together, 
and only a micrometer wire in the microscope is movable. 

Cavalleri used ten pendulums of graduated length, and found that 
sometimes one of the pendulums was agitated and sometimes another. 
Rossi observed the same with his pendulums at Rocca di Papa. It thus 
appears that the free period of oscillation of the pendulum is a disturbing 
element. 

In order to obviate the discrepancies which must arise in the use of 
various kinds of pendulums for simultaneous observations in different 
places, Bertelli and Rossi propose a normal ' tromometer,' of which a 
drawing is given. The length of the pendulum is 1^ meters, the weight 
100 grammes, and it makes forty-nine free oscillations in a minute. To 
the bottom of the pendulum is attached a horizontal disk, on the under- 
side of which are engraved two fine lines at right-angles to one another. 
These lines are observed, after total internal reflection in a glass prism 
placed immediately below the disk, by a horizontal microscope, f-irnished 
with a micrometer. The azimuth of the deflection of the vertical is 
observed by a position-circle. 

This paper also contains a description of the author's observatory at 
Rocca di Papa. It is established in a cave at 700 meters above the sea, on 
the external slope of the extinct Latian volcano. There is a large central 
l^endulum hanging from the roof, and there ai'e four others with dif- 
ferent weights and lengths hanging in tubes cut in the native rock. Only 
the ends of these pendulums are visible, and they are protected by glass at 
the visible parts. A great part of this paper is occupied with descriptions 
of seismometers, and this is outside the scope of the present Report. 

In presenting a pamphlet by Father Bertelli, entitled ' Riassunto delle 
osservazioni microsismiche, &c.,' to the Academy (' Comptes Rendus,' 
1877, vol. 84, p. 465), M. d'Abbadie summarises Bertelli's conclusions 
somewhat as follows : — 

1882. H 



98 BEPORX — 1882. 

The oscillation of the pendulum is generally parallel to valleys or 
chains of mountains in the neighbourhood. The oscillations are indepen- 
dent of local tremors, velocity and direction of wind, rain, change of 
temperature, and atmospheric electricity. 

Pendulums of different lengths betray the movements of the soil in 
different manners, according to the agreement or disagreement of their 
free-periods with the period of the terrestrial vibrations. 

The disturbances are not strictly simultaneous in the different towns 
of Italy, but succeed one another at short intervals. 

After earthquakes the ' tromometric ' or microseismic movements are 
especially apt to be in a vertical direction. They are always so when the 
earthquake is local, but the vertical movements are sometimes absent 
when the shock occurs elsewhei'e. Sometimes there is no movement at 
all, even when the shock occurs quite close at hand. 

The positions of the sun and moon appear to have some influence on 
the movements of the pendulum, but the disturbances are especially fre- 
qnent when the barometer is low. 

The curves of ' the monthly means of the tromometric movement ' 
exhibit the same forms in the various towns of Italy, even those which 
are distant from one another. 

The maximum of disturbance occurs near the winter solstice and 
the minimum near the summer solstice ; this agrees with Mallet's results 
about earthquakes. 

At Florence a period of earthquakes is presaged by the magnitude 
and frequency of pendulous movements in a vertical direction. These 
movements are observable at intervals and during several hours after 

At page 103 of the first part of the ' Bulletino ' for 1878 (?), there is 
a review of a work by Giulio Grablovitz, ' Dell' attrazione luni-solare in 
relatione coi fenomeni mareo-sismici,' MUano, Tipografia degli Ingegneri, 

1877. 

In this work it appears that M. Grablovitz attributes a considerable 
part of the deviations of the vertical to bodily tides in the earth, but as 
he apparently enters into no computations to show the competency of 
this cause to produce the observed effects, it does not seem necessary to 
make any further comment on his views. 

At page 99 of the volume for September-December, 1878, Eossi 
writes on the use of the microphone for the purpose of observing earth- 
quakes (' II microfono nella meteorologia endogena '). He begins by 
"•ivino- an account of a correspondence, beginning in 187'i>, between him- 
self and Count Giovanni Mocenigo,' of Vicenza, who seems to have been 
very near to the discovery of the microphone. When the invention of 
the microphone was announced, Mocenigo and Armellini adopted it for 
their experiments, and came to the conclusion that the mysterious noises 
which they heard arose from minute earthquakes or microisms. 

Rossi then determined to undertake observations in his cavern at 
Rocca di Papa, with a microphone, made of silver instead of carbon, 
mounted on a stone beam. The sensitiveness of the instrument could be 
regulated, and he found that it was not much influenced by external 
noises. 

The instrument was placed 20 meters underground, and remote from 

' Count jMocenigo has recently published at Yicenza a book on his observations. 
It is reviewed in Nature for July 6, 1882. 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 99 

houses and carriage-roads. It was protected against insects, and was 
wrapped up in wool. Carpet was spread on the floor of the cave to deaden 
the noise from particles of stone which might possibly fall. Having 
established his microphone, he waited till night and then heard noises 
which he says revealed ' natural telluric phenomena.' The sounds which 
he heard he describes as ' roarings, explosions occurring isolated or in 
volleys, and metallic or bell-like sounds ' [fremiti, scopii isolati o di 
moschetteria, e suoni metallici o di campana] . They all occurred mixed 
indiscriminately, and rose to maxima at irregular intervals. By artificial 
means he was able to cause noises which he calls ' rumbling (?) ov 
crackling ' [rullo o crepito]. The roaring [fremito] was the only noise 
which he could reproduce artificially, and then only for a moment. 
It was done by rubbing together the conducting wires, in the same 
manner as the rocks must rub against one another when there is an 
earthquake. 

A mine having been exploded in a quarry at some distance, the 
tremors in the earth were audible in the microphone for some seconds 
subsequently. 

There was some degree of coincidence between the agitation of the 
pendulum-seismograph and the noises heard with the microphone. 

At a time when Vesuvius became active, Rocca di Papa was agitated 
by microsisms, and the shocks were found to be accompanied by the 
very same microphonic noises as before. The noises sometimes became 
' intolerably loud ; ' on one occasion in the middle of the night, half an 
hour before a sensible earthquake. The agitation of the microphone 
corresponded exactly with the activity of Vesuvius. 

Rossi then transported his microphone to Palmieri's Vesnvian ob- 
servatory, and worked in conjunction with him. He there found that 
each class of shock had its corresponding noise. The sussultorial shocks, 
in which I conceive the movement of the ground is vertically up and 
down, gave the volleys of musketry [i colpi di moschetteria], and the 
undulatory shocks gave the roarings [i fremiti]. The two classes of 
noises were sometimes mixed up together. 

Rossi makes the following remarks : ' On Vesuvius I was put ^ ii> 
the way of discovering that the simple fall and rise in the ticking 
which occurs with the microphone [battito del orologio unito al 
microfono] (a phenomenon observed by all, and remaining inexplicable 
to all) is a consequence of the vibration of the ground.' This passage 
alone might perhaps lead one to suppose that clockwork was included in 
the circuit ; but that this was not the case, and that ' ticking ' is merely 
a mode of representing a natural noise, is proved by the fact that he 
subsequently says that he considers the ticking to be 'a telluric 
phenomenon.' . 

Rossi then took the microphone to the Solfatara of Pozzuoli, and 
here, although no sensible tremors were felt, the noises were so loud as . 
to be heard simultaneously by all the people in the room. The tickmg 
was quite masked by other natural noises. The noises at the Solfatara 
were imitated by placing the microphone on a vessel of boiling water. 
Other seismic noises were then imitated by placing the microphone on a 
marble slab, and scratching and tapping the under surface of it. 

The observations on Vesuvixis led him to the conclusion that the 
earthquake oscillations have sometimes fixed nodes and loops, for there 
were places on the mountain where no eflPects were observed. Hence, as 

H 2 



100 KEFORT— 1882. 

he remarks, although there may sometimes be considerable agitation in 
an earthquake, the true centre of disturbance may be very distant. 

In conclasion Rossi gives a description of a good method of making 
a microphone. A common nail has a short piece of copper wire wound 
round it, and the other end of the wire is wound round a fixed metallic 
support. The nail thus stands at the end of a weak horizontal spring ; 
but the nail is arranged so that it stands inclined to the horizon, instead 
of being vertical. The point of the nail is then put to rest on the middle 
of the back of a silver watch, which lies flat on a slab. The two elec- 
trodes are the handle of the watch and the metallic support. He says 
that this is as good as any instrument. The telephone is a seismological 
instrument, and therefore, strictly speaking, beyond the scope of this 
Report ; but as some details of its use have already been given, I will 
here quote portions of an interesting letter by Prof. John Milne, of the 
Imperial Engineering College of Tokio, which appeared in ' Nature ' for 
June 8, 1882. Mr. Milne writes :— 

' In order to determine the presence of these earth-tremors, at the end 
of 1879 I commenced a series of experiments with a variety of appai'atus, 
amongst which were microphones and sets of pendulum apparatus, very 
similar in general arrangement, but, unfortunately, not in refinement of 
construction, to the arrangements now being used in the Cavendish 
Laboratory. 

' The microphones wei'e screwed on to the heads of stakes driven in 
the ground, at the bottom of boxed-in pits. In order to be certain that 
the records which these microphones gave were not due to local actions, 
such as birds or insects, two distinct sets of apparatus were used, one 
being in the middle of the lawn in the front of my house, and the other 
in a pit at the back of the house. The sensitiveness of these may be 
learnt frora the fact that if a small pebble was dropped on the grass 
within six feet of the pit, a distinct sound was heard in the telephone, 
and a swing produced in the needle of the galvanometer placed in con- 
nection with these microphones. A person running or walking in the 
neighbourhood of the pits, had each of his steps so definitely recorded, 
that a Japanese neighbour, Mr. Masato, who assisted me in the experi- 
ments, caused the swinging needle of his galvanometer to close an 
electric circuit and ring a bell, which, it is needless to say, would alarm a 
household. In the contrivance we have a hint as to how earth- tremors 
may be employed as thief-detectors. 

' The pendulum apparatus, one of which consisted of a 20-lb. bob 
of lead at the end of 20 feet of pianoforte wire provided with small galva- 
nometer mirrors and bifilar suspensions, were also used in pairs. With 
this apparatus a motion of the bob relatively to the earth was magnified 
1,000 times, that is to say, if the spot of light which was reflected from 
the mirror moved a distance equal to the thickness of a sixpence, this 
indicated there had been a relative motion of the bob to the extent of 
1,000th part that amount. 

' The gi-eat evil which everyone has to contend with in Japan when 
woi'king with delicate apparatus is the actual earthquakes, which stop 
or alter the rate of ordinary clocks. 

' Another evil which had to be contended with was the wind, which 
shook the house in which my pendulums were supported, and I imagine 
the ground by the motion of some neighbouring trees. A shower of rain 
also was not without its eSects upon the microphones. After many 



ox THE MEASDREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 101 

months of tiresome observation, and eliminating all motions which by any 
possibility conld have been produced by local influence, the general result 
obtained was that there wei'e movements to be detected every day and 
sometimes many times per day. . . . 

' A great assistance to the interpretation of the various records which 
an earthquake gives us on our seismographs is what I may call a barri- 
cade of post-cards. At the present moment Yedo is barricaded, all the 
towns around for a distance of 100 miles being provided with post-cards. 
Everyone of them is posted with a statement of the shocks which have 
been felt. 

' For the months of October and November it was found from the 
records of the post-cards that nearly all the shocks came from the north 
and passed Yedo to the south-west. When coming in contact with a 
high range of mountains, they were suddenly stopped, as was inferred 
from the fact that the towns beyond this range did not perceive that an 
earthquake had occurred. This fact having been obtained, the barricade 
of post-cards has been extended to towns lying still farther north. The 
result of this has been that several earthquake origins have, so to speak, 
been surrounded or coralled, whilst others have been traced as far as the 
seashore. For the latter shocks, earthquake-hunting with post-cards has 
had to cease, and we have solely to rely upon our instruments. Having 
obtained our earthquake centres, at one or more of these our tremor 
instruments might be erected, and it would soon be known whether an 
observation of earth-tremors would tell us about the coming of an earth- 
quake as the cracklings of a bending do about its approaching breakage. 
To render these experiments more complete, and to determine the exist- 
ence of a terrain tide, a gravitimeter might be established. I mention 
this because if terrain tides exist, and they are sufficiently great from a 
geological point of view, it would seem that they might be more pro- 
nounced and therefore easier to measure in a country like Japan, resting 
in a heated and perhaps plastic bed, than in a country like England, 
where volcanic activity has so long ceased, and the rocks are, compai'a- 
tively speaking, cold and rigid, if an instrument, sufficiently delicate to 
detect differences in the force of gravity, in consequence of our being 
lifted farther from the centre of the earth every time by the terrain tide 
as it passed between (sic) our feet, could be established in conjunction with 
the experiments on earth-tremors.' 

The only account which I have been able to find of M. Bouquet de 
la Grye's observations (mentioned in the last Report) is contained in 
the ' Comptes Rendus ' for March 22, 1875, page 725. M. Bouquet 
writes : — 

' . . . The observation of the levels of our meridian telescopes put us 
on the track of a curious fact. Not only is Campbell Island subject to 
earthquakes, but it also exhibits movements when the great swell falls in 
breakers on the coast. I thought that it would be interesting to study 
this new phenomenon. The instrument, which was quickly put together, 
consisted of a steel wire supporting a weight, to which was soldered a 
needle ; the movements of the weight were amplified 240 times by means 
of a lever ; by passing an electric current through this multiplying 
pendulum, which was terminated at the bottom by a small cup of 
amalgamated tin, regular oscillations of yJ^y^jth of a mm. could be re- 
gistered. I propose to repeat these observations with a pendulum of 



102 



KEPORT 1882. 



mucli larger amplifying power, so as to try to register the variations of 
the plumb-line.' 

In a letter to me, M d'Abbadie mentions an attempt by Brunner to 
improve M. Bouquet de la Grje's apparatus, but considers that the attempt 
was a failure. 

He also tells me that Delaunay directed M. Wolf to devise an 
apparatus for detecting small deviations of the vertical, and that the 
latter, without M. d'Abbadie's knowledge, adopted his rejected idea of 
a pendulum, about 30 meters long, bearing a prism at the end by 
reflection from which a scale was to be read by means of a distant small 
refractor. The pendulum was actually set up, but the wire went on 
twisting and untwisting until Delaunay's death, and no observations were 
made with it. Our own experience is enough to show that nothing could 
have been made of such an instrument. 

M. d'Abbadie gives further explanations of a passage in his own paper 
about the arrangements for the staircases for access to and observation 
with his Nadirane. In writing the Report of 1881 I had found the 
description of the arrangements difficult to understand. 

The woodcut below is a copy of the rough diagram that he sent me. 

There were three staircases : — 

T cut in the rock; C B to ascend from the cellar-flags C D; and, lastly, 
A S to mount from the boarded ground floor, A B, to the small floor S N, 
which was hung from the roof. The two upper staircases did not touch 
the truncated cone of concrete anvwhere. 




Judging from this figure, I imagine that the concrete cone has an 
external slope of ten in one, instead of one in ten as stated in last year's 
Report ; the French expression was ' une inclinaison d'un dixieme.' 

M. d'Abbadie informs me that the apparently curious phenomenon of 
the ' ombres fuyantes,' which were observed in the reflection from the 
pool of mercury, to which we drew attention last year, was of no signifi- 
cance. It arose from the currents of air caused by a candle left standing 
on the staircase T cut in the rock. The light was required for pouring 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 103 

out the mercury, and it was left burning whilst the observation was being 
taken ; but now that this operation is done entirely from above, the 
phenomenon has disappeared. 

In a paper entitled ' Recherches sur la Verticale ' (Ann. de la Soc. 
Scient. de Bruxelles, 1881), M. d'Abbadie continues the account of his 
observations with his instrument, called by him a Nadirane. It was 
described in the last year's Report, and some further details have been given 
above. A portion of this paper refers to his old observations, and gives 
further important details as to the exact method of making observations, 
and of various modifications which have been introduced. 

Each complete observation consists of the following processes : — > 
measurement of the distance between the cross-wires and their image, 
(1) in the meridian, (2) in the prime vertical, (3) in the N.W. azimuth, 
(4) observation of barometer, (5) of thermometer, (6) of direction and 
force of the wind, (7) condition and movement of the image estimated 
with the micrometer, (8) condition of the heavens, (9) of the breakers 
called 'les Criquets,' which can be observed from the neighbouring room. 

This last is to determine whether it is possible to have a rough sea 
with a calm image ; a condition which has not hitherto been observed. 
This statement seems somewhat contradictory of the following : — 

' Aucunes des variations dans les circonstances coucomitantes n'a para 
se rattacher a I'etat de I'image qui, pendant des journees entieres, parait 
tantot belle, tantot faible, et parfois meme disparait entierement, bien que 
ce dernier inconvenient ait ete evite en grande partie par I'usage d'un 
recipient en bois a fond raine pour contenir le mercure.' I presume we 
are to understand that the roughness of the sea and the badness of the 
image is the only congruence hitherto observed. 

M. d'Abbadie's observations on the efiFect of the tides will be referred 
to in the Appendix to this Report. He then discusses the various causes 
which may perhaps influence the vertical. 

The variations of air-temperature are insufficient, because the vertical 
has been seen to vary 2"*4 in six hours. If the effects are to be attri- 
buted to variations in the temperature of the rock, it would be necessary 
to suppose that that temperature varies discontinuously, which it is 
difficult to admit. 

If it be supposed that the changes take place in the instrument itself, 
the like must be true of astronomical instruments. And there is no reason 
to admit the reality of such strange variations. 

Another cause, more convenient because more vague, is variation of a 
chemical or mechanical nature in the crust of the earth. But if this be 
so, why does the vertical ever return to its primitive position ? Another 
cause may be variation in the position of the earth's axis of rotation. 

The azimuthal variations in astronomical instruments, referred to 
by M. d'Abbadie (see a paper by Mr. Henry, vol. 8, p. 134, ' Month. Not. 
R.A.S. '), are difficult to explain without having recourse to such variation 
in the axis of rotation. 

He also tells us that Ellis (vol. 29, 1861, p. 45, ' Mem. R.A.S. ') has dis- 
cussed the Greenwich observations from 1851 to 1858. A comparison of 
the results obtained from two neighbouring meridian instruments seemed 
to show that the azimuthal variations are partly purely instrumental. 

M. d'Abbadie's paper contains diagrams illustrating the variations of 
the vertical observed with the Nadirane during nearly two years. He 
sums up the results as follows : — 



104 REroBT— 1882. 

'En resume le maximum d'ecart da sud au nord entre le fil et son 
image a ete egal a 49"'2 (this is 15"'94; it seems as though this should 
be twice the deviation of the vertical) le 30 Novembre a 8h. 43m. du 
matin. Ce meme jour, a 7h. 28m., on a la 40""1, chiffre porte ici au 
tableau, et 87'^'6 seulement a Ih. 82m. da soir. Dans I'espace de six 
heures la verticale a done varie de 2"'5 ou 0"'81 (as this is the deviation 
of the image, should not the deviation of the vertical be half as much ?). 
Le minimum de I'annee, ou 3'06, fut atteint le 19 Janvier a 3h. 3m. du 
matin, ainsi que le 21 du meme mois a midi, bien qu'on eut observe 3"44 et 
3'30 dans les matinees de ces deux jours, ainsi qu'on le voit au tableau 
ci-apres .... Pendant I'annee entiere la verticale, consideree selon le 
plan du meridien, a done varie d'un angle de 12"-45 ou4""034 .... On 
aura .... 8"'3 ou 2"' 7 pour la plus grande variation dans le sens Est- 
Ouest ou Ton nivelle les tourillons des lunettes meridiennes.' 

Towards the end M. d'Abbadie makes the excellent remark, that in 
discussing latitudes and declinations of stars, account should be taken of 
the instantaneous position of the vertical at the moment of taking the 
observation. 

In the 'Archives des Sciences,' 1881, vol. 5, p. 97, M. P. Planta- 
mour continues the account of his observations on oscillations of the soil 
at Secheron, near Geneva. The account of the earlier observations, 
which we quoted from the ' Comptes Rendus ' in our previous Report, are 
also contained in vol. 2 of the 'Archives,' p. 641. The paper to which 
we are now referring contains a graphical reproduction of the previous 
series of observations, as far as concerns the daily means. 

The new series extends from October 1, 1879, to December 31, 1880, 
the disposition of the levels being the same as was described in our last 
Report. The observations were taken at 9 a.m. and G p.m., which hours 
are respectively a little before the diurnal minimum and maximum. The 
meaning of the terms maximum and minimum were somewhat obscure in 
the ' Comptes Rendus,' but I now find that the right interpretation was 
placed on M. Plantamour's words, for maximum means for the two 
levels E. end highest and S. end highest. 

The N.S. level seems to have behaved very similarly in the two years 
of observation ; the total annual amplitudes in the two years being 4"'89 
and 4"-56 respectively. In both years this level followed, with some 
retardation, the curve of external temperature, except between April and 
October, when the curves appear to be inverted. The E.W. level be- 
haved very differently in the two years. In 1879 the E. end began to 
fall rapidly at the end of November, and continued to fall until De- 
cember 26, when the reading was — 88'''71 ; it rose a little early in 
January and then fell again, so that on January 28, 1880, the reading 
was - 89"'95. The amplitude of the total fall (viz. from October 4, 1879, 
to January 28, 1880) was 95"'80. In the preceding year the amplitude 
was only 28"'08. The E. end has never recovered its primitive position, 
and remains nearly 80'' below its point of departure. 

It is difficult to believe that so enormous a variation of level is 
normal, and one is tempted to suspect that there is some systematic error 
in his mode of observation. If such oscillations as these were to take 
place in an astronomical observatory, accurate astronomical observations 
would be almost impossible. 

I have seen nothing which shows that M. Plantamour takes any 
special precaution with regard to the weight of the observer's body, nor 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 105 

is it expressly stated that the observer always stands in exactly the same 
position, although, of course, it is probable that this is the case. It would 
be interesting, also, to learn whether any precautions have been taken for 
equalising the temperature of the level itself. To hold the hand in the 
neighbourhood of a delicate level is sufficient to quite alter the reading. 
In one of his letters to me M. d'Abbadie also remarks on the slow 
molecular changes in glass, which render levels untrustworthy for com- 
parisons at considerable intervals of time. Although we must admire 
M. Plantamour's indomitable perseverance, it is to be regretted that his 
mode of observation is by means of levels ; and we are compelled to regard, 
at least provisionally, these enormous changes of level either as a local 
phenomenon, or as due to systematic error in his mode of observation. 

In the Report for 1881 we referred to some observations by Admiral 
Mouchez, made in 1856, on changes of level. A short paper by Admiral 
Monchez on these observations will be found in the ' Comptes Rendus ' 
for 1878, vol. 87, p. 665. I now find that the observations were, in 
fact, discussed by M. Gaillot, in a paper entitled ' Snr la direction de la 
verticale a I'observatoire de Paris,' at p. 684 of the same volume. The 
paper consists of the examination of 1,077 determinations of latitude, made 
between 1856 and 1861, with the Gambey circle. 

M. Gaillot concludes that the variation from year to year is acci- 
dental, and that the variation of latitude iu the course of the year is 
represented by 



cX = + 0"-20 sin p60° (^ -_95)-| 
L 365-25 I* 



where t is the number of days since January 1. 

By a comparison of day and night observations Le concludes that 
there is no trace of a diurnal variation. On this we may remark that, if 
the maximum and minimum occur at 6 p.m. and 6 a.m. (which is, roughly 
speaking, what we found to be the case), then the diurnal oscillation 
must necessarily disappear by this method of treatment. 

Individual observations ranged from 2"-48 above to 3'''17 below the 
mean. On this he remarks : — 

' Ceux qui savent combien I'observation du nadir presente parfois de 
diflBculte dans un observatoire situe au milieu d'une grande ville, .... 
ceux-la ne trouveront pas ces ecarts exageres, et ne croiront nuUement avoir 
besoinde faire intervenir une deviation de la verticale pour lesexpliquer.' 

M. Gaillot concludes by remarks adverse to any sensible deviations 
of the vertical. 

It seems to me, however, that in the passage about the influence of 
the traflBc of a great town, M. Gaillot begs the whole question by setting 
down to that disturbing influence all remarkable deviations of the ver- 
tical. Our observations, and those of many others, are entirely adverse 
to such a conclusion. 

M. d'Abbadie, in a letter to me, also expresses himself as to the in- 
conclusiveness of M. Gaillot's discussion. 

He also tells me that M. Tisserand, in his observations of latitude in 
Japan, found variations amounting to nearly 7"; and when asked ' How he 
could be so much in error,' answered ' That he was sure of his observa- 
tions and calculations, but could not explain the cause of such variations.' 

The following further references may perhaps be useful : — Maxwell's 
paper on the 306-day inequality in the earth's rotation, which was men- 



106 EEPOET — 1882. 

tioned in the Report of last year, is in the ' Trans. Roy. Soc' of Edin- 
burgh, 1857, vol. 21, pp. 559-70, See also Bessel's ' Abhandlungen,' 
vol. 2, p. 42, vol. 3, p. 304. In ' Nature ' for January 12, 1882 (p. 250), 
there is an account of the work of the Swiss Seism ological Commission. 
The original sources appear to be a text-book on Seismology by Professor 
Heim, of Bern, the ' Annuaire ' of the Physical Society of Bern, and the 
* Archives des Sciences ' of Geneva. I learn from M. d'Abbadie that 
Colonel Orff has been making systematic observations twice a day with 
levels at the Observatory at Munich, and that Colonel Goulier has been 
doing the same at Paris, with levels filled with bisulphide of carbon. 



Appendix. 

On Variations in the Vertical due to Elasticity of the Earth's Surface. 
By G. H. Darwin, F.R.S. 

1. On the Mechanical Effects of Barometric Pressure on the Earth's Surface. 

The remarks of Signore de Rossi, on the observed connection between 
barometric storms and the disturbance of the vertical, have led me to 
make the following investigation of the mechanical effects which are 
caused by variations of pressure acting on an elastic surface. The results 
seem to show that the direct measurement of the lunar disturbance of 
gravity must for ever remain impossible. 

The practical question is to estimate the amount of distortion to which 
the upper strata of the earth's mass are subjected, when a wave of baro- 
metric depression or elevation passes over the surface. The solution of 
the following problem should give us such an estimate. 

Let an elastic solid be infinite in one direction, and be bounded in the 
other direction by an infinite plane. Let the surface of the plane be every, 
where acted on by normal pressures and tractions, which are expressible 
as a simple harmonic function of distances measured in some fixed direc- 
tion along the plane. It is required to find the form assumed by the 
surface, and generally the condition of internal strain. 

This is clearly equivalent to the problem of finding the distortion of 
the earth's surface produced by parallel undulations of barometric elevation 
and depression. It is but a slight objection to the correctness of a rough 
estimate of the kind required, that barometric disturbances do not actually 
occur in parallel bands, but rather in circles. And when we consider the 
magnitude of actual terrestrial storms, it is obvious that the curvature of 
the earth's surface may be safely neglected. 

This problem is mathematically identical with that of finding the state 
of stress produced in the earth by the weight of a series of parallel 
mountains. The solution of this problem has recently been published in 
a paper by me in the ' Philosophical Transactions ' (Part II. 1882, pp. 
187-230), and the solution there found may be adapted to the present case 
in a few lines. 

The problem only involves two dimensions. If the origin be taken in 
the mean horizontal surface, which equally divides the mountains and 
valleys, and if the axis of z be horizontal and perpendicular to the moun- 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 107 

tain chains, and if tlie axis of x be drawn vertically downwards, then the 
equation to the mountains and valleys is supposed to be 



x = — h cos 



6' 



so that the wave-length from crest to crest of the mountain ranges is 27r&. 

The solution may easily be found from the analysis of section 7 of the 
paper referred to. It is as follows : — 

Let a, y be the displacements at the point x, z vertically downwards 
and horizontally (a has here the opposite sign to the a of (44)). Let w be 
the density of the rocks of which the mountains are composed ; g gravity ; 
V modulus of rigidity, then 



1 , dW 
2v dz 



-.rib 



where W= — gwh e cos 



h J 



(1) 



these 


we 


have at once 










a = 


t'(}^i)^' 


xlb 2 

cos- 








r = 


qwh -''■"' 
2v "" 


. z 
sm- 










da 


rHi 


t!V" 


■ .T/i 2 

sin- 



6J 



(2)' 



The first of these gives the vertical displacement, the second the hori- 
zontal, and the third the inclination to the horizon of strata primitively 
plane. 

At the surface 



qwh 7 s A I 

a = ^-— b cos -, 7 = 
Zv 



da gwh 



(3) 



dz 



sm- 



Hence the maximum vertical displacement of the surface is + gwhl/2vy 
and the maximum inclination of the surface to the horizon is 

Hh cosec 1" X givhl2v seconds of arc. 

' It is easy to verify that these values of o and y, together with the value 
p = gwh e -^l'> cos zjb for the hydrostatic pressure, satisfy all the conditions of the 
problem, by giving normal pressure gwh cos zjb at the free surface of the infinite plane, 
and satisfying the equations of internal equilibrium throughout the solid. I take 
this opportunity of remarking that the paper from which this investigation is taken 
contains an error, inasmuch as the hydrostatic pressure is erroneously determined in 
section 1. The term - W should be added to the pressure as determined in (3). 
This adds W to the normal stresses P, Q, R throughout the paper, but leaves the 
difference of stresses (which was the thing to be determined) unaffected. If the 
reader should compare the stresses, as determined from the values of o, y in the text 
above, and from the value of jp given in this note, with (38) of the paper referred to, 
he is warned to remember the missing term 11'. 



108 REroRT— 1882. 

Before proceeding further I shall prove a very remarkable relation 
between the slope of the surface of an elastic horizontal plane and the 
deflection of the plumb-line caused by the direct attraction of the weight 
producing that slope. This relation was pointed out to me by Sir William 
Thomson, when I told him of the investigation on which I was engaged ; 
but I am alone responsible for the proof as here given. He writes that 
he finds that it is not confined simply to the case where the solid is 
incompressible, but in this paper it will only be proved for that case. 

Let there be positive and negative matter distributed over the horizontal 
plane according to the law wh cos {zjh) ; this forms, in fact, harmonic 
mountains and valleys on the infinite plane. We require to find the 
potential and attraction of such a distribution of matter. 

Now the potential of an infinite straight line, of line-density p, at a 
point distant d from it, is well known to be — 2/(p log d, where ji is the 
attraction between unit masses at unit distance apart. Hence the potential 
V of the supposed distribution of matter at the point x, z, is given by 

F = - 2nivhr" cos ^ log s/ [x^ + (4 - 2)2} di: 



= — f^ivlib ■ 



'sm^~\og{x' + (i'-,y} 






It is not hard to show that the first term vanishes when taken between 
the limits. 

Now put t = , so that sin - = sin — cos -+ cos — sin -, and we 

X b b b 



have 



V = luwhb sm — cos - + cos — sm - ) 

^ J_«V b b b bJl + f' 



But it is known ^ that 

{+" t sin cf, di _. f+^t cos ct., ^ 
— ^ ^7-^ = 7re '^j dt = 0. 

Therefore V=2iruw'kbe cos-. 

b 

o 

If g be gravity, a earth's radius, and c earth's mean density, 27r/t = -'^~. 

Zao 

And TT Sqwhj ""' * z . ,. 

V=-~rbe cosr- . . . (4) 

zac b 

The deflection of the plumb-line at any point on the surface denoted by 
a; := 0, and z, is clearly dVjgdz, when a; = 0. Therefore, 

,,,„,. 1 3n7ijh . z /„v 

the deflection = X -^r-^ sm - . . . (o) 

g zac b 

But from (2) the slope (or—-, when z is zero), is — ^-— ' sin -'. 

dz 2v b 

Therefore deflection bears to slope the same ratio as v/g to ^ aS. This 
' See Todhunters Int. Calc. ; Chapter on ' Definite Integrals.' 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 109 

ratio is independent of the "wave-length 2Trh of the undulating surface, of 
the position of the origin, and of the azimuth in the plane of the line 
normal to the ridges and valleys. Therefore the proposition is true of any 
combination whatever of harmonic undulations, and as any inequality may 
be built up of harmonic undulations, it is generally true of inequalities of 
any shape whatever. 

Now a = 6-37 x 10* cm., o = 5§; and ^ao = 12-03 x 10* grammes 
per square centimeter. The rigidity of glass in gravitation units ranges 
from 1-5 X 10* to 2'4 X 10*. Therefore the slope of a very thick slab of 
the rigidity of glass, due to a weight placed on its surface, ranges from 
8 to 5 times as much as the deflection of the plumb-line due to the attraction 
of that weight. Even with rigidity as great as steel (viz., about 8 x 10*), 
the slope is 1^ times as great as the deflection. 

A practical conclusion from this is that in observations with an artificial 
horizon the disturbance due to the weight of the observer's body is very 
far greater than that due to the attraction of his mass. This is in perfect 
accordance with the observations made by my brother and me with our 
pendulum in 1881, when we concluded that the warping of the soil by our 
weight when standing in the observing room was a very serious disturb- 
ance, whilst we were unable to assert positively that the attraction of 
weights placed near the pendulum was perceptible. It also gives emphasis 
to the criticisms we have made on M. Plantamonr's observations — 
namely, that he does not appear to take special precautions against the 
disturbance due to the weight of the observer's body. 

We must now consider the probable numerical values of the quantities 
involved in the barometric problem, and the mode of transition from the 
problem of the mountains to that of barometric inequalities. 

The modulus of rigidity in gravitation units (say grammes weight per 
square centimeter) is vjg. In the problem of the mountains, %vh is the mass 
of a column of rock of one square centimeter in section and of length equal 
to the heio-ht of the crests of the mountains above the mean horizontal 
plane. In the barometric problem, ivh must be taken as the mass of a 
column of mercury of a square centimeter in section and equal in height 
to a half of the maximum range of the barometer. 

This maximum range is, I believe, nearly two inches, or, let us say, 
5 cm. 

The specific gravity of mercury is 136, and therefore wh = 34 grammes. 

The rigidity of glass is from 150 to 240 million grammes per square 
centimeter ; that of copper 540, and of steel 843 millions. 

I will take vjg = 3 x 10*, so that the superficial layers of the earth 
are assumed to be more rigid than the most rigid glass. It will be easy 
to adjust the results afterwards to any other assumed rigidity. 

With these data we have^-- = -—- ; also^ ^— x -q-— = '-0117, 

2v 10* TT 10* 

lb seems not unreasonable to suppose that 1500 miles (2'4 x 10* cm.) 
is the distance from the place where the barometer is high (the centre of 
the anti-cyclone) to that where it is low (the centre of the cyclone). 
Accordingly the wave-length of the barometric undulation is 4'8 X 10* cm., 
and 6 = 4'8 X 10* -^ 6-28 cm., or, say, 6 = -8 x 10* cm. 

Thus, with these data, 3^h = 4-5 cm. 

Zv 



110 REPORT— 1882. 

We thus see that the ground is 9 cm, higher under the barometric 
depression than under the elevation. 

If the sea had time to attain its equilibrium slope, it would stand 
5 X Id 6, or 68 cm. lower under the high pressure than under the low. 
But as the land is itself depressed 9 cm., the sea would apparently only 
be depressed 59 cm. under the high barometer. 

It is probable that, in reality, the larger barometric inequalities do not 
linger quite long enough over particular areas to permit the sea to attain 
everywhere its due slope, and therefore the full difference of water-level 
can only be attained occasionally. 

On the other hand, the elastic compression of the ground must take 
place without any sensible delay. Thus it seems probable that the elastic 
compression of the ground must exercise a very sensible effect in modifying 
the apparent depression or elevation of the sea under high and low baro- 
meter. 

It does not appear absolutely chimerical that, at some future time 
when both tidal and barometric observations have attained to great 
accuracy, an estimate might thus be made of the average modulus of 
rigidity of the upper 500 miles of the earth's mass. 

Even in the present condition of barometric and tidal information, it 
might be interesting to make a comparison between the computed height 
of tide and the observed height, in connection with the distribution of 
barometric pressure. It is probable that India would be the best field 
for such an attempt, because the knowledge of Indian tides is more com- 
plete than that for any other part of the world. On the other hand we 
shall see in the following section that tidal observations on coast-lines of 
continents are liable to disturbance, so that an oceanic island would be a 
more favourable site. 

It has already been shown that the maximum apparent deflection of 
the plumb-line, consequent on the elastic compression of the earth, 
amounts to 0""0117, and this is augmented to 0"*0146 when we include 
the true deflection due to the attraction of the air. It is worthy of remark 
that this result is independent of the wave-length of the barometric 
inequality, and thus we get rid of one of the conjectural data. 

Thus if we consider the two cases of high pressure to right and low 
to left, and of low pressure to right and high to left, we see that there 
will be a difference in the position of the plumb-line relatively to the 
earth's surface of 0"'0292. Even if the rigidity of the upper strata of 
the earth were as great as that of steel, there would still be a change of 
0"-011. 

A deflection of magnitude such as 0""03 or 0"*01 would have been 
easily observable with our instrument of last year, for we concluded 
that a change of o^ro^h of a second could be detected, when the change 
occurred rapidly. 

It was stated in our previous Report that at Cambridge the calculated 
amplitude of oscillation of the plumb-line due directly to lunar disturbance 
of gravity amounts to 0"*0216. Now as this is less than the amplitude 
due jointly to elastic compression and attraction, with the assumed rigidity 
(300 millions) of the earth's strata, and only twice the result if the 
rigidity be as great as that of steel, it follows almost certainly that from 
this cause alone the measurement of the lunar disturbance of gravity 
must be impossible with any instrument on the earth's surface. 

Moreover the removal of the instrument to the bottom of the deepest 



ON THE MEASUBEMENT OF THE LUNAR DISTURBANCE OF GRAVITY. Ill 

known mine wonld scarcely sensibly affect the result, because the flexure 
of the strata at a depth so small, compared with the wave-length of 
barometric inequalities, is scarcely different from the flexure of the 
surface. 

The diurnal and periodic oscillations of the vertical observed by us 
were many times as great as those which have just been computed, and 
therefore it must not be supposed that more than a fraction, say perhaps 
a tenth, of those oscillations was due to elastic compression of the earth. 

The Italian observers could scarcely, with their instruments, detect 
deflections amounting to T-Joth of a second, so that the observed connec- 
tion between barometric oscillation and seismic disturbance must be of a 
different kind. 

It is not surprising that in a volcanic region the equalisation of pres- 
sure, between imprisoned fluids and the external atmosphere, should lead 
to earthquakes. 

If there is any place on the earth's surface free from seismic forces, 
it might be possible (if the effect of tides as computed in the following 
section conld be eliminated) with some such instrument as ours, placed 
in a deep mine, to detect the existence of barometric disturbance many 
hundreds of miles away. It would of course for this purpose be necessary 
to note the positions of the sun and moon at the times of observation, and 
to allow for their attraction. 

2. On the Disturbance of the Vertical near the Coasts of Continents due 
to the Rise and Fall of the Tide. 

Consider the following problem : — 

On an infinite horizontal plane, which bounds in one direction an 
infinite incompressible elastic solid, let there be drawn a series of parallel 
straight lines, distant I apart. Let one of these be axis of y, let the axis 
of z be drawn in the plane perpendicular to the parallel lines, and let the 
axis of x, be drawn vertically downwards through the solid. 

At every point of the surface of the solid, from 2; = to Z, let a normal 
pressure gioh (1 — 2zjl) be applied ; and from 2 = to — Z let the sur- 
face be free from forces. Let the same distribution of force be repeated 
over all the pairs of strips into which the surface is divided by the system 
of parallel straight lines. It is required to determine the strains caused 
by these forces. 

Taking the average over the whole surface there is neither pressure 
nor traction, since the total traction on the half-strips subject to traction 
is equal to the total pressure on the half-strips subject to pressure. 

The following is the analogy of this system with that which we wish 
to discuss : the strips subject to no pressure are the continents, the alter- 
nate ones are the oceans, g is gravity, lo the density of water, and h the 
height of tide above mean water on the coast-line. 

We require to find the slope of the surface at every point, and the 
vertical displacement. 

It is now necessary to bring this problem within the range of the 
results used in the last section. In the first place, it is convenient to 
consider the pressures and tractions as caused by mountains and valleys 
whose outline is given by a; = — /i (1 — 22/Z) from z = to Z, and x = 
from z = to — Z. To utilise the analysis of the last section, it is neces- 
sary that the mountains and valleys should present a simple-harmonic 



112 HEPOKT — 1882. 

outline. Hence the discontinnous function must be expanded by Fourier's 
method. Known results of that method render it unnecessary to have 
recourse to the theorem itself. It is known that — 

± 1 ;r — i a = sin + 1 sin 20 + ^ sin 39 + 

_ 1 e = — sin + i sin 29 — ^ sin 36 + .... 

-^ ,r q^ = - I cos + ^2 cos39 + i cos 59 + ... j 

The upper sign being taken for values of 9 between the infinitely small 
positive and + ir, and the lower for values between the infinitely small 
negative and — tt. 

Adding these three series together we have — 

2 I -I sin 29 + :i sin 49 + . . j + i | cos 9 + .J^ cos 39 + -^^cos 59+ . . j 

■equal to t — 29 from 9 = to + tt, and equal to zero from 9 = to — tt. 
Hence the required expansion of the discontinuous function is — 

-^^' |isin29 + i sin49+ . . .j 

- ^ ( cos + J, cos 39 + i-, cos 59 + . .1 (6) 

Avliere ^ ^ f (^) 

For it vanishes from z=: — I to 0, and is equal to — /i(l — 2r:/l) from 
s = to + Z. 

Now looking back to the analysis of the preceding section we see that 
if the equation to the mountains and valleys had been x = — /isin(;j/5), 
a would have had the same form as in (2) but of course with sine for 
cosine, and y would have changed its sign and a cosine would have stood 
for the sine. Applying then the solution (2) to each term of our expan- 
sion separately, and only writing down the solution for the surface at 
which X =■ 0, we have at once that y = 0, and 

a = 0^l\lsm2d+l^sini9+ ;^. sin G9 + . . .] 

TTV TT L 2'' 4'' 0- J 

+ ^2!^ . ?J ( COS0 + l. COS 30 + ^3 COS 50 + ... 1 (8) 

The slope of the surface is — '* or f " ; thus 
^ dz I do 



■di 
dz 



a^^gwk 1 1 cos 20 + i cos 40 + I cos 69 + . . .1 

_ ^i 2 f j^g _^ 1 j^ gg ^ 1 i^ 59 ^ _ . . j (9) 

TTU TT L 3 6" J 

The formulse (8) and (9) are the required expressions for the vertical 
depression of the surface and for the slope. 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITT. 113 



It is interesting to determine the form of surface denoted by these 
equations. Let us suppose then that the units are so chosen that 
gwhljn'^u may be equal to one. Then (8) becomes 

« = |sin2fl+lsin49+. . 



dn 



r cos 20 + ^ COS 49 + . . . 



TT ll2 



gCosff+KsCOsSe + 



}(10) 



sin0 + isin39+ . . j. .(11) 



When 9 is zero or + tt, dujdB becomes infinite, which denotes that 
the tangent to the warped horizontal surface is vertical at these points. 
The verticality of these tangents will have no place in reality, because 
actual shores shelve, and there is not a vertical wall of water when the 
tide rises, as is supposed to be the ca,sein the ideal problem. We shall, how- 
ever, see that in practical numerical application, the strip of sea-shore along 
which the solution shows a slope of more than 1" is only a small fraction 
of a millimeter. Thus this departure from reality is of no importance 
whatever. 

When 9 = or -I- 7r, 



being + when 9 = 0, and — when 9 := itn-. 



670: 



When B =■ ±^Tr, a vanishes, and therefore midway in the ocean 
and on the land there are nodal lines, which always remain in the undis- 
turbed surface, when the tide rises and falls. At these nodal lines, de- 
fined by 9 = ± ^TT, 



dn 



= -il0ge2 + 



2/1-1 

TT l 1« 3^ 



+ ^- 



} 



= - -3406 T -6108 = - -9634 and + -2702 

Thus the slope is greater at mid-ocean than at mid-land. By assuming 
9 successively as c '''' 4 ""> 3 ""> ^^^^ summing arithmetically the strange 
series which arise, we can, on paying attention to the manner in which 
the signs of the series occur, obtain the values of a corresponding to 
0. ± i^, ± i^, ± I'T, ± Itt, ± At, -!- f TT, ± f TT. The resulting values, to- 
gether with the slopes as obtained above, are amply sufficient for drawing 



a figure, as in the annexed diagram. 




w^jm^y- 



The straight line is a section of the undisturbed level, the shaded part 
being la,nd, and the dotted sea. The curve shows the distortion, when 
warped by high and low tide as indicated. 

The scale of the figure is a quarter of an inch to ^t for the abscissas, 

1882. I 



114 



REPOET 1882. 



and a quarter of an inch to unity for the ordinates ; it is of course an 
enormous exaggeration of the flexure actually possibly due to tides. 

It is interesting to note that the land regions remain very nearly flat, 
rotating about the nodal line, but with slight curvature near the coasts. 
It is this curvature, scarcely perceptible in the figure, which is of most 
interest for practical application. 

The series (8) and (9) are not convenient for practical calculation in 
the neighbourhood of the coast, and they must be reduced to other forms. 
It is easy, by writing the cosines in their exponential form, to show that 

cos + i cos 29 + ^ cos 39 + . . . = - log^ (± 2 sin 10) . . . (1.3) 
cos - i cos 20 + ^ cos 30 + . . . = loge (2 cos 10) .... (14) 

Where the upper sign in (13) is to be taken for positive values of and 
the lower for negative. 

For the small values of 0, for which alone we are at present con- 
cerned, the series (13) becomes — logg (-+; 0) and the lower loge 2. 

Taking half the diiference and half the sum of the two series we have 

1 cos 20 + 1 cos 40 + = - 1 log (± 0) - 1 log 2 ... . (15) 

COS0 + 1 cos 30 + i cos 50 + = - i log (± 0) + + log 2 . . . . (16) 

Integrating (16) with regard to 0, and observing that the constant 
introduced on integration is zero, we have 

sin + isin 30+1^ sin 50 = - 10 [log (± «)-!]+ 10 log 2 . (17) 



Then from (15) and (17) 

1 cos 20 + 1 cos 40 + 



-H 



sin + ^ sin 30 + 



»)-i(i.|l),„g._| 



•} 



(18) 



Integrating (15), and observing that the constant is zero we have, 

. = - i^ [log (± 0) - 1] - i01og2 (19) 



Isin 20 + isin 49 + 



Integrating (17) and putting in the proper constant to make the left 
side vanish when = 0, we have 



^^+^+i + 

]_3 ^ 33 ^ 53 ^ 



■ - (p -^ + Is «os 39 + . . . ) 

= _ i 92 log (± 0) + 1 02 (I + log 2) (20) 

For purposes of practical calculation may be taken as so small that 
the right-hand side of (18) reduces to — ^ log (± 29), and the right- 
hand sides of (19) and (20) to zero. 

Hence by (8) and (9), we have in the neighbourhood of the coast 



nivJi 21 

— xr2 



givh 



■L+L + L + 

13 33 ^ 53 



= ^i^ x^x 2-1037 

TTV TT' 

da qivli 1 1 rv 1 



27rz 



(21) 



ON THE MEASUREMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 115 

I shall now proceed to compute from the formulae (21) the depression 
of the surface and the slope, corresponding to such numerical data as 
seem most appropriate to the terrestrial oceans and continents. 

Considering that the tides are undoubtedly augmented by kinetic 
action, we shall be within the mai'k in taking h as the semi-range of 
equilibrium tide. At the equator the lunar tide has a range of about 
53 cm., and the solar tide is very nearly half as much. Therefore at 
spring-tides we may take h = 40 cm. It must be noticed that the high- 
ness of the tides, say 15 or 20 feet, near the coast is due to the shallow- 
ing of the water, and it would not be just to take such values as repre- 
senting the tides over large areas ; iv, the density of the water is, of 
course, unity. 

If we suppose it is the Atlantic Ocean and the shores of Europe with 
Africa, and of North and South America, which are under consideration, it 
is not unreasonable to take I as 3,900 miles or 6'28 x 10^ cm. Then 
'lirzjl =2X10-8. 

Taking v jg as3x 10^, that is to say, assuming a rigidity greater than 
that of glass, we have for the slope in seconds of arc, at a distance z from 
the sea-shore 

^_f-^, xlog,10x(8-log„.) , _ ^2,) 



= 0"-01008 (8-log,o2) 



} 



From this the following table may be computed by simple multipli- 
cation : — 

Distance from mean 

water-mark Slope 

1 cm. = 1 cm 0"-0806 

10 cm. = 10 cm -0706 

10^ cm. = 1 meter -0605 

10' cm. = 10 m -0504: 

10' cm. = 100 m -0403 

105 cm. = 1 kilom 0"-0302 

10«cm. = 10 kilom -0202 

2 X 10«cm.= 20 kilom -0170 

5 X 10«cm.= 50 kilom -0131 

10' cm. = 100 kilom "0101 



On considering the formula (22) it appears that z must be a very small 
fraction of a millimeter before the slope becomes even as great as 1'. 
This proves that the rounded nick in the surface, which arises from the 
discontinuity of pressure at our ideal mean water-mark, is excessively 
small, and the vertical displacement of the surface is sensibly the same, 
when measured in centimeters, on each side of the nick, in accordance 
with the first of (21). 

The result (5) of section 1 shows that, Avith rigidity 3 x 10*, the true 
deflection cf plumb-line dne to attraction of the water is a quai'ter of the 
slope. Hence an observer in a gravitational observatory at distance z 
from mean water-mark, would note deflections from the mean position of 
the vertical 1;^ times as great as these computed above. And as high 

i2 



116 KEPOUT— 1882. 

water changes to low, there would be oscillations of the vertical 2^ times 
as great. We thus get the practical results in the following table : — 

Distance of obser- Amplitude of 

vatory from apparent o-cillation 

mean water-mark of the vertical 

10 meters 0'-126 

100 m -101 

1 kilom '076 

lOkilom -050 

20 kilom -042 

50 kilom -035 

100 kilom -025 

It follows, from the calculations made for tracing the curve, that half- 
way across the continent (that is to say, 3,142 kilometers from either 

coast) the slope is • x -^'' x '2703 seconds of arc, = 0"'00237 ; 

and the range of apparent oscillation is 0"'006. 

In these calculations the width of the sea is taken as 6,283 kilometers. 
If the sea be nai'rower, then to obtain the same deflections of the plumb- 
line, the observatory must be moved nearer the sea in the same pro- 
portion as the sea is narrowed. If, for example, the sea were 3,142 kilo- 
meters wide, then at 10 kilometers from the coast the apparent amplitude 
of deflection is 0"-042. If the range of tide is greater than that here 
assumed (viz., 80 cm.), the results must be augmented in the same 
proportion. And, lastly, if the rigidity of the rock be greater or less than 
the assumed value (viz., 3 X 10**) the part of the apparent deflection 
depending on slope must be diminished or increased in the inverse pro- 
portion to the change in rigidity. 

I think there can be little doubt that in narrow seas the tides are 
generally much greater than those here assumed ; and it is probable that 
at a gravitational observatory actually on the sea-shore on the south-coast 
of England, apart from seismic changes, perceptible oscillations of the 
vertical would be noted. 

Sir William Thomson has made an entirely independent estimate of 
the probable deflection of the plumb-line at a seaside gravitational obser- 
vatory.^ He estimates the attraction of a slab of water, 10 feet thick 
(the range of tide), 50 miles broad perpendicular to the coast, and 100 
miles long parallel with coast, on a plummet 100 yards from the low- 
water mark, and opposite the middle of the 100 miles of length. He 
thinks this estimate would very roughly represent the state of things say 
at St. Alban's Head. He finds then that the deflection of the plumb-line 
as high tide changes to low would be ^^jro^ooth of the unit angle, or 
0"*050. The general theorem proved above, as to the proportionality of 
slope to attraction, shows that, with rigidity 3 x 10" for the rocks of 
which the earth is formed, the apparent deflection of the plumb-line would 
amount to 0"-25. 

It is just possible that a way may in this manner be opened for deter- 
mining the modulus of rigidity of the upper 100 or 200 miles of the earth's 
surface, although the process would be excessively laborious. The tides of 
the British Channel are pretty well known, and therefore it would be 
possible by very laborious quadratures to determine the deflection of the 
plumb-line due to the attraction of the tide at any time at a chosen station. 

' Thomson and Tait's Nat. Phil. § 818. 



ON THE MEASUREMENT OF THE LUNAE DISTURBANCE OF GRAVxTT. 117 

If then the deflection of the plumb-line could be observed at that station 
(with corrections applied for the positions of the sun aud moon), the 
ratio of the calculated to the observed and corrected deflection, together 
with the known value of the earth's radius and mean density, form 
the materials for computing the rigidity. But such a scheme would 
be probably rendered abortive by just such comparatively large and 
capricious oscillations of the vertical, as we, M. d'Abbadie and others, 
have observed. 

It is interesting to draw attention to some observations of M. 
d'Abbadie on the deflections of the vertical due to tides. His observatory 
(of which an account was given in the Report for 1881) is near Hendaye 
in the Pyrenees, and stands 72 meters above, and 400 meters distant, from 
the sea. He writes : ' — 

' J'ai reuni 359 comparaisons d'observations speciales faites lors du 
maximum du flot et du jusant ; 243 seulement sont favorables a la theorie 
de I'attraction exercee par la masse des eaux, et I'ensemble des resultats 
pour une di2"erence moyenne de marees egale a 2'9 metres donne un 
resultat moyen de 0''-56 ou 0""18 pour le double de I'attraction angulaire 
vers le Nord-Ouest. Ceci est conforme a la theorie, car les diS'erences 
observees doivent etre partagees par moitie, selon la loi de la reflexion ; 
mais comme il y a toujours de I'inattendu dans les experiences nouvelles, 
on doit ajouter que sur les 116 comparaisons restantes il y en a eu 57 ou 
le flot semble repousser le mercure au lieu de I'attirer. Mes resultats ont 
ete confirmes pendant I'hiver dernier par M. I'abbe Artus, qui a eu la 
patience de comparer ainsi 71 flots et 73 jusants consecutifs, de Janvier a 
mars 1880. Lui aussi a trouve un tiers environ de cas defavorables a nos 
theories admises. On est done en droit d'afiirmer que si la mer haute 
attire le plus souvent le pied du fil a plomb, il y a une, et peut-etre 
plusieurs, autres forces en jeu pour faire varier sa position.' 

We must now consider the vertical displacement of the land near the 

coast. In (21) it is shown to be ciq = ^— x ~ x 2-1037, where a^ 



TTV Tt'^ 



<o in- 



dicates the displacement coiTesponding to z = 0, 

With the assumed values, h = 40,v = 3 X 10^ 7 = 6-28 X 10^, I 
find oq ^ 5'684 cm. Hence the amj^litude of vertical displacement is 
11"37 cm. As long as M remains Constant ' this vertical displacement 
remains the same ; hence the high tides of 10 or 15 feet which are actually 
observed on the coasts of narrow seas must probably produce vertical 
oscillations of quite the same order as that computed. 

If the land falls the tide of course rises higher on the coast line than 
it would do otherwise ; hence the apparent height of tide would be h + oq. 
But this shows there is more water resting on the earth than according 
to the estimated value h ; hence the depression of the soil is greater in the 
proportion 1 + uq/Ji to unity; this again causes more tide, which reacts 
and causes more depression, and so on. Thus on the whole the augmen- 
tation of tide due to elastic yielding is in the ratio of 

This investigation is conducted on the equilibrium theory, and it 
neglects the curvature of the sea-bed, assuming that there is a uniform 

' ' Kecherches sur la Verticale,' Ann. de la Soc. Scient. de Bruxelles, 1881. 



118 REPOET — 1882. 

slope from mid-ocean to the sea-coasfc. The figure shows that this is uot 
rigorously the case, but it is quite near enough for a rough approximation. 
The phenomena of the short period tides are so essentially kinetic that 
the value of this augmentation must remain quite uncertain, but for 
the long-period tides (the fortnightly and monthly elliptic) the augmen- 
tation must correspond approximately with the ratio 

1 : fl-^J^ X 2-1037. ^ 

The augmentation in narrow seas will be small, but in the Atlantic Ocean 
the augmenting factor must agree pretty well with that which I now 
compute.' 

With the previous numerical values we have og/Zi (which is inde- 
pendent of h) equal to '1421, and 1 — uqIJi = '8579 = i very nearly. 

Thus the long-period tides may px'obalDly undergo an augmentation at 
the coasts of the Atlantic in some such ratio as 6 to 7. 

The influence of this kind of elastic yieldiilg is antagonistic to that 
reduction of apparent tide, which must result from an elastic yielding of 
the earth's mass as a whole. 

The reader will probably find it difEculfc to estimate what degree of 
jn'obability of correctness there is in the conjectural value of the rigidity, 
which has been used in making the numerical calculations in this paper. 
The rigidity has not been experimentally determined for many substances, 
but a great number of experiments have been made to find Young's 
modulus. Now, in the stretching of a bar or wire the comj^ressibility 
plays a much less important part than the rigidity, and the formula for 
Young's modulus shows that for an incompressible elastic solid the 
modulus is equal to three times the rigidity.^ Hence a third of Young's 
modulus will form a good standard of comparison with the assumed 
rigidity, namely, 3 X 10** grammes weight per square centimeter. The 
following are a few values of a third of Young's modulus and of rigidity, 
taken from the tables in Sir William Thomson's article on Elasticity'' in 
the ' Encyclopa3dia Britannica.' 

Materiil ■^ third of Young's mod. and rigidity in 

terms of lO^ grammes weight per sq. cm. 

Stone About 1-2 

Slate About 3 to 4 

Glass Kigidity 1-5 to 24 

Ice 4-7 

Copper 4 and rigidity 4-0 to .5-4 

Steel 7 to 10 and rigidity 8-4 

It will be observed that the assumed rigidity 3 is probably a pretty 
high estimate in comparison with that of the materials of which we know 
the superficial strata to be formed. 

It is shown, in another paper read before the Association at this 
meeting, that the rigidity of the earth as a whole is probably as great as 
that of steel. That result is not at all inconsistent with the probability 
of the assumption that the upper strata have only a rigidity a little greater 
than that of glass. 

_ ' It has been pointed out to me since this meeting, by Sir William Thomson, that 
this kind of augmentation of apparent tide vfill only hold true with certain distribu- 
tions of land. 

2 Thomson and Tait's Met. Phil. § 683. 

» Also published separately by Black, Edinburgh. 



ON THE MEASUKEMENT OF THE LUNAR DISTURBANCE OF GRAVITY. 119 



3. On Gravitational Observatories. 

In the preceding sections estimates have been made of the amount 
of distortion -which the upper strata of the earth probably undergo, 
from the shifting weights corresponding to barometric and tidal oscil- 
lations. These results appear to me to have an important bearing on the 
probable utility of gravitational observatories. 

It is not probable, at least for many years to come, that the state of 
tidal and barometric pressure, for a radius of 500 miles round any spot 
on the earth's surface, will be known with sufficient accuracy to make 
even a rough approximation to the slope of the surface a possibility. 
And were these data known, the heterogeneity of geological strata would 
form a serious obstacle to the possibility of carrying out such a computa- 
tion. It would do little in relieving us from these difficulties to place the 
observatory at the bottom of a mine. 

Accordingly the prospect of determining experimentally the lunar 
disturbance of gravity appears exceedingly remote, and I am compelled 
reluctantly to conclude that continuous observations with gravitational 
instruments of very great delicacy are not likely to lead to results of any 
great interest. It appears likely that such an instrument, even in the 
most favourable site, would record incessant variations of which no satis- 
factory account could be given. Although I do not regard it as probable 
that such a delicate instrument should be adopted for regular continuous 
observations, yet, by choosing a site where the flexure of the earth's 
surface is likely to be great, it is conceivable that a rough estimate might 
be made of the average modulus of elasticity of the upper strata of the 
earth for one or two hundred miles from the surface. 

These conclusions, which I express with much diffidence, are by no 
means adverse to the utility of a coarser gravitational instrument, capable, 
let us say, of recording variations of level amounting to 1" or 2". If 
barometric pi-essure, tidal pressure, and the direct action of the sun and 
moon, combined together to make apparent slope in one direction, then 
at an observatory remote from the sea-shore, that slope might perhaps 
amount to a quarter of a second of arc. Such a disturbance of level 
would not be important compared with the minimum deviations which 
could be recorded by the supposed instrument. 

It would then be of much value to obtain continuous systematic 
observations, after the manner of the Italians, of the seismic and slower 
quasi-seismic variations of level. 

I venture to predict that at some future time practical astronomers 
will no longer be content to eliminate variations of level merely by taking 
means of results, but will regard corrections derived from a special in- 
strument as necessary to each astronomical observation. 



120 REPORT— 1882. 



Report of the Covimittee, consisting of Professor Dewar, Dr. 
Williamson, Dr. Marshall Watts, Captain Abney, Mr. Stoney, 
Professor Hartley, Professor McLeod, Professor Carey Foster, 
Professor A. K. Huntington, Professor Emerson Reynolds, Pro- 
fessor Reinold, Professor Liveing, Lord Eayleigh, Dr. Schuster, 
and Professor W. Chandler Roberts {Secretary), appointed for 
the purpose of reporting tipon the present state of out Know- 
ledge of Spectrum Analysis. 

The Genesis of Spectra. By Dr. Schuster. 

It is the ambitious object of Spectroscopy to study the vibrations of 
atoms and molecules in order to obtain what information we can on the 
nature of the forces which bind them together. The vibrations we know 
must be of a very complicated nature, yet it is natural that not many 
years after Spectrum Analysis was raised to the rank of a science by the 
labours of Kirchhoff and Bunsen attempts were made to discover a law 
in the apparent irregularity with which different lines of the same element 
are distributed over the spectrum. If an atom can vibrate in more ways 
than one, it is certain that some connection must exist between the 
different periods, and this connection we may attempt to find out by trial. 
Or we may speculate on the causes which produce such vast differences 
in the chemical properties of some of the elements, while other elements 
have properties which resemble each other to an equally marked degree. 
We may be led on by such speculations to try whether we can trace any 
similarity in the periods of vibration of molecules which have similar 
chemical properties, or we may endeavour to classify the elements accord- 
ing to their spectra, and see whether such a classification would divide 
the elements into groups agreeing with those into which they have been 
divided by means of their chemical and physical behaviour. 

When different elements combine together the vibrations of the com- 
pound molecule are not obtained by the simple addition of the periods of 
the elements. The spectrum of a molecule is entirely distinct from that of 
its elements, and we may well ask the question whether we can trace in 
the spectrum of the compound the influence of the different atoms com- 
posing it. Thus, for instance, we might trace some relationship between 
the spectra of the oxides, bromides, chlorides, or iodides of a metal and 
that of the metal itself, or we may in the absorption spectrum of a salt 
trace one part to the influence of the base, the other to the influence of 
the acid. Such and similar questions have been raised and have been 
partially answered. But we must not too soon expect the discovery of 
any grand and very general law, for the constitution of what we call 
a molecule is no doubt a very complicated one, and the difficulty of the 
problem is so great that were it not for the primary importance of the 
result which we may finally hope to obtain, all but the most sanguine 
might well be discouraged to engage in an inquiry which, even after many 
years of work, may turn out to have been fruitless. We know a great 
deal more about the forces which produce the vibrations of sound than 
about those which produce the vibrations of light. To find out the 
different tunes sent out by a vibrating system is a problem which may or 
may not be solvable in certain special cases, but it would baffle the most 



ON OUR KNOWLEDGE OF SrECTBDM ANALYSIS. 121 

skilful mathematician to solve the inverse problem and to find out the 
shape of a bell by means of the sounds which it is capable of sending 
out. And this is the problem -which ultimately spectroscopy hopes to 
solve in the case of light. In the meantime we must welcome with delight 
even the smallest step in the desired direction. 

It is the object of the present report to bring together the various 
attempts which have been made to trace a connection either between the 
vibrations of the same body, between those of different compounds of the 
same body, or finally between the vibrations of similarly constituted bodies. 

I. Comiection hetiveen the different periods of Vibration of one Molecide. 

In some acoustical systems the difiTerent periods of vibration are con- 
nected together by means of a very simple law, and it was a natural idea 
to trace the same law if possible in the luminous vibrations of molecules. 
If the law holds good the periods of vibrations or the lengths of the 
waves of light sent out by molecules ought to be in the ratio of small 
integer numbers. The first published attempt to trace such a connec- 
tion is due to Lecoq de Boisbaudran, who investigated the spectrum of 
nitrogen' with special reference to this point. The spectrum in question, 
which is the one appearing at low temperatures, is made up of two sets of 
bands, one reaching fi'om the red into the green, and one reaching from 
the green into the violet. Lecoq de Boisbaudran tried to show that 
each band of the second set had a wave-length which was in the ratio of 
three to four, with a corresponding band of the first set. The author 
had, however, only a one prism spectroscope at his disposal, and the wave- 
lengths as determined by him could not possibly possess that accuracy 
which is necessary for an investigation of this nature. The more accurate 
measurements of Thalen do not bear oat Lecoq's result. Thus, for 
instance, two bands, 5064 and 6752, according to Lecoq, are nearly in the 
required ratio ; if the agreement was perfect the latter number ought to 
be 6748 ; but Thalen, though giving to the green band a number agreeing 
fairly well with Lecoq's, puts the red band at 6786, differing very con- 
siderably from 6754, the required value, if Thalen's measurement for 
the green band is used. The other coincidences pointed out by Lecoq 
are similarly disproved by more exact measurements. Inquiries such as 
those attempted by Lecoq can only be conducted with advantage when 
we have measured to the highest degree of accuracy which we can 
obtain in our best instruments, and many of the apparent harmonic ratios 
which at one time were thought to hold good had to give way when sub- 
jected to a severer test. Mr. Johnstone Stoney,^ realising this fact, 
has, however, pointed out one set of harmonic ratios which seems to hold 
good to a high degree of accuracy. We know of folir hydrogen lines in 
the visible part of the spectrum, and three of these are found to be in the 
ratios of 20 ; 27 : 32. The wave-lengths of these lines are amongst 
those best determined by Angstrom, and they were corrected by Mr. 
Stoney for atmospheric refraction. The following table exhibits the very 
remarkable coincidence. 

Table I. 

Observed Wave-length Calculated Values Differences 

h = 4102-37 . i X 131277-14 = 4102-41 . + 004 

F = 486211 . 'J^ X 131277-14 = 4862-12 . + 0-01 

C = 6563 9.^5 . -'- X 131277-14 = 6563-86 - -0 

' C. R. Ixix. p. 694 (1869). « Phil. Mag. xli. p. 291 (1871). 



122 



KEPOKT — 1882. 



A few years ago Dr. Hnggins succeeded in obtaining photographs of 
ten ultra-violet lines observed in the spectra of stars, which in the visible 
part give chiefly the hydrogen lines. These ultra-violet lines are most 
likely all due to hydrogen, and we know that this is the case with the 
four least refrangible ones. Mr. Johnstone Stoney has pointed out 
several harmonic ratios connecting them together ; the hydrogen line Hy 
near G, for instance, has a wave-length which is very nearly in the ratio 
of 35 : 32 with the one which is nearly coincident with the solar line H.' 

Mr. Johnstone Stoney ^ has also examined the absorption spectrum of 
chlorochromic anhydride. The bands of that spectrum seem to be dis- 
tributed with remarkable regularity. Mr. Stoney considers them to be 
all harmonics of one fundamental vibration. The measurements do not, 
however, seem to possess that degree of accuracy which is desirable, and 
can be obtained by our present methods. We must, therefore, suspend 
our judgment for the present on the reality of the coincidences pointed 
out by Mr. Stoney. Other writers, as, for instance, Soret,^ have fi'om 
time to time drawn attention to harmonic ratios in various spectra, and 
the author of this report'' has during the last ten years collected a lai-ge 
quantity of material bearing on the question. The results have, on the 
whole, not been favoui-able to the theoiy of harmonic ratios. In an}^ 
spectrum containing a large number of lines it is clear that, owing to 
accidental coincidences, we shall always be able to find ratios which agree 
very closely with the ratios of small integer numbers. It is only by 
means of a systematic investigation that we can find out whether these 
coincidences are due to any real cause. We must, by means of the theorj- 
of probability, calculate the number of the coincidences which we might 
expect to find on the supposition that the lines are distributed at random 
throughout the whole range of the visible spectrum. If on calculating 
out all fi-actions which can be formed in a spectrum by any pair of lines 
the number of ratios agreeing within certain limits with ratios of integer 
number greatly exceeds the most probable number, we should have reason 
to suppose that the lines are not distributed at random, but that the law 
suggested by Messrs. Lecoq de Boisbaudran and Stoney is a true one. 
The following two tables exhibit the results of an investigation which has 
been conducted on these lines. 



Table II. 



Element 


Number of 

Fractions 


Mean Value of 
Katies 


P=± 


Magnesium 

Sodium .... 
Copper .... 
Barium .... 
Iron 


18 

40 

101 

303 

10404 


■2626 
•2399 
•2430 
•2592 
•2513 


•0229 
•0154 
•0097 
■0056 
•0010 


Mean . 


10866 


•2514 


— 



' A photograph taken hy Captain Abney shows conclusively, as lias already been 
pointed out by Vogel, that the hydrogen line is a little less refrangible than H, and 
it is very likely coincident -ndth the line 3969 ? which, according to Young, falls 
within the broad shadow of H, and is always present in the chromosishere. 

2 Phil. Mag. xlii. p. 41 (1871). ^ Phil. 3Iag. xlii. p. 464 (1871). 

* Proc. Roy. Soc. xxxi. p. 337 (1881). 



ON OUR KNOAVLEDGE OF SFECTEUM ANALYSIS. 



123 



For the full explanation of Table II. we must refer to tbe paper 
which has already been quoted. The second column gives the number 
of fractions investigated for each element. The third column gives a 
number which ought to be nearly '25 (probably within the limits of the 
values of the fourth column), if the lines are distributed at random aud 
decidedly smaller than this niimber if the law of harmonic ratios is true. 

It will be seen that three out of the five elements considered, 
including the two containing the greatest number of lines, give a mean 
value greater than '25, and that in the two remaining cases the number, 
though smaller than '25, falls within the limits into which we must 
expect it to fall, on the supposition of a distribution at random. 
Table III. shows the results of a more detailed examination of the iron 
spectrum, over 10,000 fractions having been calculated and compared with 
ratios of integers smaller than 100. In order to calculate the number of 
coincidences which we might expect on the theory of probability, the 
limits had to be fixed within which we may consider a coincidence to 
have taken place. These limits must of course depend on the accuracy 
which we assign to the measurements of the lines. The results were 
worked out for two different limits, which were ± '0000505 and ± -0000755. 
When, therefore, two lines had j^eriods the ratio of which fell within the 
indicated limits of some ratio of two integer numbers smaller than 100, 
this was called a coincidence. In Table III. the columns headed ' Observed ' 
and ' Calculated ' give the number of these coincidences as actually found, 
and as calculated from the theory of probability. In the first row all 
fractions were taken into account the denominator of which is smaller 
than 10 ; in the second row the denominator is between 10 and 20, and so 
on for the other rows. 

Table III. 







Limits, ± -0000505 


Limits, ± -0000755 




Observed 


Calculated 


Observed 


Calculated 


0-10. 
10-20 . 
20-30 . 
30-40 . 
40-50 . 
50-60 . 
60-70 . 
70-80 . 
80-90 . 
90-100 




48 
180 
329 
478 
625 
777 
886 
924 
667 
253 


52 
206 
363 
521 
679 
837 
968 
896 
629 
241 


64 

250 

469 

664 

912 

1163 

1318 

1337 

989 

393 


77 

308 

544 

779 

1015 

1251 

1447 

1340 

•940 

361 


Total . 


5167 


5392 


7559 


8062 



The result seems, again, decidedly against the theory of harmonic 
ratios. For all fractions with denominator smaller than 70 the calculated 
coincidences are in excess of the observed ones. There seems, however, 
to be a greater number of ratios than we should expect which agree 
nearly with fractions the denominators of which lie between 70 and 100. 

If we compare the results given for the two different limits we find 
that the smaller limit gives results decidedly more favourable to the 
theory than the larger ones ; and this is an important fact which cannot 



124 



EEPOET 1882. 



be left out of account. For the full discussion of it we refer to the 
original paper, and only quote, in conclusion, the summary of results 
obtained : — 

1. There is a real cause acting in a direction opposed to the law of 
harmonic ratios, so far as fractions formed by numbers smaller than 70 
are concerned. 

2. After elimination of the first cause a tendency appears for fractions 
formed by two lines to cluster round liarmonic ratios. 

3. Most probably some law hitherto undiscovered exists which in 
special cases resolves itself into the law of harmonic ratios. 

It must be remarked, however, that these conclusions must stand at 
present on the evidence of the iron spectrum alone, and it is not im- 
possible that the regularities which have been discovered are due to 
accident. We can at present only say that the investigation, as far as it 
has gone, seems to point to the above conclusions. 

There is one fact which points very strongly to another yet un- 
discovered law which rules over the distribution of lines in spectra. It is 
often observed that the spectrum of some body contains two or three 
lines in close proximity, forming a characteristic group. Such doublets 
or triplets are often repeated several times in the spectrum ; yet, though 
we might expect, if the harmonic law was true, to find some simple rela- 
tions connecting the periods of these sets, such is not the case. The lines 
of sodium, for instance, are all double. In the set of lines given by 
Thalen the components approach each other as we pass to the more 
refrangible end of the spectrum more rapidly than they would if the 
lines were connected by the harmonic law. In the following table the 
wave-length of the least refrangible of each set of sodium lines is given, 
together with the distance of the two components. In addition to the 
pairs observed by Thalen, one pair in the ultra-red, photographed by 
Abney, and one pair in the ultra-violet, photographed by Cornu, ai-e 
given. 





Table IV. 




8199 


12 


Abney 


61600 


5-8 


Thalen 


5895-0 


6 


Thal&n 


5687-2 


5-8 


Thalen 


5154-8 


2-3 


Thalen 


4982-5 


. Not resolved . 


Thalen 


3301-2 


0-4 


Cornu 



Professors Liveing and Dewar' have observed some additional sets of 
double sodium lines, but the distance between the components of each pair 
does not seem to follow any law. 

The spectrum of potassium as observed by Liveing and Dewar^ 
contains, when the metal is heated in the electric arc, five groups of 
lines, each containing four lines. Though, roughly speaking, the lines 
of each set are the nearer together the shorter the wave-length, of the 
set, there seems to be no general and well-defined law. 

The most remarkable perhaps of all the groups of lines observed in 
the spectra of metals are the magnesium triplets. The well-known set of 
lines in the green is repeated three times in the ultra-violet ; but Table V. 



' Proo. Boy. Soc. xxiv. p. 398 (1879). 



' Ibidem. 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 



125 



shows that the resemblance is only a general one, and that the relative 
distances vary considerably in each set. 

Table V. 



Wave-len^'th of least 
refranyible line 


Distance from first to 
second line 


Distance from second 
to third line 


Observer 


5183-1 
3837-6 
3334-2 
3095-6 


10-9 
6-2 

4-2 
37 


53 
2-4 
3-0 
1-9 


Angstrom 
Cornu 

5» 



Tt -will be noticed that the groups come nearer and nearer together as 
they approach the violet, and that also the lines in each group are the 
closer together the more refrangible the set. Roughly speaking, the 
distance between the first and second line of each set is proportional to 
the square of the wave-length ; in order that this relation ought to hold 
rigidly, these distances for the ultra-violet sets ought to be respectively 
7'5, 4-5, 3-9. Such a relation ought to hold if the lines are successive 
harmonics of one fundamental vibration, according to Stoney's supposition. 

The fact that successive lines which belong to one vibrating system 
come nearer and nearer together as they approach the violet or ultra- 
violet end of the spectrum seems to be a pretty general one, and is well 
exemplified by the system of hydrogen lines which Huggins found in the 
star spectra. Table VI. gives the wave-lengths of the lines and their 
differences. 





Table VI. 




Hydrogen 


Solar 


Wave-length 


Difference 


Ha 


C 


6561-8 




Hj8 


F 


4860-6 


1701-2 


H7 


NeaxG 


4340-1 


502-5 


H5 


h 


4101-2 


238-9 


m 


Near H 


3969 


132-2 


HC 




.3887-5 


81-5 


Hr, 




3834 


535 


H9 




3795 


39 


H. 




3767-5 


27-5 


Hk 




3745-5 


22 


H\ 




3730-1 


15 5 


B^ 




3717-5 


12-5 


Hv 




3707-5 


10-0 






3699 


8-5 



Huggins calls the line Hf , a and continues with tlie alphabet towards tbe ultra-violet. This designation 
was chosen independently of the fact that the lines probably belonged to hydrogen. As the red hydrogen 
line usually is called Ha, we have continued the same nomenclature towards the ultra-violet. Hence the 
discrepancy with Huggins' designation. 

It has been pointed out by Johnstone Stoney that the second dif- 
ferences sho".v greater irregularities than can be accounted for by errors 
of observation, and that therefore the system of lines does not altogether 
lie on a smooth curve when plotted down with wave-lengths as ordinates, 
the ordinates lying at equal intervals of each other. Nevertheless the 
fact that these lines approach each other rapidly, making up a fluting 
on a large scale, and that generally characteristic groups when repeated 



126 



REPORT— 1882. 



several times come nearer and nearer together towards the ultra-violet, 
while at the same time the members of each group also approach, is very 
suo-crestive, and promises to furnish a safer basis for future research than 
the hypothesis of harmonic ratios. As another example illustrating the 
same fact, we may mention the absorption spectrum of iodine, where the 
distance of fluted bands of each set decreases with the wave-length. 

There is one more fact which ought to be mentioned. The fluted 
bands in spectra are often at fairly equal intervals from each other, 
but a curious change and transformation seems sometimes to occur. 
Fig. 1 is not intended to represent any particular spectrum, but simply 
to represent this transformation ; to the left a series of bauds are seen 
which have been denoted by I,, lo, &c. ; but to the right of I4 springs 
up another faint band, II,, which, being repeated, gradually gains in 
intensity until finally, by the side of Ilg, the band of the first series is no 
longer visible. 

A third series of bands, III,, III2, &c., springs up again to the 
right of the second series, and in its turn overpowers it in intensity. 
Those who are familiar with fluted band specti'a will easily call back to 
their minds the single bands like I,, the bands with weak companion 
like I4, or the double and treble bands like I7 or I9. Thalen has 



Fig. 1. 




2 



a i 



j^m, j^u^ l^n^ ijH^ J^jr^m, IsH^, J,^,m^ u^^ 



pointed out how the absorption spectrum of iodine is composed of several 
such overlapping spectra. The bands in this case shade off" towards the 
red, and the additional bands always spring up towards the violet. 
The bands approach each other very rapidly as they approach the violet 
end. The diffei-ences between corresponding bands of the second series 
are always smaller than between those of the first series, so that the 
distance between two adjacent bands of the first and second series be- 
comes larger towards the red ; the same holds good for the other series. 
Mr. Lockyer has noticed in his jjhotographs of the spectrum, which appears 
in the electric arc and seems to be due to nitrocarbon, that the least re- 
frangible of the ultra-violet bands does not seem to correspond with the 
least refrangible, but with the second band of the violet series, so that here, 
apparently, a similar change has taken place, an additional band having 
sprunf up in the least refi'angible side. It is much to be desired that 
such changes should be carefully examined in each case, as they may 
lead to most valuable results. 

The tendency to form fiutings is very remarkable. We have first the wide 
fluting formed by the hydrogen lines ; we have next the narrow flutings 
of band spectra, and this again, as in the case of iodine gas, approaching 
each other indefinitely as they go towards the violet, seems to form a 
fluting of the second order — a fluting of flutings. In the overlapping 
bauds of different series we may even recognise perhaps flutings of the 
third order. 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 127 

II. Belation of the Spectrum of an Element to tJiat of its Compounds. 

There is perhaps no other inrestigation connected with molecular 
vibrations which is of greater intei-est than that which tries to trace the 
connection between the spectrum of an element and that of its compounds. 
It was at first considered, as has already been mentioned, that an element 
preserved its spectrum when entering into combination, so that, for 
instance, the oxide of a metal would only show the metallic lines except in 
so far as oxygen lines might be visible. This idea had to be given up, but 
the absorption spectra of fluids were considered at first to be evidence in 
favour of the assumption of permanence of the spectrum of an element 
when combined with others. AV"e owe the first systematic investio-ation 
on this point to Dr. Gladstone,' who examined the absorption spectra of 
the solution of salts, each constituent of which was coloured. He came 
to the conclusion that, generally, but not invariably, the following law 
held good : ' When an acid and a base combine, each of which has a 
difierent influence on the rays of light, a solution of the resultino- salt 
will transmit only those rays which are not absorbed by either, or in 
other words, which are transmitted by both.' 

Thus, for instance, chromic acid in solution cuts off the more re- 
frangible half of the spectrum, admitting only the blue rays near F in 
thin solutions ; but they transmit the less refrangible half perfectly. 
This characteristic absorption of chromic acid remains when the acid 
is combined with such bodies as copper, nickel, ferric oxide, uranium, 
potash, and chromium ; but the salts formed by combination with the 
three first-mentioned bodies show also their own influence when combined 
with chromic or other acids by cutting off, as in copper and nickel, part 
of the red end of the spectrum, or extending, as in ferric oxide, the' blue 
absorption into the green. The characteristic absorption bands of uranium 
salts are in the blue. As the chromic acid cuts off the blue, chromate of 
uranium will not show the bands, but only a general absorption in their 
stead. The potassium salts are colourless when combined with colourless 
acids, and chromate of potash shows therefore the same spectrum as 
chromic acid. Chromate of chromium forms an exception to the rule 
for though the absorption peculiar to chromic acid exists, the absorption 
visible in ordinary chromium salts does not appear. Soret^ has confirmed 
Dr. Gladstone's conclusions with regard to the identity of the absorption 
spectraof different chromates. The chromates of sodium, potassium, and 
ammonia, as well as the bichromates of potassium and ammonia, were 
found to give the same absorption spectrum. Kor is the effect of these 
chromates confined to the blocking out simply of one end of the spectrum, 
as in the visible part, but two distinct absorption bands are seen, which 
seem unchanged in position if one of the above-mentioned chromates is re- 
placed by another. These absorption bands show themselves only in weak 
solutions ; the centre of one has a wave-length of about 3610 10"'" metres, 
while the other is wider, and reaches from 2950 to 2440 approximately in 
solutions containing about 0-1 grammes to the litre. From 2220 onwards 
the spectrum is completely blocked out. Chromic acid itself showed the 
bands, but less distinctly, and Soret does not consider the purity of the acid 
sufficiently proved to allow him to draw any certain conclusions from this 
observation. 

' Phil Mag. xiv. p. 418 (1857). 

- JiiMwthiquL' rnivemdle Arch. So. Ph. Ixi. p. 322 (1878). 



128 REPORT— 1882. 

Erhard' bas examined the absorption spectra of some salts in which 
chromium plays the part of a base. It may be said as a general rule that 
these salts absorb the yellow and yellowish-greeu and also the violet end 
of the spectrum, transmitting the blue ; the exact position of the maxi- 
mum of absorption, however, and the intensity of the absorption band, 
varies considerably with different salts, and even for the same salt with 
different temperatures, and the results are complicated by the fact that 
heating the salts produces a permanent alteration in the absorption. The 
insoluble chloride of chromium shows a behaviour differing from that of 
the other chromium salts. It transmits the yellow and more of the violet 
than the other salts. Some of the solid crystals of various chromium 
salts show fine absorption bands in the red which can also be traced in 
some of the solutions. There is therefore a general resemblance in the 
absorption of different chromium salts, but no identity. 

Dr. Gladstone has also examined the eifect of chlorine, bromine, 
and iodine when combined with different metals. The bromides of gold, 
platinum, palladium, and potassium give a spectrum which is identical 
with that of bromine water ; the same applies to a concentrated solution 
of the bromide of copper, which in addition shows the red absorption 
characteristic of copper. A dilute solution of bromide of copper shows, 
however, no absorption which can be traced to the bromine. Similar 
results were obtained with the chlorides and iodides. In pointing out 
that it is generally though not universally true that a base or an acid 
retains its absorptive properties in different combinations, Dr. Gladstone 
draws attention to the remarkable exception of ferric ferrocyanide, which 
when dissolved in oxalic acid transmits blue rays in great abundance, 
though the same rays are generally absorbed both by ferrocyanides and 
by ferric salts. 

Nitric acid and the nitrates of transparent bases such as potassium, 
sodium, and ammonia show spectra, according to Soret, which are not 
only qualitatively but also quantitatively identical ; that is to say, a 
given quantity of nitric acid in solution gives a characteristic absorption 
band of exactly the same width and darkness whether by itself alone 
or combined with a transparent base. It also shows a continuous absorp- 
tion at the most refrangible side, beginning with each of the mentioned 
salts at exactly the same point. The ethereal nitrates,^ however, give 
different results. 

Messrs. Hartley and Huntington have by photographic methods 
examined the absorption spectra of a great number of organic compounds. 
As their researches have already been referred to at length in these 
reports,' by one of the authors, we need at present only mention one or 
two of the results which most interest us from our present point of view. 
The normal alcohols were found to be transparent for the ultra-violet 
rays, the normal fatty acids less so. In both cases an increased number 
of carbon atoms increases the absorption at the most refrangible end. 
The fact that benzene and its derivatives are remarkable for their power- 
ful absorption of the most refrangible rays, and for characteristic ab- 
sorption bands appearing on dilution, led Professor Hartley to a more 
extended examination of some of the more complicated organic substances. 
He came to the conclusion that definite absorption bands are only pro- 

' Tnavpiral Dissertation, Freiburg (without date). 
[ » Brit. Ass. Be]). 1880, p. 55. ' C. B. Ixxxix. p. 747. 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 129 

duced by substances in -which three pairs of carbon atoms are doubly 
linked together, as in the benzine ring. 

In most of the cases which we have hitherto discussed, the charac- 
teristic absorption of the substance under examination extended over a 
considerable range ; the substance either blocked out altogether a large 
part of the spectrum, or at least showed absorption bands which were 
broad and increased considerably in width with increased concentration. 
When, however, absorption bands become narrower and more definite, 
so that they can be examined under high dispersive powers, their 
behaviour under different circumstances becomes more interesting, for we 
can trace smaller differences and more minute changes. 

It was Bunsen ^ who first showed that such small changes do occur, 
and he thereby led the way in a line of research which promises to be of 
great importance. While examining the absorption spectra of different 
didymium salts, he found that though all the salts showed spectra so 
nearly identical that with the ordinary one prism spectroscope they could 
easily be mistaken for each other, higher dispersive powers revealed some 
very interesting and characteristic changes. His conclusions are best 
quoted in his own words : — 

' Very remarkable and noteworthy are the small alterations in position 
which occur in the minima of brightness in the didymium spectrum, 
dependent upon the nature of the compound in which the metal occurs. 
These changes are too minute to be seen with the small, though seen 
with the large instrument. I have as yet only investigated them com- 
pletely in the case of three didymium salts, viz., the chloride, sulphate, 
and acetate. It is, however, more than probable that the same phe- 
nomena will also be found to occur with other solutions, and with the 
absorption spectra of other crystals of didymium salts, and perhaps may 
be exhibited with the luminous spectra of the oxide and other compounds 

of didymium The atomic weight of didymium chloride is 95-9, 

and that of the anhydrous acetate is 106-9. It will be noticed that all 
the groups of bands in the case of salts under examination approach 
the red end of the spectrum in the order of their increasing atomic 
weights. 

' These differences here noticed in the absorption spectra of different 
didymium compounds cannot in our present complete state of ignorance 
of any general theory for the absorption of light in absorptive media be 
connected with other phenomena. They remind one of the slight and 
gradual alterations in pitch which the notes from a vibrating elastic rod 
undergo when the rod is weighted, or of the change of tone which an 
organ-pipe exhibits when the tube is lengthened.' 

The increased lowering of the vibrations with increasing atomic 
weight of substance combined with the didymium is no doubt very sug- 
gestive, but we cannot at present assign any definite law regulating the 
displacement in different cases. Thus the difference in the wave-length 
between the bands of the chloride and acetate is nearly the same for all 
four bands, but the difference in the wave-length between the bands of 
the chloride and acetate decreases rapidly with decreasing wave-length, 
so that the yellow band is displaced about twice as much as the green 
band, and about three times as much as the bands in the blue. It follows 
from this difference in the behaviour that while the effect of the acetate 
on the yellow band is about seven times as large as that of the sulphate, 

' Phil. Maq. [41 xxxii. p. 177. 

1882. K 



130 REPORT — 1 882. 

the effect is only about twice as large on the bine band. We must refer 
to a note by Messrs. Lawrance Smith and Lecoq de Boisbaudran ' for a 
description of the spectrum of the nitrate of didymium and its changes on 
addition of nitric acid. 

Some interesting cases of this shifting of bands in different compounds 
of the same body have been found by Professor Russell,^ who has sub- 
jected the cobalt salts to a very careful and most instructive examina- 
tion. The anhydrous bromide of cobalt, for instance, was found to give 
an absorption spectrum strongly similar to that of the chloride, but there 
is a general displacement of all the bauds towards the red corresponding 
to the increased atomic weight of bromine. The effect on the most re- 
frano-ible band is stronger tlian that on the other two bands, which is 
contrary to what Bunsen has observed in the case of didymium acetate. 

Captain Abney and Lieutenant- Colonel Testing's paper* ' On the 
Influence of the Atomic Grouping in the Molecules of Organic Bodies on 
their Absorption in the Infra-red Region of the Spectrum,' contains an 
account of investigations undertaken to throw light on the effect of 
chemical combination on molecular vibrations. The importance of the 
results which they have obtained will justify a few verbal quotations. 
They distinguish a general absorption from the least refrangible end, and 
special absorptions which may consist of lines or bands. 

' Reo-ardino- the general absoi'ption we have nothing very noteworthy 
to remar-k, beyond the fact that, as a rule, in the hydrocarbons of the 
same series those of heavier molecular constitution seem to have less than 
those of lighter.' 

This effect agrees with the observation made by Professors Hartley 
and Huntington in the ultra-violet in so far as a general shifting of the 
absorption towards the red seems to take place as the number of carbon 
atoms is increased. Such a shifting would increase the general absorption 
in the ultra-violet, as observed by Professors Hartley and Huntington, 
and decrease it in the infra-red, as observed by Captain Abney and Colonel 
Festino-. Turning their attention next to the sharply defined lines, our 
author's, by means of a series of systematic experiments, come to the 
conclusion that these must be due to the hydrogen atoms in the molecule. 
' A crucial test was to observe spectra containing hydrogen and 
chlorine, hydrogen and oxygen, and hydrogen and nitrogen. 

' We therefore tried hydrochloric acid and obtained a spectrum con- 
taining some few lines. Water gave lines, together with bands, two lines 
beino- coincident with those in the specti'um ot' hydrochloric acid. 

'"in ammonia, nitric acid, and sulphuric acid we also obtained sharply- 
marked lines, coincidences in the different spectra being observed, and 
nearly eveiy line mapped found its analogue in the chloroform spectrum, 
and usually in that of ethyl iodide. Benzene again gave a spectrum 
consisting principally of lines, and these were coincident with some lines 
also to be found in chloroform. It seems then that the hydrogen, which 
is common to all these different compounds, must be the cause of the 
linear spectrum. In what manner the hydrogen annihilates the waves of 
radiation at these particular points is a question which is at present, at 
all events, an open one, but that the linear absorptions, common to the 
hydrocarbons and to those bodies in which hydrogen is in combination 

» C B. Ixxxviii. p. 1167 (1879). '^ Proc. Roy. Soo. xxxii. p. 258 (1881). 

« Phil. Trans, p. 887 (1881, iii.). 



ON OUR KNOWLEDGE OF SrECTRCM ANALYSIS. 131 

witli other elements such as oxygen and nitrogen, is due to hydrogen, 
there can be no manner of doubt.' 

' The next point that required solution was the effect of the presence 
of oxygen on the body under examination, and here we had ample material 
on which to make our observations. It apjaears that in every case where 
oxygen is present, otherwise than as a part of the radical, it is attached to 
some hydrogen atom in such a way that it obliterates the radiation between 
two of the lines which are due to that hydrogen.' . . . ' If more than 
one hydroxyl group be present, we doubt if any direct effect is produced 
beyond that produced by one hydroxyl group, except a possibly greater 
general absorption ; a good example of this will be found in cinnamic 
alcohol and phenyl-propyl alcohol, which give the same spectra as far as 
the special absorptions are concerned. . . . 

' Hitherto we have only taken into account oxygen which is not con- 
tained in the radical ; when it is so contained it appears to act differently, 
always supposing hydrogen to be present as well. We need only refer to 
the spectrum of aldehyde, which is inclined to be linear rather than 
banded, or rather the bands are bounded by absolute lines, and are more 
defined than when oxygen is more loosely bonded.' 

Perhaps the most interesting passage is that which refers to the 
detection o! the radical, and we therefore quote it in full. 

' An inspection of our maps will show that the radical of a body is 
represented by certain well-marked bands, some differing in position 
according as it is bonded with hydrogen, or a halogen, or with carbon, 
oxj-gen, or nitrogen. There seem to be characteristic bands, however, of 
any one series of radicals between 1000 and about 1100, which would 
indicate what may bo called the central hydrocarbon group, to which 
other radicals may be bonded. 

* The clue to the composition of a body, however, would seem to lie 
between A. 700 and \ 1000. Certain radicals have a distinctive absoi'ption 
aboat X 700 together with others about \ 900, and if the first be visible 
it almost follows that the distinctive mark of the radical with which it is 
connected will be found. Thus in the ethyl series we find an absorption 
at 740, and a characteristic band, one edge of which is at 892, and the 
other at 920. If we find a body containing the 740 absorption and a 
band with the most refrangible edge commencing at 892, or with the 
least refrangible edge tei'minating at 920, we may be pretty sure that 
we have an ethyl radical present. So with any of the aromatic group ; 
the crucial line is at 867. If that line be connected with a band we 
may feel certain that some derivative of benzine is present. The benzyl 
group show this remarkably well, since we see that phenyl is present, as 
is also methyl. It will be advantageous if the spectra of ammonia, 
benzine, aniline, and dimethyl aniline be compared, when the remarkable 
coincidences will at once become apparent, as also the different weighting 
of the molecule. The spectrum of nitro-benzine is also worth comparing 
with benzine and nitric acid. We should have liked to have said more 
regarding the detection of the different radicals, but it might seem pre- 
sumptuous on our part to lay down any general law on the results of the 
comparatively few compounds whichwe have examined. In our own minds 
there lingers no doubt as to the easy detection of any radical which we 
have examined, but it will require more energy and ability than we possess 
to thoroughly classify all the different modifications which, may arise. 

k2 



132 EEPORT — 1882. 

'We may say, however, it seems highly probable by this delicate 
mode of analysis that the hypothetical position of any hydrogen which is 
replaced may be identified, a point which is of prime importance in 
organic chemistry. 

' The detection of the presence of chlorine or bromine or iodine in a 
compound is at present undecided, and it may well be that we may have 
to look for its effects in a different part of the spectrum. The only trace 
we can find at present is in ethyl bromide, in which the radical band 
about 900 is curtailed in one wing. The difference between amyl iodide 
and amyl bromide is not sufficiently marked to be of any value.' 

If we compare the results obtained by Captain Abney and Colonel 
Festing with those arrived at by Professor Russell and others in the 
visible part of the spectrum, we are struck with the great persistency of 
these infra-red bands and lines. Spectra of different compounds of the 
same body may resemble each other in the visible part, but wherever the 
absorption band or line was sufficiently narrow to be looked at under high 
dispersion some difference made itself apparent, like the one discovered 
by Bunsen in the case of didymium compounds. These differences are 
generally sufficiently large to be noticed even with one prism when proper 
care is taken. It would seem very remarkable if atoms could enter into 
combination with their vibrations unchanged by the chemical force; though, 
of course, the change maybe more apparent in some parts of the spectrum 
than in others. Whether the infra-red bands are not affected at all, or 
whether only the change is so small that it has not as yet been dis- 
covered, is an open question. Oar prismatic methods would, of course, 
discover more easily a shift in the visible part than in the infra-red, but 
Captain Abney and Colonel Festing used three prisms, and there can be 
no doubt that if the displacements had been of the same order of magni- 
tude as they are with the didymium, and especially the cobalt salts, they 
could not have escaped detection. 

Alexr. Mitscherlich ' was the first to prove that compound bodies, 
when luminous, have a spectrum of their own, and do not simply show the 
supposed spectra of the elements. He followed up this important dis- 
covery by investigating the spectra of different compounds of the same 
metal, and he could not fail to be struck with the similarity which such 
spectra often present. 

Many, for instance, will instantly recognise the spectrum of the oxide 
or chloride of calcium as that of a calcium compound, without being even 
aware that these spectra present certain well-marked differences. Com- 
paring together the spectra of the fluoride, chloride, bromide, and iodide 
of barium, as they appear on Mitscherlich's map, we detect at once a 
strong similarity ; we seem to have one spectrum shifted towards the red 
with increasing atomic weight of the metalloid. At the same time the 
least refracted bands seem to be most affected and, as a consequence, the 
bands appear nearest together in the fluoride and farthest apart in the 
iodide. In the calcium and strontium salts we notice the same increase 
of wave-length in corresponding bands with increasing atomic weight, 
bat with these two metals the most refracted bands are most affected, so 
that the bands are the nearer together the higher the atomic weight. 
Mitscherlich tried to find a numerical expression for these relations, and 
he expresses the law which, according to his observation, represents the 
facts, in the following way : — 

' Pogg, Ann. cxvi. p. 499. 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 



133 



' It follows that in the haloid compounds of barium (excepting the 
fluoride) the distance between corresponding spectral lines is directly- 
proportional to the atomic weight, and that in the haloid compounds of 
calcium and strontium (excepting again the fluoride) these distances are 
inversely proportional to the atomic weights. Further, that there is such 
a point in the spectrum of each metal that the bands keep their relative 
distances from it in the diflerent compounds. Here also we must except 
the fluorides.' 

Mitscherlich's measurements were not sufficiently accurate to prove 
his statement satisfactorily, but we can easily test it by means of the 
more exact measurements of Lecoq de Boisbaudran, who has carefully 
mapped the spectra of the chloride, bromide, and iodide of barium. A 
glance at Fig. 2, which represents these spectra according to Lecoq's 

Fis:. 2. 



Barium 
chloride 



Barium 
bromide 



Barium 
iodide 



-r 1 1 1 f I 1 1 1 1 1 1 1 1 I 

■»7 4a 43 so SI S2 5J 5* SS 56 57 58 S9 SO 6/ 

measurements will show their similarity. In Table VII. the first column 
gives the wave-length of the bands seen in the spectrum of the barium 
chloride. The strongest band is denoted by o, and the order of the 
Greek letters gives the order of the intensity. In the second column a 
comparison is given between the observed wave-lengths of the spectrum 
of barium bromide, and the same wave-lengths calculated on Mitscher- 
lich's supposition that the distance between the lines is proportional to 
the atomic weight of the compound. The band a is taken as starting 
point. The third column gives the calculated value for the band jo of 
barium iodide, which compound only shows a and /3. 



Table YII. 



Barium Chloride 


Barium Bromide 


Barium Iodide 


Observed 


Calculated 


Observed 


Calculated 


Observed 


7 5313 
a 5242 
5, 5205 
5, 5171 
$ 5136 
6 5064 


5459 

5303 
6267 
6207 
5105 


5410 
5358 
5304 
5249 
' 5206 
5149 


5408 


5607 
5376 



It will be seen that for the four central bands of barium bromide the 
agreement seems good, but the two outer bands do not follow the rule, 



134 REPORT— 1882. 

for the distance between a and y and between /3 and e is actaally larger 
in the chloride than in the bromide, contrary to what holds for the re- 
maining bands. In the case of barium iodide, Mitscherlich's rule cannot 
be said to hold. 

A more satisfactory agreement could be obtained if the distances 
between the corresponding bands were made to depend, not on the 
atomic weights of the compound, but on the atomic weights of the 
metalloid in the compound ; but no object is gained at present by giving 
such rules before sufficient material has been accumulated to prove or 
disprove them. The second part of Mitscherlich's rule, which regulates 
the displacement of the bands in the different compounds, does not stand 
very well when tested by Lecoq's measurements ; the band /3 of barium 
iodide, for instance, ought, according to it, to be at 5356 instead of 5376. 

We ought to inquire whether a connection can be traced between the 
lines of a metal and that of one of its compounds. It would be possible, 
for instance, that the oxide should show its bands chiefly at such places 
at which we find lines in the metallic spectrum, and such a rule might 
be suggested by the examination of the calcium spectrum, which shows a 
characteristic group of lines exactly at the place which is filled by the 
green band of the oxide. No general rule can, however, be given, and in 
some cases even the metallic spectrum seems particularly free of lines in or 
about the place in which we find the oxide bands. There is at present no 
hope whatever of directly connecting the spectrum of a metal and that of 
its compounds, though, as was seen, we may hope to gain an insight into 
the relations of the spectra of such similar compounds as the chlorides, 
bromides, and iodides, which may be supposed to have a similar con- 
stitution. 

Some very interesting changes have been noticed in the position of 
absorption bands when certain colouring matters are dissolved in different 
liquids. We mention the names only of Hagenbach, Kraus, and Kundfc 
as having studied the question in particular cases. Two papers by 
Kundt ' and Claes ^ contain all that is known at present on the subject, 
and it will be sufficient therefore to consider them only. Kundt 
examined the position of the absorption bands of chlorophyll, anilingreen, 
cyanin, fuchsin, chinizarin, and of the colouring matter of the yolk of 
egg when dissolved in a number of liquids. His results are given in 
Table VIII., which is taken out of his paper. The solvents are arranged 
in each column in such order that with the one first on the list the 
absorption band is seen most towards the blue, while the one which 
appears last disjDlaces the band most towards the red. 

In the dissertation published by Dr. Claes we must carefully dis- 
tinguish the experimental from the theoretical part. We have at present 
no reason to doubt the accuracy of his experimental work, and as he 
used solvents and liquids partly diffei-ent from those employed by Pro- 
fessor Kundt, we give his results in Table IX. arranged in the same way 
as Table YIII. We give the results for chlorophyll in two columns ; one 
refers to the absorption baud in the red, the second to the absorption 
bands in the green. Magdala red shows different absorption bands in 
two different sets of solutions, and two columns are therefore also 
necessary. The results obtained with different didymium compounds are 
not tabulated, as they are partly due to a different order of phenomena. 

■ Wied. Ann. iv. p. 34 (1878). » Wied. Ann. iii. p. 389 (1878). 



ON OUR KNOWLEDGE OF SrECXRDJI ANALYSIS. 

Table VIII. 



135 



Chlorophyll 


Anilingreen 


Cyanin 


Fuchsia 


Chinizarin 


Yolk of egg 


Ether 


Methvl-alco- 


Methyl-alco- 


Water 


Methyl-alco- 


Methyl-alco- 




hol 


hol 




hol 


hol 


Aceton 


Aceton 


Aceton 


Methyl-alco- 
hol 


Aceton 


Aceton 


Alcohol 


Alcohol 


Alcohol 


Aceton 


Ether 


Ether 


Amyl-alcohol 


Ether 


Ether 


Alcohol 


Alcohol 


Alcohol 


Chloroform 


Chloroform 


Amyl-alcohol 


Ether 


Amyl-alcohol 


Amyl-alcohol 


Benzine 


Amvl-alcohol 


Liajroin 


Chloroform 


Chloroform 


Ligroin 


Oil of Cassia 


Lia:roin 


Chloroform 


Amyl-alcohol 


Toluol 


Chloroform 


Bisulphide 


Toluol 


Toluol 


Ligroin 


Benzine 


Toluol 


of carbon 














Benzine 


Benzine 


Benzine 


Oil of cassia 


Benzine 




Oil of cassia 


Oil of cassia 


Toluol 


Bisulphide 
of carbon 


Oil of cassia 




Bisulphide 


Bisulphide 


Oil of cassia 




Bisulphide of 




of carbon 


of carbon 


Bisulphide 
of carbon 




carbon 



In a preliminaiy examination,^ Professor Kundt had come to the 
conclusion that solvents displaced absorption bands towards the red in 
the oi'der of their dispersive powers. A look at Table VIII. will show 
that no absolute rule, however, can be given, for the order of the solvents 

Table IX. 



Chlorophyll 


Cyanin 


Chinizarin 


Fuchsin 


Eosia 


Magdala red 


I. 


11. 


I. 


II. 


Ether 


Ether 


Alcohol 


Alcohol 


Water 


Water 


Nitroben- 
zine 


Benzine 


Alcohol 


Alcohol 


Ether 


Ether 


Alcohol 


Alcohol 


Alcohol 


Bisul- 
phide of 
carbon 


Nitroben- 


Benzine 


Benzine 


Turpen- 


Nitroben- 


Turpen- 


Turpen- 




zme 






tine 


zme 


tine 


tine 




Benzine 


Nitroben- 
zine 


Nitroben- 
zine 


Benzine 




Bisul- 
phide of 
carbon 






Turpen- 


Turpen- 


Bisul- 


Nitroben- 




Nitroben- 






tine 


tine 


phide of 
carbon 


zine 




zme 






Bisul- 


Bisul- 




Bisul- 










phide of 


phide of 




phide of 










carbon 


carbon 




carbon 











is difiTerent for different colouring matters. At the same time it is cer- 
tainly remarkable that the liquids of high dispersive powers always 
stand at the bottom of the list, while those of low dispersive powers 
stand high up. Professor Kundt therefore now replaces his old conclusion 
by the less definite rule that ' When a colourless solvent has a considerably 
larger dispersive power than another the absorption band of a colouring 

' Poggendorff, Juhelbaiid. 



136 KEPORT— 1882. 

matter dissolved in it is placed more towards the red.' He divides the 
solvents into four groups. While the order of the liquids within each 
group may change, the second group will always displace the absorption 
band more towards the red than the first, the third more than the 
second, and the fourth more than the third. Dr. Claes, who also remarks 
that the order of the solvents is not strictly that of their dispersive 
powers, suggests a formula which shall correctly represent the position 
of the absorption bands in different liquids. If A. is the wave-length of 
the centre of an absorption band, his equation, when freed from tLe 
sheltering confusion of ornamental variables, runs thus — 

^'-* = "+K^ .... (1) 

In this equation i represents the dispersive constant of the liquid ; 
that is to say, the factor of the inverse square of the wave-length in the 
series which gives the refractive index as a function of the wave-length ; 
and a, /3 are two constants which, according to Dr. Claes, have to be deter- 
mined for each absorption band by means of its position in different 
liquids. Now to ordinary minds the above equation seems simply a 
restricted case of Kundt's original law that the wave-length increases 
with the dispersive power, for we can solve for X^ — h, and this quantity 
must therefore be a constant, which, on the face of it, it is not, as Dr. Claes 
himself takes some pains to prove. Yet our author shows how the same 
law in its new shape can with astonishing accuracy explain facts which to 
most minds show no regularity at all. As it is a point of some importance 
to possess a method of calculation which shall give such small differences 
between observed and calculated values as those obtained by Dr. Claes, we 
may take the trouble to point it out, especially as he might have still 
further reduced these differences had he been more careful in his calcula- 
tions with the two last decimal places. The secret consists in substituting 
in the expression on the right-hand side the observed values of X and then 
calculating the X on the left side. The differences between these two 
values Dr. Claes calls the differences between the observed and calculated 
values of \. It is easy to see how this plan works. "Write A for \^ — h, 
and call the values which A takes in the two special cases L, and L2 ; 
then in the way suggested by the author a and /3 have to be determined in 
terms of L, and Lj, and by substituting these values equation (1) 
becomes 

A = L, -f L2 - M2 .... (2) 

If we write L, + d for the observed value of A we get 

A _ L, = Lo - ^^ - -^^ 

But the difference between A — L, and d being the so-called difference 
between the observed and calculated value becomes - — ^-^ — ^ . 

As the total displacement Lo — Lj between any two bands is small, as well 
as d, this quantity is small compared to d. In other words, as long as 
A, Lj and Lg differ by small quantities, equation (2) must necessarily be true 
to quantities of the same order of magnitude, and any discrepancy must 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 137 

be of the second order of magnitude. It is needless to enter farther into 
the matter, but it is easily seen how fictitious the whole investigation of 
Dr. Claes now becomes. 

Returning for a moment to the general law discovered by Kundt, that 
the displacement of bands depends to a greater extent on the dispersive 
power of the solvent than on any other of its properties, we may, perhaps, 
suggest the way in which such a result might be brought about. The 
refractive index of a liquid does not seem to be directly connected with 
the vibrations of its molecules, for we speak of the refractive index of 
waves which are infinitely long, and connect it with the inductive capacity 
which has nothing to do with vibrations. It is otherwise with the dis- 
persion ; we know that the very colouring matters which are most sensi- 
tive as far as the displacement of bands is concerned, show the so-called 
anomalous dispersion, which only means that the nearness of an absorp- 
tion band causes an abnormally great dispersion at that point. If we are 
allowed to reason backwards and connect a great dispersive power at one 
place with a great coefficient of absorption at some point which is not too 
far removed, we might easily understand how these vibrations would in 
their turn affect the vibrations of the colouring matter and change their 
period. For it is a perfectly general rule that any spectroscopic dis- 
turbance, such as the widening of bands or appearance of high tempera- 
ture lines, is more easily produced by molecules which vibrate in similar 
jieriods than by others,' and a solvent the molecules of which can vibrate 
in similar periods to that of the colouring matter will, no doubt, produce 
a displacement of bands towards the less refrangible regions. It is true 
that the high dispersion of some liquids — such as carbon bisulphide — 
has not been traced to the influence of any specific absorption, but even 
if, as is very likely, the above explanation is not strictly correct, we seem 
to have in the vibrations of the solvent a connecting link between the dis- 
persion of a liquid and the displacement of bands which it is capable of 
producing. On the other hand it is easy to see why no perfectly general 
rule can be given ; for the influence of the solvent will not only depend 
on the vibration of its molecules but also on the closeness of the connec- 
tion between them and the molecules of the colouring matter. If there 
is any great affinity between the solvent and the colouring matter we 
should expect a great influence, and if the two bodies simply mix without 
troubling much about each other we should have no displacement at all, 
or only a very small one. The displacement of bands according to this 
view is due then, in the first instance, to the closeness of the chemical 
relation between solvent and colouring matter ; and, secondly, to the 
similarity of their vibrations. If the dispersive power of a liquid enters 
into the question it can only be owing to the fact that the vibrations of 
the Inminiferous medium and those of the colouring matter are similarly 
affected by the periods in which the molecules of the solvent are capable 
of vibrating. 

It is proved by some experiments made by Professor RusselP that 
the shifting of bands can also be produced by solution in a solid body. 
Professor Russell has proved that when chloride of cobalt is fused together 
with potassic chloride it gives a certain absorption spectrum, which may 
be obtained with small displacements of bands when the potassic chloride 

' Cf. a passage in a lecture by the author of this report before the Koyal 
Institution. 

' Proc. Roy. Soc. xxxii. p. 258 (1881). 



138 REPORT— 1882. 

is replaced by the clilorides of sodium, ammonia, or zinc. The bands 
are nearest the red with potassic chloride, and nearest the blue with zinc 
chloride. 

Before leaving this part of the report, we may just refer to some 
experiments made by Professor Melde ' to decide the question whether two 
coloui'ed liquids have the positions of their absorption bands altered when 
mixed together. He found indeed that snch an effect conld be observed, 
but all his experiments admit of an obvious explanation. To take an 
ideal case, suppose in Fig. 3 the absorption of a liquid for different waves 
of light to be graphically represented by the curve AaB, with a maximum 
at a, and suppose this liquid to be mixed with another whose curve of 
absorption is represented by CD, the simple addition of the two curves 
will produce a third curve CA'5 D with a maximum at b. This maximum 
is obviously not in the same position as before, but takes place at a wave- 
length at which the two tangents to the two original curves are inclined 
equally but in opposite directions. All the somewhat complicated rules 
deduced by Professor Melde are easily explained in this way, and he 
would have observed exactly the same phenomena if he had put his two 
liquids in front of each other instead of mixing them together. 




III. Relations of the Spectra of different Elements. 

Various efforts have been made to connect together the spectra of 
different elements. The attempts in this direction generally assume that 
certain lines in one spectrum correspond to certain lines in another 
spectrum, and the question is raised whether the atom with the higher 
atomic weight has its corresponding lines more or less refrangible. In 
the opinion of the writer of this report no definite judgment can as yet 
be given as to the success of these efforts ; some of the relations traced 
no doubt are interesting and deserve further attention, but most of them 
are far-fetched, and will very probably be proved to have no foundation 
in fact. Lecoq de Boisbaudran* has led the way in these speculations, 
and some of the similarities in different spectra pointed out by him are 
certainly of value. But whether his conclusion, that 'the spectra of 
the alkalies and alkaline earths, when classed according to their refran- 
gibilities, are placed as their chemical properties in the order of their 
atomic weights,' will stand the test of further research, remains to be 
seen. Lecoq begins by comparing together the spectra of potassium 
and rubidium, as well as those of calcium, strontium, and barium. The 
spectrum both of potassium and rubidium begins, when heated up in the 
Bunsen burner, with two red lines ; then follow, in the case of potassium, 

» Poffff. cxxiv. p. 91 (1865), and cxxvi. p. 264. ' C. H. Ixix. pp. 445, 606, 657. 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS, 139 

a group of three yellow rays, four green bands, and a line in the yellowisli- 
green (only visible in tbe spark). In the case of rubidium these are 
replaced by a group of four red rays and four double lines in the yellow 
and green. The spectrum of potassium ends with a violet line, since 
proved to be double, and the spectrum of rubidium, as is known, also 
ends with two violet lines. If we form the ratio of the wave-length of 
the centre of each of the five intermediate groups in rubidium to those 
of the corresponding group in the potassium spectrum, we obtain the 
numbers 1-0G4, 1-065, 1-056, 1-058, 1-063, which numbers are approxi- 
mately constant. The ratio of the middle of the two red rubidium lines 
to the middle of the two red potassium lines is 1-022, and the correspond- 
ing ratio of the violet lines is 1-04. If we accept the fact of corre- 
spondence of these lines we see that the atom with the higher atomic 
weight vibrates more slowly. The weak point of the comparison consists 
at present in the uncertainty as to which of all these lines and bands 
belong to the metal and which to the oxide. We could not of course 
attempt any correspondence between lines of the oxide of one metal and 
the lines of the other metal itself. Similar relations exist, according to 
Lecoq, between the two spectra we have discussed and that of calcium. 
The two blue calcium lines concluding the spectrum are again less 
refrangible than the two corresponding rubidium lines, and at the same 
time they are wider apart. There is, therefore, a progressive change, as 
pointed out by Lecoq, in the behaviour of these blue and violet lines, 
which in every case are truly metallic. In potassium they are very close 
together and in the violet ; in rubidium they are wider apart and less 
refrangible, though still in the violet ; in calcium they are still wider 
apart, and in the blue. If we connect this fact with the similar change 
which, as we have pointed out, sometimes occurs in one and the same 
spectrum, where double and triple lines go closer and closer together as 
they approach the violet, we seem certainly to have a suggestive analogy 
which may serve as the basis for further inquiries. 

We shall only follow Lecoq into his comparison between the spectra 
of the chlorides of the alkaline earths, as his comparison of the metallic 
and oxide lines seems to be uncertain. 

Both the spectrum of the chloride of calcium and that of strontium 
consists of five bands. The differences between the bands of the chloride 
of calcium gradually decrease ; they become more refrangible ; and the 
same holds for the four least refrangible bands of the spectrum of 
strontium chloride. Forming the proportion between the wave-lengths of 
corresponding bands we find that the ratios of the bands of strontium 
chloride to those of the calcium salt are 1-063, 1-065, 1-066, 1-070, 1-071, 
and these ratios are seen to increase gradually with the decrease of wave- 
lengths. The salt with the higher atomic weight vibrates, again, more 
slowly. The spectrum of baz-ium chloride resembles in its general 
arrangement that of the strontium salt, but it has six bands instead of 
five, the central band being apparently broken up into two. Other dis- 
crepancies are noticed on further inspection, and the barium bands, con- 
trary to the rule given by Lecoq, are more refrangible than those of the 
lighter metals. Lecoq gets out of the difiiculty by supposing that the 
barium chloride spectrum which we observe is not the one corresponding 
to that of the sti-ontium and calcium chloride, but that it is its higher 
harmonic, and that we are to look in the ultra-red for the true corre- 
spondence in the barium spectrum. This explanation may be correct, and 



140 BEPORT— 1882. 

DOW that, thanks to Captaiu Abney, we may photograph in the ultra-red, 
we may test its truth ; but we must observe that, if we once allow our- 
selves to take these harmonics to aid, we may arrange all our spectra 
in any order we like, for we need only assume that those which do not 
fit are higher or lower harmonics of the true spectrum. As they stand 
the spectra of the chlorides of barium, strontium, and calcium, though 
showing certain characteristic analogies, do not bear out Lecoq's theory. 

Ditte ' has tried to find an analogy between the spectra of sulphur, 
selenium, and tellurium, and to establish that the spectrum is displaced 
towards the blue as we go from the metalloid to the metal, that is to say, 
from the lighter to the heavier element. An inspection of the spectra in 
question has not led the author of this report to confirm this statement. 
The spectrum of selenium seems more contracted than the spectrum of 
sulphur, but we cannot recognise clearly any displacement towards the 
red or towards the blue. The spectrum of tellurium seems, if anything, 
more to the red than that of the other two metals. 

Messrs. Troost and Hautefeuille ^ have compared the spectra of 
carbon, boron, silicium, titanium, and zirconium, and they also come 
to the conclusion that from the metalloid to the metal the spectrum seems 
progressively to move towards the blue. 

As far as the fii-st three bodies are concerned the relation seems, at 
first sight at any rate, to have some foundation, for we have here to deal 
with three spectra which, on the whole, resemble each other in appear- 
ance, and which seem to be displaced according to the suggested law. 

Ciamician ^ has compared together the spectra of chlorine, bromine, 
and iodine. His experiments seem well conducted, and we therefore give 
his conclusions, reserving, however, every opinion as to the degree of 
certainty with which they have been established. It requires a much 
more careful experimental examination than even Ciamician has given 
to them to arrive at any proof of the reality of these analogies. The 
spectra in question are so variable with density and temperature that we 
cannot at present say whether we have to deal with a superposition of 
different spectra or simply a variation of relative intensity due to tem- 
perature. Some of Ciamician's analogies do not seem, certainly, to be 
very apparent, but the following conclusion is entitled to a place in this 
report :^ 

' The spectrum of vapour of bromine at low pressures becomes the 
more nearly like that of chlorine the smaller the pressure, while the 
spectrum of condensed bromine more nearly resembles the spectrum of 
iodine. Iodine, on the other hand, gives a spectrum resembling that of 
bromine at moderate pressures only ; at very low pressures an analogy 
with the chlorine spectrum takes preponderance over that with the 
bromine spectrum. The spectrum of highly condensed iodine vapour 
cannot well be compared with that of the other two bodies. Chlorine, 
when it is highly condensed, gives a spectrum resembling that of bromine 
at large pressures and of iodine at moderate pressures ; while at low 
pressures the spectrum of chlorine has no analogy to that of the other 
two elements. 

' If we collect together for each body all the lines which appear 
separately under different circumstances, we can establish a complete 
correspondence between the lines of the three complete spectra.' 
• C. R. Ixxii. p. 622 (1871). ^ (j_ j}^ ixxii. p. 620 (1871). 

■' Wie/i. Ber. Ixxviii. (1878). 



ON OUR KNOWLEDGE OF SPECTRUM ANALYSIS. 141 

The complete spectrum of iodine is placed most towards the blue, 
that of chlorine is placed most towards the red end of the spectrum. 

In a subsequent paper Ciamician deals further, and we believe more 
successfully, with the question. He begins by examiuiug the spectra of 
the carbon compounds. The spectrum of cjanogen consists of two sets 
of bands, one in the red and one in the blue ; the bands in the red 
resemble the nitrogen bands, the bands in the blue resemble the carbon 
bands (candle spectrum). Ciamician therefore suggests that the bands 
in the red are due to the nitrogen atoms in the cyanogen molecules, while 
the bands in the blue are due to the carbon within the same molecule. 
There can be no doubt as to the correctness of the resemblance pointed 
out by Ciamician, and the only argument which can be urged against bis 
conclusion is the uncertainty that both sets of bands belong to the same 
compound of carbon and nitrogen. There are some reasons for supposing 
that they are not ; but as yet this is an open question. The spectrum of 
carbonic oxide is very similar to that of the carbon (candle spectrum), as 
has often been shown. 

Ciamician makes a bold use of the division of the cyanogen spectrum 
into two halves, which, as just pointed out, resemble the spectra of nitro- 
gen and carbon respectively. For he thinks that we can divide the 
spectra of some of the elements similarly into two parts, one part re- 
sembling the spectrum of one, the other part resembling the spectrum of 
a second element, and this division he suggests may be due to the fact 
that such an element is really a compound body, wlaich is composed of 
the two elements to whose spectrum its own is analogous. The high 
temperature spectrum of silicium consists of a series of lines. The most 
refrangible half of the lines certainly resembles in its general arrange- 
ment to a marked degree the lines of carbon. The less refrangible lines 
Ciamician believes to resemble some of the oxygen lines, but this analogy 
does not appear very strikingly in the map which accompanies his paper. 
Silicium at low temperatures shows bands which, as pointed out by 
Messrs. Troost and Hautefeuille are very much like the carbon bands. 
Ciamician has also for the first time succeeded in obtaining two 
spectra of boron. Both the band and the line spectrum show a strikino* 
resemblance to the carbon spectra. The line spectrum of aluminium 
resembles in its most refrangible half also that of carbon, while its less 
refrangible half resembles the less refrangible half of silicium. The com- 
plete similarity of the spectra of aluminium and silicium, and that likeness 
of their most refrangible parts with the complete spectra of carbon and 
boron is the most striking analogy which has as yet been pointed out ; 
but it ought perhaps to be added that Ciamician's drawing of the boron 
spectrum does not altogether tally with the account given by Messrs. 
Troost and Hautefeuille. The line spectrum of magnesium also shows a 
likeness to the line spectrum of carbon ; and the carbon bands (candle 
spectrum) resemble certain bands seen in the spectrum of magnesium 
under certain circumstances, which according to Liveing and Dewar 
always involve the presence of hydrogen.' 

' An example may here be given as to the misunderstandings which may arise 
owing to the confusion which reigns at present in spectroscopic nomenclature. 
Messrs. Dewar and Liveing have pointed out the resemblance of the hydrocarbon 
spectrum and the hydrogen-magnesium spectrum (Proc. Boy. Soc. xxx. p. 161, 1880). 
Ciamician writes that he also discovered the resemblance ; but what Ciamician calls 
the hydrocarbon spectrum is an altogether different spectrum, presenting no resem- 



142 EEPORT— 1882. 

The likeness of the spectra of calcinm and strontium to the spectrum 
of magnesium is not so apparent, but Ciamician traces it in taking account 
only of the low temperature lines of strontium and calcium. The complete 
spectra of calcium, strontium, and barium are also homologous according 
to Ciamician — that is to say, we can find in each spectrum groups of lines 
corresponding to each group in the other two spectra. But the comparison 
seems less certain, for in spectra having such a large number of lines a 
little ingenuity will always discover certain likenesses. We do not mean 
to imply that the resemblances pointed out by Ciamician are imaginary, 
but only that spectra containing many lines ought not to be taken as tests. 
The same remarks apply to the remaining groups of elements studied by 
Ciamician, and we therefore only give his conclusions. 

1. The spectra of oxygen, sulphur, selenium, and tellurium are homo- 
logous. Corresponding groups are displaced towards the violet with 
increasing atomic weight. (This last statement seems disproved by 
Ciamician's own drawing in the case of tellurium, for out of 13 gi'oups 
of lines, the 10 last ones are displaced towards the red.) 

2. The spectra of phosphorus, arsenic, and antimony are homologous. 

3. The more refrangible parts of the spectra of the nitrogen group are 
homologous to the more refrangible parts both of the oxygen and of the 
chlorine group. 

4. The less refrangible parts of the spectra of the oxygen group are 
homologous to the less refrangible parts of the spectrum of the calcium 
group. 

The conclusion which Ciamician draws from these facts as to the con- 
stitution of the various elements and the probability of their ultimate 
decomposition lie, fortunately, outside the range of the present report. 

We add to the various facts already mentioned the great similarity 
of the spectra of zinc and cadmium, which has often struck spectro- 
scopists. 

Professors Liveing and Dewar^ have drawn attention to certain re- 
lations of wave-lengths which recur in the spectra of lithium, magnesium, 
and of some lines which are often observed in the spectrum of the chromo- 
sphere ; they draw from this fact the probable conclusion that these 
chromospheric lines all belong to the same substance. We mention this 
fact, as it is one of the first attempts to use the similarity of spectra as a 
foundation for further conclusions ; but we doubt whether many of those 
conversant with solar matters will agree with Professors Liveing and 
Dewar. The way in which these different lines appear on difl'erent 
occasions seems to suggest very strongly, if not to prove absolutely, that 
the celebrated green line of the corona belongs to a difl'erent element to 
that which gives rise to the other chromospheric lines. There is even 
a diSerent behaviour apparent between the yellow and blue line referred 

blance whatever to the spectrum which Messrs. Dewar and Liveing call the spectrum 
of hydrocarbons ; and the spectrum which Messrs. Dewar and Liveing call the 
hydrogen-magnesium spectrum is the spectrum which Ciamician calls the band- 
spectrum of magnesium ; so that when Ciamician writes that the spectrum of hydrogen- 
magnesium resembles the spectrum of hydrocarbon, he really makes an altogether 
different and independent statement when Messrs. Liveing and Dewar make the same 
remark. But Ciamician quite agrees as to the resemblance pointed out by Messrs. 
Liveing and Dewar, only he expresses the fact by saying that the spectra of the first 
order of magnesium and carbon resemble each other. 
' Proc. Boy. Soc. xxviii. p. 475 (1879). 



ON OUR KNOWLEDGE OF SPECTKUM ANALYSIS. l43 

to by Professors Liveing and Dewar, but this may only be due to a 
difference in temperature. 

No systematic attempt has hitherto been made to connect together 
the different spectra of the same element ; relations which seem to hold 
in one case seem again disproved in others, and no object therefore 
seems to be gained by entering more closely into this matter at present. 



Report of the GomTnittee, consisting of Professors Odling, 
Huntington, and Hartley, appointed to investigate by '■means 
of Photography the Ultra-Violet Spark Spectra emitted by 
Metallic Elements, and their combinations under varying con- 
ditions. Drawn top by Professor W. N. Hartley (Secretary). 

The chief objects to be gained from a knowledge of the character of the 
Spark Spectra of Metallic Elements, and of the combinations of the 
elements, are : — 

(1) A means of I'eadily identifying the metals by photographs of their 
line spectra. 

(2) A knowledge of the alterations producible in the spectra of 
metallic salts by the presence of various non-metallic elements. 

(3) A knowledge of the alterations in spectra caused by the dilation 
of metallic solutions. 

(4) A possible means of performing rapid quantitative determinations 
of metallic substances by the aid of photography, and obtaining perma- 
nent records of the results. 

All these objects have been more or less completely attained, but on 
account of the extensive inquiry which has been opened up, it is pro- 
posed on this occasion to present only a preliminary report. 

(1) In order to simplify spectroscopic work, the time of exposure 
required to produce the most characteristic spectra under various con- 
ditions, such as intensity of spark and conductivity, &c., of the electrodes 
has been carefully ascertained. 

(2) A long series of experiments has been made with the object of 
comparing the spectra of various compounds in solution with those of the 
elements they contain. In the process of photographing the spectra of 
solutions it is desirable to eliminate all foreign lines as far as possible, 
hence the selection of suitable electrodes was a matter of the first con- 
sideration. Electrodes of gold, platinum, iridium, and other metals were 
nsed, and those of gold proved decidedly the best, as containing the 
fewest lines, and the metal being a most excellent conductor of elec- 
tricity. 

All these metals are, however, useless compared with electrodes of 
graphite. The spectrum of graphite consists of eleven or twelve insigni- 
ficant lines due to the carbon, and about sixty-six lines and bands due 
to air. 

(3) In comparing the spectra of solutions of salts with those of 
metallic electrodes, it was found that in almost all cases the lines of metals 
were exactly reproduced from the solution, the graphic character being 
retained except in regard to their continuity. Discontinuous but long 



144 EEPOKT— 1882. 

lines, or in certain cases even shorb lines, appear as long lines in the 
spectra taken from solutions. 

The graphic characteristics of the lines seen in various metallic 
spectra may thus be classified as — 

1. Continuous lines. They extend the whole length of the spark, 
and are accurate representations of the spectroscope slit. 

2. Discontiyiuous lines. Those whose length is not so great as the 
distance between the electrodes. 

3. Extended lines. Sharp lines which extend above and below the 
edge of the spectrum, or, in other words, above and below the points of 
the electrodes. 

4. Blotted lines, or lines surrounded by a nimbus. 

5. Nebulous lines, or those which are destitute of the sharp clear-cut 
appearance of most metallic lines.' 

(4) Insoluble compounds give no spectra when mixed with water or 
glycerine and exposed to the spark. The non-metallic constituents of 
salts do not yield any marked series of lines, and therefore do not obscui'e 
the metallic spectra. 

(5) Experiments have been made to determine the extent of dilution 
which serves to modify in various ways the spectra of solutions of 
metallic salts, and that which finally causes the extinction of the most 
persistent line or lines. The sensitiveness of the reaction varies with 
different elements and with the period of exposure, the intensity of the 
spark, and other conditions ; I have no difficulty whatever, when work- 
ing in the manner here indicated, in recognising spectra yielded by solu- 
tions which contain no more than xTnyot'i of a^jer cent, of calcium, silver, 
copper, and ToTrT7TT^^ ^^ b. per cent, of manganese. 



Report of the Committee, consisting of Professor RoscoE, Mr. 
LoCKYER, Professor Dewar, Professor Liveing, Professor Schuster, 
Captain Abney, cwicZ Dr. W. Marshall Watts (Secretary), ap- 
jjointed to prepare a neiv series of Tables of Wave Lengths of 
the Spectra of the Elements. 

The Committee has but little to report at present. An instrument for 
the more exact performance of the process of graphical interpolation has 
been constructed for the Committee, by Messrs. Cooke & Sons, of Tork, 
at a cost of 20L This instrument has, however, only been in the hands 
of the Committee for a few weeks. 

The Committee hopes to be in a position to make a fuller report at 
the next meeting of the Association, and it desires to be reappointed. No 
further grant of money ia at present needed. 



See Scientific Transactions of the Royal Dublin Society, vol. i. ser. 2, p. 232. 



METHODS EMPLOYED IN CALIBEATION OF MERCURIAL THERMOMETERS. 145 



Report of the Committee, consisting of Professor Balfour Stewart, 
Professor EliCKER (Secretary), ami Professor T. E. Thorpe, ap- 
poliited for the purpose of reporting on the Methods employed in 
the Galihration of Mercurial Thermometers. 

[Plates I., IL, III.] 

Introduction. 

In drawing up tlie fcllowing Report the Committee have desired to pre- 
sent it in the form in which it will be most generally useful. It is there- 
fore divided into two parts. The first contains a brief description of the 
principal methods of calibration and correction which have been hitherto 
proposed, an account of the thermometers on which these methods have 
been tested by the Committee and of the apparatus employed, and a 
summary of the results arrived at. This portion therefore contains the 
facts necessaiy to enable a selection from the various methods to be made 
by persons intending to undertake the calibration or correction of a 
thermometer. The second part consists of a fully worked out example of 
each of the methods, together with remarks of a detailed character. This 
part will it is hoped be useful in facilitating the calculations required, 
especially as references to the subject of calibration in English scientific 
works are rare and meagre. 

Part I. 
General Beviern of Methods of Calibration ami Correction. 

(1) The corrections for the inequalities in the bore of a thermometer 
tube may be applied in two different ways, distinguished as methods of 
calibration and correction respectively. 

In the first the length of a column of mercury is measured in various 
parts of the tube before the scale is etched on it, and the lengths of the 
divisions are then so adjusted as to make equal differences of scale- 
readings correspond to equal volumes. In the second the tube is in the 
first instance furnished with a uniform scale, and a table of corrections 
is afterwards drawn up, by means of which the same end is attained as 
before. It will be shown hereafter that a high degree of excellence can 
be attained by the former method, but although generally used, the 
scales, even on good thermometers by well-known makers, are not, as 
a rule, sufficiently correct for \evj accurate work. They therefore 
require collection, and the process is rendered very laborious by the 
varying lengths of the divisions which have to be measui-ed and allowed 
for in the calculations. The results, too, are probably less accurate than 
they otherv.'ise would be on account of the irregular forms of the correc- 
tion curves produced by the superposition of the errors of the tube and 
scale. A uniform scale, the divisions of which are about a millimetre 
apart, seems therefore in general the most convenient. Such tubes only 
should be used as preliminary tests have shown to be of fairly uniform 
bore. 

(2) As all the methods of calibration and correction to be described 
1882. L 



146 EEPOET — 1882. 

depend upon tlie measurement of tte length of colamns of mercury in 
various parts of the tube, it is important to decide upon the best method 
of separating these ' threads ' (as they will hereafter be called) from the 
main mass of mercury in the tube and bulb. 

In general it is in the first place necessary to make the mercury run 
from the bulb into the tube, so that a column of any length can be obtained 
when the thermometer is at the ordinary temperature. To eifect this the 
instrument should be held in a vertical position with the bulb uppermost, 
and the other extremity of the tube should be cautiously tapped against 
the table. If the mercury does not start it is well, as a preliminary, to 
heat and cool the bulb several times. Tolerably rapid changes of tempera- 
ture of a few degrees will often suffice. 

The transference of the mercury from the bulb to the tube causes a 
vacuum bubble to appear in the former, and many writers, among whom 
A. von Oettingen, in a work often hereafter to be cited (' Ueber die Cor- 
rection der Thermometer insbesondere liber Bessel's Kalibrir-Methode,' 
Dorpat, 1865, p. 46) may be mentioned, recommend the separation of a 
column of the desired length by the proper manipulation of this bubble 
and a system of dexterous jei-ks. In a wide bore, if the bubble is brought 
to the junction of the tube and bulb, it is possible by a jerk to effect a 
disruption between the mei'cury contained in the one and the other re- 
spectively. It is, however, exceedingly difficult, if not impossible, to apply 
this method satisfactorily to thermometers with narrow bores, and the 
violent jerks which are required are extremely dangerous to the instru- 
ments. 

In all the experiments undertaken by the Committee, therefore, the 
separation of the thread was effected by heat. The use of a blow- 
pipe flame for this purpose has been recommended (Wiillner, ' Lehrbuch 
der Physik,' vol.iii. p. 14), but such a course is unnecessarily violent and 
risky. Instead of this, a very small flame, four or five millimetres in 
height, was used, obtained from the gas issuing from a narrow oi'ifice at 
the extremity of a piece of glass tubing drawn out fine. Into this the 
thermometer was introduced, care being taken to heat the tube equally all 
round, and the rupture was effected at the point where the heat was ap- 
plied. It is easy thus to break ofi" threads to within a millimetre of the 
leno-th aimed at. When great accuracy is important it is advisable first 
to break oS" a thread longer than that required, and then to separate from 
it a portion of the desired length. Greater steadiness of the mercurial 
column while the thermometer is being heated is thus attained. Many 
dozens of threads have been broken off in this way within the experience 
of members of the Committee without a single breakage of the instruments 
employed. 

(3) Before proceeding further it will be convenient to define certain 
terms which will be frequently used. 

The upper and loiuer ends of a thread are those furthest from and 
nearest to the bulb respectively. 

The point at which the lower end of a thread is placed when a measure- 
ment of its length is made, is called the initial point. 

When by any method the corrections are determined only for a number 
of selected (and in general approximately equidistant) points, the points 
so chosen are termed -principal points. If, when the tube has by means 
of a svstem of principal points been divided into a number of parts the 
relative volumes of which are known, these parts are further subdivided 



I 



METHODS EMPLOYED IN CALIBBATION OF MERCDEIAL THERMOMETERS. 147 

by any method in wliicli the con-ections of the principal points are taken 
as accurate, the points of subdivision are termed secondary iwints. 

The corrections for points intermediate to the principal or secondary 
points may be determined either by interpolation formulae or, as is far 
more convenient, by a graphic method. In the latter case the abscisste 
are the nncorrected scale divisions, the ordinates are the corrections to 
be applied to them, and the curves passing through the points thus deter- 
mined are called correction curves. The curves employed in this inves- 
tigation have been drawn on paper divided into millimetre squares. In 
the line of abscissae two centimetres con-esponded to one degree, while an 
ordinate of one centimetre represented a correction of 0°"01. In the case 
of second approximations it was often necessary still further to magnify 
the corrections and to represent 0°-01 by five centimetres. Time and 
trouble are saved by using an open scale. In the plates the curves are 
half the size actually used. 

If a thermometer has been corrected by several methods, it is neces- 
sary in order to compare the results to transform the correction curves, 
so that the corrections may be the same at two arbitrarily selected points. 
These, which ai-e in general at the extremities of the scale, are called the 
standard points, and a curve such that the corrections at these points are 
zero is called a standard correction curve. 

(4) The transformation of a correction curve is exactly similar to 
the conversion of a temperature from the Fahrenheit to the Centigrade 
scale. On the corrected scale equal differences of scale readings corre- 
spond to equal tube volumes. This condition will still be fulfilled — (1) if 
all the corrected readings are increased or diminished by a given amount ; 
(2) if the difference between any two readings is increased or diminished 
in a given ratio. 

Let X be any point on the scale ^ {x) its correction. To make the 
correction for the lower standard point I zero, we have to diminish all the 
readings by ^ (I). Hence ^the reading for x becomes x + (l>{x) — f (I). 

Let U and 0(U) be the upper standard point and its correction, and let 

U + 0(U) -(I + </>(!)) = N + a, 

where U — I = N. 

Hence after the scale divisions are altered in the ratio necessary to 
reduce the correction for the upper standard point to zero, the reading for 
X becomes 

{. + *Ov)-*(I)}^„. 

For facility of calculation this is thrown into the more convenient 
form — 

x + ^{x) -,p(I)-^^-i|_|a; +^{x) -./.(I)} 

= ^ + ^(^) _ ^(I)_ « ^1 _ I) |a; + <^ (a,) _ ^I) } 

approximately, 

= „. + ^,(3,) - ^(I) _ ^jo. + ^(x) - </,(!) -|a;} 

approximately, whence the transformation can, as shown hereafter, be 
easily effected. 

L 2 



148 REPORT — 1882. 

(5) Methods of calibration and correction may be divided into four 
classes; 

The first contains what may be called the step hij step method, which 
is due to Gay-Lnssac.^ In it a thread of mercury is measured in a posi- 
tion A B, then shifted to B C, so that the lower end is in the position 
previously occupied by the upper end, then measured again, and so on 
for the whole length of the tube. From these measures the corrections 
for the points B, C, D, &c. can be deduced. 

The second class contains what may be called principal point methods. 
In these a number of equidistant points are selected on the uncorrected 
scale, and the corrections for these are determined by means of threads 
the lengths of which are approximately equal to or multiples of the dis- 
tance between two consecutive points. 

Several methods are included in this class. 

Hallstrom's^ is a modification of Gay-Lussac's, in which an attempt is 
made to prevent the risk of the accumulation of ei'rors inherent in the 
use of very short threads. Two slightly different varieties of Hallstrom's 
method are described by A. von Oettingen and Pfaundler, of which the 
latter has been employed by the Committee. If the tube be divided into 
the parts A B, BO, &c. by principal points, a thread approximately equal 
to two of these parts is measured with its lower end at each of the points 
in turn. A second thread nearly equal to three of the parts is measured 
with its lower end at each of the two lowest principal points, and from 
these observations the corrections are deduced as desci'ibed in Part II. 

Dr. A. HandP has recently described a method of calibration which 
appears to differ from those of Gay-Lussac and Hallstrom only in the 
form of the calculations. 

Another method has been devised by M. Thiesen.^ The scale being 
divided into n parts by principal points, threads equal in length to 
1, 2, . . ii — 1 of these intervals are measured with their lower ends 
coincident in turn with as many of the principal points as possible, and 
hence the corrections are deduced. 

Mai'ek* has applied the method of least squares to the calculation of 
the corrections for any number of pinncipal points less than seven. 

By all these methods the corrections can be determined for as many 
points as may be desii'cd, either by taking the principal points near 
together, or by breaking up the intervals between them by secondary 
points. There is, however, one method — Rudberg's" — the essential 
feature of which is the breaking up of corrected scale intervals into 
smaller sections. This method therefore constitutes the third class, which 
may be called that of repeated subdivision. In this method the tube is 
first divided into two equal parts by measuring a thread of approximately 
half its volume, when the lower and upper ends are in turn at the 
extremities of the tube. These portions are then subdivided into three 

' See Pierre, Poffff. Annalcn, Bd. 57, S. 55t, and Ann. de Chlm. et de Phys. s^r. iii. 
iv. p. 427; Welsh, Proc. Roi/. Son. vi. p. 178, and Phil. Mag. (4) iv. p. 306 ; A. von 
Oettingen, op. cit. p. 43, Verdet, Cunr.i de Phys-iqiie, i. p. 64. 

2 See Poffff. Ann. Bd. 9,S. 535 ; Muller-Pouillet's Lckrbuch der Physik (Piaundlei) ; 
A. von Oettingen, oj>. cit. S. 51. 

' Carl's Mepertorium, Bd. xvii. Ht. 5. 

« Ibid. Bd. XV. S. 285. 

» Ibid. Bd. XV. S. 300. 

« Poffff. Annalcn, Bd. 40, S. 574 ; A. von Oettingen, ojf. cit. S. 50. 



' 



METnOUS EMPLOIED IN CALIBRATION OF MERCURIAL THERMOMETERS. 149 

by means of a thread of about one-third the whole length of the tube, 
■which is measured in the positions (see figure, p. 178) A rf) cZ e, e B, 
C/, and C g . The process can then be carried further, as described in 
the detailed account of this method. 

The fourth class of correction methods also comprises one only — ^viz., 
Bessel's — which may be called a distributed point method. 

In this all the threads are measured with their lower ends at certain 
■selected points, but as their lengths are not multiples of the distances 
between these points, but are within wide limits arbitrary, the cori-ections 
are determined at numerous points more or less irregularly distributed 
over the scale. 

In von Oettingen's modification of the method the corrections are 
finally calculated by drawing correction curves through the points deter- 
mined by each thread, and taking the means of their ordinates. Pro- 
fessors Thorpe and Riicker have introduced some changes into von 
Oettingen's method of correcting the lower and upper parts of the scale. 
An example of both systems, and a full discussion of the method are 
given in Part II. Although too detailed to be introduced here it may be 
said that the examples given prove that Professors Thorpe and Riicker's 
alterations increase the rapidity with which the method approximates to 
the true correction curve. 

All the methods above mentioned (with the exception of Handl's) 
have been tested by the Committee, and as the results are probably suSi- 
cient for the practical purpose in view, they have not extended their inves- 
tigation to several others which have been proposed by various writers. 

They may, however, refer to the plans suggested by Egen (' Pogg. Ann.' 
Bd. XI. s. 529), Rowland ('Proceedings of the American Academy of 
Arts and Sciences,' Juno 1879), and Pickering (' Physical Manipulation,' 
PartIL, p. 75). 

(6) Many of the methods of correction theoretically require that one 
or both ends of the thread should occupy definite positions in the scale. 
It is impossible, unless the tube is uniform or is perfectly corrected, 
to establish this coincidence at both ends, inasmuch as a thread which 
would comply with the condition in one part of the scale would fail to 
fulfil it in others. In the case, too, where the theoretical position of one 
end of a thread is indicated by a scale mark, the breadth of this is often 
so considerable that it is difficult to observe with accuracy the position of 
the end of a thread which is concealed by it. 

Sometimes it is impossible, and often it is inconvenient, to bring 
the thread end into its theoretical position. In cases where errors 
might be introduced by this failure to comply with the exact conditions 
of the method, they may be allowed for in two slightly diflerent ways. 

The first plan is that of farther approximation. The corrections for 
the extremities taken out from the correction curve are applied to the 
measured thread lengths, and then, by repeating the calculations with the 
corrected values, farther corrections are obtained, which must be added 
to those previously found. A second approximation is thus worked out 
in Part II. in the second example of Gay-Lussac's method (p. 166). 

In some cases, however, if the threads are not measured in their 
theoretical positions, it is convenient to avoid the necessity for a second 
approximation by the preliminary use of a correction curve drawn by any 
simple method. Let the thread end be situated at M, and let the cor- 



150 



KEPORT — 1882. 



rection be required for a neighbouring point, N". Let A' B' be an approxi- 
mate, and AB the true correction curve. (See figure below). 



Let A' M = ^1 (M) A M = ^aC^^). and so on. 
Then, if A A' = a, B B' = ^, it is evident that 

^,(M) - f,(N) = f,(M) - ^,(N) + a 



/3. 




M 



N 



Now, in the method of approximation, the assumption made in the 
first approximation is that the right-hand side of this equation is zero, or 
that frXW) = ^.(N). 

A nearer approach to the truth is reached by neglecting a — /) only, 
and obtaining the values of ^i(M) and '^i(N) from an approximate 

curve. Since the two curves in general 
differ but little, and M and N are always 
very near together, the error thus intro- 
duced is obviously in general less than that 
caused by neglecting ^i(M) — 0i(N). In 
other words, since the curves are nearly 
parallel, the diSerence between A A' and B B' 
is in general much less than that between 
M A' and N B', or M A and N B. 
— Theoretically, of course, the error due to 
the neglect of a — /3 would be greatest when 
the two curves sloped in opposite directions in the neighbourhood of M N". 
The only case, however, where a doubt as to the direction of slope could 
arise would be near to a maximum or minimum, when the whole error 
would be so small as to be negligible. 

This method, which is employed by Marek (he. cit.), is illustrated in 
the case of Rudberg's and other methods in Part II. Since by it the 
corrections at points are determined from measurements made on threads 
whose ends lie near to but not actually at them, the corrections may be 
regarded as transferred by means of the preliminary curve from the 
observed to the theoretical points, and it is convenient to refer to it as 
the method of transference. 

If the theoretical points are u and i, if the extremities of the thread 
lie at M + Am and i -f- A?', and if <l>{p.i) represents the correction at m, and 
so on, the true thread length is 

« + Am + ^ (m + Am) — [i + Ai + ^ (i + At)} . 

Here u + \u — (J, + A?!) = t say, is the uncorrected thread length, 
and thus the true thread lensrth 

= I < + { ^. (m + Am) - ./. (m) } - { ^ (i + aO _ ^ (i) } I + d> (m) - </, (i). 

The corrections within the large brackets being determined from the 
approximate curve, the expression contained in it is in this method used 
instead of t, and is referred to as the transferred thread length. 

(7) In estimating the value of any method, three points require con- 
sideration — viz. the accuracy attainable, the time and labour required, 
and the cost of the necessary apparatus. The more accurate the appa- 
ratus used, the simpler may be the method of calculation employed. 
Thus, the chief objection to the step-by-stejj and subdivision methods is 
that the errors are cumulative, and that by an unfortunate combination 
of successive errors of the same sign, considerable inaccuracy may be 
introduced. It is, however, evident that this objection would vanish if 



METHODS EMPLOYED IN CALIBEATION OF MEECUEIAL THERMOMETERS. 151 



the apparatus used for measuring the threads were sufificiently sensitive 
to make the accumulated errors of thread-measurement insensible when 
compared with the error of reading introduced when the thermometer 
is used. 

The Committee have been able to study the results produced by 
different instruments, as well as by different methods, as will appear from 
the following restmie of the observations considered in the preparation of 
this Report. 

Some time ago Professors Thorpe and Riicker obtained a number of 
mercurial thermometers for the purpose of comparison with the air ther- 
mometer. A full description of these instruments is given in Table I. :— 

Table I. 









Extent of 


Average 


Thermometer 


Owner 


Maker 


scale in 
degrees C. 


length of 
degree in m.ui. 


A 


Dr. Thorpe 


Casella 


-9 to 50 


9-3 


B 


>j 


)> 


48 „ 110 


8-9 


C 


») 


»j 


98 „ 142 


11-2 


E, 


Prof. Riicker 


») 


-11 „ 31 


12-3 


K, 


»j 


') 


21 „ 67 


111 


Ra 


j» 


)> 


55 „ 107 


10-2 


561 


Kew Committee 


Kew Observatory 


-11-5 „ 29 


12-9 


562 


»> 


)» 


19-5 „ 68 


11-2 


563 


»» 


s» 


51 „ 107 


9-5 


0. 


Owens College 


Owens College 
Laboratory 


-11 „ 30 


11-5 


0, 


JS 


>» 


21 „ 69 


9-8 


O3 


J> 


)> 


55 „ 107 


9-3 



Those numbered 561-2-3 were constructed and calibrated in the Kew 
Observatory, and those indicated by the symbols O,, Oo, O3, in the 
Physical Laboratory of the Owens College. In the case of the Kew 
instruments, the method of calculation adopted was that introduced into 
the Observatory by the late Mr. "Welsh, and explained by him in the 
' Report of the British Association ' for 1853, p. 35, which, as it is prac- 
tically the same as that of Gay-Lussac, need not be further described. 

The Owens College instruments were furnished with a uniform scale. 

In addition to the construction of the thermometers, the authorities 
of the Observatory and the Owens College undertook to perform, in 
accordance with the directions of Professors Thorpe and Riicker, the 
measurements necessary for their correction by Bessel's method. The 
appai'atus used in each case was an excellent dividing engine. The 
accuracy of the measurements and of the correction curves obtained is 
evident from the fact that the difference between any one measurement 
of the length of a mercurial thread expressed in terms of the corrected 
scale, and the mean length of that thread, equals or exceeds 0°'01 C. (i.e. 
about 0*1 m.m.), in eleven only out of a total of 880 observations made 
in all on the six instruments. 

(8) The application of Bessel's method, therefore, to the Kew instru- 
ments, afforded an excellent test of Welsh's method by which they had 
been calibrated. The result was reported to Section A of the British 
Association at York (Report 1881, p. 541), in a paper from which the 
following is an extract : — 



152 EEPORT— 1882. 

' The original calibration was so accurate that the second approxima- 
tion of Bessel's method was unnecessary in two cases, and was only 
partially carried out in the third. 

' The maximum positive and negative corrections were in the case of 

Th. 561 + 0°-004 C. and - 0°-004 C. 
„ 562 + 0°002 C. and - 0°-005 C. 
„ 563 + 0°-008 C. and - 0°-011 C. 

' As will be seen from the above description of the thermometers, the 
larger of these quantities are about equal to the limit of certainty in 
reading. 

' In no case would the calibration error in the determination of a 
difference of temperature have amounted to 0°02 C 

(9) The remainder of the thermometers, viz. A, B, C, and Ri, R,, R3, 
had been calibrated by the maker, and were corrected by Bessel's 
method in the Physical Laboratory of the Torkshire College. 

The instrument used was copied from one devised by and kindly lent 
for the purpose by Mr. T. Brown, which he has lately described to the 
Physical Society.' It consists of a wooden base to which the thermometer 
is attached parallel to a slot in which a small brass plate slides, carrying 
with it a vertical microscope furnished with a spider line. The microscope 
is moved by rackwork on the brass plate parallel to the thermometer, and 
the distance travelled is determined by a millimetre scale. Readings can 
be made by a vernier to O'l m.ni., and with the help of a lens estimations 
can be made correct to 0"02 or 0'03 m.m. In the form described by Mr. 
Brown a split object-glass is used to bring the mercury in the bore and 
the scale divisions into focus together. In that employed in this in- 
vestigation this was omitted, and the microscope was moved vertically 
by rackwork to bring the mercury and scale into view in turn. This 
worked well. Any error due to want of verticality produced in the 
measurement at one end of the thread would be compensated at the 
other, if only the direction of the tube remained the same. That it did so 
is proved by the fact that two measui^es of the same thread length rarely 
differed by more than 0'03 m.m., which was well within the limits of the 
sum of the estimation errors possible at both ends. 

This insti'ument was employed because it was believed that, with 
proper precautions, and with so accurate a method of calibration as 
Bessel's, it would serve to correct the thermometers to the required 
degree of accuracy. This anticipation has been fulfilled, and as the 
instrument is extremely convenient and relatively inexpensive, it may be 
well to state precisely the conditions under which it was used. Inasmuch 
as the thread lengths were required in terms of scale divisions, the instru- 
ment was never used to measure the entire length of a thread, but only 
the amount by which it was distant from a neighbouring scale division. 

(10) The position of the end of the thread was always determined by 
measurinsr the distance from the nearest division which was clear of the 
thread. Thus, if a and b be the extremities of the thread, and aa', be' 



a b 

the nearest scale divisions, the distances A a and b b were measured, even 
if they were much greater than A' a and b' b. 

• Phil. Mag. [5] vol. xiv. p. 59. 



METHODS EMPLOYED IN CALIBRATION OF MERCDRIAL THERMOMETERS. 153 

In what follows, the nearest division therefore means the nearest 
division beyond and clear of the thread. 

The word reading means reading on the scale of the calibrating instrn- 
ment, and in terms of millimetres. 

In a particular thermometer graduated from 55° to 107° C, the mean 
length of a degree between 55° and 75° was found to be 10'50 m.m. 

Hence, to convert readings between 55° and 75° into degrees, we have 
to multiply by jJ^„= -095. 

The corresponding factors for the whole scale were as follows : — 

Between 55° and 75° the factor = -095. 
75° and 85° „ „ = -097. 
85° and 90° „ „ = -100. 
90° and 107° „ „ = -104. 

The initial points chosen were 55°, 58°, and 61°, &c. The method of 
exhibiting the results of the measurement is shown in the accompanying 
Table II. which is made more cumbrous than in actual practice by a full 
explanation of the meaning of the figures in eacb column. 

The results of two sets of measures only are given. 

The scales of the thermometers were carefully tested in various parts, 
and it was generally found that a group of consecutive divisions, all of 
which were equal in magnitude, was bounded at either end by other 
groups, in which the length of a division difiered more or less considerably 
from that of those included in it. 

This was no doubt due to the fact that the scales were already 
adjusted by the maker to the varying dimensions of the bores, though 
not with the necessary accuracy. It was therefore possible to divide the 
scale into parts, throughout each of which the same factor could be used 
for converting the readings of the calibrating instrument (given in milli- 
metres) into degrees. An example of such a division is given above. 

It may here be stated once for all that in the case of all the thread 
lengths required for the observations detailed in Part II. the corrections 
for the varying lengths of the scale divisions were thus made. The tem- 
perature, too, was frequently observed by means of a thermometer placed 
close to that operated on, and the thread lengths were corrected by sub- 
tracting 000016 of their length for every degree Centigrade above the 
standard temperature for the set of observations in which they were made. 

The apparent mean error, taken without regard to sign of the 
thread lengths measured by this instrument is about double that of the 
more accurate instruments employed at Kew and the Owens College. In 
the case of Thermometer C, which was carefully calibrated by Bessel's 
method for the purposes of this Report, it amounts to 0°'0024, or about 
0'033 m.m. As each thread was measured only once, and required four 
readings of the vernier, this result is satisfactory. The error in the 
estimation figures obtained by the vernier is indeed much greater 
than the error of setting the cross-wire to the point to be measured. 
Additional accuracy could, of course, readily be obtained by fitting 
the eye-piece with a micrometer screw to read over 2 or 3 m.m. only. 
Inasmuch also as in the method of measurement described the sum of the 
two small quantities Aa, Bb (see p. 152), is alone required, it would be 
convenient, if a uniform scale were used, to transfer the mici-oscope 
from a to 6 by a screw or rackwork, without altering the position of the 



154 



REPORT — 1882. 










- (4^ . 








I— 1 






o 

CO 




t— ) 


*3 5 o 1 


CO 


l^ 




hH 


fcJD Jh u • 








X 


J-'>^ 




4( 












H- 1 


Distance 
between 
nearest 
cale divi- 
sions = 
ols.V.-II 




C5 




l«i 


C-1 


<M 






ma 










Qi m rr-t U ^ 11 I 


o 
o 


o 

r— 1 




3 


a a § « -p c !<< 
B 0) V. n g §2 








rn 


■^ ^ 'x 










- 










l.VII 
termi 
of 

egrees 


00 


o 




H 


o 


^ 
t^ 






o 


o 






o c: -a 










o- 








><■ 


)1. VII. 

terms 

of 
egrees 


-tl 

CO 


I «o 




1— ( 


o 


p 






d-s -« 










Q> t- 'A . • 










Distanc 

of uppe 

do.= col 

VI.-IV 










1^ 

o 






V 


iH C .- wi 








O 


P i- o -- o .-^ 










o 


o 




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o g a g .2 -1 

** -f. -r: 




















bJD^ C 










C ^ 15 O 


lO 


b* 




1—5 


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Ci 


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g = St 


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leading 
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to 






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■^ V — ^ -h -*-+- 


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METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 155 

vernier. The errors of reading would thus be reduced from four to two, 
and the maximum possible inaccuracy halved. 

(11) In order to compare experimentally the different methods of 
correction, the Committee have applied them to the same thermometer. 
The instrument selected was thermometer C, and the methods applied to 
it were those of Gay-Lussac, Hallstrom, Rudberg, Thiesen, Miirek, and 
Bessel — the latter both as modified by von Oettingen, and also with the 
additional changes introduced by Professors Thorpe and Riicker. The 
measurements were made in the Physical Laboratory of the Yorkshire 
College. 

Those for Bessel's method, and for the first example of Gay-Lussac's 
method, were performed by Professor Riicker. The remainder, together 
with much of the laborious calculation required, were kindly undertaken 
by Mr. "W. Heaton, M.A., Demonstrator in the Clarendon Laboratory of 
the University of Oxford, to whom the warm thanks of the Committee 
are due for the labour and skill which he has expended on the investiga- 
tion. It is owing to his help that they are able to present the Report 
without further delay. 

In the first place the thermometer was corrected by Gay-Lussac's 
method. The thread used was about 19 m.m. (l°-6) long. When it was 
moved the lower end was always brought veiy near to, though not into 
absolute coincidence with, the position previously occupied by the upper. 
An inspection of the curve wheit completed showfed that the errors intro- 
duced by these small deviations from the thedtetical position were abso- 
lutely negligible. The length of the thread, "together with that of the 
scale divisions in which its extremities lay, was measured twice for each 
position of the thread. As when the thread was displaced, the lower end 
lay in the same division as that which previously contained the upper, 
each division was really measured four times, and the mean of these 
values, which rarely differed by more than 0°-003, was taken as the true 
value. 

The standard correction curve obtained is exhibited in fig. I, 
Plate I. 

All the calculations, together with those required in the other calibra- 
tions to be described, are given in Part II. 

In the second application of Gay-Lussac's method to the thermometer 
the thread employed was somewhat longer, viz. about 22 m.m. (2°). 
Instead of measuring each division in which the ends lay, the scale of the 
thermometer was previously studied, and was found, as is usual in ther- 
mometers calibrated by the maker, to consist of groups of divisions of 
equal length. The values of these were determined and used as above 
described. Another difference in the application of the method was that 
it was now used as a principal point method to determine the correction 
at every second degree. As, however, the length of the thread was very 
nearly 2°, the divergence from the theory of the step-by-step method was 
small, though considerably larger than in the last case. 

To eliminate any error a preliminary curve was drawn, and the 
method of approximation applied. The distance between the positions of 
the upper and lower ends (assumed in the first approximation coincident) 
was never greater than 2-2 m.m. (0°-2), and the maximum correction 
introduced in the second approximation was 0°'007. 

In what follows the correction curve obtained by the use of the thread 
2° long was used as a first approximation curve to apply the transference 



156 



EEPORT 1882. 



of corrections above described to tlie various methods investigated. It is 
shown in fig. 1, Plate I. 

Gay-Lussac's method was also applied a third time to the thermo- 
meter. On this occasion a much longer thread 44 m.m. (4°) in length 
was used. The method of transference was used in finding the correc- 
tions, and the observations with the thread 2° long were used (for the 
sake of example) to obtain some secondary points between those found 
by the longer thread. 

The points determined are shown in fig. 1 , Plate I. 

Hallstrora's and Thiesen's methods were applied to find the corrections 
of ten principal points, Miirek's of five, Rudberg's of twelve. In all 
these the method of transference was applied. Bessel's method was also 
applied, the principal points being 2° apart. The calculations were per- 
formed twice, as above stated. 

(12) The following Table contains a statement of the number of 
thread lengths measured in the application of each of these methods. 

Table III. 



Method 


Number of measures 
required 


Total 


Number of 
points deter- 
mined by 
method alone 


Number of 
points deter- 
mined by 
method and 
preliminary 
curve 


(1) 

By method 
alone 


^ (2) ,. 
By preli- 
minary 
curves used 
in trans- 
ference 


Gay-Lussac I. 

„ II. . 
„ III. . 

Hiillstrom . 
Thiesen 
Milrek . 
Rudberg 
Bessel . 


26 
20 
10 
11 
5i 
14 
15 
1.S8 


20 
20 
20 
20 
20 


26 
20 
30 
31 
74 
34 
35 
138 


26 
20 
10 
10 
10 
5 
12 
148 


26 
20 
20 
20 
20 
20 
31 
8 



The difference in the amount of labour required by the different 
methods is not to be measured by the number of observations alone. 

In the case of the methods of Gay-Lussac and Thiesen the calculations 
are extremely short and easy ; those of Hallstrom and Rudberg are not 
lengthy, but they lack the symmetry of the two just named, and are there- 
fore less simple in application. The longest of these methods, that of 
Thiesen, may be completed in a few hours, but the calculations and curves 
which Bessel's method requires demand an amount of time which must 
be measured by days rather than hours. The operation of reducing the 
thread lengths to scale divisions, and performing the work for two full 
approximations, requires about four days' constant attention. 

It is on the other hand true that the same extreme accuracy of 
measurement is not necessary, and thus in the example given each thread 
was measured once only, instead of twice as in the case of the other 
methods. This is justified partly by the result which previous experience 
had shown to be probable, viz. that the errors made under such circum- 
stances are small. Only one of the 138 measures gives an apparent error 
as great as 0°01, and the mean is, as has been stated, 0°-0024. The 



^ 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 157 

other justification of the course adopted is that, as will immediately 
be showD, an error of measurement in Bessel's method is of relatively 
little importance. 

(13) This question is fully discussed in Part II. The following 
Table may, however, be given here. If e is the probable error of a 
single thread measurement, and me the probable error of a collection, 
the numbers in the Table are the values of m^, when ten principal points 
have been found, and are therefore proportional to the squares of the 
probable errors, or to the reciprocals of the combination weights of the 
corrections of the scale obtained by the method to which they refer. 

The probable errors of all thi-ead lengths are taken as the same, though 
measures on long threads are less reliable than those on short, on account 
of their greater mobility, and the greater value of the temperature correc- 
tions with respect to the error of reading. In the case of Rudberg's and 
Bessel's methods the numbers can only be considered as approximations. 

Table IV. 





Gay-Lussac 
















Rudberg 


Hallstrom 


Thiesen 


Bejsel 




Thread 2° 


Thread 4° 























1 


1-8 


0-9 


1-4 


M 


0-18 


010 


2 


32 


1-6 


1-8 


0-8 


018 


010 


3 


4-2 


21 


07 


11 


018 


0-10 


4 


4-8 


2-4 


0-6 


1-2 


0-18 


0-09 


5 


5-0 


2-5 


0-.5 


2-.5 


0-18 


0-09 


6 


4-8 


2-4 


0-6 


1-2 


018 


009 


7 


4-2 


21 


0-7 


4-3 


18 


0-10 


8 


3-2 


IB 


1-8 


0-8 


0-18 


0-10 


9 


1-8 


0-9 


14 


6-5 


018 


010 


10 





















To make the result of this table more obvious, the numbers have been 
plotted down and curves drawn through them in the following figure. 
The curves serve only to connect the points given by the same method. 
At these points their ordinates are proportional to the squares of the 
probable errors of the corrections. The enormous differences between 
them will be at once appreciated. Care, however, must be taken to avoid 
drawing false conclusions. The numbers have no reference to any 
approximate assumptions. They refer only to the methods as exemplified 
in this Report, e.g. for Bessel's and Thiesen's methods, with 10 threads 
and so on. Had Thiesen's method been applied to determine five 
points only, instead of ten as was actually the case, the ordinates would 
have been doubled. This points to a fundamental distinction between 
such a method as Thiesen's and Gay-Lussac's. Gceteris paribus, the larger 
the number of points corrected by the former, the more accurate is the 
correction of each, whereas in Gay-Lussac's method the reverse statement 
holds good. 

The extreme irregularity of the Hallstrom carve depends on the want 
of symmetry of the method. The extraordinary accumulation of the errors 
at the seventh and ninth points is sufficient to condemn it as presented 
by Pfaundler. 



158 



EEPORT — 1882. 



(14) Perhaps, however, more is to be learnt from the curves actually- 
obtained than from purely theoretical discussion. 

Unless the greatest care is exercised, the errors due to ' taste ' in 
drawing the curves may far exceed those produced by mere instrumental 
inaccuracies. 

An excellent example of this is afforded in the neighbourhood of the 
point 135° on Thermometer C. 

Figure 2, Plate I., gives a part of the curve obtained by the Gay- 
Lussac method with the thread l°-6 long. The points surrounded by 
circles are those obtained by the thread 4° long. The dotted line is that 
actually drawn b}'' a person unacquainted with the form of the other 
curve. Thus at 138° a difference of 0°-012 is introduced. A similar 
result was obtained with the two Gay-Lussac curves shown in fig. 1. 
The dotted curve happened to have a point at 135° where the correction 
■was found to be very low, in this agreeing with the Bessel curve, fig. 3. 



6 


















/ 


\ 


















/ 




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4 








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N 


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. 






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K 


^ 




1 


3 








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^ 


1 


\ 


\ 


\ 




•T^X^ 


\ ^ 


2. 
1 


/ 


V? 






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V 


J 


A 


A 




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f/ 


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' 


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'l 




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THieSE 


N 


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tsessEL 
5 



10 



The other curve missed this point, and gave a much higher correction 
at 136°. Probably both are nearly right. There is evidently some sudden 
change or irregularity at this part of the scale, to fully investigate which 
a number of points taken very close together would be required. 

If a thermometer is required to be accurate to 005 m.m. (0°'005) 
points must be determined at intervals not greater than 20 m.m., and 
wherever any sudden bend in the curve occurs, a secondaiy calibration 
of that part of the scale should be instituted with a shorter thread. 

(15) The following Table (V.) gives the corrections for the principal 
points as determined by all the methods. Rudberg's is omitted, as these 
points could not be directly corrected by that method. The corrections 
obtained by it are, however, plotted down in fig. 3, Plate 1. 

(16) A very careful comparison has been made between the results 
given by Bessel's and the other methods. The two methods of calculation 
applied to it are fully discussed in Part II. The result is that whereas 
at the end of the second approximation the curves disagree by nearly 



I 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 159 



Table V. 

Ill terms of 0°001. 







Gav-Lussac 




















Hallstrom 


Thiesen 


Jlarek 


Bessel 










I. 


II. 


III. 










100 























104 


121 


120 


116 


120 


121 


— 


120 


108 


loo 


155 


151 


153 


156 


156 


151 


112 


106 


109 


104 


107 


109 


— 


104 


116 


108 


116 


113 


115 


117 


116 


115 


120 


130 


136 


135 


137 


138 


— 


135 


124 


106 


112 


111 


109 


113 


112 


109 


128 


108 


111 


111 


114 


112 


— 


108 


132 


56 


60 


61 


56 


61 


62 


54 


136 


2 


10 


12 


13 


10 


— 


4 


140 
























0°"01, when the third approximation is partly carried out, that obtained 
by Professors Thorpe and Riicker's method remains virtually unaltered, 
while Yon Oettingen's is brought into agreement with it. The former, 
therefore, though somewhat the longer, is taken as the more accurate 
method. 

(17) The discrepancies between the Bessel and the second Gay- 
Lussac curve were next investigated. The extremely small effect pro- 
duced on the correction at any one point by any one measurement of a 
thi-ead length in Bessel's method, makes it possible to use these threads 
as means of comparison. The corrections for the upper and initial points 
of all the threads measured in Bessel's method were taken out both from 
the Bessel's curve, fig. 3, Plate I., and the Gay-Lussac curve, Example 2, 
fig. 1, Plate I. The thread lengths were corrected by these, and then, 
by subtracting from them the corrected mean thread lengths, the apparent 
errors of the measures were deduced. 

As ten threads were measured at each of the initial points, if the cor- 
rection for any one of these points was too high or too low, the threads 
measured at it would be too short or too long. 

This fact can be used to test the relative accuracy of the two curves. 
For instance, at 108°, the mean apparent error of the threads, when 
corrected by Bessel's curve, was + 0°-001, which would show that the 
correction of the initial point was too low, and should be changed from 
0°"151 to 0°'152. Applying similar reasoning to the other initial points, 
and to both the Bessel and Gay-Lussac curves, the following Table 
results : — 

Table VI. 
In terms of 0°-001. 



I. 


II. 


III. 


IV. 


V. 


VI. 


VIL 




Gay-Lussac 


Bessel 


Gay-Lussac 


Bessel 


Gaj'-Lussac 


Bessel 


100 








1 





1 





102 


80 


81 


1 


-1 


81 


80 


104 


121 


120 


-1 


-1 


120 


119 


106 


149 


146 








149 


146 


108 


155 


151 


-1 


1 


154 


152 


110 


142 


142 


1 





143 


142 


112 


109 


104 


-2 


1 


107 


105 


114 


115 


113 


1 


1 


116 


114 


116 


116 


115 


2 





118 


115 



160 REPORT — 1882. 

Column I. gives the principal points ; Columns II. and III. the 
corrections according to Gay-Lussac's and Bessel's curves ; Columns IV". 
and V. the mean excesses of the thread lengths, according as they are 
corrected by one or the other curve ; Columns VI. and VII., the cor- 
rections of the initial points themselves corrected by means of these 
excesses. It will be observed that the differences are reduced, but as 
the displacemeiit of each curve by the corrections is about the same, it 
is difficult to say which is the more accurate between 100° and 110". 

Another point of divergence occurring about 135°, all the threads 
whose ends fell on this part of the scale were picked out, thirteen in, 
number. Their differences from the means, expressed in thousandths, 
were, in the case of Bessel's curve, 

0, 0, -1, 6, 1, -1, 5, 4, 0, -4, -2, -G, 2; total 4, 
and in the case of Gay-Lussac's curve, 

4, 3, -1, 5, 1, 2, 1, 8, 2, 0, 1, -3, 8 ; total 31. 

This shows that the lengths given by the Gay-Lussac curve are on 
the whole too great, or that in this part it lies too high, and is the less 
accurate. On the whole, then, the Bessel curve seems to be the best, as 
theory would indicate. The extreme difficulty of obtaining an agreement 
throughout to less than 0°-005 is, however, shown by the discrepancies 
between the numbers given by Bessel's and Thiesen's methods. The 
probable error of a thread measurement is, according to the number given 
by Bessel's curve, 0°0025. Hence the probable error of a correction 
ought, according to Table IV., to be about 0°-0008 and 0°-001, according 
as it was determined by Bessel's or Thiesen's methods. They differ, 
however, in several places by 0°-005, and each receives independent con- 
firmation from one of the other methods. 

(18) The agreement in Table V. will or will not be considered good 
according to the standard of accuracy to which the readings of the 
thermometer, when in actual use, attain. 

Two members of the Committee (Professors Thorpe and Riicker) have 
frequently had occasion to read the same thermometer together, and they 
always agree to O^-Ol (O'l m.m.). This indicates a possible reading error 
of -4- 0°-005 (005 m.m.), when no lens or other aid is used. Pernet 
has~however, come to the conclusion that the distance between the fixed 
points can be determined to 0°-001, and thus Miirek and others think that 
a thermometer should be calibrated to 0°-002 at least. It may there- 
fore be convenient to lay down three standards of accuracy, defined by 
the conditions that the differences between the corrected and the true 
scales shall not exceed 0°-l m.m. (0°'01 in Thermometer C) in the first, 
0°-05 m.m. in the second, and 0°-02 m.m. in the third. 

(19) The observations on the Kew thei-mometers show that the first 
standard can be reached by a calibration conducted after Welsh's method 
with a good dividing engine. Inasmuch as the two Gay-Lussac curves 
shown in fio-. 1, Plate I., nowhere differ by more than 0°-12 m.m. 
(0°-011), except at the point 135°, where the difference could no doubt be 
reduced by a subsidiary correction near that point, the first standard is 
certainly attainable by a single Gay-Lussac correction conducted with a 
short thread and with Mr. Brown's instrument, provided that special 
attention be paid to the accurate investigation of maxima and minima. 

The second standard can be obtained with Mr. Brown's instrument 



METHODS EMPLOYED IN CALIBKATION OF MERCURIAL THERMOMETERS. 161 

either by Bessel's method or by the mean of two good correction curves 
obtained by Gay-Lussac's raethod with short threads. This last state- 
ment is proved by reference to fig. 3, Plate I. The mean Gay-Lussac 
curve and the Bessel's curve are there shown side by side, and it will be 
observed that at the points where the Bessel's correction differs moat 
from Thiesen's, the mean curve diminishes the difference. As the Bessel 
and the Thiesen curves do not differ by more than 0'007, nor the Bessel 
and the mean Gay-Lussac curves by more than 0°"00o, the latter may 
certainly be taken as correct to within this limit. 

There seems, too, no doubt that any of the principal point methods 
will, with Mr. Brown's instrument, and the methods of approximation or 
transference used as in this Report, give the principal points correct to 
O^'OOS. Among these the preference is certainly due to Thiesen's. It 
must, however, be remembered that the points corrected by these methods 
in this paper are too far apart to enable accurate curves to be drawn. 
They are suflBciently numerous to enable a comparison between the 
methods to be made, which is all that was desired. If they are used 
to determine points nearer together the number of measurements required 
and the labour of calculation rapidly increase. 

It seems therefore better to use these methods only as auxiliaries to 
a short-thread Gay-Lussac curve. 

This should be drawn as a first approximation, the length of the 
thread being a sub-multiple of the distance between the principal points 
determined by the more elaborate method. The corrections at these 
points should then be found, applying the method of transference by 
means of the Gay-Lussac curve, and, finally, the measures made on the 
short thread should be used to determine secondary between the prin- 
cipal points. The third standard of accuracy is more difficult of attain- 
ment. The discrepancies between Bessel's and Thiesen's figures in 
Table V. prevent certainty that either curve is correct to less than 0°'002. 
The method of least squares, as applied by Marek, does not seem to 
produce numbers differing by more than O'OOl from those given by 
Thiesen's method. The application of such calculations to so small a 
number of measures is, indeed, of doubtful utility. 

The thread-lengths measured at Kew do not after correction, when 
treated as above described (p. 159) to discover residual errors in the 
initial points, anywhere show signs of an error as great as 0°'002. The 
same statement, however, holds good for Bessel's curve, obtained in 
this Report with Mr. Brown's instrument, and yet, as has just been 
shown, it is difficult to feel certain that it is correct to 0°"002. On the 
whole, therefore, there can be no doubt that this standard of accuracy 
can be reached only by the most accurate apparatus and most perfect 
methods. 

The second standard in which the error of calibration is less than the 
error of an unassisted-eye reading of the thermometer is that which will 
probably be most generally aimed at. 

For this purpose the Committee, after considerable experience of 
Bessel's method on the part of some of its members, are (if an instru- 
ment such as Mr. Brown's or a dividing engine is used) decidedly in 
favour of the use of less laborious processes. The extreme length of the 
calculations required by Bessel's method is in itself a serious drawback — 
an undetected error may vitiate many hours' work. The sanae or a less 
amount of time spent in obtaining independent correction curves by Gay- 
1882. . M 



162 REPORT — 1882. 

Lussac's method, and taking the mean, would give an equally good 
result with much less trouble in calculation. 

(20) On the whole, then, the Committee think that, if the following 
rules are obeyed, an accuracy of 0°*05 m.m. in the correction of a 
thermometer scale can be attained. 

I. If a dividing engine is used, select principal points about 40 m.m. 
apart. ^ 

Correct by measures on a thread about —m.m. long, employing Gay- 

Lussac's as a principal point method. If necessary apply a second 
approximation. 

This will probably be sufficiently accurate. It may, however, be well 
to check by using a thread 40 m.m. long to redetermine the principal points 
accordino" to Gay -Lussac's method, applying the method of transference 
by means of the curve obtained with a short thread. Combine the results 
of the two sets of measures at the principal points, giving to the values 
obtained by the two threads weights proportional to their lengths. 

Use the shorter thread to determine secondary points. Examine 
further any maxima or minima in the neighbourhood of which the 
curves slope steeply. 

The total number of measures which would be required to apply this 
method to Thermometer C would be ten on the long and thirty on the 
short thread. 

II. If an instrument such as Mr. Brown's is used, reading to 0"1 m.m. 
on the vernier and to less by estimation. 

Select principal points about 40 m.m. apart. 

Apply Gay-Lussac's method twice by measurement on threads 20 and 

— m.m. long respectively. Use the method as a principal point method, 
o 

and make the points originally selected principal poinis for both correc- 
tion curves. 

If necessary, apply a second approximation in each case. 

If the two curves obtained agree to within O'l m.m. their mean will 
probably be as accurate as is desired. In taking the mean the weight 
assigned to each should be proportional to the thread-length. If, however, 
greater certainty is desired, it may be well to determine the principal 
points, either by Gay-Lussac's method, using a thread 40 m.m. long, or 
by Thiesen's. 

In the former case combine the three curves at the principal points, 
giving the weights 6, 3, and 2 to the corrections obtained by the longest, 
intermediate, and shortest threads respectively. 

If Thiesen's method is employed and there are n principal points, the 
weights assigned to the three corrections of the r*** principal point will be 

3 nr {n - r), 3 (w - 1), and 2 {n - 1) 
to that given by Thiesen's method and those obtained by Gay-Lussac's 
with the longer and shorter thread respectively. This gives so great a 
preponderance to Thiesen's method that unless the discrepancies are very 
great the corrections at the principal points practically depend upon it 
alone. 

' The numbers given in these rules refer to a thermometer about 400 m.m. long, 
on which ten principal points are to be found. They can readily be modified so as to 
apply to instruments of other dimensions. 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 163 

If these rules are applied to the numbers in Table V. the correction 
at the principal points are found to be 

118, 153, 106, 113, 134, 110, 110, 60, and 10, 

as given by the three Gay-Lussac curves, and 

121, 156, 109, 117, 138, 113, 112, 61, and 10 

by the Thiesen curve. 

As these nowhere differ by more than 0004, and by that only near a point 
where the Thiesen curve is certainly in error (116°), and as they nowhere 
differ fi-om the results given by Bessel's curve by more than O'OOS, except 
at 136, where the cause of the difference has been explained, it follows 
that both methods attain the second standard of accuracy. The three 
Gay-Lussac curves would involve altogether sixty thread-measurements ; 
the Thiesen and two Gay-Lassac curves would involve 104, so that on the 
whole it would seem better to adopt the former plan, and if when the 
calculation is concluded there seems any reason to doubt the result, to 
make another Gay-Lussac correction-curve, and include it in obtaining 
the final results. 

The general result of the investigation may, therefore, be summed up 
as follows — that labour is saved, and equal accuracy is obtained, by the 
repetition of the simplest method of correction (Gay-Lussac's) instead 
of the employment of more elaborate and, theoretically, more perfect 
schemes. 

Part II. 
Details of Calculations, with Examples of each Method. 

(21) The following system of symbols will be adopted. 

The upper and initial points of a thread will be indicated by the 
letters u and i. 

An uncorrected thread-length is therefore v, — i, indicated by t. 

The corrections at any point x to the first, second, &c., degrees of 
approximation are indicated by ^jj (x), (p2 (a;), &c. Since the calculations 
often give the differences between these quantities, it is convenient to 
define 

f (^^) = 92 (^) - <P\ («) 

and so on. 

A corrected thread- length is indicated by T, which is defined by the 
equation 

'J: =, u + 9 (u) - (i + 9 (i)) 

In principal point methods it is convenient to follow Thiesen (Zoc. 
citS) in the use of the symbol S, such that 

B(x + l) = (t,(x + l) -9 (x), 

where the symbols on the right refer to the x + V^ and x^^ principal 
points respectively. 

In cases where the true positions of the thread-ends are not coincident 
with their theoretical positions, the latter are often indicated by u and i,. 
the actual positions by ?t + Am, and-i +Ai. 

When in a step-by-step method the correction is referred to the mean 
point between the positions of the upper end of the thread and that of 
the lower end, when next shifted, that mean point may be indicated by u. 

M 2 



164 EEPoitT— 1882. 

The symbol r indicates the transferred thread-length defined in Part I. 
(p. 150) by the equation. 

T = t + I ^(ii + A m) - (p(u) - [</.(i + A {) -i>(i)] j . 

In the case of principal point methods it is often best to indicate the 
position of a thread by reference to the principal points nearest to which 
its extremities lie. Let the principal points be numbered from o upwards 
in the direction of increasing scale readings, and let u' and i' be the 
numbers indicating the principal points nearest to the upper and lower 
ends of the thread respectively. By the substitution of these quantities 
for u and ^ the above system of symbols will apply without further 
change. In cases, therefore, where ambiguity might otherwise arise, 
1', 2', &c. mean not the first, second, &c. scale division or degree, but the 
principal points numbered 1, 2, &c. Where no ambiguity is to be feared 
the dashes may be dispensed with. 



Gay-Lussac's Method. 
Thermometer C. 

(22) The following is an example of as accurate a compliance with 
the strict conditions of this method as is possible with Mr. Brown's 
instrument. 

The lower end of the thread was always moved into the same division 
and generally into the same part of that division as that in which the 
upper end previously lay. The correction is applied to the mean of these 
two positions. The thread-length was always measured twice in each 
position, together with the lengths of the divisions in which the extre- 
mities lay. The length of each division was therefore measured four 
times, twice when the upper and twice when the lower end of the thread 
lay in it. The mean of these four readings, which rarely differed by more 
than 0°"003, was taken as the true length. 

In Table VII., Columns I. and II. give the positions in terms of 
uncorrected scale-divisions of the lower and upper ends of the thread. 
Column III. gives the difierences between these quantities or the un- 
corrected thread-lengths (<). 

Hence, if the successive values of t be indicated by i,, ^21 &c., and if T 
be the corrected thread-length 

f T - <, = (99-66) - .i.(9805) = (99-66), 
(1) <^ T - ^o = ^(101-27) - V(99-66) = 0(101-27), 
[ T - ^3 = 0(102-89) - 0(101-27) = c(102-89), 
and so on. 

If, therefore, (98-05) = 0, 

0(99-66) =c(99-66), 
(101-27) = ^(101-27) + 0(99-66), 
and so on. 

Now there are 26 of the equations (1), and addition gives 
26 T - (i, +;,, + .... + ha) = 0(141-85) - 0(98-05). 
But the corrections of these two points may be taken as zero. Hence T 
is the mean of the uncorrected thread-lengths. 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 165 

In Column IV., therefore, are the means of the readings in Columns 
I. and II., or the points to which the corrections are to be applied («). 
In Column V. are the values of c(u) obtained by subtracting each of the 
numbers in III. from their mean. 

In Column VI. are the values of ^(«) obtained by taking the sum of 
all the c's up to c(n). 

Table VII. 



I. 


II. 


III. 


IV. 


V. 

In terms 


VI. 

ofO°-001 


i 


u 


t 


u 


s(rc) 


*(«) 


98-048 


99-656 


1-608 


99-66 


55-9 


55-9 


<)9-663 


101-269 


06 


101-27 


57-9 


113-8 


101-274 


102-891 


17 


102-89 


46-9 


160-7 


102-893 


104-522 


29 


104-55 


34-9 


195-6 


104-571 


106-219 


48 


106-23 


15-9 


211-5 


106-250 


107-909 


59 


107-93 


4-9 


216-4 


107-947 


109-625 


78 


109-65 


-141 


202-3 


109-667 


111-367 


1-700 


111-37 


-36-1 


166-2 


111-378 


113046 


1-668 


11305 


-4-1 


1621 


113-058 


114-723 


65 


114-75 


-1-1 


1610 


114-781 


116-443 


62 


116-45 


1-9 


162-9 


116-462 


118-120 


58 


118-14 


5-9 


168-8 


118-159 


119-814 


55 


119-84 


8-9 


177-7 


119-865 


121-526 


61 


121-54 


29 


180-6 


121-560 


123-247 


87 


123-25 


-23-1 


157-5 


123-262 


124-939 


77 


124-95 


-13-1 


144-4 


124-959 


126-628 


69 


126-62 


-5-1 


139-3 


126-623 


128-279 


53 


128-28 


7-9 


147-2 


128-278 


129-964 


86 


129-96 


-22-1 


12.5-1 


129-949 


131-640 


91 


131-65 


-27-1 


98-0 


131-663 


133-357 


94 


133-35 


-30-1 


67-9 


133-350 


135050 


1-700 


135-05 


-36-1 


31-8 


135057 


136-710 


1-653 


136-75 


10-9 


42-7 


136-789 


138-451 


62 


138-46 


1-9 


44-6 


138-462 


140144 


82 


140-15 


-18-1 


26-5 


140157 


141-847 


90 


141-85 


-26-1 


•4 


T = 1-6639 



In order to obtain a standard curve from the numbers given in the 
above Table, a few points were plotted down in the neighbourhood of 
100° and 140°, and the curve drawn through them. 

The corrections at these points were 0°-069 and 0°-028 respectively, 
i.e. in the notation used above (p. 147) 

f (i) = 0-069, a = - 0-041, - = - 0-001025. 

N 

The largest value of ^(a;) = 0-216. Hence the largest value of 
-i0(*) - fO)} is - 0-001 X 0-188 = - 0-0002, 

N 

which is negligible, as is the largest value of —^ x. 
Hence the formula reduces to 

X + </>(.-0 - 0(i) - - .-c = .?; + ^(a;) - 0-069 + "001025 x. 

N 



166 KEPORT— 1882. 

The ordinates of the standard curve are therefore easily obtained by 
subtracting 0'069 from the numbers in Column VI. of the above Table 
VII., and adding the number of degrees above 100 in Column IV. multi- 
plied by -001025. 

It is unnecessary to give the whole of the remainder of the calcula- 
tions ; but, as examples, the corrections for 104'55 and 135'05 may be 
taken, all the numbers being in terms of 0°'001 :— 

f (104-55) = 195-6 - 69 + 4-6 = 131 
<t> (135-05) = 31-8 - 69 + 35-1 x 1-025 
.= 31-8 — 69 + 36 = — 1 approximately. 

The standard curve thus obtained is the dotted curve in Plate I. 
fig. 1. 

Gat-Lussac. — Example II. 
Used as a principal point method with second approximation. 

TJiermometer G. 

(23) Another example of the application of Gay-Lussac's method 
-was carried out in a somewhat different way. 

It was now used to determine the corrections of points 2° apart — i.e. 
as a principal point method. 

,The thread-ends always lay in the divisions next to the principal 
point, and as a first approximation the differences between the corrections 
at the extremities of the thread and at the principal points were neg- 
lected. 

The calculation for the first approximation is carried out exactly as in 
the last case. There were twenty-one principal points — -viz. 100°, 102°, 
104°, &c. These were numbered from to 20, as shown in the Column 
headed u' in Table VIII. Columns I. and II. give the positions of the 
upper and lower ends of the thread ; Column III. their differences, or the 
uncorrected thread-lengths ; Columns IV. and V. the values of S («') and 
(u') obtained exactly as in the last example : — • 

With these values of (u') an approximate correction curve was 
drawn, and the corrections for the positions of the upj^er and lower ends 
of the thread were taken out in Table IX., Columns I. and II. 

Then, since the corrected thread-length 

= <i + (l> (u + Am) — <P (i + Ai), 

the differences of the numbers in Columns II. and I. are entered in III., 
and these, when added to the corresponding numbers in Column III., 
Table VIII., give the corrected thread-lengths entered in Table IX., 
Column IV. The numbers in Columns V. and VI. are obtained exactly 
like those in Columns IV. and V. in Table I. ; and, by adding the values 
of (/)' (t/) in Table II. Column VI. to those of ^ (u') in Column V. 
Table I., the values of fi ('^*') ^re found. 

It will be noticed that the differences between the values of f (u') 
and 02 (^<') are not inconsiderable. 

The curve obtained is drawn in Plate I. fig. 1. It is used, hereafter, 
as a first approximation curve for obtaining transferred thread-lengths in. 
the other methods. 



METHODS EMPLOYED IN CALIBKATION OF MERCURIAL THERMOMETERS. 167 

Table VIII. 
(1st Approximation.) Corrections in terms of 0°'001. 





I* 


II* 


III. 


IV. 


V. 


u' 


i' + Ai' 


u' + A«' 


t 


5(„') 


*("') 


1 


0-036 


1-908 


1-872 


•0754 


75-4 


2 


2-050 


3-958 


1-908 


•0394 


114-8 


3 


4-049 


5-969 


1-920 


•0274 


142-2 


4 


6-021 


7-962 


1-941 


•0064 


148-6 


5 


8-024 


9-985 


1-961 


--0136 


135-0 


6 


9-978 


11-958 


1-980 


-0326 


102-4 


7 


12026 


13-966 


1-940 


-0074 


109-8 


8 


14012 


15-958 


1-946 


-0014 


111-2 


9 


16012 


17-949 


1-937 


-0104 


121-6 


10 


18-050 


19-988 


1-938 


-0094 


1310 


11 


20-034 


21-978 


1-944 


•0034 


134-4 


12 


22-036 


24011 


1-975 


--0276 


106-8 


13 


24-016 


25-968 


1-953 


-•0056 


101-2 


14 


26-044 


27-985 


1-941 


•0064 


107^6 


15 


28-060 


30-031 


1-971 


-•0236 


840 


16 


29-971 


31-948 


1-977 


--0296 


54-4 


17 


31-957 


33-941 


1-984 


--0366 


17^8 


18 


34-030 


35-987 


1-957 


--0096 


8-2 


19 


36-011 


37-951 . 


1-940 


•0074 


15-6 


20 


38028 


39-991 


1-963 


-•0156 


0-0 



T = 1-9474. 
* The numbers in these columns are diminished by 100, thus 2-05 means 102-05. 







Table 


IX. (Second Approximation.) 


• 






I. 


n. 


IIL 


IV. 


V. 


VI. 


VII. 




Corrections from first 


Corrections 


Thread- 




.(.'(«') = 




u' 


curve (in -001"") 


of thread- 


lengths cor- 


«'(«') 


4>-zW) - 


<!>i{u') 




<i>{i' + A J') (<i(»«' + A u') 


lengths. 


rected. 




*(«') 




1 


2 


72 


70 


1-942 


4-9 


4-9 


80 


2 


76 


115 


39 


47 


- •I 


4^8 


120 


3 


117 


142 


25 


45 


1-9 


6-7 


149 


4 


143 


149 


6 


47 


- -1 


6-6 


155 


5 


149 


135 


- 14 


47 


- -1 


6-5 


142 


6 


135 


102 


- 33 


47 


- 1 


6-4 


109 


7 


102 


110 


8 


48 


- 1-1 


5-3 


115 


8 


110 


111 


1 


47 


- -1 


5-2 


116 


9 


111 


121 


10 


47 


- -1 


5-1 


127 


10 


122 


131 


9 


47 


- -1 


5-0 


136 


11 


132 


134 


2 


46 


-9 


5-9 


140 


12 


134 


107 


- 27 


48 


- 1-1 


4-8 


112 


13 


107 


101 


- 6 


47 


- -1 


4-7 


106 


14 


101 


108 


7 


48 


- 1-1 


3-6 


111 


15 


108 


83 


- 25 


46 


•9 


4-5 


89 


16 


85 


54 


- 31 


46 


•9 


5-4 


60 


17 


54 


19 


- 35 


49 


- 2-1 


33 


21 


18 


17 


8 


- 9 


48 


- 1-1 


2-2 


10 


19 


8 


17 


9 


49 


- 2^1 


-1 


16 


20 


16 





- 16 


47 


- -1 


00 






To = 1-9469 



168 REPOBT— 1882. 

Gay-Lussac— Example III. 
Application of method of transference. 

Determination of secondary points. 

(24) In this case a thread about 4° long was used, and the principal 
points were taken 4° apart. The thread having been accurately broken 
off, the transfer corrections are small. The curve determined in the last 
example was used as an approximation to determine them. The positions 
of the upper and lower ends are given in Columns II. and I. Table X. ; 
their difference, or the uncorrected thread-length, in Column III. From 
this the transferred thread-length 

T=t+ (<p (u + Au) - <p (u)) - if (i + M) - cp (0), 

is calculated in Columns IV., V., and VI., and from these the corrections 
of the principal points are determined as before. 

This example offers a means of illustrating the determination of 
secondary points. Let Pq and P be two principal points between which 
n secondary points are to be determined. This may be done by apply- 
ing Gay-Lussac's method to the interval by means of a thread=one n + 1"* 
of the distance between Pg and Pj. If this thread has been used to 
determine an approximate correction curve, transferred thread-lengths can 
be used, and the equations 

T-r,=ni)-^(Po) 
T-r2 = .^(2)-0(l) 
T - 73 = (3) - ^ (2) 

&c. = &c. 
T-r„ + . = ./.(P,)-0 W 
give by addition 

{n + 1) T = 7, -t- 72 + 73 -f- 4- r„, + , -f (PO - (Po) 

Whence T can be determined, and the calculations proceed exactly as 
before, except that T is not the mean of the transferred thread-lengths. 
The calculations of a few points will suffice, the thread used in Example 
II. being employed to bisect the intervals between the principal pointa 
obtained in the present example. 

Thus in Table XI., Column I. gives the principal and secondary 
points numbered as in Table VIII., Example 2. Column II. gives the un- 
corrected thread-lengths taken from the same Table. Columns III. and 
IV. give the values of the quantities by which the transference is 
effected, taken from the continuous curve in Plate I., fig. 1. Column VI. 
gives the value s oi Z correct to O'OOl taken from Table X., Column VII. 
Column VII. gives the values of T, i.e. of ^{rj + T2 + f(Pi)}. Column 
VIII. gives T — 7, and in Column IX. the corrections are finally ob- 
tained, as given by the formula. 

The points given by this thread are indicated in Plate I., fig. 1. 



JIETHODS EMPLOYED IN CALIBBATION OF MERCURIAL THERMOMETERS. 169 



M 

hi 
n 



VII. VIII. 


■-^..^ 

o 

o 

O 

6 

O 


«oc<)oo-*otONoo-<»<o 

f-HlOO^HCOi-H^HCOr-l 


1 


LO in h- j-, A -* l o oo « 
^1 1 1 1 1 


1 


^-1 


h 


tOtOO>5^0tO-'(MOrtl 
C5t^0 005CO-^tOtDOq 

CO "^ "^ "^ ^ ^ ^ ^ "^ "^ 


CO 

1—1 


K- 


+ •«■ 

-e- 


-0-001 

-0001 
-0-002 
-0-001 


1 




1 

/— ^ 

+ 

-e- 


-0001 
-0001 


1 




H4 


«0 10 O IM O b- — < -*l C3 lO 
03(:^COOG5CO-HCDO<M 
O^Of-Hf— lOi— 1»— I'-^rHr— 1 

CC '+' "^ ^ ^ ^ ^ ^ ^ "^ 


1 


HH 


S 

+ 


OO^Hf— lOt-Hl-HT-Hf— <r-* 

■*a)c<)«bc-»'obCTtbo 

O r-li-HtJq<M'MCOC0--»< 

T— 1 


1 


hH 


<l 

+ 


O 05 (M t- o Tji cc CO in o 

poscsOwspoooo 

O CO b- (Tl O O -* OD M =b 

o .-H i-H e^ ?■> (M CO CO 

T— 1 


1 




8 


•*C0(M«0O-*<00(M«DO 
O rH|-l(MC<INCl?CO^ 


1 



m 





el- 


o ^ 


1— ( 


1 


o o 


k 


II + 
+ 

^— .— ' 


to 00 

»— 1 .— ( 


l-H 




^H CO 
»— 1 


Is; 


h 


05 t- C5 r-l . 
to O rt -J* o 
CO OS a: 02 ^ 
Al f^ At Al 

b" »-"' b" b-' 


1— 1 


■5-C 

^ -e- 

vS 1 


0-1 

o 

<? . . . 6 

oo oo <^ 

1 


1— ( 


■0- 

1 

< 

+ 


o oo o 


»— 1 
t— 1 


~ 


IM CO O i-H i-l 
t^ O IM ^ to 

CO Ci C5 C2 C5 


HH 


~s 


.-H <M CO ■* lO 



170 



EEPOKT 1882. 



Hallsteom's Method. 
i Thermometer C. 

(25) In the application of Hallstrom's method the principal points 
were taken 4° apart, and a thread about 8° long was measured with its 
lower point in the neighbourhood of each of them, and a thread about 
12° long, with its lower end in the neighbourhood of the first two. 
S and (T have with respect to this longer thread the same meanings as 
T and r for the shorter. The Gay-Lussac curve drawn in a continuous line 
in Plate I., fig. 1, was used to effect the transference. Then the follow- 
ing equations were obtained : — 

S = ^3 + </'(3')-0(O) .... (1) 

! S = a, + f (4') - <p (1') .... (2) 

T = r, + ^ (2') - V> (0) .... (3) 

T = r, + cp(3')-<p(V) .... (4) 

&c.= &c. 

T = 7,0+ 0(10')- 0(8') .... (11) 

Hence, remembering that o (n) = (p («) — (p {n — ,) from (1) and (2). 

.: c (4') = a (1') + .73 - ff, 

= a (1') + y (4') say 
Similarly from the other equations : — 

ra - r3 = c (3') - c (1') .'. o (?,') = 3 (1') + r, - rg = 3 (1') + y (3') say 
- c (2') = c (4;) - (r; - rj 

= I (1') + ^3 — (^4 — (''3 — '■4) 

= a (1') + y (2') say 
can be expressed in terms of c (1'). If 



73 -r, = 3(4')-, -(2') 



c s 



Similarly all the other 

(0') and (10') are taken = zero, 

3(1') + 3(2') + 



+ 3 (10') = 0. 



Table XII. 
Thread I. 



I. 


II. 


III. 


IV. 


V. 


VI. 








In- 


001° 




100-022 


111-767 


11-745 


+ 1 


+ 2 


11-746 


4-015 


15-874 


11-859 

Thread 



II. 





11-859 


0020 


7-688 


7-668 


+ 1 


+ 1 


7-668 


4-019 


11-852 


7-833 





H-1 


7-834; 


8019 


15-878 


7-859 








7-859 


12-017 


19-808 


7-791 








7-791 


16030 


23-854 


7-824 





+ 2 


7-826 


20-025 


27-869 


7-844 








7-844 


24013 


31-885 


7-872 





+ 2 


7-874 


28-015 


35-937 


7-922 








7-922 


32014 


39-890 


7-876 





+ 1 


7-877 



Hence, if all the nine equations which give the c's in terms of 3 (1') 
be added, it follows that 

- 10 3 (1') =■ y (2') + y (3') + + y (10'). 



METHODS EMPLOYED IN CALIBBATION OF MEECURIAL THEllMOMETEBS. 171 

Hence, c (1') is known, from it all the other o's can be deduced, and 
the corrections at the principal points are obtained at once from the 
equation 

V^ (h') = HI') + H2') + +H«')- 

Table XII. gives the calculations necessary for finding the transferred 
thread-lengths. Columns I. and II. give the positions of the lower and 
upper ends of the thi-ead. Column III. the uncorrected thread-lengths. 
Columns IV. and V. give the values of ^ (i' -f A i') — <b (i') and 
<l> {u' + Au') — <j>{u'). Column VI. gives the transferred thread-length 
obtained by adding V. to III. and subtracting IV. 

Table XIII. gives the details of the determination of all the 2's in 
terms of c (1'). 

Column II. gives the transferred thread-lengths when the upper ends 
lie near the principal points indicated in Column I. 

Column III. contains the values of o-.-. — <tj, r, — r,, r, — rj, and 



'4) 



r3» 



'4' 



so on. 



Column IV. contains the equations between the o's obtained as 
above. 

In Column V. the right-hand sides are transformed so as to contain 
Z (!') and constants only. 

Table XIII. 



I. 


II. 


III. 


IV. 


V. 


u' 


<r or T 


In -001° 






3' 


] 1-746 


_ 





, . 


4' 


11-859 


- 113 


8(4') = S(l') - 113 


= S(l') - 113 


2' 


7-668 


— 


— 


— 


3' 


7-834 


- 166 


8(3') = S(l') - 166 


= 8 (1') - 166 


4' 


7-859 


- 25 


8 (2') = 8 (4') + 25 


= S(l') - 88 


5' 


7-791 


68 


8 (.5') = S (3') + 68 


= 8(1')- 98 


6' 


7-826 


- 35 


8 (6') = 5 (4') - 35 


= 8 (1') - 148 


T 


7-844 


- 18 


8 (7') = 8 (5') - 18 


= S(l') - 116 


8' 


7-874 


- 30 


8 (8') = 5 (6') - 30 


= 8(1')- 178 


9' 


7-922 


- 48 


8 (9') = 8 (7') - 48 


= 8 (1') - 164 


10' 


7-877 


45 


8(10')= 8(8') + 45 


= 8 (1') - 133 


10 8(1')= 1204 



Table XIV. 



1 -^■ 


II. 


III. 


1 "' 


«(«') 


*(«') 


1' 


120-4 


120-4 


2' 


32-4 


152-8 


3' 


- 45-6 


107-2 


4' 


7-4 


114-6 


6' 


22-4 


137-0 


6' 


- 27-6 


109-4 


7' 


4-4 


113-8 


8' 


- 57-6 


56-2 


9' 


-43-6 


12-6 


10' 


- 12-6 






The value of S (!') obtained by dividing the sum of the constants by 
10 is found to be 120-4. 



172 



EEPORT — 1882. 



Using this number, the values of o («') are found in Table XIV., 
Column II., whence in Column III. the corrections for the principal 
points are found in the usual way. 



Thiesen's Method, 
Thermometer G. 

(26) If the principal points be numbered from to n, Herr Thiesen 
employs a series of threads, the lengths of which are approximately equal 
to 1, 2, . . Ji — 1 times the distance between two consecutive principal 
points. He deals with untransferred thread-lengths. In the following 
example, however, transferred thread-lengths have been used, but as 
the method of transference has been fully illustrated, it is unnecessary to 
exhibit the calculations. Each thread gives a number of equations of 
the form 

T = r,, + <!> {u') - f (0) 

(1) T = r,,^,+f(u + l)-<t>(V) 

T = r,,+ o + 0(n + 2)-<?.(2') 
and so on. 

By subtracting each equation from that which precedes it, the follow- 
ing are obtained : — 

and so on. 

Now, the thread whose length is equal to the distance between two 

principal points can be measured in n positions, and hence from it n — 1 

equations of the series (2) can be obtained. Similarly, the thread the 

length of which is twice the distance between consecutive principal points 

gives n — 2 equations ; and in all there are 

■ ^ n (n — 1) 

ji - i + u - 2 + +1 = -^ 

equations between the c's. 

These are combined to find their values as follows. 

A table is prepared, of which the following is a symbolical repre- 
sentation : — 



i' 


?«' = 1' 


2' 




&c. 


1' 
2' 
3' 

71 


5(1') -5(1') 
5(1') -5(2') 
5(1') -5(3') 

5(i')-5(«') 


5(2') -5(1') 
5 (2') -5 (2') 
8(2') -5 (3') 

5 (2') - 5 («') 


5 (3') - 5 (1') 

&c. 


&c. 


— 


S(l') 


S(2') 


S(3') 


&c. 



The differences of the b's are given by equations (2). On adding all 
the numbers in any column, say the ?**', an expression of the form 

n S (r') - {? (!') -f h (2') + + a («')} = S (/) 

is obtained. But if (p (0') = <p (n') = 0, the expression in the bracket 
vanishes, and hence nc (/•') = S(r'). 

The h's being known, the values of (j) may be found as usual. 



I 



METHODS EMPLOYED IN CALIBBATION OF MERCURIAL THERMOMETERS. 173 

Table XV. 



i' 


I. 

T 






11. 

In -001° 


u' 






Thread J. 









3-096 








1 


1 


4-076 






- 80 


2 


2 


4-159 






- 83 


3 


3 


4-102 






57 


4 


■1 


4-090 






12 


5 


5 


4-136 






- 46 


6 


6 


4-111 






25 


7 


7 


4-161 






- 50 


8 


8 


4-160 






1 


9 


9 


4-123 






37 


10 






Thread IT. 









7-668 








2 


I 


7-834 






-166 


3 


2 


7-859 






- 25 


4 


3 


7-791 






68 


5 


4 


7-826 






- 35 


6 


5 


7-844 






- 18 


7 


C 


7-874 






- 30 


8 


7 


7-922 






- 48 


9 


8 


7-877 






45 


10 






Thread III. 









11-746 








3 


I 


11-859 






-113 


4 


2 


11-874 






- 15 


5 


3 


11-852 






22 


6 


4 


11-862 






- 10 


7 


5 


11-932 






- 70 


8 


(5 


11-956 






- 24 


9 


7 


11-968 






- 12 


10 






Thread TV. 









15-935 








4 


1 


16-037 






-102 


5 


2 


16-097 






- 60 


6 


3 


16046 






51 


7 


4 


16-103 






- 57 


8 


5 


16183 






- 80 


9 


C 


16-164 






19 


10 






Thread V. 









19-640 








6 


1 


19-778 






-138 


6 


2 


19-815 






- 37 


7 


;{ 


19-823 






- 8 


8 


4 


19-881 






- 58 i 


9 


5 


19-908 






- 27 1 


10 






Thread VI. 









23-991 








G 


I 


24-118 






-127 


7 


2 


24-195 






- 77 


8 


;5 


24-202 






- 7 


9 


4 


24-220 


Thread 


VII. 


- IS 


10 





27-775 








7 


I 


27-953 






-178 


8 


2 


28-034 






- 81 


9 


:$ . 


27-995 






39 


10 






Thread VIII. 









32-661 








8 


1 


32-838 






-177 


9 


2 


32-887 






— 49 


10 



174 



REPORT 1882. 



In the example worked out, the lengths of the thread employed were 
approximately 4°, 8°, 12° . . 32°. In strict accordance with the method 
as just explained, a thread 36° long ought also to have been used. It 
was, however, found difficult to manipulate so long a thread. Herr 
Thiesen points out that a number of thi-eads less than the largest possible 
number may be used, and the plan adopted below can easily be extended 
in a case where more than one thread is wanting. 

Table XV. gives in the first and last columns the numbers of the 
principal points between which the thread was measured. Column I. 
gives the transferred thread-lengths. Column II. the differences between 
the consecutive values of -. 

Thus, Thread I. gives in accordance with equations (2) 



Thread II. gives 



c (2') - c (V) 

a (3') - c (2') 

a(3')-^(l') = 
a (4') -0(2') = 



: - 80 

: - 83, &C. 

- 166 

- 25, &c. 



These numbers are tabulated in Table XVI. 

Thus 2 (2') — c (1') is entered in Column 2, Row 1. 

„ ?(3')-o(2') „ „ 3, „ 2. 

and so on. 





Table XVI.— Val 


ues of 


c (u') 


— S (i') in terms of 


•001°. 




»■' 


m' = 1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


1 





-80 


-166 


-113 


-102 


-138 


-127 


-178 


-177 




2 


80 





- 83 


- 25 


- 15 


- 60 


- 37 


- 77 


- 81 


-49 


3 


166 


83 





57 


68 


22 


51 


- 8 


- 7 


39 


4 


113 


25 


- 57 





12 


- 35 


- 10 


— 57 


- 58 


-18 


5 


102 


15 


- 68 


- 12 





- 46 


- 18 


- 70 


- 80 


-27 


6 


138 


60 


- 22 


35 


46 





25 


- 30 


- 24 


19 


7 


127 


37 


- 51 


10 


18 


- 25 





- 50 


- 48 


-12 


8 


178 


77 


8 


57 


70 


30 


50 





1 


45 


9 


177 


81 


7 


58 


80 


24 


48 


- 1 





37 


10 




49 


- 39 


18 


27 


- 19 


12 


- 45 


- 37 





S (1//) 


1081 


.347 


-471 


85 


204 


-247 


- 6 


-516 


-511 


34 


5 («.') 


121-2 


34-7 


-47-1 


8-5 


20-4 


-24-7 


-0-6 


-51-6 


-51-1 


-9-7 


<P («') 


121-2 


155-9 


108-8 


117-3 


137-7 


113 


112-4 


60-8 


9-7 





It will be seen that the squares in Column 10, Row 1, and Column 1, 
Row 10, are blank. This results from the fact that no measures were 
taken with a thread 36° long. 

By adding the numbers in the different columns, the values of all the 
o's, except o (1) and c (10) are found as previously explained. 

By adding Column I., however, the equation, 

9 (1') - {o (V) + c. (2') + + a (9')} = 1081 i 

is obtained, or ' 

9 S (1') + 8 (10') = 1081, 

Similarly, Column 10 gives ' j 

9 c (10') + c (V) = 34. ' 

Whence c (1') = 121-2 c (10') = - 9-7. 



methods employed in calibration of mebcurial thermometers. 175 

Marek's Method. 
Thermometer G. 

(27) Thiesen's method supplies, as has already been shown, more 
equations than there are unknown quantities. Marek has, therefore, 
applied the method of least squares to measurements made in this way 
up to and including the case in which the tube is divided into six 
intervals. 

As the formulte are somewhat lengthy, those only will be given which 
suflBce for the correction of four points. First, let the tube be divided 
into five parts by principal points numbered from to 5 (in this case the 
dashes will be omitted). Let r,„- be the transferred thread-length 
measured between the ^t*^'* and i"^ principal points of a thread equal 
approximately to the interval between them, and let the measurements 
be made as in Thiesen's method, and let threads equal to 1, 2, 3, and 4 
intervals be measured with their lower ends at as many principal points 
as possible. 

Finally, let f (0) = f (5) = 0, then 




'■52 
'•41 
'■30 


= 24-220 
= 24-195 
= 23-991 


'•51 

'"40 


= 32-887 
= 32-661 



In applying these formulae to Thermometer C the principal points 
would be 100°, 108°, 116°, &c. Hence, taking from the tables of thread- 
lengths given in Thiesen's methods those which are multiples of 8° in 
length, and which are measured with their lower ends at their principal 
point, the following values are obtained : — 

r5, = 7-877 . r53 = 16-164 

743=7-874 . 742 = 16-103 

732 = ''■826 . 731 = 16-097 

721 = 7-859 . 720 = 15-935 
710=7-668 

■whence, from the above formnlee, 
(0) = 0,<p (1) = 156, <p (2) = 116, <i, (3) = 112, 9 (4) = 62, <[, (5) = 0. 

If it be required to halve these intervals a thread about 4° long must 
be used, and the calculations are exactly similar to those given in the 
third example of Gay-Lussac's method. 

Let Pi and Pq be any two of the principal points where corrections 
^ (Pi) and ^ (Po) have just been determined. Let 7,, 73 be the trans- 
ferred thread-lengths of a thread about 4° long, measured with its lower 
and upper ends near each of them in turn, and then the correction for the 
point half-way between them is 

M^2-'-l+^(Pl)+^(Po)}. 



176 



EEPOET 1882. 



As an example has already been given of the determination of 
secondary points, it is unnecessary to carry the calculation farther. 



Rudberg's Method. 
Thermometer C. 

(28) A general outline of Rudberg's method has already been given. 
A thread approximately equal to half the length of the tube is measured 
with each end in turn at one of the extremities, i.e. in the thermometer 
used at 100° and 140°. 

Thus, if T be the true thread-length, and t^, t^ the uncollected lengths, 
and if when the lower end is at 100° the upper end is at 120° + a, and 
when the upper end is at 140° the lower end is at 120° + /3, two equations 
are obtained as follows : — 

T = i, + (120 + o) - (100), 
T = <2 + ^(14O)-0(12O + /3). 

Now, (j> (100) = (p (140) = 0, as these are the standard points, and, as 
a and ft are small, Rudberg assumed^ (120 + a) = ^ (120 + [3) = f (120), 
when 2^(120) = i!o-/i. 

The considerable inaccuracies which may be introduced by these 
assumptions are obviated by the method of transference. 

Thus, since the successive fractions into which the scale may be 
divided by Rudberg's method are ^, g-, yV, &c., and as in this example it 
was determined to divide the scale into twelve parts, the principal points 
are 

100°, 103°-3, 106°7, 110°, 113°-3, 116°- 7, &c. 

In Table XYII., Columns I. and II. give the positions of the lower 

Table XVII. 

Thread I. 



I. 


11. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 














Expre 


ssed in 






i + Aj 


u + ^u 
119-960 


t 


t 


V. 


terms o 


f 0-001° 


T 




100-052 


19-908 


■ 100 


120 


2 





19-906 


(1) 


119-767 


139-936 


20-169 


120 


140 


-1 


1 


20-171 


(2) 








Thread II. 


* 








100-0.38 


112-930 


12-892 


100 


113-3 


1 


-1 


12-890 


fS) 


113-.S40 


126-350 


13-010 


113-3 


126-7 





-1 


13-009 


(4) 


126-738 


139-843 


13105 


126-7 


140 





2 


13-107 


(5) 


106-836 


119-854 


13-018 


106-7 


120 


1 





13-017 


(6) 


119-849 


132-939 


13-090 


120 


133-3 





7 


13-097 


(7) 








Thread III. 










100-043 


116-537 


16-494 


100 


116-7 


1 


-1 


16-492 


(8) 


116-4.51 


133-136 


16-685 


116-7 


133-3 


-1 


3 


16-689 


(9) 


106-830 


123-473 


16-643 


106-7 


123-3 


-1 


-3 


16-641 


(10) 


113-022 


129-651 


16-629 


113-3 


130 


-1 


5 


16-6.35 


(11) 


119-937 


136-666 


16-729 


120 


136-7 








16-729 


(12) 


103-358 


119-939 


16-581 


103-3 


120 


1 





16-580 


(13) 


109-81.5 


126-460 


16-645 


110 


126-7 


2 





16-643 


(14) 


123-235 


139-965 


16-730 


123-3 


140 


1 


1 


16 730 


(15) 



METHODS EMPLOYED IX CALIBRATION OF MERCURIAL THERMOMETERS. 177 

and upper ends of the threads ; Column III. the uncoxTected thread- 
lengths ; Columns IV. and V. the principal points near the ends of the 
threads to which the corrections are to be transferred ; Columns VI. and 
VII. give the transfer corrections for the lower and upper ends of the 
threads; Column VIII. the transferred thread-length. Thus, from the 
first thread, 

T = 19-908 + i> (119-960) - </. (100-052), 
= 19-908 + {<!> (119-960) - </> (120)}, 
- {<!> (100-052) - <l> (100)} + f (120) - f (100), 
= 19-908 + - -002 + f (120) - <p (100), 
= 19-906 + <p (120) - <l> (100). 

From this table the following equations are obtained :— 

19-906 + </) (120) - <p (100) = 71 (1) 

20-171 + (j> (140) - <^ (120) = ri (2) 

12-890 + <i> (113-3) - </) (100) = r. (3) 

13-009 + i> (126-7) - <p (113-3) = r^ (4) 

13-107 + <l> (140) - ./. (126-7) = t^ (5) 

13-017 + <J> (120) - (/. (106-7) = T2 (6) 

13-097 + <p (133-3) - <j> (120) = t^ (7) 

16-492 + (j> (116-7) - f (100) = 73 (8) 

16-689 + f (133-3) - f (116-7) = 73 (9) 

16-641 + <!» (123-3) - f (106-7) = 73 (10) 

16-635 + ^ (130) - <l> (113-3) = 73 (11) 

16-729 + f (136-7) -</) (120) =73 (12) 

16-580 + </. (120) - f (103-3) = 73 (13) 

16-643 + f (126-7) - f (110) = 73 (14) 

16-730 + </. (140) - (123-3) = 73 (15) 

From (1) (2) since <{> (100) = <j> (140) = 0. 

^^,,0^^20071-29:906^ -133 (a) 

From (3) (4) (5) by addition 

3 72 = 39-006 or t^ = 13-002 

Hence from (3) (4) (5) (6) (7) 

f (113-3) = -112 (/3) 

(126-7) = -105 (y) 

</. (106-7) = -148 (g) 

<t> (133-3) = -038 (0 

From (8) and (9) by addition 

33-181 + ^ (133-3) - il> (100) = 2 73. 

Hence, since ^ (133 3) = -038, and ^ (100) = 0, 73 = 16-6095. 
Hence, from the equations given by thread III., 

<f> (116-7) = -1175 
from (10) <!> (123-3) = -1165 1 _ .,,g, 

from (15) <!> (123-3) = -1205 / ^^^^ - i J O'^ 

^ (130) = -0865 

f (136-7) = -0135 

f (103-3) = -1035 

^ (110) = -1385 
1882. N 



178 



EEPORT — 1882. 



The corrections as thus obtained are inserted in Table XVIII., 
Column I. In Column II. are given (for the sake of comparison) the 
corrections calculated from the observed instead of the transferred thread- 
lengths. The greatest difference is 0°-005. 



Table XVni. 






I. 


II. 


100 








103-3 


104 


101 


106-7 


148 


147 


110 


139 


136 


113-3 


112 


110 


116-7 


118 


117 


120 


133 


131 


123-3 


119 


117 


126-7 


105 


102 


130 


087 


092 


133-3 


038 


043 


136-7 


014 


013 


140 









This example will have made Rudberg's method clear. The correction 
for the middle part, C, of a tube A B, is obtained by measuring a thread 
approximately equal to A C or B C with its extremities at A and B in 
turn. 

A C B 

A thread approximately equal to ^ the length of tube is measured in 
the positions A d, d e, e B. Hence its true length and the corrections at 
d and e are found. By then measuring it in the positions C/ and C g, 



d e 

since its length and the correction for C are kno-wn, the corrections for 
f and g are found, and the tube is thus divided into six parts. 



f d eg 

Next, to divide the tube into 12 parts, a thread = -fh of its length 
is taken. The true length of this and the correction for h are determined 



A 



h c Jc I 



m B 



/ 



d 



9 



by measuring it in the positions A 7j, li g, as the corrections of A and g 
are known. An independent value of the length and the correction for 
% may be found by measuring fk, k B. In the present case the two 
values of the length differ only by O'OOIS. That determined from Ag 
has been used. By measuring forwards from d and C the corrections for 
I and m are found, and by measuring backwards from e and C, those for 
n and o. 

To divide the scale into 24 parts a thread ^^ of its length would be 
used, and so on. 



merhods elirloyed in calibration of mkkcdiual thermometers. 179 

Bessel's Methol» 
(As modified hij A. von Oettingeii). 

(29) For a full theoretical discussion of this method, reference must 
be made to von Oettingen's work, ' Ueber die Correction der Thermometer 
insbesondere ilber Bessel's Kalibrir-Methode ' (Dorpat, 1865), which has 
been frequently cited. It will be sufficient here to describe the method, 
and to refer to some points in which it seems open to criticism. 

A scries of equidistant points are selected, extending over the whole 
length of the thermometer-scale. The first of these should be at or near 
the lowest point on the scale, and if (as in the examples here given) ten 
threads are used, the tenth should be near the middle of the scale. Hence, 
if the distance between any two consecutive points is taken as the number 
of entire degrees or of half-degrees, which is most nearly equal to -^^ of 
the whole scale, the conditions will generally be fulfilled with sufficient 
accuracy. A mercurial thread is then measured in terms of scale-divisions, 
when the lower end coincides in turn with as many of the initial points 
as its length will allow, and this operation is repeated with ten threads 
of different lengths. 

The conditions which these threads must fulfil as to length are — that 
when the lower end of the shortest is brought to the first initial point, 
the upper end shall not reach the tenth initial point (practically, several 
threads should satisfy this condition), and that when the lower end of the 
longest is brought to the tenth initial point, the upper end shall be at, or 
nearly at, the top of the scale. 

The longest thread will thus be measured at ten initial points, and 
some of the shorter threads will be measured at more. A convenient 
arrangement is to take the shortest thread about ^, and the longest 
about ^, of the whole length of the scale. 

Observations other than those in which the end of the thread lies at 
one of the ten initial points nearest to the bulb are, in the ensuing calcu- 
lations, treated differently from the rest, and will be called the additional 
observations. 

Tables XIX. and XX. give the thread-lengths obtained in the case of 
Thermometer C from the first ten initial points and from the additional 
observations respectively. For the reasons given above, the lower ends 
of the threads were not coincident with, but only very close to, the initial 
points. The error introduced by this fact will be discussed hereafter. The 
initial points are given in Column 0, the thread-lengths in Columns 
I. to X. 

Tables XXI. and XXII. are obtained from II. and III. by adding the 
thread-lengths to the initial points, and thus give approximately what 
would be the readings for the upper ends of the threads if the lower ends 
coincided exactly with the initial points. 

These tables give the direct results of the measures. It remains to 
deduce from them the scale-errors, and it will be convenient to follow 
von Oettingen's notation closely. Let Vj. be the mean of the numbers in 
the ¥^ column of Table XXI., H^ the mean of the numbers entered in 
Columns I. to X. of the same table. Let M be the mean of all the 
numbers entered in Columns I. to X. of Table XXL, which is obtained 
by taking the mean either of the ten V^'s, or of the ten H,.'s ; and, lastly, 

n2 



180 



EEPORT — 1882. 



O 



« 


1. 


td 




H 




W 


."^ 


S 


'■;s 


O 


c> 




^ 


(^ 




b) 


^» 


M 


« 


H 


s 




.«> 




bi 


M 


1 


1— 1 




M 


S 




Ci 


» 




h-1 

CO 


ts 


■< 




H 





I. 


— (COCC(^OO-*<t^'MCI0<M 
(M.-Hlo^HiOCO»O00Cv|(M 

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t^ t-- l^ t^ t-^ t^ b- b^ t- b- 


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t- 

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lo o ib »h lb »h tb >b »b »b 

C-] M Kl Kl c-l (N S<1 C-l (M (M 


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lO 

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in 

t— 1 




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t- 

00 

oo 

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o 

CJ 




t— CC^^00CO-**CO^^(M(M 
(M OO »0 O 10 lO lO >C ff; <M 

■^--i-icococomcoco-ti 


1 

CO 


IV. V. 


O O CO lO CO <?q C5 1-0 t^ lO 

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CO 
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C5l~C0C0C:COlM— It H 

CTC0C0COt--H_t-05C0 
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lb lb lb lb lb »b lb lb »b ib 


10 

lb 


»— 1 

h- 1 


Ol 00 10 t- lO t— CO CO -+' 00 

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(MCCCO-^^-+<-+l^--t*-^ 

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00 

CO 

m 

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t-lOt-OCO(MOCOO— ' 
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lO 
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oo 

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s 




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O CO 
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o o 


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t- C-. 05 h- O 
CO CO 00 CO Ci 

lb lb lb lb lb 

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1— ( 


lO I- CO O CO CO 
oo CO 10 CI CI lO 
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M CO « cb oo M 

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t- t- t- l'^ t- t- t- b- t- 


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^HdCICIClClCOCOCO 






METHODS i:MPLOYED IN CALIBRATION OF MEllCURIAL THERMOMETERS. 181 



!^ 



-Htoosoo^occcO'^co 
oococcc:oo^H«5oo^H 

<MCC-^^»OOCDiOlOCO 
m O b- O -^ CO "b b- 05 -^ 

iMc^i>4CMCccf:cococo-a< 



1^ 



.-H 50 05 t- '.-r "O -t< C2 IS 00 

tOlSC^It^COCOOllOtOGO 
CO-*iO»SO«00?DOO 

IMIM<MC<1C0C0CCC0C0-* 



Cit~t-i— IC000C2OOO 

<NC^<MS^c>ic(;cccococo 



l>--*ll0l--rH00OOO«0 
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t^CO-H00eC^CO-H(MiM 
CI OO O O iQ >--; lO lO C5 <M 

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t-c^T^coibb-Cif^cbo 

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tOCOOSOCOOSt^-^OOr-i 

tcb-t^ooooooooooooo 
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i-Hr-li-HC^CllMCliqCOCO 



030CO!Ot— ^ — t^OCO 
ip!£>l^t^t^0OO0t--b-CO 

coibt-c^-^cbih^-cif^ 
t-if-ii— ii— icqucjiqcico 



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f— (^if:t-*C5T^o^»nw65 

I— t,i— t ^H f— ( r-l ^ CJ CI CM CI 



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ic^t-ooooooQOt— coop 

t^c-'--tcbibh-di»^cb»b 

-^ rt .-I rJ rt CI O CI 



CiCOCOOS^HCOOO-^-^tO 

t~-COCCOCOCOOtOCOOi 

cpt-ooososo^oaoooooo 

l-^ b- CS "^ K "b t- OS -^ CO 
^ ^ rt rt rt CJ C) 



OOOCI-fCOOOOCl'^tO 

C500000^-i— i^H,-H 






pa 
« 
Eh 






(—1 


o 
in 
o 




o ^ 

O CO 
CO 00 

CO o 
CO "Jl 


> 


37-427 
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> 


05 O t^ 00 

CO to to to 

CS OS OS C5 

-* tb ci) o 

CO CO CO '^ 


1— ( 


00 CO t^ CI C5 

t^ Ci c:5 t- o 

00 GO 00 OO C5 

W lb b- CS r^ 

CO CO CO CO ^ 




lO t^ to o to o 

00 CO lO CI O lO 
■^ lO lO lO lO >o 
.^ CO lb b- 02 .^ 

CO CO CO CO CO "^ 




ot^ooostoiaooo 

CI ^ t- 00 01 03 OS 00 
00 00 OO 00 OO OO 00 oo 

»^02T^cblbb-05»^ 
CICICOCOCOCOCO'*! 


hH 


t^OOt^OStOt HCICO 

i-lrt^-t-WOStOlO-* 

ibb-6s.^n5ibt-c5rlH 

C100COOTCOCOCO-* 


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>— tCldCiCICICOCOCO 



182 



EEPORT 1882. 



let Uj.,. be the number entered in the r*'^ row of the h^^ column (the 100, 
which for shortness has been omitted, being of course included). 

The symbolical representation of Table XXI., with the Vs, &c., intro- 
duced, is therefore 






I. 


II. 


in. 


— 


X. 




ho 


Up, 




U3,, 


— 


U.0-, 


H„ 




V, 


V. 


V3 


— 


v,„ 


M 



where 



M = Yl 



+ V, + +V,o_H, +H, + +H 



in 



10 



10 



Now, von Oettingen proves (loc. cit. p. 9), that 

^U,,.= H,. + V,-M-U,,. 

An alternative plan is, however, better — viz., to make use of Table 
XIX. instead of Table XXI., inasmuch as the numbers employed are 
smaller. Let /.i be the mean of the initial points, and let Ji,., v^., in and %^ 
have the same significations with respect to Table XIX. as the corre- 
sponding large letters have to Table XXI. Then 

H,. = i, + h,., V/, — ^L + i\., M = n + m, U,.,. = i, + u,,,. 

.'. by substitution in the above formula, 

fl> (U;,,) = h,. + Vk - »«' - «<■-■• 

The values of all the four quantities on the right-hand side of this 
equation are given in Table XIX. 

Table XXIII. contains the values of v^ — %.,., and in the last column 
of h,. — m. 

Table XXIV. is obtained by adding the values of h^ — rti to those of 
V)i — V,.,. — e.g. in Column I. 176 — 191 = — 15, and so on. 

Table XXIV., therefore, contains the corrections according to the 
formula for the scale readings given in corresponding situations in 
Table XXI. A curve is then drawn, with the scale divisions in Column I., 
Table XXI. as abscissae, and the corresponding corrections in Column I, 
Table XXIV. as ordinates, and similar curves are drawn for each of the 
other threads. 

They are shown in fig. 1, Plate II., drawn in continuous lines, and 
numbered to correspond with the column and thread from which Ihey 
are deduced. The scale of the curves in the plates is one-half of that 
actually employed. The mean of the ordinates of these curves for every 
degree above the highest initial point is then taken, and a curve with 
these quantities as ordinates is drawu, tluis forming part of the^^rs^ mean 
cm-ve. It is shown in fig. 2, Plate II., drawn in a continuous line. It will 
be observed that the fii-st correction curves do not extend to the lower 
and of the scale. The corrections for this are obtained from the initial 



^e*" 



-^95:: 



\Z'- 



ir 



M 



2: 



5^ 



Plate IL 



f^ 



g 



Fi|- 



2^ 



2: 



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~z 



_14C 



5 



:2-S: 



:2^. 



W 



;^f=: 



11^.: 



- z? 



'=^: 



=5 




itrri JBustraiina (he. RqK I m 



■troiing (he, kefK ( VI Uu MeU ode finfjlo^f t tl c Uxl b t f CM iinalllunD U re ^ 



J 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 183 



XI 





1 


.— 1 1—1 

1 1 1 




>< 


1 1 1 1 1 1 






(M .-H 1-1 

1 1 1 1 1 1 




1— t 


(M-:H^ ,--t£il>00COO0 
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^ 


1— 1 


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1 1 I 1 1 1 1 






I— 1 1— 1 I— 1 
1 1 1 1 1 1 


N 

/A 

i 
1 


> 


"^"^ 1 1 1 1 1 1 


•ii 

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S— ' 




1 1 1 1 1 1 1 




1— 1 


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1 1 1 1 1 1 1 






^'^ 1 1 1 1 1 II 




HH 


^^ 1 1 1 1 1 1 1 




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05000 0'— tr^T-H^^ 



I 

> -5 

XI + 
XI s 

H II 

0- 



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1 1 1 1 t 1 


1— 1 


—■lOCOlOrHiMOO^CCtO 
1 1 1 1 1 


1— H 
)— I 


•Ht-eoec-HeoososOcO 
CO cq l-H N -*< CO 

! 1 1 1 1 




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•-H ^1 »— 1 (M f-H -^*H I— ( 

III 


l-H 


QOO'-li-IO«Ot^«OCOCO 
<M l-H rt ^ (M CO 

1 III 


> 


C3^coiotOi-iiOT-(coia 

III 1 1 




CO CO rt (M <M 1-1 

i 1 1 


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1— t 


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CO CO CT .-H (M T-H (M C^ 

1 1 1 1 


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1 1 1 1 1 


1— I 


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1 1 1 1 1 


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184 



EEPORT — 1882. 



points. It is proved by von Oettingen that the correction for an initial 
point i,. is given by 

f (i,.) := H^ — i,. + constant 
= h,. + constant. 

Now, if the assumption is made that the correction for the highest 
initial point is accurately given by the first mean curve, the corrections 
for the initial points are readily found by adding to the values of h^ in 
Table XIX., or /;,. — m in Table XXIII., the quantity which is necessary 
to make /^lo or /i,o — m equal to the correction thus obtained from the 
curve. 

Thus, in the example under discussion, the ordinate of the first mean 
curve at 116° is — -024. To make the value of ^,o — m — viz. -079 — 
equal to this, -103 must be subtracted from it. Hence the correction for 
98° is — -191 — -103 = - -294, and so on. The quantities so obtained 
are plotted down in fig. 1, Plate II., and produce the first initial point 
curve (PQ R). 

In order to combine this with the portions of the upper point cor- 
rection curves which extend below 116°, von Oettingen gives to it equal 
weight with them, takes the mean, and thus completes the first approxi- 
mation correction-curve. 

The corrections for the initial points thus determined are inserted in 
Table XXV. :— 

Table XXV. 





Corrections of initial points expressed in terms of 


=•001 




Correction of 116 from fig. 1 = - 24 






/(-TO for lie . . . = 79 




98 




-294 


108 


-4.S 


100 




-22.5 


110 


-40 


102 




-141 


112 


-68 


104 




- 94 


114 


-44 


lOG 




- 60 


116 


-24 



Table XXVI. 

Corrections of Upper Ends from, mean curve I. (Jiff. 2., Plate II.) exjjressed 

'in terms of 0°-001. 






I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


X. 


AV 


98 


- 40 


-18 


-44 


-39 


-29 


-13 


2 


19 


25 


20 


-11-7 


100 


- 17 


-23 


-42 


-26 


-18 


9 


22 


25 


8 


8 


- 5-4 


102 


- 24 


-48 


-27 


- 6 


5 


26 


24 


8 


14 


20 


- 0-8 


104 


- 49 


-36 


-10 


15 


24 


19 


8 


13 


23 


17 


2-4 


106 


- 35 


-25 


11 


26 


23 


8 


16 


23 


5 


- 6 


4-6 


108 


- 25 


- 5 


26 


13 


7 


20 


23 


6 


-14 


-25 


2-6 


110 


- 4 


15 


18 


9 


17 


18 


3 


-13 


-39 


-39 


- 1-5 


112 


16 


26 


8 


22 


22 


- 4 


-14 


-37 


-30 


-18 


- 0-9 


114 


26 


13 


20 


14 


1 


— 22 


-39 


-32 


-12 


-12 


- 4-3 


116 


12 


9 


17 


- 9 


-15 


-40 


-28 


-12 


-18 


-25 


-10-9 


^''fc = 


-14-0 


-9-2 


-2-3 


1-9 


3-7 


21 


1-7 


0-0 


-3-8 


-6-0w'= 


-2-59 



METHODS EMPLOTED IN CALIBRATION OF MERCURIAL THERMOMETERS. 185 





s 




^. 




«^ 








"« 




« 




t. 


)— 1 




1— 1 


i 


^ 








fa 




« 






•-i 





1 1,1,11 




a:c<t(Nir:cococoocooo 
' ' Mill' 


!3 


OOO OO00-*00OO 
(M (M >-l ^ ^ 


1 


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II II 


>i 


C'l r-l IM (M i-H CC 1-1 i-H 
1 II 1 


1— ( 


Mil' 


t— J 
> 


1 1 ' M ' 




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C*I IM 1 rt 1-1 1 i-( -H CO 

II ' M ' 


t— ( 

> 


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1-1 1 !M — 1 1 i-i i-l SM -*! 

' 1 1 ' II 


> 


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CC iM 1 IM -H 1 1-1 I-l 1-1 

' 1 1 ' II 


> 


1 II ' II 


1— t 
H- 1 


iMOioooccooooc-ic: 

■*-*C^ i-IO^CTi-lCli-l 

M 1 II 1 


1— < 

1— t 


1-1 m (M rt 1 IM « <M 1-1 
1 II 1 


NH 


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1 II 1 


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C500000I— ii— li— ii— 1 



X 



w •« 






II 



y, 


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1 II 1 


H- 1 


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1 1 1 I 


1— « 

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> 


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II ' ' 1 ' 


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1 (M fM 1 11-1 1—1 CO (M 

' 1 1 ' ' 1 


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1-1 CI 1-1 1-1 1-1 iM CO 

III II 


> 


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C<1 1— 1 1—1 1—1 f— 1 1— 1 1—1 

II II 


r>- 


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186 



EEPOET 1882. 



The entire continuous curve in fig. 2, Plate II., made up partly of tlie 
initial point curve, partly of the first mean curve, partly of the two com- 
bined, is called the first approximation curve. 

(30) If a second approximation is required, the theoretical procedure 
is to insert in Table XXI. the corrected values of the initial and upper 
points as given by the first mean curve. Hence, to deduce a corrected, 
Table XIX., and to proceed as before. 

A considerable saving of labour can, however, be effected by dealing 
with the corrections in the quantities in Table XXI. alone, instead of 
with the quantities themselves. 

Thus the corrections for the upper ends of the thread taken from the 
first approximation curve are entered in Table XXVI. 

In Tables XXVII. and XXVIII. the same operations are performed 
upon these as are performed in Tables XXIII. and XXIV. npou those in 
Table XIX. Hence a series of numbers are obtained by which the correc- 
tions in Table XXIV. would have been altered had the measurements 
been made with the scale corrected to the first approximation instead of 
with the uncorrected scale. 

By adding the numbers in Tables XXIV. and XXVIII. the quantities 
entered in Table XXIX. are obtained, which constitute the corrections or 
the second approximation for the upper points. 



Table XXIX. 






I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


X. 


98 


2 


-3 


-2 


-1 


-5 


— 2 


2 


3 


3 


3 


100 








5 


-7 


— 2 


-5 





-1 





5 


102 


-7 


-4 


2 


-4 


_2 


-1 


-4 





10 


•J 


104 


-5 





3 


-5 





-1 





5 


3 


3 


106 


-5 


-1 





4 


-6 


1 


-6 


8 


-1 


6 


108 


-2 


1 


-2 


-5 


1 


3 


5 


-4 


3 


-6 


110 


1 


-1 


-4 


2 


3 


2 


2 


5 


—2 


-6 


112 


-2 


3 


-1 


3 


5 


2 


3 


-10 


-3 


1 


114 


8 


-3 


-1 


r, 


4 


-1 


-3 





-7 


-8 


116 


4 


6 


2 


5 


6 


1 


4 


-4 


-10 


-13 



The numbers in Table XXIX. are plotted down in fig. 3, Plate II., 
and the mean of the ordinates of the curves is taken as in the first 
approximation, and these when added to those of the first mean curve 
form the second mean curve. 

It is, however, necessary below 116° to combine these curves with 
the corrected initial point curve. It has been shown that if f(ir) be the 
coi'rection for the r* initial point, <p(i,.) = h,. = h^ — i,. plus a constant 
which, as differences only are required, may for the present be neglected. 
Now, by taking the mean of the initial and upper point curves at that 
part of the scale where they overlap, ^(iV) is changed into 

'/'(v) = f(i) + '^r, 

where -cr,. is the difference at that point hetween the first mean curve and the 
first initial point curve. 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 187 

The analogue of Table XXII. in the second approximation would there- 
fore be drawn up as under : — 



Initial points. 


I. 


II. 


ho + *(^lo) + •=^10 


«1.10 + <f'(«i.io) 


&C. 
&C. 

&c. 



Hence the correction for the r^^ initial point (omitting the constant) 
would be : 



10 



0«l,r + «2»- +....+ 1tlO„) + jTj {^(«I,r) + ^(«2n) + + </'(»I0„-)} 



Bat 



— (U^„ + U.2„. + + Iho,,-) = H, = ^(C) + ir, 

plus a constant which may be neglected, and 



1 r, 



10 



{^(»i.,-) + ^(«2»-) + + fi^ho„y,■. 



is equal to the quantity entered in Table XXVI. as h',.. 

Hence ^'(iV) = Z^',- — '^,- 

The values of -ra-,. taken out from the first mean and first initial point 
curves in figs. 2 and 1, Plate II. are entered in Table XXVII. In the 
next column are the differences between the values of h',. — m' and •zr-,.. 

The additional correction for 11G° from the second upper point curves 
is — -002. Hence, by adding 6 to the values of h',. — in' — tn,., the 
ordinates of the second initial point curve are obtained which are entered 
in the last column of Table XXVII. By taking the mean of these and 
the upper point curves where they overlap, the following second approxima- 
tion corrections are obtained in Table XXX. 



Table XXX. 
Corrections of initial 2>oints {second ap2}i'oximatio')i) expressed in terms o/C-OOl. 



98 


- 3 


108 


- 7 


100 


3 


110 


- 5 


102 


8 


112 


- 4 


104 


11 


114 


- 2 


106 


-5 


116 


_ 2 



In order still further to correct the upper part of the scale, the follow- 
ing method is adopted. The full corrections for the initial and upper 
points are taken out from the second mean curve and entered in Table 
XXXI. 

If to any mean thread-length, i.e. to the value of v,. obtained in 
Table XIX., the mean correction for its upper points be added, and that 



188 



KEPOBT — 1882. 



XI 

m 
■< 





















s 
1 


1—1 1-H 








II [1 






ii 












-^ 






b--4<oooot^iO(Mcqci 


CO 




^ 


-rt<t>-.— (i— (lOG^r^OlOG^ 


1 




< 


III 1 1 II 


Jl 






t>05-*<^(NOD«05000 


05 




H 


rH C9 C>) d -^ r-H (M CO 
1 1 1 1 i 1 


1 






-foot^050(Neooioos 


00 




>< 


"M i-l(M >-l-*mrt<M 


■* 




1— ( 


1 1 1 1 1 


1 


•^ 








N 

* 

» 


j * 


t^^OOtDt^t^OlMCOCO 


IM 


h- C 


i-Hoi i-Hcq rt-jtcoi-i 


o 




> 


1 1 1 1 


1 


t2 








1 








. 


o-HMooa>50ioc^^oo 


oo 


N 


> 


1 1 1 


a 








c- 








'fi^ 








i"' 




-*l~.OCOC3«(MO«-* 


-*l 






■-I (M T-c (M IM (M ^ 


•fo 


> 


1 1 1 


<M 


"h 








!~ 








<u 








s 




eqo5C(3m^coo«o-*-* 


o 


> 


CC i-H C<) (M <?5 <M 1-1 
1 1 1 


•* 


'« 








s; 








« 








.*^ 




cqosi^iMto^^ot^co 


I>1 

1^4 




> 


III 1 


S 








"^ 
















, 


05ioo-^0«omo5-i*<— 1 


o 




■*-*ia2.-if-l(Mi-( (MM 


CO 


hH 


1 1 1 1 


1 


^ 
























t3 






to 




, 


mt — fOcoocoONi-i 


r-H 






(MlMlO-*liM i-liqt-irt 


•-H 




t-H 


1 1 i 1 1 1 


1 








O) 






incCOSlOOOOOlOrHtOi-l 


t^ 




, 


■* (M cq »o m ^q i-H M rt 


■-H 






1 1 1 1 1 1 1 + + + 


1 








CO 














h~(MCOCOOCi5^iOI>.t~ 


-* 






OicMCOCO-^C-ICOloeOIM 


OJ 






IM (M .-H 






-&■ 


1 1 1 1 1 1 1 1 1 1 


1 








^ 




o 


aoc>'>'\'^<ot^O>o^'^^ 






CiOOOOOi-Hi— ii— ii— ( 


s 









^1 



o 

o 

o 

O 



8. 



XI 
X 
X 

H 

m 
«i 






^ 



l-H 


^ 1 1 1 i i 1 1 1 


1— < 


S5 1 1 1 1 1 1 1 


1-^ 


ggS M 1 1 1 1 


> 


gg^S Mill 


1— 1 


-*< -S< CO oo 10 1 1 1 1 
N •* ^ rH iO 1 1 1 1 


1— 1 


lO t- «0 O «0 50 

-* CO CO CO to 1 1 1 


1—1 


C5CqC5O«--<0i-IC5 
0-) (M -»( •* 'it •* CO 1 

1 1 1 


1— 1 


!OU3-r«tOeO-*.-IC50 
rH^^T-ti— l-^eOCOrHi— 1 

1 1 


O 


000<MrHeOCOON-t< 
i-ilM(M3-1iNIMeOCOC0 



o 1-5 


eoo50-*ot-«ococot^ 

C0'»<a510C0O00.-l00CTl 

csoo^oogs-jHt-iotpio 
t-05co>btbaiO(>i-*ib 

f— If-Hi— (»-H<M(MC<I(M 


a 

o 

"§ 

(-1 


OOCO(Mt~Ot-t-^Ot- 

t^OOOiOCSOSO^CiOSOO 

opooooopoo 


13 

o 5J 


lOCOOOl^i-lOOOCOO 

ioeoa>iocO'HoortC5.-i 

COfr-COIr-QOCO«3-*>Oip 

h'05co»bcbc506i'rttib 
t-li-li-Hi-l(M<NCqiM 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 189 

for its initial points (both taken from Table XXXI.), be subtracted, the 
corrected thread-length is obtained. These are exhibited in Table XXXII. 

The errors of tlie additional measures (given iu Table XXXIII.) are 
obtained by subtracting the corrected thread-lengths from the uncorrected 
lengths given in Table XX. 

If now the corrections for the lower ends of the additional measures 
f .2(1',.) be taken out from the second mean curve, the corrections for the 
upper ends can be calculated. 



Table XXXIV. 
Correctians for Initial and Upper Points of Additional 3feasicres, in terms o/0°-001. 



0. 


*2(0 


I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


118 


- 4 


12 


2.-) 


1 


-28 


-43 


-24 


-18 


-31 


120 


15 


30 


17 


-32 


-29 


-15 


-15 


-30 




122 


26 


12 


- 3 


-40 


-17 


-11 


-33 






124 


10 


- 6 


-30 


-20 


- 8 


-28 








126 


12 


-31 


-35 


-24 


-43 










128 


27 


-37 


-19 


-39 












130 


14 


-17 


-27 














132 


- 6 


-25 


-45 














134 


-36 


-46 

















The values of ^o (^-) ^^'^ entered in Column I., Table XXXIV., and 
by subtracting from these the numbers in Table XXXIII., the upper 
point corrections are obtained. 

The corrections given by each thread are plotted down in fig. 4, Plate 
II. ; and the curve shown in fig. 5 is obtained by taking the mean of their 
ordinates. 

It agrees closely with the second mean curve. Where they diverge, 
as in the neighbourhood of 134° and 140°, the mean is taken and plotted 
down in fig. 2, Plate II., in the curve drawn thus : : 

The curve thus finally attained must next (for purposes of comparison) 
be converted into a standard curve. 

The corrections for 100° and 140° are : - 0-223 and 
respectively. 

Hence, in accordance with the formula given in Part I., p 
following quantity must be added to the corrected readings : — 



- 0-022 
147, the» 



0-223 



201 r . . / N , a.ooQ 0'201 



Now 




•^ {x) + 0-223 - 



0-201 
40 



■] 



only amounts to 0-001 if the quantity inside the brackets = "2. 

The values of </> («) 4- 0-223 are given in Column III. of the following 
Table XXXV. They exceed •! when a; is > 2. As x increases, however^ 

the quantity — - — x becomes greater, and at about 125° it reduces the 
expression below -1. On the other hand, the last significant figure of the 

numerator in the fraction — —— introduces a term >-0005 when x 

40 

is >20. 



190 



EEPORT— 1882. 



On the whole, therefore, if the expression be written in the form 
0'223 — 'OOo X — "001, the last term being only nsed when x is > 2, no 



error amounting to O'OOl will be made. 



Table XXXV. 



I. 


11. 


III. 


IV. 


V. 


100 


-223 











101 


-177 


46 


- 5 


41 


102 


-134 


89 


- 10 


79 


103 


-lOG 


117 


- 16 


101 


104 


- 84 


139 


- 21 


118 


105 


- 59 


164 


- 26 


138 


&c. 










138 


- 16 


207 


-191 


16 


139 


- 17 


206 


-196 


10 


140 


- 22 


201 


-201 





141 


- 31 


192 


-206 


- 14 



The corrections for the initial points which will be required afterwards 
are as follows : — 

Table XXXVI. 



100 





110 


141 


102 


79 


112 


107 


104 


118 


114 


115 


106 


151 


116 


115 


108 


159 


— 


— 



Bessel's Method. 
FurtJie)' Modifications in the Calculations. 

(.31) Having thus described Bessel's method as modified by von 
Oettingen, it is necessary to indicate some points in which it appears to be 
susceptible of improvement. 

The most obvious objection is that the scale is corrected by dif- 
ferent methods in different parts, and with varying degrees of ac- 
curacy. 

In the first approximation, the middle part of the scale is corrected by 
observations on all the ten threads, the upper part by observations on 
three, two, and at last on one only. It is true that in the second approxi- 
mation the additional measures are introduced, but the corrections for 
the lower ends of these are of unequal value. Thus the correction 
at 124° is determined from 9 curves, that at 1.34° is found from 5. The 
latter must, therefore, be the more uncertain, and this uncertainty will be 
as it were transmitted to the upper ends of the threads measured at these 
points in the additional observations. 

At the lower end of the scale matters are still more unsatisfactory. 
In the opinion of von Oettingen (loc. cit., p. 14), the corrections for 
the initial points are of the same value as those for the upper ends of 
the threads. If this be so, only four points are corrected between 98° and 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 191 

105°, while 33 determinations of the corrections of equal value are made 
between 122"^ and 129°, without including the additional observations. 

Such an arrangement of the experiments is evidently unsatisfactory. 
It will be hereafter shown that von Oettingen has probably under- 
estimated the value of the corrections of the principal points, but making 
all allowance for the much higher value which should probably be 
assigned to them, there can be no doubt that the correction is either 
determined unnecessarily often in the middle of the scale, or at too great 
intervals in the lower part. 

It appears, then, that the extremities of the scale are the portions 
upon the corrections of which least reliance can be placed. This is 
especially unfortunate. Delicate thermometers are now commonly 
graduated for a part only of the range between 0° and 100° C. As, there- 
fore, such instruments can have at the most but one fixed point, the 
temperature value of a scale division must be determined by comparing 
them at two temperatures with another instrument upon which the other 
fixed point can be read. If two thermometers do not cover the whole 
range between the freezing and boiling points, the comparison may have 
to be made by several intermediate steps. Each instrument in a set of 
such thermometers is, therefore, constructed so as to overlap those which 
read above and below it. To avoid the necessity for having too many 
thermometers, this overlap rarely exceeds one-fourth of the scale and is 
often less. Hence the errors in the absolute measurements made by a 
given thermometer will be several times greater than the errors made in 
the measurement of the temperature- difference necessary to determine the 
value of the overlap. The extremities of such thermometers should, 
therefore, be the most carefully corrected, and yet it is here that the 
method under discussion is weakest. 

Objection may also be taken to the method of grafting the initial 
point correction curve with those portions of the correction curves for 
the upper points which affect the same part of the scale. 

Von Oettingen, referring to an example in which eight threads were 
used, says (he. cit., p. 14) : ' Fiir die Curve der arithmetischen Mittel . . . 
sind ausser den 64 Verbesserungen der 8 mal 8 oberen Fadenenden, noch 
die enimal 8 Correktionen der unteren Enden hinzugenommen. In der 
That haben diese Verbesserungen dasselbe Grewicht wie der oberen Enden.' 

This view appears open to objection. It is quite true, as von Oettingen 
adds, that the expressions obtained by him for the corrections of an upper 
and a lower point both contain the same assumptions, which are only 
approximately true — viz., that the sum of the errors of any row and of any 
column are separately = 0. 

But he determines the ei'ror of the topmost initial point (116) from 
the means of the curves of the upper points. To this, therefore, the full 
weight, 10 (if 10 threads are used), must be assigned. 

In using the formula (p (i'g) — ([> ('i,o) = /ig — 7i,o, the only quantity 
neglected is the difference of the means of the corrections of the upper 
points in the ninth and tenth rows. Now, since the upper points in these 
rows extend over nearly the same part of the scale, the difference of these 
quantities — i.e. //'t, — /i',o — must be small. In the example given it 
amounts to 0°'007. Hence (/> (uj) must be known with considerable 
accuracy. The value of f (ig) will be more doubtful, and so on. On 
the other hand, the weight 10 is perforce assigned to corrections given 
by the initial point curve at the lower end of the scale, inasmuch as no 



192 



EEPORT — 1882. 



othera are available. It seems, tberefore, unreasonable to entrust the cor- 
rection entirely to the initial point curve up to the point where the first 
upper point curve overlaps it, and then suddenly to regard it as of equal 
value to this, which is itself only one out of ten carves which are used to 
determine the correction in the centre of the scale. 

Experiment fully confirms this view. In no case, either of examples 
worked out by members of the Committee or of those given by von 
Oettingen, do the corrections given by the initial point-curve differ on a 
first approximation from the values they ultimately assume so much as 
do many of those given by the upper point curves. 

(32) In calibrating their thermometers, therefore. Professors Thorpe 
and Riicker thought it better to weight the initial point curve 10, the 
upper point curves being weighted 1, to introduce the additional measures 
in the first approximation, and to determine the initial point of any 
additional measure with full accuracy before using it to determine the 
error of its upper point. 

For this purpose the calculations were carried on exactly as in the 
previous method up to and including Table XXIV., and the upper point 
and initial point curves were drawn. The mean ordinates of the upper 
point curves were calculated from the highest initial point (116°) up to 
the point where the first upper point curve ended (123°). The means of 
the lower parts of the upper point curves and of the initial point curve 
were then taken, giving the latter the weight 10, and thus the fii-st mean 
curve was formed from 98° to 123°. It is given in fig. 1, Plate III. 

The additional observations were now at once introduced, and the 
calculations required the gradual building up of five Tables at the same 
time. The highest point given by Thread I. is at 123°-9 ; hence the 
corrections for the initial points and for all the upper points on Thread I. 
were taken out from the first mean curve and entered in Table XXXVII., 
in the columns headed f {{) and I. respectively. 



Table XXXVII. 

Corrections of U^per and Initial Points from Mean Curve I, Jiff- 1, Plate III., 
expressed in terms of(i°QQ\. 






*(0 


I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


X. 


h' 


98 


-291 


-61 


-39 


-63 


-47 


-32 


-13 


2 


19 


24 


18 


-18 


100 


-225 


-38 


-34 


-51 


-25 


-18 


9 


22 


25 


9 


11 


- 9 


102 


-140 


-35 


-61 


-26 


- 7 


6 


26 


23 


9 


17 


22 


- 3 


104 


- 94 


-61 


-44 


-10 


14 


24 


18 


8 


16 


24 


19 


1 


106 


- 56 


-43 


-25 


11 


26 


22 


11 


18 


24 


7 


- 3 


5 


108 


- 36 


-24 


- 5 


26 


12 


8 


22 


24 


8 


-12 


-24 


4 


110 


- 37 


- 4 


15 


16 


13 


19 


20 


5 


-10 


-35 


-34 


1 


112 


- 62 


15 


26 


11 


24 


23 


- 1 


-13 


-34 


-25 


-16 


1 


114 


- 41 


26 


12 


22 


15 


4 


-20 


-36 


-27 


-11 


-13 


- 3 


116 


- 24 


12 


12 


19 


- 5 


-14 


-35 


-23 


-11 


-22 


-32 


-10 




-101 


-21 


-14 


- 3 


2 


4 


4 


3 


2 


- 2 


- 5 


m'=-3 



The mean of the ^ (i)'s subtracted from the mean of the numbers in 
Column I. gives the correction on the mean value of Thread I. given m 



late in. 




SjioUiswoodc S; C' LitK.Londo'n. 









j!.uLi-i_LLiiiJ-i-LLiii:iiun f riJii.m4444J4rr: 

l-ig.I. IltMtli Mrdtnt (r^.x«M„pUIlP ' ' H 1 1 1 



Qntimiaia /^iru: /&»( of^mdiiiotitiii Qirvr 
:— PoUtil Line Satoul 

Ml irfr'TtJ /fliiu A. 




lii. Lj'iA-i- i<ant au-vsB n 

Sreaid initiat point ctave A'.T.V.tf 

Ml ,,iu-,T,i II- E F 



I 






if 



^^ 



^m 







ffig 



M 



rUiistixKiri,/ (/if /(iport m cJu McchciUi anplcyed in die Ca/ibratim oT Aftntaial ntet-numie^s. 



M& 



-■-fc 



:-;si 



iilffi^if^ss 



i-iSi. 



rig^ 



■^^^^mm^ 



gfeS 



METHODS EMPLOYED IN CALIBRATION OF MERODIIIAL THERMOMETERS. 193 

Table XXXVIII. Hence the corrected value of Thread I. is obtained aa 
in Table XXXVIII. 

Table XXXVIII. 
Corrected Mean Lengths of Threads. 



Uncorrected 
Length from 
Table XIX. 


Correction 


Corrected 
Length L 


Uncorrected 
Letigth from 
Table XIX. 


Correction 


Corrected 
Length L 


7-855 

9-766 

13-398 

15-757 

16-831 


-080 
•087 
-098 
•103 
•105 


7-935 

9-853 

13-496 

15-860 

16-936 


19-310 
20-089 
22-420 
24-593 
25-510 


•105 
•104 
•103 
-099 
-096 


19-415 
20-793 
22-523 
24-692 
25-606 



Subtracting this mean thread-length from the uncorrected lengths 
given in Table XIX., the errors of the additional measures of Thread I. 
are found, and entered in Column I., Table XXXIX. 

The corrections of the initial point.'^ between 116 and 122 beino- 
known from the first mean curve, which is complete up to 123, they are 
entered in Table XL., and by subtracting from these the errors of the 



Table XXXIX. 

Errors of Additional Mcasitres = Jj — Z, in terms of 0°-001. 






I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


Vlll. 


118 


-18 


-33 


-11 


18 


33 


12 


7 


17 


120 


-17 


- 6 


41 


38 


24 


22 


38 




122 


12 


25 


60 


37 


31 


51 






124 


14 


36 


24 


12 


32 








126 


41 


43 


30 


49 










128 


62 


42 


60 












130 


29 


37 














132 


17 


35 














134 


8 

















additional measures in Table XXXIX., the corrections for the upper 
points of the first three additional measures of Thread I. are found and 
entered in Column I., Table XL. The points to which these correspond 
are given in Column I., Table XXI., and by their aid the correction curve 
given by Thread I. can be prolonged as in fig. 2, Plate III. 

Using this prolongation, the mean curve can now be prolonged for 
two or three degrees by means of all the ten curves — viz., nine in fio-. 1, 
Plate II., and one in fig. 2, Plate III. — i.e., it is prolonged far enough 
to take out, as in Column II., Table XXXVIL, all the corrections for the 
upper points of Thread II. The same process can then be repeated with 
this thread, and thus gradually all the ten curves, by means of which the 
first mean curve is constructed, are formed — the initial point of each 
additional measure being determined, with the full accuracy of which 
the first approximation is capable. 

(33) The second approximation is then carried out in exactly the 
same way. 

1882. 



194 



EEPORT 1882. 



Tables XLl. and XLIl. are obtained from Table XXXVII., Table 
XLIII. from Tables XXIV. and XLII. The corrections for the initial 

Table XL. 
Correction for Initial and Tipper Points of Additional 3Ieasii/res, in terms (»/'O°'0Ol. 






*(0 


I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


118 


- 3 


15 


30 


8 


-21 


-36 


-15 


-10 


-20 ■ 


120 


17 


34 


23 


-24 


-21 


- 7 


- 5 


-21 




122 


26 


14 


1 


-34 


-11 


- 5 


-25 






124 


11 


- 3 


-25 


-13 


- 1 


-21 








126 


13 


-28 


-30 


-17 


-36 










128 


25 


-37 


-17 


-35 












130 


14 


-15 


-23 














132 


- 6 


-23 


-41 














13i 


-29 


-37 

















points are obtained as previously described (p. 187), and entered in Table 
XLIV. ; and the second mean curve is completed as before up to 123°. 



Table XLI. 

Derived from Tahle XXXVII. {In terms t)/0=-OOI). 






I. 


II. 


III. 


IV. 


V. 

36 


VI. 


VII. 


VIII. 


IX. 


X. 

-23 


/('-. — m 


m-- 


h',. — m' 
— a,- 


98 


40 


25 


50 


49 


17 


1 


-17 


-26 


-15 





-15 


100 


17 


20 


48 


27 


22 


- 5 


-19 


-23 


-11 


-16 


- 6 





- 6 


102 


14 


47 


23 


9 


- 1 


-22 


-20 


- 7 


-19 


-27 











104 


40 


30 


7 


-12 


-20 


-14 


- 5 


-14 


-26 


-24 


4 





4 


106 


22 


11 


-14 


-24 


-18 


- 7 


-15 


-22 


- 9 


- 2 


8 


5 


3 


108 


3 


- 9 


-29 


-10 


- 4 


-18 


-21 


- 6 


10 


19 


7 


7 





110 


-17 


-29 


-19 


-11 


-15 


-16 


- 2 


12 


33 


29 


4 


4 





112 


-36 


-40 


-14 


-22 


-19 


5 


16 


36 


23 


11 


4 


5 


- 1 


114 


-47 


-26 


-25 


-13 





24 


39 


29 


9 


8 





3 


- 3 


IIG 


-33 


-26 


-22 


7 


18 


39 


26 


13 


20 


27 


— 7 





- 7 



Table XLIT. 

<|)'(U<.,.) = c'a. - ?('*.,. + h,! - m'). In terms of 0°-001. 





I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


X. 


98 


25 


10 


35 


34 


21 


2 


-14 


-32 


-41 


-38 


100 


11 


14 


42 


21 


16 


-11 


-25 


-29 


-17 


-22 


102 


14 


47 


23 


9 


- 1 


-22 


-20 


- 7 


-19 


-27 


104 


44 


34 


11 


- 8 


-16 


-10 


- 1 


-10 


-22 


-20 


106 


30 


19 


- 6 


-16 


-10 


1 


- 7 


-14 


- 1 


6 


108 


10 


— 2 


-22 


- 3 


3 


-11 


-14 


1 


17 


26 


110 


-13 


- 25 


-15 


- 7 


-11 


-12 


2 


16 


37 


33 


112 


- 32 


-36 


-10 


-18 


-15 


9 


20 


40 


27 


15 


114 


-47 


-26 


-25 


-13 





24 


39 


29 


9 


8 


116 


-40 


-33 


-29 





11 


32 


19 


6 


13 


20 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 195 



Table XLIII. 

</>(Uiv) + <^(U>It) = 'P'A'^tr). In terms of 0°-001 . 






I. 


II. 


III. 



IV. 


V. 


VI. 


VII. 


VIII. 


IX. 


X. 


98 


10 


7 


1 


-8 


-6 


-3 


- 1 








100 


11 


3 


10 


-11 


— 5 


-6 


— 2 


— 2 


— 2 





102 


— 5 


2 


_ 2 


- 5 


-4 


-1 


-4 


- 1 


7 


6 


104 


- 1 


2 


1 


— 5 


-1 


1 





3 


3 


1 


106 


- 3 


— f") 





o 


-4 


1 


-6 


10 





5 


108 


- 8 


— 2 


- 1 


— 2 


2 


5 


7 


_ 2 


5 


-4 


110 


- 3 


-3 





1 


4 


5 


4 


7 


-1 


-7 


112 


- 6 





- 3 


3 


6 


3 


5 


- 9 


-4 


2 


114 


3 


— 5 


_ 2 


6 


3 


1 


-3 


- 1 


-4 


-4 


IIG 


— 2 


-1 





2 


C 


-1 


1 


_ 2 


-3 


-4 



Table XLIV. 
Mean Ordinates from Initial and Ujjjyer Point Carves, in terms o/O'-OOl. 



106 


5 


111 


1 


107 


3 


112 





108 


2 


113 





109 


1 


114 


-1 


110 


1 


115 


-4 






116 


-6 



The additional measures are then a^ain introduced. Let L, L and 
X + Z, be an uncorrected measure of the length of a thread, and the 
means of the ten ordinary measures of the same thread correct to a first 
and second approximation respectively. 

Let (j> (m), <!) (i), ^., («) and ^2 (*') be the corrections for the upper 
and initial points of the thread, correct to a first and second approxima- 
tion respectively. 



Hence, 



L + ^2 («) — 02 (0 = ^ + ^ ; 



but ^2 («) = 00 + 0' 00, and ^0 (0 = (0 + 0' (0- 

.-. <p' {u) = (i) + f (i) + Z _ {L - i + (u)} . 

To apply this formula, Table_ XLV. is found from the second mean 
curve, exactly as Table XXXVIT. was found from the first — i.e. the 
columns ^ (i) and I. are completed and their means taken. As before, 
the difference between t), and the mean of the 0(»)'s gives the correction 
for the mean value of Thread I., and thus the corrected length of that 
thread is found as in Table XLVI. Tlie difference between the corrected 
lengths in Tables XLVI. and XXXVIII. give the values of I, which are 
given in the last column of Table XLVI. The values of the corrections 
for the upper points of the additional threads are then taken out from 
the first mean curve and entered in Table XLVII. ; and these, being 
added to the corresponding values of L — i in Table XXXVIII. , give 
the values of L — L + ^ (it) entered in Table XLVIII. 

02 



196 



KEPORT — 1882. 



Table XLV. 

Corrections of Initial and Upper Points from corrected Mean Curve. 
In terms o/0°-001. 






*2(0 


I. 
-56 


II. 


III. 


IV. 


V. 
-35 


VI. 


VII 


VIII. 


IX. 


X. 


h" 


h"-m" 


98 


-309 


-36 


-52 


-47 


-16 


-2 


16 


24 


16 


-19 


-16 


100 


-229 


-35 


-34 


-51 


-30 


-22 


4 


20 


25 


8 


11 


-10 


— 7 


102 


-138 


-34 


-60 


-31 


-9 





25 


23 


8 


18 


26 


-3 





104 


-88 


-61 


-44 


-13 


11 


22 


16 


9 


17 


28 


21 


1 


4 


106 


-51 


-42 


-30 


6 


26 


21 


11 


20 


28 


9 


1 


5 


8 


108 


-31 


-30 


-7 


26 


11 


10 


25 


27 


11 


-9 


-23 


4 


7 


110 


-35 


-7 


11 


14 


13 


21 


23 


9 


-8 


-36 


-35 


1 


4 


112 


-62 


12 


26 


11 


28 


27 


3 


-11 


-35 


-23 


-14 


2 


5 


lU 


-42 


26 


10 


26 


19 


8 


-19 


-37 


-26 


-11 


-12 


-2 


1 


116 


-30 


11 


13 


22 





-12 


-36 


— 22 


-11 


-21 


-32 


-9 


-6 




-102 


— 22 


-15 


-4 


2 


4 


4 


4 


3 


-1 


-4 


-3 





Table XLVI. 

Corrected Mean Lengths of Threads (second apjjroj:imation'). 



Uncorrected length Cor 


•ection 


Corrected length 


Difference between 2nd 
and Ist approxs. = 


7-855 


080 


7-935 


■000 


9-766 


087 


9-853 


-000 


13-398 


098 


13-496 


-000 


15-757 


104 


15-861 


-001 


16-831 


106 


16-937 


•001 


19-310 


106 


19-416 


■001 


20-689 


106 


20-795 


•002 


22-420 


105 


22-525 


•002 


24-593 


101 


24-694 


•002 


25-510 


098 


25-608 


•002 



Table XLVII. 

Corrections for Upjicr Points of Additional Pleasures from 1st Mean Curve 







fo- 


, Plate III. In terms of 0°- 


001. 









I. 


il. 


III. 


IV. 


V. 
-36 


VI. 
-17 


VII. 


VIII. 


118 


13 


24 


-2 


-28 


-11 


-19 


120 


25 


15 


-21 


-33 


-21 


-13 


-23 




122 


14 


-5 


-34 


-13 


-11 


-31 






124 


-6 


-28 


-16 


-14 


-24 








126 


-29 


-33 


-12 


-37 










128 


-32 


-13 


-32 












130 


-13 


-14 














132 


-14 


-36 














134 


-37 

















The second mean curve being completed up to 123° enables the first 
three values of </> (i) + ^' (/) to be taken out in Table XLIX. ; ajjd by 



METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 197 



means of Table XLVIII., and the values of I, the corrections for the 
npper points of the first three additional measni-es of Thread I. are 
found. By this means the curve given by Thread I. is prolonged, and 
the operation of completing the second mean curve is carried out in a 
manner similar to that adojited in the first approximation. 

Table XLVIII. 
■L - L + <p (it). In terms of 0°-001. 






I. 


II. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 


118 


- 5 


- 9 


-13 


-10 


- 3 


- 5 


- 4 


— 2 


120 


8 


9 


20 


5 


3 


9 


15 




122 


26 


20 


26 


21 


20 


20 






121 


8 


8 


8 


- 2 


8 








126 


12 


10 


18 


12 










128 


30 


29 


28 












130 


16 


23 














132 


3 


- 1 














131 


-29 

















Table XLIX. 

Corrections for Upper Points of Additional Threads j^^tted down in Curves in fg. 4, 

Plate III. 





<f,(0 + <p'(i) 


+ l- 


(L - Z 


+ <J>(«))- In terms of 0°-001. 







* (0 + no 


I. 


11. 


III. 


IV. 


V. 


VI. 


VII. 


VIII. 






l = Q 








1 


1 


1 


2 


2 


118 


- 6 


-1 


3 


7 


5 


— 2 








-2 


120 


13 


5 


4 


-7 


9 


11 


5 







122 


26 





6 





3 


7 


7 






124 


9 


1 


1 


1 


12 


2 








126 


14 


2 


4 


-4 


3 










128 


29 


-1 





1 












130 


17 


1 


-6 














132 


- 3 


-6 


-2 














134 


-30 


-1 

















The curve must now be made to pass through the standard points. 
This operation is performed as in the previous example, the formula 
in this case beino: 



0-230 - 



0-215 f ^ ^ / N ^ n oQn 0-215 

s a; + ^ (a;) + 0-230 — — x 



40 



40 



} 



It is unnecessary to give details, 
points are : — 

Table L, 



The correction for the initial 



100 





110 


140 


102 


81 


112 


102 


104 


119 


114 


111 


106 


146 


116 


113 


108 


151 


— 


— 



198 REPORT— 1882. 

The curve is exhibited in fig. 3, Plate I. 

(34) On oomparing the two methods a glance at the first and second 
approximation curves in fig. 2, Plate II., and fig. 1, Plate III., establishes 
a primd-facie case in favour of that adopted by Professors Thorpe and 
Rlicker. In von Oettingen's method there is a considerable difference 
between the two curves at the part affected by the additional measures, 
and also at the points where the initial and upper point curves overlap. 
In the curve obtained by the second method, the agreement is perfect at 
the top of the scale, and very much better in the neighbourhood of the 
overlap. The greatest difference occurs at the points which the previous 
discussion indicates as the weakest — namely, the lower initial points. 
The much closer agreement between the values of h',. — m', and of 
Ji'^ — i)i' — 'w,., exhibited in fig. 3, Plate III., than between those in 
fig. 3, Plate II., is also a point in favour of attributing the weight 10 to 
the initial point curve. 

It is, however, possible to submit the differences in the neighbour- 
hood of the overlap to a closer investigation. The values of h'' in Tables 
, XXXI. and XLV. enable the correction of the initial points to be carried 
a stage further. It follows from the investigation of the correction of 
the initial points already given (p. 187) that, just as in the first appi-oxi- 
mation, the process of combining the initial and upper point curves 
changes ^ (i^) into (l> (i,.) + -nr,. ; so, in the second approximation, it will 
change (p' (i,.) into (j)' (/,.) + •ct',.. Hence, if ^p' (/,.) is the difference be- 
tween the second and first mean curves at the o-^^ initial point, 

^' (Q = f (V) + -'- 
, By a method similar to that by which the correction Avas obtained in 
the second approximation, the third correction is now found to be 

</." (i) = H,. - i + h'^ + -,V {f (n,„.) + i>' (u,„) + &c.} 

I Now, since in Tables XXXI. and XLV. the whole correction is taken 
out — i.e. (j>2 («) — and not merely the difference between the first and 
second approximations — i.e. (j)' (?;). 

i J^'r + tV [f (^h,r) + I'' (Mo„.) + &C.} = h" ,. ; 

and since <j> (v) = H^ — i„ 

and ^\. = ^P' (i) - f (i,), 

it follows that <}>" (i,) = h'\. - ■nr, - i/.' (?,). 

As -ra-,. + \p' (v) is the difference between the second mean curve and 
the first initial point curve, this expression is exactly comparable with 
that obtained in the first approximation. 

In Table LI. the values of (p" (r,.) are calculated according to both 
methods. 

The values of <(>" (i,.) reqiiire the addition or subtraction of a constant 
in order to bring the curves given by them into agreement at one point 
with that obtained from the second mean curves. The cori'ected curves 
could then be made to pass through the standard points. 

As, however, the values of ({>" (/,.) are ncai'ly the same at 100° and 
116°, and as the resulting corrections ai'e very small, no appreciable 
error will be committed if they ai^e considered as applied directly to the 
standard curves. A third approximation to the corrections of the initial 



METHODS EMPLOYED IN CALIBRATION OF MERCUBIAL THERMOMETERS. 199 

points may therefore be obtained, under conditions such that the two 
methods may bo compared by adding to the values of ^" (i,.) the correc- 
tions for the initial points taken from the standard curves, together with 
the constants (K) necessary to make the corrections at 100° zero. 
This operation is performed in Table LII. 



Table LI, 

Expressed in tervis of 0°-001. 

VoN Oettingen. 





from Table XXXI. 




'i-Xir), 






from Table XXVII. 


from Curves 
fig. 2, Plate 11. 


*"(v) 


98 


-15 





- 4 


-11 


100 


- 7 





2 


- 9 


102 


- 2 





8 


-10 


104 


2 





10 


- 8 


106 


5 


25 


- 7 


-13 


108 


3 


28 


- 8 


-17 


110 


- 2 


14 


- 5 


-11 


112 





18 


- 5 


-13 


114 


— .5 


10 


- 3 


-12 


116 


-13 





- 3 


-10 



Thorpe and Euckee. 





h"r, 

from Table XLV. 




V-'Cv), 






from Table XLI. 


from Curves 
fig. 1, Plate III. 


-*"('V) 


98 


-19 





-15 


-4 


100 


-10 





- 5 


-5 


102 


- 3 





2 


-5 


104 


1 





5 


-4 


106 


5 


5 


4 


-4 


108 


4 


7 


2 


-5 


110 


1 


4 


1 


-4 


112 


2 


5 





-3 


114 


- 2 


3 


- 1 


-4 


116 


- 9 





- 6 


-3 



Table LII. 





Von Oettingen 


Thorpe and Eiicker 


Second approxm. 


Third approxm. 


Second approxm. 


Third approxm. 




from Table XXXVI. 


A' = 9 


from Table L. 


A'=5 


100 














102 


79 


78 


81 


81 


104 


118 


119 


119 


120 


106 


151 


147 


146 


147 


108 


159 


151 


151 


151 


110 


41 


139 


140 


141 


112 


107 


103 


102 


104 


114 


115 


112 


111 


112 


116 


115 


114 


113 


115 



200 EEroET— 1882. 

In Table LII., the last three columns are in virtnal agreement, while 
the second difiPers from all of them in that the correction in the neighbour- 
hood of 108° is too great. This is exactly what would occur on the 
assumption that von Oettingen had not given sufficient weight to the 
initial jioint curve. 

The maximum error would occur in the neighbourhood of the point 
where the initial and upper point-curves first overlap, as there, owing to 
the small number of the upper point-curves, the errors introduced by 
them would be most important. The nature of the error would be such 
that the correction carves would be deflected too far in the direction of 
the upper point-curves, and finally it Avould be eliminated by a sufficient 
number of approximations. 

All these conditions are fulfilled. The overlap begins at 106. At 
that point there is a sudden increase in the difference between the first and 
second approximations, which is a maximum at 108°. The upper point- 
curves lie above the initial point-curve ; and the second apj^roximation, 
given by von Oettingen's method, lies above the third. The third 
approximation agrees very closely with the second and third approxima- 
tions obtained by Professors Thorpe and Riicker's method, which are them- 
selves in virtual agreement. 

The upper part of von Oettingen's curve is, however, for the most 
part above that obtained by the other method, and this error is no doubt 
due to the less rapid approximation obtained by ranking the initial point- 
curve as equal to one of the upper point curves only. 

On these grounds, therefore, the curve calculated, on the supposition 
that the initial point-curve is equivalent in value to ten of the upper 
point-curves, will be taken as the standard. 

(35) Only one other point with regard to Bessel's method requires 
investigation, viz. the error introduced by the measurement of the thread, 
not at, but near, the principal points. Let the true lengths of the divi- 
sions on which the upper and lower ends of a thread lay be 1 -H c?„ and 
1 + di. Let y be the fraction of the division in which the lower end lay 
by which that end was distant from the principal point. Had the thi-ead 
been pushed back through this distance its length would have been 
increased by ?/((?„ — d^. 

All the numbers in Tables XX. and XXI. must therefore be increased 
by this amount. Assuming y to have a mean value y throughout, and 
inserting this correction in the formula on p. 182, it is easily proved that 
the added correction of U^^ is 

y[^^rd. - d,^ - 1 S,c7„ _ _!_ S„ S.cZ„}, 

where S,. d„ and S^, d,,, are the sums of all the values of d„ in the r"^ row, 
and the ¥^ column respectively, and S^. S,. c?„, is the sum of all the values 
of c7„. 

The correction for the r^^ initial point is increased by y {S,.(7„ — d,] . 

On taking out the values of d^ and d^ from the curves in fig. 1, Plate 
III., it is found that the largest correction for any upper point is 
0-002y, and for any initial point Q-OOoy, and since the value of y is about 
0-3, the error introduced cannot exceed 0°001. The mean curves may, 
therefore, as far as this error is concerned, be taken as correct to 0°001, 
and it has therefore been neglected. 



METHODS EiirLOYED IN CALlBItATIOxN OF MEECURIAL THERMOMETERS. 201 



Effect of Errors in Measurement of Threads. 

(3G) The errors introduced in a correction-method depend partly upon 
the magnitude of the false assumptions made in the method itself, partly 
upon errors in the measurement of thread. 

It has been shown that the former may be obviated to a great extent 
by approximation or transference ; it remains to investigate the latter. It 
has been thought better to treat of this subject by itself in oi-der to avoid 
the complication which it introduces into the discussion of the various 
methods. It is proposed here to investigate tlae probable errors of the 
corrections of the principal points in terms of the errors in the thread- 
measurements. The probable error of a thread-measurement will be 
considered the same in all cases and taken = e. It must, however, be 
remembered that, in all probability, for reasons already given, long 
threads are less accurately measured than short. 

Gat-Lussac's Method, 

The equations (1) (p. 164) show that in the case of Gay-Lussac's 
method the correction for the r*** principal point is 

v V n. — r 

a/; "V ™m V 1- / ' vn / V r/ ' yn i [^ .' V )* 

V'VjV rl — -.[ l^ ^1 Jf — ^1 fj; ^,-+1 '.,■ ^1 f.r' 

n n n 

Hence if e,. be the probable error of the correction at this point, since all 
the ^s are independent measures 

E,.^ =: — (n — r)e^ + —!- re^ = -^— ~ e^. 

Hence if rt = 10 the squares of the probable errors at the first, second, 

9 16 
&c., points are proportional to — , -— , &c. 

These numbers are plotted down and give the curve indicated in the 
figure on p. 158. 

Rudbeeg's Method. 

It will be sufficient to consider the case of division into six parts. 
The above formulae give at once 

g2 2 

3 — o"' ^2 — ^4 — o ^ • 

Since the shorter thread is found as the mean of three independent 

measures its (probable error) ^ = — , and since this thread is measured 

o 

independently of 0(3), and ^(1) is found from the equation 

where all the quantities on the right are independent 
{p.e. 0(1))2 = J -f e2 + J ^ 1.83 e\ 

A curve is drawn through the points thus obtained in the figure on p. 158. 



202 



REPORT — 1882. 



Hallstkom's Method. 

In the case of Hallstrom's method the relation between the corrections 
and the thread-lengths are more complex. They may, however, be 
obtained as follows. In Table LIII. the first column gives the various 
B's, the other columns the coefficients with which r's and o-'s occur in 
the expressions for them. 

Thus, for instance, ? (2) = ^ (1) + 0-3 — o-^ — tj + 7-4, and so on. 
These are obtained from the formulte given above (p. 170), and from them 
10^' 1 is found. Using the value thus obtained, and remembering that 
(p (n) = (1) + (2) + . . . . + ^ (i(.),the values of them's are found in 
Table LIV. These have been checked by comparison with Table XIV. 

Table LTII. 

Probable errors. 



I. 


«(1) 


0-3 


<^i 


To 


T3 


'■4 


Tj 


TO 


T? 


T3 


■^0 


TIO 


8(1) 






















8(2) 






— 1 




— 1 


1 














8(3) 








1 


— 1 
















8(4) 






-1 




















8(0) 








1 


— 1 


1 


— 1 












8(6) 






— 1 










— 1 










6(7) 








1 


— 1 


1 


— 1 




-1 








8(8) 






— 1 










— 1 


] 


-1 






8 (9) 








1 


— 1 


1 


— 1 




-1 


1 


-1 




8(10) 


= 


5 


-5 






4 




— 1 


1 


-1 


1 


-1 
-1 


.-.-10 8(1) 


4 


-5 




-1 




-1 





Table LIV. 

Probable Errors. 



























Sum of 


I. 


-•5 


<^4 


T„ 


■^5 


•"4 


^5 


•^0 


■'I 


■'% 


TO 


TIO 


Squares of 
Coefficients 


<I>(1) 


•5 


-•4 


•5 


-•4 




•1 




•1 




•1 


1-10 


</.(2) 






-•8 




•0 




•2 




•2 




•2 


0-80 


<|>(3) 


-•5 


•5 


— •2 


-•5 


— 2 




■3 




•3 




•3 


1-10 


.?.(4) 






-•6 




-•6 




•4 




■4 




■4 


1-20 


<|)(5) 


-•5 


•5 




— •5 




- 1 


•5 




•5 




•5 


2-50 


</>(6) 






-•4 




-•4 




-•4 




•6 




•6 


1-20 


I- (7) 


-•5 


•5 


•2 


-■5 


■2 


- 1 


1 


- 1 


■7 




■7 


4-30 


</>(8) 






— •2 




— '2 




— "2 




-•2 




•8 


0-80 


<;>(9) 


-•5 


•5 


•4 


-•5 


•4 


- 1 


•9 


- 1 


•9 


- 1 


•9 


6-50 


</>(10) 







































Since now each of the <t's and r's is an independent measure, it is 
evident that the square of the probable error of the correction of a 
principal point = square of probable error of a measurement X the 
sum of the squares of the coefiicients in Table LIV., and is therefore 
proportional to the number given in the last column of that Table. 



METHODS EJirLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 203 

A curve is, as usual, drawn in the figure on p. 158. If an bypotlieti- 
cal 7-, is introduced, the correction may be expressed by the following 
formulae. 

For the odd points, 



0-5 (ff^ — 0-3) - 0-5 (7, — rj + 74) + 71 

+ j^ I '■2 + '■4 + 'G + • • ■ • + 1-10 I 

- {"1 + '■3 + • • • • + ^n}, 
and for the even points, 

J^ I 5^2 + '•4 + •••• + '■10 I - I "2 + -4 +....+ r„ j , 

where in each case n is the number of the principal point. 



Thiesen's Method. 

In the case of Thiesen's method the relation between the corrections 
and the measures is simpler. Suppose the observations complete — i.e. no 
threads to be wanting. 

Referring to the table on page 172, it is evident that the correction for 
the J-* principal point is the sum of all the columns up to and including 
the r*^ divided by 10. But the figures in any rectangle of which the O's 
form the diagonal cancel one another. Thus the correction for any 
point is one-tenth of the sum of the figures in all the columns np to the 
r^^ with the rectangle in question cut off. 

For instance, if in Table XVI. (p. 174), the blank space be filled up 
with the correct number afterwards found, the correction for i, is one- 
tenth the sum of the figures. 

102 15 - 68 - 12 

138. 60 - 22 35 

127 "37 — 51 10 

178 77 8 57 

177 81 7 58 

, 131 49 - 39 18 

All the numbers in any diagonal sucb as that through which the 
line is drawn are obtained from the same thread. They are the 
differences of successive thread-lengths, and therefore their sum depends 
only on the first and last. In other words, the number of independent 
measures used in finding the corrections is twice the number of the 
diagonals, i.e. it is in all cases 18. 



Hence (probable error of correction)^ = — 2e^="18e^. 
The curve is drawn in the figure on p. 158. 



Marek's Method. 

Marek gives the formulae for finding the probable error of a correcfion. 
When, as is the case worked out, the tube is divided into five parts, the 
(2?. e's) ^ are 

0- 0-29 e2 0-28 e2 0-2-8e2 •0-29 e2 



204 EEroET— 1882. 

These are, of course, not comparable with the others above obtained, as 
the subdivision of the tube is different. 

If the tube is divided into five jDarts by Thiesen's method the (p. e)^ 
= 0-32e2. 

Bessel's Method. 

The above method is not strictly applicable to Bessel's corrections, 
but it may be approximately applied as follows : — 

Each value of h,. depends on 10 independent measurements. Hence 

{p. e. h,y = — , &c. 

Each value of ^ (Uir) depends on 100 measures. 

Ten of these arc introduced with the coefficient O'l in r^., ten (of 
which one is common to this and last group) with the coefficient O'l in 
h^, and 100 with the coefficient — 0*01 in the m. One, viz., U/^^ itself, 
appears again with the coefficient — 1. Hence 81 will have the 
coefficient — 001, 18 will have the coefficient 0'09, and 1 the coefficient 
— 1 + 0"2 — 001 ^ — '81. Hence the probable error of a single thread- 
correction is : — 

{81 X 0-0001 + 18 X 0-0081 + (-81) '-} e^ = -81 e\ 

a result which strongly confirms the view expressed above as to the rela- 
tive values of the initial point and other corrections. 

Let it next be supposed that all the corrections in the diagonal which 
passes from the lower left to the upper right-hand corner of Table XIX. 
(p. 180), refer to the same point. 

Hence the final correction will be the mean of the ten. These are not 
independent. Each number in the Table will occur ten times. 

Ten, viz., the numbers in the diagonal, will have the coefficient — 081 
once, and — O'Ol nine times. Their coefficients in the mean will therefore 
be — 0-09. The remaining ninety will have the coefficient 0-09 twice, 
and — 0-01 eight times. Their coefficients in the mean will therefore be 



o 



^ I 0-18 -0-08 I =0-01 



Hence the probable error of the correction will be e^, multiplied by 

10 X (009)2 + 90 X (0-01)2 ^ 0-081 + 0-009 = 0-09. 

For comparison with the other methods referred to, it would be better 
to take Bessel's method with five principal points 4° apart. The probable 
errors of an initial point, and a mean upper point, would then be 0-2 e^ and 
*15 e^, respectively. 



ox THE EARTHQUAKE PHENOMENA OF JAPAN. 205 



Second Report of the Committee, consisting of Sir A. C. Eamsay, 
Mr. Thomas G-ray, and Professor John Milne {Secretary), 
appointed for the puiyose of investigating the Earthquake 
Phenomena of Japan. Drawn up by the Secretary. 

The^ seismological work which I have been engaged upon since the 
British Association, in 1881, generously placed in my hands a grant of 
25Z. as an assistance towards the investigation of the earthquake pheno- 
mena of Japan, has been partly the continuation of experiments and 
observations on which I was previously engaged, and partly an endeavour 
to carry out experiments which are more or less new. 

The results of a portion of this work have already been published in 
the 'Transactions of the Seismological Society of Japan.' The o-reater 
portion, however, of the observations which have been made are still in a 
rough form, and considerable time and labour will have to be expended 
upon them before they are ready for publication. The results to which 
many of these observations lead are, however, sufficiently well defined to 
be described in general terms, and this I propose to do in the followino- 
brief report. The order in which the various investigations are referred 
to is as nearly as possible the same as that which was followed in my first 
report to this Association. They are as follows : — 

I. Determination of tie areas from luUcli the shakings so often felt in 
ToTcio and YoJcohama emanate. 

In my first report it was stated that the origins of three earthquakes 
had been located near to or in the Bay of Yedo, at no great distance from 
Yokohama. Owing to the fact that there was often a confusion of normal 
and transverse vibrations, or to the fact that even if the ground moved 
backward and forward in a definite direction this did not of necessity 
correspond to the direction of a line connecting the point of observation 
and the origin, the origins of many other earthquakes which had been felt 
had not been determined. 

During the last year, in consequence of my having established at 
various places a number of instruments which give graphical records of 
all the prominent vibrations of an earthquake, instead of simply indicating 
the extent and direction of the maximum disturbance, I have been 
enabled to determine approximately the origins of a considerable number 
of disturbances. The instrument here referred to I call a pendulum 
seismograph. It is described in Vol. IV. of the ' Transactions of the 
Seismological Society.' 

These instruments have been distributed as follows : — 

^ 1. With F. Kinger, Esq., at Nagasaki, 550 geo. miles W.S.W. from Tokio. 

2. „ St. John Browne, 

Esq., „ Kobe, 240 „ W. by S. „ 

3. „ A. Owston, Esq., „ Yokohama, 15 „ SW bv S 

4. „ W. H. Talbot, Esq., „ „ „ „ ,/ ' ;; 

5. „ A Japanese gentle- „ Chiba, 17 ,, E. by S. 

man, 
6- .» ,, „ „ Kisaradzn, 15 „ S.E. by S. 

7. „ „ „ „ Kamaishi, 120 „ N.N.E. " 

8. At my own house, „ Hakodate, 375 „ N. by E. 

9. ,, F. Fukushi, Esq., „ Saporo 450 „ N. bv e' 
10. _ _ _ Tokio. ^ 



206 REPORT — 1882. 

Examples of the records obtained from these instruments, which 
records are written on plates of smoked glass that are subsequently var- 
nished and photographed, are given with the description of the instru- 
ment. The greater number of earthquakes which have been recorded 
in Tokio have also been recorded in Yokohama, Chiba, and Kisaradzn. 
Now and then the same earthquake has also been recorded in Kamaishi, 
and now and then even in Hakodate and Saporo. In no instance during 
my seven years' i-esidence in Japan have earthquakes, even when they 
have originated so near to Yokohama as to destroy chimneys and to 
completely unroof houses, been propagated so far sonth as Kobe. So 
far as ordinary earthquakes are concerned Kobe belongs to a special 
seismic area. Nagasaki in a similar manner is independent of all the 
other districts where seismographs have been placed. The reason why 
an ordinary earthquake in North-Eastern Japan is unable to spread far 
beyond Yokohama towards the south-west apparently depends upon the 
fact that in going southwards it is intercepted by many high and 
broad tracts of mountainous country. For a similar reason these same 
earthquakes are unable to cross the central backbone of the island, and so 
disturb the inhabitants upon the eastern shores. These facts have been 
illustrated in a very remarkable manner during the last year by an 
analysis of some hundreds of communications which I have received from 
various parts of North Japan. 

These communications were obtained by sending to the Government 
offices at all the important towns within a radius of from 60 to 100 
miles of Yedo bundles of post-cards, with a request that every week one 
of these cards should be returned with a statement of the earthquakes 
which had been felt. The result obtained by the examination of these 
communications showed that a great number of earthquakes came from 
the north-east, and hardly ever passed the ranges of mountains to the west 
and south-west. Subsequently the boundary of the post-card area was 
extended farther to the north, and the result which was obtained showed 
that many earthquakes came from the sea on the east._ The general 
results obtained by this system of investigation are exhibited in a seis- 
mological atlas which is being prepared for North Japan, in which the 
area "shaken by every shock has been tinted, the dark tints indicating 
where the shock was most severely felt, or where there were a number 
of shocks at short intervals corresponding to the single shock felt at 
more distant localities. The information to be derived from this series 

of maps is — i • i • 

1st. An approximate origin for many of the shocks, which is of great 

value as a check upon the records of instruments and an assistance to 

their interpretation. 

'2nd. In North-Eastern Japan there appear to be several^ seismic 

centres, and from these centres ordinary disturbances only radiate into 

surrounding districts, the boundaries of which are sharply defined by 

certain ranges of mountains. 

3rd. The greater number of seismic centres appear to be beneath the 

ocean. • • j. j 

4th. In the case of heavy shocks, and shocks which have originated 

some distance out at sea, the disturbance may be felt over the whole ora 

great portion of North-Eastern Japan, from Saporo and even Nemuro in 

the north to Yokohama in the south. 

5th. Although disturbances may be felt for several hundreds of miles 



ON THE EARTUQUAKE PHENOMENA OF JAPAN. 207 

along the eastern shores of Japan, it is seldom that they cross the moun- 
tains to the north-western coast, which is singiilarlj free from earthquakes 

One inference to be drawn from the above observations is that the 
disturbance, as felt upon the land, is to a great extent superficial, and on 
reaching the mountains is either destroyed by reflections and refractions 
or else absorbed by their mass. ' 

In the case of earthquakes where there were prominent vibrations 
having a definite direction, a prolongation of lines parallel to these 
directions through the observation stations has given intersections 
corresponding with the locality in which we should seek for the origin of 
the disturbance from the records of the post-cards. When prominent 
movements in two or more directions had been recorded, the one which 
had to be taken to represent the normal motion was indicated by the 
approximate origin shown by the post-cards. 

These determinations were further checked by time observations 
usually made in Yokohama, Tokio, and Chiba. Sometimes they were 
also made m Saporo and Hakodate. Assuming these time observations 
to have been correct, and the velocity of an earthquake to be constant it 
is theoretically possible by several methods to determine the orio-in of a 
disturbance. Although these methods fail in practice, chiefly o'Win? to 
the fact, which I will speak of presently, that the assumed velocity is not 
constant, the observations lead to very sure and practical deductions as 
to the direction m which we are to look for the origin of a shock. 

II. Velocity of Propagation of an Earthquake Wave. 

The observations which l" have been enabled to make upon the 
velocity with which earthquake motion is propagated are dependent upon 
the accuracy of time observations made at the localities just mentioned 
In iokio and Yokohama the observations were usually made automa- 
tically, by means of an instrument (which I have described in Vol IV of 
^\^ '<l?.^°'^r^*',°''',?^*^®. Seismological Society of Japan,' under the name 
of a Time Taker ), which gives a record of the time of a disturbance 
without stopping or retarding the clock from which it was taken. At Chiba 
and Kumagai the records were taken by telegraph operators by means of 
watches which I provided for them. At the remaining stations the 
observations were made similarly. All watches and clocks were from 
time to time compared with a telegraphic signal sent daily from the 
Meteorological Department in Tokio throughout Japan. The only ex- 
ceptions wereHakodate and Saporo, where the observations were made 
at observatories well provided with the necessary means of obtainincr 
accurate local time. ° 

The conclusions which these observations lead me to draw are— 

1. Different earthquakes, although they may travel across the same 
district, do so with different velocities, varying between several hundreds 
and several thousands of feet per second. 

2. The same disturbance is propagated with a decreasing velocity 
travelling very much more quickly across districts which are near to the 
origm than across districts which are far removed. 

3. The greater the initial force producing a disturbance the .Greater 
the velocity of propagation. ° 

As examples of the observations which have led to these deductions I 
quote the lollowing : — 

1. The earthquake of October 25, 1881. 

The origin of this was about 41° N. lat. and 144° 15' E. long. From 



208 EEPORT— 1882. 

tbe Hakodate homoseist this shock travelled at the rate of about 
10,219 feet per second to reach Tokio. Between Tokio and Yokohama 
the rate of propagation appears to have been about 4,500 feet per second. 

2. The earthquake of February 6, and two disturbances on March 1,1881. 
These disturbances, like that of October 25, appear to have travelled 

in a straight line through Tokio and Yokohama. Their velocities of propa- 
gation were respectively about 3,900, 1,900, and 1,400 feet per second. 

3. The earthquake of February 16, 1881. 

This shock appears to have originated in Yedo Bay, about eight miles 
east of Yokohama. From the Yokohama homoseist the velocity with 
which the shock travelled on to Tokio was about 2,454 feet per second. 

4. The earthquake of March 11, 1881. 

This disturbance originated at a place about nineteen miles S.S.W. 
from Chiba. The shock was a severe one. From the Tokio homoseist 
it appears to have travelled at the rate of 2,200 feet per second on to 
Yokohama. 

No doubt, notwithstanding the care which has been taken to have 
the time observations correctly recorded, it is possible that there may be 
errors due, for instance, to observers or instruments at the different 
stations making their records at different portions of the disturbance. 
Also there may be differences in the calculated velocities due to differences 
in the topographical and geological nature of the districts traversed by 
the disturbance. 

Although causes such as these may lead to a want of accuracy in the 
calculations which are here presented, I still regard the results of these 
calculations as indicating general laws. This view appears to be confirmed 
by the analysis of a table of earthquake velocities which I have compiled from 
the writings of various earthquake investigators, and also from the result of 
experiments on artificially produced disturbances yet to be referred to. 

III. The Kature of EarthqtiaJie Motion. 

In my first report to this Association I stated, 1st, that although the 
upper portions of buildings may at the time of an earthquake move 
through a considerable distance, the actual motion of the ground does not 
usually exceed a few millimetres, and is often under one millimetre ; 
2nd, the backward and forward motions of the ground are very irregular, 
both as regards period and amplitude ; 3rd, that there are seldom more 
than two or three vibrations per second ; and 4th, that the motion often 
takes place in more than one direction. 

To these observations, which have received further confirmation from 
records of earthquakes taken during the past year, I may add that in 
certain earthquakes where there are one or more prominent vibrations or 
what might be called shocks — 

1st. That the motion of the ground imvards towards the origin of the 
disturbance is usually much greater than the motion outwards. 

2nd. That the velocity, and consequently the acceleration of an earth 
particle for the inward motion, is usually very much greater than for 
the outward motion. 

In certain instances these two characters — which are of great import- 
ance, not only as indicators of the side from which the disturbance came, 
but also as indicators of the nature of the cause of the disturbance — I 
have sometimes observed, not simply in one or two vibrations of a dis- 
turbance, but in nearly all the vibrations which were sufficiently well 
defined to be analysed. 



ON THE EAUTIIQUAKE PHENOMENA OF JAPAN. 209 

"Further, it may he added that certain semi-vibrations have been 
described by the pointer of the seismograph moving across a movin"" 
record receiver in the direction of its motion, which have the anomalous 
appearance of having- been described in less than no time. 

From these observations it_ would appear that it is hardly safe for us 
to regard the backward and forward motion of the earth as simple 
harmonic motions, and maximum velocities and accelerations calculated 
upon such an assumption may possibly lead to false results. 

TV. An endeavour to find out the relative extent and variation in 
direction of the motion of an earthquake at neighbouring points in a given 
area, the contour and geological structure of ivhich is irregular. 

To work ont this problem seven similar seismometers were distributed 
on the hills and in the valleys near my house. The chief difficulty which 
had to be overcome in this investigation was to obtain a type of seismo- 
meter which, whilst magnifying the actual motion of the ground, was 
sufficiently simple to allow of a number being employed, and which, when 
under the same conditions, would give the same result. The results of 
experiments to find such an instrument are given in Vol. III. of the 
'Transactions of the Seisraological Society.' The seismometers which 
were chosen consisted of heavy pendulums suspended in cases to shield 
them from currents of air. Against the bobs of these pendulums, in grooves 
at right angles to each other, slips of wood were placed. At the time of 
an earthquake these, being pushed against the pendulum by the motion 
of the stands on which they rested, caused pointers which were attached 
to them by one thread of a bifilar suspension to swing round and o-ive a 
magnified representation of the motion which had taken place. 

The so-called hills surrounding the plain of Tokio are irregular, flat- 
topped spurs, jutting out from an elevated plateau about 100 feet hio-h 
into the flat plain on which a great portion of the city of Tokio is situ- 
ated. The area over which the seismometers were distributed had a 
radius of about a quarter of a mile. Two of the seismometers were 
placed on the top of the spurs, two'wex-e placed near together on the side 
of a spur, whilst three were placed at diSerent points on the plain. 

The results obtained from the records of fourteen small earthquakes 
are : — 

1st. That the maximum amplitude of motion and the direction of 
motion at all the stations were different. 

2nd. The greatest motion was experienced upon the flat ground, and 
the least upon the hills and their flanks. 

These results have been confirmed by observations made with other 
instruments. For instance, one of Professor Ewing's bracket seismographs 
at the University, situated on the flat ground of Tokio, usually records a 
much larger amplitude of motion than seismographs constructed on similar 
principles placed at my own house, situated on a small plateau half-way 
up the side of a hill about a mile distant from the University. Also the 
duration of a distui-bance is longer on the low ground than it is upon the 
high ground. As an example, the earthquake of March 11, 1882, may 
be quoted. At the University this disturbance lasted about 41- minutes 
the maximum amplitude of motion being 8 millimetres; at my "house the 
motion could only be traced upon the moving plate on which it was 
recorded for a period of about 1^ minute, and the maximum amplitude 
was about 3 millimetres. That there is less disturbance npou the hills 
than in the plain at Tokio is a fact that has long been recoo-nised bv the 
1882. p c o J 



210 REPORT— 1882. 

Japanese. It -was especially remarked at the time of the destructive 
earthquake of 1854. 

In Yokohama, sixteen miles to the S.E., -where the high and low 
ground has almost exactly the same topographical character as at Tokio, 
the rule appears to be reversed. This was clearly evident in February 
1880, when the shattering of chimneys, unroofing of houses, and destruc- 
tion generally was almost wholly confined to the high ground. In 
Hakodate the rule appears to be like that for Tokio — namely, that the 
greatest disturbance is felt upon the low ground. 

In consequence of the great difference in motion observed in places 
which are adjacent to each other, I have hitherto been unable to make 
any satisfactory determination of the manner in which an earthquake 
dies out as it radiates from its cpicentrum, although on many occasions I 
have obtained a number of diagrams for the same earthquake from 
distant stations. 

"V. Experiments on artificially produced Earthquakes. 

In 1881, in conjunction with Mr. Thomas Gray, I made experiments 
upon a series of artificial earthquakes produced by allowing a heavy iron 
ball to fall from various heights up to 35 feet. 

During the past year I continued these experiments on a larger and 
more satisfactory scale, the disturbances being produced by charges of 
dynamite exploded in bore-holes usually about 10 feet deep. In the first 
two sets of experiments the vibrations resulting from the explosions were 
simultaneously recorded upon moving glass plates at three stations. 

In consequence of the great increase in the intensity of the initial 
disturbance as compared with that obtained from the falling ball, the result- 
ing diagrams showing the backward and forward motions of the ground 
were much larger, and, therefore, better fitted for analysis than those 
which had been obtained pi-eviously. It also became possible to place 
the observation stations at greater distances apart, and thus errors in the 
calculation of velocity arising from inaccuracy in time observations were 
considerably reduced. 

The results obtained were a confirmation of results which had been 
previously obtained. They were, briefly — 

1. A graphic separation of normal and transverse vibrations. 

2. A determination of the relative amplitudes and periods of these 
vibrations at various points. 

3. The determination of the manner in which these vibrations became 
extinguished. 

4. The velocity with which these vibrations were propagated. 
To these observations the following may be added : — 

5. Vibrations, especially those performed in a normal direction, take place 
more rapidly near to the commencement of a disturbance than at the end. 

6. The greatest motion of the ground, as shown by the normal vibra- 
tions, is inwards towards the origin of the disturbance. 

7. The direction in which the ground moves with the greatest velocity 
is also imvards towards the origin of the disturbance. 

8. The motion does not appear to be simple harmonic. 

9. The vertical motion is not due to a direct shock, but to a surface 
nndulation. 

10. The velocity of propagation of a disturbance is not constant, but 
varies with the distance from the origin. 

The last observation led to three new sets of experiments being 
undertaken, the chief object of which was to determine the velocity with 



ON TUB EAKTHQTTAK.E PHENOMENA OF JAPAN. .211 

which vibrations of various descriptions were propagated. The arrange- 
ments were automatic. The charges were fired electrically, and as the 
disturbance passed successive stations electric circuits were broken and a 
mark made upon the surface of a smoked glass plate which was moving 
at a known rate. 

The results, which have not yet been worked out in detail, are gene- 
rally as follows : — 

1. The velocity of propagation of both normal and transverse vibra- 
tions is a function- of the initial force creating the disturbance ; or, 
briefly, the greater the charge of dynamite the greater the velocity. 

2. The velocity of propagation of both normal and transverse vibra- 
tions is greater between points near to the origin than between points 
which are distant. Near to the origin this velocity decreases much more 
rapidly than it does at a distance. 

When writing on this subject, I shall refer to the work done in this 
direction by Mr. Robert Mallet and by General Abott. 

VI. Experiments to determine the relative motion of two neighhouring 
points of ground. 

In these expei'iments two stakes were driven in the ground at various 
distances apart up to about 2 ft. 6 in. ' Sometimes the stakes were so 
placed that a continuation of the line joining them passed through the 
origin of the disturbance, and sometimes they were placed at right angles 
to such a direction. Fixed horizontally upon the head of one of the stakes 
was a light rigid bar, from the end of which a light index hung vertically. 
This index at a short distance below its point of suspension, which was a 
universal joint, was caught by a second universal joint at the end of a bar 
passing from the second stake. So long as the two heads of the stakes 
synchronised in their motions, it was assumed that the universal joints at 
the ends of the bars would keep vertically beneath each other, and the index 
which they supported would remain perpendicular. If, however, there 
was a want of synchronism, the lower end of the index would give a 
multiplied representation of their relative displacements. In all cases it 
was found that there was a considerable relative motion in the direction 
of the origin. 

The chief practical value of this experiment was to see how far we 
are justified in placing two portions of a seismograph upon different 
stakes. It also shows that a building, although it may be small, may not 
be moved as a whole, but may suffer considerable racking. 

VII. Experiments on the Production of Earth Currents. 

From near the scene of the explosions a telegraphic communication 
was established across a deep moat up to a hill where the mechanical' 
disturbances were practically not observable. Each end of this circuit 
was put to earth by means of two long crow-bars, and in the circuit on 
the hill one of Clark's diff'erential galvanometers was arranged. As 
either of the crow-bars was raised or depressed it was found that the 
current passing through the galvanometer varied, sometimes being positive 
and sometimes being negative. At a certain depth, which was found by trial,, 
the needle of the galvanometer remained at zero, and it was in this way 
that the adjustment to ' no current ' was made previous to an explosion. 

When the explosion took place, one earth bar being at distances of 
from 10 to 50 feet, a considerable current was always produced, and the 
needle of the galvanometer swung with violence until it reached a stop. 
The direction of swing was, in the few experiments which were made,, 



212 REPORT — 1882. 

always constant. Sometimes the needle remained permanently deflected, 
and at otlier times it gradually fell back towards zero. 

These currents I regard as being due to a mechanical disturbance of 
one of the earth bar.s, causing a difference of contact with the soil ; and, 
in consequence of this, an alteration iu the moisture, oxidation surface, 
&c., at one end of the circuit, thus giving rise to a difference of potential 
relatively to the other end of the circuit. 

No doubt actual earthquakes act upon the earth plates of telegraphic 
lines in a similar manner, but the currents which are in this way pro- 
duced at the time of an earthquake are due to different causes than those 
which appear sometimes to have preceded earthquakes by considerable 
intervals of time. 

In the experiment upon artificial earthquakes ray thanks are especially 
due to Mr. T. Fujioka and Mr. M. Kuwabara, of the Imperial College of 
Engineering, and not least of all to Mr. John Reid, agent of Nobel and 
Co., and to Mr. Denys Larrieu, who not only furnished me -with dyna- 
mite, but on several occasions also gave me their personal assistance. 

The great difficulties which had to be overcome in making these 
experiments, as, for instance, obtaining dynamite from the Government 
stores, its transportation, its storage, the difficulties in obtaining a piece 
of ground on which to experiment, manufacturing the necessary instru- 
ments, obtaining telegraphic wire and firing apparatus, the making of 
electric fuses, the anxiety lest accidents should occur, the training of a 
body of assistants, the putting in of bore-holes, the almost unexceptionally 
bad weather which had to be encountex'ed on days for which permission 
had been obtained, &c., have already been referred to in a letter to this 
Association. 

For the use of the ground where the experiments were performed and 
for the loan of numerous tents for the places where the instruments were 
established, and for a body of attentive servants, my thanks are due to His 
Excellency General Yamada, Minister of the Interior, and to Mr. Arai 
Ikunosuke, Director of the Meteorological Department. For the loan of 
telegraph wire, firing apparatus, and other instruments I tender my 
thanks to the directors and officers of the Department of Public Works, 
especially the Department of Imperial Telegraphs, the ^aval and War 
Departments, and the Imperial College of Bngineei-ing. 

Although several good diagrams of actual earthquake motion were 
obtained, in consequence of my instruments being continually removed 
for the purpose of making experiments on artificial disturbances, each set 
of which took several weeks' prepax'ation, many earthquakes were passed 
by unrecorded. Had the instruments, however, been continually in their 
places, the records would not have been so numerous as in previous years, 
the last season being comparatively a poor one — there only being between 
May 1881 and May 1882 fifty-seven shocks, as compared with eighty 
which were felt during the corresponding period of the previous year. 

The greatest activity was in February and March. 

Although earthquake disturbances were comparatively few in the 
Tokio area, the records obtained by the help of post-cards from the 
districts north of Tokio show that during certain months there was in 
North Japan an activity greater than was anticipated. In fact, judging 
from the records which were obtained although the season was a poor 
one, it was calculated that, taking Japan as a whole, there were every 
year, on the average, two or three shocks per day, a number as great 
as that which is usually assigned for the whole world. 



ON THE CIRCULATION OF UNDERGROUND WATERS. 213 



Eighth Report of the Goni'rnittee, consisting of Professor E. Hull, 
the Eev. H. W. Crosskey, Captain Douglas Galton, Professors 
Gr. A. Lebour and J. Prestwich, and Messrs. James Glaisher, 
E. B. Marten, W. Molyneux, Gr. H. Morton, W. Pengelly, 
James Plant, James Parker, I. Egberts, C. Fox Strangways, 
Tuos. S. Stooke, Gr. J. Symons, W. Topley, Tylden- Wright, 
E. Wethered, W. Whitaker, and C. E. De Eance {Secretary), 
appointed for the purpose of investigating the Circidation of the 
Underground Walers in the Permeable Formations of England, 
and the Quality and Quantity of the Water supplied to various 
Towns and Districts from these for')nations. 

Eight years have elapsed since this Committee commenced to investigate 
the circulation of underground waters, and the quantity and character of 
water supplied to towns and districts so derived. 

From 1874 to 1878 the Triassic and Permian formations were alone 
under consideration ; in that year the Jurassic rocks were added to the 
scope of the enquiry, which at the York meeting was enlarged to include 
the whole of the permeable rocks in England and Wales. 

The Triassic and Permian rocks of Devonshire are described in the 
first, fifth, and sixth reports ; of Somersetshire in the first ; of Leicester- 
shire in the first, fourth, and fifth ; of Warwick in the second, fourth, 
and seventh ; of Nottingham in the second and sixth ; of Cheshire in the 
second, fourth, and fifth; of Lancashire in the first, second, third, fourth, 
sixth, and seventh ; of Yorkshire in the first, second, third, sixth, and 
seventh ; of Shropshire in the sixth. ^ 

Through the removal to South Africa of the member of the Committee 
taking charge of Staffordshire, this district is still incomplete, but some 
information as to the Bui'ton-on-Trent area is given in the first report. 

In Devonshire the enquiry was carried on by Mr. Pengelly, F.R.S., 
supplemented by details obtained by Mr. Stooke, C.E. The Triassic rocks 
of the district have been made the object of careful study by Mr. W. A. E. 
Ussher. From his investigations it would appear that the sequence ex- 
hibited has more in common with the Trias of the French side of the 
English Channel than with that of the midland counties. In Devonshire 
and Somersetshire the sandstones and conglomerates appear to have been 
deposited in a distinct basin to that north of the Mendips, the Keuper 
marls being alone common to the two districts. 

The basin south of the Mendips is remarkable for having a series of 
marls intercalated in its sandstones, called by Mr. Ussher the ' Middle 
Marls ' ; these underlie sandstones beneath the Keuper marls. The con- 
glomerates have a distinctly local character, and when present are plenti- 
fully water-bearing, as are the sandstones, though to a somewhat less 
extent. 

Private supplies are obtained by wells at Torqnay, where the water- 

' Beport of Brithli Association for 187.5 (Bristol) contains first report ; that for 
1876 (Glasgow) the second; that for 1877 (Plymouth) the third; that for 1878 
(Dublin) the fourth ; that for 1879 (Sheffield) the fifth ; that for 1880 (Swansea) the 
sixth ; and that for 1881 (York) the seventh. 



214 EEPOET— 1882. 

level is 168 feet above the sea ; at Teignmoutli ; at Dawlish, -where the 
water-level is 71 feet above the sea ; and at Bramford Speke, near Exeter. 

Near Exeter the Lyons Holt spring issues at 126 feet above sea-level, 
yielding towards the town supply 47,000 gallons daily of very pure water, 
which is extensively used for drinking-fountains. 

The following gives an abstract of the facts, of the more important 
wells in the Exeter district : — 



Locality 


Depth 


Water-level 


Quantity gallons 




feet 


above sea 


in 24 hours 


Lunatic Asylum, Exminster 


473^ 


13 


200,000 


Bridge Mills, Silverton 


217 


— 


180,000 


Hele Paper Works 


120A 


60 


259,000 


City Brewery 


270 


. no inf. . 


4,000 


Treus Weir 


340 





250,000 


Kensham Mills, Hele . 


200 


. . 70 . 


170,000 



Higher up the valley of the Exe and its tributaries private supplies 
■are obtained at Crediton. 

North is the watershed separating the streams flowing into English 
and Bristol Channels. 

At Willington a well 230 feet above the sea is sunk to a depth of 
48| feet ; only a small quantity of water is pumped from it. 

At Taunton numerous private wells give a supply of rather hard water 
from the New Red Sandstone. 

At Somerton hard water is obtained from a well 129^ feet deep ; the 
White Lias is said to occur in it at 90 to 99 feet. 

At Wembdon a private well in triassic conglomerate yields hard 
water to a well 30 feet deep, at 60 feet above the sea. 

At Wookey, near Wells, 70 feet above the sea, a private well, 33 feet, 
yields a constant supply, uninfluenced by the seasons as to quantity, but 
decreases 9 feet in level after dry weather. 

In Bristol the wells vary in depth from 60 to 300 feet, some only pene- 
trating peat and gravel, others passing through triassic marls, whilst a 
few penetrate the coal measures. 

At Braysdown Colliery, near Bath, a shaft 500 yards deep, passing 
iihrough New Red Sandstone and coal measures, yielded water at the 
•bottom of the pit containing 1,008 grains of common salt, or 1,440 parts 
iper 100,000. 

In the Tiverton Coal-i^it, near Bath, 16,800 gallons per 24 hours are 
yielded by plastic shale in the Blue Lias, 130 feet above the White Lias, 
whicli is 12 feet thick, resting on 23 feet of Rhsetics, lying on the New 
Red Marl ; the water contains 112 parts per 100,000 of common salt. 

The Tyning Pit, Radstock, intersected a spring yielding 864,000 
gallons per day at 200 feet from the surface, at the bottom of the Red 
Marls. 

At Kilmersdon New Coal Shaft, Writhlington, a 10-feet shaft inter- 
sected a spring at 253^ feet. On cutting through a hard base of stone the 
water rose 99 feet in 24 hours, and stands at this level, yielding 98,400 
gallons per day of hard water. The section passed through was liassic 
clay, black and blue marl 78 feet ; 34 feet of ' red ground,' with bands of 
blue stone ; conglomerate 5 feet ; red beds 4 feet ; then conglomerate 
again ; the remainder of the section is not given. The late Mr. Charles 
Moore considered the last, 5 feet 4 inches of the Lias, in this section to 
belong to the Rhsetic beds. 



ON THE CIRCULATION OF UNDERGROUND WATERS. 215 

In reference to the information furnished by Mr. Taunton as to the 
Thames and Severn Canal, it may be well to state that the outcrop of the 
oolitic rocks has an average breadth on the dip of 25 miles. The base of 
the Oolites resting on the Lias reaches its highest point near Chipping 
Campden, 1,032 feet above the sea, on the watershed between the Thames 
and Severn basins. This, south of the Seven Wells, the source of the 
Churn, runs somewhat east of the base of the Oolite, causing the surface 
drainage of the oolitic tract around Minchinhampton, Dursley, and 
Wotton-under-Edge to flow into the basin of the Severn. It is probable 
also that a portion of the underground drainage does so also, notwith- 
standing the general south-easterly dip, from the basement level of the 
Oolites, varying in the direction of the strike, owing to the denudation 
of the escarpment being unequal, the Oolite to the south having been 
worn back much further down the dip, and consequently to a lower 
elevation than at Chipping Campden, descending from 1,030 at the 
latter place to 212 feet in the Stroud valley, or about 800 feet in 25 miles. 
South of this valley the level rises slightly, so that a partial discharge of 
underground drainage takes place in this valley, which is immediately 
west of the point in the Thames and Severn vratershed which is pene- 
trated by the canal connecting the two basins. 

Of the 25 miles of average outcrop of oolitic rocks measured on the 
dip, only about 8 consist of impermeable deposits — viz., the Fuller's Earth, 
the Oxford Clay, and the Kimmeridge Clay, — so that two-thirds of the area 
may be considered to be of a permeable character. The vertical section 
of the Oolites is as follows : — 

Portland Oolite — 

Kimmeridge Clay ....... — 

Coralline Oolite ........ — 

Oxford Clay 300 

Cornhrash 8 

Forest Blarhle 30 

Great Oolite 200 

Inferior Oolite ........ 264 

WarwicJcsliire information. — The southern and western portion of the 
Warwickshire coalfield is overlaid by Permian rocks consisting of reddish- 
brown and purple sandstones, intercalated with marls in lenticular beds, 
rising to a height of 622 feet at Cowley Hall, which forms part of the 
watershed between the tributaries of the Trent to the north, and those of 
the Avon on the south. 

Though the surface-drainage of this Permian area flows in opposite 
directions, that portion of the rainfall percolating into the ground has a 
uniform gradient to the south, the base of the Permians, where they rest 
on the coal measures west of Atherstone, being 470 feet above the sea, 
and 170 feet under the Mithurst Tunnel of the Midland Railway, being a 
fall of 50 feet per mile, while at Warwick the tops of the Permians are 
18C feet above the sea, and as they are not less than 800 feet thick, their 
base is probably about 600 feet below the sea-level, giving a further fall 
of 786 feet in 18 miles, or a fall of 4.3 feet per mile. 

Examining the district more minutely, it is seen that though the 
Permians do not always lie conformably on the coal measures, yet 
there is a general conformity, and a synclinal flexure traversing the 
coal measures from north to south is shared by the overlying Permians, 
which have synclinal dips towards the axis of an average amount of 3°, 



216 



liEPORT 1882. 



or about 270 feet per mile from the edges of the basin towards the axis, 
which occurs more to the eastern than the western margin. 

The fault throwing in the coal measures of Arley "Wood is believed to 
be connected with the fault throwing back the outcrop of the main part 
of the coalfield at Broomfield Park ; but of this there is no evidence, and 
as the dips in the Permian show the flexures to be present on both sides 
of the supposed fault, its existence is very doubtful. If it occurred, and 
were a watertight barrier, the water percolating into the sandstones to 
the west of Atherstone and flowing south would be thrown out in a line 
of springs, which is not the case ; and there is no doubt that the waters 
travelling in the porous portion of the system flow south to Leamington 
and Warwick, where a portion of the supply is utilised. South of this 
point the Permians are concealed by triassic, liassic, and oolitic rocks 
in the direction of Banbury. Southwards the Permians probably wedge 
out before the Trias, which continue into the Thames basin ; the water 
travelling down the dip planes of the Permian, where that formation thins 
out, probably enters the overlying triassic sands, and, prevented from rising 
higher by the Keuper marls, probably flows a considerable distance under 
the Thames basin, where its outlet being checked by the thinning out of 
the Lower Trias against the Palaeozoic ridge, causes the subterranean 
Trias to be fully charged with water in a stationary condition, and thus 
limits the amount of absorption in the area of absorption. 

Between the base of the Permian and the Spirorhis limestone is 
a thickness of 150 feet, and between it and the first workable coal is a 
further 500 feet, of which a large portion consists of Permian sandstone 
fully charged with water, which was met with in sinking the Exhall 
Colliery. 



Appendix I. — Millstone Grit Wells. 

Collected by Mr. C. E. De Ranee. 

From Messrs. Mather and Piatt, Salford Ironworks, Manchester. 

Description and thickness of each Stratum hored through at Messrs. 
J. 8f E. Gru7idy's, Bury. 

Well 15 ft. deep 
ft. in. 

At 



ft. in. 




1.5 from surface 


45 


»J 


64 2 


ft 


65 


y> 


67 


>> 


85 


>» 


88 


»» 


90 6 


>i 


93 6 


)) 


103 


i> 


117 6 


)> 


119 6 


j> 


124 6 


y> 


125 


j» 


144 


t* 


145 


n 


227 10 


)> 


229 6 


)) 


258 


tt 


268 


>> 



(48 yds.) 



ft. 


in. 






30 


of Blue metal 


19 


2 


» 


Black shale and rock 





10 


)) 


Coal 


2 





)> 


White rock 


18 





»5 


Dark grey rock 


3 





)> 


Black rock 


2 


6 


J» 


Dark grey rock 


3 





is 


Brown rock 


9 


6 


tt 


Blue metal 


14 


6 


99 


Dark grey rock and blue metal 


2 





99 


Coal 


5 





99 


Fire-clay 





6 


J) 


Brown rock 


19 





fj 


Blue metal 


1 





») 


Coal 


82 


10 


99 


Dark grey rock 


1 


8 


)» 


Fine clay and white rock 


28 


6 


»> 


White rock 


10 





}} 


do. and a few partings 


10 





») 


do. 



ON THE CIRCULATION OF UNDERGROUND WATERS. 



217 



Well 15 ft. 


deep. 


ft. in. 




At 278 from surface 


,. 281 




.. 288 6 




. 290 




„ 290 8 




„ 295 6 




„ 303 




„ 304 6 




„ 312 




„ 315 




315 from surface 



ft. 


in. 


3 


of Dark brown rock 


7 


6 „ White rock 


1 


6 „ Millstone rock 





8 „ Dark brown rock 


4 


10 „ do. 


7 


6 „ White rock 


1 


6 „ Dark brown rock 


7 


6 „ White rock 


3 


„ Shale or blue metal 



300 Total depth bored 



Collected by Mr. C. E. De Ranee. 

From Mr. A. Timmins, Stud. Inst. C.E., Runcorn. 



1. Leyland Local Trial Boring for Water, Clayton-le-Woods. 

3, 5 feet well to 

11 inch boring to . 



10 

3a. None. 4. 14^ feet from surface. 
Brown, county analyst, Jan. 28, 1882. 



4a. Same. 



la. Dec. 1881. 

64 feet 
120 feet 
150i feet 

Made by Dr. Campbell 



Total solid matter 

Organic carbon 

Organic nitrogen (Dr. Frankland's method) 
Ammonia ....... 

Ammonia for organic matter 

Nitrates and nitrites .... 

Total combined nitrogen . . . • . 

Combined chlorine 

Hardness 24, of which 20'1 was temporary. 



Surface soil 
Sandy gravel 
Boulder clay 
Ferruginous earth 
Fine light sand . 
Coarse gravel 
Micaceous clay . 
Purple shale 
Ferruginous sandstone 
Uniform sandstone 
Brown mould 
Purple shale 
Purple sandstone 
Bronze shale 
Purple shale 



Parts per 100,000 
37-4 
•093 
•019 
•015 
•008 
•046 
•078 
302 



ft. 
3 

13 

30 
1 
2 
5 
5 
1 
3 

27 
5 

19 

13 
3 

20 



m. 





























6 



150 6 



Appendix II. — Triassic Wells. 

Collected by Mr. Thos. S. Stooke, Assoc. M. Inst. C.E. 
From Mr. Edwin Parry, Engineer to Messrs. Marshall, the proprietors 
of the said well. October 19, 1881. 

1. In the mill-yard belonging to Messrs. Marshall, Shrewsbury, la. 1837. No. 
2. About 240 feet. 3. 60 feet ; from the bottom of the well are two bore-holes 50 
yards deep, through \yhich the whole supply comes, 9 in. diam. 3a. The well enters 



218 EEPORT— 1882. 

the rock 11 ft. 4. 40 feet of water in well which we have pumiced out in an hour. 
10 hours. 5. 250,000 gallons. 6. Some slight variation in rainy weather. Yes ; it 
has diminislied aboiit one-fourth. 7. Yes. Appears to rise when Severn is in flood. 
8. Only the hardness ; by Clarke's test 18°. 9. 48 feet of clay and sand. Eed 
sandstone to bottom of bore. lo. Yes. 11. Yes, by cast-iron cylinders. 12. Geo- 
logical Survey shows a fault N.W. close to the well. 13. No. 14. No. 15. No. 

Collected by Mr. Thos. S. Stooke. 

From Mr. C. Hy. Kynaston, Brewei', Wem, Salop. 

1. Sunk 17 feet. Bored from bottom diameter of hole 3 inches, la. 1878. No. 
3. 17 feet, 6 feet, and 100 feet. 3«. None. 4. 14 feet from surface. 2 hours. 
4(7.. 14 feet from surface. 5. From 4 to .5,000 gallons. 6. Does vary a little in 
September and October, when it is the lowest. 7. Yes ; in about 24 hours. 8. 
None. Used for brewing purposes. 9. None; gravel, then blue claj^ down to water, 
1.5 inches of sand 100 feet from surface fi-om which the water came. — T. S. S. 12. 
None, 13. None. 14. Not within 17 miles. 15. No. 

Collected by Mr. Thos. S. Stooke. 

1. At Messrs. Marshall & Co.'s Bleach Works, Hanwood. 1«. In progress. 3. 
€8 feet ; 4 feet 6 diam. 3a. None. 4. Pases to top. 5. 48 gallons per minute. 
7. No. 8. Soft. 9. Eed marl and blue-grey sandstone. lO. No. 15. No. 

Collected by Mr. Thos. S. Stooke. 

From Mr. R. E. Johnston, C.E., Engineer Office, G.W.R. and L.N.W. 
Joint Railways, Birkenhead. 

1. Steam Shed, "Wellington G.W. &: L.N.W. joint railway companies, la. 
Finished August 1875. 2. Above 350 feet. 3. 18 feet below soil level ; 36 feet 
below original surface. Bore-hole 163 feet below original surface. 3a. None. 
■4. One foot below rail-level. After pumping 14 feet below rail-level. Two hours. 
4a. One foot below rails, or 19 feet below surface-level; at present time height of 
water 18 feet. 5. 204,000 gallons per day of 24 hours. 6. Notbing perceptible. 
7. Slightlj', after several days' rain. No information. 8. Good for general pur- 
poses. 

9. Drift . . , 45 feet 

Sandstone . . . . . . . . 78 „ 

Eed marl 22 „ 

ita. In sandstone. lO. Yes. 11. Yes. 12. None. 13. None. 

Collected by Mr. Thos. S. Stooke. 
From Lient.-Col. Drake, R.E. 

1. Barrack enclosure, Shrewsbury, la. March 1882. No. 2. -I-239-01- O.D. 

3. Total depth 93 feet ; diameter 37 feet x 6 feet 3 inches and 56 feet x 5 feet 
5 inches. Bore-hole 243 feet 6 inches x 5^ inches diameter. 3a. No drift-ways. 

4. 75 feet to surface of water. 4(7. 75 feet, which it maintains. 5. 175,000. 7,000. 
6. No variance has been detected. 7. No. The water in well stands 6 feet 4 inches 
above adjoining Eiver Severn. 

8. Lime . . Large . . Ammonia . . Trace 
Magnesia . Present . Nitric acid . Large 
Chlorine . „ . ' . Nitrous acid . Trace 
Sulph. Acid SO^ „ . . Oxidisable matter Present 
Phosphoric acid None . . Iron . . . None 

Hardness. 

Fixed 7°-35 

Temporary 5°-40 

ft. in. 

9. Soil 3 

Coarse gravel 7 

Eed sand ... .... 3 

Yellow loam 2 

Fine red sand 35 ; 



ON THE CIRCULATION OF UNDERGROUND WATERS. 



219 



1 





3 





5 





13 





3 





11 





157 


6 



ft. in. 
Coarse gravel 
Fine sand. 
Fine gravel . 
Stonj' red clay 
Blue stiff stony clay 
Coarse gravel 
Red sandstone 

9a. Principal yield of water from last 50 feet of boring. lO. First spring of water 
met in last gravel bed-75 to 86 feet. 11. No. 12. Yes; a large fault trending 
E.N.E. to due west. 13. No. 14. No knowledge of any. 15. Not aware of any. 

Information given by Mr. E. B. Marten, Member of the Committee, 
Engineer to Stourbridge Waterworks Co., &c. : — 

1. WoUaston Station of the Stourbridge Waterworks at Coalbournbrooke, between 
Wordsley and Stourbridge, on the road to WoUaston Hall, and between Canal and 
River St'our, just under the Platts on Ordnance Survey. 1«. 1880, July 44 ft. deep, 
and bore-hole 179 ft. ; May 1882 sunk 20 ft. deeper. 2. 218 ft. above sea-level. 
3. Well 44 ft. from surface; bottom of bore-hole 179 ft. from surface. 3a. No 
drift- ways. 4. Water rises over the surface, and flows into River Stour. If pumped 



Fig. 1 




thattJif P/c/iij)A- drar,' froTTi it 

emptjr well fills in 25 minutes. If pumped down 4 ft. it rises and overflows in 3 
minutes. A pipe fixed in bore-hole can be shut off from the well, and the water 
rises 10 or 12 ft. above the surface in good volume, but it has not been tested as to 
what height of ijipe would prevent overflow. 4(/. The first 10 ft. only vrere drj-, and 
then the water increased very fast. 5. 600,000 when pumped about 20 ft. below sur- 
face ; average 300,000 gallons per day at about 4 ft. below surface. 6. No variation 
can be observed, and no diminution. 7. Rain makes no difference ; ordinary level 
stands about 10 ft. above River Stour, which io about 100 yds. away. 8. Practically 
the same as at Jlill lileadow. The waterworks were originally set out here, but 
moved nearer the town to a well still used, and which has served for 20 years. 9. 
This drift then all Upper Mottled Sandstone. 9a. Red sandstone rock is of uniform 



220 



REPORT — 1882. 



texture, a little more at about 43 ft. from surface. 10. No surface spring in drift, 
but if holes are made they fill with water. 11. Land springs are coffered out. 12. 
No faults are seen near the well. 13. No brine. 14. No. 15. No. 16. The new 

red sandstone occupies a large area from the western boundary fault of the South 
Stafford.shire coalfield to Enville, and forms the gathering ground for this well. It 
has few large streams on it, as it is so permeable that the rainfall percolates easily. 
There are no large towns on this area, but villages and gentlemen's country seats, 
including Enville Hall, Lord Stamford's, and the famous Sheep Walks. The rock is 
full of water, which overflows along the banks of the river, and the long overflow 
has formed springs or wells in the sandstone escarpment, one of which is called the 
' bottomless pit,' from the persistency of the outflow of the water in great volumes 
at all seasons uniformly. This company purchased the right to run a heading at 
50 ft. below the surface from the Wollaston well under this escarpment to another 
site at Tack Farm, half a mile away, but the bore-hole has yielded all that is needed 
without any chance of river water getting into the well. The Wollaston site was 
that originally chosen for the works, but it was considered that the same condition 
would appertain at Mill Jleadow, the site near the town, although no sign of a spring 
was then seen. It was found exactly as conjectured, and answered for town supply 
for 20 years, and being between the town and reservoir a much less outlay was 
sufficient. 

Stom-bridge "Waterworks (continued) : — 

1. At the Mill Meadow Pumping Station, near Stourbridge, i mile N.E. of centre 
of town. la. Sunk in 1856 to depth of 50 ft., with a bore-hole 20 ft. from the 
bottom of the well. In 1871 it was deepened to 50 ft., with bore-hole 80 ft. deeper, 

and drif t-waj"S made ; two other shafts were 
also sunk for convenience. 2. Surface of 
the ground or engine-house floor 237 ft. 
above the sea (Ordnance datum). 3. 50 ft. 

' to bottom of the well. 130 ft. to bottom 

of bore-hole. 3a. 44: ft. Length about 

40 j'ards. 4. Water would rise to the sar- 

into the Eiver Stour, but a drain-pipe is put into the river about 

When pumping 300,000 gallons per day it sinks 20 ft. and 

When pumping 550,000 gallons 30 ft., and recovers in four 

to surface and flowed over, and would do so again. 







Fig. 



A 



¥ 



face and flow over 

10 ft. from the surface, 

fills again in two hours. 

hours. 4a. The water rose 

5. About 600,000 gallons per 24 hours. 6. No ditference in seasons. After 15 years 

it was tested and found to yield exactly the same quantity. 7. Local rain does not 

affect it. It stands 10 ft. above the River Stour. 



Ha ilway Well 



M rijr 



JfewJieS/ Sandstone 
Z.3. ' 



8. Carbonate of lime . . . 

Sulphate of lime 
Sulphate of magnesia 
Chloride of sodium and alkalies 
Organic matter 

Loss ..... 

Degree of hardness 




Measure 



Grs. per gal. 
. 15-23 
. 0-47 
. 1-67 
1-76 
. 2-07 
•77 
. 17-2 



21-95 
This site was chosen as it was conjectured that the rock was as overflo-wing as the 
more distant site at Wollaston originally chosen. This has been suffused in 20 years, 



ox THE CIRCULATION OF UNDERGROUND WATERS. 221 

antl being between the town and the high-level reservoirs it saved much outla}-. Tlie 
gathering- ground for this well is supposed to be the Clent Hills, and the large sand- 
stone area of Hagley and Clent Heath. 9. No drift. Well was commenced in the 
dock. The new red sandstone, 3 ft. 9a. Water comes chiefly out of the bore-lioles. 
lO. No springs, but if any hole was made it would fill with water. 11. As the 
well is generally full land-springs cannot come in. New pumping stations are pur- 
chased to prevent the need of drawing down this water permanently. 12. The 
Western boundary fault of the S. S. coalfield, 200 yards to east. 13. No brine 
springs. 14. None near. 15. No wells stopped because of brine. 16. Two wells 
near are also shown on the sketch. 

Woherhamj^ton Waterworks. 

(From Memorandum taken Inj Mr. E. B. Marten when he was JResident Engineer to 

Wolrerhanqrton Waterworks, during which time this Shaft 7vas sunk. Section is 

given in Vertical Sections, Sheet 50 of the Geological Surrey.) 

1. At Goldthorn Hill in Wolverhampton, on high ground where Service Reservoir 

is placed, la. 1853 ; not altered since. 2. 506 above mean sea-level. 3. 800 ft. ; 

8 ft. diam. ; 340 ft. bore-hole ; 640 ft. altogether. There are two shafts near to each 

other. One used for sinking and the other for pumping. 3a. 240 ft. main driftway 

S90 ft. long to the west branch, 330 ft. to the south. Total 1,330 ft. 4. The greater 

part of theWater was at 240 ft., and the pumps were shortened to that point. Water 

had to fill the headings when it rose, and so it took some time. 4«. No note of this 

to be found. There was not much until 240 ft. 

5. January to June 1852 . . 26,615,888 gallons pumped 

July to December . - . i'8,095,268 

Total 1852 . . . 54,711,156 

January to June 185S . . 36,981,792 gallons pumped 
July to December . . . 48,808,261 

Total 1853 . . . 85,790,050 

This was nearly all that could be pumped. 6. Only being used for local supply of 
some high-level houses there is not much pumped out. 7. I believe not. 8. No 
certain information, but average quality of sandstone water. 9. See No. 50, pit 
section Geological Survey. The shaft is in Permian strata, and near Western boun- 
dary of S.S. coalfield, which is ^ mile to the east. 9a. Chiefly in 240 ft. water- 
bearing strata. lO. No ; it is on a hill. 11. All surface water is kept out. 12i 
The great boundary fault of S.S. Coalfield, h mile to East. 13. The bore-hole 
yielded strong brine. 14. No. 15. No 16. Not much used now, but perfectly 
good water, the borehole being stopped up. 

"Wolverhampton Waterworks (continued) : — 
{Fro7)i Memorandum taken hi/ Mr. E. B. MaHen when he was Engineer to the 
Wolfcrhamjjt.on Waterworks Company.) 
1. Tettenhall, 2^ miles west of Wolverhampton. 1«. 1847. Not altered since. 
2. 372 Ordnance datum. 3. 136 ft. 10 ft. diam. oval to suit pumps. 2 other 
shafts for convenience. 3«. 130 ft. about \ mile in different directions under the 
company's land. 4. From 5 to 19 ft., according to pumping. See paper attached 
with results of some years' pumping. 4a. See above details. 5. Full quantity 
possible was pumped during the years of which details are given. 

Mr. Marten's Notes of Wolrerhampton Waterworks Well at Tettenhall, 

Avgiist 4, 1882. 







Average 


Depth of Water 




Total Pumped 


per day 


in Well 




Kals. 


gals." 


ft. in. 


1847 June to Dec. 


. 8,571,596 . 


. 42,224 . 


. 19 6 


1848 J^an. to Dec. 


, 20,095,110 . 


. 57,636 . 


. 17 1 


1849 


. 37,495,670 . 


. 102,727 . 


. 16 fi 


1850 


. 56,484,162 . 


. 154,750 . 


. 8 


1851 


. 61,804,904 . 


. 169,328 . 


. 8 


1852 


. 56,474,656 . 


. 154,725 . 


. 7 


1853 


. 61,44.5,.5.52 . 


. 168,344 . 


. 6 


1854 


. 57,206,412 . 


. 156,812 . 


. 5 



222 EEPORT — 1882. 

6. No. 7. No. 8. No certain information, but good average sandstone water. 
9. On a hill. No drift, all sandstone 5 ft. Section would be sent if desired. 9a. 
Towards the bottom. lO. No. 11. No land springs, as well was on a hill. 12. 
No. 13. No. 14. No. 15. No. 16. The well is not now so much used, as the 
Cosford works described by Mr. H. J. JIarten supplj- most of the water. 



Farticulars of a Bore-hole sunh tmder Mr. H. J. Marten's superintendence for 
the Waterworlis belonging to the Corporation of Wolrerhamjyton. 

By Mr. Henry J. Marten, M. Inst. C.E. 

1. The Bore-hole in question is situate at the Cosford Pumping Station 
of the "Wolverhampton Corporation Waterworks, about nine miles distant 
from Wolverhampton along the old turnpike road leading from Wolver- 
hampton to Shrewsbury, and is sunk through the upper soft red, and the 
conglomerate, into the lower soft red measures of the New Red Sandstone 
formation. 

la. The boring was commenced in June, 187G, and completed in 
December, 1877, and it has not been deepened since. 

2. The approximate height of the present surface of the ground above 
mean sea-level is 200 feet. 

3. The total depth of the bore-hole from the present surface of the 
ground is 918 feet 9 inches, of which 534 feet is 24 inches in diameter, 
and the remainder, 384 feet 9 inches, is 15 inches in diameter. 

The bore-hole is fitted at the top with a cast-iron guard pipe which 
rises about 3 feet above the present surface of the ground, with an opening 
in it at a depth of 4 feet, and another at between 16 and 17 feet below 
the present surface of the ground, through which, by means of sluices, 
the water rising up the bore-hole can be turned either into an adjoining 
brook or into the engine well. 

3a. There are no horizontal driftways. 

4. When not being drawn upon the water rises in the guard pipe 
described in reply to question 3, to a height of about 1 foot above the 
present surface of the ground, or 9 feet above the natural, or original, 
surface of the ground. At this level, which is denominated the summit 
level, the artesian force of the deep springs supplying the bore-hole is 
balanced by the head of water attained in the guard pipe, and everything 
is at rest. On opening the sluice 5 feet below this point the natural 
discharge from the bore-hole is at the rate of 480,000 gallons a day. On 
opening the lower sluice in the guard pipe, so as to reduce the outflow 
point to the level of the water in the engine well, or 14 feet below summit 
level, the natural discharge is at the rate of 830,000 gallons a day. On 
pumping down the water in the bore-hole to a depth of 27 feet below 
summit level, the yield is at the rate of 1,320,000 gallons a day, and at 
31 feet below summit level, it is at the rate of 1,420,000 gallons a day. 
On ceasing to pump and shutting the sluices, the water rises in the bore- 
hole to summit level in a few minutes. 

4a. Excepting for experimental purposes, the water in the bore-hole 
has not been permanently pumped down below the engine well level, and 
when not drawn upon the height at which the water now stands is the 
same as when the well was first sunk. 

5. The average discharge at engine well level is between 800,000 and 
900,000 gallons a day, and this quantity is daily pumped from that level. 

6. The level of the water does not appear to vary with the seasons to 



ON THE CIRCULATION OF UNDERGROUND WATERS. 223 

any appreciable extent, and it has not diminislied since the bore-hole was 
completed. 

7. The ordinary level is not affected by local rains. The summit level 
to which the water rises is about 5 feet above the surface of the water in 
the River Worf, a stream which is within a dozen yards of the bore-hole. 

8. The analysis of the water is as under : — 

Grains per gallon 

Total solid matter 18-970 

Albuminoid ammonia 0-000 

Free ammonia ......... 0-000 

Nitrogen, as Nitrates and Nitrites 0-059 

Chlorine 0-980 

Hurtful metallic impurity none 

Transparency good 

Hardness — Temporary 6-46 

„ Permanent 6-69 

„ Total 13-15 

The water does not contain any marked peculiarity. 

9. The section of the rocks passed through is as under : — 

ft. in. It. in. 

Drift nil. 

Upper Mottled Sandstone 461 6 

Pebble Beds :— 

Upper pebble beds ..... 165 6 
Argillaceous marl rock . . . . 85 

Lower pebble beds 128 

378 6 

Lower Mottled Sandstone (not bottomed) ... 78 9 

918 9 

The Pebble Beds, it will be seen, are here divided into upper and 
lower beds by a thick bed of argillaceous marl. The lower pebble 
bed was of so obdurate a character that 2,000 blows with a heavy cutter 
weighing nearly one ton, and falling 5 feet each stroke, only penetrated 
one foot through it. 

9a. The principal springs intercepted were in the upper soft red 
rocks. There is generally a large flow from the springs in the lower 
soft red rocks, but in this case the artesian force at command at the 
engine well level was not sufHcient to liberate them to any appreciable 
extent. The object ia view in opening a communication through the 
argillaceous marl and conglomerate beds into the lower soft red rocks 
was to ensure a supply from the last-named beds in the event of the 
engine well being lowered, a work now being carried out. TZ^'''"''^ 

10 and 11. There is no drift rock over the site of the bore-hole, 

12. There are no large faults in the neighbourhood of the bore-hole. 
The borehole is situate in the central portion of the downfall trough 
between the Shropshire and Staffordshire coalfields — the boundary 
faults of which are respectively eight and nine miles from the bore-hole. 

13. There was a very slight briny ooze, estimated at about 300 gallons 
a day, from the argillaceous marl beds into the bore-hole. 

14. There are no salt springs in the neighbourhood. 

15. No wells or borings have been discontinued in the neighbourhood 
in consequence of the water being more or less brackish. 

16. The bore-hole required no casing in it from top to bottom. The 
bore-hole, which was sunk by rope-boring machinery, supplied by Messrs. 



224 EEPORT — 1882. 

Mather and Piatt, of Mancliester, cost 2,315?., or at the rate of aboufc 
21. 10s. per foot ran. The total expense, including the last-named amount 
— the balance valve, the fuel for engines, guard pipe and sundry labour, 
was about 3,700L 



Particulars of WaterworJcs Well sunk under superintendence of Mr. Henry 
J. Marten, M. Inst. C.E., for the supply of Tamworth and the sur- 
rounding district with water. 

1. The well is situate at Hopwas, about 2 miles to the west of Tam- 
worth, and is sunk in the conglomerate beds of the New Red Sandstone 
formation. 

la. The well was sunk in the year 1879, and has not been deepened 
by sinking or boring since that date. 

2. The approximate height of the surface of the ground is 306 feet 
above Ordnance datum. 

3. The depth from the surface of the ground to the bottom of the 
well which is 10 feet in diameter, is 168 feet, and there is no bore-hole. 

3a. There are no horizontal drifts. 

4. Before pumping, the water stood at 1 29 feet below the surface of 
the ground. The number of hours elapsing before ordinary level is 
restored depends upon the extent and duration of the pumping. 

4a. The well was sunk practically di-y, until a depth of 168 feet below 
the surface of the ground was reached, when, through the marl floor of 
the well at that depth a large spring was met with, the initial inflow of 
which was at the rate of about 1,500,000 gallons a day, and its artesian 
force such that in a veiy few minutes it rose to a height of 39 feet above 
the bottom of the well, or, as before stated, to 129 feet from the surface 
of the oTOund, at which point it remained stationary, and to which point 
it rises when not drawn upon by pumping. 

5. Durino- an experimental test extending over a period of 59 days, 
from September 21 to November 19, 1881 , the pumps were kept continu- 
ously at work day and night, and during that time the total quantity of 
water raised from the well was 61,000,000 gallons, or rather over 
1 000 000 callous a day. This continuous pumping at the i-ate named 
lowered the water in the well 28 feet 7 inches, or to a depth of 157 feet 

7 inches below the surface of the ground, leaving a depth of 10 feet 
5 inches in the well. On the cessation of pumping the water rose 

8 inches in 30 seconds, or at the rate of 945,000 gallons a day, and at 
the end of 8 days it had regained 14 feet 2 inches of the loss of level. In 
3 weeks (notwithstanding occasional pumping for the supply of about 
800 houses then laid on), it had risen to a level some few inches higher 
than the point at which it stood before the experimental test was made. 
The averao'e quantity pumped for the supply at present of between 1,100 
and 1,200 houses is about 55,000 gallons jjer diem. 

6. There is no decided information available as to whether the water- 
level varies with the seasons. I am of opinion that it does, though only 
to a limited extent. The well having only been regularly drawn upon for 
water supply purposes for less than a year, and that at a rate very far 
within the margin of its average yield, affords no experience at the 
present time on the point whether the yield is diminishing or not. 

7. The ordinary water-level is not affected by local rains. It stands 



ON THE CIRCULATION OF UNDERGROUND WATERS. 225 

about 177 feet above mean sea-level, or 11 feet above the ordinary- 
summer level of the river Tame, about half a mile distant. 

8. The analysis is as under : — 

_ , , Grains per arall. 

1 emporary hardness 6-13 

Permanent „ ' 3.5Q 

Total „ '.'.;; 9-63 

Chlorine •••••...... 1-61 

Total solids ..'.'. 25-06 

The v^ater contains no marked peculiarity. 

9. The section of the rock passed through is as under : — 

a. Soil, sand, and gravel 16 6* 

b. Red marl, with layers of sandstone . . . . .' 15 ] 1 

c. Hard conglomerate rock 5 7 

d. Argillaceous marl rock 39 11 

e. Fissured sandstone . , 139 

/. Argillaceous marl rock 5 

ff. Light fissured sandstone rock 30 4 

A. Red marl, with layers of greyish blue stone, and balls of 

marl of same colour with dark spot in centre, called ' fish- 
eyed ' marl 410 

Total 168 

9a. As stated in reply to 4a, the well was practically dry until the 
spring referred to was tapped, at a depth of 168 feet from the surface ; 
though a little water oozed out at the bottom of the fissured sandstone 
rock ' jf ' in the preceding answer. 

A singular phenomenon occurred with respect to one of the fis- 
sures situate in this rock at 115 feet from the surface of the ground. 
When first opened down to, a violent current of wind (simply atmo- 
spheric air) rushed from it, which gradually spent itself, and was fol- 
lowed thereafter at one time by an in-draught, succeeded at another by 
an out-draught. It was observed that these variations of direction were 
coincident with barometrical changes — i.e. when the barometer was rising 
there was a decided indraught from the well into the fissure ; and, on the 
contrary, while the barometer was sinking there was a decided out- 
draught from the fissure into the well. It is evident, therefore, that the 
fissure must be connected with large cavernous passages. Changes in 
the weather were accurately foretold by watching the behaviour of a 
candle-flame when placed near the fissure ; but the workmen were dis- 
inclined to place much faith in its indications until an active outflow 
during the whole of one day was succeeded at night by one of the most 
violent storms of the period. 

10. The cover-drift over the rocks contains no sprino-s. 

11. There are no land springs to keep out of the well. 

12. There is a large down-throw fault between the well and the river 
Tame, which brings the Keuper Marl beds face to face with the con- 
glomerate beds in which the well is sunk. 

13. No brine springs were passed through in making the well. 

14. There are no salt springs in the locality. 

15. No wells or borings in the neighbourhood have been discontinued 
in consequence of the water being more or less brackish. 

16. The well is lined with brick in cement to within about 2 feet of 
the bottom. Its cost was 793Z. 15s. 6d. 

1882. Q 



226 



EEPOET 1882. 



Information collected by Mr. James Plant, T.G.S. 
From Mr. H. W. Pochin. 

1. Croft, Leicestershire. This is an underground spring in greenstone rock at 
bottom of a deep cutting. 1«. Begun 1880. Water struck January 1, 1882. 2. 
About 320 ft. 3. 110 ft. 4 and 4a. Water issues constantly at the end of the 
fissure, and has been running without ceasing for eight months. 5. A pump is now- 
used which discharges 100,000 gallons every ten hours. 6. Quantity is the same as 
when first struck. 7. Is below the level of the Kiver Soar, which runs close bj-. 
8. No proper analysis yet made, but water very soft. 

9. Lower boulder clay 

Upper white Keuper sandstone .... 
Red marl separated by thin floors of white sand- 
stone ......... 

Total 130 

These beds lie on the worn and rounded surface of the greenstone, at an angle of 
about 20° dipping S.E. 9a. Greenstone. lO. None seen. 12. No. 13. No. 14. 
No. 15. No. 16. Six photographs have been taken, and will show the deep spring 
ssuing out of the rock. 

Information collected by Mr. James Plant. 
From the Hinckley Local Board. 

1. Hinckley Wharf, near Hinckley, Leicestershire. la. Boring of 10 inches 
diameter commenced Nov. 1881. 2. 813 ft. 3. Depth from surface of 10 inches 
diameter 160 feet, depth below this 540 feet of 7 inches. Total depth 700 feet. 4. 
The mean height at which the water stands in the bore-hole varies from 630 to 680 
feet. 5. Over 1,000 gallons were taken out of the bore-hole, which filled up again 
in about two hours. 6. See No. 4. 7. Water-level is above the bed of the Kiver 
Anker, which is about 2 miles S.W. of the bore-hole. 8. No analysis yet made. 



ft. 


in 


8 





30 





92 






9. Hinckley Wharf Soring 


, commenced Kor. 1881. 


Character of Kocks 


Thickness 
of Beds 


Total 
Depth 


Remarks 




ft. 


in. 


ft. 


in. 




Soil 


1 





1 







Middle glacial sands . 


30 





31 







Lower boulder clay . 


50 





81 







Red boulder clay 


7 





88 





Many pebbles. 


Upper Keuper sandstone . 


12 





100 





Much denuded. Band fine 
crystallised gypsum 6 in. 


Red and blue marl with gypsum 


10 


9 


110 


9 




Red marl and gypsum 


69 


8 


180 


5 




Grey sandstone .... 


1 


I 


181 


6 




Red marl and gypsum 


26 


11 


208 


5 




Grey sandstone . 


1 


6 


209 


11 


6 in. crystallised gypsum. 


Red marl and gypsum bands 


96 


7 


306 


6 




Grey sandstone .... 





9 


307 


3 


5 in. gypsum. Verj' abun- 
dant water. 


Red marl and gypsum bands 


46 


5 


353 


8 


3 in. gypsum. 


Grey sandstone .... 


1 





354 


8 


4 in. gypsum. 


Red marl and gypsum 


41 





395 


8 




Grey rock, mottled marl and 












gypsum 


100 


4 


496 





At 484 ft. crystallised gyp- 
sum 3 in., being last band 
of gypsum. 


Red micaceous sandstone 


11 





507 





Top of Waterstones. Fine 
clay or wayboard \ in. 


Soft micaceous red sandstone . 


4 


c 


611 


6 





ON THE CIRCULATION OF UNDEKGEOUND WATEES. 



227 



Character of Rocks 


Thickness 
of Beds 


Total 
Depth 


Remarks 


Mottled marly sandstone (mica). 


5 


6 


517 





\ in. wayboard. 


Grey mottled marly sandstone . 


15 


1 


532 


1 


Ripple marks. 


Soft red sandstone 


11 


7 


543 


8 




Red sandstone .... 


c 


10 


550 


6 


Fine red clay, wayboard. 


Red sandstone .... 


10 


6 


561 





Fine red clay, wayboard 
1 in. 


Red sandstone (mica) 


5 


5 


566 


5 




Fine red clay .... 


4 





570 


5 




Red sandstone .... 


9 





579 


5 




Fine red clay .... 


1 





580 


5 




Red sandstone .... 


7 





587 


5 




Fine red clay .... 





6 


587 


11 




Grey sandstone (mica) 


2 


5 


590 


4 




Fine red clay .... 


5 


1 


595 


5 




Light red sandstone (mica) 


6 





601 


5 




Red sandstone .... 


2 





603 


5 


Wayboards 1^ and 6 in. 


Soft white sandstone, with small 












yellow iron spots . 


18 


4 


621 


9 




Hard white coarse sandstone 












with false bedding . 


i 


1 


625 


10 




Soft white sandstone with small 












iron stains .... 


7 


5 


633 


3 




Hard white siliceous sandstone . 


2 


2 


635 


5 




Hard red siliceous sandstone 


3 


6 


638 


11 




Soft white clay .... 


3 


4 


642 


3 




Red micaceous sandstone and 












red sandy marl 


6 


8 


648 


11 




Red marl and sandstone . 


11 


4 


660 


3 




White and brown sandstone 


11 


6 


671 


9 




Brown micaceous sandstone and 












strong red marl 


10 


6 


682 


3 


Wayboard. 


Red micaceous sandstone and 












strong red marl 


6 





688 


3 


Wayboard. 


Soft red clay .... 


O 


6 


690 


9 




Brown micaceous sandstone 





7 


691 


4 




Soft red clay .... 


1 


6 


692 


10 




Brown sandstone 





10 


693 


8 




Red clay 


2 


1 


695 


9 




Red sandstone .... 


1 


2 


696 


11 




Red clay ..... 


1 


7 


698 


6 




Red and brown micaceous sand- 












stone ..... 


4 





702 


6 




Red clay 


2 


2 


704 


8 




Red micaceous sandstone . 





6 


705 


2 





lO. Yes. H. Entirely out. 12. One great fault three miles to the W. is known, 
and another large one suspected four miles to the E. These faults run from N. W. to 
S.E. 13. No. 14. No. 15. No. 16. Several chalybeate sjarings formerly existed 
(shallow wells penetrating into the drift), they arc all now disused but one. 

Collected by Mr. E. Wethered, C.E. 

From Mr. J. N. Taunton, C.E., F.G.S., Engineer to the Thames and 
Severn Canal. 

1. Thames Head, three miles south-west of Cirencester. la. About 1793. 
2. 364 feet. 3. 63 feet depth of well ; shape oval 15 ft. x 10 ft. No bore-hole below- 
bottom of well. 3a. Original di'ift-way 30 yds. subsequently extended down the 
valley some 500 j-ards tailing into cutting about 17 feet in depth. 4. and 4a. The 

k water-level varies from 30 to 53 feet below the surface, according to the seasou and 
pumping. When the engine pumps continuously it usually lowers the water-level 



228 EEPORT — 1882. 

gradually in a dry season 3 or i inches a week. As the springs break in the neigh- 
tourhood the water rises rapidly. There does not appear to be any material change 
in the normal level of the water. 5. The quantity of water pumped from 1,500,000 
to 3,.500,000 gallons per diem. 6. Ai^art from the continuous pumping for the 
supply of the summit-level of the Thames and Severn Canal the water-level is 
determined by that in the gravel in the bed of the adjoining valley, and rises and 
falls with it. No perceptible diminution during the last 30 j'ears. 7. Not affected 
except by long-continued rains in the Cotteswold District on the N.W. 9. Section 
sent herewith. 9a. In the basement beds of the Great Oolite. lO. See section. 
11. See section. 12. No. 13. No. 14. No. 



Appendix III. — Jurassic Wells. 

Collected by Mr. C. Eox Strangways. 

From Lieut.- Col. W. F. Walker, R.E., York. 

1. Towthorpe Common, near York. Xa. January to April 1870. No. 2. 60 feet. 
3. The well consisted of a bore-hole 9 inches in diameter and 311 feet -1 inches deep. 
This was subsequently plugged, leaving the present depth 210 feet. 3<7,. None. 
4 and 4a. Enquiry will be made on these points. 5. Not tested. After 72 hours 
continuous pumping no diminution in supplj' was perceptible. 6, Little or no 
variation is observed in the shallow wells of the locality. Experiment not tried in 
deep boring. 7. Only temporarilij affected. Ordinarily stands \h feet above the 
level of the water in the I^ors, the nearest river, a. Two copies of the results of the 
analysis of this water are attached, that marked No. 1 being the result of the first 
analysis, and that marked No. 2 being the result of the analysis after plugging for 
about 100 feet had been resorted to. 

Analysis No. I. 

From Towthorpe, York. I Drawn December 20, 1879. 

Source, Artesian well, 311 ft. 4 in. deep. | Eeceived December 26, 1879. 

Physical Characters. 

Colour (through 36 in.) . Faintly yellow. | Lustre ...... Fair. 

Turbidity . . . None. ' Taste 

Sediment . . . Present. Smell None. 

Hardness. 

Fixed 66°-50 

Temporary or removable 26°-25 



Total .... 92°-75 

Quantitative Chemical Analysis. 

Parts per 1.000,000 

Oxygen required for oxidisable organic matter . 0'5600 

Ammonia, free 0-4940 

Ammonia, albuminoid ...... None. 

Nitric acid (NO3) 0-2297 

Nitrous Acid (NO,^) None. 



Total nitrogen included in nitrates and nitrites . 00519 

Grains per Gallon 

Volatile organic matter 0-4357 

Ammonium nitrate 0-1517 

Sodium nitrate 0*1566 

Sodium chloride 2-5689 

Sodium carbonate 5-0000 

Calcium carbonate 14-8000 

Calcium sulphate ... . . 77-9800 



ON THE CIRCULATION OF UNDERGROUND WATERS. 



229 



Magnesium sulphate . 
Sodium silicate . 
Aluminium and iron phosphates 
Water with calcium suljihate 

Total solids 

Total solids .... 
Total solids by evaporation 



Grains per Gallon 
2.^-729.5 

1-9485 

2-8300 
10-3209 



Difference 
microscopic examination of the sediment 



141-9218 

141-9218 
141-8500 



grit 



0-07] 8 

The microscopic examination of the sediment shows mineral 
and sand, some crystalline particles, probably carbonate of lime, a little 
mycelium of fungi, but no trace of animal or vegetable life. 

This water is quite unfit for a water-supply on account of the large 
quantity of lime, magnesia, and sulphuric acid. Perhaps if the borings 
were continued farther a softer water might be obtained. 

Attention is called to the case of the Clifton Asylum Well, where the 
solids are now only about 20 grains, whereas I believe that previous to 
deepening the water was too hard to use. 

F. De Chaumont, M.D., F.R.S., 
Laboratory, Army Medical School, Professor of Military Hygiene, 

Eoj-al Victoria Hospital, Netley, Army Medical School. 

January 24, 1880. 



Analysii 
From Towthorpe, York. 
Source, -^vell 210 feet. 


! No. II. 

Dra-wn April 10, 1880. 
Keceived April 14, 1880. 
Examined April 20, 1880. 




PhTjsical Charracten. 




Colour (through 18 ins 

Turbidity 

Sediment 


.). Slightly yello-sv. 
. None. 
. Large. 


Lustre . . . . 

Taste . 

Smell . . . . 


. Very good. 
. Good. 
. None. 




Chemical Analysis. 




Qualitative ( 


water unconcentrated). 




Lime . 
Magnesia . 
Chlorine 

Sulphuric acid . 
Phosphoric acid . 


. Very large. 
. Very large. 
. Trace. 
. Very large. 
. None. 


Ammonia , 
Nitric acid . 
Nitrous Acid 
Oxidisable matter 
Iron or lead 


. Large. 
. Large. 
. None. 
. Trace. 
. None. 


Fixed 
Tempora 


Hard 

■y or removable 
Total 


ness. 

Degrees of Clark's Scale 
. 57°-75 
. 30°-15 


Quantitative. 


. 87° 


•50 



Grains per Gallon 
Volatile matter (by incineration and after re-carbonating) . 17500 

Parts per 1,000,000 
Oxygen required for oxidisable organic matter . 0-5800 

Ammonia, free 0-4548 

Ammonia, albuminoid ...... 0-0960 

Nitric acid (NO3) 8-5529 

Nitrous acid (NO2) 0-2300 

N.B. — These constituents, with the oxidisable 
organic matter indicated by the oxygen required 
are included in the Volatile Matter. 

Total nitrogen included in nitrates and nitrites 1-5497 



230 REPORT— 1882. 

Grains per Gallon 

Chlorine 1-6368 

Calcium carbonate 20' 1000 

rixed hard salts . . ' 67-7500 

Sulphuric acid (SO^) 53-0 880 total partly included in fixed^ 

hard salts . . 

Alkaline carbonates ........ 

Sodium or other metal (combined %Yith CI or SO,) not in- 
cluded in fixed hard salts 

Silica, alumina, iron, kc. 



54-5632 



Total solids (by evaporation) .... 135-8000 

_ Microscopic Characters. — The microscopic examination shows only a little 
mineral grit. No trace of animal or vegetable life. 

Eemarks. — The -water has improved a little since plugging, and justifies further 
plugging, as originally suggested, to the level of the green sand. 

J. L. Notter, M.D., F.C.S. 
Laboratory, Army Medical School, Assistant Professor of Military Hygiene 
Eoyal Victoria Hospital, Netley. 
April 23, 1880. 

ft. iu. 

9. Top sand 4 6 

Fine clay 15 

Boulder clay 15 

Loamy sand 6 

Fine warp clay 9 

Grey sand 10 

Boulder clay . 4 

Green sand 16 

Green sand with layers of blue bind . , .18 

Blue bind or marl 19 

Light green sand with blue bind . . . . 35 

White sandstone 5 

Blue bind 10 

Red marl ........ 2 

White sandstone 810 

Blue marl 6 

White sandstone 23 

Blue marl 3 

Variegated sandstone 60 

Red marl 3 



310 
Note.— The actual depth is 311 ft. 4 in., but 1 ft. 4 in. has been lost in taking- 

the various dimensions. See remark opposite 3, as to plugging. 

lO. Yes ; the drift is full of water. 11. Yes. 12. No. The strata are those of 

the Vale of York. 13. None. 14. None. 15. None ; as far as we know. 

Collected by Mr. C. Fox Strangways. 
From Mr. J. W. Woodall, J.P., F.G.S. 

1. Salton, near Malton, York, N. Riding. Xa. 1880. No. 2. 150 ft. 3. 316. 
About 4 in. 3a. None. 4. Flows out at surface, ftff. Flows out at surface. 5. 
Not been tested. 7. A few feet above the Rye ; 3 or 4 ft. 8. No analysis has been 
made, but it is slightly sulphureous. 9. Fluviatile drift 15 ft. Kimmeridge clay, 
about 295 ft. lO. No. 11. Yes. 

Appendix TV.— By Mr. E. Wethered, F.G.S., F.C.S. 
The Porosikj and Density of Rocks. 
My first object in commenciug a series of observations on the porosity 
of rocks was with a view of investigating the lithological changes which 



ON THE CIRCULATION OF UNDERGROUND WATERS. 231 

are brought about by tbe percolation of water through them. But while 
engaged in work of this kind, one is struck with the great volume of 
water which the rocks of the earth are capable of absorbing, and a know- 
ledge of this is important both as regards water-supply and the suit- 
ability of stone for building purposes. Much information on the subject 
has already been obtained by the investigations of the Rivers Pollution 
Commission, the Commission on "Water Supply, and on the Selection and 
Decay of Stone for the Houses of Pai'liament. Also by the Committee 
appointed by the British Association for the Investigation of the Circula- 
tion of Underground Waters, and by Mr. De Ranee, C.E., F.Gr.S., in his 
book on the Water Supply of England and Wales. 

The method which I have adopted for arriving at the results con- 
tained in this paper is that recommended by Dr. Sterry Hunt in the 
Geological and Chemical Essays. ^ The portions of rock selected for the 
work were struck off by a blow with a hammer. By this means I was 
enabled to get clear and natural surfaces exposed. The whole of the 
results obtained are given in the annexed table. 

The Arenaceous JRochs. — The oldest rocks which I have examined are 
those of the Old Red, and all the specimens were selected personally. 
Taking first the Old Red Sandstone we get an average specific gravity 
of 2"61, but the specimens from near Bristol have a decidedly lower 
specific gravity compared with others which are given. Excluding the flags 
from Caithness, the volume of water absorbed by a cubic foot of the rock 
is 0-707 of a gallon, or 59,000,000 gallons to the square mile 3 feet thick. 
The specimen of flags from Caithness absorbed much less Avater, and I 
found the same thing to apply to Old Red flagstones from other districts. 
The conglomerate beds are more absorbent than the sandstones : the 
average specific gravity is 2-58 and the volume of water absorbed by a 
cubic foot 0-805 of a gallon, or 67,000,000 gallons to a square mile .3 feet 
thick. 

I next take the Millstone Grit. The specimens from Bristol, South 
Wales, and the Forest of Dean were selected personally, and for those 
from Sheffield I am indebted to the kindness of Dr. Sorby, P.R.S. The 
Millstone Grit which underlies the Bristol coalfield is something like 
1,000 feet thick ^; the chemical composition, the mean of five analyses, 
is as follows : — 

Silica 97-80 

Alumina ......... '47 

Oxide of Iron -80 

Lime ......... -44 

Carbon . -17 

Carbonic acid -39 

Moisture -22 



100-29 

In some of the specimens of this grit, microscopically examined, the 
grains of silica appear to cement themselves together, and so closely, 
that it is difficult to distinguish their outline. The gi-ains are, for the 
most part, sub-angular, and are either colourless or have a slight pink 
tinge imparted by oxide of iron. The specific gravity averages 2-60, 
and the amount of water absorbed by a cubic foot of the rock is O'OSO of 
a gallon, equal to 6,000,000 gallons to a square mile 3 feet thick. 

' Pages 165-7. 

^ Proc. Bristol NaUt/ralists' Society, 1875-6, page 336. 



232 



REPORT — 1882. 



Two typical specimens of Millstoue Grrit were selected from Pertyrcb, 
South Wales ; one a coarse variety and the other with grains averaging 
about O'OIO of an inch in diameter. There is a slight lithological differ- 
ence when compared with the same formation around Bristol, and 
chemically it is a little more argillaceous, as shown by the following 
analysis : — 

Silica 96-63 



Alumina . 

Oxide of iron 

Lime 

Carbonic acid 

Carbon . 

Moisture . 

Alkalies not estimated 



]-15 
•70 
•55 
•20 
■30 
•10 



99G3 

The specific gravity may be taken at 2^57, the volume of water 
capable of being absorbed by a cubic foot of the rock 0-290 of a gallon, 
or 23,000,000 gallons to a square mile 3 feet thick. 

The specimens of Millstone Grit from Sheffield resemble lithologically 
those of South Wales, though a person acquainted with the formations 
in the two districts would probably be able to distinguish between them. 
The grains composing the grit in the neighbourhood of ShefiBeld, 
according to Dr. Sorby, 'are, on the whole, extremely angular.' ' The 
specific gravity averages 2'59, and the volume of water absorbed per 
cubic foot of rock is 0-504 of a gallon, equal to 42,000,000 gallons to a 
square mile 3 feet thick. 

Two samples of Millstone Grit were collected from the Forest of 
Dean coalfield ; one from the southern outcrop and the other from the 
northern. We here get a very different lithological character when com- 
pared with the same formation at Bristol and in South Wales, and a 
very much larger volume of water is absorbed. The rock resembles a 
Trias sandstone more than the Millstone Grit, but in chemical com- 
position there is practically little difference, as is shown by the following 
analysis of a specimen from Drybrook : — 

Silica 98-06 

Alumina -30 

Oxide of iron , . -50 

Lime -33 

Carbon -20 

Carbonic acid -30 

Alkalies Trace 



99^69 



The specific gravity of tlie Forest of Dean Millstone Grit averages 
2-63, the volume of water absorbed by a cubic foot of the rock is 0854 of 
a gallon, or 71,000,000 gallons to a square mile 3 feet thick. Though I 
have given the average volume of water absorbed, it will be seen, on 
reference to the tabulated list, that the results obtained from the two 
specimens examined differ considerably. In the case of the one absorb- 
ing the greatest quantity of water, the grains composing it were but 
slightly cohesive, but in the other case the rock was of a more compact 
character. 



Quarterly Journal Geol. Society, 188, page 64. 



ON THE CIRCULATION OF UNDERGROUND WATERS. 233 

Referring to the upland surface water from the Millstone Grit and 
the non-calcareous portions of the coal measures, the Royal Com- 
missioners on Rivers Pollution say in their sixth report,' ' Many of the 
larsre manufacturing towns of Lancashire and Yorkshire are supplied 
with water for potable and manufacturing purposes, by the storage in 
vast reservoirs of the upland drainage from these formations. Being 
but slightly absorbent they yield to the impounding rivulets and streams 
a large proportion of the actual rainfall.' Though the Millstone Grit 
may be but slightly absorbent in the localities named, yet this character 
cannot be established as a rule by which one can be guided. In the case 
of the Bristol coalfield it applies, but when we come to the Forest of 
Dean we find the reverse to be the case. The Millstone Grit of the West 
of England serves as a good illustration of the variability of rocks in 
different localities, especially as regards the volume of water which is 
capable of being stored in them. 

The next rocks examined were those of the Pennant Grit. It is 
necessary here to lay stress upon the definite article, as ' the Pennant ' is 
confined to the middle coal-measui-es of Bristol, and is also extensively 
developed in the Somersetshire and South Wales coalfields. There are, 
however, beds of grit in the lower coal-measures of Bristol, which are 
lithologically true Pennants. The Pennant Grit is a compact blue rock, 
made up of angular grains. The following is the mean analysis of seven 
samples taken from my paper on the ' Composition of the Pennant Gi-it.' ^ 

Silica- ■ . 84-96 

Alumina ■i'34 

Oxide of iron ........ 4'55 

Lime 1-29 

Carbon 286 

Carbonic acid ........ 1'33 

Magnesia "05 

Water -58 

99-96 

The specific gravity of the Pennant averages 2'67, the water absorbed 
by a cubic foot of the rock 0"150 of a gallon, and by a square mile 3 feet 
thick 12,000,000 gallons. Speaking of deep wells in the Coal Meastires, 
the Rivers Pollution Commissioners say : ^ The proportion of mineral 
impurity present in the deep well-water is always large, but varies within 
wide limits. The water was found to contain, ' as a rule, larger pro- 
portions of organic elements (organic carbon and organic nitrogen) than 
are met with in similar waters obtained from other strata,' the average 
proportion being 0'153 parts per 100,000 parts, or 'lO? grains per gallon, 
I quite endorse what the Commissioners say in respect to water from 
the coal-measures generally, but where we have a great thickness of 
rock, as in the case of the Pennant around Bristol and Swansea, I think 
there may be an exception to what has been stated. Some years ago, 
it was proposed to supply a portion of Bristol with water from the 
Frampton Cottrell iron mines, which are in the Pennant, and the 
analyses made of the water showed it to be of good quality. Considering 
the quantity of water which this rock is capable of storing, the quality 

' Page 40, part 2. 

- Journal of the Cliem. Society, 1882, page 79. 

' Sixth Keport, page 91. 



234 EEPOBT— 1882. 

becomes a matter of great importance to villages and towns in the 
vicinity. 

The only specimen of Triassic sandstone which I have had an oppor- 
tunity of examining is that of the Banter, from Heidelberg, Germany. 
The specific gravity was 2'55, and the volume of water absoi-bed by a 
cubic foot of the rock was 0'838 of a gallon, equal to 70,000,000 gallons to 
a square mile 3 feet thick. Mr. I. Roberts, F.G.S.,' has made observations 
on the porosity of the Bunter from the Pebble Bed of Everton, and found 
the absorption to be 0"733 of a gallon of water to the cubic foot of rock. 

The Calcareous Rocks. — Coming to the calcareous rocks which I have 
examined, I have classed among them the Magnesian Conglomerate, 
which I take first. The average specific gravity is 2 '73, and the volume 
of water absorbed by a cubic foot of rock varies between 0"082 and 
0-368 of a gallon, or between 6,000,000 and 30,000,000 gallons to a square 
mile 3 feet thick. This rock is extensively used for building purposes, 
and a knowledge as to the porosity of the various beds is therefore 
important in this respect as well as for water supply. It would appear 
from the specimens which I have examined, that the finer the conglo- 
merate the more water there is absorbed. 

Of the Magnesian Limestone, two specimens were examined, both 
selected from the same locality. The average mean specific gravity is 
2'77, the water absorbed by a cubic foot of the rock 1'031 gallons, and by 
a square mile 3 feet thick, 86,000,000 gallons. 

The Magnesian Limestone is much more porous than the Carboniferous 
Limestone, which I take next. All the specimens were obtained per- 
sonally, the first three from the lower shales. These gave a specific 
gravity of 2' 71, with a porosity of 0'028 of a gallon of water to a cubic 
foot of rock, which is equal to 2,000,000 gallons to a square mile. The 
specific gravity of the specimens representing the limestone gave an 
average of 2'70. The volume of water absorbed by a cubic foot was '043 
of a gallon, or 3^ million gallons to a square mile 3 feet thick. From 
these comparisons it would seem that the lower shales are least porous. 
Considering the large volume of water which these rocks supply, their 
not being porous will seem contradictory ; the fact is, however, that the 
water finds its way through joints and fissiires, dissolving away the lime- 
stone, and sometimes forming subterranean reservoirs. 

We next come to rocks which are very pervious ; some of them, so far 
as their absorption of water is concerned, may be compared to an ordinary 
sponge. The rocks to which 1 allude are those of the Oolites. The 
specimens of the Great Oolite were personally selected from near Bath. 
The average specific gravity is 2'52, the water absorbed by a cubic foot 
of rock 1'706 of a gallon, or 142,000,000 gallons to a square mile 3 feet 
thick. The soft variety is the most absorbent. The specimens of Inferior 
Oolite were personally selected from near Cheltenham, with the exception 
of one from near Bath. As this rock is so extensively used for building 
and on account of the great volume of water which the beds contain, I 
have examined a number of representative specimens, but the variation 
in the porosity is so great that no reliable average can be given of the 
volume of water capable of being absorbed. The bed which absorbed 
the least was a hard variety of Oolite taken from below the Pisolite bed 
of Leckhampton Hill, near Cheltenham ; and the bed which absorbed the 
most was a soft variety of freestone from the same locality, but higher 
' Fourth Report Underground Water Committee, page 16. 



ON THE CIRCDLATION OF UNDERGROUND WATERS, 235 

up in the series. The first of these gave 0"146 of a gallon to the cubic 
foot, or 13,000,000 gallons to the square mile 3 feet thick ; and the second 
2'202 gallons to the cubic foot, or 184,000,000 gallons to a square mile 
3 feet thick. We may, therefore, take it that the yield of water from 
the Inferior Oolite varies between those limits. 

The Relation of Specific Gravity to Porosity. — In the report on Selec- 
tion and Decay of Stone of the Houses of Parliament in 1839 ^ it is said 
that the specimens of rock which had the greatest specific gravity absorb 
the least quantity of water, though there are individual exceptions. I 
cannot say that my observations bear out this rule, and I doubt whether 
any such rule can be laid down. 

The Relation of the Size of Grains composing a Rock to the Porosity. — • 
In the tabulated results I have given a column in which the size of the 
grains composing the rocks is given. The object of this was to ascer- 
tain whether any relation existed between the size of the grains and the 
porosity. In the sandstones and grits there appears to be no connection 
whatever, hut in the Magnesian Conglomerate the finer the material of 
which a bed is made up the more water there seems to be absorbed. 
In the case of the Oolites the more compact the rock the less porous ib 
becomes. 

The Privity of the Water. — On account of shallow well-water being 
almost invariably contaminated with organic matter, the Royal Commis- 
sioners on Rivers Pollution have classed shallow well-water as dangerous. 
On the other hand, deep well-water is classed as wholesome. It is, there- 
fore, clear, that if shallow well-water is dangerous and deep well-water 
wholesome, there must be a purifying process going on during the 
percolation of water through the strata. I have given the analyses of 
samples of Millstone Grit and of the Pennant Grit, and on an examination 
of these it will be seen that the grits are pi-actically composed of grains of 
silica. There is, therefore, nothing in the chemical composition of the 
rock which could purify the water except mechanically, and in order 
to get rid of organic contamination there mast be oxidation. We must, 
therefore, look to another source than the chemical composition of the rock 
for the oxidising agent, and I think it will be found in the air absorbed 
by the water and in the air contained by the rock. The water in the 
strata is constantly being drained by springs, wells, and outlets by which 
the water-level is reduced. During a dry period, then, the interstices 
of the upper portions of porous rocks must be either occupied by air or 
there must be a vacuum. The former of these two conditions is the most 
probable, and it seems reasonable to assume that the oxygen of this air 
must oxidise any organic matter contained in water percolating through 
the earth. I have made observations with a view of ascertaining the 
volume of air absorbed by certain rocks. I have endeavoured to arrive at 
the result by displacing the air contained in given specimens by water. I 
have found the volume of water absorbed, and reduced it to the weight of 
air, assuming that water at 62° F. is 819'4 times heavier than air at the 
same temperature. By this means I find that a cubic foot of Inferior 
Oolite, absorbing 1 gallon of water, would, in the event of complete 
drainage off of the water, absorb 0'16 of its volume of air. In short, we 
find in the rocks of the earth much the same process going on naturally 
as the London water companies are doing artificially for the filtration of 

> Page 36. 



236 



EEPOET 1882. 



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s t r 



238 EEPOEX — 1882. 

the London water-supply. The following is a section of the filter beds 
of the Chelsea Waterworks, for which I am indebted to the manager, 
Mr. Lott :— 

ft. iu. 

Fine sand 3 6 

Shells' 4 

Shingle 2 

Coarse shingle - 2 2 

Total' 8 

The chemical analysis of the top bed of the filter, which does the 
work, gave the following : — 

Silica 90'05 

Alumina "40 

Oxide of iron 6'90 

Carbonaneous matter ... . . -70 

Carbonic acid 1'50 

Magnesia "01 

Alkalies trace 

Moisture "26 

99-97 

' "'The rate of filtration is 2 gallons per hour.'* By comparing the 
chemical analysis of the filter-bed with those of the Millstone Grit and of 
the Pennant Grit, it will be seen that to all practical purposes the analyses 
are the same. There is nothing in the chemical composition of the filter 
which can oxidise the organic impurities of the Thames water passing 
through, but the oxidation is effected by air between the gi-ains of sand 
with perfect effect. It is much the same with water percolating through 
the rocks of the earth ; it comes in contact with air collected in the 
interstices. With such rocks as the Mountain Limestone, however, where 
the water yielded comes through fissures and joints in the strata, and does 
not percolate, it is a question whether the purifying process would be 
always satisfactory. 

Appendix V. — List of Queries circulated. 

1. Position of well or shafts with which you are acquainted ? la. State date at 
which the well or shaft was originally sunk. Has it been deepened since by sinking 
or boring ? and when ? 2. Approximate height of the surface of tlie ground above 
Ordnance Datum (mean sea-level) ? 3. Depth from surface to bottom of shaft or 
well with diameter ? Depth from surface to bottom of bore-hole, with diameter ? 
3a. ^ Depth from the surface to the horizontal drift-ways if any ? What is their 
len'oth and number ? 4. Height below the surface, at which water stands before 
3JxA after pumping. Number of hours elapsing before ordinary level is restored after 
pumping ? 4«. Height below the surface at which the water stood when the well 
was first sunk, and height at which it stands now when not pumped ? 5. Quantity 
capable of being pumped in gallons per day of 24 hours ? Average quantity daily 
pumped ? 6. Does the water-level vary at different seasons of the year, and to what 

' To keep the upper layer from mixing with the lower. 

'^ Gradually increases in coarseness towards the base to prevent the pipes which 
carry off the water from becoming clogged. 

3 The arenaceous material is taken from the Thames, and is well cleansed by a 
powerful hose playing upon it. , , . , ^ 

* Colonel Bolton's Report for February, 1882, for which I am indebted to the 
courtesy of Colonel Bolton. 



ON THE CONVEBSION OF SEDIMENTARY MATERIALS. 239 

extent ? Has it diminished during the last ten years ? 7. Is the ordinar}' water-level 
ever affected by local rains, and, if so, in how short a time ? And how does it stand 
in regard to the level of the water in the neighbouring streams, or sea ? 8. Analysis 
of the water, if any. Does the water possess any marked jjecidiarity ? 9. Section 
with nature of the rock passed through, including cover of Drift, if any, with thioh- 
itess ? 9«. In which of the above rocks were springs of water intercepted ? lO. 
Does the cover of Drift over the rock contain surface springs ? 11. If so, are these 
land springs kept entirely out of the well ? 12. Are any large faults known to 
exist close to the well ? 13. Were any Irine springs passed through in making 
the well? 14. Are there any salt springs in the neighbourhood? 15. Have any 
wells or borings been discontinued in your neighbourhood in consequence of the 
water being more or less brackish ? If so, please give section in reply to query No. 
9. 16. Kindly give any further information you can. 



Re'port of the Committee, consisting of Dr. H. C. Sorby, Professor 
W. Eamsay, and Professor W. J. Sollas, appointed for the pur- 
pose of investigating the Conditions under which ordinary Sedi- 
mentary Materials may he converted into Metamorphic Rocks. 
Drawn up by Professor W. J. Sollas {8ecretary\ 

The Committee have entered upon this investigation by commencing a 
.study of the effect of highly-elevated temperatures and pressures on the 
solubility of minerals and chemical compounds ordinarily insoluble in water. 

They have succeeded in obtaining a simply constructed tube, in which 
the experimental substances can be heated in the presence of water to a 
high degree of temperature (300-400° C.) without the escape of steam. 
The tube consists of cast iron, is 4 in. long, with an internal diameter of 
5 in., and walls | in. thick ; the mouth is closed by a conical iron stopper 
ground to fit, and secured by screws and nuts to a marginal flange ; to 
ensure complete tightness a washer of copper, or other soft refractory 
metal, is introduced before screwing up. 

Silica is the first substance which has been selected for examination, 
and the experiments with it have only recently been taken in hand. They 
have been conducted by Mr. Hunter, under the supervision of Professor 
Ramsay, in the laboratory of University College, Bristol. 

(1) A fragment of colourless, transparent quartz was reduced to fine 
powder, placed in a cage of platinum wire gauze, and so introduced into 
the tube, along with 10 cubic centimetres of water. The tube was then 
closed, and heated by a Bunsen's burner to a temperature of 300° C. for 
two days. There was no sign of action ; no residue was left on evapora- 
tion of the water, and the surface of the quartz retained its lustre. 

(2) Some powdered chalcedony taken from a clear hyaline specimen 
was similarly treated. It was slightly attacked, and on evaporation a 
distinct residue was left. 

(3) Some chemically pure silica was next prepared by precipitation 
from sodium silicate with hydrochloric acid, evaporation to dryness, 
thorough washing, and subsequent ignition. After ignition it was placed 
in the experimental tube, and heated to 300° C. for two days. At the 
conclusion of the experiment the impalpable powder of silica was found 
to have caked together into a white opaque granular mass. On examina- 



240 KEPOKT— 1882. 

tion tinder the microscope it was found to have passed into a state of 
glass. The glass itf.elf is transparent and colourless, and hard enough to 
scratch ordinary window-glass ; it is, however, filled with innumerable 
oval and tubular cavities, so as to resemble pumice, and it is to these 
that it owes its whiteness and opacity when seen by the unassisted eye. 
It is now in process of chemical examination. 

It is proposed to continue these experiments on silica, particularly 
under much higher temperatures than those hitherto employed, and to 
extend them to other substances. 



Report of the Committee, consisting of the late Professor A. Leith 
Adams, Professor W. Boyd Dawkins, Dr. John Evans, Mr. Gr. H. 
KiNAHAN, and Mr. K. J. Ussher {Secretary), appointed for the 
purpose of carrying out Explorations in Caves of Carboniferous 
Limestone in the South of Ireland. 

"Within the past three months attempts have been made to effect an 
entrance from the face of the scarp into the series of caves discovered and 
reported on last year (1881) in the rock called the Carrigmurrish, but 
after a careful survey had been made, and levels taken from the several 
branches of the caves by Mr. DufEn, County Surveyor (whose kind assist- 
ance we wish specially to acknowledge), it was found that the caves lay 
at so low a level as to make such a mode of access to them practically 
impossible. The onlj' enti-ance to them continues to be by the difhcult 
descent within the rath on the top of the rock. A series of trial pits 
were then sunk with candle-light in the several branches of the caves. 
Beneath the stalagmite floor was iu all cases a deep layer of tenacious 
clay, passing into gravel when the pits were sunk to the depth of about 
six feet. No animal remains nor other relics occurred in these trial pits. 

It is therefore probable that the only objects of interest that will be 
yielded by excavations on the Carrigmurrish will be found in the kitchen- 
midden of the rath, much of which remains untouched. 

Our next operations were conducted in the Bone cave of Ballyna- 
mintra, which yielded remains of man associated with those of Irish elk 
and bear in 1879, as reported in the ' Proceedings of the Royal Irish. 
Academy for 1880,' and more fully in the ' Transactions of the Royal 
Dublin Society for 1881.' 

In this cave a new chamber was cleared out down to the level of the 
stalagmite floor, and a portion of the latter was broken up, but as yet with- 
out result. Beyond this chamber, however, a new series of chambers, 
were discovered in which no excavations have been made. 

Excavations have therefore been carried on during the past season 
only to a very limited extent, owing to unusual demands on time and 
labour for other purposes. The amount expended in wages, &c., is but 
two pounds. 

The ossiferous caverns in the county of Waterford have not, however, 
been exhausted. The Shandon Cave, which yielded so many fossil 



ON THE PREPARATION OF A GEOLOGICAL MAP OF EUROPE. 241 

remains of mammoth, bear, horse, reindeer, and other animals, remains ia 
great part unexplored since the excavations of our late lamented friend 
Professor A. Leith Adams in 1875. He was then prevented from prose- 
cuting his work further by the danger of the impending roof coming away 
in fragments, the rock being full of horizontal splits, so that layers of 
stone are ready to fall if disturbed from beneath. Professor Leith Adams 
was anxious to resume the exploration of this great cavern, which has 
been so fruitful in Pleistocene mammalia, and stated it as his opinion that 
the superincumbent rock should first be wholly removed for a distance of 
fifty feet along the face of the cliff, taking the present mouth of the cave 
as the centre, and as far in as Cullen's Chamber might extend. The cliff 
is over twenty feet in height, so that such an undertaking would involve 
considerable outlay, including compensation to the occupier of the ground. 
If, however, your Committee could undertake to have the work quarried 
at sixpence a cartload, the stone thus obtained might be sufficient recom- 
pense for the injury to land and fences. A very large quantity of stone 
would have to be removed, which could be done during the winter 
months, leaving the floor of the cavern open for excavation before next 
summer. It is difficult to estimate the probable expenses of this work. 
To do it effectively the cave should be properly opened up by the total 
removal of its roof. Professor Leith Adams expended 401. on the portion 
that he excavated in 1875, without having to remove any of the roof, as 
his operations were conducted near the mouth. A sum of 50Z. seems to 
be required for the work now proposed. 



I 



Report of the Committee, consisting of Sir A. C. Ramsay, Professor 
J. Prestwich, Professor T. McK. Hughes, and Mr. W. Topley, 
appointed to assist in the preparation of an International 
Geological Map of Europe. Drawn up hy Mr. W. Topley 
{SecretaryX 

Since the appointment of the Committee last year considerable progress 
has been made with the Geological Map of Europe. The International 
Geological Congress met at Bologna on September 26 last. Two 
members of this Committee, Professor Hughes and the Secretary, 
attended the meeting. The discussions extended over five days, but it is 
only with those immediately referring to the Map that this Committee is 
concerned. 

The Congress resolved to prepare and publish a Geological Map of 
Europe, with so much of Asia and Africa as comes within the border : 
the map to be published at Berlin on the scale of 1 : 1,500,000 (about 
23 miles to the inch). A Committee to carry out the work was appointed 
as follows : — 

MM. Beyrich and Hauchecorne for Germany (Directors of the Map). 

M. Daubree for France. 

M. De Moeller for Russia. 

M. Giordano for Italy. 

1882. R 



242 EEPOKT— 1882. 

M. Mojsisovics for Austria-Hungary. 

Mr. Topley for England. 

M. Renevier, as Secretary of the Original Committee on Map Colour- 
ing. 

The details of the execution of the map were left to the Committee, as 
also were some questions relating to colouring. The Congress, however, 
decided upon the following colours : — 

Rose carmine for crystalline schists, whenever there is no certain 
proof that they are of Cambrian or Post- Cambrian age. 

Bright rose colour for rocks of Pre-Cambrian age. 

Pale rose colour for crystalline rocks of indeterminate age. 

Violet for Trias. 

Blue for Jurassic (the Lias a darker tint.) 

Green for Cretaceous. 

Yellow for Tertiary, the higher beds being the lighter shades. 

The subdivisions of a system are to be represented by shades of the 
colour adopted, the darker shade representing the older subdivision. 
Divisions may also be shown by reserved spaces of white or by lines. 

The lettering for sedimentary rocks to be based on the Latin alphabet - 
for eruptive rocks on the Greek alphabet. 

The monogram of a system to be formed by the initial capital of the 
name of the system ; subdivisions to be denoted by the initial small 
letter of its name in addition to that of the system. Smaller divisions to 
be denoted by figures, one denoting the oldest example : — Silurian, S ; 
Ludlow, SI ; Upper Ludlow, &\ 

The use of palteontological, orographical, chronological, petro graphi- 
cal, and geotechnical signs is recommended. 

The arrangements finally made for the publication of the map are as 
follows : — Reimer and Co., of Berlin, are the publishers. The map will 
be issued in forty-nine sheets (7 by 7) ; the size of the entire map when 
joined together will be rather over 12 ft. by 10 ft. The British Isles are 
contained witliin two sheets, with a slight extension of the south-west of 
Ireland beyond the map-margin. The southern sheet contains a large 
part of the north and north-west of France. 

The cost of engi'aving and colouring the map, including the prepara- 
tion of 1,000 complete copies, is estimated at 4,000Z. To meet this expense 
contributions will be given by the various Governments of Europe. 
England's share of the expense is 400Z., for which 100 copies of the com- 
plete map will be given. The Royal Society has voted the first instal- 
ment of 751. from the Government grant ; and has also given 75Z. towards 
the cost of preparing the map in England so as to be ready for engraving, 
and of printing the reports of the various sub-committees on Geological 
Nomenclatui'e, &c. 

England is also to supply the requisite information for the topography 
and geology of Palestine. 

The engraving of the map is well advanced. Streams and railways 
are given in great detail ; the names of places of geological interest will 
be inserted ; also the names of the mountain chains and the heights of 
the chief summits (in metres). 



ON THE ERRATIC BLOCKS OF ENGLAND, WALES, AND IRELAND. 243 



Tenth Report of the GoTnmittee, consisting of Professor J. Prest- 
wiCH, Professor T. McK. Hughes, Professor W. Boyd Dawkins, 
Professor T. Gr. Bonney, Dr. Crosskey, Dr. Deane, and Messrs. 
C. E. De Eance, D. Mackintosh, K. H. Tiddeman, J. E, Lee, 
James Plant, W. Pengelly, H. Gr. Fordham, and W. Terrill, 
appointed for the purpose of recording the position, height 
above the sea, lithological character's, size, and origin of the 
Erratic Blocks of England, Wales, and Ireland, reporting other 
matters of interest connected with the same, and taking measures 
for their preservation. Drawn up by Dr. Crosskey, Secretary. 

The Committee liave received the following accounts of Erratic Blocks 
examined during the past year : — 

Yorkshire. — Mr. "Woodall has examined a number of boulders brought 
from the bottom of the JN^orth Sea north of Flamborough Head, and gives 
the following account of their position and character : — 

North of Flamborough Head large numbers of boulders are found 
strewing the bottom of the North Sea ; but they are arranged very much 
in a belt, which is approximately parallel to the existing coast, at a 
distance of twenty to forty miles from the land. The outer or eastern 
edge of this belt is not well defined ; but on the western side it would 
appear to have a sharper boundary, as the marks used by the trawlers 
to avoid the boulders show that the line is well marked. 

While preserving a line parallel to the existing coast, it is curious to 
note that just opposite to the mouth of the Tees the inner edge of the 
' rough ground ' — by which name this belt is known to the fishermen — 
makes a sharp bend to the eastward, coinciding almost exactly with 
a line drawn down the Tees Valley. I venture to suggest that this 
large belt of erratic blocks is connected with the history of the giant 
glacier which descended the Tees Valley, bringing, among other stones, 
masses of the well-known Shap Fell granite. The boulders that I have 
seen brought on shore — having been trawled up by the smacks — are 
either of Shap granite or carboniferous limestone, and of these I have 
examined from sixty to seventy specimens. The rough ground — as far as 
I am aware — extends from the coast of Northumberland to the mouth of 
the Humber. While the boulder clay on the coast line contains blocks 
of carboniferous limestone and Shap granite, the glacial deposits in the 
valley of the Rye and Derwent — south of the Cleveland Moor district 
•^are composed of oolitic and liassic detritus, and are very different 
from those on the coast, though only a few miles distant from each 
other. 

Warwickshire. — A remarkable group of erratic blocks has been ex- 
posed in some excavations made for building purposes in Icknield Street, 
Birmingham, between Key Hill and Hockley Hill. The section occurs 
on the N.W. slope of the hill on which it is exposed, and consists of 
7 feet or 8 feet of glacial drift (the height slightly varying at different 
points), which immediately rests on an irregular and broken surface of 
the new red sandstone of the district, and is composed of about 1 foot 
6 inches of surface soil. The ' drift ' itself consists of erratic blocks,, 

n2 



244 KEPORT— 1882. 

intermixed with nnmeroas round and oval stones and pebbles, together with 
small gravel, sand, and clay. In different parts of the section these 
materials occur in varying proportions, a light clay generally pre- 
dominating. The erratic blocks, however, so pervade the whole bed, 
and so thoroughly constitute a component part of it, that tjjey cannot 
have been dropped into it either singly or by twos and threes. They 
must all have travelled together, for a certain distance at any rate, and 
have been brought down together to the spot at which they are found. 
They consist of — 

Fel sites. 

Felspathic ashes. 

Shales and flagstones. 

Quartz conglomerates. 

Fragments of quartzite. 

Millstone grits (with Stigmaria). 

Fossiliferous calcareous sandstones of Llandovery age. 

The felsites and the felspathic ashes are the most abundant, and the 
Llandovery sandstones are the rarest. No granite has been found in 
this gi'oup of erratics. 

The sizes of the blocks vary. The measurements of a few of the 
largest are as follows : — 

20 in. X 20 in. x 8 in. ; 26 in. x 15 in. x 14 iu.; 28 in. X 29 in. 
X 10 in. ; 32 in. x 18 in. x 16 in. 

Some are subangular ; a not inconsiderable proportion are well 
smoothed, although they can hardly be said to be highly polished ; and 
on a few striae may be traced. 

Professor C. Lapworth has examined the specimens, and recognises a 
large number as being of rocks that occur m situ at the Berwyn Hills ; 
others may be found in the Arenig range. 

The condition of the new red sandstone rock on which the boulders 
rest is most remarkable. The sandstone rock is broken up ; and large 
fragments of it have been lifted up out of their position and thrust into 
the middle of the drift. At one point in the section a part of the rock 
has been lifted up almost like an arm, and still remains united with the 
basement mass, while the drift fills the V-shaped hollow. A lai-ge erratic 
block is seen close to the extreme end of the uplifted arm of the basement 
rock. 

The evidence of violence is complete. The breaking up of the sand- 
stone rock, the uplifting of parts of it en masse, and the carrying away 
of fragments, are facts as patent as the presence of the erratic blocks 
themselves. 

The Secretary of the Committee has had photographs of the section 
prepared, to be preserved with specimens of the erratic blocks found. 

The Rev. W. Tuckwell has called the attention of the Committee to 
some very interesting boulders at Stockton, near Rugby, about equi- 
distant from Leamington, Rugby, and Coventry. The dimensions of the 
largest boulder are 4 ft. x 2 ft. 4 in. x 2 ft. 2 in. It is in part angular, 
but some portions are rounded. One end is planed into two level 
slabs. No distinct striations can be traced. The direction of its longest 
axis is almost exactly N. and S. It is composed of granite from Mount 
Sorrel, Leicestershire. It is quite isolated, and rests upon the lower 
middle lias clay. Its height above the sea is 289 feet. Through the 



ON THE ERRATIC BLOCKS OF ENGLAND, WALES, AND IRELAND. 245 

efforts of Mr. Tackwell, measures have been taken for the pre- 
servation of this remarkable boulder. It has been moved from the 
roadside, where it was in great danger of being injured, placed upon a 
bed of concrete, and will be protected by railings. 

A second boulder, also composed of Mount Sorrel granite, has been 
dug up from 5 feet below the surface in Nelson & Co.'s lime- works, 
half a mile to the N. of the boulder just described. 

Its dimensions are 1 ft. 8 in. x 1 ft. 8 in. x 1 in. 

In the same lime-works, and at about the same depth, a boulder 
of quartzite has also been Ibund. 

Its dimensions are 2 ft. 6 in. X 2 ft. 5 in. x 1 ft. 3 in. 

Fragments similar to this last boulder have been found in considerable 
quantities ; and from what the workmen say it appears that in past years 
many similar boulders have been discovered, and have been broken up 
in order that they might be got out of the quarrymen's way. 

Leicestershire. — Mr. W. Jerome Harrison has sent the Committee the 
following note on a Leicestershire boulder which has travelled north- 
wards : — 

In the construction of the sewerage for the Clarendon Park Estate, 
near the Victoria Park, on the east side of the town of Leicester, some 
interesting sections of the drift were laid bare, which I examined in 
June 1880. Much of the drift exposed was of a loamy nature, containing 
erratics of moderately large size, and overlying, though with no well- 
marked line of demarcation between, the well-known great chalky 
boulder clay which spreads so widely in this district. 

Among the travelled rocks contained in this deposit I particularly 
noticed one angular block identical in appearance with the syenitic rock 
which forms Enderby Knoll (4 miles south-west of Leicester), and Croft 
Hill (about 2 miles farther in the same direction). These South Leicester- 
shire syenites are well-characterised, and being somewhat abnoi'mal their 
identification is easy. 

The surface of the Clarendon Park Estate is about 300 feet above 
sea-level ; wLile Enderby Knoll is about 350 feet, and Croft Hill 450 feet 
(these heights are approximations only). The block which I saw on the 
Clarendon Park Estate measured about 3^ x 2 x Ih ft., and would 
weigh about three-quarters of a ton ; it was irregular in shape and very 
angular. As it did not interfere with the direct line of the sewer it was 
not removed, but was covered in.' 

Mr. J. Plant adds the following to his previous reports on the erratic 
blocks of this county : — 

Boulder in the parish of Aylestone (Ord. Map, 63 S.E.), in a field 
opposite the third milestone S. of Aylestone. Its dimensions are 7 ft. 
X 6 ft. X 4 ft. About one-third of the boulder is buried in the ground. 
It is angular, and not known to have been moved by man. Longest axis, 
N.N.E. No striations are visible. It is granite from Mount Sorrel, 

' The facts seem to the writer to show (1) that a submergence followed the retreat 
northwards of the great chalky boulder clay ; (2), that when this submergence 
amounted to about 350 or 400 feet, the bosses of syenite wi|^ occur in South 
Leicestershire stood as little islands above the sea ; (3), that ' coast ice ' formed on 
the margins of these islands, on which blocks of rock, detached by the frost, fell ; 
and (4), that a current running northwards carried at least one of these blocks 
down the Soar Valley and dropped it where it now lies, on the eastern brow of the 
Valley at Leicester. 



246 KEPOET — 1882. 

distance 9 miles due north, and no rock like it occurs in same locality. 
It may be noted that it lies due south of the ' St. John's Stone ' and 
the ' Holy Stone ' mentioned in former i-eports, and would mark the 
line of the meridian. It is about 250 feet above the sea-level. A large 
photograph, 12 in. by 10 in., has been taken of it. It is connected with 
what are supposed to be 'middle glacial sands,' which appear to be 
the wreck of the ' Upper Keuper sandstone ' (found in situ near them) ; 
these glacial sands being spread in long sheets, or ridges. It rests upon 
sandy drift. The weight of the boulder is about 10 tons. 

At Beasley's Farm, Aylestone, is a group of boulders. The smallest 
is 1 ft. 9 in. X 1 ft. 3 in. X 10 in., and the largest 3 ft. X 1 ft. 9 in. 
X 1 ft. 8 in. They are subangular. Rocks of the same character as the 
boulders (which are for the most part coarse sandstones), occur at Garrat's 
Hill, 3 miles N.W. Some smaller blocks, composed of millstone grit, must 
have come 40 miles from the N.W. The group is about 250 feet above 
sea-level. About an acre is covered by the boulders. There are seven 
large blocks of sandstone within an area of about 20 square yards. They 
are found in upper boulder clay lying upon middle glacial sands. A 
large photograph, 12 in. by 10 in., has been taken of this sand quarry. 

At the Clay-pit, Saffron Lane (Ord. Map, 63 N.E.), is a group 
of boulders. The smallest is 1 ft. cube, the longest 4 ft. x 3 f t. 6 in 
X 2 ft. The following are the dimensions of fifteen : 4 ft. x 3 ft. 6 in 

" in. X 1 ft. 6 in. ; 3 ft. 3 in. X 2 ft. x 1 ft. 
; 1 ft. 6 in. x 1 ft. x 10 in. ; 1 ft. x 1 ft. 6 in 
X 2 ft. X 1 ft. ; 1 ft. 8 in. X 1 ft. X 1 ft. 
2 ft. X 1 ft. 8 in. X 1 ft. ; 2 ft. X 1 ft. 8 in 
ft. 3 in. X 8 in. ; 1 ft. 6 in. x 1 ft. x 1 ft. 
2 ft. X 1 ft. 6 in. X 1 ft. They are rounded, 
angular, and subangular. ]\Iany of the smaller boulders are striated on 
both sides. They are derived from Mount Sorrel, Markfield, Hartshill, 
Ashby Coalfield, South Derbyshire, and places near Eelvoir Castle. The 
distance fi'om which these boulders have travelled ranges from miles to 
40 miles. Of the blocks counted and measured, thirteen are granite 
from Mount Sorrel of both the red and white variety. Of the remainder, 
■one is a block of black basaltic-looking rock, which may have come from 
the Hartshill range, Warwickshire ; the other is syenite from Markfield. 
The remaining twenty-two smaller blocks (not measured) are millstone 
grit, mountain limestone, chert, hard calcareous grits of the upper portion 
of the lower lias, and basaltic rocks. The group is about 230 feet above 
sea-level. The area opened is between 5 and 6 acres, and the boulders 
have gradually sunk to the bottom of the clay-pit, as the overlying 
' drift ' in which they are found was gradually removed so as to get at 
the marl underneath, and now they lie scattered over the pit. Thirty- 
seven have been counted, and fifteen of them measure as stated above. 
These blocks are found in middle sands and lower boulder clay, which 
vary from 6 to 10 feet in depth, and rest upon the Upper Keuper Marl. 
Two large photographs have been taken, showing some of these boulders 
lying upon the red marl floor, and the lower boulder clay upon the 
red marl. 

On turnpike road opposite the New Gasworks, Aylestone (Ord. map, 63 
N.E.) was found a group of three boulders. The smallest is 4 ft. X 3 ft. 
X 3 ft.; the largest 6 ft. X 3 ft. 6 in. x 3 ft. They are subangular. The 
large face of one of tlie boulders is ground smooth, and has a number of 



x 2 


ft 


; 4 


ft 


X 2 


ft. 9 


3 ft. 


X 


2 ft. 


X 


1ft. 


4 in. ; 


X 1ft. 


1 in. ; 


2 ft 


6 in. 


2 ft. 


X 


1ft. 


4 


in. X 


1ft.: 


X 1 


ft 


.; 1 


ft. 


8 in. X 1 


1ft. 


5 


in. X 


1ft. X 


6 in. ; 



ON THE EREATIC BLOCKS OF ENGLAND, WALES, AND IRELAND. 247 

striae in various directions. They are derived from Markfield, 6 miles N. W. 
They are syenite, much decomposed by the decay of the felspar, and are 
about 210 ft. above the sea-level. They were found in making a sewer 
at a depth of about 4 ft. from the surface, resting upon the Upper Keuper 
Marl. As they stretched from side to side of the excavation the two 
large ones had to be blasted to sret them out. The blocks have been 
removed to the Museum Grounds at Leicester. 

At Knighton, on the estate of Clarendon Park (Ord. Map, 63 N.E.), 
is a group of boulders. The smallest is 1 ft. 6 in. x 1 ft. 6 in. x 1 ft.; 
the largest 2 ft. 6 in. x 2 ft. X 2 ft. They are rounded, angular, and 
subangular. Some of the lower lias blocks are polished, rounded, and 
striated on both sides. These striations are in various directions. The 
distances of the rocks from which they were derived are as follows : 
About 20 miles N.B. for the lias blocks ; 6 miles N.W. for syenites and 
gi'anites ; 10 miles W. for greenstones. They consist of calcareous grita 
from the upper beds of lower lias ; granites, syenites, and greenstones are 
in greatest number. The group is about 300 ft. above the sea-level. The 
boulders from this locality extend over nearly 100 acres of ground, and 
some of them have been described in former reports. They have been 
found in making streets and sewers and digging foundations of houses, 
lying in upper boulder clay and middle glacial sands. 

In the parish of Thurnby (Ord. map, 63 N.E.) is a large collection 
of boulders. The smallest is a cube of 1 ft. ; the largest 6 ft. X 2 ft. 
X 1 ft. 6 in. Many are rounded and subangular. The majority are 
scratched with shallow scratches on both, sides of the longer face at 
various angles. They are derived from South Derbyshire, about 40 miles 
N.W. They are composed of mountain limestone, millstone grit, and 
permian rocks. The group is about .500 ffc. above the sea-level. The 
greater portion of these boulders (of whicli there are many thousands 
under a cubic foot) were turned out in making a tunnel on a new line 
of railway from Leicester to Melton. An excavation was made in lower 
boulder clay, which including the tunnel extended about 3 miles. This 
lower boulder clay was found to be 80 ft. deep in the tunnel-shaft, and rested 
on the black shales of the middle portion of the lower lias. Boulders 
have been found in the adjoining villages, and have been described in 
former reports. 

Shropshire. — The Committee have received from Mr. Luff a valuable 
report upon the group of erratic blocks found in the neighbourhood of 
Clun, Shropshire. 

Professor Lapworth has examined a series of specimens, and describes 
them as Lower Llandovery grits and shales belonging to the Plinlimmon 
group of central Wales. The hills from which they have been derived are 
all south of Bala, and situated almost due west from their present position. 

The following are the most remarkable among a large number of. 
boulders. The ' Great Boundari/ Stone,' marking the boundary of Clun 
and Treverward townships. It is on Rock Hill, 52° 24' 28" N.L. ; 
3° 3' 40" W.L., on the estate of Earl Powis. Its dimensions are 
6 ft. X 6 ft. X 2"5 ft. No striations can be detected, but it is angular 
and polished on one face. It is a cleaved flagstone, and has travelled 
from a point south of Machynlleth. It rests upon a bed of clay and rubble 
above the Upper Ludlow rock. Height above the sea, 1,152 ft. 

The ' Black Hill JBoidder; 52° 24' 40" N.L.; 2° 59' 50" W.L. 



248 REPORT— 1882. 

This boulder may be calculated to contain from 8 to 10 cubic 
feet, and is subangular. It is a pebble grit belonging to the Plin- 
limmon group, and may have come, according to Professor Lapworth, 
from the neighbourhood of Rhaydr. So far as can be observed, it rests 
upon the same limit of bed as the Great Boundary Stone. Its elevation 
above the sea is 1,327 feet, and it is the highest of all the boulders of the 
group. 

The ' 10 Feet Boulder.'—This boulder is a pebbly grit of the Plin- 
limmon group, and is very remarkable in many respects. 

It lies on the Clun Hill, near Pen-y-wern, 52° 24' 20" N.L., 3° 0' 30" 
W.L., at an elevation of about 1,160 feet above the sea. It measures 
10 ft. X 3 ft. X 3 ft., and weighs probably between 6 and 7 tons. It bears 
every evidence of having stood upright in the ground for a very long 
time. The base is tolerably angular and well-preserved, but the sides 
and apex are much Aveathered. About 4 ft. from the base it is deeply 
undercut, apparently all round, exactly as we should expect such a block 
to be where (on the ground-line) it had been most exposed to the combined 
influence of moisture and frost. 

About 120 yards distant, at the highest point of the hill it stands on, 
is a clump of young firs. Old inhabitants remember, before the trees 
were planted, a circle of stones (foreign-looking boulders), some 30 yards 
in diameter, existed here. The farmers, finding this piece of ground 
useless for agricultural purposes, carted the refuse of their fields — loose 
stones and weeds — on to it, and afterwards the firs were planted. 
Distinct traces of the stone circle are still to be seen.' 

The work of destruction among boulders is still going on with great 
rapidity. Many specimens are heard of as having existed some years 
ago, of which now no trace can be found. The Committee appeal, there- 
fore, to observers in all parts of the country to assist them in completing 
the record upon which they are engaged. 

' Mr. LufE sends the following memorandum on the Clun 10 Feet Boulder : — 

' A line drawn from the centre of this circle to the base of the boulder, if pro- 
longed, on one side would meet the 23oint of lowest sunrise (December 21), and 
on the other that of latest sunset (June 21). This I have tested by mariner's 
comiaass, making careful allowance for variation of the needle, and higher elevation 
of the opposite hills, and also by observation of sunset on and about the longest 
day. The boulder lies on the S.E. side of the circle, and in my opinion has been 
used as a gnomon to indicate the point at which the sun would be first seen on the 
shortest day. A spot more favourable for the observation or worship of that luminary 
could hardly be imagined. It is the centre of an amphitheatre of hills, the valleys 
are out of sight, and nothing is in view but hill-top below, and the dome of heaven 
above. 

' It is impossible to say who first erected this rude obelisk, or worshipped at this 
circle, but associated with them on the same range of hills are many clearly Neolithic 
remains, nicely polished flint arrow-heads, flint cores, and broken fragments. 

' It is to be hoped this interesting stone may be preserved as a monument of a 
bygone age.' 



ON FOSSIL POLYZOA. 249 



Third Report of the Committee, consisting of Dr. H. C. Sorby, 
and ]\Ir. G-. E. Vine, appointed for the purpose of reporting 
on Fossil Polyzoa (Jurassic Species — British Area only). 
Drawn up by Mr. Vine {Secretary). 

A PARTIAL examination of the Jurassic Polyzoa was made by Goldfuss,' 
but I am not aware whether he had any English examples of the types 
described and figured by him. With the exception of the Aulopora all 
the types are foreign, and I do not find any reference to British species 
in his text. In the ' Geological Manual ' of De la Beche, published in 
1832, a list of species is given, but only two are named as found within 
the British area — Cellipora orhiculata, Goldfuss (= Berenicea, Lamouroux), 
and Millepora straminea, Phill. In the ' Geology of York,' ed. 1835, 
Phillips gave three species only — M. straminea, Gellaria SmitJdi,'^ Scar- 
borough, and an undescribed Betepora (?). When, in 1843, Professor 
Morris published his ' Catalogue of British Fossils,' there was a large in- 
crease of species, but many of these had not been thoroughly worked. 
In 1854, Jules Haime examined critically the whole of the Jurassic 
Polyzoa then known, and many English naturalists furnished him with 
material from their own cabinets so as to enable him to correlate British 
and foreign types. Lamouroux, Defranc, Milne-Edwards, Michelin, 
Blainville, and D'Orbigny have published descriptions of Jurassic species,. 
and a list of these, so far as I am able, will be given at the end of this 
report. Professor D. Braun, by the publication of his paper on species 
found in the neighbourhood of Metz, added materially to our knowledge 
of French Jurassic types, and later foreign authors, Damortier, Waagen 
and others, have increased the number of described species. Since the 
publication of Haime's work much valuable material has been accumu- 
lating in the cabinets of collectors, and I would willingly draw up a. 
monograph if desired to do so. In the meantime I offer, in the following 
report, a rather compact analysis of genera and species known by name 
or otherwise to the palEeontologist. 

Classification. — Haime's arrangements of the Jurassic Polyzoa is very 
simple ; all his species, excepting two, are placed in one family, the Tubu- 
liporidce. In the ' Crag Polyzoa,' 1859, Mr. Busk gave a synopsis of 
the ' Cyclostomata,' arranged in eight family groups, which Avere made 
to include several Mesozoic types. This arrangement, with a slight 
alteration, was followed by Smitt, Busk to some extent accepting the 
modification for the arrangement of recent Cyclostomata in his later 
work ('Brit. Mus. Cat.' pt. iii. 1875). The Rpv. Thomas Hincks 
(' Brit. Marine Polyzoa,' 1880) disallows the family arrangement of Busk 
in so far as it relates to British species. The Tubidiforidce, Hincks, in- 
clude, in part, three of the families of Bask. In this report I shall 
follow Hincks as far as I am able to do so, as many of the Jurassic 
species may be included in the family Tuhidiporidce as now described. 
It will, however, in the present state of our knowledge at least, be im- 

' Petrifacta Germania, 1826-1833. - Hijipothoa (?), Morris's Catalogue. 



250 REPORT— 1882. 

possible to arrange the species stratagraphically, as many, having the 
same type of cell, range from the Lias upwards. As far as I am able to 
do so I shall give the range of the species, beginning, of course, with the 
lowest strata. 

Class POLTZOA. 

Sub-order Ctclostomata, Busk. 

Fam. I. CkisiiDvE, Busk. 

No fossils belonging to this family are at present known to have existed 
in the Jurassic epoch. 

Fam. II. 1880. TuBULiPORiDif;,' Hincks. 

' Zoarium entirely adherent, or more or less free and erect, multiform, 
often linear, or flabellate, or lobate, sometimes cylindrical. Zocecia 
tubular, disposed in contiguous series or in single lines. Omcium, an 
inflation of the surface of the zoarium at certain points, or a modified 
cell.' (Vol. i. p. 424.) 

1. Stomatopora, Bronn. 4. Entalophora, Lamx. 

2. TuBULiPORA, Lamarck. 5. Diastopora, „ (pars). 

3. Idmonea, Lamouronx, 

1825. Stomatopora, Bronn. 
1821. Alecto, Lamx.; 1826, Aulopora (pars), Goldf. 

1 have already done partial justice to the uniserial Stomatopora, found 
in the Palaeozoic rocks ^ of this and other countries. I have again 
studied the species described by James Hall, Professor Nicholson, and 
myself, and I cannot, at present, detect any generic character in the 
species that may be used by the systematic paleontologist to separate 
the PalfBozoic from the Massozoic types. I must, therefore, regard the 
Btomatoporoi of the two epochs as one, though the sequence is broken in 
the Palgeozoic — no species having as yet, I believe, been recorded from 
the Carboniferous series of this or any other country. 

Jules Haime has already pointed out the striking differences between 
the Alecto of Lamx. founded upon A. dicJwtoma and the Devonian 
Aulopora ; but I have not been able to verify his strictures regarding 
the exclusion of the latter from this group. It may be possible, however, 
to find that corals and polyzoa have been unwittingly united in some of 
our identifications. Haime gives seven different Jurassic species as 
found in the Lias and Oolite of this and other countries. As far as my 
material will justify the assumption, I claim for our British area the 
following charactei'istic types. As they are somewhat different I give the 
characters of our own species and varieties. 

I. Stomatopora antiqua, Haime. 
(pi. vi. fig. 7,^ Jurassic Bryozoa). 

Zoariuvi branching dichotomously, branches contorted, very rarely 
anastomosing. Zocecia uniserial ; lateral zoo3cia given off from either 

' For SjTionyms see British Marine Polyzoa. 

2 Brit. Assoc. Report, 1881. Silurian Uniserial, Stomatopora and Ascodictya. 
' Notes on the Wenlock Polyzoa,' QuaH. Journ. Geol. Soc. Nov. 1881, Feb. 1882. 

^ The references to Haime's work, Bryor,narcs Fossilcst de la, Formation jurasse. 



ON FOSSIL POLTZOA. 251 

the first or second cell of the branch, which in tux-n forms the base of a 
new branch ; cells generally uniform in size, sometimes swelling towards 
the distal extremity ; older cells slightly rugose, or granular ; oral 
extremity raised at times with circular or semi-circular orifices ; two 
cells average from three-quarters to one line in length. 

Locality, 8fc. — Lower Mid. Lias, Fenny Compton, on Gryi}liCBa incurva. 
Cabinet of Mr. Walford. {Aledo dichotoma. Beesley.) 

Stomatopora dilatans montUvaltaformis (new variety). Zoarium, 
adherent, slightly ramified, consisting of short stem of nniserial zocecia, 
Avhich gradually widens so as to form dilated branches, but of very 
irregular form. Zooeoia, punctate, depressed ; orifice circular, slightly 
raised ; cells passing from uni- to tri-serial, and each cell measuring 
about half a line in length. 

Locality. — Lower Mid. Lias, Cherrington. 

Habitat. — On Montliualtia Victoria. — Cab. Mr. Walford. 

The peculiar habit and cell-character of this type is so distinct from 
the former, that, after many grave thoughts, I have decided to give it the 
above name. On the same coral are specimens of Diastopora. 

Stomatopora Waltoni, J. Haime. 
(pi. vi. fig. 3, Haime). 

This species is found adherent to specimens of Biastopora from the 
Bradford clay, and also from the Cornbrash of Stanton. It assumes 
many peculiar habits, but the cell-arrangement generally is a rather con- 
«tant feature. Sometimes it approaches the character of 8. diclwtomoides, 
D'Orb., at other times that of the recent 8. gramdata, M.-Ed. To the 
latter species Hincks' assigns a remote ancestry, and it is a difficult 
matter to say nay to his synonyms, and range in time, as all the nniserial 
Stomatoporce may be closely related. My own specimens from the Green- 
sand are too fragmentary to allow of a very close comparison. 

Localities, ^'c. — Approaching 8. dlchotomoides, D'Orbigny's type, Great 
Oolite, Kidlington. Adherent to Terebratida maxillata. Cabinet of Miss 
Gatty. 8. Waltoni type, Bradford Clay, and Cornbrash, Bradford and 
Stanton, Wilts. My own cabinet. 

In our modern classification (Hincks) we have a sub-genus, Proioscina, 
which links together the genei'a 8tomatopora and Tnhulipora. Haime's 
second genus is also called Prohoscina, but there seems to me to be a great 
diflference between the recent and fossil species. The type of the recent 
sub-genus 8tomatopora incrassata, Smitt, is a very peculiar species as 
regards the cells, and I know of no Jurassic type that can compare with 
it. The type of Haime's genus is the Cellepora echinata, Munster or 
Goldfuss. This latter species is a Tertiary type from Astrupp, and I fail 
to recognise any species in the British area that can compare with this 
either. Seeing that D'Orbigny applies the term Prohoscina and Idmonea 
indifferently for certain species ; that Busk places the sub-genus with his 
Alecto ; and that Hincks practically disallows the division, it seems to 
me only a matter of very questionable convenience to retain it. There 
are, however, certain as yet undescribed types in both the Inferior and 

' Brit. Marine Polyzoa, vol, i. p. 426. 



252 EEPORT— 1882. 

Great Oolite tbat are really passage forms — evolutionary stages — which 
can neither be claimed as Stomatopora nor Tubulipora, and much less as 
Diastopora. With the exception of one species, I believe— the P. David- 
soni, Haime, from the Great Oolite of Hampton Cliffs — all the other 
types are from the foreign Jurassic areas. I cannot in my material re- 
cognise P. Davidsoni, but I have drawings of species lent to me from 
the cabinets of Mr. Longe (Inferior Oolite), Mr. Walford, and Miss 
Gatty (Great Oolite) — that one would naturally place in this genus. The 
one type, especially from Mr. Longe's cabinet from the Inferior Oolite of 
Cleave, near Cheltenham, in some of its chai'acters approaches the 
P. Jacquuti, Haime, from the Inferior Oolite, Montveaux. There are 
other characters which would separate them widely. The same may be 
said of a very beautiful type in the cabinet of Mr. Walford, procured from 
the base of the Great Oolite. The species are adherent, as Haime de- 
scribes, and meshes are formed by the inosculation of the branches, but 
the cell characters and arrangements appear now as Stomatopora, and 
anon as Idmonea ; and I can well understand the confusion that was 
painful for Haime to note, when he says, ' The CelUpora, ccJiinata, Gold- 
fuss, appears to me to be the first fossil known to be referred to the 
division (Proboscina). Tlie others, principally those of the Crag, have 
been described as Diastopora or else as Tuhulipora, either by Michelin or 
by Lonsdale. D'Orbigny has at first shown them under the name of 
Idmonea, and afterwards that of Prohoscina, originally applied by Audouin 
in 1826, He criticises Milne-Edwards for having called Criserpia a 
species, which he, D'Orbigny, confounds with Prohoscina.'^ 

The true Idmonea as an erect Jurassic type I do not know, though 
we meet with specimens partly adherent and partly erect in the cre- 
taceous series. In the ' Catalogue of British Fossils,' Professor MottIs gives 
Idmonea triquetra, Lamx., as found in the Great Oolite, Bradford, and 
Haime describes the same species in his text, aud figures it (pi. vii. fig. 
1, a.h). I notice the same Idmonea arrangement of cells as in many 
undescribed species of Stomatopora (?) at present lying dormant in the 
cabinets of collectors and students, and it is very ditficult to conceive 
where these shall be placed in our modern classification, if we destroy the 
genus Proboscina as a passage group, or get rid of Idmonea other than as 
an erect type. Busk says ' Zoarium usually erect,' speaking of the 
fam. Idmoneid^. Hincks, however, gives more latitude in his diagnosis 
of the genus Idmonea, for he says ' Zoarium erect and ramose, or (rarely) 
adnate.' Seeing that this latitude exists of partly adnate and partly 
erect types in the work of one of our greatest systematists, I strongly 
advise our local students to seek to throw light upon the origin of this 
unique type of Cyclostomatous Polyzoa. The Idmonea triquetra is at 
present unknown to me, and I can only point out the lines along which 
research can be made. 

There is yet another type given by Haime to which I must direct 
particular attention. This is the Terehellaria of Lamouroux. I have 
been unable to refer to the original works for a description of the genus, 
but this has been done for me by George Busk, Esq., F.R.S., to 
whom 1 am indebted for the following very valuable particulars of the 
genus and species. 

' Jules Haime, Jurassic Bryozoa, Genus Proboscina. 



I 



ON FOSSIL POLYZOA. 25 i 



Terebellaria, Lamouroux. 

' A fossil, dendroid polypary, composed of cylindrical scattered 
branches, spirally twisted from left to right, or from right to left in- 
differently; pores prominent almost tubular, numerous, disposed quin- 
cnncially, and more or less inclined according to their position with the 
spires.' 

Lamouroux says the genus should be placed after the Millepores and 
before the Spiroporce, remarking ' that the Spiroporre have the cells or the 
pores projecting as in Terebellaria, but that this character is observable . 
only in well-preserved specimens. When the prominent part of the spire 
has been worn by attrition, it looks like a narrow riband wound round 
the branch.' 

Two species are described by the author, T. ramosissima and T. 
antilopa, from the Terrain a polypes at Caen. 

Hagenow's description is the same, but he includes in the genua 
Ceriopora spiralis, Goldfuss. 

D'Orbigny adopts the genus of Lamouroux with the following 
character: — 

' Colony entirely fixed by the base, whence spring thick cylindrical 
dichotomous branches, often very numerous, and forming a dendroid 
growth. Each branch presents three parallel spiral zones, which begin 
at th*e end of the branch in a projection formed exclusively of the germs 
of cells.' He enumerates four species — T. gracilis, D'Orb.; T. antilopa, 
Lamx.; T. ramosissima, Lamx.; and T. tenuis, D'Orb. 

The peculiar habits of the species are remarkable. Haime says, 
' The (colonial) development proceeds by layers of testules (cells), which 
superpose themselves by following a spiral line, and they increase after- 
wards downwards, covering themselves more and more.' In the figs. 
of pi. vi. typical features of the species ai-e given, but the very peculiar 
spiral habit of T. ramosissima shown in transverse section, and the 
checked winding habit of T. antilopa, shown in longitudinal section, 
which will be further alluded to, may be seen in the figures of Lamou- 
roux, of which Mr. Busk has furnished me with tracings. 

The fossils which ordinarily pass for species of Terehellaria in the 
cabinets of collectors are a very curious group that may be more closely 
studied. My own studies are made fi'om specimens from the Cornbrash, 
and Bradford Clay of Bradford and Stanton, Wilts, and it is from this 
locality that the School of Mines specimens were obtained. 

To properly master the details of colonial growth, it will be necessary 
to isolate a single colony. The one furnished by Haime as a specimen of 
a young colony on stone shows a tapering pi'oximal point, gradually 
widening by the addition of cells, till a certain fanlike shape is arrived 
at. A similar growth to this is found in young colonies of Diastopora. 
If superficially examined it will be seen that the cells are peculiarly 
arranged, beautifully punctured, with an orifice sometimes circular, at 
other times semi-circular, and sometimes the cell characters of portions 
of the colony bear a resemblance to Bidiastopora ramosissima of D'Or- 
bigny. A complete and critical examination of the type will show that 
any fragment of stone or shell is sufficient to form the nucleus of a colony. 
It begins with a primary cell and then enlarges in a spiral direction, but 
to what extent the riband-like growth would be carried without a check 



254 REPOET— 1882. 

I am unable to say. In another direction a similar colony will be de- 
veloped, the distal cells of which will ultimately meet and coalesce, both 
colonies striking out in fresh directions till met by another check, the 
growth not always being in an upward direction. The dendroid 
character of species is perfectly accidental. 

With regard to the proper location of the type authorities differ. Pro- 
fessor Busk places it in the family Idmonidce. In referring to Heretopora 
(' Crag Polyzoa,' p. 121) he says, ' Milne-Edwai-ds, in his second edition of 
Lamarck, 1836, placed amongst the heterogeneous Polypiers foramines, 
Pustulopora, Ohrysaora, Theonoa, and Terebellaria.' Jules Haime places 
the genus immediately after Idmonea and before Berenicea, and it is near 
to, or, if need be, as a sub-genus of, Diastopora that I would be inclined 
to leave it. In accordance with this I think it will be best to redescribe 
the species. 

Terebellaeia ramosissima, Lamx. 
1816. Millepora, William Smith. — (Clay over Upper Oolite.) 
Terebellaria. — (Of authors generally.) 

Zoarium, a thin riband-like layer of cells encrusting foreign bodies, or 
coiling itself upon its own previously formed zoaria, ultimately assuming 
a spiral, ramose, dendroid or massive form. Zooecia slightly elongated, 
sometimes disposed in spiral lines, rather more produced at the distal 
than at the proximal part of the cell ; peristome thick, orifice circular, 
occasionally semi-circular, front of cell finely punctured. Ocecia, an 
enlarged globose cell, having beneath the orifice a semi-civcular cluster 
of punctures definitely arranged. 

Localities. — My own cabinet, Cornbrash, Stanton, Wilts ; Forest Marble 
Box; Bradford Clay, Bradford, Wilts ; Mr. Walford's cabinet, rich from 
several localities ; School of Mines. 

Genus Diastopora, Lamx. 
Sy. with Berenicea (pars), Lamx. 

I am willing to accept this genus, in its wider sense, as defined by 
Hincks ; yet I hardly think that it will be possible to include the whole 
of the foliaceous forms of the Jurassic period in one group. In this 
report I shall adhere to the arrangement of Busk, as I have done in my 
two papers on the Diastoporidas, keeping the foliaceous types for distinct 
study. At the same time I am willing to admit that in getting rid of one 
difficulty in our grouping we open the door to admit others. Haime 
admits both the encrusting and foliaceous types ; accepting the genus 
Berenicea for the encrusting, and Diastopora for simple-foliaceous and 
retiform species. Professor Braun, in his Jurassic studies, separates the 
species Diastopora foliacea from the group and establishes another, which 
he calls Elea, claiming for his type certain peculiarities which have been 
entirely overlooked by authors. It is very certain that the more closely 
we examine Jurassic Polyzoa and compare them with modern species of 
the genus Diastopora, the more divergent the types appear; and although 
we would rather accept a simple than an elaborate classification, still 
there are limits beyond which it is not wise to go. 

The genus Berenicea was established by Lamouroux, and included in 
it, beside the fossil species, B. diluviana from the environs of Caen — two 



ON FOSSIL POLTZOA. 255 

living species. These, Haime says, he could not find in the Caen Museum ; 
consequently they are not determinable by their figures alone. The 
Zoarium is adherent-encrusting, and formed of superimposed layers ; the 
development commences in a simple manner, and is radiating or fanlike. 

The Diasiopora of Haime has a Zoarium with a large base, elevated, 
foliaceous or frondescent, sometimes reticulated, formed of ascendant 
leaves folding back upon themselves, and closely cemented in such a 
manner as to present often two shelving planes of cells. Then the planes 
are united by a laminated calcareous epidermis.^ 

Diastopora foliacea, of Lamx., covers two distinct types. One has been 
well worked out by Professor Braun,- and upon this he seeks to estab- 
lish the family Operculata, order Eleina, naming his type Elea foliacea. 
The other species Milne-Edwards named D. Lamouroiixi ; and it forms 
with D. Waltoni, Haime, the Diastopora simples of Edwards. The next 
section of Haime and Edwards includes the whole of the Biserial species. 
For these Blainville, in 1830, or rather for a section of the now recog- 
nised species, founded the genus Mesenteripora, still retained by Busk in 
the Crag Polyzoa and Cyclostomata,^ and in his list of Polyzoa collected 
by Captain H. "W". Fielden (' Jour, of Linnjean Soc' 1880), and also by 
Mr. Waters. Blainville's genus is again rechristened by D'Orbigny, and 
becomes Bidiastopora ; establishing for the D. lamellosa a special genus 
which, he calls Latero-multelea. 

Genus Diastopora, Lamouroux. 
Sy. with Berenicea (pars), Lamx., ' Expos. Meth.' 1821. 

Hainae figures and describes five species of Berenicea and fourteen 
Diastopora as present in the Jurassic series. I shall only notice those 
species which are found in the British area. 

I have already, in a previous paper,* drawn attention to four types 
of Diastopora {Berenicea, Haime), not previously noticed by authors. 
They are 

1. D. stomatoporides, Vine. 3. D. oolitica, Vine. 

2. D. ventricosa ,, 4. D. cricopora „ 

These species range from the Lias to the Great Oolite ;. and for par- 
ticulars, details, and description I refer the reader to the paper itself. 

Before leaving this purely descriptive part, I wish to speak of a 
paper ' On the Relation of the Bscharoid Forms of Oolitic Polyzoa,' by 
Francis D. Longe, F.G.S.^ In this paper Mr. Longe very ably discusses 
certain peculiarities of cell- character, showing their apparent relationship 
to the Escharoid forms of the Cheilostomata ; especially drawing the 
attention of the palaeontologist to the opercula of the Oolite species. 

There are many discrepancies in our modern classification of the 
Polyzoa ; and Mr. Longe has, by the publication of this paper, increased 
our knowledge of their number. Seeing that the whole of the remarks 
are founded upon facts gleaned from a comparative study of Oolitic 
specimens, we cannot do more than accept the hints and illustrations, 
and work them into our future histories rather than ignore them altogether. 

' Italics mine. 

* Die Bryozoa des Mittleren Jwa, 1879. ' BHt. Mus. Cat. pt. iii. 

* Further notes on the family JDiastoporida, Bnsk, Quart. Jour. Geo. Soc, August 
1881. 

* Geological Magazine, January 1881. 



256 KEPOBT— 1882. 

I cannot, however, see my way clearly at present to accept without a 
demur his conclusions. As a ' suggestive sketch of the genealogical 
arrangement of certain famiUes,' Mr. Longe offers the following : — 

' Race DiASTOPOEiD^. 

' Families or genera represented in the Oolites : — 
' Creeping. — Biastopora. 

' Foliaceous. — Bidiastopora, Mesenteripora, Elea, EscJiara. 
' Dendroid. — Cricopora, Melicertttes, Entaloplwra.'' 

The remaining portion refers to species found in the Chalk and sub- 
sequent periods. 

DlASTOPORA DILUVIANA. 

Berenicea diluviana, Lamx. B. diluviana, Haime. 
Berenicea dihcv., or Biastoiwra diluv. of authors generally. 
Bepto-multisparsa diluv., D'Orb. 

This species is present in the Inferior and also in the Great Oolite, 
and the name should be restricted to the thin, papyraceous specimens 
which encrust, with varying habits, stones and shells. The Zoarium, in 
its youngest stage, begins with a primary cell, which gi-adually increases 
in size till a small fanlike outline is reached, some of the cells turning to 
the right, others to the left of the primary one. After this the Zoarium 
is of varying habit, and all the cells are deeply immersed, and specimens 
appear like a continuous coeniceum, very much punctured, the peristomes 
only rising but very slightly above the surface. The cells are distinct, 
and in very sheltered parts of the Zoarium the distal portion of the tube 
is much produced. 

Localities. — Inferior Oolite abundant at Cleave, near Cheltenham. 
Cabinets of Mr. Longe and my own. 

DlASTOPORA MICROSTOMA, Michelin. 

Berenicea microstoma, Haime, pi. vii. fig. 3, a.d. 

„ undtdata, D'Orb. (Pal.), Prance. 
Bepto-multisparsa microstoma, D'Orb. 

I feel certain that this species, though much smaller in the cells, has 
at times been identified with the one above. It is only on very rare 
occasions that the two could be possibly confounded. The most distin- 
guishing features of this species are the proliferous habits and the small- 
ness of the cells. Some of the cells, too, appear like those of Biastopora 
Lucensis. 

Localities. — Abundant in the Great Oolite, generally encrusting spe- 
cies of Terehrattda. The cabinet of Mr. Walford very rich. Haime 
gives Hampton Cliffs as one of the localities from which he obtained 
his specimens. 

I wish to draw particular attention to this species on account of its 
peculiar proliferous habits. Many of the fresh colonies originate from 
some of the marginal cells of the older colony. They begin with a 
primary cell as ordinary Biastopora, and the zoarium very soon assumes 
a fanlike, then a circular, habit. Newer colonies also cover the older 
ones, and the innumerable growths give a very thick appearance to the 
blended Zoaria. 



ON FOSSIL POLYZOA. 257 

Another British species is given by Haime : — 

Diastopora Lucensis (Berenicea, pi. vii. fig. 4, a.c). 

:= „ diluviana, Milne-Ed. 

=:Mt(Uisparsa Luceana, D'Orb. 

Localities. — Hampton Cliffs, Walton ; Bradford Clay and Cornbrash, 
Laycock. 

II. BiSERiAL Diastopora, Milne-Ed. 

Mesenteripora, Blainville ; Bidiastopora, D'Orb. ; Ditaxia, Hagenow. 

It is well that the encrusting and biserial Diastopora should be sepa- 
rated, but not widely so. In the choice of the above names I havo 
selected the simplest — Blastopores biserialaires of Milne-Edwards — because 
it has the precedence of the Bidiastopora of D'Orb. Busk — in the ' Crag 
Polyzoa'and in the ' Brit. Mus. Cat.' pt. iii. — has chosen Blainville's 
name for this division of the group. 

My chief objection to Blainville's term for the biserial species may be 
found in the diagnosis as given by Busk : ' Cells in two layers, parted by 
a calcareous septum.' In all the specimens figured in ' Crag Polyzoa ' ' 
of Mesenteripora meandrina the transverse sections of the folia,ceous zoa- 
rium are shown to have this septum very distinct. In many of Haime's 
figures where cross sections are given, the septa are also shown to be 
present. It seems to me, judging from the foliaceous specimens in my 
own cabinet, that this ' calcareous septum ' is only an apparent, and not 
a real character. If sections are made in a line with the cells, the only 
axis visible is that made by sections of the cell-walls. In a cross section 
of the foliations there is an apparent septal division, but the more closely 
this is examined the less real will it be. The septal divisions of D. scohi- 
nula, D. Terquemi, and D. cervicornis, as given by Haime, show one, two, 
and three sections of cells on either side of the septal line ; and specimens 
of Inferior Oolite species found in the neighbourhood of Cheltenham are 
in many respects of a similar character. As I have been able to examine 
only a very limited number of species, I should be glad to have more 
detailed information if students of our Oolitic Polyzoa will address their 
attention to this point. Meanwhile, by selecting the divisional name of 
Milne-Edwards I shall not commit myself to any generic name dependent 
upon a questionable structural character. 

Jules Haime, after very careful working, saw reason for establishing 
fourteen species of biserial Diastopora, the whole of which are not found 
in the same horizon in either this or other countries. Leaving D.foliacea 
and X*. Lamourouxii we have nine foliaceous species as common to the 
Jui'assic Fauna generally. Some of these range from the Inferior to the 
Great Oolite and the Cornbrash ; whilst others, so far as observation at 
present favours us, are confined to one horizon only. Two species given 
by Haime — D. Michelini, Blainville, and D. Eudesana — ^range from the 
Inferior Oolite through the Great Oolite ; and, according to Busk, is 
possibly identical with the Mesenteripora meandrina found amongst the 
Crag Polyzoa, and in recent Arctic fauna. I cannot assert positively that 
the species are identical, or that we ought to accept all the synonyms of 
Busk : still there is great probability in their favour ; but the fi-ag- 
ments of Busk will bear no comparison in point of size with the fin& 

' riatos xvii. fig. 2 ; xviii. fig. 4 ; and xx. fig. 2, pp. 100, 1 10. 
1882. S 



258 EEPORT— 1882. 

specimens from the Jurassic formations in the cabinet of Mr. Longe. The 
cells are very similar in character, both in their worn and in their perfect 
state. 

Two other species — D. WrigUi (D. foUacea of Mor. Catalogue), and 
D. Mettensis — are both Inferior Oolite types ; the first ranging from the 
Inferior to the Great Oolite in this country. The B. Wrighti also may be 

the Bidlastopora and Mesenteripora meandrina of D'Orb. Mr. Lono-e 

who has made careful observations on the species — has selected for illus- 
tration the most typical features of cell arrangement and character of the 
two types ; and Dr. Woodward, in the beautiful plate which illustrates 
Mr. Longe's paper on the ' Escharoid Forms of Oolitic Polyzoa,' ' has 
doneample justice to the selection. A comparison of the two types of 
cell in figs. 2 and 3 of that plate will give special details of structure 
sufficient to justify Haime in their separation as species. It must not be 
supposed, however, that the character and arrangement of the cells are 
always so clearly defined as in the plate. The cells vaiy very much, and 
it may be possible to find similarly shaped cells to these in other species 
of the Oolitic Diastopora. 

Haime gives us another type of Diastopora cell as found in a species 
in the Inferior Oolite of this country, and also in the Great Oolite of Ran- 
ville and Caen. In the plate already referred to (fig. 4) Mr. Longe has- 
selected for typical illustration a specimen from Caen. Haime calls it D. 
lamellosa, Mich., and gives as its synonyms Elea, Multelea and Latere- 
mtdtelea Banvilliana, D'Orb. and Eschara Banvilliana - of Michelin. 
Relying upon the evidence of Mr. Longe, I cannot help but select his 
opinion on this type. Speaking of the illustration, pi. 11, fig. 4, ' Geo. 
Mag.' Jan. 1881, he says, ' I have little doubt but that this form is the 
JEschara Ranvilliana of Michelin. In his figure the areolation is slightly 
more angular than in the part shown in (my) figure. Jules Haime has 
classed a somewhat similar form as B. lamellosa. D'Orbigny's EscJiara 
or Elea triangularis is evidently a very similar form.' ^ The type of cell 
I am not familiar with as a British species. 

In the Biastopora Waltoni, Haime, and in the B. Bavidsoni, Haime, one 
from the Inferior Oolite near Cheltenham and the other from the Great 
Oolite Hampton Cliffs, we have types of cells far from being unique. The 
same may be said of the cells of B. Eudesana, Haime, also a Great Oolite 
type. _ The same peculiarity of cell structure and arrangement may be 
found in some of the adherent or encrusting Biastopora, as in the more 
richly developed foHaceous species, but whether the foliaceous species as 
a whole are developed from the encrusting forms I am unable to say. In 
all probability they may have been so, and this would justify the Rev. 
T. Hincks in breaking up the artificial divisions and classifying the 
foliaceous and the encrusting species under one generic term. 

In the B. cervicornis,^ Michelin, of which species the Bidlastopora and 
Elea cervicornis of D'Orb. are synonyms, we have very insufficient data to 
deal with. It is said to occur both in the Great Oolite of Ranville, and in 
the Bradford Clay of Pound Hill. I am not acquainted with the species 
as a British type. 



' Geological Magazine, January 1881. 

* A beautiful illustration of this type is o-iven in Nicholson's Palceontclogy, vol. i, 
420, fig. 270. ■'^ r. vy, r 

' Geo. Mag., January 1881, pp. 33, 34 ; descriptive text of fig. 4. 

* For illustration, see Nicholson's Palceontology, vol. i. p. 431, fig. 272. 



ON FOSSIL POLTZOA. 259 

Many valuable foliaceous types are in the cabinet of Mr. Longe, and 
a few are in the Musenm of the School of Mines, and in the Cambridge 
Museum. Some few of Mr. Louge's specimens I have been allowed to ex- 
amine, and I have five species in my own cabinet. These I have examined 
both in the mass and in sections before drawing up the details furnished 
in this report. It is high time that a monograph of British Jurassic 
Polyzoa should be undertaken by some competent authority before the 
masses of material at present in the hands of private collectors are again 
scattered, as previous collections have been, without note or comment. 
Besides my own specimens I have examined many in the cabinets of 
Mr. Walford and his friends. If these could be compared with the type 
specimens named by Haime, a more valuable addition to Paleontology 
could be made than we at present possess. In the work of Professor 
Phillips, ' Geology of the Valley of the Thames, 1871,' it is painful to 
read his remarks on the Polyzoa of the various formations laid bare in 
the valley. Speaking of Liassic Polyzoa, he says, ' specimens have been 
observed at Fenny Compton.' Of the Infei'ior Oolite, ' Insufficiently 
examined in the series.' In the Great Oolite only four species are given 
— Alecto dichotoma ; Cricopora straminea, Phill. ; Diastopora diluviana, and 
Terehellaria ramosissima. 

Of the Oxford Oolitic Period, Phillips says, ' The rarity of Polyzoa in 
the Oxford Oolites and Clays is somewhat remarkable, and appears to 
be in some way related to the even more remarkable rarity of Brachio- 
poda, on whose shells in the Bath Oolites so many of these beautiful 
objects ai'o found.' ' In the Cretaceous system (p. 434), a list of nearly 
fifty species of Polyzoa is given by the author as occurring in the valley 
of the Thames. 

I have before me a very valuable series of notes compiled by Mr. 
Walford, on species of Polyzoa found in his own neighbourhood. If other 
students would undertake to furnish notes of a similar character of other 
localities, a compilation of the range of types would be easily made. As it 
is we have insufficient data and ill-digested identifications to deal with. 

1821. Genus Spiropora, Lamouroux. 

1822. Intricaria, Defranc. 1830. Cricopora, Blainville. 1840. MEir— 
CERITITES, Roeraer. 1850. Entalophora, D'Orbigny. 1853. Cricopora, 
Spiropora, Tubigera,Mei,iceritites, Laterotubigera, Entalophora, D'Orb. 
Palaeontology. 

I have already vindicated by use and preference the retention of this 
genus for species of Palaeozoic Polyzoa.^ I still retain the name for 
species of the genus very common in the Mesozoic rocks. I have also 
given the synonyms with their dates of genera intended to supersede 
Lamouroux's original term. It may be as well to define and limit the 
genus as applicable for the reception ofPalaeozoic, Mesozoic, and Cainozoic 
species. I am not aware that any recent species of Polyzoa can be in- - 
eluded in the group. 

' Zoarium dendroid with dichotomous branches. Zocecia elongated,, 
closely connected laterally, but less distinct at the base, perforated with, 
very small and round pores . . . Peristomes circular, more or less pro- 

' Pp. 123, 239, 302. 

^ 'Notes on the Wenlock Polyzoa,' Quart. Jour, of Geo, Soc. February 1882, 
pp. 43-68. 

S2 



260 REPORT — 1882. 

iecting, forming at the sui'face of the branches circles which ordinarily are 
not complete, and each of them constitutes one of the turns of a spire 
many times interrupted. These rings appear more regular when they are 
distant from each other ; when they are crowded they are often difficult 
to recoEfnise.' ^ 



■'o 



Spiropora Liassica, Tate. ' Geological Magazine,' 1875. 

This species has been very well described by Professor Tate in the 
above magazine. I have seen the type specimen, which is in the Museum 
of Practical Geology. But my own specimens, given to me by Mr. Walford, 
are different from the types of Tate. The zoarium is more flattened 
and the cells are longer and more irregular. The type of cell approaches 
nearer to that of Diastopora stomatopor ides, Yine ('Jour, of Geol. Soc' 
August, 1881), than that of ordinary Spiropora. 

Localities. — Leptena beds of Moy., King's Sutton. Amm. spinatus 
beds (Beesley). 

Haime admits eight accredited species, but only three are present in 
our British area. />'. straminea, Phill. ; S. ccespifosa ; and <S. Bajocevsis. 

Spiropora straminea. 
Millepora straminea, Phill., ' Geo. of York,' pi. ix. fig. 1. 

This species as figured and described by Phillips in the above work is 
that ordinarily mot with in fragments. The zoarium is dendroid, variously 
branched, branches anastomosing so as to form an intricate amalgamation 
of branches, all of which are of the ordinary size. Zooicia tubular, arranged 
in series spirally, peristomes circular, slightly raised. 

This species is widely distributed, ranging from the Lower Oolite to 
the Greensand , and on account of the very peculiar habit of the amalgama- 
tion of the branches it received from Defranc the name of Intricaria. 
Blainville gave two species the name of Cricopora, because the cells are 
arranged in rings. This is the character o? Ceriopora verticillata, Goldfuss, 
which is given as a synonym of the species by Professor Braun. It has 
also received the name of Latero-tnbigera from D'Orb., but Professor 
Braun prefers to adopt the generic name of Entalopliora for the two 
species described by him as found in the middle Jura of the neighbour- 
hood of Metz. 

Localities. — Inf. Oolite, Peagrit, Cheltenham. Great Oolite, Scar- 
borough, Phillips, ' rare in this stratum.' 

Spiropora c^spitosa, Lamouroux. 
Cricopora, Blainville. Entalophora, Professor Braun. 

This species is distinguished by much thinner and more slender 
branches. The spiral arrangement of the cells is somewhat similar, but 
the tufted character is a distinguishing feature. 

Localities. — Inferior Oolite, Base of Oolitic Marl., Nutgrove station. 
Morris cites Hampton and Bradford. 

' Haime's Jurassic Bryozoa. One passage has been left out respecting ' trans- 
verse ulaphragms,' which I have not been able to verify. 



O.N FOSSIL POLYZOA. 261 



Entalophora cellaeoides, Lamx. (Pustulopora, Nicholson.) 
Plate ix. fig. 8, a. b. Haime's 'Jurassic Bryozoa.' 

This species is described by Haime as above. It is very different from 
any of the Spiropora described by him, and he says that an ' incomplete 
example was furnished to him by Walton, procured from Hampton Cliff.' 
I am not acquainted with the type. 

Judging from the figures given by Nicholson (p. 430, ' Paleontology,' 
vol. i.), this is a true Entalophora, well deserving of separate recognition. 
Under any circumstances it could not be confounded with Spirupora. 

Fam. III. HoRNEEiD^. Hincks. 

This family contains only one genus, Hornera. There is no repre- 
sentative of the family, in Brit. Jurassic Rocks at least, and I am not aware 
of any recorded species of the genus in Foreign Oolites. As the Rev. Thomas 
Hincks says that ' the genus Hornera is connected with Tubuliporidj:, 
through Idmonea,' to which it bears in many points a very close resem- 
blance,' in all probability early types of the genus, as defined by him, 
may yet be found in either the Jurassic or Cretaceous rocks. The Sipho- 
dictyum, of Lonsdale, is given as one of the synonyms of Hornera.^ 

Fam. IV. LiCHENOPOBiD^. 

This is the last family given by Hincks in which Jurassic Polyzoa can 
be placed. The genus Lichenopora of Defranc has also a number of 
synonyms, but as species of the genus are rare in the Oolites, we find 
only one recorded. Haime says the genus has not been represented until 
now, other than by Tertiary or Cretaceous fossils. In Lichenopora 
PhiUipsii, dsrived from the Great Oolite of Hampton Cliff, the zoarium is 
disciform, very slightly elevated, and adherent only by the middle of its 
inferior face. The upper surface resembles a fungus, with unequally 
developed rays formed of a series of long zooecia, ordinarily doubled. The 
peristomes are polygonal, regular, and closely connected. 

Species of the genus, in all probability the same as above described, are 
found in the Inferior Oolite, but too indistinct for description. 

Another peculiar genius of Lamouroux's is accepted by Haime — 
Apsendesia — in which to place two species of Jurassic Polyzoa. In his 
synoptical arrangement of the Polyzoa Cyclostomata, Busk places this 
genus in the family Theonoidje : ' Zoarium massive sub-globose, or 
irregular; zooecia contiguous crowded.' Haime describes in the foreign 
Oolites two species — A. cristata, Lamx., and A. clypeata, Lamx. I 
have no means of studying these, but Professor Braun, in his paper, places 
as the synonyms of Apsendesia — Defrancia and PeJagia. In his descrip- 
tion of the i'ascictdaria of the Crag — one of the genera of THEONOiPiE — 
Mr. Busk places Apsendesia (pars), Blainville ; questioning its affinity 
with Lamouroux's type, as one of the synonyms of the Fascicidaria of 
Milne-Edwards. Facially the specimens of Lichenopora found in our own 
Oolites may bear some resemblance to the figures of Haime, but as there was 
some confusion in the mind of Blainville when drawing up the characters 
of the genus Apsendesia, the student will do well to refer to the ' Crag 

' Brit. Maiine Polyzoa, vol. i. p. 467. * Hid. 



262 REPORT— 1882. 

Polyzoa ' (p. 139) for a description of Fascicularia, as given by Busk, and 
its relationship to Apsendesia cristata, Lamx. 

Since the above was written, Mr. Walford has kindly furnished me 
with the following note on this genus, and of species in his own cabinet. 

^Apsendesia cristata, Lamx. The Barford, Oxon, specimen agrees 
fairly with Haime's description, excepting that it seems to be attached 
not by a central base, but to be adherent by its whole breadth. It seems 
to be more regular than most of the forms figured. 

' Locality. — On the inside of shells ; Inferior Oolite. 

' Apsendesia, sp. The fasciculse are rather coarser, slightly sinuous, 
and less numerous than in the species mentioned above. 

' Locality. — On stones ; Inferior Oolite ; Stowe-on- the- Wold.' ' 

There are still several genera described by Haime which, on account 
of their rarity, have not been so closely studied. One of these — Fascicu- 
lipora, a genus of the family Frondiporida, Busk — has assigned to it a 
species F. Waltoni, Haime. It is found in the Great Oolite at Hampton 
Cliff. This genus is still represented by at least two species in the 
Australian and South Patagonian Seas. In the Crag Polyzoa three 
species are described under the generic term of Fungella, Hagenow, in the 
family Ceeioporida, Busk. 

Theonoa, Lamx., is represented by three species, one of which — -T. Boiver- 
hanhii, Haime — is found in the Inferior Oolite of Cheltenham, both by 
Bowerbank and by Walton. 

The genus Gonstellaria was founded by Dana, and is probably synony- 
mous with Stellipora, Hall, and Radiopora, D'Orb. I am not acquainted 
with the type in our English Oolites. The only example known — 
G. Terquemi, Haime — was discovered in the Infra Oolite (Metz) by 
M. O. Terqueim. The zoarium is encrusting, with short zuascia, erect, 
prismatic, slightly unequal in width, of two kinds : the one more erect, 
disposed in a double or triple or radiating series ; the other very short, 
occupying the interval of the rays. Two recent species of Radiopora, 
D'Orb., are given by Busk, and one — B. cristata — in some respects answers 
to the description of the Oolitic species as given by Haime. Radiopora 
is placed in the Ctclostomata, pp. 34-35, with the Discoporellida. In 
placing the G. Terquemi in the genus Gonstellaria, Haime says, ' I do not 
find any essential difference between the Palaeozoic Fossils and those of 
the secondary period, which D'Orbigny calls Radiopora, and they are 
bound, without doubt, to form one and the same genus.' - 

The genus Ghilipora is one of the Heteroporida types, and it, too, is 
founded upon a single unique example. There are, however, characters 
about the peristome and also the interjacent openings of G. guernoni, 
Haime, altogether at variance with the known types of British Heteropora. 
The specimen was found at Ranville, in the Great Oolite. 

1835. Neuropora, Bronn. 

Chrysaora, Lamx. Filicaria, D'Orb. 

Species belonging to this genus are present in our British Oolites, in 
the Bradford Clay, and Cornbrash, but I have not been able to secure 
specimens to operate upon so as to study the internal characters. 
Dumortier describes several species from the Middle Lias, Haime de- 
scribes three from the Great Oolite of Ranville and Hampton Cliffs, and 

' Letter, June ] , 1882. - Jurassic Bryozoa, p. 206. 



ON FOSSIL POLYZOA. 263 

Professor Braun says that it extends from the Lower Lias onward into 
the White Jnra and also into the Great Oolite of Ranville. It is also 
found about Metz. Through the kindness of Professor Roemer of Breslau 
I have had supplied to me the species of Ceripora, Goldfuss, which are 
referable to this genus, but the types diflfer in many particulars from our 
own species. 

One peculiar type is separated from the genus Neuropora by Haime, 
and is made the Oolitic type of the genus Acanthopora, D'Orb. It is 
the Ghrysaora spinosa of Michelin. A specimen of the genus Semycitis — 
another Ghrysaora type — was found by Walton at Bath. The British 
species of Neuropora and allies are — 

Neuropora spmosa, Lamx. := Ghrysaora spinosa. 

„ dumicornis „ = „ dumicornis. 

and Geriopora angulosa, Quen. 

,, Befrancii, Haime. 

1834. Heteeopoea, Blainville. 

We have now left one group of Oolitic Fossils which within the last 
few years have been more closely studied than any of the others, because 
of their supposed relationship with the Palaeozoic Monticulipora. 

In his ' Petrifactions of Germany,' Goldfuss placed in the genus Oerio- 
jpora three species, which he describes and figures ' as containing large and 
small openings on the surface of the branches. These were Geriopora 
anomalopora, C. cryptopora, and G. dichotoma, all of which were from the 
Mastricht beds of Astrupp or Nantes. In 1834 M. de Blainville separated 
these from the Geriopora of Goldfuss, and established another one for their 
reception which he called Heteropora, assigning as essential structures the 
two sorts of openings, but giving very few details respecting the genus. 
After this Milne-Edvvai-ds added to them Millepora dumitosa and corigera, 
Lamouronx. In his 'Miocene Fossils of North America,' ^ Mr. Lonsdale 
oomplained of the inadequate description of Blainville as not having in 
it sufficient details ' to enable an opinion to be formed of its complete 
characters, or of the nature of the minor openings.' This error was to 
some extent rectified by Lonsdale, and we owe to him the merit of being 
the first author who clearly indicated upon sufficient grounds the real 
zoological position of the genus. Jules Haime, in his ' Jurassic Bryozoa ' 
(pp. 207-8), redescribes the genus, and as his diagnosis has particular 
j?eference to Oolitic types, I reproduce a portion of his description. 

' Zoarium of variable form, but chiefly dendroid. 

' Zooecia apparently united by some lamellar prolongation of the walls, 
whence result some intermediary tubes, the terminal aperture of which 
has been closed by a thin calcai'eous pellicle, but which perhaps were 
themselves intended to become young cells. When externally examined 
two different sets of openings are seen, varying in size, sometimes circular, 
at other times polygonal. . . . There are fundamental differences between 
the peristomes of the true cells and those of the intermediary openings ; 
still, the matter of the young cells is very uncertain, and is not of any 
specific value (?).' 

In accordance with this decision, Haime admitted only two species — 
Heterojiora conifera and H. pustulosa- — where Michelin admits seven, and 
D'Orbigny eight. 

' Petrifactions, pi. x. fig. 1-5, fig. 3, fig. 9, &;c. 
- Quart. Jour. Geo. Soc. vol. i. p. 500 (1845). 



264 



EEPORT — 1882. 



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266 BEPOET— 1882. 

In Ms classical ' Monograph of the Fossil Polyzoa of the Crag' (1859), 
Professor Busk very much simplifies the diagnosis of Haime, because, as 
I think, the types of the ' Crag ' were more suitable for this purpose than 
those of the Cretaceous or Oolitic periods. 

'■ Zoaritmi erect, cylindrical, undivided or branched ; surface even, 
furnished with openings of two kinds : the larger representing the orifices 
of the cells, and the smaller the ostioles of the interstitial canals or tubes.' 
' Crag Polyzoa,' p. 120. 

Since this was written species of recent Heteropora have been dis- 
covered and described by A. W. Waters, E.G. S.,' from the neighbourhood 
of Japan, and by Professor Busk from the neighbourhood of New Zealand,^ 
and a critical study of these species has thrown some little light upon 
particular structures in the Oolitic types. I fail, however, to detect, either 
in the descriptions of the recent, or in my own investigations of the 
ancient type, any evidence, or characters, that would be sufficient to 
establish a link between Monticuli'pora and Heteropora, or, in other words, 
between Tabulate Corals (which have intercellular ; openings like Hetero- 
pora) and Polyzoa. Yet it is very strange that in the Mesozoic epoch we 
should have well-developed types like Heteropora which we are content 
to call Polyzoa, and yet be unable to associate them with Palteozoic species 
having similar external characters. But it is so, and without seeking to 
do violence to structural evidence we must wait for future light by simply 
working and watching. 

Professor H. AUeyne Nicholson, F.L.S., in his two works on the 
' Structure and Affinities of the Tabulate Corals of the Palaeozoic Period,' 
1879, p. 256 ; and in the ' Structure and Aflinities of the Genus Monti- 
culipora,' 1881, p. 62, has gone into the whole question of the apparent 
affinity of Heteropora and Monticulii^ora. As the whole of his remarks 
are founded upon structural evidence I willingly refer the student to the 
elaborate details furnished by the author. Generally I agree with Pro- 
fessor Nicholson, but much yet remains to be done in the correlation of 
the Mesozoic and Pateozoic types. 

To Mr. Walford, F.G.S., of Banbury, and Mr. F. G. Longe, F.G.S., 
my thanks are due for help by suggestions and the loan or gift of speci- 
mens.^ I also thank Mr.' Robert ^Etheridge, F.G.S., and Mr. Newton, 
F.G.S., for allowing me to examine specimens in the School of Mines. 

The preceding list of the ranges of types may help the student of our 
Jurassic Polyzoa, and many of the blanks in the columns may ultimately 
be filled in. 

References to letters in the various columns : — H., Haime ; W., Wal- 
ford ; M., Morris' Catalogue. In the last column the figures refer to the 
figures at the tops of the columns. 

I shall be glad to receive from any student of British or Foreign 
Fossil Polyzoa a list of species which are known to be present in their 
own neighbourhood, for the purpose of compiling a complete list of species, 
or as far as possible complete. 

' ' On the Occurrence of Recent Heteropora; Jour, of Rmj. Microscoi). Sue. 1879 
(June). 

■- 'OnEecent Species of Ileteropora; Jour, of Linn. Sue. 'Zoology,' vol. xiv. (1879). 



267 



Preliminary Report of the Comonittee, consisting of Professor W. 
C. Williamson, and Mr. Wm. Cash (Secretary), on the Flora of 
the ' Halifax Hard Bed,^ Lotver Coal Measures. 

The present Report is on the fossil plant-remains, whiclL are found in a 
singularly perfect state of preservation in a thin bed of impure coal in 
the ' gannister ' series of Halifax and its neighbourhood, in the county 
of York. 

Our observations relate to an examination of specimens from numerous 
coal-pits situated on an area extending from the vicinity of Bradford on 
the north to Sheffield and district on the south. 

Many of the pits in the district now indicated are no longer worked, 
partly on account of the reduced price of coal of late years and partly 
because the iron pyrites brought up in working the coal (which was 
formerly sold for chemical purposes) has been superseded by the im- 
portation of sulphur at a cheap rate from Italy and other countries. 

These influences have acted adversely upon your Committee, since 
some of the best pits for the special ' coal balls ' in which the coal plants 
are found have been closed. Still, we have to report the acquisition of a 
goodly number of ' coal balls ' which await examination. Before their 
contents can be properly studied they will have to be cut into thin slices 
preparatory to microscopical investigation. Already we have prepared 
upwards of one hundred microscopical slides for cai-eful study. 

Halifax appears, so far as our observations go, to be the centre of this 
rich Carboniferous flora. The bed in which the fossils are found is 
two feet three inches thick in the neighbourhood of Halifax, and consists 
of an impure coal, which in many places is thickly studded with nodules, 
or, as they are locally called, ' coal balls.' These are composed chiefly 
of carbonate of lime, some carbonate of magnesia, along with smaller 
quantities of oxide and sulphide of iron, sulphates of soda and potash, 
and a little silica. These nodules contain imbedded rootlets, stems, 
leaves, Lepidostrobi, spores, and occasionally the mycelium of fungi. 

The state of preservation of the fossils is very remarkable ; the tissues 
of the plants are infiltrated with carbonate of lime and the cell- walls 
are carbonised, so that in thin slices prepared for the microscope the 
minutest details are clearly defined. 

The roof of the ' hai^d bed ' is a thin stratum of shale filled with the 
flattened valves of a bivalve shell (Aviculopecfcen) ; above this is a bed of 
shale with numerous calcareous nodules, coated and often impregnated 
with iron pyrites, and containing fossil shells of the genera Aviculo- 
pecten, Goniatites, Nautilus, Orthoceras, and others, a very prevalent 
fossil being Goniatites Listen. The base of the bed is composed of 
' gannister,' and abounds in Stigmarian roots. 

In the northern part of our district around Bradford the * coal balls ' 
are scarce, and so highly charged with iron pyrites that plant-remains 
suitable for microscopical examination very rarely occur. The same 
remark applies to Huddersfield, and in a somewhat less degree to the 
southern area around Hazlehead and Shefiield. 

The three most prolific localities are situated at Sunny Bank, South- 
owram, at Sugden Pit, Bradshaw, and near BUand, all of which are in 
the immediate neighbourhood of Halifax, but unfortunately the two 



268 REPORT— 1882. 

latter pits are now closed, whilst the number of nodules brought up 
from the Sunny Bank Pit is much restricted. The state of preservation 
of the fossils is, however, most excellent, surpassing in this respect even 
those from the famous Oldham and other Lancashire beds. 

So far as we have been able to study the fossils collected daring 
the past year, we succeeded in throwing considerable light upon the 
structure of Aster opliyllites (^Myriopliylloides') Williamsoni, upon Calamo- 
stachys Binneana, especially in relation to the structure of its central 
axis, upon a hitherto undescribed form of Kaloxylon, upon Lyginodendron 
Oldhamium, and several other minor forms of plants, the structure and 
affinities of Avhich are as yet imperfectly understood. Indeed, an enor- 
mous amount of work remains to be done. We have already a very large 
number of objects with the structure of which we are well acquainted 
but the true botanical relations of which are entirely unknown to us. 
In the case of some of these, persevering research has already enabled us 
to ascertain those relations, and we doubt not that a continuance of that 
perseverance will sooner or later enable us to throw a definite light upon 
many of those whose botanical history is yet obscure. 

The following is a list of plant-remains from the Halifax hard 
seam : — 

Lepidodendron Selaginoides. Kachiopteris insignis. 

„ Harcourtii. „ robusta. 

Sigillaria. ,, di-upsilon. 

Stigmaria ficoides. Kaloxylon Hookeri. 
Favularia. „ nov. sp. 

Dadoxylon. Trigonocarpon olivjeforme, 

Diploxylon. Lagenostoma ovoides. 
Lyginodendron Oldhamium. „ physoides. 

Lepidostrobus insignis. Cardiocarpon anomalum. 
Lepidostrobi (several forms). ■ „ Butterworthi. 

Traquaria (auctorum). Zygosporites brevipes. 
Calamites. „ longipes. 

Calamostachys Binneana. ,, oblongus. 

Amyelon radicans. Oidospora anomala. 

„ radiatus. Sporocarpon asteroides. 
Astromyelon. „ tubulatum. 

„ (Myriophynoides)Williamsoni. „ ornatum. 

Rachiopteris Lacattii. „ elegans. 

„ bibractiensis. „ pachyderma. 

„ aspera. „ compactum. 

„ duplex. Peronosporites antiquarius. 

„ tridentata. Cistopus (?) carbonarius. 

„ cylindrica. Stomata (Cordaites (?)). 

We have to express our indebtedness to those indefatigable woi-kers, 
Messrs. Binns and Spencer, of Halifax, for valuable assistance given in 
the investigation of the Halifax fossil flora. 



INFLUENCE OF BODILY EXERCISE ON THE ELIMINATION OF NITBOGEN. 269 



Report of the Committee, consisting of Dr. Pye-Smith, Dr. M. 
Foster, and Dr. Burdon Sanderson, appointed for the pu7pose 
of investigating the Influence of Bodily Exercise on the Elimina- 
tion of Nitrogen {the experiments conducted by Mr. North). 

In presenting an account of the expenditure of the grant of 501. made 
to us last year for the purpose of investigating the effect of muscular 
labour on the elimination of nitrogen, we beg to submit the following 
statement of the present position of tlie inquiry. 

The subject naturally divides itself into two parts — (1) The analysis 
of the ingesta and excreta, and (2) the work. The experiments under 
the former head have been carried out with funds derived from another 
source, and have arrived at a point at which it becomes desirable to 
employ some means by which the relative amount of work done at 
diffei'ent times can be compared with the utmost practicable exactitude. 

The grant has been expended in providing a machine for this purpose, 
and for certain accessories. 

The machine consists essentially of an arrangement by which a 
weight — the amount of which can be regulated — may be raised through 
a known distance and then allowed to fall to its position of rest. 

Without entering into a detailed account of the apparatus it will 
suffice here to describe the arrangement by which the muscular recoil at 
the end of the stroke is got rid of. 

As will be seen in the accompanying photographs,' the force is exerted, 
not directly upon the weight, but upon a cam keyed on to the same axis 
as the pulley which carries the weight. By means of this cam the work 
at the end of the stroke rapidly diminishes to practically nothing, and in 
consequence there is no muscular recoil. The handle by which the weight 
is raised carries an automatic clutch so arranged that, when the weight 
has been raised to a certain point, it is released. The descent of the 
handle by its own weight causes the clutch to part an eye on the end of 
the rope attached to the cam, and the operation can then be repeated. 
The apparatus has been so constructed that the work can be done in any 
position, from the vertical to the horizontal. The photographs show it 
arranged for the latter. 

The machine is completed and ready for use, and Mr. North hopes 
during the ensuing year to be able to make a number of experiments 
Avith it upon the effect of varying amounts of work upon the elimination 
of nitrogen. 

" These have not been engraved, as they represent the machine in a state not 
quite perfected. 



270 EEPOKT — 1882. 



First Report of the Committee, consisting of Professor Flower, 
Dr. Beddoe, Mr. Brabrook, Mr. F. Gtalton, Mr. J. Park Harri- 
son {Secretary), Dr. Muirhead, Greneral Pitt-Rivers, Mr. F. W. 
RuDLER, and Mr. Charles Roberts, aiypointecl for the purpose of 
obtaining Photographs of the Typical Races in the British Isles. 

Owing to the accumulation of observations of height, weight, and 
other physical characteristics of the inhabitants of the British Isles, the 
discussion of which required the undivided attention of the Anthropo- 
metric Committee, the acquisition of photographs undertaken by them in 
1876 was last year transferred to a Committee of the Anthropological 
Department. 

The photographic portraits already collected have been handed over 
to the new Committee, and will assist materially in determining the 
values of crosses in different parts of the country. Some, obtained under 
exceptionally favourable circumstances, and especially seventeen portraits 
of Shetland islanders, well illustrating the Scandinavian element in the 
population, and presented by Dr. Muirhead, may be safely termed 
typical. 

The scientific hearing of the subject. — A clear definition of racial 
features, illustrated by examples, will, the Committee believe, prove of 
considerable importance in connection with more than one social question. 

1. First ; as tending to allay national animosities springing from a 
belief in the preponderance of some one race ; and, in connection with 
this affording a safe basis for generalisation, in the place of deductions 
depending on doubtful traditions and insufficient historical data. 

2. A correct description of the main racial types would also afford an 
opportunity of testing in a more complete manner than is now practic- 
able the truth of views, believed to be extensively held, on the. subject of 
racial tendencies and proclivities. 

3. Indirectly ; by indicating the way in which features, and more 
especially profiles, of human beings should be observed, it would lead to 
a more exact description of criminals and deserters ; resulting, it cannot 
be doubted, in more frequent arrests. At present, so little attention is 
paid to the subject that photographs of prisoners are taken solely in full 
face • and the description of recruits for the military rolls is confined, so 
far as their features are concerned, to the colour of the hair and eyes. 

The popular view regarding the possihility of a. survival of racial features 
at the present day. — Before proceeding further, the Committee think it 
will be well to notice an objection, not infrequently made, that European 
populations are now too mach mixed to allow of racial types being recog- 
nised. This is not the belief of anthropologists generally. Professor 
Rolleston — whose loss this Committee has especial reason to deplore — 
expressed no uncertain opinion on the subject in his address to the 
Anthropological Department at Bristol. ' At once, upon the first inspec- 
tion of a series of crania, or, indeed, of heads, from such a (mixed) race,' 
he said it was evident that ' some were referable to one, some to another, 
of one, two, or three typical forms : ' also that intercrossing has left the 
originally distinct forms still in something like their original indepen- 
dence, ' and in the possession of an overwhelming numerical representa-. 



ON THE TYPICAL KACES IN THE BRITISH ISLES. 271 

tion : ' and Professor His was quoted as having arrived at a similar con- 
clusion from an investigation of the ethnology of Switzerland.' 

Professor Kollmann, too, of Bale, believes that it is quite possible to 
distinguish original or main racial characteristics in a mixed population, 
owing to a capacity in skulls and facial skeletons to joreserve their 
pristine types long after the colour of the hair and eyes have changed 
by crossing. A complete fusion of component elements, the distinguished 
Professor is convinced, never absolutely occurs. 

'Reversion to original types. — Besides, however, these composite forms, 
eminent anthropologists recognise a law through the operation of which 
reversion takes place, under favourable circumstances, to original types. 
Drs. Beddoe, Barnard Davis, Flower, Rolleston, Thurnam, and Turner, 
in this counti'y, and Morton, Broca, Quatrefages, Retzins, and Virchow, 
abroad, are in accord in believing, from craniological evidence, that the 
characteristics of prehistoric races exist at the present day ; Professor 
Quatrefages, than whom the Committee believe there could not be 
a safer authority, even affirming that representatives of the fossil types of 
man are still to be found amongst us.'- 

Height, and colour of the hair and eyes, insufficient as evidence of race. — 
Assuming the correctness of Professor Kollmann's deductions that hair 
and eyes (permanent in a pure race) change by crossing more easily than 
skull-forms ; dark tints, except under conditions of intensity, joined with 
diminutive stature and complete doHchocephalism, such as unmistakably 
point to the race styled Iberian, simply indicate, according to the 
index of nigrescence established by Dr. Beddoe, more or less mixture in 
blood. Where, too, the hair and eyes are light, and the stature tall, in 
the absence of information respecting the features generally, it would be 
impossible to pronounce any individual to be Celt or Saxon, Dane or 
Swede. 

Birth of parents and grandparents in the same locality no proof of race. 
An experiment made for the purpose of ascertaining how far the birth 
of parents and the grandparents, on both sides, in certain districts would 
assist in the selection of pure local types, resulted in the conclusion that 
the requirement mentioned, though securing the absence of recent foreign 
admixture, failed as a sufficient test, by affording no evidence that move- 
ments had not occurred in the population at an earlier date. 

Photographic portraits obtained under the above-mentioned conditions 
do not, as a fact, assist materially in the definition of racial character- 
istics ; the features exhibit moi'e than one type even in districts supposed 
to have been peopled by a given race ; though, owing to the law already 
alluded to, pure types may be sought for, and would more frequently be 
found amongst such populations than elsewhere. 

This, and other considerations, led a sub- Committee, in 1880, to 
collect in preference, from different localities, a certain number of portraits, 
all of which exhibited similar features ; and then an equal jiumber dis- 
tinguished by characteristics in all respects diffisrent from the first series, 
but equally homogeneous. They presented contrasts which appeared to 
be racial. 

Method of Identification of Types adopted hy the Committee. — Approaching 
the subject from the standpoint of comparative physiognomy alluded to 
in the last paragraph, but experimenting in the first instance on the facial 

^ Brit. Ass. Rep, 1875, p. 148. * Crania Ethnica, p. 28. 



272 EEPORT— 1882. 

skeletons of skulls obtained from ancient tumnli and cemeteries in different 
parts of the British Isles, it was found on superimposing tracings of the 
skeleton profiles of the three main types figured in the ' Crania Britannica,' 
that the brows of the Brachycephalic, round-barrow type were more 
prominent, and the nasal bones more angular and sharply projecting, than 
those of the Dolichocephalic, long-barrow type ; whilst brows and nasals 
in the Teutonic skulls (and especially those of the Saxons proper) 
were respectively smooth and little prominent. The main characteristics 
in the profiles of the Round-barrow man and the Teuton would clearly 
have been the high bridge of the nose of the former, and the absence 
of an arched nose in the Saxon. 

Similar results were obtained from measurements of skulls in the 
Anatomical Museum at Cambridge, purchased from Dr. Thurnam by 
Professor Humphry, and presented by him to that University. Also some 
skulls in the Museum of the Royal College of Surgeons, and the Greenwell 
collection at Oxford, have been measured and found to exhibit the same 
contrasts. Mr. Harrison, who obtained the measurements for the infor- 
mation of the Committee, found that the mean difference in projection 
of the nasal bones in skulls from the round-barrows, as measured from 
the basion to fixed points on the dorsum and the nasion, or root of the 
nasal bones, is about twice that observed in purely Teutonic crania. In 
the fine collection of true Saxon skulls from Wiltshire, obtained by General 
Pitt-Rivers, the principal characteristics are a rounded forehead and 
smooth brow, and but little projection in the nasals ; and this in the male 
as well as the female skulls. 

The points of contrast in the skeleton features of the two races were 
noticed by Dr. B. Davis ; but owing to Saxons and Angles being at the 
time he wrote considered equally Teutonic, the differences observed in 
some of the examples selected by him to illustrate types, are not so 
strongly mai'ked as in others. Dr. Beddoe and Mr. David Mackintosh, 
it should be mentioned, both consider the Anglian features to have 
heen more prominent than the Saxon. — When proceeding to define tribal 
differences and crosses, the nasal forms will, with other features, be sub- 
jected by the Committee to more minute examination.' 

The above facts having been sufiiciently ascertained, it was easy to 
compare the skeleton features of the Round-barrow man and the Saxon 
with profiles of living subjects in this and neighbouring countries pre- 
sumably inhabited by similar populations. Whenever the osseous and 
other features were found to correspond, at the same time that they 
differed entirely from other equally well-marked types, it was assumed 
that the characteristics belonged to distinct races. 

In the following definitions the three main types in this country are 
designated by capital letters, intended to be used as symbols when discuss- 
ing racial crosses. 

First, the Dolichocephalic Dark Type, A. — The definition of the short, 
narrow-headed race shown by Dr. Thurnam and Professor Boyd Dawkins 
to have preceded the so-called Celts, and termed by them Iberian (^ the 
Silurian of Professor RoUeston), is at present incomplete. The forehead, 

' Professor Flower, speaking of the racial value of the nasal bone, when describing 
the cranial characters of the natives of the Fiji Islands, says: — 'The nose is one of 
the most important of the features as a cliaracteristic of race, and its form is very 
accurately indicated by its bony framework ' {Jour. Antfirop. Inst, vol. x. p. 160) 
Dr. Droca defines six forms. 



ON THE TYPICAL RACES IN THE BRITISH ISLES. 273 

however, appears to have been fairly vertical ; the brows prominent ; the 
nasal bones lon^ and straight; the lower jaw weak (Rolleston) ; and the 
hair and eyes dark. Statistics of the colour of the hair and eyes, collected 
by Dr. Beddoe, show that this race exerted a much wider influence on the 
population than is usually supposed. A number of photographs, which, 
it is believed, represent varieties of the type, have been placed on cards. 

Second, the BrachicepJialic Fair Ti/pe, B. — The principal character- 
istics of this race consist in the prominence of the brow and supra-nasal 
ridges ; a slightly receding forehead ; sharply projecting nasal bones, 
causing a high-bridged or arched nose, without undulation ; a long, oval 
face ; high cheek-bones ; and a prominent fine chin. From Mr. Park 
Harrison's observations the lips of this type appear to be thin, and the 
ear pear-shaped, with no proper lobe, the fossa being continuous. 

The above features are found associated with light hair and eyes, 
and a stature above the average. 

This type includes Belgic, Cymric, and Danish varieties, which further 
observation, the Committee believe, will in course of time enable them to 
differentiate : as also the Anglian, Jutish, and Frisian types. They have 
selected several portraits, which present common characteristics. 

The definition of Type B agrees in all the main points with descrip- 
tions given some years ago by Dr. Beddoe, Mr. David Mackintosh, and 
Mr. Hector Maclean, as well as with Dr. RoUeston's deductions in the 
appendix to ' British Barrows,' 

Third, the Suh-Dolichocephalic Fair Type, C. — The Committee believe 
that the following is a correct definition of true Saxon features. Brows 
smooth ; forehead rounded and vertical ; nasal bones short and straight ; 
nose not arched, ending in more or less of a bulb; face elliptical, rounded; 
cheek-bones broad ; chin rounded ; lower part of face wide ; eyes promi- 
nent, in colour blue or bluish-grey ; lips moulded ; ears flat, with formed 
lobes ; face and frame well-covered. Height aboiit the average. 

The definition accords with Schadow's pure German (Teutonic) type, 
and with the Saxon type of Beddoe and Mackintosh. 

Photographs conforming in all respects to the above characteristics 
have been obtained from Sussex and several other English c